دانلود رایگان مقاله آنالیز توزیع احتمال واکنش متحد دو زمینه آکوستیک نا مطمئن هیبریدی

Abstract

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.

5. Conclusion

For the response probability distribution analysis of the acoustic field with limited information, two types of hybrid uncertain models have been introduced. The first type of hybrid uncertain model is the hybrid probabilistic and interval model. In the hybrid probabilistic and interval model, the uncertain parameters with and without sufficient information to construct the corresponding probability distributions are treated as probabilistic variables and interval variables, respectively. The second type of hybrid uncertain model is the interval probabilistic model. In the interval probabilistic model, the uncertain parameters are treated as probabilistic variables whose distribution parameters may be treated as interval variables. The common element of two hybrid uncertain models is that probability variables and interval variables exist simultaneously. Based on this common element, an inverse mapping hybrid perturbation method (IMHPM) is proposed for the unified response probability distribution analysis of two hybrid uncertain acoustic fields. In the proposed method, the responses of two hybrid uncertain acoustic fields are converted to invertible functions of probability variables based on the stochastic perturbation analysis. And then, the change-of-variable technique is introduced to calculate the response probability distributions. Last, the variational ranges of the response probability distributions are estimated by the interval perturbation technique. Numerical results on a U-shaped tube verify that the lower and upper bounds of the response probability distribution yielded by IMHPM can be used to determine an interval in which the potential response probability distributions of the acoustic field under either of two hybrid uncertain models are included. Furthermore, the numerical results also show that the computational efficiency of IMHPM is very high, when compared with the Monte-Carlo method. Hence, IMHPM can be considered as an effective and efficient engineering method to quantify the effects of parametric uncertainties on the sound pressure response of two hybrid uncertain acoustic fields.