THE DEVELOPMENT AND REPRESENTATION OF OCCUPANT PERFORMANCE IN BUILDING EVACUATION MODELING Except where reference is made to the work of others, the work described in this dissertation is my own or was done in collaboration with my advisory committee. This dissertation does not include proprietary or classified information. Rani A. Muhdi Certificate of Approval: Gerry Dozier Gerard Davis, Chair Associate Professor Assistant Professor Computer Science and Software Industrial and Systems Engineering Enginering Kent Oestenstad Saeed Maghsoodloo Associate Professor Professor School of Public Health Industrial and Systems Engineering University of Alabama at Birmingham Joe F. Pittman Interim Dean Graduate School THE DEVELOPMENT AND REPRESENTATION OF OCCUPANT PERFORMANCE IN BUILDING EVACUATION MODELING Rani A. Muhdi A Dissertation Submitted to the Graduate Faculty of Auburn University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Auburn, Alabama May 10, 2008 iii THE DEVELOPMENT AND REPRESENTATION OF OCCUPANT PERFORMANCE IN BUILDING EVACUATION MODELING Rani A. Muhdi Permission is granted to Auburn University to make copies of this dissertation at its discretion, upon request of individuals or institutions and at their expense. The author reserves all publication rights. Signature of Author May 10, 2008 Date of Graduation iv VITA Rani A. Muhdi, son of Abdullah and Neema (Deeb) Muhdi, was born in Amman, Jordan on January 29, 1977. He graduated from Saraj High School in 1994 and began his undergraduate at The University of Jordan in September of 1994. In June 1999, he earned a Bachelor of Science in Industrial Engineering. Following graduation, he worked for Al- Ganim Group. In 2000, he joined the Graduate School at East Tennessee State University in the Department of Industrial Engineering Technology. After completing a Masters of Science in 2002, he enrolled in the PhD program in Industrial and Systems Engineering at Auburn University to pursue a research interest in occupational safety and ergonomics. He married Yazmin A. Ali, daughter of Aziz Ali and Yara Landa on December 17, 2002. v DISSERTATION ABSTRACT THE DEVELOPMENT AND REPRESENTATION OF OCCUPANT PERFORMANCE IN BUILDING EVACUATION MODELING Rani A. Muhdi Doctor of Philosophy, May 10, 2008 (Master of Science, East Tennessee State University, 2002) (Bachelor of Science, The University of Jordan, 1999) 179 Typed Pages Directed by Jerry Davis Occupant characteristics are considered important features incorporated into most evacuation models. The relative scarcity of evacuation experiments in the literature, contributes to some extent to the continuous challenge of occupant data representation in computer evacuation models. Such a challenge is even more significant when modeling occupant behavior and performance responses to fire conditions since deteriorating conditions influence the occupants? adoption of new responses. The primary objective of this research was to bridge the gap between the development and representation of occupant data pertaining to crawling, one of the more important responses to evacuation in fire and smoke conditions. This research investigated occupant crawling speed compared to walking, and the effect of occupant characteristics; gender and body composition (BMI), on crawling in evacuation. vi The study also examined the impact of route design on evacuation times for crawling movements by comparing evacuation time for a straight route to an indirect route design, and the influence of occupant characteristics on evacuation time for occupants crawling such an indirect route. After that, the current study looked into the relationship between crowd density and occupant crawling movement, by examining the impact of occupant configuration (number of occupants) and exit access width on crowd walking and crawling speeds on a flat surface. The last part of the research focused on the application of evolutionary computation techniques in building designs for walking and crawling egress, which has been evaluated by evolving the location and number of exits required to minimize evacuation time. The results suggest a significant difference between normal walking and normal crawling speeds. Normal walking is performed at a faster rate than normal crawling. Further, gender and body composition significantly impact individual crawling speed as well as individual evacuation time when crawling an indirect route, since they are unique characteristics to the individual. Exit access width is significant to crowd crawling speed, whereas occupant configuration plays less of a factor. The study demonstrates a significant difference in crawling speeds at different exit access widths. The relationship between crowd crawling speed and density is best described by a quadratic regression model. Finally, evolutionary computation techniques can be used to find optimal building designs for walking and crawling egress. The designs are evaluated by evolving the best exit configuration(s) to minimize total evacuation time. However, the reliability of these techniques depends on the accuracy of the evacuation models utilized. The techniques have the potential to be implemented in more complex designs. vii ACKNOWLEDGEMENTS I wish to express my gratitude to my committee chair, Dr. Jerry Davis, for his guidance, wisdom, inspiration, as well as confidence in me through this learning process. I truly admire his research skills which helped make this work possible. My appreciation is also directed to Dr. Gerry Dozier, Dr. Kent Oestenstad, and Dr. Saeed Maghsoodloo for their responsiveness and support. My sincere appreciation is extended to Dr. Steven Gwynne, whose unique combination of brilliance and practical application inspired and challenged me to expand my intellectual capabilities. I would also like to thank Dr. Volker Schneider from Integrierte Sicherheits-Technik, Mr. Christian Rogsch from Bergische Universit?t Wuppertal, and Mr. Timo Korhonen from VTT Technical Research Centre of Finland for their assistance. In addition, thanks are due to the Deep South Center for Occupational Health and Safety, the National Institute for Occupational Safety and Health (NIOSH), and the Educational and Scientific Foundation of the Society of Fire Protection Engineers (SFPE) for their funding support. My sincere thanks go to my family and friends for their constant support and encouragement, especially my wife, who has been most supportive and patient throughout this journey. Above all, I am grateful to the Glory of God, who has blessed my life with many wonderful people and great opportunities; ?For God is full of bounty to mankind, but Most of them are ungrateful? The Noble Qur?an, 2: 243. viii Style manual or journal used: Fire Technology, Springer Netherlands Journal of Fire Sciences, SAGE Publications, Inc. Fire Safety Journal, Elsevier Science Ltd. Safety Science, Elsevier Science Ltd. Computer software used: Minitab 15.1.1.0, Microsoft Word 2003, Microsoft Excel 2003, Microsoft PowerPoint 2003, and AutoCAD 2006 ix TABLE OF CONTENTS LISTS OF TABLES....................................................................................................... x LISTS OF FIGURES ..................................................................................................... xi CHAPTER 1. INTRODUCTION ................................................................................. 1 CHAPTER 2. A REVIEW OF THE DEVELOPMENT AND REPRESENTATION OF OCCUPANT MOVEMENT DATA IN EVACUATION MODELS.......... 5 CHAPTER 3. THE EFFECT OF OCCUPANT CHARACTERISITCS ON CRAWLING SPEED IN EVACUATION ........................................................ 26 CHAPTER 4. THE IMPACT OF EXIT ROUTE DESIGN ON EVACUATION TIME FOR CRAWLERS .................................................................................. 39 CHAPTER 5. THE DEVELOPMENT OF MOVEMENT-DENSITY RELATIONSHIP FOR CRAWLING................................................................ 53 CHAPTER 6. THE APPLICATION OF EVOLUTIONARY COMPUTATION IN LAYOUT DESIGN FOR WALKING AND CRAWLING EGRESS ......... 69 CHAPTER 7. CONCLUSIONS ................................................................................... 99 REFERENCES .............................................................................................................. 104 APPENDICES ............................................................................................................... 127 x LIST OF TABLES Table 1 ? Reviewed evacuation models that specify the sources of movement data .... 11 Table 2 ? Default values of movement input data to building evacuation models........ 20 Table 3 ? Mean normal walking and crawling speeds (m/s) ......................................... 34 Table 4 ? Individual normal crawling data.................................................................... 35 Table 5 ? Mean crawling evacuation times for straight and indirect routes.................. 47 Table 6 ? Individual evacuation time data for crawling in an indirect route................. 49 Table 7 ? Density and speed values reported in crowd movement studies ................... 55 Table 8 ? Crowd normal walking and crawling speeds (m/s) at different configurations and exit access width levels................................................. 62 Table 9 ? Crawling body dimensions for U.S. male adults aged 19 ? 29 years (mm) ................................................................................................... 81 Table 10 ? Comparison between total evacuation times of 100 simulation runs produced by ASERI and the potential field model .............................. 83 Table 11 ? The percentage of the solution with a certain number of exits.................... 91 Table 12 ? Summary of the evacuation simulation runs for walking............................ 97 Table 13 ? Summary of the evacuation simulation runs for crawling........................... 97 xi LIST OF FIGURES Figure 1 ? The approach to identify and classify occupant movement sources in evacuation models........................................................................................ 10 Figure 2 ? Default occupant movement speeds in evacuation models .......................... 28 Figure 3 ? Age-adjusted prevalence of overweight and obese among U.S. adults, age 20-70 years ............................................................................................ 29 Figure 4 ? A 100-ft test track with a subject in the crawling position........................... 32 Figure 5 ? Probability plots of mean walking and crawling speeds .............................. 34 Figure 6 ? Graphical summary of crawling speed......................................................... 36 Figure 7 ? Indirect test track (route) with a subject in the crawling position ................ 45 Figure 8 ? Probability plots of mean evacuation times on straight and indirect routes. 48 Figure 9 ? Graphical summary of individual evacuation time for crawlers in an indirect route........................................................................................ 50 Figure 10 ? Test track with adjustable widths ............................................................... 60 Figure 11 ? Normality test of crowd walking speed...................................................... 64 Figure 12 ? Main effect plot of exit access width on crowd crawling speed................. 65 Figure 13 ? Study observation at (a) 3-ft, (b) 4-ft, and (c) 5-ft wide exit access width ............................................................................................... 66 Figure 14 ? The relation between crawling speed and density on a flat surface ........... 67 xii Figure 15 ? The approach to implementing evolutionary computation into an evacuation simulation model .......................................................... 73 Figure 16 ? The layout design of the banquet hall......................................................... 77 Figure 17 ? A range of anthropometric measurements and body sizes adopted in people movement studies........................................................................ 78 Figure 18 ? An approximation of crawling length (sagittal plane)................................ 80 Figure 19 ? Crawling dimensions based on CAESAR measurements (transverse plane)........................................................................................ 80 Figure 20 ? Mathematical representation of occupant crawling shape and size............ 81 Figure 21 ? Pseudocode structure of an EC................................................................... 84 Figure 22 ? Best exit locations of the EDA and GGA solutions for walking................ 92 Figure 23 ? Best exit locations of the PSO solution for walking................................... 92 Figure 24 ? Best exit locations of the EDA solution for crawling................................. 93 Figure 25 ? Best exit locations of the GGA solution for crawling ................................ 93 Figure 26 ? Best exit locations of the PSO solution for crawling ................................. 94 Figure 27 ? Probabilities of best exit locations for walking .......................................... 94 Figure 28 ? Probabilities of best exit locations for crawling......................................... 95 1 CHAPTER 1 INTRODUCTION The ongoing trend of advancing knowledge in building designs and structures has raised major concerns for occupant safety. Innovative methods and approaches are needed to understand and assess these complex designs to assure occupant safety and verify compliance with standards and guidelines. Traditionally, verification has been demonstrated through full-scale building evacuation drills. Although structural designs and evacuation procedures can be somewhat controlled during a full-scale evacuation experiment, and some similarities between real emergencies and experimental evacuation drills have been established [1], this option faces challenges in finding representative target populations, controlling the level of unpredictable variability, and dealing with ethical, practical, and financial difficulties [2, 3] to provide accurate evacuation data to the designs. A promising alternative to conquer these challenges and assess occupant safety lies in computer evacuation models. Generally, a model is a representation of reality without the presence of reality itself [4]. In the context of evacuation, it refers to a close and fairly accurate approximation of real evacuation processes and features. Computer evacuation models not only assess the efficiency of evacuation processes by controlling 2 challenges presented in evacuation drills, but also simulate the dynamic interaction between occupant, structure, and the environment. One of the more important features incorporated into most evacuation models, relates to occupant characteristics. According to the Life Safety Code ? [5], occupant characteristics are defined as the abilities or behaviors of people before and during a fire. Both regulations and fire safety codes, and the need for more reliable and validated computer evacuation models, suggest further attempts to understand and model occupant behavior and performance characteristics in fire [6]. The complexity of modeling occupant characteristics during evacuation, and the relative scarcity of evacuation experiments in the literature, contribute to some extent to the continuous challenge of occupant data representation in computer evacuation models. Research Objective It is apparent from the literature, as reported in Chapter Two of this dissertation, that there is a gap between the way occupant data is developed and the manner in which it has been represented in computer evacuation models. This gap is even broader when modeling occupant behavior and performance responses to fire conditions. The deterioration of environmental conditions and the interaction of occupants with such conditions influence the adoption of new responses such as moving through or redirecting away from smoke [7, 8]. Crawling represents another response that occupants choose, or are forced to choose, to avoid heat and smoke. The presence and movement of smoke and fire have been incorporated into several computer evacuation models [9-17]. In order for existing and new models to have 3 the potential to accurately simulate the impact of fire and environmental conditions on human behavior and performance responses during evacuation, it is vital to meticulously develop and represent appropriate occupant data for these responses. Simulating these responses, and others, enhances the ability of evacuation models to accurately evaluate the robustness of building designs and ultimately assess occupant safety. The specific aim of this research is to bridge the gap between the development and representation of occupant data as it pertains to crawling, one of the important responses to evacuation in fire and smoke conditions. The astonishing lack of crawling data in literature poses fundamental challenges for evacuation modelers to integrate and validate the crawling behavior into computer evacuation models. It is, however, beyond the scope of this dissertation to investigate the likelihood of crawling, but rather focus on occupant performance once the decision to crawl has been made. Format of the Dissertation This dissertation is organized following the publication format. The manuscript chapters constitute the body of the dissertation. Chapters 1 and 7 are the traditional dissertation introduction and overall conclusions, respectively. Chapters 2, 3, 4, 5, and 6 are stand-alone manuscripts reporting methods, discussions, and results. Chapter 2 is a comprehensive literature review of the development and representation of occupant movement in evacuation models. Due to the special arrangement of this format, a brief literature review of the most relevant literature will be provided in each of the remaining manuscripts. Chapter 3 reports on preliminary experiments conducted to investigate crawling speed compared to walking, and the influence of occupant characteristics 4 (gender and body composition) on speed reduction for occupants when crawling. Chapter 4 assesses the impact of exit route design on evacuation time for crawlers. Chapter 5 investigates the relationship between crawling speed and crowd density, and its representation in evacuation models. The development of occupant walking and crawling data in Chapters 3 has been employed by a software application utilizing an evolutionary computation approach to examine the effect of occupant crawling on evacuation planning (Chapter 6). The overall conclusions reached as a result of this research are presented in Chapter 7, along with a summary of the recommendations made, and the study limitations. The appendices contain information regarding the recruitment of human subjects, protocols adopted through the study, summaries of the data collected, and detailed statistical analyses supporting the results presented in the manuscript chapters. 5 CHAPTER 2 A REVIEW OF THE DEVELOPMENT AND REPRESENTATION OF OCCUPANT MOVEMENT DATA IN EVACUATION MODELS Abstract. As evacuation models evolve, occupant performance data plays a key role in the development, functionality, and validation of these models. Despite the implementation of advanced computational and modeling techniques, evacuation models continue to quantify and predict occupant movement in normal and emergency conditions. This paper investigates the sources of occupant movement data on which evacuation models are based. After critically reviewing 62 different evacuation models, it is evident that there is a trend among models to utilize limited movement data sources. The sources most frequently used are nonemergency experimental studies, fire tests and incidents reports. The impact of these sources is strongly dependent upon the representation of occupant movement data in the models. The review reveals a gap between the way movement data is developed and the manner in which it has been utilized in the models. This review is an attempt to move forward the discussion of movement data experimentation and dissemination. 6 1. Introduction As evacuation models are increasingly becoming a part of an innovative approach to assess occupant safety, model developers are faced with the challenge of demonstrating that their models accurately represent human physical abilities and behaviors during emergency conditions. Historically, two reasons have contributed to the challenge of representing occupant characteristics in evacuation models: (1) modeling occupant parameters for emergency evacuation based on non-emergency data [1], and (2) the relative scarcity of evacuation studies designed and conducted for modeling [2]. Evacuation models might characterize occupant parameters for emergency evacuations observed from nonemergency ones without foundation for their assumptions. The First International Symposium on Human Behavior in Fires in 1998 called for fewer, better, and universally accepted building evacuation models. Shields and Proulx [3] therefore suggested a strategic approach for the future development of models; calling for universal evacuation protocols in experimental studies, and modeling validation procedures to generate better quality data. The lack of real evacuation data is attributed to ethical, practical, and financial difficulties [4]. The complexity of modeling occupant characteristics demands not only a vast amount of occupant data to improve the accuracy of evacuation models, but also a systematic comparison between experimental data and model predictions to provide more useful information to end users, investigate the uncertainty and variability in input and output data, and enhance the validation of models [5, 6]. Further, the advanced development of computational and modeling techniques has made the models capable of 7 simulating conditions and situations that are yet to be supported by the experimental data available. One of the important response characteristics of occupants identified by the Life Safety Code ? [7] is the speed of movement (mobility), which is determined by individual physical capabilities and other crowding phenomena. The movement of occupants is a key element to the development, functionality, and validation of evacuation models. As sophisticated evacuation models continue to emerge, quantifying and predicting occupant movement remains a fundamental element in estimating the required evacuation time to reach safety (exit). Since the work of Predtechenskii and Milinskii [8] and Fruin [9] in quantifying human movement in nonemergency conditions, the number of building evacuation models has significantly increased. Attempts to review the movement of occupants have essentially progressed into two groups: (1) some attempts have concentrated solely on reviewing the occupant movement data (values) obtained from evacuation studies, and (2) other reviews have discussed occupant movement techniques implemented in evacuation models as part of reviewing the functionality of those models. The first group has resulted in a limited number of movement data reviews due to the relative scarcity of evacuation studies in the literature. For instance, Fahy and Proulx [10] summarized occupant data on walking speeds to feed the development and validation of evacuation models. An extended study by Lord et al. [11] reported an extensive literature review of data related to occupant walking speeds on horizontal surfaces and up and down stairs. Although the sources and values of occupant movement 8 were reported in the studies, both reviews fell short in relating their findings to evacuation models. Previous model reviews (the second group) have presented occupant movement in terms of the development and functionality of evacuation models. Kuligowski & Peacock [12] described the representation of occupant movement techniques in several evacuation models. The review discussed occupant movement data of 28 models but failed to categorize the data by source or type, since the primary focus of the review was primarily on modeling methods. Despite the valuable information these reviews present to model developers, fire safety engineers, and architects, none of the reviews (in both groups) has fully addressed the representation of the sources of movement data in evacuation models, or linked the implementation of data explicitly to the development of models. The purpose of this review is to categorize the models according to the movement data employed in order to identify the gap between the development of the data in evacuation studies and its representation in the evacuation models. Therefore, it is quite important to distinguish between investigating movement data available in the literature and the data actually implemented in the models [10, 11]. 2. The Review Approach The significant increase in the number of building evacuation models has resulted in a variety of evacuation model reviews [2, 4, 12-18]. The development of models at the time a review was conducted, the availability of models for commercial applications, and basically the existence of models in the literature are among some of the apparent reasons behind considering certain evacuation models for review over others. 9 The model selection criterion for this review is defined as any system or methodology, referred to in building evacuation research, used to calculate, simulate, or evaluate evacuation processes, is considered a candidate for review. Figure 1 depicts a suggested approach to help survey available building evacuation models to particularly address the sources of occupant movement data in the models. An intensive literature review of 62 evacuation models was conducted using the selection criterion. The surveyed models were then categorized into: (1) models that incorporate occupant data in terms of sources, measures, or functionality, along with other elements of the evacuation process (46 models), and (2) models that focus on the structure of the model and the interaction of evacuation elements without providing specific occupant data descriptions (16 models). Out of the 46 models that feature occupant data, only 34 models (Table 1) specifically address the sources of occupant movement data. The review further discusses the representation of those sources in the models. The review is solely based on evacuation literature and personal contacts with model developers and evacuation researchers. 10 Figure 1. The approach to identify and classify occupant movement sources in evacuation models. Start Approach Occupant data? End Approach Apply model selection criterion Identify sources of occupant movement data Categorize occupant data Examine models for occupant data Identify building evacuation models Occupant movement S 1 S n Sources of occupant data Sources? Yes (46) Yes (34) (62) models S 2 No (16) Representation in evacuation models No (12) 11 Table 1 Reviewed evacuation models that specify the sources of movement data Model and Reference(s) 1. Allsafe [19] 2. ASERI [20] 3. Burstedde?s Model [21] 4. CRISP III [22] 5. Daoliang?s Model [23] 6. EESCAPE [24] 7. EGRESS [25, 26] 8. EgressPro [27] 9. EMBER [28] 10. Escape and Rescue model [29] 11. ESM [30] 12. EVA [31] 13. EvacSim [32] 14. Exit89 [33] 15. EXITT [34] 16. EXODUS [35, 36] 17. Firescape [37] 18. FPETool [38] 19. GridFlow [39] 20. Johnson?s Model [40] 21. Kirchner?s Model [41] 22. Lizhong?s Model [42] 23. Magnetic Model [43] 24. MASSEgress [44] 25. PATHFINDER [45] 26. SGEM Model [46] 27. Simulex [47] 28. Social Force Model [48] 29. Song?s Model [49] 30. STEPS [50] 31. Takahashi?s Model [51] 32. TIMTEX [52] 33. VEgAS and Myriad [53, 54] 34. WAYOUT [55] 12 3. Sources of Occupant Movement Data in Evacuation Models Human movement research in building evacuation has been underway for nearly 40 years. Some of the earliest research quantifying the movement of people is the work of Pedtechenskii and Milinskii [8], and Fruin [9]. Studies have been mainly conducted under normal conditions due to the danger inherent in emergency environments. Consequently, building evacuation models deploy nonemergency occupant movement and density data due to the lack of representative data under emergency conditions. Therefore, the movement of occupants in the models is generally unimpeded unless occupants become closer in a high density situation. This changes the speeds and flow rates assigned to individuals during evacuation based on the density of the available space. After intensive review of available models, the sources of occupant movement data can be classified into two distinct groups: experimental studies, and fire tests and incident reports. 3.1. Experimental studies The majority of the reviewed models obtain their occupant movement data from a number of nonemerget experimental studies [8, 9, 56-67]. Tests and observations from those studies have been implemented to establish movement algorithms for several evacuation models such as EgressPro [27], EvacSim [32], GridFlow [39], PATHFINDER [45], TIMTEX [52], and WAYOUT [55]. Furthermore, the nonemergent studies have provided many of the reviewed models with default values for a range of occupant movement parameters. Examples of these parameters include unimpeded velocities, movement probabilities, average empirical velocities, adjusted travel speeds, and movement through exits, stairs, routes, and smoke conditions. The following 13 classification of evacuation models and their movement values is based on the occupant movement parameters developed in those experimental studies. 3.1.1. Unimpeded and adjustable speeds (speed vs. density) In the evacuation model Egress [25, 26], the default value of average speed (0.9 m/s), standard deviation (0.424 m/s), alternative haste factors of 1.5 m/s and 0.6 m/s for emergency and unconcerned crowd movement situations, respectively, and probability values are all based on the work of Predtechenskii and Milinskii [8]. The movement speed is adjusted as crowd density changes. Occupant flow is calculated as a function of density, which shows similarity to some experimental data [8, 9, 63]. The maximum density in the model is set at 5 occupants/m 2 . EgressPro [27] uses calculations from Nelson and MacLennan [61]. The program also predicts the flow of groups of persons in an emergency based on the relationship between speed of movement and the population density. Shen [30] introduced the evacuation simulation model (ESM) with adjusted travel speeds of occupants based on density. When density is less than 0.54 persons/m 2 , the speed adopts the free walking speed value of 1.19 m/s. When density is greater than 3.8 persons/m 2 , the occupants are moving at a much slower rate. The results are also given by Nelson and MacLennan [61]. The model EESCAPE [24] does not assign fixed values to the flow density or velocity for each individual or separate group but considers them to be a single group of a certain mean density on each section of the escape route. The model uses density on each component of the escape route to calculate the speed of the occupant through the escape route based on the work of Pauls [62] and Predtechenskii and Milinskii [8]. It also provides predictions of the time required for the total evacuation of high-rise buildings 14 via staircases based on the work of Kendik [68]. Total evacuation times for a certain flow density on the means of escape are determined based on a mathematical method developed by Predtechenskii and Milinskii [8]. Exit89 [33] also employs Predtechenskii and Milinskii?s work [8] on movement through doors and down stairs using density calculations. The model?s unimpeded horizontal emergency speed and optimal density are set at 1.36 m/s and 0.92 m 2 /m 2 , respectively. The evacuation model SGEM [46] and Simulex [47] implement the findings of Ando et al. [56] to represent individual unimpeded speeds. The walking speed of an individual in SGEM [46] is a function of crowd density. Unimpeded speed is considered when there is no other person in a 1.12 m 2 area around an evacuee. In the evacuation model Simulex [47], each individual is assigned a random walking speed between 0.8 and 1.7 m/s. Other specific unimpeded speeds in the model are 1.35 m/s ? 0.2 for males, 1.15 m/s ? 0.2 for females, 0.9 m/s ? 0.3 for older adults, and 0.8 m/s ? 0.3 for children. The evacuation model MASSEgress [44] includes five population types; median, adult male, adult female, child, and elderly. The model currently shows the differences between the five population types in terms of mobility. Each population type represents a typical segment of the human population. Average walking velocity and maximum running velocity on a level surface are obtained from Eubanks and Hill [58] and Thompson et al. [66]. TIMTEX [52] applies data from tests and observations [8, 9, 62] to provide a foundation for fluid flow equations. These equations estimate evacuation time based on the relationship between population density and speed of movement. The model uses the equations specified in the SFPE Handbook [61] to move occupants through corridors and 15 stairs. When queuing occurs, the model assumes that the upper floors dominate the flow. The model accounts for an evacuation efficiency factor of 0.68 for delay in decision to egress and the time for people to reach the corridor and move towards an exit. The flow ascending stairs (10% slower than the flow descending) and default speed of 64% of common stairs are based on Pauls [62]. Finally, the occupant movement and density of WAYOUT [55] is also based on the findings of Predtechenskii and Milinskii [8]. 3.1.2. Empirical and constant speeds Burstedde?s model [21] employs an empirical average velocity of 1.3 m/s based on the work of Weidmann [67]. In the evacuation model EVA [31], walking pace on a level surface is set at approximately 1.5 m/s ignoring different agent speeds. As a result, each agent in the model moves at a constant simulated speed. The formulated natural movement was based on pedestrian steps. When considering other modes of transport such as wheelchair, bicycle, or car, the natural movement would differ. The intended paces of movement used in Johnson?s model [40]; walk, fast walk, and run are all based on Pauls [62]. The intended pace of movement used in the model is one of three options: walk at 1 m/s, fast walk at 1.5 m/s, and run at 2 m/s. In the evacuation model GridFlow [39]; the movement?s algorithms employed are based on Nelson and MacLennan [61]. Each occupant is assigned an unimpeded walking speed. The default walking speeds are assigned from a theoretical normal distribution ( =? 1.19 m/s, =? 0.3 m/s). Finally, Lizhong?s model [42] applies the average empirical velocity of a normal human (in a nervous state) at 1.5 m/s [8]. 16 3.1.3. Speeds in smoke conditions The work of Boyce et al. [57], Jin [59], and Jin and Yamada [58] provide EXITT [34] and buildingEXODUS [35, 36] with travel speeds in normal and smoke conditions. EXITT [34] applies normal travel speed for each occupant at 1.3 m/s. If the fire is serious, a faster normal speed of 1.69 m/s (30% increase) is assigned. When assisting other occupants, walking speed becomes 0.65 m/s (50% of normal). If the fire is considered serious during assisting others, the speed increases to 0.84 m/s. A value of 0.78 m/s (60% of normal) is assigned if smoke is thick and depth of the lower layer is less than 1.5 m. The value becomes 0.52 m/s when assisting others in smoky conditions. On the other hand, buildingEXODUS [35, 36] implements a default fast walk of 1.5 m/s, while walk, leap and crawl are at engineering judgments of 0.9, 0.8, and 0.2 of the fast walk, respectively. The default value of flow rate is set at 1.33 occupants/m/sec with an indefinite range. 3.1.4. Hydraulic flow speeds The physical attributes of EvacSim [32]; maximum horizontal and stair speeds, use a bilinear travel speed model as proposed by Nelson and MacLennan [61] based on the findings of Fruin [9], Pauls [62], and Predtechenskii and Milinskii [8]. The model travel speed for disabled occupants also uses the same speed model, but incorporates a different horizontal and stair maximum velocities. Finally, the model PATHFINDER [45] also follows the hydraulic flow model of Nelson and MacLennan [61] but tracks occupant movement and position individually by room or floor to find bottlenecks and queues in designs. 17 3.2. Fire tests and incident reports Fire tests and incident reports represent another major source of occupant movement data. For example, the model Allsafe [19] bases its functions on actual incidents determined through studies conducted by SINTEF on large fire incidents. Likewise, EMBER [28] imitates the dynamic movement of rescue personnel and occupants using horizontal and vertical travel speeds. The rate of occupant movement is obtained from fire tests in single-family dwellings in Los Angeles [69]. Finally, the assumptions of Firescape [37] are based on the analysis of the Beverly Hills Supper Club fire. 4. The Representation of Movement Data in Evacuation Models Occupant movement data in the reviewed models can be determined by the model users or obtained from pre-defined values or statistical distributions. Many evacuation models are designed to allow users to modify the default movement values. Users can adjust occupant movement data in a number of models by either specifying movement speed values or defining statistical parameters of probability distributions used to generate such values. However, such flexibility given to the end user does not imply that the user can impact the movement algorithms developed in the design phase of these models, but rather the input variables of movement for specific simulation runs. The following is a description of occupant movement representation in some of the reviewed models. In the Escape and Rescue model [29]; pre-defined speeds are assigned to 15 occupant types ranging from occupants requiring staff assistance to those moving alone. 18 The time scale in Kirchner?s model [41] corresponds to a pre-determined empirical speed. Similarly, an occupant movement of one grid each time step results in a pre- assigned average speed for Song?s model [49]. Takahashi?s model [51] and STEPS [50] assume constant walking speeds that can be input by the user. Alternatively, uniform and normal distributions have been used to generate random occupant movement values for evacuation models. Velocities in the Magnetic model [43] are decided by random values generated from a normal distribution, while positions are decided by uniform random values set to each group to increase velocity as occupants move toward an exit. The social force model [48] also assumes a normally distributed speed that is compatible with empirical data. Walking speeds in Daoliang?s model [23] range according to a uniform distribution. The movement speed of each occupant in Firescape [37] is determined by a random perception of risk to provide a weight for the subjective estimate of the situation. Finally, in the model CRISP III [22], the user defines the movement speeds for different classes of people by selecting a probability distribution and its statistical parameters (i.e., mean and standard deviation) for each class. The model then randomly assigns a speed value to each person depending on the defined probability distribution. Similarly, occupant movement in the model ASERI [20] is an individual input or generated from a statistical distribution. 5. Discussion It is apparent that there is a general trend toward specific sources of occupant movement data in building evacuation models. The impact of these sources is strongly 19 dependent upon the representation of occupant input data and how the models actually implement such data. For instance, an average speed of 1 m/s collected in experimental settings, and subsequently used in an evacuation model does not imply that the model will run a speed of 1 m/s during the evacuation process. The extensive employment of experimental data demonstrates the need to focus on the development and representation of such data in evacuation models. The foregoing review exhibits a wide range of occupant movement represented in evacuation models. Table 2 summarizes some default values of occupant movement in some evacuation models. The variability in occupant data is also reflected in the sources from which it was drawn. For example, the measurements of Predtechenskii and Milinskii [8] on speed and density sometimes show a significant change in speed at the same density level. This inconsistency has also been shown by Fruin [9] when measuring average free-flow walking speeds for males and females. 20 Table 2 Default values of movement input data to building evacuation models Model Movement Condition/Type Value (m/s) Source Burstedde unimpeded 1.30 Weidmann [67] Daoliang walk U~[0.5-1.50] pre-determined by developers unimpeded N~(0.9, 0.424 2 ) haste factor (emergency) 1.50 EGRESS haste factor (non-emergency) 0.60 Predtechenskii and Milinskii [8] resident 0 1.50 residents 1A, 6A 1.00 residents 3C, 6B, 6C, 30A, 30B, 30C 0.75 residents 10 0.67 residents 1B, 20, 40 0.50 resident 3A 0.30 Escape & Rescue resident 3B 0.15 pre-determined by developers ESM unimpeded 1.19 Nelson and MacLennan [61] EVA unimpeded horizontal (emergency) 1.50 Sutherland et al. [65] Exit89 unimpeded horizontal (emergency) 1.36 Predtechenskii and Milinskii [8] unimpeded 1.30 fast speed (serious fire conditions) 1.69 assisting others (minor fire danger) 0.65 assisting others (serious fire) 0.85 unimpeded (minor smoke conditions) 0.78 EXITT assisting others (serious smoke) 0.52 Jin [59] 21 fast walk 1.50 walk 1.35 leap 1.20 EXODUS crawl 0.30 Jin [59] unimpeded on flat pathways 1.27 FPETool unimpeded on stairs (ascending) 0.20 pre-determined by developers GridFlow unimpeded N~(1.19, 0.30 2 ) Nelson and MacLennan [61] walk 1.00 fast walk 1.50 Johnson/ Firescape run 2.00 Pauls [62-64] Kirchner maximum 1.3 Burstedde et al. [21] Lizhong nervous state 1.50 Predtechenskii and Milinskii [8] average flat walking (median) 1.30 average flat walking (adult male) 1.35 average flat walking (adult female) 1.15 average flat walking (child) 0.90 average flat walking (elderly) 0.80 maximum flat running (median) 4.10 maximum flat running (adult male) 4.10 maximum flat running (adult female) 4.10 maximum flat running (child) 3.40 MASSEgress maximum flat running (elderly) 2.75 Thompson et al. [66] and Eubanks and Hill [58] SGEM walk 1.40 pre-determined by developers 22 walk U~[0.80-1.70] unimpeded (male) U~[1.15-1.55] unimpeded (female) U~[0.95-1.35] unimpeded (elderly) U~[0.60-1.20] Simulex unimpeded (child) U~[0.50-1.10] Ando et al. [56] desired N~(1.34, 0.26 2 ) leaving a room (relaxed) 0.60 leaving a room (normal) 1.00 Social Force leaving a room (nervous conditions) 1.50 pre-determined by developers Song unimpeded 1.00 pre-determined by developers STEPS walk 1.00 pre-determined by developers 23 The review also reveals that the global representation of movement data is sometimes extracted from experimental studies that are limited in scope, conditions, or controls but then applied to a variety of scenarios in the models, functioning under very different assumptions. The default stair speeds used in some models are obtained from Fruin [8] who studied movement and behavior of 700 people on stairs considering gender, age, stair angle, riser height, and tread depth. However, the study involved only two specific stair dimensions; indoor (7 inch riser, 11.25 inch tread, 32 o slope), and outdoor (6 inch riser, 12.0 inch tread, 27 o slope). In another representation, the travel speeds obtained from Boyce et al. [57] and Shields et al. [70] were collected from a small number of participants, a wide range of variability in values, and simple experimental designs with low levels of control. Another finding from this review is that occupant data is sometimes extrapolated beyond the results of the sources upon which it is based. The speed ratios of evacuating in smoke conditions implemented in some models are based on Jin [59], where 31 participants (14 males and 17 females) performed simple mathematical calculations while walking in a smoke-filled corridor. Using those results, buildingEXODUS [35, 36] applied engineering judgments to establish speed ratios for walk, leap, and crawl. The crawling ratio was established from extrapolated data [59] although crawling was never conducted in the study. Similarly, the speed ratios in EXITT [34] for serious fire conditions, assisting other occupants, and high smoke concentrations are also extracted from the same study [59]. The compatibility of movement data with their respective models was also noted as a potential issue. In the evacuation model Simulex [47], individuals are assigned 24 random walking speeds between 0.8 and 1.7 m/s. This is intended to represent a population that contains an even distribution of males and females, with ages ranging from 12 to 55 years. The model does not demonstrate the fitness of such data to all populations although its results correlate with real life values of crowd flow. Information about the nature of the data, the subjects from which the data was generated, or data validation was not provided. 6. Conclusion Since the initial efforts to model evacuation scenarios some 40 years ago, significant progress has been made in understanding and modeling human behavior and performance characteristics in evacuation. Regardless of the complexity of computational techniques implemented in current advanced building evacuation models, occupant data always plays, along with other evacuation elements, a fundamental role in the development, functionality, and validation of these models. In general, models have managed to incorporate occupant performance data through the presentation of occupant movement. This review was performed to investigate and compile the available sources of human performance data values employed in 34 building evacuation models 1 . It is evident from this review that there is a conspicuous trend among evacuation models to obtain occupant movement data from certain sources. The influence of these sources on the development of the models obviously varies with the variety of ways they are employed in the models. Some sources of occupant data such as experimental 1 The author acknowledges that some models were not considered for this review due to the difficulty of obtaining occupant information, or the late appearance of such information in the literature at the time this review was conducted. 25 research on human movement in nonemergency conditions and fire incidents and reports are engaged at the early design phase of the models. On the contrary, some advanced evacuation models provide users with a level of flexibility to alter occupant input data to the models. However, the flexibility does not diminish the importance of other sources in the development of those models. In summary, the review implies that there is a gap between the way occupant movement data is developed in the literature and the manner in which it has been represented in the models. The scarcity of occupant data has encouraged evacuation modelers to apply these limited sources of movement to situations different from those which the data was generated for. The mismatch between data and its applications in the models has also extended to model validation despite the fact that models functionality could be affected. 26 CHAPTER 3 THE EFFECT OF OCCUPANT CHARACTERSITICS ON CRAWLING SPEED IN EVACUATION Abstract. The movement of occupants is a key element to the development of evacuation models which estimate the required evacuation time to reach an exit. The deterioration of environmental conditions influences occupants to adopt new responses. This study investigates crawling movement as a physical response to environmental conditions in fire. The study investigates occupant crawling speed compared to walking, and the effect of occupant characteristics; gender and body composition (BMI), on crawling in evacuation. Eighteen subjects (9 males and 9 females) within the 19-29 age stratum participated in the study (normal, overweight, and obese body composition). The findings indicate a statistical significance between normal walking and crawling speeds. Further, the study statistically demonstrates that both gender and body composition significantly impact individual crawling speed as they are unique individual characteristics. More research is needed to better understand the effect of age group, mobility capabilities, and fatigue on crawling speed. The study concludes that the development of crawling data and its representation in evacuation models will enhance the accuracy of evacuation models, and better evaluate the safety of evacuees. 27 1. Introduction Evacuation models are becoming a promising alternative to the challenges of full- scale evacuation drills, used to assess the safety of occupants and building designs and structures [1]. Regardless of the complexity or techniques used, evacuation models incorporate occupant characteristics in their attempt to accurately represent the evacuation process and its features. According to the Life Safety Code ? [2], occupant characteristics refer to the abilities or behaviors of people before and during a fire. An important occupant characteristic during fire evacuation that the Code identifies is speed (mobility), which is a key element in the representation of human physical abilities in evacuation models [3]. The work of Predtechenskii and Milinskii [4], Fruin [5], and many others [6-17] in quantifying human movement has significantly contributed to the representation of occupant physical characteristics in evacuation models. The findings of these studies have provided the models with a range of movement speeds (Figure 2). The deterioration of environmental conditions during a fire, in terms of heat and smoke, and the interaction of occupants with such conditions influence the adoption of new behavioral and physical responses [18-21]. One of the physical responses to smoke and heat that occupants choose, or are forced to choose, is crawling. Despite the extensive literature on quantifying human movement, little research has been conducted on human physical abilities to crawl during evacuation. Muhdi et al. [22] compared normal and maximum crawling velocities to walking. The study suggested further research focusing on certain occupant characteristics. Another study conducted by Nagai et al. [23] compared experimental and simulated evacuation processes of walkers and crawlers through an exit. A similar study [24] investigated, experimentally and via 28 simulation, the phenomenon of counterflow for both walkers and crawlers in a hall. Both studies [23, 24] focused on the evacuation process without emphasizing on occupant characteristics. In light of the significant absence of crawling data in the literature, it is necessary to conduct some basic experiments to further investigate occupant crawling speed compared to walking, and the effect of occupant characteristics on walking and crawling in evacuation. Figure 2. Default occupant movement speeds in evacuation models. One of the characteristics that is of particular interest in this study is body composition, known as Body Mass Index (BMI). The index is a screening tool that provides a reliable indicator of body composition, and it is primarily used to classify people in one of four distinct weight categories: underweight (BMI < 18.5), normal (18.5 < BMI ? 25.0), overweight (25.0 < BMI ? 29.9), and obese (BMI ? 30.0). According to 29 the 1999-2002 National Health and Nutrition Examination Survey (NHANES), an estimated 65 percent of U.S. adults are either overweight or obese [25]. This indicates a 16 percent increase compared to the age-adjusted overweight estimates obtained from the 1988-1994 NHANES III. Figure 3 compares the findings of the 1992-2002 NHANES to NHANES II and III. Figure 3. Age-adjusted prevalence of overweight and obesity among U.S. adults, age 20-70 years. 2. Methodology 2.1. Objective and Hypotheses The purpose of this study is to examine the effect of occupant characteristics, in terms of gender and body composition (BMI) on walking and crawling in evacuation. The hypotheses for the study are: 47% 56% 65% 15% 23% 31% 0% 15% 30% 45% 60% 75% NHANES II (1976-80) NHANES III (1988-94) NHANES (1999-02) Survey Percent Overweight or obese (BMI > 25.0 Obese (BMI > 30.0) 30 Hypothesis 1: There is no significant difference between individual normal crawling speed (NC) and individual normal walking speed (NW) on a flat surface for both healthy (cognitively and physically) males and females within the 19 ? 29 age stratum. SpeedWalkingNormalSpeedCrawlingNormal SpeedWalkingNormalSpeedCrawlingNornal H H ?? ?? ? = : : 1 0 Hypothesis 2: There is no significant difference between individual normal crawling speed on a flat surface for healthy (both physically and cognitively) males within the 19 ? 29 age stratum and individual normal crawling speed on a flat surface for healthy (both physically and cognitively) females within the same age stratum. FemalesforSpeedCrawlingNormalMalesforSpeedCrawlingNormal FemalesforSpeedCrawlingNormalMalesforSpeedCrawlingNormal H H ?? ?? ? = : : 1 0 Hypothesis 3: Individual normal crawling speed on a flat surface for both healthy (cognitively and physically) males and females within the 19 ? 29 age stratum is unaffected by their body composition (BMI). nCompositioBodyObeseforCrawlingNormal nCompositioBodyOverweightforCrawlingNormalnCompositioBodyNormalforCrawlingNormal nCompositioBodyObeseforCrawlingNormal nCompositioBodyOverweightforCrawlingNormalnCompositioBodyNormalforCrawlingNormal H H ? ?? ? ?? ?? == : : 1 0 2.2. Experimental Design In order to test these hypotheses, a mixed-factor analysis was constructed with the level of significance (?), set at 0.05. The factors in this study were activity (walking, crawling), BMI (normal, overweight, obese), and gender (male, female). The response or 31 dependent variable was speed, measured in m/s. For each factor, three replicates (n = 3) were recorded. 2.3. Subjects The analysis of variance (ANOVA) for the study indicates that a total of 18 college subjects (9 males and 9 females) within the 19-29 age stratum were recruited to participate in the study. The age stratum was selected based on the classification of the Civilian American and European Surface Anthropometry Resources (CAESAR) [26, 27]. Subjects were required to read and sign an informed consent form (Appendix 3.1) approved by the Auburn University Office of Human Subjects Research Institutional Review Board (IRB) prior to participating in the study. Each gender group included 3 subjects with a 18.5 ? BMI < 25.0, 3 subjects with a 25.0 ? BMI < 30.0, and 3 subjects with a BMI ? 30.0. Subjects? BMI measures were compared to CAESAR?s median BMIs for the same age stratum. Additionally, subjects completed a physical activity questionnaire (Appendix 3.2) to demonstrate their physical ability to participate in the study. 2.4. Equipment A 100-ft test track (Figure 4) was constructed with safety cones and barrier tape. The length of the track represents the travel distance limit for a common path in a sprinklered educational occupancy or double the distance limit for dead-end paths during evacuation, as specified by the Life Safety Code ? [2]. The track was marked every 20 ft. The start and finish lines were set 10 ft from the beginning and the end of the track, respectively, to overcome any performance acceleration or deceleration. Six photo sensors were mounted along the track and connected to a digital timer, which was linked 32 to a computer through an Ethernet cable. Time to perform each activity (normal walking and normal crawling) was recorded to the nearest 0.01 second. Three sets of adjustable knee pads and three sizes of gloves (small, medium, and large) were provided for the subjects to perform the crawling activity. A general anthropometry kit was used to measure subjects? height and weight. Also, a Polar? Heart Rate monitor was used for heart rate monitoring of the subjects. Figure 4. A 100-ft test track with a subject in the crawling position. 2.5. Protocol Subjects performed the study individually based on a random schedule. Once at the track site, the study?s procedure (Appendix 3.3) was explained in detail. After signing the informed consent form, the subject?s height and weight were measured, and the heart rate monitoring equipment was put on the subject in a private waiting area. The subject was then asked to rest until his/her resting heart rate was reached. After that, the participant was guided to the start line. Next, the researcher instructed the participant to walk down the test track at a normal pace. Six time measurements (t 0 ? t 5 ) were recorded 33 and stored electronically. After crossing the finish line, the participant was escorted to the waiting area again. In order to perform the next activity (normal crawling), the subject received a brief verbal description of the activity. After that, the subject was fitted with appropriate knee pads and gloves to eliminate any possible burns or injuries that may occur due to friction with the floor. When a standing resting heart rate level was reached again, the subject was directed to the starting line. Upon the request of the researcher, the participant crawled at a normal pace until reaching the finish line. Another six time measurements were taken and stored simultaneously. 3. Results The purpose of the study is to examine the effect of occupant characteristics (body composition and gender) on walking and crawling. Appendix 3.4 summarizes the data for the study. The mean individual normal walking and crawling speeds on a flat surface for males and females are shown in Table 3. In order to test the hypotheses, a normality test is conducted for walking and crawling speeds (Figure 5). At ? = 0.05, the p-values for the normal distributions for walking and crawling speeds (p walking = 0.326, p crawling = 0.753) provide a good fit for each activity. As a result, conducting a two-sided t-test to compare between walking and crawling means is reasonable. A test of the population variances provides enough evidence to claim that the two populations have unequal variances. Thus, it is rational to assume unequal variances when using a two- sample t-test. The t statistic exceeds t ? (17.31 > 2.069), which implies that there is a 34 significant difference (p << 0.0005) between normal walking and normal crawling speeds (hypothesis 1) as illustrated in Appendix 3.5. Table 3 Mean normal walking and crawling speeds (m/s) 0.83 0.810.90 0.770.79 0.77 0.73 0.650.76 0.79 0.71 0.650.76 0.74 0.67 1.29 1.32 1.271.36 1.37 1.34 0.790.86 0.86 1.48 1.51 1.48 1.67 1.61 1.40 1.42Overweight Obese Walking Females Normal 1.73 1.70 1.80 1.62 1.46 Crawling Males Body Composition Males Females 1.91.81.71.61.51.41.31.21.1 99 95 90 80 70 60 50 40 30 20 10 5 1 Mean Walking (m/s) Pe r c e n t 0.950.900.850.800.750.700.650.60 99 95 90 80 70 60 50 40 30 20 10 5 1 Mean Crawling (m/s) Pe r c e n t Figure 5. Probability plots of mean walking and crawling speeds. 35 In order to test hypotheses 2 and 3, further analysis was conducted on the crawling data. Table 4 lists crawling speeds for 18 subjects (9 males and 9 females). In reality, the levels of gender (males, females) and the levels of body composition (normal, overweight, obese) cannot be crossed since body composition is nested under gender. The subjects are also nested under both gender and body composition. In other words, each subject performed crawling for a specific gender type and body composition. Therefore, studying full-level combinations and their interactions is impracticable; rather a balanced nested design is applied because of equal number of levels of BMI within each gender type and equal number of replicates. A repeated measures ANOVA was conducted to examine the source of variability in crawling speed. The ANOVA table in Appendix 3.6 indicates that there is significant evidence for gender and body composition on crawling speed at ? = 0.05. However, there is no significant evidence for subjects (blocks). Table 4 Individual normal crawling speed data 0.89 0.93 0.86 0.82 0.77 0.85 0.84 0.85 0.90 0.76 0.86 0.88 0.88 0.84 0.85 0.78 0.79 0.81 0.71 0.77 0.81 0.71 0.70 0.78 0.84 0.74 0.78 0.75 0.77 0.78 0.72 0.80 0.86 0.68 0.70 0.74 0.78 0.74 0.77 0.64 0.63 0.67 0.74 0.74 0.75 0.64 0.68 0.70 0.76 0.78 0.75 0.54 0.70 0.69 Crawling Males Females Body Composition Normal Overweight Obese 36 4. Discussion This study investigated occupant crawling speed as compared to walking, and the effect of occupant characteristics on crawling in evacuation. It has been statistically shown when tested with a two-sample t-test that mean crawling speed is significantly less than mean walking speed (p<0.0005). Individual normal crawling speed presented in this study not only matches the findings of other crawling studies [22, 23], but also fits the normal distribution since the p-value is greater than the level of significance ? (0.720 > 0.05) as illustrated in Figure 6. The mean of the crawling speed is 0.77 (95% confidence interval of 0.75 and 0.79 m/s), while the standard deviation is 0.08 (95% confidence interval of 0.065 and 0.096 m/s). This finding is vital to model developers to represent occupant crawling in evacuation models by incorporating the most reliable human performance data possible without relying on theoretical crawling data. 0.90.80.70.6 Median Mean 0.790.780.770.760.750.74 1st Quartile 0.71136 Median 0.77148 3rd Quartile 0.84102 Maximum 0.93330 0.74795 0.79034 0.74472 0.78450 0.06529 0.09588 A-Squared 0.25 P-Value 0.720 Mean 0.76914 StDev 0.07767 Variance 0.00603 Skewness -0.283481 Kurtosis 0.260050 N54 Minimum 0.54243 Anderson-Darling Normality Test 95% Confidence Interval for Mean 95% Confidence Interval for Median 95% Confidence Interval for StDev95% Confidence Intervals Figure 6. Graphical summary of crawling speed. 37 Further, the study revealed that occupant characteristics; gender and body composition, are major determinants of occupant normal crawling speed, accounting for about 80% of the variance in crawling speed (R 2 = 79.94%). The ability to simulate these characteristics, and others, will improve the accuracy of evacuation models. However, it is important to state that these characteristics are unique for each occupant (within- subjects). Therefore, nested ANOVA was conducted with subjects being nested under body composition and gender. This result poses an immense challenge to model developers to represent occupant unique physical characteristics in evacuation models. 5. Conclusions Occupant movement data plays a key role in the development of evacuation models. Despite the implementation of advanced modeling techniques, evacuation models continue to quantify and predict occupant movement in normal and emergency conditions. The present study investigates crawling movement as a physical response to environmental conditions in fire. The study compares individual crawling to individual walking speeds and the influence of occupant characteristics (gender and body composition) on the speed reduction for occupants when crawling. The findings of the study indicate a statistical difference between normal walking and crawling speeds. Furthermore, the study demonstrates statistically that both gender and body composition significantly impact individual crawling speed as they are unique characteristics to every individual. 38 Although the study, to the best knowledge of the author, is the first to report the effect of occupant characteristics on normal crawling in evacuation, future crawling studies should be conducted with larger samples with a focus on certain occupant characteristics such as age group and mobility capabilities. Research is also needed in crawling on different types of surfaces and under different degrees of crowd levels to quantify crowd crawling. Another need lies in studying the effect of fatigue on crawling, and its representation in the adaptive decision making process in response to evacuation. Since the current study focuses on normal crawling, there was no effect of fatigue on human performance. However, the effect would be more obvious in longer test areas and under actual emergency environmental conditions. Finally, the development of crawling data and its representation in evacuation models will enhance the robustness of engineering procedural designs, improve the accuracy of evacuation models, and better evaluate the safety of evacuees. 39 CHAPTER 4 THE IMPACT OF EXIT ROUTE DESIGN ON EVACUATION TIME FOR CRAWLERS Abstract. According to the Life Safety Code ? , the distance between the exit access and the exit is a function of the occupants, type and number of obstructions, and the type of hazard. This study investigates the impact of route design on evacuation times for crawling movements. The study compares evacuation time for a straight route to an indirect route design, and the influence of occupant characteristics (gender and body composition) on evacuation time for occupants crawling an indirect route. Eighteen subjects (9 males and 9 females) in the 19-29 age stratum participated in the study (normal, overweight, and obese body composition). The findings indicate a statistical difference between evacuation time for crawling in a straight route and an indirect one. Furthermore, the study reveals that both gender and body composition have a significant impact on individual evacuation time when crawling in an indirect route. The representation of different route designs in evacuation models can provide architects with a better understanding of occupant individual and global views of buildings, which further enhances the robustness of their designs. 40 1. Introduction According to the Life Safety Code ? [1], means of egress refers to ?a continuous and unobstructed way of travel from any point in a building or structure to a public way consisting of three separate and distinct parts: (1) the exit access, (2) the exit, and (3) the exit discharge.? Since the exit access includes, according to the Code, all occupied floor spaces that lead to an exit, it comprises more floor area that either of the other distinct parts of the means of egress. As sophisticated building evacuation models continue to emerge, quantifying and predicting occupant movement from the exit access to the exit remains a fundamental element in calculating evacuation time. In order to assess the methods of occupant movement through a building and simulate a building enclosure, it is important to examine how models represent occupant perception of means of egress. In their comprehensive review of 28 evacuation models, Kuligowski & Peacock [2] classified the occupant view of buildings into individual and global perspectives. Occupants with an individual view are usually unaware of a building?s exit access and await external knowledge to move toward the exit. On the contrary, a global view provides occupants with the best familiarity of the exit and exit access. Regardless of the approach adopted to represent the occupant view of buildings and means of egress, occupant movement from the exit access to an exit in the models can be carried out implementing any of the following: 1. Single route movement. Some evacuation models [3-6] make only one exit available to occupants during evacuation. Therefore, occupant view of the building means of egress is global. 41 2. Efficient route selection. During this approach, the occupants move to an exit according to the most efficient route that would result in a minimal evacuation time, which may not be necessarily the shortest route to an exit. Occupant view to exit access in these models [7-10] is also considered global. 3. User-defined route. Model users can either specify each occupant?s exit choice (exit familiarity) [11-16], or define a default percentage of occupants to use a certain exit [17-21]. In both cases, occupants view means of egress individually. 4. Nearest distance route selection. This is probably the most common method model designers implement to identify occupant movement to exit [18-26]. The shortest distance between each occupant and an exit is updated throughout the evacuation process. However, model users can alter the nearest exit route selection of occupants by indicating environmental conditions or exit congestion. It is this final approach, where occupants chose the nearest exit that will be further examined in this study. The Life Safety Code ? [1] dictates the maximum distance limit that occupants travel from their location in a building to the nearest exit. The travel distance is measured horizontally along the centerline of the natural trail of travel curving around obstructions. According to the Code, the maximum permitted travel distance is a function of several factors. Some of which are the number, age, and physical condition of occupants, type and number of obstructions, and type of hazard. 42 2. Methodology 2.1. Objective and Hypotheses The purpose of this study is to evaluate the impact of turns (changing directions) to avoid obstructions on evacuation time for crawlers and compare that to the time needed to crawl in a straight exit route, free from obstructions. The impact of occupant characteristics (gender and BMI) on evacuation time for crawlers to change directions is also investigated. The hypotheses for the study are: Hypothesis 1: There is no significant difference between time to evacuate in a straight path (route) and time to evacuate in an indirect route (changing directions) during evacuation for healthy (both physically and cognitively) crawlers (males and females) within the 19 ? 29 age stratum. pathindirectevacuatetotimepathstraightevacuatetotime pathindirectevacuatetotimepathstraightevacuatetotime H H ,,1 ,,0 : : ?? ?? ? = Hypothesis 2: There is no significant difference between time to evacuate at a normal pace in an indirect route for healthy (cognitively and physically) males within the 19 ? 29 age stratum and time to evacuate at normal pace for healthy (cognitively and physically) females within the same age stratum. femalespathindirectevacuatetotimemalespathindirectevacutetotime femalespathindirectevacuatetotimemalespathindirectevacautetotime H H ,,,1 ,,,,0 : : ?? ?? ? = Hypothesis 3: Time to evacuate in an indirect path for both healthy (cognitively and physically) males and females within the 19 ? 29 age stratum is unaffected by their body composition (BMI). 43 ncompositiobodyobesepathindirectevacuatetotime ncompositiobodyoverweightpathindirectevacuatetotimencompositiobodynormalpathindirectevacuatetotime ncompositiobodyobesepathindirectevacuatetotime ncompositiobodyoverweightpathindirectevacuatetotimencompositiobodynormalpathindirectevacuatetotime H H ,, ,,,,1 ,, ,,,,0 : : ? ?? ? ?? ? ? = = 2.2. Experimental Design In order to test these hypotheses, a mixed-factor analysis is constructed with the level of significance (?), set at 0.05. The factors in this study are route type (crawling in a straight route, crawling in an indirect route), BMI (normal, overweight, obese), and gender (male, female). The response or dependent variable is time, measured in seconds. For each factor, three replicates (n = 3) will be recorded. 2.3. Subjects The analysis of variance (ANOVA) for the study indicates that a total of 18 college subjects (9 males and 9 females) within the 19-29 age stratum were recruited to participate in the study. The age stratum was selected based on the classification of the Civilian American and European Surface Anthropometry Resources (CAESAR) [27, 28]. Subjects were required to read and sign an informed consent form (Appendix 3.1) approved by the Auburn University Office of Human Subjects Research Institutional Review Board (IRB) prior to participating in the study. Each gender group included 3 subjects with a 18.5 ? BMI < 25.0, 3 subjects with a 25.0 ? BMI < 30.0, and 3 subjects with a BMI ? 30.0. Subjects? BMI measures were compared to CAESAR?s median BMIs for the same age stratum. Additionally, subjects completed a physical activity questionnaire (Appendix 3.2) to demonstrate their physical ability to participate in the study. 44 2.4. Equipment A 100-ft test track (Figure 7) was constructed with safety cones and barrier tape. The length of the track represents the travel distance limit for a common path in a sprinklered educational occupancy or double the distance limit for dead-end paths during evacuation, as specified by the Life Safety Code ? [1]. The track consisted of five-90 o turns (changes of direction), and was marked every 20 ft. The start and finish lines were set 10 ft from the beginning and the end of the track, respectively, to overcome any performance acceleration or deceleration effect. Six photo sensors were mounted along the track and connected to a digital timer, which was linked to a computer through an Ethernet cable. Time to perform normal crawling in both routes (straight and indirect) was recorded to the nearest 0.01 second. Three sets of adjustable knee pads and three sizes of gloves (small, medium, and large) were provided for the subjects to perform the crawling activity. A general anthropometry kit was used to measure the subjects? height and weight. Also, a Polar? Heart Rate monitor was used for heart rate monitoring of the subjects. 45 Figure 7. Indirect test track (route) with a subject in the crawling position. 2.5. Protocol Subjects performed the study individually based on a random schedule. Once at the track site, the study procedure (Appendix 4.1) was explained in detail. After signing the informed consent form, the subject?s height and weight were measured, and the heart rate monitoring equipment was put on the subject in a private waiting area. The subject 46 was then asked to rest until his/her standing resting heart rate was reached. After that, the subject was fitted with knee pads and gloves to eliminate any possible burns or injuries that may occur due to friction with the floor. Next, the researcher instructed the participant to crawl down the indirect test track (changing directions) at a normal pace following the centerline of the natural path of travel, as defined by the Code. The length of both test tracks (straight and indirect) was identical, i.e., 100 ft. When a standing resting heart rate level was reached again, the subject was directed to the starting line to crawl at a normal pace until reaching the finish line. Six time measurements (t 0 ? t 5 ) were recorded and stored electronically. After crossing the finish line, the participant was escorted to the waiting area. 3. Results The main purpose of the study is to evaluate the impact of turns (changing directions to avoid obstructions) on evacuation time for crawlers and compare that to the time needed to crawl (an identical distance) in a straight exit route, free from obstructions. Additionally, the effect of crawlers? gender and BMI on evacuation time when traveling in an indirect route is examined compared to a direct one. Appendix 4.2 summarizes evacuation times of crawling (in seconds) in both route types. The mean crawling evacuation times on a flat surface for males and females are shown in Table 5. In order to test the hypotheses, a normality test is conducted for mean evacuation times in the straight and indirect routes (Figure 8). At ? = 0.05, the p-values for the normal distributions for mean crawling times in straight and indirect routes (p straight = 0.341, p indirect = 0.315) indicate that, at 0.05 ? level, there is evidence that both sets of data 47 follow the normal distribution. As a result, conducting a two-sided t-test to compare between the means of evacuation time for crawling in straight and indirect routes is statistically reasonable. Since the same activity is performed in both routes (normal crawling), it is rational to assume equal variances when using a two-sample t-test. However, a test of the population variances confirms such rationale of equality between variances. The t statistic exceeds t ? (|-2.56| > 2.069), which implies a significant difference (p = 0.015) between the mean times to evacuate crawling in straight and indirect routes (hypothesis 1) as illustrated in Appendix 4.3. Table 5 Mean crawling evacuation times for straight and indirect routes 47.24 47.43 41.00 45.24 46.73 47.28Obese 39.97 47.17 45.48 39.85 47.85 47.69 38.59 43.23 43.09 44.89 40.75 Overweight 39.93 41.77 42.06 44.47 38.76 39.71 44.41 43.92 39.45 35.33 36.90 38.98 40.58Normal 34.08 37.53 37.69 35.51 38.52 36.13 Body Composition Straight Route Indirect Route Males Females Males Females 48 5045403530 99 95 90 80 70 60 50 40 30 20 10 5 1 Mean crawling time in a straight route Pe rc e n t 52.550.047.545.042.540.037.535.0 99 95 90 80 70 60 50 40 30 20 10 5 1 Mean crawling time in an indirect route Pe r c e n t Figure 8. Probability plots of mean evacuation times on straight and indirect routes. In order to test hypotheses 2 and 3, further analysis was conducted on the evacuation times crawling an indirect route. Table 6 lists evacuation times for 18 subjects (9 males and 9 females) crawling an indirect route. In reality, the levels of gender (males, females) and the levels of body composition (normal, overweight, obese) cannot be crossed since body composition is nested under gender. The subjects are also nested under both gender and body composition. In other words, each subject performed crawling for a specific gender and body composition type. Therefore, studying full-level combinations and their interactions is impracticable; rather a balanced nested design is applied because of equal number of levels of BMI within each gender and also equal number of replicates. A repeated measures ANOVA was conducted to examine the source of variability in evacuation time. The ANOVA table in Appendix 4.4 indicates that there is significant evidence for gender and body composition on time to evacuate crawling through an indirect path at ? = 0.05. However, there is no significant evidence for subjects (blocks). 49 Table 6 Individual evacuation time data for crawling in an indirect route 37.23 36.18 39.66 38.38 41.26 38.70 39.20 39.06 38.67 41.86 39.45 40.43 37.21 35.54 35.65 40.14 41.49 40.61 43.35 40.34 42.48 44.33 45.10 43.98 44.17 43.34 45.72 42.30 45.20 44.27 43.20 41.32 44.75 45.04 45.65 43.97 47.02 45.52 43.89 47.13 46.94 48.21 44.59 46.83 48.77 46.23 47.85 47.76 47.37 46.90 48.81 47.05 47.91 46.77 Obese Overweight Body Composition Indirect Route Males Females Normal 4. Discussion This study investigated the impact of turns (changing direction) on evacuation time for crawlers compared to the time required to crawl (an identical distance) in a straight path, and the effect of occupant characteristics on time to evacuate crawling an indirect route. It has been statistically demonstrated when tested with a two-sample t-test that mean time to crawl in an indirect route is significantly greater than mean time to crawl in a straight route (p = 0.015 < ? = 0.05). Individual time to evacuate crawling an indirect route presented in this study does not fit the normal distribution since the p-value is slightly less than the level of significance ? (0.045 < 0.05) as illustrated in Figure 9. The mean time to evacuate was 43.24 sec (95% confidence interval of 42.23 and 44.24 sec), while the standard deviation was 3.69 sec (95% confidence interval of 3.10 and 4.55 50 sec). This indicates that occupants react to changes in route design differently, especially when adopting new physical responses (such as crawling) to deteriorating environmental conditions. 48464442403836 Median Mean 45.044.544.043.543.042.542.0 1st Quartile 40.290 Median 43.975 3rd Quartile 46.785 Maximum 48.810 42.230 44.243 42.017 45.079 3.100 4.553 A-Squared 0.76 P-Value 0.045 Mean 43.237 StDev 3.688 Variance 13.600 Skewness -0.411523 Kurtosis -0.856970 N5 Minimum 35.540 A nderson-Darling Normality Test 95% Confidence Interval for Mean 95% Confidence Interval for Median 95% C onfidence Interval for StDev 95% Confidence Intervals Figure 9. Graphical summary of individual evacuation time for crawlers in an indirect route. Further, the study revealed that occupant characteristics; gender and body composition, are major determinants of evacuation time of crawlers in an indirect route, accounting for about 90% of the variance in evacuation time (R 2 = 92.21%). The ability to simulate these characteristics, and others, will improve the accuracy of evacuation models. However, it is important to state that these characteristics are unique for each occupant (within-subjects). Therefore, nested ANOVA was conducted with subjects being nested under body composition and gender. 51 5. Conclusions Occupant movement from the exit access to the exit remains a fundamental element in calculating evacuation time. Evacuation models rely on a variety of movement algorithms to represent occupant view of building design, enclosure, and means of egress. The present study investigated the impact of route design on evacuation time for crawling as a physical response to environmental conditions in fire. The study compared crawlers? evacuation times for a straight route to an indirect route design, and the influence of occupant characteristics (gender and body composition) on evacuation time for occupants crawling an indirect route. The findings of the study indicated a statistical difference between evacuation time for a straight route and an indirect one. Furthermore, the study showed statistically that both gender and body composition significantly impact individual evacuation time when crawling an indirect route as they are unique characteristics to every individual. Although the study, to the best knowledge of the author, is the first to report the effect of occupant characteristics on indirect route design for normal crawling in evacuation, future crawling studies should be conducted with larger samples with a focus on certain occupant characteristics such as age group and physical conditions. Research is also needed in crawling on different types of surfaces and under different degrees of crowd levels to quantify crowd view of means of egress. Another need lies in studying the effect of fatigue on crawling as occupants try to avoid obstacles during evacuation, and its representation in the adaptive decision making process in response to evacuation. Since the current study focuses on normal crawling, there was no effect of fatigue on 52 human performance even in different route designs. However, the effect would be more obvious in longer test areas and under actual emergency environmental conditions. Further, the finding of the study is vital to validate the algorithms employed in the models to quantify and predict occupant movement throughout building enclosure by comparing the most reliable human performance data available to model output for a given route design without relying on hypothetical data. Finally, the development of crawling data and its representation in different route designs will provide architects with a more realistic understanding of occupant individual and global views of building enclosure to further enhance the robustness of their designs. 53 CHAPTER 5 THE DEVELOPMENT OF MOVEMENT-DENSITY RELATIONSHIP FOR CRAWLING Abstract. Occupant movement in evacuation models has been simulated and predicted based on a number of variables, including crowd density. This study investigates the relationship between crowd density and occupant crawling movement, as a physical response to environmental conditions in fire. This is conducted by examining the impact of occupant configuration (number of occupants) and exit access width on crowd walking and crawling speeds on a flat surface. The findings of the study suggest that exit access width is significant to crowd crawling speed, whereas occupant configuration plays less of a factor. The results further demonstrate that there is a significant difference in the crawling speed at the different levels of the exit access width due to the effect of crowd density. The relationship between crowd crawling speed and density is best described in the study by a quadratic regression model. The study concludes with the need to continuously develop new predictive movement methods, or enhance existing ones in order to cope with the level of detail required to ensure occupant safety. In light of the significant absence of crawling data in the literature, this study contributes to the improvement of the accuracy and functionality of occupant movement in existing and future evacuation models. 54 1. Introduction A lack of real evacuation data poses a challenge to the development and representation of occupant movement in evacuation models. As a result, researchers have been driven to configure and apply predictive approaches to overcome such obstacles [1]. One of the approaches that has been commonly applied to simulate occupant movement in evacuation models is based on occupant density. The relationship between crowd density and horizontal walking speed has been previously developed from observations and experiments in different crowd places, namely public buildings [2], walkways [3-7], railway stations [8], stairs [2, 3, 9, 10], and queues [3]. Table 7 summarizes density and speed values reported in some of these studies. The findings from crowd movement research have significantly contributed to the development of movement algorithms in a number of evacuation models. Some evacuation models in which the relationship between density and crowd speed has been implemented are; buildingEXODUS [11, 12], CRISP II [13], EESCAPE [14], Egress [15], ESM [16], EvacSim [17], Exit89 [18], PATHFINDER [19], and Simulex [20]. The successful implementation of such relationship (walking speed vs. density) in evacuation models is currently limited to walking. The deterioration of environmental conditions in evacuation influences occupants to adopt new behaviors [21-24]. The representation of these behaviors in evacuation models in terms of density and speed introduces more realistic movement algorithms to evaluate the consequences of these behaviors on model outcomes, and hopefully to enhance the robustness of evacuation procedures and building designs. One of the responses that occupants choose, or are 55 forced to choose, is to avoid heat and smoke by crawling. The purpose of this study is to examine the relationship between crowd crawling speed and crowd density. Table 7 Density and speed values reported in crowd movement studies Study Density (persons/m 2 ) Crowd movement Speed (m/s) Ando et al. [8] 0.8 Free 1.4-1.6 1. Non-contact 0.5-1.0 4 Restricted (stagnation) < 0.5 Fruin [3] 0.4 Adjustable 1.3-1.4 Nelson and MacLennan [9] 0.54 Comfortable 1.2 3.8 Slow ? 0 Older [6] 4 Restricted 0.3 Pauls [10] 0.54 Independent 1.25 4-5 Restricted (standstill) ? 0 Polus et al. [7] 0.1 Free 1.3 2.2 Jammed 0.7 2. Crawling Data in the Literature An exhaustive review of the literature on occupant crawling revealed a significant shortage of the development of crawling data in human performance studies and its representation in evacuation models. Muhdi et al. [25] conducted one of the few performance studies in evacuation that measured normal and maximum crawling and walking speeds. Their results suggest that maximum walking is performed at a significantly higher rate than normal walking, whereas normal crawling is performed at a significantly lower rate than normal walking. Maximum crawling, on the other hand, showed no significant difference compared to normal walking. The average normal 56 walking speed in the study was measured at 1.32 m/s (4.33 ft/s), while maximum walk, normal and maximum crawl were 163%, 54%, and 111% of normal walking, respectively, or 2.15, 0.71, and 1.47 m/s (7.05, 2.33, and 4.82 ft/s). Another study by Nagai et al. [26] compared experimental and simulated evacuation processes of walkers and crawlers through an exit. Individual crawling speed was measured at 0.73 m/s (2.4 ft/s), which is comparable with that of Muhdi et al. [25]. The study further demonstrated the effect of initial density (number of occupants/maximum capacity) on mean flow rate (persons/sec) for both walkers and crawlers through different exit widths. A similar study [27] investigated, experimentally and via simulation, the phenomenon of counterflow for both walkers and crawlers in a hall. The researchers obtained the mean crawling speed by averaging all individuals? crawling speeds. Each individual speed was calculated based on crawling distance, which was measured from an individual?s initial position to the other end of the hall. Therefore, in the Nagai et al. study [27], the relationship between crawling speed and density reflects individual crawling speed and not crowd crawling speed as influenced by density. With respect to crawling movement being incorporated into evacuation models, to the best knowledge of the author, only buildingEXODUS [11, 12] simulates crawling behavior during evacuation. The model assumes standing and crawling heights of 1.7 and 1 m, respectively, and applies a default empirical crawling speed of 0.3 m/s (0.98 ft/s), which is 20% of its default fast walking speed of 1.5 m/s (4.92 ft/s). A crawling speed of 0.3 m/s (0.98 ft/s) is significantly less than the findings of Muhdi et al. [25] and Nagai et al. [26], i.e., 0.71 (2.33 ft/s) and 0.73 m/s (2.4 ft/s), respectively. Therefore, in an attempt to incorporate crawling data into evacuation models, Muhdi et al. [28] employed the 57 crawling data found in Muhdi et al. [25] and Nagai et al. [26] into buildingEXODUS [11, 12] to test the accurate representation of crawling speeds in the model. The researchers emphasized the importance of incorporating reliable occupant data into evacuation models to verify the model outcomes, and suggested the development of a density-speed relationship for crawlers to improve upon the model?s representation of crawling movement. 3. Methodology 3.1. Objective and Hypotheses The purpose of this study was to investigate the relationship between crowd crawling speed and crowd density. This is accomplished by examining the impact of the number of occupants (occupant configuration) and width of the exit access on crowd normal walking and crawling speeds. The hypotheses for the study are: Hypothesis 1: Crowd normal walking speed of healthy (cognitively and physically) occupants (males and females) within the 19 ? 29 age stratum is unaffected by the width of the exit access (W). n n WatSpeedWalkingNormalCrowdWatSpeedWalkingNormalCrowdWatSpeedWalkingNornalCrowd WatSpeedWalkingNormalCrowdWatSpeedWalkingNormalCrowdWatSpeedWalkingNornalCrowd H H ??? ??? ??? === ...: ...: 21 21 1 0 Hypothesis 2: Crowd normal walking speed of healthy (cognitively and physically) occupants (males and females) within the 19 ? 29 age stratum is unaffected by occupant configuration (number of occupants). occupantsnforSpeedWalkingNormalforSpeedWalkingCrowdoccupantsforSpeedWalkingCrowd occupantsnforSpeedWalkingCrowdforSpeedWalkingCrowdoccupantsforSpeedWalkingCrowd H H ??? ??? ??? === ...: ...: 321 320 58 Hypothesis 3: Crowd normal crawling speed of healthy (cognitively and physically) occupants (males and females) within the 19 ? 29 age stratum is unaffected by the width of the exit access (W). n n WatSpeedCrawlingNormalCrowdWatSpeedCrawlingNormalCrowdWatSpeedCrawlingNornalCrowd WatSpeedCrawlingNormalCrowdWatSpeedCrawlingNormalCrowdWatSpeedCrawlingNornalCrowd H H ??? ??? ??? === ...: ...: 21 21 1 0 Hypothesis 4: Crowd normal crawling speed of healthy (cognitively and physically) occupants (males and females) within the 19 ? 29 age stratum is unaffected by occupant configuration (number of occupants). occupantsnforSpeedCrawlingNormalforSpeedCrawlingCrowdoccupantsforSpeedCrawlingCrowd occupantsnforSpeedCrawlingNormalforSpeedCrawlingCrowdoccupantsforSpeedingCrowdCrawl H H ??? ??? ??? === ...: ...: 321 320 3.2. Experimental Design In order to test these hypotheses, a mixed-factor analysis was constructed with the level of significance (?), set at 0.05. The study design considered two activities (walking, crawling), three exit access widths (W 1 = 3, W 2 = 4, W 3 = 5 ft) and five configurations (C 1 = 2, C 2 = 4, C 3 = 5, C 4 = 7, C 5 = 9 occupants). Each configuration is designed with consideration of gender and BMI. The response or dependent variable is speed, measured in m/s. For each factor, two replicates (n = 2) were recorded. 3.3. Subjects The analysis of variance (ANOVA) for the study required a total of 20 college subjects within the 19-29 age stratum recruited to participate in the study. The age stratum was selected based on the classification of the Civilian American and European Surface Anthropometry Resources (CAESAR) [29, 30]. Subjects were required to read and sign an informed consent form (Appendix 5.1) approved by the Auburn University 59 Office of Human Subjects Research Institutional Review Board (IRB) prior to participating in the study. Five of the males are classified as having a normal weight (18.5 ? BMI <25.0), four overweight (25.0 ? BMI <30.0), and one obese (BMI ? 30.0), whereas, for the female group, seven are normal (18.5 ? BMI <25.0), two are overweight (25.0 ? BMI <30.0), and one is obese (BMI ? 30.0). The proportion of males and females, as well as, BMI within each gender, is rational to the national data for the 19 ? 29 age stratum obtained by CAESAR [29, 30], which is provided in Appendix 5.2. The combination of gender and BMI categories was randomly selected from the sample without replacement within each configuration, but with replacement between configurations. Additionally, subjects completed a physical activity questionnaire (Appendix 3.2) to demonstrate their physical ability to participate in the study. 3.4. Equipment A 50-ft test track (Figure 10) was constructed with adjustable widths. The length of the track represents the distance limit for dead-end paths during evacuation, as specified by the Life Safety Code ? [31]. The start and finish lines were set 10 ft from the beginning and the end of the track, respectively, to overcome any performance acceleration or deceleration effect. Six photo sensors were mounted along the track and connected to a digital timer, which was linked to a computer through an Ethernet cable. Time to perform each activity (normal walking and normal crawling) was recorded to the nearest 0.01 second. Three camcorders were mounted along the track to capture a length of 10 ft each. Adjustable knee pads and gloves were provided for the subjects to perform the crawling activity. A general anthropometry kit was used to measure the subjects? 60 height and weight. Also, a Polar? Heart Rate monitor was used for heart rate monitoring of the subjects. Figure 10. Test track with adjustable widths. 3.5. Protocol Subjects were randomly assigned to configurations, track width, and activities. Once at the track site, the study?s procedure was explained in detail (Appendix 5.3). After signing the informed consent form, the subject?s height and weight were measured, and the heart rate monitoring equipment was put on the subject in a private waiting area. The subjects were then asked to rest until his/her standing resting heart rate was reached. After that, the subjects were fitted with knee pads and gloves to eliminate any possible burns or injuries that may occur due to friction with the floor during the crawling activity. Next, the researcher instructed the participants to walk down the test track at a normal pace. Six time measurements (t 0 ? t 5 ) were recorded and stored electronically. After crossing the finish line, the participants were escorted to the waiting area. The normal walking activity was then repeated at three different track widths. 61 In order to perform the next activity (normal crawling), the subjects were received a brief verbal description of the activity. Once resting heart rate level was reached again, the subjects were directed to the start line. Upon the request of the researcher, the participants crawled at a normal pace until reaching the finish line. Another six time measurements were taken and stored. The normal crawling activity was also repeated at three different widths. 4. Results The purpose of the study was to investigate the relationship between crowd crawling speed and crowd density. Further, the study examined the impact of occupant configuration (number of occupants) and the width of the exit access on crowd normal walking and crawling speeds. Table 8 summarizes crowd walking and crawling speeds on the flat surface at different configurations and exit access widths. In order to test hypotheses 1 and 2, a general linear model of crowd walking versus configurations and exit access widths was performed in Minitab (Appendix 5.4). The analysis of variance (ANOVA) for crowd walking speed, using adjusted sum of squares, indicated that the width of the exit access was statistically significant (p << 0.0005) to crowd walking speed, whereas occupant configuration was statistically insignificant (p = 0.420 > ?). The effect of occupant configuration on crowd walking speed was further analyzed. All 10 pairwise comparisons among levels of occupant configuration; C 1 = 2, C 2 = 4, C 3 = 5, C 4 = 7, C 5 = 9 occupants, were evaluated. The results in Appendix 5.4 reveal that none of the levels of occupant configuration was statistically significant with respect to crowd walking speed. 62 Table 8 Crowd normal walking and crawling speeds (m/s) at different configuration and exit access width levels C 1 = 2 1.23 1.19 1.22 1.22 1.25 1.27 C 2 = 4 1.18 1.24 1.27 1.30 1.19 1.14 C 3 = 5 1.23 1.20 1.27 1.25 1.17 1.18 C 4 = 7 1.26 1.21 1.20 1.27 1.10 1.15 C 5 = 9 1.28 1.20 1.28 1.33 1.14 1.15 C 1 = 2 0.71 0.72 0.74 0.74 0.66 0.63 C 2 = 4 0.65 0.71 0.70 0.81 0.69 0.68 C 3 = 5 0.66 0.68 0.76 0.77 0.68 0.66 C 4 = 7 0.69 0.66 0.75 0.81 0.62 0.64 C 5 = 9 0.68 0.63 0.76 0.73 0.64 0.66 Crawling W 3 = 5 Activity Configuration (occupants) Exit access width (ft) W 1 = 3 W 2 = 4 Walking The interaction between occupant configuration and exit access width was significant (p = 0.014 < ?). This implies that occupant configuration has no effect on crowd walking speed. However, when the effect of occupant configuration is examined at different levels of exit access width, it is concluded that this is not the case. In other words, occupant configuration has an effect on crowd walking speed, but it depends on the level of exit access width. Therefore, the knowledge of the interaction between the 63 occupant configuration and the exit access width is more useful than the knowledge of the main effect of each factor independently. Next, the impact of exit access width and occupant configuration on crowd crawling speed was examined (hypotheses 3 and 4). The analysis of variance (ANOVA) for crowd crawling speed, illustrated in Appendix 5.5, indicated that the width of the exit access was statistically significant (p << 0.0005) to crowd crawling speed, whereas occupant configuration was statistically insignificant (p = 0.712 > ?). As a result, the effect of occupant configuration on crowd crawling speed was further analyzed. The pairwise comparisons among levels of occupant configuration with respect to crowd crawling speed; C 1 = 2, C 2 = 4, C 3 = 5, C 4 = 7, C 5 = 9 occupants, revealed similar results to crowd walking speed; none of the levels of occupant configuration was statistically significant. Furthermore, the interaction between occupant configuration and exit access width was insignificant (p = 0.406 > ?). This implies that occupant configuration has no effect on crowd crawling speed even when examined at different levels of exit width access. 5. Discussion This study examined the impact of the occupant configuration (number of occupants) and the width of the exit access on crowd normal walking and crawling speeds. It has been demonestrated that the exit access width is significant to both crowd walking and crawling speeds (p<0.0005). However, the occupant configuration is insignificant to both speeds (p crowd walking = 0.420 and p crowd crawling = 0.712). Crowd walking speed presented in the study fits the normal distribution. At ? = 0.05, the p-value 64 for the normal distribution for crowd mean walking speed (p walking = 0.795 > ? = 0.05) providing a good fit of normality for crowd walking (Figure 11). The mean of the walking speed is 1.22 (95% confidence interval of 1.20 and 1.24 m/s), with a standard deviation of 0.05 (95% confidence interval of 0.04 and 0.0 m/s). 1.301.251.201.151.10 Median Mean 1.251.241.231.221.211.201.19 1st Quartile 1.1800 Median 1.2200 3rd Quartile 1.2700 Maximum 1.3300 1.1987 1.2393 1.1923 1.2500 0.0432 0.0730 A-Squared 0.23 P-Value 0.795 Mean 1.2190 StDev 0.0543 Variance 0.0029 Skewness -0.140984 Kurtosis -0.453714 N30 Minimum 1.1000 Anderson-Darling Normality Test 95% Confidence Interval for Mean 95% Confidence Interval for Median 95% Confidence Interval for StDev 95% Confidence Intervals Figure 11. Normality test of crowd walking speed. The study further revealed that none of the occupant configuration levels had an impact on crowd crawling speed (p-values >> ?). Thus, the focus has been on the exit access width. Pairwise comparisons among levels of the exit access width were conducted. The results in Appendix 5.5 demonstrate that there is a significant difference of crowd crawling speed at the exit access width of 3 ft when compared to that at 4 ft (p = 0.001 << 0.05), while it is statistically insignificant at 5 ft exit access width. In other words, at any occupant configuration level, crowd crawling speed increases at the 4-ft 65 exit access width, but then decreases at a larger exit access width (5 ft). Figure 12 illustrates the effect of the levels of the exit access width on the mean crowd crawling speed. 543 0.750 0.725 0.700 0.675 0.650 Exit Access Width (ft) M ean C r o w d C r aw l i n g S p eed ( m / s ) Figure 12. Main effect plot of exit access width on crowd crawling speed. Observations from the study indicate that two crawlers can barely fit in the 3-ft wide exit access (Figure 13a), which results in a mean crowd crawling speed of 0.68 m/s. When the width increases to 4 ft (Figure 13b), the two crawlers can now comfortably move along the track at a faster speed (0.76 m/s). When the exit access width is extended to 5 ft (Figure 13c), it is expected that crawling speed would either increase or remain similar to that in 4-ft width. On the contrary, crowd crawling speed has decreased significantly (0.66 m/s) due to the fact that more crawlers could line up in parallel. 66 (a) (b) (c) Figure 13. Study observation at (a) 3-ft, (b) 4-ft, and (c) 5-ft wide exit access width. The primary conclusion of those observations is that the location of crawlers with respect to the exit access width affects the density of crawlers, which is also critical to crowd crawling speed calculations. In order to calculate the crowd density, the number of crawlers in a unit area has been captured through the camcorder as crawlers pass through the designated area along the test track. Appendices 5.6 and 5.7 show the calculations of crowd density and the regression analysis, respectively. The relationship between crowd crawling speed and crowd density is shown in Figure 14. The quadratic model (p-value = 0.004) appears to provide a good fit to the data. The R 2 indicates that crowd density accounts for 42.7% of the variability in crowd crawling speed. )/( ),/( 1503.02909.07973.0 2 2 mpersonsDensityCrowdd andsmSpeedCrawlingS where ddS = = ?+= (1) 67 2.001.751.501.251.000.750.50 1.1 1.0 0.9 0.8 0.7 0.6 Crowd Density (Occupant/m2) C r ow d C r a w l i ng S p e e d ( m / s ) S 0.0593124 R-Sq 42.7% R-Sq(adj) 37.0% Regression 95% CI 95% PI Crowd Crawling Speed = 0.7973 + 0.2909 Crowd Density - 0.1503 Crowd Density**2 Figure 14. The relation between crawling speed and density on a flat surface. 6. Conclusions Occupant movement in evacuation models is commonly based on the density of the space, which is currently limited to walking speed on flat surfaces and stairs. The present study investigates the relationship between crowd density and occupant walking and crawling movement. The latter is a physical response to environmental conditions in fire. This is accomplished by examining the impact of occupant configuration (number of occupants) and exit access width on crowd walking and crawling speeds on a flat surface. The findings of the study statistically show that the exit access width is significant to both crowd walking and crawling speeds, whereas occupant configuration is insignificant to both speeds. The results further demonstrate that there is a significant difference in crawling speed at different levels of the exit access width. This implies that the density of 68 the crawlers affects crawling speed. The relationship between crowd crawling speed and density is best described in a quadratic regression model. Finally, there is a need to continuously develop new predictive movement methods, or enhance existing ones in order to cope with the level of detail required to ensure occupant safety. In light of the significant absence of crawling data in the literature, this study contributes to the field of fire safety by providing experimental data for use in evacuation models, improving the accuracy and functionality of existing and future models, and introducing a realistic movement algorithm to evaluate the consequences of crawling on model outcomes. The ability to directly assess the impact of fire and smoke conditions upon evacuee performance requires the use of more sophisticated computational tools and reliable evacuation and fire data. 69 CHAPTER 6 THE APPLICATION OF EVOLUTIONARY COMPUTATION IN LAYOUT DESIGN FOR WALKING AND CRAWLING EGRESS Abstract. According to the Life Safety Code ? , building design and structure must provide protection to the occupants of a building in order to reach safety. As evacuation models are implemented to understand and assess building designs to assure occupant safety, the effectiveness of such evaluation relies heavily on the models? ability to reflect the detailed interaction between the occupant, building design, and environment. The purpose of this study is to demonstrate the application of evolutionary computation techniques, namely the Estimation of Distribution Algorithm (EDA), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO), in building design for walking and crawling egress. This has been undertaken by evolving the optimal placement and number of exits required to minimize evacuation time. The algorithms are applied to a layout known to be in compliance with the Life Safety Code ? . The best exit configurations are presented for each algorithm. The performance of the algorithms varies by activity. A comparison between the algorithms? performance is also drawn. The study suggests that the algorithms have the potential to be implemented in more complex design problems. The study further suggests the need to validate the configurations found by the algorithms by conducting actual evacuation drills. 70 1. Introduction Evacuation procedures and planning present a challenge to building occupants and emergency responders during evacuation and rescue operations. The challenge is partially caused by the creative designs and complex structures that exist in modern buildings. The ongoing trend of advancing knowledge in building designs and structures has raised major concerns for occupant safety. Innovative methods and approaches are needed to understand and assess these designs to assure occupant safety and verify building compliance with standards and guidelines. Traditionally, prescriptive codes have been applied to building designs to establish occupant safety without the need to demonstrate the level of safety achieved, or the effectiveness of evacuation procedures [1]. A more recent approach to evaluate occupant safety in building designs lies in the application of performance-based assessment techniques such as expert analysis, engineering (hydraulic) calculations, and evacuation drills [2]. The application of these techniques introduces major obstacles to safety engineers. For instance, expert analysis is a qualitative technique rather than a quantitative one, and is based on individuals? sole experience and judgment, engineering calculations consider a number of simplifying assumptions, which ignore the representation of evacuation behavioral complexity, and evacuation drills present ethical, practical, and financial difficulties to safety engineers. A potential alternative to these challenges and obstacles lies in computer-based evacuation models. The development of evacuation models in the last three decades has mainly contributed to the assessment of occupant safety and evacuation procedures in a variety of building designs, under a range of environmental conditions. The effectiveness of such evaluation relies mainly on the models? ability to reflect the detailed interactions 71 between the occupant, building design, and environment. The deterioration of environmental conditions during a fire, in terms of heat and smoke, and the interaction of occupants with such conditions influence the adoption of new behavioral and physical responses [3-6]. A number of studies [1, 2, 7-9] have suggested crawling as a physical response to a descending hot layer of smoke. As a result, it is important to understand the robustness of evacuation procedures and the consequences of encountering such response when assessing building designs based on the standards and guidelines of the Life Safety Code ? [10]. According to the Code, the components of a building design and structure must provide protection to the occupants of a building in order to reach safety. The Code uses the term means of egress to reflect the compliance of those components with standard and guidelines. The Code defines means of egress as ?a continuous and unobstructed way of travel from any point in a building or structure to a public way consisting of three separate and distinct parts: (1) the exit access, (2) the exit, and (3) the exit discharge.? In addition, the geometry of a building, the location of exits, and the number of exits influence the means of egress for all those occupying a building. The purpose of this study was to evaluate the application of evolutionary computation techniques, namely the Estimation of Distribution Algorithm (EDA), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO), in building designs to assess the means of egress for walking and crawling occupants by evolving the location and number of exits required to minimize total evacuation time. 72 2. The Approach In order to examine the effect of occupant crawling on building design in terms of the optimal placement and number of exits, an evacuation model needs to be developed. The layout selected for this study, a ballroom, is representative in terms of the area, number of occupants, exit width, and occupant load factor to be in compliance with the Life Safety Code ? [10]. Occupant walking and crawling speeds for the model were employed from experimental studies (Chapter 3 of this dissertation). Occupant sizes and anthropometric measurements were obtained from the Civilian American and European Surface Anthropometry Resources (CAESAR) [11, 12]. For validation purposes, the performance of the evacuation simulation model was then compared to another well- known evacuation model, namely ASERI. Finally, several evolutionary computation techniques were implemented to investigate the optimal location and number of exits that minimized the overall evacuation time. Figure 15 illustrates the approach followed in this study. 3. The Development of the Evacuation Model Since the keystone work of quantifying people movement in nonemergency conditions [13, 14], a growing body of research has been recognized in modeling building evacuation in both normal and emergency conditions. Kuligowski [15] reported that the development of the first generation of computer evacuation models started in the mid 1960s. Since then, the number of evacuation models has significantly increased mainly due to advancing computational techniques and the availability of evacuation data [16]. 73 Figure 15. The approach to implementing evolutionary computation into an evacuation simulation model. Model Validation Walking & crawling experiments & CAESAR data (19 ? 29) age stratum Individual walking and crawling speeds Quantitative Data Body size for walkers & crawlers Building evacuation scenario (compliant with Safety Code) Geometry/drawing/ interior layout/exits Qualitative & Quantitative Data Occupant physical attributes/location Occupant behavioral attributes Evacuation procedures Start Approach Evacuation Simulation Model Modeling method/structure Occupant movement/behavior Input data to model Output representation Evolutionary Computation End Approach Simulation Results ASERI 74 Evacuation models vary in structure, computation method, and complexity. The simplest model structure utilizes straightforward calculational methods to estimate evacuation times. The next level of complexity is network flow (flow-based) evacuation models, which represent paths and exits by arcs and nodes, respectively [17]. Although network models are useful to minimize distance to exit(s) and/or evacuation time, they lack the ability to represent the stochastic nature of the evacuation process caused by the human and hazard elements. The most complex models are the ones that incorporate occupant performance and behavioral variables into the evacuation process. In these models, a set of attributes are assigned to each occupant (agent) to assess the optimal escape route. The simulation is usually performed in a series of time steps to track occupant movement and decision-making (behavior). 3.1. The Model Structure In order to evaluate the application of evolutionary computation techniques in building designs for walking and crawling occupants, an evacuation model is needed to simulate occupant movement and behavior. Helbing and Moln?r [18] suggested that occupant motion can be realistically described using a mathematical model named the social forces model. The main effects that determine the motion of an occupant are reaching a certain destination at certain period of time, which requires desired direction and velocity, and a repulsive effect which is the influence of an occupant on others or that provided by a boundary. The evacuation model in the study was based on a simplified framework of the social forces model, namely the artificial potential field approach [19]. In the model, an exit location creates an attractive force for an occupant, while obstacles/barriers and other 75 occupants act as repulsive forces. The resultant force acting on an occupant forms a potential field, whose gradient drives the occupants at every time-step of the simulation. In order to calculate the movement of an occupant, each force is inversely proportional to the square of the distance between the occupant and the source of the force. If A, O, and E denote the set of all attraction, obstacle, and occupant vectors, respectively, and ),( qpd rr represents the Euclidean distance between vectors p r and q r , then, for a given occupant position, the resultant force acting on that occupant )( pF r is calculated as shown in Equation 1. The gradient of F is calculated according to Equations 2, 3 and 4. To compute the direction of movement, the current F? is averaged with the previous one, as shown in Equation 5. In order to determine occupant change in location during a time step, the gradient vector is normalized and multiplied by the occupant speed. ??? ? ? ?? ??= Oo pe EeAa epdopdapd pF r rr rr rrrrrr r 222 ),( 1 ),( 1 ),( 1 )( (1) y F x F F ? ? ? ? =? , ??? ? ? ?? ?? ? ?? ? ?? = ? ? Oo pe Ee xxxx Aa xx epd ep opd op apd ap x F r rr rr rrrrrr 444 ),( )(2 ),( )(2 ),( )(2 (2) (3) (4) ??? ? ? ?? ?? ? ?? ? ?? = ? ? Oo pe Ee yyyy Aa yy epd ep opd op apd ap y F r rr rr rrrrrr 444 ),( )(2 ),( )(2 ),( )(2 ( ) 2 1 tt avg FF F ?+? =? ? (5) 76 The repulsive forces acting on an occupant from obstacles/barriers and other occupants diminish when the distance to the occupant exceeds a pre-determined minimum value. The obstacle o r and occupant e r vectors are checked at every time step of the simulation. When the distance is within 0.03 m (0.1 ft), the contribution of those particular repulsive vectors are included in the summation of the resultant force. The minimum distance applied here is more conservative when compared to that applied in other studies [20-21], where a distance of 0.08 m (0.26 ft) is considered to activate the repulsive forces on an occupant. The model also accounts for trampled and/or crushed occupants during the evacuation process. At each simulation time-step, the model checks each occupant for overlapping by other occupants or obstacles by a distance of the occupant radius. Therefore, dead occupants do not obstruct the movement of the other ones since they no longer act as repulsive forces. 4. The Layout Design The layout design for this study consists of a small banquet hall (39? x 22?); with 7 fixed obstacles, and 24 occupants, as illustrated in Figure 16. The area of the room, number of occupants, and occupant load factor are all in compliance with the Life Safety Code ? [10]. The effect of the layout symmetry on the level of difficulty in searching for an optimal solution is yet to be explored. This is because of the unexpected number of local minima in the artificial potential field in the evacuation simulation. The possible exit locations are determined by calculating how many 3-ft wide doors would fit along each wall without separation. If a wall does not allow an integral number of doors, the set of doors are centered along the wall with the excess space placed 77 in each corner. The doors are then numbered starting with the far left door along the north wall and continuing clockwise. In this way, the presence or absence of the exits is represented by a one-dimensional Boolean array. Although this approach is limited to a set of fixed door locations, it uses a fixed-length encoding scheme to represent a variable number of doors. In all, the room had the potential for 35 specific exit door locations. Figure 16. The layout design for the banquet hall. 5. Occupant Size and Shape Representation The size and shape of individuals in an evacuation model influence occupant movement, density, and response to surroundings. Many evacuation models rely on movement techniques to model the dynamic of spatial systems during the evacuation process, where a discrete environment is updated in steps according to global rules. As a result, occupant shape is a critical element of that spatial system representation and 78 dynamic environment. Meanwhile, the size of individuals assesses the method of movement throughout a building and simulates the presence of occupants and building enclosure such as walls, rooms, exits, corridors, stairs, and obstacles. The majority of the models obtain their occupant shape and size from anthropometric studies [22, 23], or people movement research [13, 14, 24-26]. The scarcity of civilian anthropometric data led researchers to seek alternative anthropometric measurements to represent occupant shape and size in evacuation models. Predtechenskii and Milinskii [13] and Ando et al. [27] observed a projected area of people based on the average dimensions (measurements) of a person?s width and breadth obtained at the shoulder and chest levels, respectively, while Fruin [14] applied shoulder breadth and body depth measurements obtained from U.S. Army human factors design recommendations. Figure 17 exemplifies a range of anthropometric measurements and body sizes adopted in some crowd movement studies. Figure 17. A range of anthropometric measurements and body sizes adopted in people movement studies. Fruin [14] 95th %-ile of fully clothed male worker (a = 0.58 m, c = 0.33 m, area = 0.150 m 2 or 1.62 ft 2 ) U.S. Army human factors design manual (a = 0.61 m, c = 0.46 m, area = 0.22 m 2 or 2.36 ft 2 ) Predtechenskii and Milinskii [13] caxarea 4 ? = , a = shoulder breadth, c = body depth Adult in summer dress (a = 0.46 m, c = 0.28 m, area = 0.1 m 2 ) 79 On the contrary, crawling modeling studies (1, 2, 7-9] and evacuation models [28, 29] have never taken anthropometric measurements into consideration when simulating crawlers size and shape. Thus, as reliable observations of civilian anthropometric measurements are becoming more available due to advanced modern technologies, it is essential to incorporate recent and reliable anthropometric measurements into evacuation models. The most comprehensive and reliable source for civilian anthropometric data available to date is that of the Civilian American and European Surface Anthropometry Resources or CAESAR [11, 12]. The CAESAR project is an international anthropometric survey that collected 3-D whole body scans for two postures; standing and seated, using a cyberware WB4 scanner. The project measured more than 13,000 3-D scans taken from 4,431 subjects sampled from the U.S., Canada, Netherlands, and Italy, and classified into three age strata; 18 ? 29, 30 ? 44, and 45 ? 65. The anthropometric body measurements of CAESAR were used in this study to model walkers and crawlers physical attributes. According to the Human Engineering Guide to Equipment Design [30], the crawling position is achieved when a subject rests on their knees and flattened palms with arms and thighs perpendicular to the floor and feet comfortably extended and spaced. Crawling length is measured from the most rearward point on the foot (the tip of the longest toe-first or second digit) to the most forward point on the head (vertex). Since CAESAR did not collect data on crawling length, an approximation (Equation 6) has been developed from CAESAR body dimensions (Figure 18). The range of movement for ankle extension is based on data from Barter et al. [31]. For simplicity, crawler width is represented in the study from the CAESAR shoulder breadth (bideltoid) dimension (Figure 19). 80 Figure 18. An approximation of crawling length (sagittal plane). Figure 19. Crawling dimensions based on CAESAR measurements (transverse plane). )}cos({ extensionanklexlengthfootmalleoluslatteralright toEpicondylefemorallateralrightheightsittinglengthCrawling + +? (6) 81 The only representation of crawler shape in evacuation literature was found in Nagai et al. [7, 8], where crawlers were represented by a 0.4 m x 0.8 m-rectangular grid. For the purpose of this study, crawler shape is approximately represented by three circles attached in a linear configuration; a leading circle for the head and shoulder, and two ?following circles? for the lower back and extremities, respectively as illustrated in Figure 20. In order to simulate crawling movement in the potential field model, ?the following circles? contribute to repulsive forces to other leading circles but not to other attached circles. The anthropometric estimates of crawling body dimensions for U.S. male adults aged 19 ? 29 years, based on CAESAR data, are presented in Table 9. Figure 20. Mathematical representation of occupant crawling shape and size. Table 9 Crawling body dimensions for U.S. male adults aged 19 ? 29 years (mm) Dimension ? ? 95th %ile Crawling Length 1531 69 1669 Crawling Width (Shoulder Breadth-bideltoid) 494 34 562 Hip Breadth (sitting) 375 36 447 447 mm 447 mm 562 mm 1669 mm 82 6. Model Verification and Validation One of the most challenging tasks facing evacuation model developers is the verification and validation of their models. According to Banks et al. [32], verification relates to the correct structure of a model by comparing the computer representation to the conceptual model, whereas validation attempts to confirm that the model is a true representation of a real system. With respect to evacuation models, verification can be conducted by testing the performance and functionality of various modules of the computer model. This includes checking the code to examine the performance of model components, and testing a series of model capabilities to ensure the accurate representation of the model functionality [33]. In this study, the evacuation simulation model has been verified by inspecting its code routinely and assessing its ability to perform scenarios with expected outcomes. The majority of evacuation modeling literature has concentrated on model validation, assuming verification is an integral part of the development phase of the model. Evacuation models have been validated against building code requirements [34], fire drills and movement experiments [35-41], literature on past evacuation trials [42-44], or other evacuation models [45, 46]. For the purpose of this study, the evacuation simulation model has been validated against another evacuation model, ASERI [35]. The selection of ASERI is due to its continuous space structure, occupant behavior and movement representation, ability to import CAD drawings, and visualization capability. The layout utilized for the study, with two random locations of 3-ft exit door (scenarios are illustrated in Appendix 6.1), has been run by both models. Since ASERI is not designed to model crawling, the validation has been conducted for walking. 83 The input data to the models are occupant speed and body size. Occupant speed is normally distributed with a mean of 1.5 m/s and a standard deviation of 0.16 m/s, based on the results from Chapter 3 of this dissertation. However, since ASERI uses normal distributions that are limited at the boundaries given by the standard deviation, the standard deviation of occupant movement in ASERI is set at 0.48 m/s to contain over 99% of the speed distribution. Occupant size is represented by a circle with a diameter equivalent to 95 percentile U.S. male adults aged 19 ? 29 years representing shoulder breadth (bideltoid), based on U.S. CAESAR data (Table 9). Once the input data were identified for each model, total evacuation times resulted from 100 simulation runs, for each scenario, have been compared (Appendix 6.2). The results shown in Table 10 reflect reasonable outcomes. In scenario 1, where the exit door is located in the middle bottom of the banquet hall, the potential field model under-predicted the average total evacuation time by 1.4 sec in comparison with ASERI. In scenario 2, where the exit door is placed in the bottom right of the banquet hall, the potential field model over-predicted ASERI?s average total evacuation time by 0.9 sec. Table 10 Comparison between total evacuation times of 100 simulation runs produced by ASERI and the potential field model Scenario 1 Scenario 2 ASERI Potential Field Model ASERI Potential Field Model Min 9.2 7.4 11.6 11.3 Max 12.8 14.8 14.4 16.6 Average 11.0 9.6 12.9 13.8 84 7. Evolutionary Computation (EC) Evolutionary computation is the discipline devoted to the design, development, and analysis of problem solvers based on natural selection [47]. Evolutionary computation techniques have been applied to a range of design, scheduling, and optimization problems [48]. Figure 21 illustrates the basic structure of an EC. A set (population) of candidate solutions (individuals) for the optimization problem is randomly initialized and evaluated with respect to an objective function. The evaluation function assigns candidate solutions fitness values corresponding to how well the solutions optimize the problem. After the initial population is evaluated, a subset of the population is chosen to become parents for the next generation, allowing the selected parents to create offspring through procreation operators such as crossover and mutation. The procreation operators modify and combine the genetic composition of the parents to create offspring. A subset of the offspring is evaluated and selected for inclusion in the next generation of the population. This process is repeated until some stopping criterion is reached; the discovery of an optimal solution or exceeding a maximum number of iterations. Figure 21. Pseudocode structure of an EC. 85 7.1. Estimation of Distribution Algorithms Estimation of Distribution algorithms (EDAs) attempt to leverage the statistical properties of the fitness landscape in order to create children. In EDAs, there are neither crossover nor mutation operators. During each generation, the new population is created by sampling the probability distribution of the current population. For binary-coded chromosomes, the EDA makes use of the probability distribution function of selected individuals. For real-coded chromosomes, the probability density function is used instead [49]. In both cases, a set of parents is selected from the population. The probability distribution/density function is calculated for the set, and used to create a new population of offspring. EDAs operate along one dimension at a time when creating children (offspring). Essentially, for binary-coded chromosomes along a particular dimension, a random parent is selected, and its gene value is used to create the child gene. For the real- coded chromosomes along a particular dimension, the mean and standard deviation of the set of the parent genes are calculated. Each child gene (along that dimension) is created according to Equation 7, where i denotes the offspring (child) number, dim represents the dimension, and N(0,1) is the standard normal random variable, which differs for each offspring by sampling the probability density function for the set of parents. )1,0(. dimdimdim, Noffspring i ?? += 7.2. Genetic Algorithms Genetic Algorithms (GAs) were developed by John Holland through his work in simulating natural evolution using binary strings (chromosomes), which represent candidate solutions for the problem of interest [50]. The GA starts with a population of (7) 86 randomly generated chromosomes. The population goes through a series of generations. During each generation, a set of chromosomes from the population is selected, through some selection strategy, to become the parents in the next generation. Once the parents are chosen, they are exposed to one or both of the genetic operators; crossover and mutation. During crossover, the chromosomes of two parents are mixed to form one or more offspring. On the other hand, mutation modifies the chromosome of a single parent to produce an offspring. The modification typically entails some type of random change applied to one or more of the alleles (i.e. components) of the chromosome. Once the genetic operators are applied to the parents, a set of offspring is produced. Finally, the GA determines which of the offspring and parents survive to the next generation. 7.3. Particle Swarm Optimization Algorithm Particle Swarm Optimization (PSO), developed by Kennedy and Eberhart, is inspired by the movement and behavior of bird flocks and insect swarms to solve optimization problems [51]. In the PSO model, each particle is composed of three vectors ,, px rr and v r which represent the particle?s current location, best location found, and velocity, respectively. The vectors are of the same dimensionality as the search space, and each particle maintains a value corresponding to the fitness of the x r vector and a value corresponding to the fitness of the p r vector. As the particles in the swarm move through the search space, their velocities are updated according to Equation 8. ()( ) ( )( ) idididididid xgRxpRvv ?+?+= 1,01,0 2211 ?? (8) 87 In the equation, id v is the velocity of the ith particle along the dth dimension. The g vector represents the best location found by the particles in the current vector?s neighborhood, and R 1 (0, 1) and R 2 (0, 1) are random numbers in the interval [0, 1]. Finally, 1 ? and 2 ? are two constants that control the influence of the individual and global best locations, respectively, on the particle?s velocity. These values are often referred to as cognitive and social learning rates [52]. After the velocity vector and the particles? location are updated, the fitness of the new location is evaluated and compared to the fitness of the particle?s personal best location. If the new location is better, then it becomes the new personal best location for the particle. 8. Methodology 8.1 Evaluation Function The assessment of the fitness of a candidate solution with respect to evaluating a set of exit locations required several criteria. The most important one is total evacuation time, which is defined as the time needed for all occupants to leave the banquet hall. Another element to take into account is the number of occupants who are crushed to death in their attempt to evacuate. The penalty for a crushed occupant, in the fitness function, is significantly higher than that for an occupant who is unable to escape by the end of the allotted simulation time. This is because a crushed occupant has no chance of escaping regardless of time. Since the algorithm would likely generate solutions where each occupant has a door nearby, which is noncompliant with the Life Safety Code ? guidelines, the third and final element of the fitness function is the number of exit locations. 88 In order to calculate the fitness value of a given configuration of exit locations, the simulation evacuation model was set at a maximum simulation time (T max ). The limit values for walking and crawling maximum evacuation times resulted from 100 simulation runs (Appendix 6.3) of a single-exit configuration, located in the middle of the lower wall of the banquet hall (Scenario 1 in Appendix 6.1). Such a configuration was reported to be a common best solution among similar studies; Garret et al. [53] and Muhdi et al. [54]. The T max limits for walking and crawling were set at 10,000 and 35,100 milliseconds (ms), respectively. Each limit value represents three standard deviations from the mean of its 100 simulation runs of each activity (? + 3?). Two different fitness functions were applied, depending on the number of occupants able to evacuate. At any simulation run, when all occupants safely evacuate the banquet hall in a time less than the allotted maximum evacuation time (t < T max ), the fitness value for a configuration of exits is calculated according to Equation 9, where n represents the number of exit doors in a configuration. The fitness function favors configurations with n ? 2 due to the high penalty score against configurations with three or more exits. If some occupants are unable to evacuate due to trampling to death or running out of time, the fitness score is computed via Equation 10, where a represents the number of evacuees who are still alive but could not escape in the time allowed, and d represents the number of evacuees who are trampled to death. Thus, the fitness function penalizes for long evacuation times, the number of occupants who are crushed, and configurations with three or more exits. )2)2,(max(000,10 ?+ nt (9) 89 )2)2,(max(000,105.1 maxmax ?+?+? ndTaT For each walking or crawling evacuation simulation run, occupant walking and crawling speeds were drawn randomly from normal distributions, obtained from Chapter 3 of this dissertation, with ? walking = 1.5, ? walking = 0.16, ? crawling = 0.77, and ? crawling = 0.08 m/s. The evaluation function (evacuation simulation) was run 10 times for a given layout configuration to establish a 95% upper bound for the 10 fitness values based on the mean and standard deviation of the fitness evaluations (fitness upper = fitness fitness skx .+ ). The k value is 3.981, obtained from Jay L. Devore, Probability and Statistics for Engineering and Sciences, 7 th edition. 8.2 Encoding Scheme Each chromosome in the population was encoded as an array of N binary values, where N denotes the maximum number of exits that may be located along the perimeter of the banquet hall. The binary values represent whether a door should be placed at that location of the room or not (0 for no door, 1 for door). 8.3 EC Setup An elitist EDA was used to search for the best layout configuration. This indicates that the best individual for each generation was allowed to survive. The EDA was constructed with a population size of 100. For the GA, the initial population of 78 individuals was generated in a binary format, similar to that in Garret et al. [51]. A binary tournament was used to select parents. This implies that two individuals were randomly chosen from the population, their fitness values were compared, and the individual with the lower fitness value became a parent. Each pair of parents then underwent a uniform crossover, at the rate of 100%, to generate offspring. No modifications have been made (10) 90 on the offspring (mutation rate was set at 0%). The PSO was applied with 100 particles, a global neighborhood, and constriction coefficient. Updates were done asynchronously. The cognition and social rates were 2.8 and 1.3, respectively. 8.4 Experimental Setup For a given layout configuration, each EC was executed for 30 independent runs with a maximum of 25000 function evaluations per run. The EC used the upper bound of the fitness evaluation to evolve solutions. Hence, 2500 different individuals were evaluated by the EC, and each individual was assessed 10 times, giving a total of 2500 x 10 = 25000 function evaluations. 9. Results The purpose of this study was to evaluate the application of Estimation of Distribution Algorithm (EDA), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO), in building designs to dictate the means of egress for walking and crawling occupants. This has been conducted by evolving the location and number of exits required to minimize total evacuation time. Each algorithm produced 30 runs of best exit configurations, which were often unique solutions to the evacuation planning problem. Therefore, each run of the EC returned the best suggested exit location. Appendix 6.4 lists all 30 solutions for each algorithm, along with their function evaluations, fitness values, and exit locations, for walking and crawling, respectively. For both activities, two of the algorithms (EDA and GGA) produced 2-exit best solutions, while PSO yielded a 3-exit solution. The exit locations varied by algorithm and activity. For walking, the best exit locations for the EDA and GGA were 13 and 19, whereas for 91 the PSO solution, the best exit locations were 10, 17, and 21. On the other hand, the best exit locations for crawling were 3 and 13 for the EDA, 19 and 29 for the GGA, and 12, 17, and 21 for the PSO. Table 11 lists the percentage of the 30 solutions that have number of exits equivalent to that found in the best exit configuration. Figures 22 through 26 illustrate the best exit locations of EDA, GGA, and PSO solutions for both activities. The similarity between best solutions found by each algorithm was captured based on the probability calculations of each of the 40 exit locations being selected by all of the 30 runs of a single algorithm. Figures 27 and 28 present the probabilities of best exit locations for all 30 runs of each algorithm for walking and crawling, respectively. Figure 27 clearly shows that there is at least 20% chance that all three algorithms would choose exit location 17 in their best solution for the walking activity. However, such a chance decreases to 10 % for crawling when exit 19 or 29 is chosen, as shown in Figure 28. The maximum probability values of best exit locations range from 0.27 to 0.37 for walking, and 0.27 and 0.47 for crawling. Appendix 6.5 provides the probability values for all exit locations classified by activity and algorithm type. Table 11 The percentage of the solutions with a certain number of exits Number of Exits EDA GGA PSO EDA GGA PSO 2 96.7 83.3 0 100 100 0 3 3.3 16.7 20 0 0 16.7 4 - - 23.3 - - 16.7 5 -40 -20 6 or more - - 16.7 - - 46.6 Walking Crawling 92 Figure 22. Best exit locations of the EDA and GGA solutions for walking. Figure 23. Best exit locations of the PSO solution for walking. Exit Location 13 Exit Location 19 Exit Location 17 Exit Location 10 Exit Location 21 93 Figure 24. Best exit locations of the EDA solution for crawling. Figure 25. Best exit locations of the GGA solution for crawling. Exit Location 13 Exit Location 3 Exit Location 19 Exit Location 29 94 Figure 26. Best exit locations of the PSO solution for crawling. 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 Exit Location Pr o b a b ili ty EDA GGA PSO Figure 27. Probabilities of best exit locations for walking. Exit Location 17 Exit Location 12 Exit Location 21 95 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 Exit Location Pr o b a b ili ty EDA GGA PSO Figure 28. Probabilities of best exit locations for crawling. 10. Discussion This study examined the application of evolutionary computation algorithms in evacuation planning to determine the location and number of exits required to optimize evacuation time. Although the algorithms undertook the same planning problem (banquet hall), their performance in finding best configurations differed for both walking and crawling occupants. For walking, both the EDA and the GGA required significantly fewer mean function evaluations and achieved lower mean fitness values than the PSO when tested with a two-sample t-test at ? of 0.05 (p << 0.0005). However, there was no significant difference in mean function evaluations or fitness values between the EDA and the GGA. In regard to crawling, the PSO needed significantly less mean function evaluations than the EDA and the GGA (p = 0.001 < ? = 0.05). However, a comparison between mean fitness values for crawling revealed that the EDA and GGA significantly 96 achieved lower mean fitness values than the PSO (P << 0.0005). Appendices 6.6 and 6.7 provide the t-test comparisons of mean function evaluations and fitness values for walking and crawling, respectively. Once the best exit configurations were found, the evacuation process was then simulated 1000 runs to compare the average total evacuation time and number of casualties for each activity. Such comparisons further confirm the quality of the best configuration found by each algorithm. Tables 12 and 13 summarize the results of the simulation runs for walking and crawling, respectively. For the walking activity, the EDA and GGA best exit configurations resulted in a total evacuation time that is significantly longer than that found by the PSO due to the extra exit location (2 exits for the EDA and GGA vs. 3 for the PSO). However, the evacuation simulation runs revealed that the number of casualties resulted is significantly less for the EDA and GGA than that for the PSO (P << 0.0005). Such observation clearly indicates that the location of exits in walking is more important to the evacuation planning problem than the number of exits when the number of exits in a solution is relatively low. For the crawling activity, the best exit configurations found by the EDA and the GGA (Figures 24 and 25) were almost similar because of the symmetrical geometry of the design problem. Therefore, there is no significant difference in total evacuation times for crawling between the two solutions (P = 0.221 > 0.05). However, since the best exit solution found by the PSO is located on the right side of the hall, it takes occupants more time to reach the exits. As a result, total evacuation time is significantly longer for the PSO in comparison with the EDA and GGA. The longer it takes to reach the exits, the less congestion levels are at the exits, which results in fewer casualties, as shown in Table 13. Appendices 6.8 and 6.9 illustrate 97 the t-test comparisons of mean total evacuation time and number of casualties for walking and crawling, respectively. Table 12 Summary of the evacuation simulation runs for walking Evac. Time (ms) Number of Casualties Evac. Time (ms) Number of Casualties Min 6400 0 5300 0 Max 9600 2 8500 3 Mean 7759.7 0.22 6683.5 0.47 St. Dev 613.5 0.46 505.0 0.62 Exit Configuration (13,19) (10,17,21) Table 13 Summary of the evacuation simulation runs for crawling Evac. Time (ms) Number of Casualties Evac. Time (ms) Number of Casualties Evac. Time (ms) Number of Casualties Min 14900 0 14300 0 14400 0 Max 22700 3 23800 3 29100 2 Mean 17690.8 0.31 17759.5 0.34 18877.5 0.11 St. Dev 1219.4 0.54 1288.4 0.58 1778.9 0.31 Exit Configuration (3,13) (19,29) (12,17,21) 11. Conclusions The study has demonstrated the application of evolutionary computation techniques, namely Estimation of Distribution Algorithm (EDA), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO), in building designs to dictate the means 98 of egress for walking and crawling occupants. For both activities, the EDA and GGA generated 2-exit best solutions, while the PSO found 3-exit best solutions. The performance of the algorithms to find such solutions has varied by activity. For walking, it has been shown that there was no significant difference between the three algorithms in terms of function evaluations. However, the EDA and GGA outperformed the PSO in fitness values. For crawling, the PSO required significantly less function evaluations than the other two algorithms but resulted in greater fitness values. The study suggests that the EDA is particularly well-suited to solve such evacuation planning problem. Finally, although the algorithms are applied to a relatively simple design problem, they have the potential to be implemented in more complex designs. However, since such implementation is solely dependent on the outcome of the evacuation model used, a continuous development of evacuation models with accurate representation of occupant performance and behavior characteristics is highly needed, especially in deteriorating environmental conditions. There is also a need to constantly develop new predictive crawling movement methods to cope with the level of detail required in evacuation crawling. In light of the significant absence of occupant size and shape for crawling occupants in the literature, further research is needed to investigate the impact of crawling on the interaction between occupants during evacuation. Another future work is the validation of the design suggestions found by the algorithms in real evacuation scenarios. 99 CHAPTER 7 CONCLUSIONS 1. Introduction Computer evacuation models are a promising alternative to evaluate occupant safety and verify a building?s compliance with standards. The effectiveness of such evaluation relies exclusively on the models? ability to accurately demonstrate the dynamic interaction between occupant characteristics, building design, and environmental conditions. One of the important features incorporated into most evacuation models, relates to occupant characteristics. Regulations and fire safety codes, and the need for more reliable and validated computer evacuation models, suggest further attempts to understand and model occupant behavior and performance characteristics in fire. The complexity of modeling occupant characteristics during evacuation, and the relative scarcity of evacuation experiments in the literature, contribute to some extent to the continuous challenge of occupant data representation in computer evacuation models. It is apparent from the literature that there is a gap between the development and representation of occupant data in the models. The gap is even broader when modeling occupant behavior and performance responses to fire conditions since deteriorating conditions influence the occupants? adoption of new responses. 100 2. Summary of Findings An attempt has been made in this research to bridge the gap between the development and representation of occupant characteristics pertaining to crawling, one of the more important responses to evacuation in fire and smoke conditions. A review of the literature revealed an astonishing lack of crawling data in evacuation research, which poses fundamental challenges for evacuation modelers to integrate and validate the crawling performance and behavior into evacuation models. In order to bridge the gap between the development and representation of occupant crawling data, this research investigated occupant crawling speed compared to walking, and the effect of occupant characteristics; gender and body composition (BMI), on crawling in evacuation. The study then examined the impact of route design on evacuation times for crawling movements by comparing evacuation time for a straight route to an indirect route design, and the influence of gender and body composition on evacuation time for occupants crawling such as an indirect route. After that, the current study looked into the relationship between crowd density and occupant crawling movement, by examining the impact of occupant configuration (number of occupants) and exit access width on crowd walking and crawling speeds on a flat surface. The last part of the research focused on the application of evolutionary computation techniques in building designs for walking and crawling egress, which has been evaluated by evolving the location and number of exits required to minimize evacuation time. The results of the research can be summarized as follows. 1. Occupant movement data plays a key role in the usefulness of evacuation models. The development of crawling data and its representation in evacuation models 101 enhance the accuracy of evacuation models, and better evaluate the safety of evacuees. 2. There is a significant difference between normal walking and normal crawling speeds. Further, gender and body composition significantly impact individual crawling speed as they are unique characteristics to the individual. 3. The findings reveal a difference between evacuation times when crawling in different routes. Both gender and body composition have a significant impact on individual evacuation time when crawling an indirect route. The representation of different route designs in evacuation models can provide architects with a better understanding of occupant individual and global views of buildings, which might further enhances the robustness of their designs. 4. Exit access width is significant to crowd crawling speed, whereas occupant configuration plays less of a factor. The study demonstrates that there is a significant difference in crawling speeds at different exit access widths due to crowd density. 5. The relationship between crowd crawling speed and density is best described by a quadratic regression model. In light of the significant absence of crawling data in the literature, such a relationship contributes to the improvement of the accuracy and functionality of occupant movement in existing and future models. 6. Evolutionary computation techniques can be used to find optimal building designs for walking and crawling egress. The designs are evaluated by evolving the best exit configuration(s) to minimize total evacuation time. However, the reliability of 102 these techniques depends on the accuracy of the evacuation models utilized. The techniques have the potential to be implemented in more complex designs. 3. Limitations of Study It is as important to discuss the limitation of a research study, as it is to discuss the findings. The limitations of the study can be categorized as follows. 1. Participant representation: The experimental part of the study was based on a limited sample. The recruited subjects were in the 19-29 age stratum and healthy (both physically and cognitively). No consideration was given to other age groups or mobility capabilities. 2. Experimental settings: The experiments were conducted in a controlled environment. As in real evacuation scenarios, confounding variables may have an impact on the results. For instance, the crawling activity was performed on a smooth, dry, and flat surface. Testing crawling on a variety of surface textures (different coefficients of friction) and the presence of heat and smoke could result in more realistic performances. Another limitation of this study, related to experimental settings, was the examination of only two characteristics (gender and BMI). The impact of additional physiological characteristics such as heart rate, energy expenditure, and fatigue would provide evacuation models with more accurate representation of crawling. 3. The evacuation model constructed for the application of evolutionary computation incorporated a limited number of occupant performance and behavior attributes. Further, the evolutionary computation approach described in this study is not 103 applicable to all existing evacuation models. The integration of such approach has to be incorporated in the early design stages of evacuation models. 4. Recommendations for future research Future research should be conducted with larger samples with a focus on certain occupant characteristics such as age and mobility capabilities. Research is also needed in crawling on different types of surfaces and under different degrees of crowd levels to quantify crowd crawling. Another need lies in studying the effect of fatigue on crawling, and its representation in the adaptive decision making process in response to evacuation. Since the current study focuses on normal crawling, there was no effect of fatigue on human performance. However, the effect would be more apparent in longer test areas and under actual emergency environmental conditions. There is also a need to continuously develop new predictive movement methods, or enhance existing ones in order to cope with the level of detail required to ensure occupant safety. 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Umphress, ?The Application of Evolutinary computation in evacuation planning,? in Proceedings of the 9th International IEEE Conference on Intelligent Transportation Systems, Toronto, Canada, 2006. 127 APPENDICES 128 APPENDIX 3.1 INFORMED CONSENT 129 130 131 132 APPENDIX 3.2 PHYSICAL ACTIVITY QUESTIONNAIRE 133 APPENDIX 3.3 INDIVIDUAL WALKING AND CRAWLING PROCEDURE Purpose: To study and evaluate the effect of occupant characteristics on physical activities performed during evacuation. Method: 1. Read and sign informed consent. 2. Allow researcher to measure and record your height and weight. 3. Allow researchers to explain the procedure (researcher?s protocol). 4. Put on the Polar? Heart Rate Monitor (female research assistant available) 5. Rest for 5 min. 6. When instructed, walk at your normal pace down the test track. 7. Rest until your heart rate reaches a resting level. 8. Put on knee pads and gloves. 9. When instructed, crawl at your normal pace (Note: the crawling position means that you are supported with your knees and flattened palms. Your arms and thighs should be perpendicular to the floor and your feet are comfortably extended and spaced). 10. Rest and remove the knee pads and gloves. 11. Conclude the trial. 134 APPENDIX 3.4 PARTICIPANTS DATA IIII Walking 1.63 1.80 1.77 1.73 Crawling 0.89 0.93 0.86 0.90 Walking 1.67 1.77 1.68 1.70 Crawling 0.84 0.85 0.90 0.86 Walking 1.67 1.87 1.87 1.80 Crawling 0.88 0.84 0.85 0.86 Walking 1.45 1.49 1.50 1.48 Crawling 0.71 0.77 0.81 0.77 Walking 1.43 1.54 1.56 1.51 Crawling 0.84 0.74 0.78 0.79 Walking 1.48 1.50 1.47 1.48 Crawling 0.72 0.80 0.86 0.79 Walking 1.35 1.38 1.29 1.34 Crawling 0.74 0.74 0.75 0.74 Walking 1.31 1.41 1.39 1.37 Crawling 0.74 0.74 0.75 0.74 Walking 1.35 1.34 1.38 1.36 Crawling 0.76 0.78 0.75 0.76 Walking 1.51 1.62 1.72 1.62 Crawling 0.82 0.77 0.85 0.81 Walking 1.68 1.66 1.67 1.67 Crawling 0.76 0.86 0.88 0.83 Walking 1.55 1.59 1.67 1.61 Crawling 0.78 0.79 0.81 0.79 Walking 1.40 1.31 1.50 1.40 Crawling 0.71 0.70 0.78 0.73 Walking 1.35 1.46 1.46 1.42 Crawling 0.75 0.77 0.78 0.77 Walking 1.47 1.45 1.47 1.46 Crawling 0.68 0.70 0.74 0.71 Walking 1.33 1.25 1.30 1.29 Crawling 0.64 0.63 0.67 0.65 Walking 1.33 1.31 1.31 1.32 Crawling 0.64 0.68 0.70 0.67 Walking 1.23 1.28 1.30 1.27 Crawling 0.54 0.70 0.69 0.65 AverageSubject Gender BMI Activity Obese Obese Overweight Overweight Overweight Obese Obese Normal Normal Normal Female Female Female Normal Normal Overweight Overweight Overweight Obese Obese Female Female Female Female Male Male Female Female 17 18 Male Normal Male Male Male Male Male Male 13 14 15 16 9 10 11 12 Replicates 1 2 3 4 5 6 7 8 135 APPENDIX 3.5 TEST FOR EQUAL VARIANCES AND TWO-SAMPLE T-TEST Test for Equal Variances: Mean Walking, Mean Crawling 95% Bonferroni confidence intervals for standard deviations N Lower StDev Upper Mean Walking 18 0.117030 0.162172 0.259025 Mean Crawling 18 0.050901 0.070535 0.112660 F-Test (Normal Distribution) Test statistic = 5.29, p-value = 0.001 Levene's Test (Any Continuous Distribution) Test statistic = 10.67, p-value = 0.002 Two-Sample T-Test and CI: Mean Walking, Mean Crawling Two-sample T for Mean Walking vs Mean Crawling N Mean StDev SE Mean Mean Walking 18 1.491 0.162 0.038 Mean Crawling 18 0.7689 0.0705 0.017 Difference = mu (Mean Walking) - mu (Mean Crawling) Estimate for difference: 0.7217 95% CI for difference: (0.6354, 0.8079) T-Test of difference = 0 (vs not =): T-Value = 17.31 P-Value = 0.000 DF = 23 136 APPENDIX 3.6 GENERAL LINEAR MODEL: CRAWLING SPEED General Linear Model: Crawling Speed versus G, BC, BLKs Factor Type Levels Values G fixed 2 1, 2 BC(G) fixed 6 1, 2, 3, 1, 2, 3 BLKs(G BC) fixed 18 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 Analysis of Variance for Crawling Speed, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P G 1 0.066287 0.066287 0.066287 37.20 0.000 BC(G) 4 0.175055 0.175055 0.043764 24.56 0.000 BLKs(G BC) 12 0.014224 0.014224 0.001185 0.67 0.772 Error 36 0.064150 0.064150 0.001782 Total 53 0.319717 S = 0.0422132 R-Sq = 79.94% R-Sq(adj) = 70.46% Unusual Observations for Crawling Speed Crawling Obs Speed Fit SE Fit Residual St Resid 16 0.722132 0.794130 0.024372 -0.071998 -2.09 R 31 0.757424 0.829482 0.024372 -0.072058 -2.09 R 52 0.542429 0.645986 0.024372 -0.103557 -3.00 R R denotes an observation with a large standardized residual. 137 APPENDIX 4.1 INDIVIDUAL WALKING AND CRAWLING PROCEDURE Purpose: To study and evaluate the impact of exit route design and occupant characteristics on evacuation time for crawlers Method: 1. Read and sign informed consent. 2. Allow researcher to measure and record your height and weight. 3. Allow researchers to explain the procedure (researcher?s protocol). 4. Put on the Polar? Heart Rate Monitor (female research assistant available) 5. Rest for 5 min. 6. When instructed, walk at your normal pace down the indirect test track. 7. Rest until your heart rate reaches resting level. 8. Put on knee pads and gloves. 9. When instructed, crawl at your normal pace down the indirect test track (Note: the crawling position means that you are supported with your knees and flattened palms. Your arms and thighs should be perpendicular to the floor and your feet are comfortably extended and spaced). 10. Rest and remove the knee pads and gloves. 11. Conclude the trial. 138 APPENDIX 4.2 PARTICIPANTS CAWLING DATA IIII Direct 34.26 32.66 35.31 34.08 Indirect 37.23 36.18 39.66 37.69 Direct 36.28 35.95 33.75 35.33 Indirect 39.20 39.06 38.67 38.98 Direct 34.50 36.09 35.95 35.51 Indirect 37.21 35.54 35.65 36.13 Direct 42.78 39.54 37.46 39.93 Indirect 43.35 40.34 42.48 42.06 Direct 36.14 41.28 38.85 38.76 Indirect 44.17 43.34 45.72 44.41 Direct 42.21 38.23 35.32 38.59 Indirect 43.20 41.32 44.75 43.09 Direct 39.20 41.11 39.59 39.97 Indirect 47.02 45.52 43.89 45.48 Direct 41.04 41.42 40.53 41.00 Indirect 44.59 46.83 48.77 46.73 Direct 39.88 39.26 40.42 39.85 Indirect 47.37 46.90 48.81 47.69 Direct 37.24 39.35 35.99 37.53 Indirect 38.38 41.26 38.70 39.45 Direct 40.24 35.63 34.82 36.90 Indirect 41.86 39.45 40.43 40.58 Direct 39.28 38.58 37.71 38.52 Indirect 40.14 41.49 40.61 40.75 Direct 43.04 43.40 38.86 41.77 Indirect 44.33 45.10 43.98 44.47 Direct 40.73 39.48 38.93 39.71 Indirect 42.30 45.20 44.27 43.92 Direct 44.79 43.49 41.40 43.23 Indirect 45.04 45.65 43.97 44.89 Direct 47.91 48.17 45.43 47.17 Indirect 47.13 46.94 48.21 47.43 Direct 47.57 44.84 43.30 45.24 Indirect 46.23 47.85 47.76 47.28 Direct 56.19 43.48 43.89 47.85 Indirect 47.05 47.91 46.77 47.24 18 Female Obese 16 Female Obese 17 Female Obese 14 Female Overweight 15 Female Overweight 12 Female Normal 13 Female Overweight 10 Female Normal 11 Female Normal 8MaleObes 9MaleObes 6 Male Overweight 7MaleObes 4 Male Overweight 5 Male Overweight 2MaleNormal 3MaleNormal Replicates Average 1MaleNormal Subject Gender BMI Route Type 139 APPENDIX 4.3 TEST FOR EQUAL VARIANCES AND TWO-SAMPLE T-TEST Test for Equal Variances: Straight, Indirect 95% Bonferroni confidence intervals for standard deviations N Lower StDev Upper Straight 54 3.54141 4.31554 5.49885 Indirect 54 3.02627 3.68779 4.69897 F-Test (Normal Distribution) Test statistic = 1.37, p-value = 0.256 Levene's Test (Any Continuous Distribution) Test statistic = 0.08, p-value = 0.776 Two-Sample T-Test and CI: Mean Straight, Mean indirect Two-sample T for Mean Straight vs Mean indirect N Mean StDev SE Mean Mean Straight 18 40.05 3.86 0.91 Mean indirect 18 43.24 3.61 0.85 Difference = mu (Mean Straight) - mu (Mean indirect) Estimate for difference: -3.19 95% CI for difference: (-5.72, -0.65) T-Test of difference = 0 (vs not =): T-Value = -2.56 P-Value = 0.015 DF = 34 Both use Pooled StDev = 3.7380 140 APPENDIX 4.4 GENERAL LINEAR MODEL: TIMES TO EVACUATE IN AN INDIRECT ROUTE General Linear Model: Indirect Route versus G, BC, BLKs Factor Type Levels Values G fixed 2 1, 2 BC(G) fixed 6 1, 2, 3, 1, 2, 3 BLKs(G BC) fixed 18 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 Analysis of Variance for Indirect Route, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P G 1 31.495 31.495 31.495 20.19 0.000 BC(G) 4 600.739 600.739 150.185 96.25 0.000 BLKs(G BC) 12 32.383 32.383 2.699 1.73 0.101 Error 36 56.171 56.171 1.560 Total 53 720.788 S = 1.24912 R-Sq = 92.21% R-Sq(adj) = 88.53% Unusual Observations for Indirect Route Indirect Obs Route Fit SE Fit Residual St Resid 22 44.5900 46.7300 0.7212 -2.1400 -2.10 R 24 48.7700 46.7300 0.7212 2.0400 2.00 R R denotes an observation with a large standardized residual. 141 APPENDIX 5.1 INFORMED CONSENT 142 143 144 APPENDIX 5.2 A PROPORTIONAL COMPARISON BETWEEN CAESAR AND THE STUDY SAMPLE CAESAR (563 subjects) Sample (20 subjects) BMI 271 males (48%) 292 females (52%) 10 males (50%) 10 females (50%) Normal 131 (48%) 201 (69%) 5 (50%) 7 (70%) Overweight 100 (37%) 58 (20%) 4 (40%) 2 (20%) Obese 40 (15%) 33 (11%) 1 (10%) 1 (10%) 48% 50% 69% 70% 37% 40% 20% 20% 15% 10% 11% 10% 0% 10% 20% 30% 40% 50% 60% 70% 80% C AESAR Sample C AESAR Sample Males Females P e r cen t a g e Normal Overweight Obese 145 APPENDIX 5.3 CROWD WALKING AND CRAWLING PROCEDURE Purpose: To study and evaluate the impact of the number of occupants and the width of an exit access on crowd normal walking and crawling speeds. Method: 1. Read and sign informed consent. 2. Allow researcher to measure and record your height and weight. 3. Allow researchers to explain the procedure (researcher?s protocol). 4. Put on the Polar? Heart Rate Monitor (female research assistant available) 5. Rest for 5 min. 6. When instructed, walk, in a group, at your normal pace down the test track. 7. Rest until your heart rate reaches a resting level. 8. When instructed, walk again, in a group, at your normal pace down the test track (different track width). 9. Rest until your heart rate reaches a resting level. 10. Put on knee pads and gloves. 11. When instructed, crawl at your normal pace (Note: the crawling position means that you are supported with your knees and flattened palms. Your arms and thighs should be perpendicular to the floor and your feet are comfortably extended and spaced). 12. Rest until your heart rate reaches a resting level. 13. When instructed, crawl again, in a group, at your normal pace (different track width) 14. Rest and remove the knee pads and gloves. 15. Conclude the trial. 146 APPENDIX 5.4 GENERAL LINEAR MODEL: CROWD WALKING SPEED VS. OCCUPANT CONFIGURATION AND EXIT ACCESS WIDTH General Linear Model: Walking versus Occupant Configuration, Exit Access Width Factor Type Levels Values Conf fixed 5 1, 2, 3, 4, 5 W fixed 3 1, 2, 3 Analysis of Variance for Walking, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Conf 4 0.0040533 0.0040533 0.0010133 1.04 0.420 W 2 0.0379800 0.0379800 0.0189900 19.44 0.000 Conf*W 8 0.0287867 0.0287867 0.0035983 3.68 0.014 Error 15 0.0146500 0.0146500 0.0009767 Total 29 0.0854700 S = 0.0312517 R-Sq = 82.86% R-Sq(adj) = 66.86% Tukey Simultaneous Tests Response Variable Walking All Pairwise Comparisons among Levels of Conf Conf = 1 subtracted from: Difference SE of Adjusted Conf of Means Difference T-Value P-Value 2 -0.01000 0.01804 -0.554 0.9797 3 -0.01333 0.01804 -0.739 0.9438 4 -0.03167 0.01804 -1.755 0.4327 5 0.00000 0.01804 0.000 1.0000 Conf = 2 subtracted from: Difference SE of Adjusted Conf of Means Difference T-Value P-Value 3 -0.00333 0.01804 -0.185 0.9997 4 -0.02167 0.01804 -1.201 0.7510 5 0.01000 0.01804 0.554 0.9797 Conf = 3 subtracted from: 147 Difference SE of Adjusted Conf of Means Difference T-Value P-Value 4 -0.01833 0.01804 -1.016 0.8441 5 0.01333 0.01804 0.739 0.9438 Conf = 4 subtracted from: Difference SE of Adjusted Conf of Means Difference T-Value P-Value 5 0.03167 0.01804 1.755 0.4327 Tukey Simultaneous Tests Response Variable Crawling All Pairwise Comparisons among Levels of W W = 1 subtracted from: Difference SE of Adjusted W of Means Difference T-Value P-Value 2 0.07800 0.01327 5.879 0.0001 3 -0.02300 0.01327 -1.734 0.2255 W = 2 subtracted from: Difference SE of Adjusted W of Means Difference T-Value P-Value 3 -0.1010 0.01327 -7.613 0.0000 148 APPENDIX 5.5 GENERAL LINEAR MODEL: CROWD CRAWLING SPEED VS. OCCUPANT CONFIGURATION AND EXIT ACCESS WIDTH General Linear Model: Crawling versus Occupant Configuration, Exit Access Width Factor Type Levels Values Conf fixed 5 1, 2, 3, 4, 5 W fixed 3 1, 2, 3 Analysis of Variance for Crawling, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Conf 4 0.0018867 0.0018867 0.0004717 0.54 0.712 W 2 0.0560467 0.0560467 0.0280233 31.84 0.000 Conf*W 8 0.0078533 0.0078533 0.0009817 1.12 0.406 Error 15 0.0132000 0.0132000 0.0008800 Total 29 0.0789867 S = 0.0296648 R-Sq = 83.29% R-Sq(adj) = 67.69% Unusual Observations for Crawling Obs Crawling Fit SE Fit Residual St Resid 9 0.700000 0.755000 0.020976 -0.055000 -2.62 R 10 0.810000 0.755000 0.020976 0.055000 2.62 R R denotes an observation with a large standardized residual. Tukey Simultaneous Tests Response Variable Crawling All Pairwise Comparisons among Levels of Conf Conf = 1 subtracted from: Difference SE of Adjusted Conf of Means Difference T-Value P-Value 2 0.00667 0.01713 0.3892 0.9946 3 0.00167 0.01713 0.0973 1.0000 149 4 -0.00500 0.01713 -0.2919 0.9982 5 -0.01667 0.01713 -0.9731 0.8630 Conf = 2 subtracted from: Difference SE of Adjusted Conf of Means Difference T-Value P-Value 3 -0.00500 0.01713 -0.292 0.9982 4 -0.01167 0.01713 -0.681 0.9576 5 -0.02333 0.01713 -1.362 0.6590 Conf = 3 subtracted from: Difference SE of Adjusted Conf of Means Difference T-Value P-Value 4 -0.00667 0.01713 -0.389 0.9946 5 -0.01833 0.01713 -1.070 0.8185 Conf = 4 subtracted from: Difference SE of Adjusted Conf of Means Difference T-Value P-Value 5 -0.01167 0.01713 -0.6812 0.9576 150 APPENDIX 5.6 CROWD DENSITY AND CRAWLING SPEED DATA # Occupant W (ft) L (ft) Area (m 2 ) Density (occ/m 2 ) Time (sec) Speed (m/s) 1 3 6 1.67 0.60 1.90 0.96 1 3 6 1.67 0.60 2.00 0.91 1 3 6 1.67 0.60 1.90 0.96 2 3 8 2.23 0.90 3.00 0.81 2 3 8 2.23 0.90 2.73 0.89 2 3 6 1.67 1.20 1.90 0.96 2 3 6 1.67 1.20 1.97 0.93 2 3 6 1.67 1.20 1.90 0.96 2 3 6 1.67 1.20 2.07 0.88 2 3 6 1.67 1.20 1.87 0.98 3 3 8 2.23 1.35 2.57 0.95 3 3 8 2.23 1.35 2.73 0.89 2 3 4 1.11 1.79 1.37 0.89 4 3 8 2.23 1.79 3.27 0.75 4 3 8 2.23 1.79 2.67 0.91 4 3 8 2.23 1.79 2.80 0.87 2 4 6 2.23 0.90 2.00 0.91 3 4 6 2.23 1.35 1.93 0.95 4 4 8 2.97 1.35 2.83 0.86 5 4 8 2.97 1.68 2.83 0.86 4 5 6 2.79 1.44 1.87 0.98 7 5 8 3.72 1.88 3.47 0.70 151 APPENDIX 5.7 REGRESSION ANALYSIS: CROWD CRAWLING SPEED VS. CROWD DENSITY Polynomial Regression Analysis: Crowd Crawling Speed (m/s) versus Crowd Crawling Density (occ/m 2 ) The regression equation is Crowd Crawling Speed = 0.7973 + 0.2909 Crowd Density - 0.1503 Crowd Density 2 S = 0.0593124 R-Sq = 42.7% R-Sq(adj) = 37.0% Analysis of Variance Source DF SS MS F P Regression 2 0.052397 0.0261983 7.45 0.004 Error 20 0.070359 0.0035180 Total 22 0.122756 Sequential Analysis of Variance Source DF SS F P Linear 1 0.0356769 8.60 0.008 Quadratic 1 0.0167197 4.75 0.041 152 APPENDIX 6.1 LAYOUT DESIGNS FOR THE VALIDATION PROCESS Scenario (1) Scenario (2) 153 APPENDIX 6.2 TOTAL EVACUATION TIMES FOR ASERI AND THE POTENTIAL FIELD MODEL ASERI Potential Field Diff. ASERI Potential Field Diff. 1 11.6 9.0 2.6 14 15.2 -1.2 2 11.6 8.3 3.3 12 12.4 -0.4 3 11.2 10.2 1.0 12.8 12.9 -0.1 4 10.8 9.1 1.7 14 13.4 0.6 5 11.2 9.1 2.1 13.6 14.9 -1.3 6 11.2 8.7 2.5 13.6 13.1 0.5 7 10.4 8.7 1.7 13.2 14.9 -1.7 8 11.2 13.1 -1.9 12.8 12.5 0.3 9 10.4 8.8 1.6 12 11.8 0.2 10 10.8 10.0 0.8 12.4 14.5 -2.1 11 10.4 8.3 2.1 13.6 12.9 0.7 12 11.6 9.3 2.3 12.4 12.2 0.2 13 12.0 8.7 3.3 12.8 13.6 -0.8 14 10.8 8.0 2.8 12.4 16 -3.6 15 10.8 9.3 1.5 14 12.5 1.5 16 10.8 11.3 -0.5 13.2 14.9 -1.7 17 10.8 10.2 0.6 12.8 15.4 -2.6 18 11.6 10.2 1.4 12.8 14.2 -1.4 19 10.4 7.5 2.9 12.4 13.4 -1 20 11.2 10.1 1.1 12.8 13.8 -1 21 12.0 8.4 3.6 12.8 13.1 -0.3 22 11.2 9.5 1.7 12.4 13.2 -0.8 23 11.6 10.0 1.6 13.6 12.5 1.1 24 11.6 9.0 2.6 12.8 12.9 -0.1 25 10.0 9.6 0.4 13.2 11.9 1.3 26 11.6 9.3 2.3 12.8 12.3 0.5 27 10.8 8.7 2.1 13.6 13 0.6 28 10.8 9.5 1.3 13.2 16.6 -3.4 29 11.6 8.2 3.4 12.4 12.7 -0.3 30 10.8 9.7 1.1 14.4 15.3 -0.9 31 10.8 10.0 0.8 14.4 11.7 2.7 32 10.4 10.0 0.4 12.8 14.3 -1.5 33 11.2 8.1 3.1 12.8 14.9 -2.1 34 10.8 9.1 1.7 12 12.9 -0.9 35 11.6 8.8 2.8 12.4 13.1 -0.7 36 11.6 8.1 3.5 13.6 12.6 1 37 10.8 9.2 1.6 12.8 15.3 -2.5 38 11.2 10.2 1.0 12.8 13.3 -0.5 39 11.6 9.1 2.5 14 12.8 1.2 40 9.6 8.8 0.8 13.2 13.3 -0.1 41 11.2 10.9 0.3 12 12.2 -0.2 42 10.0 10.3 -0.3 12.4 14.3 -1.9 43 10.8 9.4 1.4 12.4 13.9 -1.5 44 10.0 9.6 0.4 14 12.7 1.3 45 11.2 9.7 1.5 11.6 14.9 -3.3 46 10.4 8.8 1.6 12.8 14.9 -2.1 47 10.4 8.6 1.8 12 13.8 -1.8 48 11.6 10.4 1.2 12.8 13.8 -1 49 11.2 8.8 2.4 12 12.3 -0.3 50 10.8 9.3 1.5 12.8 11.6 1.2 Scenario 1 Scenario 2 Run # ASERI Potential Field Diff. ASERI Potential Field Diff. 51 10.8 10.1 0.7 12.8 13.3 -0.5 52 10.4 9.0 1.4 14 14.7 -0.7 53 9.2 9.1 0.1 13.2 13.1 0.1 54 11.2 8.7 2.5 13.2 15.3 -2.1 55 10.8 9.1 1.7 12.8 11.9 0.9 56 10.8 10.9 -0.1 12.8 13.9 -1.1 57 12.0 8.9 3.1 13.2 14.9 -1.7 58 12.0 8.7 3.3 12.4 13.1 -0.7 59 10.4 13.9 -3.5 12.4 15.5 -3.1 60 11.2 8.7 2.5 12.8 14.5 -1.7 61 11.6 8.5 3.1 12.8 14.1 -1.3 62 11.2 10.3 0.9 13.2 13.1 0.1 63 12.0 9.3 2.7 12 14.9 -2.9 64 9.2 8.9 0.3 12.4 15.3 -2.9 65 10.8 13.7 -2.9 12 16.4 -4.4 66 12.0 11.6 0.4 12.4 13 -0.6 67 12.0 10.1 1.9 12.4 14 -1.6 68 10.4 7.9 2.5 13.2 13.7 -0.5 69 11.2 11.8 -0.6 12 15.7 -3.7 70 10.8 9.0 1.8 13.2 13.6 -0.4 71 10.4 8.3 2.1 12.8 12.9 -0.1 72 10.8 11.9 -1.1 12 12.8 -0.8 73 10.4 8.9 1.5 12.8 13.1 -0.3 74 9.6 11.7 -2.1 12.8 14.6 -1.8 75 10.8 9.8 1.0 13.6 14.3 -0.7 76 11.2 14.8 -3.6 12.8 13.1 -0.3 77 10.4 8.3 2.1 14 12.3 1.7 78 11.2 9.2 2.0 12.8 16.3 -3.5 79 11.6 8.5 3.1 12 13.8 -1.8 80 10.8 9.7 1.1 12.4 14.2 -1.8 81 11.6 9.7 1.9 12.8 14.6 -1.8 82 10.4 9.3 1.1 12.4 13.1 -0.7 83 11.6 12.5 -0.9 12.4 12.6 -0.2 84 12.8 9.2 3.6 12.8 15.4 -2.6 85 11.2 8.6 2.6 13.2 13.8 -0.6 86 11.2 9.0 2.2 12.4 14.1 -1.7 87 11.2 10.5 0.7 13.2 14 -0.8 88 12.4 13.0 -0.6 13.2 16.5 -3.3 89 11.6 8.4 3.2 12.4 14.8 -2.4 90 10.0 7.4 2.6 13.2 13.8 -0.6 91 10.4 8.0 2.4 14 11.3 2.7 92 11.6 8.0 3.6 12.8 13.9 -1.1 93 10.8 10.1 0.7 13.2 14.9 -1.7 94 11.2 10.0 1.2 13.2 11.4 1.8 95 11.2 10.1 1.1 12 14.2 -2.2 96 10.8 10.2 0.6 12.8 15.5 -2.7 97 12.4 8.7 3.7 12.4 13.4 -1 98 11.6 7.9 3.7 13.6 13.2 0.4 99 10.8 10.3 0.5 13.6 12.8 0.8 100 11.6 8.6 3.0 12.4 14.9 -2.5 Scenario 1 Scenario 2 Run # 154 APPENDIX 6.3 BASELINE EVACUATION RUNS FOR A SINGLE-EXIT CONFIGURATION Walking Crawling 1 9100 31000 2 7400 28500 3 8200 27800 4 8400 29100 5 8100 29300 6 8700 28600 7 8700 28700 8 9200 29800 9 7900 30500 10 7500 28900 11 8900 29400 12 7900 33200 13 7500 29300 14 8200 32300 15 8900 32900 16 8300 32600 17 8300 29900 18 9200 31900 19 8900 29000 20 7900 28000 21 8400 31000 22 7200 30200 23 7800 30000 24 8500 30000 25 8800 28200 26 8000 27500 27 7800 29500 28 7500 30400 29 8800 32700 30 7900 28200 31 7800 31300 32 8900 30300 33 7600 32800 34 8900 30200 35 7900 28700 36 7600 27900 37 8700 29600 38 8100 29500 39 8400 31300 40 7700 26800 41 7900 29300 42 8000 27400 43 8700 28200 44 8400 30700 45 9100 30500 46 8600 27200 47 8400 29400 48 9000 26600 49 7800 27900 50 8200 28500 Run # Evacuation Time in milliseconds Walking Crawling 51 7600 28500 52 8600 26400 53 8700 32000 54 7500 27200 55 8100 33600 56 8300 28100 57 8500 27500 58 7900 27700 59 8100 29400 60 8100 29100 61 7900 29800 62 8300 32300 63 9400 29600 64 7900 30500 65 8700 27700 66 8500 28500 67 8600 29700 68 7500 29800 69 8100 29000 70 8400 28900 71 7900 31700 72 8200 27400 73 7900 29000 74 7900 26600 75 8700 28600 76 9400 28500 77 9300 32900 78 7900 30700 79 8100 25700 80 8700 26200 81 7400 32200 82 7200 27800 83 9000 33000 84 8400 27300 85 8000 31400 86 8600 29500 87 8400 28100 88 8000 26700 89 8100 32200 90 8300 30000 91 9300 28500 92 7900 27600 93 7600 25600 94 9400 26300 95 8200 26500 96 8700 27900 97 9000 32300 98 8900 29100 99 8300 31800 100 8300 29600 Run # Evacuation Time in milliseconds 2.350983 4.1904 29385 7.98933 6.533 8293 =+ = = =+ = = crawlingcrawling crawling crawling walkingwalking walking walking ?? ? ? ?? ? ? 155 APPENDIX 6.4 EC RESULTS OF EDA, GGA, AND PSO FOR WALKING Function Evaluation Fitness Value Exit Location (0 - 39) Function Evaluation Fitness Value Exit Location (0 - 39) Function Evaluation Fitness Value Exit Locations (0 - 39) 1 1353 16914 (3,30) 2496 16914 (3,19,28) 2200 22897 (18,23,30) 2 2337 15324 (14,18) 2574 13260 (11,19) 2200 17409.1 (10,17,21) 3 2460 15374 (13,19) 2340 9849 (15,16) 2500 27776.9 (1,10,15,20) 4 2460 15314 (13,18) 2418 16557 (15,18) 2000 36271.5 (16,17,27,28,33) 5 2091 15354 (16,17) 2574 13399 (14, 18) 1700 42215.8 (1,7,10,22,23) 6 2214 15323 (16,17) 2418 17155 (4,15,21) 2300 38808 (6,16,29,35) 7 1845 9712 (14,17) 2184 18968 (17,30) 2100 35444.8 (2,12,16,39) 8 1968 16827 (16,17) 2574 8248 (13,19) 2400 35157.3 (1,6,7,21,28) 9 2583 15343 (14,17) 2262 15320 (15,18) 1200 46440.8 (0,4,6,8,10,14) 10 2460 17451 (14,17) 2106 20046 (5,17) 2200 44936.4 (1,14,24,25,26,35) 11 2583 15379 (11,18) 2574 13599 (14,17) 2300 46029.3 (8,9,11,13,29,30) 12 2460 16562 (15,17) 2028 17531 (17,21) 2100 37266.5 (3,8,16,18,33) 13 1968 20255 (5,10) 2106 16580 (15,18) 2000 45403.2 (4,16,19,24,27,38) 14 1353 8753 (13,19) 2262 17406 (15,30) 1800 23189.6 (10,15,16) 15 2583 15400 (13,21) 1404 19071 (13,17,19) 2500 22832.3 (5,8,13) 16 1845 15392 (13,19) 1248 13525 (13,21) 2300 27068.3 (1,3,8,9) 17 1722 18490 (11,15) 2106 13620 (15,18) 2500 17818.7 (12,17,18) 18 1722 8802 (13,19) 2262 15000 (5,13) 2100 37734 (3,4,10,24) 19 2583 9184 (13,19) 1872 15376 (19,29) 1900 36535.9 (0,5,13,29) 20 2583 9849 (13,19) 2496 13656 (15,16) 1400 37341.6 (11,17,22,27,33) 21 2337 18575 (5,11) 2262 15335 (13,18) 2000 34665.7 (4,6,12,24,28) 22 1476 13313 (13,19) 936 15340 (15,16) 1600 36708.3 (8,10,20,22,24) 23 2583 16238 (5,13,28) 2496 15337 (2,29) 2300 22410.9 (5,15,27) 24 1107 13131 (13,21) 1794 15323 (13,19) 2300 45466.8 (6,7,17,26,36) 25 1968 15499 (11,19) 2418 13283 (14,18) 1300 50523.6 (3,6,12) 26 2091 18663 (15,18) 1638 17615 (14,17,30) 1800 36654.3 (3,29,37,39) 27 1353 16913 (11,19) 936 17926 (2,29) 1900 35985.7 (8,13,25,27,31) 28 2214 18903 (16,22) 2028 23123 (13,22,25) 1900 43244.1 (3,22,30,31,35) 29 2583 15257 (15,17) 2106 17668 (12,17,18) 1900 26023.1 (7,10,18,22) 30 1353 20072 (2,27) 1248 13160 (13,19) 900 53023.9 (5,13,14,16,17,38) ? 2074.6 15252.1 2072.2 15639.7 1986.7 35442.8 ? 467.8 3212.2 485.5 2947.9 397.2 9622.9 PSOGGAEDA Run 156 EC RESULTS OF EDA, GGA, AND PSO FOR CRAWLING Function Evaluation Fitness Value Exit Locations (0 - 39) Function Evaluation Fitness Value Exit Locations (0 - 39) Function Evaluation Fitness Value Exit Locations (0 - 39) 1 1845 23979 (11,18) 2106 20194 (11,19) 1800 88702.2 (14,16,18,22) 2 2214 24955 (1,29) 1560 20978 (11,18) 2100 157439.8 (9,10,13,14,28,33) 3 1353 23628 (13,21) 2574 21758 (13,18) 800 147439.1 (3,16,22,27,35) 4 1722 21906 (2,31) 2496 22583 (14,21) 1200 89368.35 (9,26,39) 5 2583 21562 (2,29) 2184 23950 (14,18) 1000 161090.3 (20,25,27,28,29,35) 6 1353 21910 (3,28) 1950 19979 (14,18) 2200 56996.02 (2,9,13) 7 1230 21083 (3,28) 1560 22571 (11,21) 2400 255171.7 (4,6,8,11,17,19,25,26,38) 8 1599 19789 (13,19) 2184 23550 (15,22) 1200 121905 (1,8,9,11,30) 9 2337 21039 (2,30) 1638 18765 (19,29) 1300 220956.3 (0,4,7,12,15,18,26,32) 10 1722 20728 (3,13) 1950 19959 (3,29) 1300 115330.3 (6,7,15,25,38) 11 2460 18310 (3,13) 2574 20381 (3,30) 1400 122422.1 (3,10,11,29,38) 12 2583 24792 (15,17) 2574 22547 (10,17) 1100 181892.5 (3,4,9,19,27,30) 13 1722 21947 (3,29) 2184 19235 (13,29) 2000 113173.7 (5,12,13,34) 14 2583 18759 (3,13) 2418 19496 (3,19) 2500 153062.6 (7,15,19,25,26,30) 15 1599 21168 (4,28) 2184 20838 (13,18) 1800 186765 (5,6,10,15,19,21,22) 16 1845 19776 (13,29) 2574 23403 (15,18) 2500 187481.7 (3,7,15,24,25,33) 17 1599 20271 (13,19) 1950 29199 (15,21) 900 81313.64 (1,16,20) 18 2583 19231 (3,13) 1638 24241 (14,17) 1900 128457.2 (3,4,30,36,38) 19 2214 25583 (15,17) 2184 22244 (10,18) 1500 82126.51 (7,22,28,33) 20 2460 43467 (19,30) 2574 25604 (15,17) 2300 57459.17 (12,14,19) 21 2583 23780 (14,17) 2028 24854 (14,17) 1100 189783.9 (2,6,10,12,19,32,33) 22 2460 23812 (14,22) 2418 20560 (3,13) 2500 188662.7 (2,6,9,15,32,35) 23 1599 19314 (13,19) 2418 23889 (15,18) 2500 181302.4 (5,9,13,20,28,35) 24 1599 20901 (13,19) 1638 19833 (11,21) 2400 92469.21 (14,24,25,29) 25 1599 20728 (1,13) 2340 22278 (15,22) 2300 88358.79 (10,11,18,22) 26 1968 19877 (19,28) 2340 21614 (14,18) 2100 122185.7 (15,16,18,23,24) 27 1599 19133 (13,19) 2574 19774 (11,21) 2100 154812.5 (3,14,24,31,34,39) 28 2583 18589 (13,19) 2496 24175 (15,17) 2200 54719.33 (12,17,21) 29 2583 21982 (16,22) 2340 23065 (14,21) 1600 228525.3 (3,8,9,10,28,34,35,39) 30 2583 19211 (13,19) 2418 24358 (15,18) 1800 159528.5 (15,18,19,27,29,30) ? 2025.4 22040.4 2202.2 22195.8 1793.3 138963.4 ? 468.9 4526.8 335.1 2303.9 549.6 53256.9 PSO Run EDA GGA 157 APPENDIX 6.5 BEST LOCATION PROBABILITIES OF EXIT LOCATIONS EDA GGA PSO EDA GGA PSO 0 0.00 0.00 0.07 0 0.00 0.00 0.03 1 0.00 0.00 0.17 1 0.07 0.00 0.07 2 0.03 0.07 0.03 2 0.10 0.00 0.10 3 0.03 0.03 0.20 3 0.23 0.13 0.23 4 0.00 0.03 0.13 4 0.03 0.00 0.13 5 0.10 0.07 0.13 5 0.00 0.00 0.10 6 0.00 0.00 0.20 6 0.00 0.00 0.17 7 0.00 0.00 0.13 7 0.00 0.00 0.17 8 0.00 0.00 0.23 8 0.00 0.00 0.10 9 0.00 0.00 0.07 9 0.00 0.00 0.27 10 0.03 0.00 0.27 10 0.00 0.07 0.20 11 0.17 0.03 0.07 11 0.03 0.17 0.13 12 0.00 0.03 0.13 12 0.00 0.00 0.17 13 0.37 0.27 0.17 13 0.47 0.13 0.13 14 0.13 0.13 0.10 14 0.07 0.23 0.17 15 0.13 0.30 0.10 15 0.07 0.27 0.27 16 0.13 0.10 0.23 16 0.03 0.00 0.13 17 0.27 0.23 0.20 17 0.10 0.17 0.07 18 0.13 0.27 0.13 18 0.03 0.33 0.17 19 0.30 0.23 0.03 19 0.30 0.10 0.27 20 0.00 0.00 0.10 20 0.00 0.00 0.10 21 0.07 0.10 0.07 21 0.03 0.20 0.07 22 0.03 0.03 0.17 22 0.07 0.07 0.17 23 0.00 0.00 0.07 23 0.00 0.00 0.03 24 0.00 0.00 0.20 24 0.00 0.00 0.13 25 0.00 0.03 0.07 25 0.00 0.00 0.20 26 0.00 0.00 0.07 26 0.00 0.00 0.13 27 0.03 0.00 0.17 27 0.00 0.00 0.13 28 0.03 0.03 0.10 28 0.13 0.00 0.17 29 0.00 0.10 0.13 29 0.13 0.10 0.13 30 0.03 0.10 0.10 30 0.07 0.03 0.17 31 0.00 0.00 0.07 31 0.03 0.00 0.03 32 0.00 0.00 0.00 32 0.00 0.00 0.10 33 0.00 0.00 0.10 33 0.00 0.00 0.20 34 0.00 0.00 0.00 34 0.00 0.00 0.07 35 0.00 0.00 0.10 35 0.00 0.00 0.17 36 0.00 0.00 0.03 36 0.00 0.00 0.03 37 0.00 0.00 0.07 37 0.00 0.00 0.00 38 0.00 0.00 0.07 38 0.00 0.00 0.13 39 0.00 0.00 0.07 39 0.00 0.00 0.10 Max 0.37 0.30 0.27 Max 0.47 0.33 0.27 Walking Crawling Exit Location Exit Location 158 APPENDIX 6.6 T-TEST COMARISONS OF MEAN FUNCTION EVALUATIONS AND FITNESS VALUES FOR WALKING Two-Sample T-Test and CI: Fun. Eval. (W-EDA), Fun. Eval. (W-GGA) Two-sample T for Fun. Eval. (W-EDA) vs Fun. Eval. (W-GGA) SE N Mean StDev Mean Fun. Eval. (W-EDA) 30 2075 468 85 Fun. Eval. (W-GGA) 30 2072 485 89 Difference = mu (Fun. Eval. (W-EDA)) - mu (Fun. Eval. (W-GGA)) Estimate for difference: 2 95% CI for difference: (-244, 249) T-Test of difference = 0 (vs not =): T-Value = 0.02 P-Value = 0.985 DF = 58 Both use Pooled StDev = 476.7106 Two-Sample T-Test and CI: Fun. Eval. (W-EDA), Fun. Eval. (W-PSO) Two-sample T for Fun. Eval. (W-EDA) vs Fun. Eval. (W-PSO) SE N Mean StDev Mean Fun. Eval. (W-EDA) 30 2075 468 85 Fun. Eval. (W-PSO) 30 1987 397 73 Difference = mu (Fun. Eval. (W-EDA)) - mu (Fun. Eval. (W-PSO)) Estimate for difference: 88 95% CI for difference: (-136, 312) T-Test of difference = 0 (vs not =): T-Value = 0.78 P-Value = 0.436 DF = 58 Both use Pooled StDev = 433.9231 Two-Sample T-Test and CI: Fun. Eval. (W-GGA), Fun. Eval. (W-PSO) Two-sample T for Fun. Eval. (W-GGA) vs Fun. Eval. (W-PSO) 159 SE N Mean StDev Mean Fun. Eval. (W-GGA) 30 2072 485 89 Fun. Eval. (W-PSO) 30 1987 397 73 Difference = mu (Fun. Eval. (W-GGA)) - mu (Fun. Eval. (W-PSO)) Estimate for difference: 86 95% CI for difference: (-144, 315) T-Test of difference = 0 (vs not =): T-Value = 0.75 P-Value = 0.458 DF = 58 Both use Pooled StDev = 443.5210 Two-Sample T-Test and CI: Fit. Val. (W-EDA), Fit. Val. (W-GGA) Two-sample T for Fit. Val. (W-EDA) vs Fit. Val. (W-GGA) N Mean StDev SE Mean Fit. Val. (W-EDA) 30 15252 3212 586 Fit. Val. (W-GGA) 30 15640 2948 538 Difference = mu (Fit. Val. (W-EDA)) - mu (Fit. Val. (W-GGA)) Estimate for difference: -388 95% CI for difference: (-1981, 1206) T-Test of difference = 0 (vs not =): T-Value = -0.49 P-Value = 0.628 DF = 58 Both use Pooled StDev = 3082.8921 Two-Sample T-Test and CI: Fit. Val. (W-EDA), Fit. Val. (W-PSO) Two-sample T for Fit. Val. (W-EDA) vs Fit. Val. (W-PSO) N Mean StDev SE Mean Fit. Val. (W-EDA) 30 15252 3212 586 Fit. Val. (W-PSO) 30 35443 9623 1757 Difference = mu (Fit. Val. (W-EDA)) - mu (Fit. Val. (W-PSO)) Estimate for difference: -20191 95% CI for difference: (-23951, -16431) T-Test of difference = 0 (vs not =): T-Value = -10.90 P-Value = 0.000 DF = 35 Two-Sample T-Test and CI: Fit. Val. (W-GGA), Fit. Val. (W-PSO) Two-sample T for Fit. Val. (W-GGA) vs Fit. Val. (W-PSO) 160 N Mean StDev SE Mean Fit. Val. (W-GGA) 30 15640 2948 538 Fit. Val. (W-PSO) 30 35443 9623 1757 Difference = mu (Fit. Val. (W-GGA)) - mu (Fit. Val. (W-PSO)) Estimate for difference: -19803 95% CI for difference: (-23537, -16069) T-Test of difference = 0 (vs not =): T-Value = -10.78 P-Value = 0.000 DF = 34 161 APPENDIX 6.7 T-TEST COMARISONS OF MEAN FUNCTION EVALUATIONS AND FITNESS VALUES FOR CRAWLING Two-Sample T-Test and CI: Fun. Eval. (C-EDA), Fun. Eval. (C-GGA) Two-sample T for Fun. Eval. (C-EDA) vs Fun. Eval. (C-GGA) SE N Mean StDev Mean Fun. Eval. (C-EDA) 30 2025 469 86 Fun. Eval. (C-GGA) 30 2202 335 61 Difference = mu (Fun. Eval. (C-EDA)) - mu (Fun. Eval. (C-GGA)) Estimate for difference: -177 95% CI for difference: (-388, 34) T-Test of difference = 0 (vs not =): T-Value = -1.68 P-Value = 0.099 DF = 52 Two-Sample T-Test and CI: Fun. Eval. (C-EDA), Fun. Eval. (C-PSO) Two-sample T for Fun. Eval. (C-EDA) vs Fun. Eval. (C-PSO) N Mean StDev SE Mean Fun. Eval. (C-EDA) 30 2025 469 86 Fun. Eval. (C-PSO) 30 1793 550 100 Difference = mu (Fun. Eval. (C-EDA)) - mu (Fun. Eval. (C-PSO)) Estimate for difference: 232 95% CI for difference: (-32, 496) T-Test of difference = 0 (vs not =): T-Value = 1.76 P-Value = 0.084 DF = 58 Both use Pooled StDev = 510.8316 Two-Sample T-Test and CI: Fun. Eval. (C-GGA), Fun. Eval. (C-PSO) Two-sample T for Fun. Eval. (C-GGA) vs Fun. Eval. (C-PSO) N Mean StDev SE Mean 162 Fun. Eval. (C-GGA) 30 2202 335 61 Fun. Eval. (C-PSO) 30 1793 550 100 Difference = mu (Fun. Eval. (C-GGA)) - mu (Fun. Eval. (C-PSO)) Estimate for difference: 409 95% CI for difference: (172, 645) T-Test of difference = 0 (vs not =): T-Value = 3.48 P-Value = 0.001 DF = 47 Two-Sample T-Test and CI: Fit. Val. (C-EDA), Fit. Val. (C-GGA) Two-sample T for Fit. Val. (C-EDA) vs Fit. Val. (C-GGA N Mean StDev SE Mean Fit. Val. (C-EDA) 30 22040 4527 826 Fit. Val. (C-GGA 30 22196 2304 421 Difference = mu (Fit. Val. (C-EDA)) - mu (Fit. Val. (C-GGA) Estimate for difference: -155 95% CI for difference: (-2026, 1715) T-Test of difference = 0 (vs not =): T-Value = -0.17 P-Value = 0.868 DF = 43 Two-Sample T-Test and CI: Fit. Val. (C-EDA), Fit. Val. (C-PSO) Two-sample T for Fit. Val. (C-EDA) vs Fit. Val. (C-PSO) N Mean StDev SE Mean Fit. Val. (C-EDA) 30 22040 4527 826 Fit. Val. (C-PSO) 30 138963 53257 9723 Difference = mu (Fit. Val. (C-EDA)) - mu (Fit. Val. (C-PSO)) Estimate for difference: -116923 95% CI for difference: (-136881, -96965) T-Test of difference = 0 (vs not =): T-Value = -11.98 P-Value = 0.000 DF = 29 Two-Sample T-Test and CI: Fit. Val. (C-GGA), Fit. Val. (C-PSO) Two-sample T for Fit. Val. (C-GGA vs Fit. Val. (C-PSO) N Mean StDev SE Mean 163 Fit. Val. (C-GGA 30 22196 2304 421 Fit. Val. (C-PSO) 30 138963 53257 9723 Difference = mu (Fit. Val. (C-GGA) - mu (Fit. Val. (C-PSO)) Estimate for difference: -116768 95% CI for difference: (-136673, -96863) T-Test of difference = 0 (vs not =): T-Value = -12.00 P-Value = 0.000 DF = 29 164 APPENDIX 6.8 T-TEST COMARISONS OF MEAN TOTAL EVACUATION TIME AND NUMBER OF CASUALTIES FOR WALKING SIMULATION RUNS Two-Sample T-Test and CI: Evac. Time_1, Evac. Time_2 Two-sample T for Evac. Time_1 vs Evac. Time_2 SE N Mean StDev Mean Evac. Time_1 1000 7767 562 18 Evac. Time_2 1000 6684 505 16 Difference = mu (Evac. Time_1) - mu (Evac. Time_2) Estimate for difference: 1084.0 95% CI for difference: (1037.1, 1130.9) T-Test of difference = 0 (vs not =): T-Value = 45.34 P-Value = 0.000 DF = 1973 Two-Sample T-Test and CI: Casualties_1, Casualties_2 Two-sample T for Casualties_1 vs Casualties_2 N Mean StDev SE Mean Casualties_1 1000 0.222 0.457 0.014 Casualties_2 1000 0.471 0.618 0.020 Difference = mu (Casualties_1) - mu (Casualties_2) Estimate for difference: -0.2488 95% CI for difference: (-0.2965, -0.2011) T-Test of difference = 0 (vs not =): T-Value = -10.23 P-Value = 0.000 DF = 1841 165 APPENDIX 6.9 T-TEST COMARISONS OF MEAN TOTAL EVACUATION TIME AND NUMBER OF CASUALTIES FOR CRAWLING SIMULATION RUNS Two-Sample T-Test and CI: Evac. Time_3, Evac. Time_4 Two-sample T for Evac. Time_3 vs Evac. Time_4 SE N Mean StDev Mean Evac. Time_3 1000 17691 1219 39 Evac. Time_4 1000 17760 1288 41 Difference = mu (Evac. Time_3) - mu (Evac. Time_4) Estimate for difference: -68.7 95% CI for difference: (-178.7, 41.3) T-Test of difference = 0 (vs not =): T-Value = -1.22 P-Value = 0.221 DF = 1998 Both use Pooled StDev = 1254.3708 Two-Sample T-Test and CI: Evac. Time_3, Evac. Time_5 Two-sample T for Evac. Time_3 vs Evac. Time_5 SE N Mean StDev Mean Evac. Time_3 1000 17691 1219 39 Evac. Time_5 1000 18878 1779 56 Difference = mu (Evac. Time_3) - mu (Evac. Time_5) Estimate for difference: -1186.7 95% CI for difference: (-1320.5, -1052.9) T-Test of difference = 0 (vs not =): T-Value = -17.40 P-Value = 0.000 DF = 1768 Two-Sample T-Test and CI: Evac. Time_4, Evac. Time_5 Two-sample T for Evac. Time_4 vs Evac. Time_5 166 SE N Mean StDev Mean Evac. Time_4 1000 17760 1288 41 Evac. Time_5 1000 18878 1779 56 Difference = mu (Evac. Time_4) - mu (Evac. Time_5) Estimate for difference: -1118.0 95% CI for difference: (-1254.2, -981.8) T-Test of difference = 0 (vs not =): T-Value = -16.10 P-Value = 0.000 DF = 1820 Two-Sample T-Test and CI: Casualties_3, Casualties_4 Two-sample T for Casualties_3 vs Casualties_4 N Mean StDev SE Mean Casualties_3 1000 0.314 0.538 0.017 Casualties_4 1000 0.336 0.584 0.018 Difference = mu (Casualties_3) - mu (Casualties_4) Estimate for difference: -0.0220 95% CI for difference: (-0.0713, 0.0273) T-Test of difference = 0 (vs not =): T-Value = -0.88 P-Value = 0.381 DF = 1984 Two-Sample T-Test and CI: Casualties_3, Casualties_5 Two-sample T for Casualties_3 vs Casualties_5 N Mean StDev SE Mean Casualties_3 1000 0.314 0.538 0.017 Casualties_5 1000 0.105 0.310 0.0098 Difference = mu (Casualties_3) - mu (Casualties_5) Estimate for difference: 0.2090 95% CI for difference: (0.1705, 0.2475) T-Test of difference = 0 (vs not =): T-Value = 10.64 P-Value = 0.000 DF = 1595 Two-Sample T-Test and CI: Casualties_4, Casualties_5 Two-sample T for Casualties_4 vs Casualties_5 167 N Mean StDev SE Mean Casualties_4 1000 0.336 0.584 0.018 Casualties_5 1000 0.105 0.310 0.0098 Difference = mu (Casualties_4) - mu (Casualties_5) Estimate for difference: 0.2310 95% CI for difference: (0.1900, 0.2720) T-Test of difference = 0 (vs not =): T-Value = 11.04 P-Value = 0.000 DF = 1519