Response analysis and reliability-based design optimization of structural-acoustic system under evidence theory

Evidence theory has a strong ability to deal with epistemic uncertainties whose precise probability distributions cannot be determined according to limited information. For response analysis of the structural-acoustic system under evidence theory, a numerical method named as vertex Taylor expansion moment method (VTPEMM) is proposed. In VTPEMM, the response of the structural-acoustic system in each focal element combination of evidence variables is expanded by the first-order Taylor series and its variational range is evaluated at vertexes of focal elements of evidence variables. Then, a moment method of probability theory is developed to calculate variational ranges of expectation and variance of response. For optimization of the structural-acoustic system under evidence theory, an evidence reliability-based design optimization (RBDO) strategy is developed. In the evidence RBDO, the objective function is efficiently estimated by VTPEMM. To efficiently evaluate the reliability constraint condition, an evidence-based reliability analysis technique (EBRAT) is proposed. A numerical example is provided to investigate the effectiveness of the proposed numerical analysis and optimization techniques.