Nondeterministic Kriging for Probabilistic Systems with Mixed Continuous and Discrete Input Variables

Abstract

This paper presents a nondeterministic kriging (NDK) method to approximate the response of probabilistic systems with mixed continuous and discrete input variables. The proposed method approximates both epistemic (extrinsic) and aleatory (intrinsic) uncertainties in addition to the mean response of a system. Kriging is a popular metamodeling method for approximating the responses of computationally demanding systems along with prediction variances. However, conventional kriging fails to perform with nondeterministic data sets with replications. The recently developed NDK method addresses those challenges in the continuous input space. Currently, kriging is often used for approximations in probabilistic systems with mixed continuous and discrete input variables as well. Therefore, this study aims to fill the gap in the NDK method for probabilistic systems with mixed continuous and discrete input variables. Herein, the aleatory uncertainty is assessed using locally weighted regression (LWR). The proposed method uses a combination of continuous and discrete kernels to capture the effects of mixed inputs. The effectiveness of the newly proposed NDK method was demonstrated using a set of probabilistic analytical cases and engineering applications. The proposed method provides separable information about aleatory and epistemic uncertainties, which are beneficial in design optimizations and sequential explorations of probabilistic systems, especially with large-scale experiments and computer simulations with randomness.