Uncertainty quantification of 3D acoustic shape sensitivities with generalized nth-order perturbation boundary element methods

This paper presents a novel perburbation-based method for uncertainty quantification of acoustic fields and their shape sensitivities. In this work, the frequencies of impinging acoustic waves are regarded as random variables. Taylor’s series expansions of acoustic boundary integral equations are derived to obtain $n$th-order derivatives of acoustic state functions with respect to frequencies. Acoustic shape sensitivity is obtained by directly differentiating acoustic boundary integral equation with respect to shape design variables, and then the $n$th-order derivatives of shape sensitivity with respect to random frequencies are formulated with Taylor’s series expansions. Based on the $n$th-order perturbation theory, the statistical characteristics of acoustic state functions and their shape sensitivities can be evaluated. Numerical examples are presented to demonstrate the validity and effectiveness of the proposed algorithm.