认知不确定二维声场的响应特性数值分析

针对声学参数存在认知不确定性的问题,为实现认知不确定声场声压响应的预测。提出了解决二维认知不确定声场的有限元法(Evidence Theory-based Finite Element Method,ETFEM),引入证据理论,采用焦元和基本可信度的概念来描述认知不确定参数,基于摄动法的区间分析技术,推导了认知不确定声场声压响应的标准差、期望求解公式。为验证本文方法的可行性。以认知不确定参数下的二维管道声场模型和某轿车二维声腔模型为例进行了数值计算,对比离散随机变量得到认知不确定参数的声场分析结果和相应的随机声场所得分析结果,研究表明:该方法能够有效的处理认知不确定参数下的二维声场,为工程问题中噪声预测提供可靠的分析模型。 

Numerical analysis of the 2D acoustic field with epistemic uncertainty

Aiming at the problem that the epistemic uncertain parameters exist in a acoustic field, an evidence theory- based finite element method (ETFEM) is proposed by introducing the evidence theory, in which the focal element and basic probability assignment (BPA) are used to describe the epistemic uncertainty. In order to alleviate the computational cost, the interval analysis technique based on perturbation method is adopted to acquire the approximate frequency response amplitude bounds for each focal element. The corresponding formulations of intervals of expectation and standard deviation of the approximate frequency response amplitude with epistemic uncertainty are deduced. The sound pressure response of a 2D acoustic tube and a 2D car acoustic cavity with epistemic uncertain parameters are analyzed by the proposed method. The proposed method is verified through the comparison of the analysis results of random acoustic field with that of epistemic uncertain acoustic field in which the epistemic uncertain parameters are obtained by discretizing the random parameters. Thus, the proposed method can analyze the 2D acoustic field with epistemic uncertainty effectively and provide a reliable model for noise prediction, which has good prospects of engineering application.