Uncertainty and multi-criteria global sensitivity analysis of structural systems using acceleration algorithm and sparse polynomial chaos expansion

Abstract

Sparse polynomial chaos expansion (PCE) can be used to emulate the stochastic model output where the original model is computationally expensive. It is a powerful tool in efficient uncertainty quantification and sensitivity analysis. Structural systems are usually associated with high dimensional and probabilistic input. The number of candidate basis functions increases significantly with input dimension, resulting in high computational burden for establishing sparse PCE. In this study, acceleration techniques are integrated to formulate an algorithm for efficient computation of sparse PCE (ASPCE). The integrated algorithm can improve efficiency of computational process compared with conventional greedy algorithm while ensuring the satisfying predictive performance. Once the sparse PCE model is obtained, the statistic moments, probability density function of stochastic output, and global sensitivity index could be computed efficiently. Traditional PCE based global sensitivity analysis only assesses the sensitivity on individual structural performance criterion. Assessing the global sensitivity considering multiple criteria is challenging as the sensitive parameters may not be consistent for different performance criteria. To address this issue, a two-stage multi-criteria global sensitivity analysis algorithm is proposed by coupling ASPCE and the technique for order preference by similarity to ideal solution (TOPSIS). A holistic global sensitivity index is proposed to identify the sensitive parameters incorporating multiple performance criteria. In order to illustrate the efficiency, accuracy, and applicability of the proposed approach, two illustrative cases are presented.