Test Planning and Validation through an Optimized Kriging Interpolation Process in a Sequential Sampling Adaptive Computer Learning Environment

Abstract

This dissertation explores Kriging in an adaptive computer learning environment with sequential sampling. The idea of this Design for Kriging (DFK) process was first mentioned in [1] titled “Kriging for Interpolation in Random Simulation”. The idea presented by [1], paved the way for continued research in not only applications of this new methodology, but for many additional opportunities to optimize and expand research efforts. The author proposes several advancements to the above process by introducing a novel method of interpolation through an advanced Design for Kriging (DFK) process with cost considerations, advanced initial sample size and position determination, search techniques for the pilot design, and standardized variogram calculations. We use the terminology variogram over semivariogram as described by [2]. The resulting applications in this research are two-fold. One is to use this process in the upfront experimental design stage in order to optimize sample size and Factor Level Combination (FLC) determination while considering the overall budget. The other application is the use of sampled empirical and interpolated data to form a representative response dataset in order to perform statistical analyses for validation of Monte Carlo simulation models. The DFK process is defined as: Define factor space, boundaries, and dimensions Determine initial sample size through cost considerations and estimation variance analysis. Determine FLCs by a space filling design performed by an augmented simulated annealing algorithm Observe responses, with replication if required, at the initial sample size and FLC selection After sample responses have been observed, perform Kriging interpolation at n_K^U where n_K^U is some number of unobserved FLCs Calculate the estimation variance Based on the results from steps 3-5, identify the next x^c candidate input combination set, {x_i^c,x_(i+1)^c,…,x_(n_K^U)^c}, based on budget considerations and variance reduction, and repeat steps 3-5 using {x_i^c,x_(i+1)^c,…,x_(n_K^U)^c} After an acceptable prescribed accuracy measurement level is achieved or budget is exhausted, Krige the n_K^A observations to achieve a representation of the underlying response function After DFK process is completed, statistically compare a verified Monte Carlo estimated response dataset (Y^MC) with the combination of the Kriging metamodel response dataset (Y^K) and the actual response data Y^S, to assess the model against the combined response dataset Y.