基于空时相关阵联合对角化的子空间DOA估计

为提高空间相关噪声场中的目标方位估计性能,提出一种基于空时相关阵联合块对角化的子空间方位估计算法.具体利用Jacobi旋转矩阵法对一组空时相关阵联合近似对角化,用联合对角化特征向量矩阵和特征值修正MUSIC(Multiple Signal Classification)等子空间算法.理论和仿真结果表明,在非相关噪声场中,基于联合对角化的子空间算法性能与常规子空间算法基本一致;而在相关噪声场中,联合对角化特征向量法能显著减小方位估计方差,提高估计性能.     

基于临界特征值的MDL信源数欠估计分析方法

针对最小描述长度准则下的信源数欠估计问题,提出了一种基于临界特征值的欠估计分析方法,通过对信源数估计算法进行分析,给出了临界特征值的求解表达式及唯一性证明。相比现有方法,临界特征值方法可对不同漏检数下的欠估计边界进行预测,并评估阵列参数对信源数估计性能的影响。为解决大漏检数下的临界特征值的求解复杂问题,提出了一种近似方法,分析了近似误差的影响因素。仿真数值实验结果表明,临界特征值方法可准确描述算法在不同漏检数下的欠估计边界,为基于信息论准则的信源数估计算法提供了一种新的具有普适性的分析手段。     

基于协方差矩阵Toeplitz重构的MUSIC算法的波达方位估计方法

针对传统波达方向（Direction of Arrival, DOA）估计方法通过空间平滑对相干信号进行处理损失阵列孔径的问题，文章提出了一种基于协方差矩阵托普利兹（Toeplitz）矩阵重构的多重信号分类（Multiple Signal Classification, MUSIC）算法的波达方位估计方法。该方法首先根据阵列接收数据的协方差矩阵及其翻转矩阵来构造新协方差矩阵，并利用新协方差矩阵构造Toeplitz矩阵，然后对其进行特征值分解，得到Toeplitz矩阵的噪声子空间，利用噪声子空间求出信号空间谱，通过谱峰搜索估计入射信号的方位角。文中方法拓展了阵列孔径，增加了可估计相干信号的数量，提升了方位估计的性能，提高了阵列的空间分辨率。仿真和湖上实验数据处理结果表明，文中方法可估计出更多的相干信号，而且在低信噪比、少快拍以及信号入射角度间隔较小时仍然具有良好的方位估计性能。     

空间非平稳噪声下圆阵的修正Capon算法

在空间非平稳噪声环境下,利用估计的噪声相关矩阵对圆阵接收数据相关矩阵进行预处理,可以消除非平稳噪声对方位估计的影响。再利用修正Capon算法,可以突破瑞利限的限制,且不需要知道信源数,从而实现目标的高分辨方位估计。仿真结果证实了该方法的有效性。     

协方差矩阵的相关法Toeplitz改进算法

提出一种基于均匀线形阵列的相关Toeplitz矩阵构造方法,建立了两种Toeplitz矩阵的构造方式,结合子空间法形成一种相干信源方位估计的高分辨方法。具体将接收阵列各阵元与参考阵元输出信号做相关,获得一组相关向量,应用相关Toeplitz矩阵构造算法构造阵列输出的Toeplitz矩阵,从而得到去相干的相应接收阵列的协方差矩阵,最后再应用高分辨子空间估计方法完成相干信源方位估计。仿真结果表明：所采用的相关Toeplitz矩阵构造算法达到了很好的去相干效果,并将Toeplitz近似化方法改进成为无偏估计方法,显著提高了相干信源方位估计的精度,并使Toeplitz矩阵构造的计算量减少到原方法的1/M。     

MUSIC与MNM在均匀圆阵的方位估计性能比较

圆阵作为具有360o全向方位角搜索能力的阵型,可以同时对信源方位角和俯仰角进行分辨,因此,采用圆形基阵的系统有更广的空间搜索能力。多重信号分类法（MUSIC）和最小模算法（MNM）同属于子空间分解类算法,具有不受阵型限制的优点。就二者在均匀圆阵（UCA）方位估计性能上进行了比较研究,结果表明：随着信噪比或阵元数的增加,MUSIC性能均要优于MNM。     

一种基于特征分析的强干扰抑制方法

水声环境中微弱目标往往被掩盖在强干扰的旁瓣中而无法检测。研究如何抑制强干扰,提高输出信噪比,对提高声呐探测性能具有重要意义。假设干扰能量远大于目标信号能量。首先,对接收数据协方差矩阵进行特征分解,其中最大特征值对应的特征向量属于干扰特征向量。然后利用正交投影方法将阵列接收数据向干扰子空间的正交子空间投影,将干扰数据去除,从而达到抑制强干扰的目的。数值仿真和海试数据验证结果表明,该强干扰抑制方法能够很好地抑制强干扰,提高目标信号输出信噪比和目标方位估计可靠性,可为后续的目标被动定位创造有利条件。     

基于压缩感知的旋转式基阵DOA估计

提出旋转基阵方法,达到增加虚拟阵元的效果,再利用压缩感知理论进行阵列信号方位估计(DOA)。此方法可降低阵列流形矩阵相关性,提高多信号恢复算法成功率,且具有高分辨率。信源个数大于阵元个数时,该方法仍能成功对各信源方向进行估计。     

基于协方差扩展PM算法的波达方向估计

针对基于传播算子方法(Propagator Method, PM)的水听器阵波达方向(Direction of Arrival, DOA)估计在低信噪比或者小快拍数时性能变差的问题,文章提出一种改进的基于PM算法的水听器阵方位估计方法。该方法利用信号子空间的旋转不变性特征对协方差矩阵进行扩展和重构,通过分块协方差矩阵的子矩阵得到传播算子矩阵。通过传播算子矩阵构造扩展噪声子空间,然后利用信号子空间与噪声子空间的正交性估计空间谱。仿真实验和湖上实验的结果表明：相较于传统PM方位估计算法,文中算法在低信噪比或者小快拍情况下具有较好的方位估计性能,在信噪比为0 dB时,文中方法比传统PM算法均方根误差减少0.6°;在快拍数为150时,比传统PM算法的均方根误差减少0.1°。     

岸基水听器阵列阵形估计方法研究

阐述了基于时延估计的阵形估计方法的基本原理,该方法比基于传感器测量和基于匹配场处理的方法具有更强的适应性和较高的精度.对比分析了单辅助信源和双辅助信源的相应的阵形估计方法,其中单信源方法用装配间距近似各个阵元间的实际间距.对已有海试数据阵形估计处理的结果表明,阵列弯曲不大时,单源方法可以得到与双源方法相当精度的估计结果,用估计阵形进行空间谱分析,进一步说明了结果的有效性.基于时延估计的阵形估计方法对长水听器阵列的应用及阵形估计具有较大应用价值.     

An invariant subspace‐based approach to the random eigenvalue problem of systems with clustered spectrum

The repeated or closely spaced eigenvalues and corresponding eigenvectors of a matrix are usually very sensitive to a perturbation of the matrix, which makes capturing the behavior of these eigenpairs very difficult. Similar difficulty is encountered in solving the random eigenvalue problem when a matrix with random elements has a set of clustered eigenvalues in its mean. In addition, the methods to solve the random eigenvalue problem often differ in characterizing the problem, which leads to different interpretations of the solution. Thus, the solutions obtained from different methods become mathematically incomparable. These two issues, the difficulty of solving and the non‐unique characterization, are addressed here. A different approach is used where instead of tracking a few individual eigenpairs, the corresponding invariant subspace is tracked. The spectral stochastic finite element method is used for analysis, where the polynomial chaos expansion is used to represent the random eigenvalues and eigenvectors. However, the main concept of tracking the invariant subspace remains mostly independent of any such representation. The approach is successfully implemented in response prediction of a system with repeated natural frequencies. It is found that tracking only an invariant subspace could be sufficient to build a modal‐based reduced‐order model of the system. Copyright © 2012 John Wiley & Sons, Ltd.     

声场-结构耦合系统特征值敏度研究

基于有限元模型分析了声场-结构耦合系统的左、右特征向量关系式，证明声场-结构耦合系统左特征向量可用右特征向量的分量来表示，基于此分析推导出声场-结构耦合系统的特征值敏度表达式。以一矩形声场-结构耦合系统为实例进行计算，基于Nastran对声场-结构耦合系统进行模态分析，用其内部的DAMP语言编程计算了特征值敏度。结果验证了该方法的有效性及正确性。     

A new stochastic residual error based homotopy approach for stability analysis of structures with large fluctuation of random parameters

The large fluctuation of uncertain parameters introduces a great challenge in the stability analysis of structures. To address this problem, a novel stochastic residual error based homotopy method is proposed in this article. This new method used the concept of homotopy to reconstruct a new governing equation for stochastic elastic buckling analysis, and the closed-form solutions of the isolated buckling eigenvalues and eigenvectors are obtained by the stochastic homotopy analysis method. On this basis, a pth order origin moment of the stochastic residual error with respect to the elastic buckling equation is defined. Then, the optimal form of the homotopy series can be determined automatically by minimizing the pth order origin moment, which overcomes the disadvantage of highly relying on sample values of the existing homotopy stochastic finite element method. Moreover, the proposed method is developed to deal with the stochastic closely spaced buckling eigenvalue problem. Three mathematical examples and three buckling eigenvalue examples, including a variable cross-section column, a 7-story frame, and a Kiewitt single-layer latticed spherical shell, are performed to illustrate the accuracy and effectiveness of the proposed method by comparing with the existing methods when dealing with large fluctuation of random parameters.     

Iterative solution of the random eigenvalue problem with application to spectral stochastic finite element systems

A new algorithm for the computation of the spectral expansion of the eigenvalues and eigenvectors of a random non‐symmetric matrix is proposed. The algorithm extends the deterministic inverse power method using a spectral discretization approach. The convergence and accuracy of the algorithm is studied for both symmetric and non‐symmetric matrices. The method turns out to be efficient and robust compared to existing methods for the computation of the spectral expansion of random eigenvalues and eigenvectors. Copyright © 2006 John Wiley & Sons, Ltd.     

一种改进的稳健高分辨力DOA估计算法

介绍了一种基于最大后验概率准则的约束最优空间处理(Spatial Processing-Optimized and Constrained,SPOC)DOA算法。这种算法将阵列接收到的空间能量近似为来自远场的密集分布的独立信号源发出的信号,在极限情况下,这些点源是连续分布的。算法应用最大后验概率准则,在满足接收信号能量不变的情况下,使得接收到的总功率最小,通过估计每个点源的能量完成对来波方位的估计。算法只针对单快拍数据进行处理,因此避免了目标运动以及环境非平稳性带来的影响。针对算法在低信噪比下不稳定的缺点,使用对角加载技术(diagonal loading)进行了改进,增强了算法的稳健性。使用单个发射换能器和接收水听器进行了水池实验,实验显示DL-SPOC算法相比于MVDR、CBF等算法拥有更高的角度分辨力。     

基于解析模式分解的密集工作模态参数识别

长大跨度的桥梁结构或者高层建筑的工作环境振动响应中经常包含密集的模态成分,并会出现模态叠混现象,而传统的信号分析方法往往难以识别结构的密集模态参数。提出一种基于解析模式分解理论与随机减量技术相结合的方法识别环境激励下的结构密集模态参数。对于工作环境激励下的结构振动响应,通过随机减量技术可以提取结构的自由振动响应,利用解析模式分解方法对具有密集模态的自由振动响应进行有效的分解,对每一阶自由振动响应利用最小二乘拟合方法识别出频率与阻尼比。通过两层框架的数值模拟以及对密集频率的密集程度指数和信号时程长度等参数分析,其结果表明通过随机减量技术提取的自由振动响应可以有效的减少模态叠混的影响,虽然提取的自由振动响应的时程长度比实际的信号时程要短,然而解析模式分解仍然能够十分有效的对短时程具有密集模态成分的信号进行有效的分解。最后,通过对一具有密集模态的36层框架的数值模拟,以及对一具有密集模态的3层框架的振动台实验,验证该方法可以有效的识别出环境激励下的结构密集模态参数。     

A method for modal reanalysis of topological modifications of structures

A method for structural modal reanalysis for three cases of topological modifications, the number of degrees of freedom (DOFs) is unchanged, decreased, and increased, is presented. In this method, the newly added DOFs are linked to the original DOFs of the modified structure by means of the dynamic reduction so as to obtain the condensed equation. The methods for forming the stiffness and mass increments, Δ K and Δ M , resulting from the three cases of topological modifications of structures are discussed. The extended Kirsch method is used to improve the accuracy of the starting solutions of the initial structure. And then, the eigenvectors of newly added DOFs resulting from topological modification can be recovered. At last, the Rayleigh–Ritz analysis is used to evaluate the eigenvalues and eigenvectors for the modified structure. Three numerical examples are given to illustrate the applications of the present approach. The results show that the proposed method is effective for structural modal reanalysis of three cases of the topological modifications and it is easy to implement on a computer. By comparing with previous method, it can be seen that the present method can give good approximate eigenvalues and eigenvectors, even if the topological modifications are very large. Copyright © 2005 John Wiley & Sons, Ltd.     

Highly efficient general method for sensitivity analysis of eigenvectors with repeated eigenvalues without passing through adjacent eigenvectors

It is well known that the sensitivity analysis of the eigenvectors corresponding to multiple eigenvalues is a difficult problem. The main difficulty is that for given multiple eigenvalues, the eigenvector derivatives can be computed for a specific eigenvector basis, the so-called adjacent eigenvector basis. These adjacent eigenvectors depend on individual variables, which makes the eigenvector derivative calculation elaborate and expensive from a computational perspective. This research presents a method that avoids passing through adjacent eigenvectors in the calculation of the partial derivatives of any prescribed eigenvector basis. As our method fits into the adjoint sensitivity analysis , it is efficient for computing the complete Jacobian matrix because the adjoint variables are independent of each variable. Thus our method clarifies and unifies existing theories on eigenvector sensitivity analysis. Moreover, it provides a highly efficient computational method with a significant saving of the computational cost. Additional benefits of our approach are that one does not have to solve a deficient linear system and that the method is independent of the existence of repeated eigenvalue derivatives of the multiple eigenvalues. Our method covers the case of eigenvectors associated to a single eigenvalue. Some examples are provided to validate the present approach.     

Fitting Systems of Linear Differential Equations Using Computer Generated Exact Derivatives

The problem of estimating coefficients and initial values in a system of linear differential equations from observations on linear combinations of the system's responses is addressed. Using the Gauss-Newton algorithm, the reqllired function values are obtained by expressing the system's solution in terms of the eigenvalues and eigenvectors of its coefficient matrix aud its initial values. Differentiating this solution gives expressious for the required function derivatives in terms of these same eigenvalues and eigenvectors. The advantage of this approach is that it, uses exact analytic expressions for the required function values and derivatives rather than resorting to numerical integration or secants. An application to compartment, analysis is considered aud results are compared with those obtained by using the SAAM program of Berman and Weiss.     

Generalized rank annihilation method using similarity transformations.

Recently several papers have described the generalized rank annihilation method; however, in some cases complex eigenvalues and eigenvectors may appear when the generalized eigenproblem is solved. When complex eigenvalues and eigenvectors are encountered, the results cannot be used to estimate pure component profiles (e.g. spectra or chromatograms). In this paper, a similarity transformation is used to transform complex eigenvalues and eigenvectors into real eigenvalues and eigenvectors, thereby permitting spectra and profiles of pure constituents to be estimated. The modified GRAM method is illustrated with simulated and real data.