Hybrid uncertain analysis of acoustic field with interval random parameters

For the acoustic field prediction without sufficient information, an interval random model is introduced to treat with the uncertain parameters in which the probability distribution parameters of random variables are modeled as interval variables instead of given precise values. Based on the interval random model, the hybrid uncertain acoustic dynamic equilibrium equation is constructed and a hybrid uncertain analysis method is proposed. In the proposed method, the interval random matrix and vector are expanded by the first-order Taylor series and the sound pressure response vector is obtained by the matrix perturbation technique. A monotonic analysis is conducted for the sound pressure response vector and based on it the lower and upper bounds of the sound pressure response vector are obtained by the vertex method. According to the response bounds, the intervals of expectation and variance of the sound pressure response vector are calculated by the random interval moment method. Two numerical examples which include a simple problem with explicit expression and a complex engineering application are presented to demonstrate the effectiveness of the present method.