A Novel Sparse Polynomial Expansion Method for Interval and Random Response Analysis of Uncertain Vibro-Acoustic System

Abstract

For the vibro-acoustic system with interval and random uncertainties, polynomial chaos expansions have received broad and persistent attention. Nevertheless, the cost of the computation process increases sharply with the increasing number of uncertain parameters. This study presents a novel interval and random polynomial expansion method, called Sparse Grids’ Sequential Sampling-based Interval and Random Arbitrary Polynomial Chaos (SGS-IRAPC) method, to obtain the response of a vibro-acoustic system with interval and random uncertainties. The proposed SGS-IRAPC retains the accuracy and the simplicity of the traditional arbitrary polynomial chaos method, while avoiding its inefficiency. In the SGS-IRAPC, the response is approximated by the moment-based arbitrary polynomial chaos expansion and the expansion coefficient is determined by the least squares approximation method. A new sparse sampling scheme combined the sparse grids’ scheme with the sequential sampling scheme which is employed to generate the sampling points used to calculate the expansion coefficient to decrease the computational cost. The efficiency of the proposed surrogate method is demonstrated using a typical mathematical problem and an engineering application.