Novel symmetric divergence based importance measures for engineering simulation models under uncertainty

Abstract

Uncertainty importance assessment of engineering simulation models provides information on how difference sources of uncertainty in the model inputs contribute to the uncertainty in the model output. This paper develops new importance measures based on symmetric statistical divergences, including the symmetric Kullback-Leibler (SKL) divergence and Jensen-Shannon divergence (JSD). These measures aim at assessing the global sensitivity of individual inputs, the joint effect of multiple inputs, the impact of uncertainty on specific output regions of interest, and the influence of input uncertainty on the reliability of engineering system performance. The Mathematical properties of the new importance measures are explored and compared with the conventional asymmetric Kullback-Leibler divergence (KLD) based measure. The analysis indicates that the proposed measures preserve the flexibility of the KLD based measure while addressing its limitations in terms of robustness and interpretability. A comparative study investigates the proposed JSD and SKL based measures, alongside the KLD based importance measure, the moment-independent δ_i index, and Sobol's indices, through two numerical cases and a composite beam example. The results demonstrate that the new importance measures not only ensure calculation accuracy and efficiency, but also exhibit improved robustness compared to the asymmetric approach. Finally, the proposed importance measures are applied to a quayside container crane structure to analyze how uncertainties in the input parameters affect the system's performance and reliability.