Hybrid Uncertain Analysis for Exterior Acoustic Field Prediction with Interval Random Parameters

For exterior acoustic field problems that lack sufficient information to construct precise probability distributions, an interval random model is introduced to deal with the uncertain parameters. In the interval random model, the probability variables are employed to treat the uncertain parameters, whereas some distribution parameters of random variables are modeled as interval variables instead of precise values. Based on the interval random model, the interval random finite element equation for exterior acoustic fields is established and a hybrid uncertain analysis method is presented to solve the exterior acoustic field problem with interval random variables. In the presented method, by temporarily neglecting the uncertainties of interval variables, a first-order stochastic perturbation method is adopted to calculate the expectation and the variance of the response vector. According to the monotonicity of the expectation and variance of the response vector with respect to the interval variables, the lower and upper bounds of the expectation and variance of the response vector can be calculated by the vertex method. In addition, in order to ensure accuracy of the proposed method, the subinterval technique is introduced and investigated. The numerical example of a square flexible shell model is presented to demonstrate the effectiveness of the proposed method.