Effective and scalable uncertainty evaluation for large-scale complex system applications

Effective uncertainty evaluation is a critical step toward real-time and robust decision-making for complex systems in uncertain environments. A Multivariate Probabilistic Collocation Method (M-PCM) was developed to effectively evaluate system uncertainty. The method smartly chooses a limited number of simulations to produce a low-order mapping, which precisely predicts the mean output of the original system mapping up to certain degrees. While the M-PCM significantly reduces the number of simulations, it does not scale with the number of uncertain parameters, making it difficult to use for large-scale applications that typically involve a large number of uncertain parameters. In this paper, we develop a method to break the curse of dimensionality. The method integrates M-PCM and Orthogonal Fractional Factorial Designs (OFFDs) to maximally reduce the number of simulations from 2^2m to 2^{⌈log2(m+1)⌉} for a system mapping of m parameters. The integrated M-PCM-OFFD predicts the correct mean of the original system mapping, and is the most robust to numerical errors among all possible designs of the same number of simulations. The analysis also provides new insightful formal interpretations on the optimality of OFFDs.