模糊随机参数二维声场数值计算

解决声场参数同时具有模糊性和随机性的问题,实现模糊随机声场声压响应的预测,引入了信息熵理论,利用信息熵的等效转换,将模糊随机声场转化为纯随机声场或者纯模糊声场进行求解,推导了基于摄动法的二维随机声场和模糊声场的有限元计算公式。以模糊随机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,所得结果与蒙特卡洛法(Monte Carlo Method)所预测声压变化范围基本一致,同时,转化为纯随机声场和纯模糊声场所求得声压响应变化范围也基本一致,说明了本文方法计算结果的准确性。因此本文方法能很好地应用于模糊随机参数下二维声场的预测,具有重要的工程应用价值。     

概率盒框架下混合认知不确定声场的响应预测

针对含概率盒-证据混合认知不确定参数声场的响应预测问题,提出了一种概率盒框架下的改进区间蒙特卡洛方法。该方法首先将混合认知不确定参数转换为纯概率盒形式,然后结合有限元方法推导出混合认知不确定声场的盖根鲍尔多项式代理模型,再采用蒙特卡洛方法求解代理模型得到声压响应。以含概率盒-证据混合认知不确定参数的二维管道声场模型和卡车乘客舱声腔模型为例,计算结果表明混合认知不确定参数影响下的声压响应为概率盒形式,其包括声压响应极值和相应的概率信息,并且所提方法较常规混合离散方法效率更优,较基于一阶摄动法的区间蒙特卡洛方法准确性更高。研究结果表明:所提方法可以有效预测混合认知不确定声场的声压响应,并可进行声学性能的风险和保守估计。      

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。      

不确定声场分析的二阶区间摄动有限元法

针对一阶区间摄动有限元法在声场参数不确定程度增大时误差过大的缺陷,在二阶Taylor展开的基础上推导了声学二阶区间摄动有限元法,并将其应用于区间不确定声场的声压响应分析。该方法先对声学区间有限元方程的声压响应向量进行二阶Taylor展开,获取声压响应的二阶近似响应向量;再根据二次函数极值定理获得声压响应向量的上下界。二维管道声场与轿车声腔模型的数值分析算例表明,与一阶区间摄动有限元法相比,二阶区间摄动有限元法有效提高了计算精度。因此二阶区间摄动有限元适合不确定度更大的区间不确定声场声压响应分析,具有良好的工程应用前景。     

半自由声场的全息重建和预测技术研究

在半自由声场中,实际测量声压为直达声压和反射声压的叠加,而声压为标量,很难直接将其中直达声压成分分离出来,因而不能简单地用常规的方法来直接进行声源重建和声场预测。在充分地考虑到反射声压的情况下,建立了半自由声场环境下反射面为刚性和非刚性时的声场全息重建和预测理论模型,并通过实例验证了此模型的可行性和正确性。结果表明:此方法有效地解决了半自由声场中进行声场全息重建和预测时所存在的声压反射问题,从而扩充了声全息重建和预测技术的应用范围;采用分布源边界点法作为全息变换算法,提高了声全息重建和预测的速度、精度和稳定性。     

不确定声场分析的二阶区间摄动有限元法

针对一阶区间摄动有限元法在声场参数不确定程度增大时误差过大的缺陷,在二阶Taylor展开的基础上推导了声学二阶区间摄动有限元法,并将其应用于区间不确定声场的声压响应分析。该方法先对声学区间有限元方程的声压响应向量进行二阶Taylor展开,获取声压响应的二阶近似响应向量;再根据二次函数极值定理获得声压响应向量的上下界。二维管道声场与轿车声腔模型的数值分析算例表明,与一阶区间摄动有限元法相比,二阶区间摄动有限元法有效提高了计算精度。因此二阶区间摄动有限元适合不确定度更大的区间不确定声场声压响应分析,具有良好的工程应用前景。      

标量波传播问题的双互易精细积分法

为避免使用计算多种特征频率下的声场响应，采用双互易方法将边界积分方程中时间二次导数项的域积分转化为边界积分.首先，将计算场点配置在边界上并考虑边界条件，可以获得由内部节点上声压量线性表示的边界节点上的物理量；其次，将计算场点配置于域内离散节点上，将所得边界积分方程组中关于边界物理量用内部节点的声压量线性表示，获得关于声压量的二阶常微分方程组；第三，引入声压变化速度作为未知量，将二阶常微分方程组转化为一阶常微分方程组；最后，采用精细积分法精确求解常微分方程组.数值算例验证了双互易精细积分法的正确性和稳定性.     

二维声场预测的快速多极基本解法

传统基本解法在二维大规模模型的声场求解过程中,系统方程形成和求解的计算量正比于自由度N的二次方O(N2)和三次方O(N3),求解效率低;为此,引入快速多极子算法并采用广义极小残差法迭代求解,提出一种用于二维声场预测的快速多极基本解法。对无限长圆柱体及二维类车体辐射模型的仿真结果表明,当N为3000时,分别采用快速多极基本解法与传统基本解法求解所需的时间比值约为百分之四,且N越大比值越小;最终实现系统方程的形成和求解的计算量降低到正比于自由度O(N),提高了对二维大规模模型声场预测计算效率。      

适用于任意形状封闭空间的声场预测相干模型

针对现有几何声学的方法对封闭空间内声场进行预测时在中低频段出现较大误差的问题,该文提出一种近似圆锥声束追踪法和相干反射场理论相结合的声场预测新模型。在近似圆锥声束追踪法基础上,考虑声束轴线在边界多次反射时声压和相位的改变,最后计算不同声波之间的干涉效应,建立一种适用于任意形状封闭空间的声场预测相干模型。利用该模型对某一矩形封闭空间进行声场预测,通过对边界元法、Raynoise软件相干和非相干算法的预测结果和本模型的数值模拟结果对比。结果表明,文中提出的方法和边界元法的计算结果在中低频段非常吻合,两者的计算结果平均绝对误差为1.1 d B。本模型在中低频率下与同样考虑了相位的Raynoise相干算法相比有更好的准确性,在较高频率上,本模型计算结果与Raynoise相干算法计算结果非常吻合。     

浅海相干声场不确定性研究

提出一种采用随机响应面法求解浅海中含不确定参数波动方程的方法.将海洋环境不确定参数表示为标准随机变量,利用Hermite多项展开式表示相干声场的随机响应,用概率配点法求解随机多项式系数后,获得相干声场的近似表达式.通过与Monte Carlo法、声场位移法比较,表明本文方法计算精度和效率较高.     

Numerical analysis of the 2D acoustic field with fuzzy-random parameters

Regard for the fuzziness and the randomness in some acoustic fields,a method for the numerical analysis of the 2D acoustic field with Fuzzy-Random parameters was proposed based on the equivalent conversion of information entropy.In the proposed method,a fuzzyrandom acoustic field was treated as a pure fuzzy acoustic field or a pure random acoustic field by transforming all the variables into fuzzy variables or random variables.Perturbation finite element methods for analyzing the two-dimensional acoustic fuzzy and random field are deduced.The sound pressure response of a 2D acoustic tube and the 2D acoustic cavity of a car with fuzzy-random parameters were analyzed by the proposed method and the Monte Carlo method,the results show that the proposed method can be well applied to the numerical analysis of the 2D acoustic field with fuzzy-random parameters,and has good prospect of engineering application.     

Numerical analysis of the 2D acoustic field with epistemic uncertainty

Aiming at the problem that the epistemic uncertain parameters exist in an 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 reduce the computational cost,the interval analysis technique based on perturbation method is adopted to acquire the approximate sound pressure response bounds for each focal element.The corresponding formulations of intervals of expectation and standard deviation of the sound pressure response 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.Numerical analysis results show that the proposed method can analyze the 2D acoustic field with epistemic uncertainty effectively,and has good prospect of engineering application.     

Modified sub-interval perturbation finite element method for 2D acoustic field prediction with large uncertain-but-bounded parameters

Based on the sub-interval perturbation analysis, a modified sub-interval perturbation finite element method is proposed to determine the bounds of sound pressure in the 2D acoustic field with large uncertain-but-bounded parameters. In the proposed method, the inversion of the invertible sub-interval dynamic stiffness matrix is approximated by a modified approximate interval-value Sherman–Morrison–Woodbury formula to overcome the drawbacks arising from the dependency phenomenon of parameters and the unpredictable effect of neglecting the higher order terms in Neumann series. The modified sub-interval perturbation procedures are implemented in a numerical finite element framework. Numerical results on a 2D acoustic tube and a 2D acoustic cavity of a car with large uncertain-but-bounded parameters evidence the remarkable accuracy and effectiveness of the proposed method.     

Hybrid uncertainty propagation of coupled structural–acoustic system with large fuzzy and interval parameters

Based on the finite element framework and uncertainty analysis theory, this paper proposes a first-order subinterval perturbation finite element method (FSPFEM) and a modified subinterval perturbation finite element method (MSPFEM) to solve the uncertain structural–acoustic problem with large fuzzy and interval parameters. Fuzzy variables are used to represent the subjective uncertainties associated with the expert opinions; whereas, interval variables are adopted to quantify the objective uncertainties with limited information. By using the level-cut strategy and subinterval methodology, the original large fuzzy and interval parameters are decomposed into several subintervals with small uncertainty level. In both FSPFEM and MSPFEM, the subinterval matrix and vector are expanded by the Taylor series. The inversion of subinterval matrix in FSPFEM is approximated by the first-order Neumann series, while the modified Neumann series with higher order terms is adopted in MSPFEM. The eventual fuzzy interval frequency responses are reconstructed by the interval union operation and fuzzy decomposition theorem. A numerical example evidences the remarkable accuracy and effectiveness of the proposed methods to solve engineering structural–acoustic problems with hybrid uncertain parameters.     

A collocation reliability analysis method for probabilistic and fuzzy mixed variables

The main bottleneck of the reliability analysis of structures with aleatory and epistemic uncertainties is the contradiction between the accuracy requirement and computational efforts.Existing methods are either computationally unaffordable or with limited application scope.Accordingly,a new technique for capturing the minimal and maximal point vectors instead of the extremum of the function is developed and thus a novel reliability analysis method for probabilistic and fuzzy mixed variables is proposed.The fuzziness propagation in the random reliability,which is the focus of the present study,is performed by the proposed method,in which the minimal and maximal point vectors of the structural random reliability with respect to fuzzy variables are calculated dimension by dimension based on the Chebyshev orthogonal polynomial approximation.First-Order,Second-Moment(FOSM)method which can be replaced by its counterparts is utilized to calculate the structural random reliability.Both the accuracy and efficiency of the proposed method are validated by numerical examples and engineering applications introduced in the paper.     

Proper orthogonal decomposition and cluster weighted modeling for sensitivity analysis of sound propagation in the atmospheric surface layer

Outdoor sound propagation predictions are compromised by uncertainty and error in the atmosphere and terrain representations, and sometimes also by simplified or incorrect physics. A model's predictive power, i.e., its accurate representation of the sound propagation, cannot be assessed without first quantifying the ensemble sound pressure variability and sensitivity to uncertainties in the model's governing parameters. This paper describes fundamental steps toward this goal for a single-frequency point source. The atmospheric surface layer is represented through Monin-Obukhov similarity theory and the acoustic ground properties with a relaxation model. Sound propagation is predicted with the parabolic equation method. Governing parameters are modeled as independent random variables across physically reasonable ranges. Latin hypercube sampling and proper orthogonal decomposition (POD) are employed in conjunction with cluster-weighted models to develop compact representations of the sound pressure random field. Full-field sensitivity of the sound pressure field is computed via the sensitivities of the POD mode coefficients to the system parameters. Ensemble statistics of the full-field sensitivities are computed to illustrate their relative importance at every down range location. The central role of sensitivity analysis in uncertainty quantification of outdoor sound propagation is discussed and pitfalls of sampling-based sensitivity analysis for outdoor sound propagation are described.     

空间声场全息重建的波叠加方法研究

提出了基于波叠加法的近场声场全息技术，并将其用于任意形状物体的声辐射分析.在声辐射计算问题中，边界元法是通过离散边界面上的声学和位置变量来实现，而波叠加方法则通过叠加辐射体内部若干个简单源产生的声场来完成.因而，基于波叠加法的声全息就不存在边界面上的参数插值和奇异积分等问题，而这些问题是基于边界元法的声全息所固有的.与基于边界元法的声全息相比较，基于波叠加法的声全息在原理上更易于理解，在计算机上更容易实现.实验结果表明：该种全息技术在重建声场时，具有令人满意的重建精度. 关键词： 声全息 逆问题 波叠加方法 正则化方法