Sensitivity Analysis of Random and Interval Uncertain Variables Based on Polynomial Chaos Expansion Method

Abstract

The problem of characterizing the sensitivity indices of structural performance considering random and interval uncertainty variables simultaneously is analyzed. Data-driven polynomial chaos expansion (PCE) is established to treat random variables with arbitrary input uncertainty information, and subsequently extended to consider interval uncertainty variables simultaneously. An adaptive-sparse polynomial chaos expansion calculation algorithm is proposed to determine the appropriate polynomial coefficients based on the available uncertainty information of random and interval uncertainty variables. Subsequently, the local and total sensitivity indices of random and interval uncertainty variables are calculated directly using the constructed PCE model. Two numerical and engineering examples are presented to demonstrate the effectiveness of the proposed approach. Compared with the results of the Monte Carlo simulation method, the proposed approach yields excellent results with significantly reduced computational effort in the three examples.

Keywords

• Sensitivity analysis
• polynomial chaos expansion
• random variables
• interval variables