本文選題：聲學數(shù)值計算 + 證據(jù)理論��； 參考：《湖南大學》2014年碩士論文

【摘要】：隨著計算機性能和數(shù)值計算方法的快速發(fā)展,研究人員可以采用數(shù)值計算方法來預測產品的噪聲性能。聲學有限元法(Finite Element Method, FEM)是在聲學Helmholtz方程的基礎上,對聲場進行有限元離散,并構建聲學系統(tǒng)控制方程來求解聲學響應,能夠有效的處理中低頻段的穩(wěn)態(tài)聲場和結構-聲場耦合問題。不確定性普遍存在于工程實際之中,從不確定性的產生原因來看,可將其分為隨機不確定性和認知不確定性。聲學問題中環(huán)境狀態(tài)、模型穩(wěn)定性、數(shù)值簡化、制造誤差和人為因素都是不確定性的主要來源。當前不確定聲學有限元研究主要采用隨機模型和區(qū)間模型來分析參數(shù)的不確定性,對于聲學參數(shù)的認知不確定性問題還缺乏相關研究。 本文針對聲學參數(shù)中的認知不確定性問題,引入證據(jù)理論表述參數(shù)的認知不確定性,提出了一種基于證據(jù)理論的聲學有限元法(Evidence Theory-based Finite Element Method of Acoustic Fields, ETFEM),并將其推廣到認知不確定參數(shù)作用下的穩(wěn)態(tài)聲場和殼結構-聲場耦合系統(tǒng)分析之中。 論文主要研究工作如下 (1)建立了穩(wěn)態(tài)聲場FEM分析模型和殼結構-聲場耦合分析的FEM/FEM模型。在聲學波動方程和有限元建模方法的基礎上,推導了穩(wěn)態(tài)聲場有限元法的計算公式；采用殼單元表述薄壁結構,推導了殼結構-聲場耦合分析的FEM/FEM法,并以MATLAB軟件平臺為基礎,編寫了聲學響應的數(shù)值計算程序。 (2)系統(tǒng)分析了區(qū)間模型、隨機模型和模糊模型的局限性,引入證據(jù)理論來系統(tǒng)表述參數(shù)的認知不確定性和隨機不確定性。通過焦元和基本可信度分配(Basic Probability Assignment, BIA)的概念來表述參數(shù)的最小分布范圍及其分布概率；采用D-S證據(jù)合成準則處理多變量信息和沖突信息,并以整體可信度區(qū)間來表征認知不確定系統(tǒng)響應的“風險預測結果”和“保守預測結果”。 (3)考慮聲場參數(shù)存在的認知不確定性,基于證據(jù)理論和有限元法,推導了認知不確定聲場分析的ETFEM法。采用沖突信息表述參數(shù)認知不確定性的一般情況,結合攝動法和區(qū)間分析技術,給出了聲壓響應期望和標準差的求解公式。以管道聲場和汽車聲腔模型為例,驗證了ETFEM方法處理認知不確定聲場問題的可行性和有效性。 (4)應用ETFEM方法處理殼結構-聲場耦合分析的認知不確定性問題,考慮結構參數(shù)和聲學參數(shù)同時存在認知不確定性,推導了耦合聲場聲壓響應期望值和標準差的求解公式。三維殼結構-聲場耦合分析的結果表明,ETFEM方法能夠處理認知不確定參數(shù)作用下的結構-聲場耦合系統(tǒng),具有良好的工程應用前景。 本文對不確定聲學問題的數(shù)值分析方法進行了探討,采用認知不確定性來綜合表征參數(shù)的非概率不確定性,提出了解決認知不確定聲學問題的ETFEM法,研究成果能夠有效的應用于不確定聲學問題的數(shù)值計算,具有重要的工程應用價值。
[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.
【學位授予單位】：湖南大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：TB53

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