Novel Evaluation Methods for Complex Systems via Adaptive Sequential Exploration of Variables Interactions

Abstract

The complex and coupled behavior of variables in the currently developing Generation IV reactors and Small Modular Reactors is becoming a major incentive to seek efficient design methods. This research develops and validates new methods to evaluate systems with various degrees of variables’ interactions using basic knowledge in variables’ directions of effect and an adaptive number of experiments. The methods replace the commonly used assumption of negligible interactions with a broader assumption of monotonic variables’ effects. The assumption was evaluated using studies of other physical systems’ regularities, and is expected to be significantly present in physical systems.

Four methods were developed and analyzed in this dissertation. Three of the introduced methods utilized an adaptive sequential spanning tree concept with a method specific criterion to construct piecewise multidimensional surfaces or subtrees. Each method then used a specific approach to project the results within the subtrees. The fourth method is an expansion to an existing method to explore any order of interactions through the introduction of a new domain of parameters. Three of the four methods significantly outperformed the common orthogonal arrays methods that rely on a uniform distribution of experiments in the design domain. Two of the three methods significantly outperformed the third method and were used in the dissertation’s application. The strength of the applicable methods was demonstrated through their application to two examples from literature, each of which has a different degree of variables’ monotonic behavior. The most applicable method of the two most effective methods was used to decouple the effects of fourteen variables on six performance characteristics in the design of a Small Modular Reactor version of the Advanced Pressurized Water Reactor AP1000. The methods’ application succeeded in finding the most important main effects and interactions of each performance characteristic. The performance of the methods’ application to three performance characteristics was compared to the performance of fractional factorial designs. The methods were found to significantly reduce the projection error when the assumption of variables’ monotonic behavior is valid.