基于证据理论和有限元法的不确定声学数值分析方法研究

发布时间：2018-04-13 08:10

本文选题：声学数值计算 + 证据理论　；参考：《湖南大学》2014年硕士论文

【摘要】：随着计算机性能和数值计算方法的快速发展,研究人员可以采用数值计算方法来预测产品的噪声性能。声学有限元法(Finite Element Method, FEM)是在声学Helmholtz方程的基础上,对声场进行有限元离散,并构建声学系统控制方程来求解声学响应,能够有效的处理中低频段的稳态声场和结构-声场耦合问题。不确定性普遍存在于工程实际之中,从不确定性的产生原因来看,可将其分为随机不确定性和认知不确定性。声学问题中环境状态、模型稳定性、数值简化、制造误差和人为因素都是不确定性的主要来源。当前不确定声学有限元研究主要采用随机模型和区间模型来分析参数的不确定性,对于声学参数的认知不确定性问题还缺乏相关研究。本文针对声学参数中的认知不确定性问题,引入证据理论表述参数的认知不确定性,提出了一种基于证据理论的声学有限元法(Evidence Theory-based Finite Element Method of Acoustic Fields, ETFEM),并将其推广到认知不确定参数作用下的稳态声场和壳结构-声场耦合系统分析之中。论文主要研究工作如下 (1)建立了稳态声场FEM分析模型和壳结构-声场耦合分析的FEM/FEM模型。在声学波动方程和有限元建模方法的基础上,推导了稳态声场有限元法的计算公式；采用壳单元表述薄壁结构,推导了壳结构-声场耦合分析的FEM/FEM法,并以MATLAB软件平台为基础,编写了声学响应的数值计算程序。 (2)系统分析了区间模型、随机模型和模糊模型的局限性,引入证据理论来系统表述参数的认知不确定性和随机不确定性。通过焦元和基本可信度分配(Basic Probability Assignment, BIA)的概念来表述参数的最小分布范围及其分布概率；采用D-S证据合成准则处理多变量信息和冲突信息,并以整体可信度区间来表征认知不确定系统响应的“风险预测结果”和“保守预测结果”。 (3)考虑声场参数存在的认知不确定性,基于证据理论和有限元法,推导了认知不确定声场分析的ETFEM法。采用冲突信息表述参数认知不确定性的一般情况,结合摄动法和区间分析技术,给出了声压响应期望和标准差的求解公式。以管道声场和汽车声腔模型为例,验证了ETFEM方法处理认知不确定声场问题的可行性和有效性。 (4)应用ETFEM方法处理壳结构-声场耦合分析的认知不确定性问题,考虑结构参数和声学参数同时存在认知不确定性,推导了耦合声场声压响应期望值和标准差的求解公式。三维壳结构-声场耦合分析的结果表明,ETFEM方法能够处理认知不确定参数作用下的结构-声场耦合系统,具有良好的工程应用前景。本文对不确定声学问题的数值分析方法进行了探讨,采用认知不确定性来综合表征参数的非概率不确定性,提出了解决认知不确定声学问题的ETFEM法,研究成果能够有效的应用于不确定声学问题的数值计算,具有重要的工程应用价值。
[Abstract]:With the rapid development of computer performance and numerical calculation methods, researchers can use numerical methods to predict the noise performance of products.Acoustic finite Element method (FEMM) is a finite element method to discretize acoustic field based on acoustic Helmholtz equation, and the control equation of acoustic system is constructed to solve the acoustic response.It can effectively deal with the steady state sound field and structure-sound field coupling problem in low and medium frequency band.Uncertainty generally exists in engineering practice, which can be divided into stochastic uncertainty and cognitive uncertainty.Environmental state, model stability, numerical simplification, manufacturing error and human factors are the main sources of uncertainty in acoustic problems.At present, the uncertain acoustic finite element analysis mainly uses stochastic model and interval model to analyze the uncertainty of the parameters, but there is no related research on the cognitive uncertainty of acoustic parameters.Aiming at the problem of cognitive uncertainty in acoustic parameters, this paper introduces evidence theory to express the cognitive uncertainty of parameters.In this paper, an acoustic finite element method based on evidence theory is proposed, which is based on evidence Theory-based Finite Element Method of Acoustic Fields, and is extended to the analysis of steady-state sound field and shell structure-acoustic coupling system under the action of uncertain cognitive parameters.The main research work of this thesis is as follows1) the FEM analysis model of steady-state sound field and the FEM/FEM model of shell structure-acoustic field coupling analysis are established.On the basis of acoustic wave equation and finite element modeling method, the calculation formula of steady-state sound field finite element method is derived, the shell element is used to express thin-walled structure, the FEM/FEM method of shell structure-acoustic field coupling analysis is derived, and the MATLAB software platform is used as the foundation.A numerical calculation program for acoustic response is developed.(2) the limitations of interval model, stochastic model and fuzzy model are systematically analyzed, and the evidence theory is introduced to describe the cognitive uncertainty and stochastic uncertainty of parameters systematically.The minimum distribution range and distribution probability of parameters are expressed by the concept of focal element and basic Probability assignment (Bia), and the multivariable information and conflict information are processed by D-S evidence synthesis criterion.The "risk prediction result" and "conservative prediction result" of the cognitive uncertain system response are represented by the global confidence interval.3) considering the cognitive uncertainty of acoustic field parameters, the ETFEM method for the analysis of cognitive uncertain acoustic field is derived based on the evidence theory and finite element method.By using conflict information to describe the general situation of cognitive uncertainty of parameters and combining the perturbation method and interval analysis technique, the formulas for solving the expectation and standard deviation of sound pressure response are given.The feasibility and effectiveness of the ETFEM method in dealing with the problem of cognitive uncertain sound field are verified by taking the pipe sound field and the vehicle acoustic cavity model as examples.In this paper, ETFEM method is used to deal with the cognitive uncertainty in the coupled analysis of shell structure and sound field. Considering the cognitive uncertainty of both structural parameters and acoustic parameters, the formulas for calculating the expected value and standard deviation of acoustic pressure response of coupled sound field are derived.The results of three-dimensional shell structure-acoustic field coupling analysis show that the ETFEM method can deal with structure-acoustic field coupling systems under the action of cognitive uncertain parameters, and has a good prospect of engineering application.In this paper, the numerical analysis method for uncertain acoustic problems is discussed. The non-probabilistic uncertainty of parameters is represented by cognitive uncertainty, and a ETFEM method is proposed to solve the acoustical problem of cognitive uncertainty.The research results can be effectively applied to the numerical calculation of uncertain acoustic problems, and have important engineering application value.
【学位授予单位】：湖南大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TB53

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