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。     

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。     

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.     

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。     

Numerical approach for quantification of epistemic uncertainty

In the field of uncertainty quantification, uncertainty in the governing equations may assume two forms: aleatory uncertainty and epistemic uncertainty. Aleatory uncertainty can be characterised by known probability distributions whilst epistemic uncertainty arises from a lack of knowledge of probabilistic information. While extensive research efforts have been devoted to the numerical treatment of aleatory uncertainty, little attention has been given to the quantification of epistemic uncertainty. In this paper, we propose a numerical framework for quantification of epistemic uncertainty. The proposed methodology does not require any probabilistic information on uncertain input parameters. The method only necessitates an estimate of the range of the uncertain variables that encapsulates the true range of the input variables with overwhelming probability. To quantify the epistemic uncertainty, we solve an encapsulation problem, which is a solution to the original governing equations defined on the estimated range of the input variables. We discuss solution strategies for solving the encapsulation problem and the sufficient conditions under which the numerical solution can serve as a good estimator for capturing the effects of the epistemic uncertainty. In the case where probability distributions of the epistemic variables become known a posteriori, we can use the information to post-process the solution and evaluate solution statistics. Convergence results are also established for such cases, along with strategies for dealing with mixed aleatory and epistemic uncertainty. Several numerical examples are presented to demonstrate the procedure and properties of the proposed methodology.     

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。     

某型艇近场噪声和自噪声数值计算

采用结构有限元软件NASTRAN和声学边界元软件SYSNOISE,对某型艇振动与声学特性数值计算问题进行了研究。通过基于全船三维有限元分析模型的频响分析计算,获得该船结构振动响应特性参数。以振动频响分析计算结果作为声学边界条件,考虑球面点噪声源的影响,建立了全船三维边界元声学分析模型;并采用间接边界元法,对某型艇近场和自噪声声学特性进行了计算。所得计算结果与该船实测数据进行了对比,证明本文计算方法是可行的。     

Numerical analysis of the magnetic field for arbitrary magnetic susceptibility distributions in 2D.

We describe a numerical technique for calculating the 2D magnetic field in arbitrary magnetic susceptibility distribution. The technique we used is the explicit finite difference method with an addition of the Du Fort-Frankle algorithm. The proposed algorithm is unconditionally stable and has excellent convergence properties. For simple geometries, numerical results were compared against analytical solutions and appeared to be in excellent agreement.     

Numerical simulation of acoustic field under mechanical stirring

The present study analyzes the effect of stirring on ultrasonic degradation experiments through acoustic field distribution, which provides a guidance for further improvement of the degradation rate of organic solutions. It is known that in order to eliminate the standing wave field formed by ultrasonic radiation in the water tank, the liquid in the water tank needs to be stirred and the corresponding distribution of acoustic field is simulated by using the finite element method(FEM).The standing wave leads to an uneven distribution of the acoustic field when it is not stirred, and disappears after being stirred, which increases the cavitation area in the ultrasonic cleaning tank. Then, the degradation experiment with agitation is carried out. The experimental results show that the degradation rate of the solution is higher than that when there is no agitation, which confirms the importance of the acoustic field distribution to ultrasonic degradation. In addition, it is clear that with the increase of the stirring speed, the degradation rate increases first and reaches a maximum at 600 rpm before decreasing. Finally, the distribution of flow field is simulated and analyzed.     

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.     

锥型热声谐振管内非线性声场的数值模拟研究

从声学角度出发,考虑粘性耗散、非线性效应及管型结构变化的影响,利用伽辽金法,对锥型热声谐振管内的一维声场进行了数值模拟研究,对谐振管结构参数对声场的影响进行了分析,给出了锥型管内压比随谐振管结构参数变化的规律,通过与圆柱型直管的比较,揭示了锥型管在抑制谐波及提高压比等方面的优越性。     

软地层随钻测井仪器偏心情况下低频四极子源 激发波场的数值分析*

为了探索测井仪器偏心对随钻低频四极子波场的影响,利用有限元法(多物理场耦合有限元软件包)对软地层井孔中随钻仪器偏心情况下低频四极子声源激发的波场进行了数值模拟。通过对随钻四极子测井波形的分析可知,当采用低频随钻四极子偏心声源激发时,测井波列中除传播速度与低速地层横波速度相当的地层四极子波模式外,还存在一个幅度非常低、传播速度略高于井孔流体中声速的模式波,该模式被对应钻铤弯曲波模式,且该模式波的幅度随着随钻四极子源偏离井孔中心距离的增大呈二次方规律增大,地层四极子模式波幅度呈三次方规律增加。     

Numerical analysis of 2D tunable HIS on GaAs support

Numerical analysis of the dispersion characteristics of a 2D tunable periodic structure in microstrip technology is presented. The high relative dielectric constant gallium-arsenide (GaAs) substrate hosts the embedded active FET switches, allowing dynamic changes in the propagation conditions of the electromagnetic wave. The position, the aperture of band-gaps and hence the value of the effective dielectric constant can be controlled. These effects will be monitored through the change of the scattering parameters for different numbers of repetition of the unit cell in the transverse direction.     

Numerical analysis of the Burgers’ equation in the presence of uncertainty

The Burgers’ equation with uncertain initial and boundary conditions is investigated using a polynomial chaos (PC) expansion approach where the solution is represented as a truncated series of stochastic, orthogonal polynomials.     

Numerical and experimental analysis of uncertainty on modal parameters estimated with the stochastic subspace method

Modal parameters of structures are often used as inputs for finite element model updating, vibration control, structural design or structural health monitoring (SHM). In order to test the robustness of these methods, it is a common practice to introduce uncertainty on the eigenfrequencies and modal damping coefficients under the form of a Gaussian perturbation, while the uncertainty on the mode shapes is modeled in the form of independent Gaussian noise at each measured location. A more rigorous approach consists however in adding uncorrelated noise on the time domain responses at each sensor before proceeding to an operational modal analysis. In this paper, we study in detail the resulting uncertainty when modal analysis is performed using the stochastic subspace identification method. A Monte-Carlo simulation is performed on a simply supported beam, and the uncertainty on a set of 5000 modal parameters identified with the stochastic subspace identification method is discussed. Next, 4000 experimental modal identifications of a small clamped–free steel plate equipped with 8 piezoelectric patches are performed in order to confirm the conclusions drawn in the numerical case study. In particular, the results point out that the uncertainty on eigenfrequencies and modal damping coefficients may exhibit a non-normal distribution, and that there is a non-negligible spatial correlation between the uncertainty on mode shapes at sensors of different locations.     

Resonant frequency method for the measurement and uncertainty analysis of acoustic and elastic properties

A resonant frequency method is proposed to determine the bar speed and the Poisson's ratio of a rod several meters long of the kind often used for manufacturing power sonic transducers and mechanical horns in mass production. This method is shown to be robust in a field test and with high resolution for estimation of the bar speed. The uncertainty (standard deviation/average) for the bar speed and the Poisson's ratio can be reduced by appropriately selecting the mode number pairs and increasing the mode number. In this study, the uncertainties of the bar speed and Poisson's ratio are less than 0.043% and 2.9%, respectively. The resonant frequency method is verified by comparing the dilatational wave speeds calculated by elastic theory with those from experiments, the difference between them being less than 0.17%.     

Numerical simulation of acoustic excitations in an imperfect 1D superlattice

Features of the propagation of acoustic excitations in an imperfect 1D superlattice have been studied within the virtual crystal approximation. The dependence of the lowest acoustic band gap width of an imperfect (disordered in the composition and layer thickness) two-sublattice 1D phonon crystal on the concentration of impurity layers has been numerically simulated.     

Numerical analysis of tonal airfoil self-noise and acoustic feedback-loops

In this study the role of acoustic feedback instabilities in the tonal airfoil self-noise phenomenon is investigated. First, direct numerical simulations are conducted of the flow around a NACA-0012 airfoil at Re=1×10⁵ and four angles of attack. At the two lowest angles of attack considered the airfoil self-noise exhibits a clear tonal contribution, whereas at the two higher angles of attack the tonal contribution becomes less significant in comparison to the broadband noise. Classical linear stability analysis of time-averaged boundary layer profiles shows that the tonal noise occurs at a frequency significantly lower than that of the most convectively amplified instability wave. Two-dimensional linear stability analysis of the time-averaged flowfield is then performed, illustrating the presence of an acoustic feedback loop involving the airfoil trailing edge. The feedback loop is found to be unstable only for the cases where tonal self-noise is prominent, and is found to self-select a frequency almost identical to that of the tonal self-noise. The constituent mechanisms of the acoustic feedback loop are considered, which appear to explain why the preferred frequency is lower than that of the most convectively amplified instability wave.     

基于FW-H方程的Hartmann哨辐射声场数值研究*

该文基于声类比法,通过求解FW-H方程,对不同喷口与谐振腔位置关系的Hartmann哨的声场分布进行了分析,计算了不同位置关系的Hartmann哨的声指向性。得到了以下结论:喷口与谐振腔位置关系对Hartmann哨的发声基频几乎不产生影响。对称位置关系的Hartmann哨的声场呈对称趋势,且在垂直于喷流方向上达到最大;非对称位置关系的Hartmann哨不再呈现对称趋势。Hartmann哨的最大声压级随着偏离对称位置的距离的增加有小幅增加,最大声压级出现的方向向着谐振腔方向移动。     

Pekeris waveguide comparisons of methods for predicting acoustic field amplitude uncertainty caused by a spatially uniform environmental uncertainty (L)

Acoustic field calculations in underwater environments are often uncertain because the environmental parameters required for such calculations are uncertain. This letter compares the accuracy of direct simulations, the field shifting approximation, and polynomial chaos expansions for predicting acoustic amplitude uncertainty in 100-m-deep Pekeris waveguides having spatially uniform uncertain water-column sound speed. When this sound speed is Gaussian-distributed with a standard deviation of 1 m/s, direct simulations and polynomial chaos expansions, based on 21 field calculations, are more accurate than the field shifting approximation, based on two field calculations. This ranking reverses as the sound-speed standard deviation increases to 20 m/s.