海洋—声学耦合过程不确定性快速预报

针对海洋声速空间非均匀和时变条件下的声场不确定性快速预报问题,根据海洋-声学耦合模式预报声速场时空变化过程,获取声速垂直结构不确定性分布规律,提出经验正交函数-随机多项式展开方法,以降低不确定参数维度,得到声场不确定性分布.数值计算表明该方法在保证同等精度的同时可大幅减少计算量,相比常规随机多项式展开方法计算效率可提高2个数量级,且计算量不随声速剖面复杂程度变化而改变.经海上实验验证,结果表明该方法可实现环境不确定性条件下的声场及其不确定性的快速预报。      

浅海不确定声场的随机多项式展开法研究

为获得求解浅海不确定声场的普适模型,建立了随机多项式展开法与Helmholtz方程的非嵌入式耦合模型,其间运用概率配点法求解多项式系数。针对仅当海水深度不确定时的Pekeris波导、声速剖面和海深均不确定时的Pekeris波导以及下限深度不确定温跃层等几种情形,计算了传播损失概率密度分布。结果表明所建模型对声场计算模型普适性强,计算精度和计算效率高,可用于研究含多个不确定环境参数、声速剖面复杂的浅海环境中声传播的不确定性。      

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.     

多项式混沌展开的浅海水声环境参数敏感度分析*

水下声场是海洋环境参数的非线性函数,因此环境参数的不确定性必然会引起水下声场预测的不确定性,从而导致与声场预测相关的声呐探测和水声通信等设备性能的下降。该文将Sobol敏感度指数的计算与多项式混沌展开方法相结合,将敏感度指数表达为环境条件的函数,利用Q范数约束的双曲截断方案来减少多项式项数,有效地分析了设定的"浅海负梯度温跃层"信道中8个环境参数及其交互效应对水下声传播的影响。结果表明,沉积层声速是低频远距离声场不确定性分布的最主要贡献参数,同时对于下发下收的情况,声源深度的影响程度随着声源频率增加而逐渐增大。最后应用射线理论从海底反射的角度解释了各个环境因素影响程度差异的具体原因。该文的研究对水声通信和探测系统在浅海不确定环境下的性能预报研究具有重要的参考意义。     

一种更具普适性的浅海不确定声场快速算法

非嵌入式随机多项式展开法是目前性能最优的一种不确定声场快速算法,但配点的选择对算法计算精度影响较大,且当计算随不确定海洋环境参数变化剧烈的声场输出时,需采用分段概率配点法等特殊方法处理。基于Kriging模型提出了一种新的浅海不确定声场快速算法,首先给出了该算法的理论推导,然后通过数值计算验证了算法性能,并给出具体的物理解释,结果表明:在同等条件下,新算法的计算精度较非嵌入式随机多项式展开法更高;无需针对声场输出随不确定海洋环境参数的变化情况采取特殊处理过程;克服了非嵌入式随机多项式展开法为提高计算精度将随机多项式展开至非常高的阶数,从而增加计算量的不足;较非嵌入式随机多项式展开法,其样本点的选择简单易行,且可直接计算误差,因此,本文算法较非嵌入式随机多项式展开法普适性更强。     

基于双曲线截断混沌多项式展开的地磁感应电流敏感度分析

地磁感应电流(GIC) 可能会引起变压器直流偏磁从而威胁电力设备和电网的安全。鉴于GIC计算所需的很多输入参数是不确定变量, 全面评估电网GIC水平及对电网的威胁有必要研究GIC的不确定度及GIC对输入变量的敏感度。基于混沌多项式展开(PCE) 提出了一种GIC的不确定度量化方法, 利用双曲线截断技术进一步提高了计算效率, 计算了GIC对输入参数的敏感度指标。以新疆750kV规划电网为例, 利用提出的方法对GIC进行了不确定度量化, 得到了GIC的均值和标准差等统计量。根据混沌多项式系数计算了Sobol敏感度指标, 得到了GIC对电场幅值和电网直流电阻等输入参数的敏感度。与蒙特卡罗法(MC) 相比, 此方法在保证精度的前提下大大提高了计算效率。     

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.     

嵌入随机多项式的抛物方程不确定声场快速算法

为了得到准确且高效计算起伏海洋介质中随机声场的算法,本文将随机多项式展开嵌入到宽角抛物方程声场计算模型(简称RAM模型)中,发展了一种不确定声场的快速算法.其计算结果比使用嵌入随机多项式的窄角抛物方程准确,计算时间小于作为参考的蒙特卡洛方法.在仿真算例中,随机多项式展开法对声强均值、方差、概率密度的计算准确;在一定的随...     

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。      

动态水声环境不确定性的预报与估计

水声环境具有强烈的时空易变性,为了解其变化中的规律和产生的不确定性,将POM海洋数值模型和水声传播模型FOR3D进行耦合,建立海洋—声学耦合数值模式。对海区的温盐等环境参数和水下声场进行预报,给出了典型断面的温度垂直结构、实验海区声速剖面和传播损失。同时,采用集合卡尔曼滤波(EnKF)方法结合海洋—声学耦合数值模式分析了水声环境的不确定性,对不同深度与频率下,传播损失的均值与满足90%的可能区间进行了计算,同时给出了不同点声速、传播损失、声纳作用距离的不确定性直方图。和实验数据的对比结果表明该方法具有较高的有效性,能对水声环境的不确定性进行合理的预报与估计。     

基于多项式混沌方法的场线耦合响应不确定度量化

在传输线场线耦合的计算中,由于辐射场可能从不同方向入射,入射方位角和入射仰角会在一定范围内变化,可以将其看作不确定变量,因此传输线的响应也呈现出不确定性。针对输入参数服从非典型分布的情况,应用多项式混沌方法对传输线场线耦合频域响应进行不确定度量化。结合入射方位角和仰角的物理意义,给出其服从的分布类型并构建相应的正交多项式基底,并对该模型的传输线方程进行多项式混沌展开。最后结合含两个不确定参数的传输线场线耦合算例,给出远端电流响应的统计信息,对比蒙特卡罗方法,验证了该方法的正确性和高效性。     

On using polynomial chaos for modeling uncertainty in acoustic propagation

The use of polynomial chaos for incorporating environmental variability into propagation models is investigated in the context of a simplified one-dimensional model, which is relevant for acoustic propagation when the random sound speed is independent of depth. Environmental variability is described by a spectral representation of a stochastic process and the chaotic representation of the wave field then consists of an expansion in terms of orthogonal random polynomials. Issues concerning implementation of the relevant equations, the accuracy of the approximation, uniformity of the expansion over the propagation range, and the computational burden necessary to evaluate different field statistics are addressed. When the correlation length of the environmental fluctuations is small, low-order expansions work well, while for large correlation lengths the convergence of the expansion is highly range dependent and requires high-order approximants. These conclusions also apply in higher-dimensional propagation problems.     

海洋-声学耦合模式捕捉水声环境不确定性

考虑到海洋环境的时空变化对水声环境不确定性的影响,建立了海洋-声学耦合数值模式,实现了并行计算。该模式将声学计算纳入到运动的海洋中,从而实现了对水声环境的动态预报和估计。同时,采用集合预报方法对典型断面的温度垂直结构、实验海区声速剖面和传播损失进行预报,并给出了声速剖面的预报误差、不同深度与频率下,传播损失90%的概率区间以及声速、传播损失、声呐作用距离的不确定性直方图。结果反映了海洋时空变化对水声环境不确定性的影响,量化了水声环境中不确定性的大小。实验结果表明该方法可以刻画海洋动态变化引起的水声环境不确定性,并对其进行了量化和描述。      

Capturing uncertainties of the underwater acoustic environment based on an ocean-acoustic coupled model

Considering the uncertain effects of temporal and spatial changes in the marine environment on the underwater acoustic environment,we established an ocean-acoustic coupled numerical model and performed a parallel calculation.This model incorporated acoustic calculations into the dynamic ocean,thereby achieving a dynamic forecasting and assessment of the acoustic environment.Furthermore,we adopted the ensemble prediction method to predict the vertical structure of temperature in a classic cross-section,the sound speed of the cross-section of the investigated sea area,and transmission losses.We gave the prediction errors of the sound speed profile as well as the 90%probability interval of transmission losses and the uncertainty histograms of the sound speeds,transmission losses,and sonar ranges at different depths and frequencies.The results reflected the influence of marine temporal and spacial variations on the uncertainties of the underwater acoustic environment,and the results also quantified the uncertainties of the underwater acoustic environment parameters.The experimental results indicate that the method used in this study is able to delineate and quantify the uncertainties of the underwater acoustic environment caused by marine dynamic changes.     

Acoustic field and array response uncertainties in stratified ocean media

The change-of-variables theorem of probability theory is applied to compute acoustic field and array beam power probability density functions (pdfs) in uncertain ocean environments represented by stratified, attenuating ocean waveguide models. Computational studies for one and two-layer waveguides investigate the functional properties of the acoustic field and array beam power pdfs. For the studies, the acoustic parameter uncertainties are represented by parametric pdfs. The field and beam response pdfs are computed directly from the parameter pdfs using the normal-mode representation and the change-of-variables theorem. For two-dimensional acoustic parameter uncertainties of sound speed and attenuation, the field and beam power pdfs exhibit irregular functional behavior and singularities associated with stationary points of the mapping, defined by acoustic propagation, from the parameter space to the field or beam power space. Implications for the assessment of orthogonal polynomial expansion and other methods for computing acoustic field pdfs are discussed.     

Multiple-array passive acoustic source localization in urban environments

In many situations of interest, obstacles to acoustic wave propagation such as terrain or buildings exist that provide unique challenges to localization. These obstacles introduce multiple propagation paths, reflections, and diffraction into the propagation. In this paper, matched field processing is proposed as an effective method of acoustic localization in a two dimensional scattering environment. Numerical techniques can be used to model complex propagation in a space where analytical solutions are not feasible. Realistically, there is always some uncertainty in model parameters that in turn can adversely affect localization ability. In particular, uncertainty in array location, sound speed, and various parameters affecting inter-array coherence only are investigated. A spatially distributed, multiarray network is shown to mitigate the effects of uncertainty. Multiarray inverse filter processing techniques are evaluated through perturbation of uncertain model parameters. These techniques are more accurate and flexible to implement than other matched field processing methods such as time reversal.     

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。      

A Chebyshev–Lagrangian method for acoustic analysis of a rectangular cavity with arbitrary impedance walls

A general Chebyshev–Lagrangian method is proposed to obtain the analytical solution for a rectangular acoustic cavity with arbitrary impedance boundary conditions. The originality of the present paper is the successful attempt of applying orthogonal polynomials, such as Chebyshev polynomials of the first kind, to the analysis of a rectangular sound field with general wall impedance. The sound pressure is uniformly expressed as triplicate Chebyshev polynomial series which is independent in each direction. The Chebyshev polynomial series solution is obtained using the Rayleigh–Ritz procedure after considering the influence of boundary impedance on the cavity as the work done by the impedance surfaces in the Lagrangian function. The accuracy and reliability of the proposed method are validated against the analytical solutions and some numerical results available in the literature. Excellent orthogonality and complete properties of the Chebyshev polynomials ensure the rapid convergence, numerical stability, high accuracy of the current solution. The simplicity and low computational cost of the present approach make it preferable to obtain the results of complex models even in the relative high frequency range by choosing enough truncated terms in the sound pressure expression. Numerous cases with various uniform or non-uniform impedance boundary conditions are analyzed numerically and some of the results can be used as benchmark. It is shown that the impedance boundary condition can effectively influence or modify the acoustic characteristics and response of a cavity.     

自回归状态空间模型下时变声速剖面跟踪方法

讨论了一种适用于浅海的时变声速剖面跟踪方法。该方法将时变水体声速剖面的反演问题建模为由描述声速剖面时变特性的状态方程与包含声压场局部测量信息的测量方程组成的状态-空间模型,提出利用自回归分析拟合方法将声速场扰动建模为高阶自回归演化模型,并通过集合卡尔曼滤波序贯地估计时间演化的海洋声速场。利用2001年亚洲海实验环境与声速测量数据,仿真分析了基于高阶自回归演化模型的时变声速剖面集合卡尔曼滤波估计方法。结果表明,相比于利用传统随机游走状态演化模型的估计方法,该改进方法可有效降低声速的跟踪误差,并且在较低信噪比条件下仍具有较好的跟踪性能。      

Tracking of time-evolving sound speed profiles with an auto-regressive state-space model

An approach for time-evolving sound speed profiles tracking in shallow water is discussed.The inversion of time-evolving sound speed profiles is modeled as a state-space estimation problem,which includes a state equation for predicting the time-evolving sound speed profile and a measurement equation for incorporating local acoustic measurements.In the paper,auto-regression(AR) method is introduced to obtain a high-order AR evolution model of the sound speed field time variations,and the ensemble Kalman filter is utilized to track the sound speed field.To validate the approach,the accuracy in sound speed estimation is analyzed via a numerical implementation using the ASIAEX experimental environment and the sound velocity measurement data.Compared with traditional approaches based on the state evolution represented as a random walk,simulation results show the proposed AR method can effectively reduce the tracking errors of sound speed,and still keep good tracking performance at low signal-to-noise ratios.