A unified model approach for probability response analysis of structure-acoustic system with random and epistemic uncertainties

The uncertainties of structure-acoustic system can be generally characterized as the random uncertainty and the epistemic uncertainty. Traditional methods for response analysis of structure-acoustic system with hybrid random and epistemic uncertainties are developed by integrating different mathematical theories, such as the probability theory and the interval analysis. In this paper, the Evidence-Theory-based Unified Uncertain Model (ETUUM) is introduced to deal with hybrid random and epistemic uncertain structure-acoustic problem. In ETUUM, both epistemic and random uncertainties are modeled by using evidence theory. For uncertainty quantification of ETUUM of structure-acoustic system with hybrid random and epistemic uncertainties, a new hybrid uncertainty analysis method named as the Evidence-Theory-based Arbitrary Polynomial Chaos Method (ETAPCM) is proposed. In ETAPCM, the response of ETUUM in the range of variation of the uncertain parameter is approximated by the arbitrary Polynomial Chaos (aPC) expansion, through which the uncertainty property of the response can be efficiently obtained. As the aPC expansion can provide a free choice of the polynomial basis, the optimal polynomial basis of polynomial chaos expansion for the epistemic uncertain parameter and the random parameter with arbitrary probability distribution can be obtained by using aPC expansion. The effectiveness of the proposed methodology has been investigated by comparing it with the conventional polynomial chaos and evidence theory based hybrid uncertainty analysis method as well as the probability theory based hybrid uncertainty analysis method.