不确定声固耦合系统的数值分析与优化方法研究

发布时间：2018-06-16 17:10

本文选题：声固耦合系统 + 有限元法　；参考：《湖南大学》2015年博士论文

【摘要】：声固耦合系统广泛存在于汽车、轮船、飞机、潜艇和航天器等运载工具之中。声固耦合系统的结构振动所产生的中低频噪声是上述运载工具的主要噪声来源之一。基于声固耦合系统声学性能分析的优化设计技术是控制结构中低频噪声最直接和最有效的方法。传统的声固耦合系统的分析与优化一般是基于确定系统参数，并借助经典CAE技术和优化方法进行求解。然而，在许多实际工程问题中，制造、装配和测量的误差，环境的变化莫测和外部激励的不可预测等因素引起的不确定性广泛存在于声固耦合系统。大多数情况下，这些不确定性因素的影响较小，但当它们耦合在一起时，则可能导致实际声固耦合系统的响应产生较大偏差，甚至导致反相现象的出现。以不准确的声固耦合系统响应为基础，对声固耦合系统进行优化，可能导致优化后的声固耦合系统无法满足给定设计要求。要实现不确定声固耦合系统的有效分析与优化，首先须借助不确定性理论构建不确定声固耦合系统的数值分析模型，并提出相应的不确定数值分析算法，以研究不确定性因素对声固耦合系统响应的影响；再依据不确定性因素对声固耦合系统响应的影响，建立不确定声固耦合系统的优化模型，并提出相应的高效优化算法，以实现不确定声固耦合系统的高效优化设计。为此，本文拟从单一不确定模型（随机模型和区间模型）入手，逐步深入到混合不确定模型（随机与区间混合不确定模型和区间随机模型），并在此基础上对不确定声固耦合系统的数值分析与优化算法进行系统性研究。论文完成的主要研究工作包括：（1）建立了变量变换随机摄动有限元法，可用于随机声固耦合系统响应分析。变量变换随机摄动有限元法采用一阶摄动技术将声固耦合系统的响应近似为随机变量的线性函数；接着，采用变量变换技术计算响应的概率密度函数；最后，在响应概率密度函数的基础上，根据置信区间的定义计算响应的置信区间。某随机壳结构声固耦合系统的数值分析结果表明：变量变换随机摄动有限元法能有效地分析随机声固耦合系统响应的概率密度函数和置信区间。（2）提出了修正区间摄动有限元法，，可用于区间声固耦合系统的响应分析。区间摄动有限元法以一阶Taylor级数展开和一阶Neumann级数展开为基础；子区间摄动有限元法将区间变量划分为若干个子区间，再采用区间摄动有限元法和区间并集运算求解区间声固耦合系统的响应变化范围；修正区间摄动有限元法以一阶Taylor级数展开和修正Neumann级数展开为基础。某壳结构声固耦合系统的数值分析结果表明：区间摄动有限元法仅适用于不确定区间较小的声固耦合系统响应分析；子区间摄动有限元法通过将区间变量划分为若干个子区间，可有效提高区间声固耦合系统的分析精度，但其计算成本随着子区间数的增加呈指数形式增加；修正区间摄动有限元法通过考虑高阶Neumann级数项，能在小幅增加计算成本的条件下，大幅提高区间声固耦合系统的分析精度。（3）建立了混合摄动顶点法，可有效且高效地分析随机与区间混合不确定声固耦合系统响应的期望和方差变化范围。混合摄动顶点法将随机与区间混合不确定声固耦合系统的响应近似为随机变量和区间变量的线性函数，接着，根据响应与区间变量的线性关系，采用顶点法计算响应的上下界；然后，采用随机矩技术计算响应上下界的期望和方差，并以上下界的期望为期望的上下界，以上下界的方差为方差的上下界。某壳结构声固耦合系统的数值分析结果表明，混合摄动顶点法与大样本下混合摄动Monte-Carlo法的计算精度相同，但混合摄动顶点法的计算效率远高于大样本下混合摄动Monte-Carlo法。（4）提出了区间随机摄动顶点法，可用于区间随机声固耦合系统响应分析。区间随机摄动顶点法在区间摄动技术和随机摄动技术的基础上提出区间随机摄动技术，将区间随机声固耦合系统的响应近似为区间随机变量和区间变量的线性函数；再根据响应与区间变量的线性关系，采用顶点法计算响应的上下界；最后采用随机矩技术计算响应上下界的期望和标准差，并以上下界的期望为期望的上下界，以上下界的方差为方差的上下界。某壳结构声固耦合系统和某汽车内声场的数值分析结果表明：区间随机摄动顶点法能有效且高效地预测区间随机声固耦合系统响应期望和方差的变化范围。（5）构建了混合不确定模型（随机与区间混合不确定模型和区间随机模型）下声固耦合系统的嵌套优化模型；提出了优化模型目标函数和约束条件的混合摄动-随机矩法和混合摄动-变量变换法，实现了嵌套优化模型向单层优化模型的转换。板结构声固耦合系统优化设计结果表明：混合摄动-随机矩法和混合摄动-变量变换法能有效且高效地计算混合不确定优化模型的目标函数与约束条件；采用混合不确定优化方法对混合不确定声固耦合系统进行优化，能有效降低声固耦合系统的声压响应，改善混合不确定声固耦合系统的声学性能。（6）提出了区间摄动波函数法，可用于区间声场低频和中频响应分析；提出了混合摄动波函数法，可用于随机与区间混合不确定声场低频和中频响应分析。三维声腔模型的数值分析结果表明，与区间摄动有限元法相比，区间摄动波函数法能更有效地预测区间声场低频和中频响应的上界；与混合摄动有限元法相比，混合摄动波函数法能更有效地在低频和中频段预测随机与区间混合不确定声场响应期望与标准差的上界。本文对不确定声固耦合系统的数值分析与优化方法进行了深入系统地研究，针对不确定声固耦合系统的低频响应数值分析问题，提出了变量变换随机摄动有限元法、修正区间摄动有限元法、混合摄动顶点法和区间随机摄动顶点法；针对混合不确定声固耦合系统低频响应的优化设计问题，提出了基于混合摄动-随机矩法和混合摄动-变量变换法的混合不确定声固耦合系统低频响应优化方法；针对不确定声场中频响应的数值分析问题，提出了不确定声场中频响应数值分析的区间摄动波函数法和混合摄动波函数法。用本文方法分别对板壳结构声固耦合系统、汽车内声场和三维声腔模型进行了数值分析，结果验证了本文方法的有效性和高效性。
[Abstract]:Sound solid coupling systems are widely used in vehicles, ships, aircraft, submarines and spacecraft. The low and low frequency noise produced by the structural vibration of the sound solid coupling system is one of the main sources of noise. The optimal design technique based on the acoustic performance analysis of the sound solid coupling system is the most low frequency noise in the control structure. The analysis and optimization of the traditional sound solid coupling system is generally based on determining the parameters of the system and using the classical CAE technology and the optimization method. However, in many practical engineering problems, the error of manufacturing, assembly and measurement, the unpredictable changes of the environment and the unpredictability of external excitation are caused by many practical engineering problems. Uncertainty exists widely in sound solid coupling systems. In most cases, these uncertainties are less affected, but when they are coupled together, they may lead to a larger deviation in the response of the actual sound solid coupling system and even the emergence of a reverse phase phenomenon. The optimization of the combined system may lead to the optimization of the acoustic structure coupling system which can not meet the specified design requirements.
In order to realize the effective analysis and optimization of the uncertain sound solid coupling system, the numerical analysis model of the uncertain sound solid coupling system must be constructed with the help of the uncertainty theory, and the corresponding uncertain numerical analysis algorithm is put forward to study the influence of the uncertain factors on the response of the sound solid coupling system, and then the acoustic solid is based on the uncertain factors. With the influence of the coupling system response, the optimization model of the uncertain sound solid coupling system is set up, and the corresponding efficient optimization algorithm is proposed to achieve the efficient optimization design of the uncertain sound solid coupling system. This paper, starting with a single uncertain model (random model and interval model), is gradually going deep into the mixed uncertainty model (random and area). Based on the mixed uncertainty model and interval stochastic model, the numerical analysis and optimization algorithm of uncertain acoustic structure coupling system are systematically studied.
The main research work completed in this paper includes:
(1) a variable transformation stochastic perturbation finite element method is established for the response analysis of the stochastic acoustic coupling system. The variable transformation random perturbation finite element method is used to approximate the response of the sound solid coupling system to the linear function of the random variable by the first order perturbation technique; then, the variable transformation technique is used to calculate the probability density function of the response; finally, the variable transformation technique is used to calculate the probability density function of the response. On the basis of the response probability density function, the confidence interval of the response is calculated according to the definition of confidence interval. The numerical analysis results of a random shell structure sound solid coupling system show that the probability density function and confidence interval of the response of the random sound solid coupling system can be effectively analyzed by the variable transformation random perturbation finite element method.
(2) the modified interval perturbation finite element method is proposed for the response analysis of the interval acoustic solid coupling system. The interval perturbation finite element method is based on the first order Taylor series expansion and the first order Neumann series expansion. The interval perturbation finite element method is used to divide the interval variables into several subregions, and then the interval perturbation finite element method and the interval method are used. The interval perturbation finite element method is based on the first order Taylor series expansion and the modified Neumann series expansion. The numerical analysis results of the acoustic solid coupling system of a shell structure show that the interval perturbation finite element method is only applicable to the sound solid coupling system with small uncertain interval. The subinterval perturbation finite element method can effectively improve the analysis precision of the interval sound solid coupling system, but the calculation cost increases exponentially with the increase of the number of subinterval, and the modified interval perturbation finite element method can be added to a small amplitude by considering the higher order Neumann series term. The accuracy of interval acoustic structure coupling system is greatly improved under the condition of cost.
(3) a mixed perturbation vertex method is established, which can effectively and efficiently analyze the expectation and variance range of the response of the stochastic and interval mixed uncertainty sound solid coupling system. The mixed perturbation vertex method approximated the response of the random and interval uncertain acoustic solid coupling system to a linear function of the random variable and the interval variable, followed by the response. With the linear relation of the interval variables, the upper and lower bounds of the response are calculated by the vertex method. Then, the expectation and variance of the upper and lower bounds of the response are calculated by the random moment technique, and the expectation of the above lower bounds is the upper and lower bounds of the expectation, and the variance of the above lower bounds is the upper and lower bounds of the variance. The computational accuracy of the dynamic vertex method and the mixed perturbation Monte-Carlo method under the large sample is the same, but the calculation efficiency of the mixed perturbation vertex method is much higher than the mixed perturbation Monte-Carlo method under the large sample.
(4) an interval random perturbation vertex method is proposed, which can be used for the response analysis of an interval random sound coupled system. Interval random perturbation vertex method is applied to the interval perturbation technique and random perturbation technique. The interval random perturbation technique is proposed to approximate the response of the interval random sound solid coupling system to the interval random variable and the interval variable. According to the linear relationship between the response and the interval variable, the upper and lower bounds of the response are calculated by the vertex method. Finally, the expectation and standard deviation of the upper and lower bounds of the response are calculated by the random moment technique, and the expectation of the above lower bounds is the upper and lower bounds of the expected. The variance of the above lower bounds is the upper and lower bounds of the variance. The numerical analysis of the internal sound field shows that the interval random perturbation vertex method can effectively and efficiently predict the variation range of the response expectation and variance of the interval random sound solid coupling system.
(5) the nested optimization model of the acoustic solid coupling system under the mixed uncertainty model (random and interval mixed uncertainty model and interval random model) is constructed, and the mixed perturbation random moment method and mixed perturbation variable transformation method are proposed to optimize the target function and constraint conditions of the model, and the transformation of the nested optimization model to the single layer optimization model is realized. The optimal design results of the sound solid coupling system of the plate structure show that the mixed perturbation random moment method and the mixed perturbation variable transformation method can effectively and efficiently calculate the objective function and constraint conditions of the mixed uncertain optimization model, and the hybrid uncertain optimization method is used to optimize the mixed uncertain sound solid coupling system effectively. The sound pressure response of the acoustic structure coupling system improves the acoustic performance of the mixed uncertain acoustic solid coupling system.
(6) the interval perturbation wave function method is proposed, which can be used for the analysis of the low frequency and intermediate frequency response of the interval sound field. A mixed perturbation wave function method is proposed, which can be used to analyze the low frequency and intermediate frequency response of the random and interval uncertain sound fields. The numerical analysis results of the three-dimensional sound cavity model show that the interval perturbation finite element method is compared with the interval perturbation finite element method. Compared with the mixed perturbation finite element method, the mixed perturbation wave function method can more effectively predict the upper bound of the expectation and the standard deviation of the random and interval uncertainty of the acoustic field response.
In this paper, the numerical analysis and optimization method of the uncertain acoustic solid coupling system are systematically studied. In order to solve the problem of the low frequency response of the sound solid coupling system, the variable transformation random perturbation finite element method, the modified interval perturbation finite element method, the mixed perturbation vertex method and the interval random perturbation vertex method are proposed. For the optimal design of low frequency response of mixed uncertain sound solid coupling system, a low frequency response optimization method based on mixed perturbation random moment method and mixed perturbation variable transformation method for mixed uncertain sound solid coupling system is proposed. In view of the numerical analysis problem of the medium frequency response of the uncertain sound field, the uncertainty of the medium frequency response number of the sound field is proposed. The interval perturbation wave function method and the mixed perturbation wave function method are used to analyze the acoustic solid coupling system of the plate and shell structure, the internal sound field and the three-dimensional sound cavity model of the car respectively. The results verify the effectiveness and efficiency of the proposed method.
【学位授予单位】：湖南大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TB535

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