Unified response probability distribution analysis of two hybrid uncertain acoustic fields

For the response analysis of uncertain acoustic fields with limited information, two hybrid uncertain models have been developed. One is the hybrid probability and interval model in which the probability and interval variables exist simultaneously. The other one is the hybrid interval probability model in which some distribution parameters of probability variables are expressed as interval variables. For the unified response probability distribution analysis of acoustic fields under two hybrid uncertain models, an inverse mapping hybrid perturbation method (IMHPM) is proposed. In IMHPM, the responses of two hybrid uncertain acoustic fields are converted to invertible functions of probability variables based on the Taylor series expansion. According to the inverse mapping relationships between responses and probability variables, the formal expressions of the response probability distributions are yielded on the basis of the change-of-variable technique. The variational ranges of the response probability distributions are estimated by the interval perturbation technique. The effectiveness and efficiency of the proposed method for the unified response probability distribution analysis of two hybrid uncertain acoustic fields are investigated by a numerical example.