A polynomial expansion approach for response analysis of periodical composite structural-acoustic problems with multi-scale mixed aleatory and epistemic uncertainties

The response analysis of periodical composite structural-acoustic problem with multi-scale mixed aleatory and epistemic uncertainties is investigated based on homogenization method in this paper. The aleatory uncertainties are presented by bounded random variables, whereas the epistemic uncertainties are presented by interval variables and evidence variables. When dealing with the combination of bounded random variables, interval variables and evidence variables, enormous computation is needed to estimate the output probability bounds of the sound pressure response of the periodical composite structural-acoustic system. To reduce the involved computational cost but without losing accuracy, by transforming all of the bounded random variables and interval variables into evidence variables appropriately, an evidence-theory-based polynomial expansion method (EPEM) is developed in which the Gegenbauer series expansion is employed to approximate the variation range of the response with respect to evidence variables. By using EPEM, the probability bounds of the response can be obtained efficiently. A numerical example is used to validate the proposed method and two engineering examples are given to demonstrate its efficiency.