A probability-box-based method for propagation of multiple types of epistemic uncertainties and its application on composite structural-acoustic system

Abstract

The response analysis of the composite structural-acoustic systems with multiple types of epistemic uncertainties is investigated in this paper. Based on the available information for the uncertain parameters, the multiple types of epistemic uncertainties refer to probability-box (p-box) variables, evidence variables and interval variables. The proposed development focused on an efficient computation of the output bounds of the cumulative distribution function of the sound pressure response when dealing with the combination of p-box variables, evidence variables and interval variables. To reduce the involved computational cost but ensuring the accuracy, all evidence variables and interval variables are transformed into p-box-form variables. Then, a modified interval Monte Carlo method (MIMCM) is developed to estimate the bounds of the cumulative distribution function of the system response. In MIMCM, a sparse Gegenbauer polynomial surrogate model is established with focus on the efficiency and accuracy and then applied for the interval analysis in each iteration. A numerical example and two engineering examples with respect to multiple types of epistemic uncertainties are carried out to illustrate the accuracy and efficiency of the MIMCM by conducting comparisons with traditional algorithms. The ability of the proposed method for risk and conservative reliability analysis is also investigated.