一种声发射信号方位角自适应监测算法*

四阶累积量可用于声发射信号处理,结合盲波束形成算法可对声发射信号的方位角进行估计。由于四阶累积量的计算量较大,采用迭代计算的思想,提出一种基于四阶累积量的自适应声发射信号方位角监测算法。与改进前的算法相比,自适应算法的计算复杂度和所需存贮空间均显著降低,可用于声发射信号的方位估计和监测。计算机仿真及实测数据分析均验证了算法的有效性。     

四阶累积量对角切片法提取舰船辐射噪声特征

从理论上分析了四阶累积量的特性,由此将四阶累积量分为三部分:第一为三次频率（相位）耦合部分的四阶累积量,第二是双对频率（相位）耦合（ω1+ω=ω3+ω4）部分的四阶累积量,第三为无上述两种耦合部分的四阶累积量。在此基础上,用四阶累积量的对角切片分析并提取了实际舰船辐射噪声的三次频率（相位）耦合特征、双对频率（相位）耦合特征以及子带“能量”分布特征,并将这些特征送入神经网络分类器对舰船进行分类识别,取得了A,B,C三类舰船正确识别率分别为92.5％,92.7％,88.6％的良好效果,从而验证了该方法的有效性和实用性。     

水声信号稀疏重构的高阶累积量波达方向估计

高阶累积量具有高斯噪声抑制和阵元扩展特性,将高阶累积量引入水声信号的方位估计中,提出了离格稀疏贝叶斯学习重构的高阶累积量测向算法。该方法利用高阶累积量对高斯噪声的自然盲性,计算阵列信号四阶累积量来滤除高斯噪声,使阵元在原来的结构上扩展了一倍;并构造出选择矩阵剔除了四阶累积量中的冗余项,能再一次的扩展阵元,得到的新观测模型具有更好的统计性能;最后利用空域稀疏性,推导出四阶累积量下的离格稀疏表示模型,采用贝叶斯学习解算出源信号的最大后验概率,实现了目标方位估计。数值仿真和海试实验数据表明,该方法在相邻声源方位间隔为4°的情况下分辨概率可达到95%以上,在信噪比大于-5 dB时目标方位估计的均方根误差在1°以内,可显著抑制背景噪声干扰,在多声源密集分布条件下也能准确、稳健的对水声目标方位进行估计。      

利用累积量理论量化双模压缩贝尔态的非高斯特性

根据相空间函数的累积量理论,提出了玻色量子态非高斯性的量化工具.利用该量具研究了四个压缩贝尔纠缠态的非高斯特性.结果表明:高斯操作能显著的改变这些态的非高斯特性.此外,也研究了这些量子态二阶关联函数的四阶累积量.     

利用累积量理论量化双模压缩贝尔态的非高斯特性（英文）

根据相空间函数的累积量理论,提出了玻色量子态非高斯性的量化工具.利用该量具研究了四个压缩贝尔纠缠态的非高斯特性.结果表明:高斯操作能显著的改变这些态的非高斯特性.此外,也研究了这些量子态二阶关联函数的四阶累积量.     

典型概率密度背景下四阶累积量波束形成的阵增益

在理论上零均值高斯分布噪声的四阶累积量恒等于零,而实际噪声和混响的概率密度是影响四阶累积量波束形成技术性能的关键问题。本文针对海洋环境噪声与海底混响的瞬时幅度分布,分别推导了四阶累积量波束形成阵增益函数;建立了阵增益与阵元数、海洋环境噪声和海底混响统计特性的四阶矩和二阶矩及输入信噪比的关系;确定了与常规波束形成阵增益之间存在临界信噪比,高于临界信干比时四阶累积量波束形成可以获得比常规波束形成更高的阵增益与分辨率。实验数据处理结果验证了四阶累积量波束形成阵增益和分辨率理论结果的一致性。      

分数阶状态空间系统的稳定性分析及其在分数阶混沌控制中的应用

基于Lyapunov稳定性理论,针对分数阶状态空间系统模型,提出一种稳定性判定方法,并给出了数学证明. 运用该稳定性理论无需求解平衡点,而方便地选择出控制项,对分数阶状态空间系统进行控制. 本文以分数阶统一混沌系统作为控制对象,将所提出的稳定性理论应用于该系统的控制中,仿真结果验证了该理论的有效性. 关键词： 分数阶 状态空间系统 稳定性 统一混沌系统     

基于改善空间关联性的混沌控制

基于混沌信号的统计特性，提出了一种通过改善混沌信号的空间关联性实现混沌控制的方法.以Hénon离散混沌系统和四阶Chua's电路超混沌连续系统为例进行了数值研究，验证了这种控制方法的有效性.结果表明， 通过改善混沌信号之间的空间关联性， 混沌系统能以较快的速度收敛到它的平衡点或多种周期轨道. 关键词： 混沌控制 空间关联性 Hénon系统 四阶Chua's电路     

声矢量锥形阵的高阶累积量波达方向估计

为解决信源在较低信噪比情况下的测向分辨率问题,提出阵列可扩展的声矢量锥形阵测向算法。算法基于四阶累积量的阵列扩展和高斯噪声抑制特性,计算声矢量传声器不同输出分量的四阶累积量,使其在三维方向上扩展与原阵型结构相同的虚拟阵,从而构造包含角度信息的旋转不变矩阵进行测向。推导给出了算法的克拉美罗界,理论分析了算法性能受信噪比、采样快拍以及入射声源俯仰角的影响。仿真实验验证了该算法较常规声矢量阵ESPRIT算法有更优的噪声抑制能力及更高分辨的DOA估计性能。      

基于Liao氏吸收边界条件的四阶FDTD算法

建立了在空间上用四阶差分的时域有限差分法的 Liao氏吸收边界,证明了四阶差分具有比二阶差分更小的数值色散.空间上用四阶差分的时域差分法将有助于人们对尺寸较大的物体如光纤等光波导的数值分析.     

Array gain of fourth-order cumulants beamforming under typical probability density background

The fourth-order cumulant of zero mean Gaussian distribution noise always equals to zero theoretically.In practice the probability density of noise and reverberation is the key problem to performance of the fourth-order cumulant beamforming technique.In this paper,the array gain functions of the fourth-order cumulant beamforming are deducted considering the instantaneous amplitude distribution of the ambient sea noise and bottom reverberation respectively.And the relationships are determined between array gain and the factors including the number of the array elements,the fourth-order and second-order statistical properties of the noise and reverberation,and the input signal-to-noise ratio.It is also verified that there is a critical signal-to-interference ratio and the fourth-order cumulant beamforming can obtain higher gain and resolution than the conventional beamforming method when the ratio is larger than it.The results of experiment data processing demonstrate that the gain and the resolution of the fourth-order cumulant beamforming coincide with the theoretic.     

Behavior and finite-size effects of the sixth order cumulant in the three-dimensional Ising universality class

The high-order cumulants of conserved charges are suggested to be sensitive observables to search for the critical point of Quantum Chromodynamics(QCD). This has been calculated to the sixth order in experiments.Corresponding theoretical studies on the sixth order cumulant are necessary. Based on the universality of the critical behavior, we study the temperature dependence of the sixth order cumulant of the order parameter using the parametric representation of the three-dimensional Ising model, which is expected to be in the same universality class as QCD. The density plot of the sign of the sixth order cumulant is shown on the temperature and external magnetic field plane. We found that at non-zero external magnetic field, when the critical point is approached from the crossover side, the sixth order cumulant has a negative valley. The width of the negative valley narrows with decreasing external field. Qualitatively, the trend is similar to the result of Monte Carlo simulation on a finite-size system. Quantitatively, the temperature of the sign change is different. Through Monte Carlo simulation of the Ising model, we calculated the sixth order cumulant of different sizes of systems. We discuss the finite-size effects on the temperature at which the cumulant changes sign.     

Critical Binder cumulant of two-dimensional Ising models

The fourth-order cumulant of the magnetization, the Binder cumulant, is determined at the phase transition of Ising models on square and triangular lattices, using Monte Carlo techniques. Its value at criticality depends sensitively on boundary conditions, details of the clusters used in calculating the cumulant, and symmetry of the interactions or, here, lattice structure. Possibilities to identify generic critical cumulants are discussed.     

Cumulant functions in optical coherence theory

Cumulant functions are introduced to describe the statistical state of a radiation field. These functions are simply related to the optical coherence functions but have some interesting features. It is shown that if the cumulant functions of all orders greater than some numberN ₀ vanish then they also vanish for all orders greater than 2. Thermal field is the only field having this property. This property holds whether the field is described by a classical stochastic process or by a quantum density operator. Further the particular operator ordering used in defining these cumulant functions for the quantized field affects only the second order cumulant function. To describe the statistical state of a vector field such as partially polarized or unpolarized radiation, one would need to introduce cumulant tensors.     

Photon number cumulant expansion and generating function for photon added- and subtracted-two-mode squeezed states

For the first time, we derive the photon number cumulant for two-mode squeezed state and show that its cumulant expansion leads to normalization of two-mode photon subtracted-squeezed states and photon added- squeezed states. We show that the normalization is related to Jacobi polynomial, so the cumulant expansion in turn represents the new generating function of Jacobi polynomial.     

DOA estimation for uniform circular array without the source number based on beamspace transform and higher-order cumulant

Fourth-order cumulant is one of most widely used high-order cumulant for direction of arrival (DOA) estimation due to its ability of expanding the virtual array aperture as well as suppressing Gaussian noise. To address the two-dimensional (2D) DOA estimation problem, we propose a modified MUSIC scheme for uniform circular array (UCA) in this paper. Firstly, the fourth-order cumulant of UCA is considered to construct a new propagator, resulting in the elimination of a priori knowledge of the number of signals. Secondly, the UCA is transformed by beamspace transformation, reducing the time computational complexity of the algorithm since the two-dimensional grid search and singular value decomposition are avoided. And finally a low-rank recovery algorithm is adopted to improve the accuracy regarding the limited snapshots scenario. The numerical simulations validate the superiority of the proposed method.     

Fluctuation symmetry in a two-state Markov model

We show that the scaled cumulant generating and large deviation function, associated to a two-state Markov process involving two processes, obey a symmetry relation reminiscent of the fluctuation theorem, independent from any conditions on the transition rates. The Legendre transform leading from the scaled cumulant generating function to the large deviation function is performed in an ingenious way, avoiding the sign problem associated to taking a square root. Applications to the theory of random walks and to the stochastic thermodynamics for a quantum dot are presented.     

A novel algorithm for underwater moving-target dynamic line enhancement

When we use a traditional adaptive line enhancer (ALE) algorithm to detect an underwater moving target, there are two disadvantages: the ability to suppress colored Gaussian noise is low and the lower the SNR is, the worse the performance of the ALE algorithm. In order to greatly overcome these disadvantages, we take full advantage of the capability of higher order cumulants to alleviate the effect of colored Gaussian noise and develop a fourth order cumulant non-diagonal slice-based adaptive dynamic line enhancer (FOCNDSBADLE) algorithm and fourth order cumulant diagonal slice-based adaptive dynamic line enhancer (FOCDSBADLE) algorithm. The adaptive filtering coefficients of these algorithms are indirectly updated by the instantaneous fourth order cumulant slices. It is shown that these slices are comprised of noiseless sinusoids if the input signals are comprised of sinusoids corrupted by Gaussian noise. Therefore these algorithms are fit to handle highly colored Gaussian noise. Simulation tests are carried out using the measured data radiated by the underwater moving target. Simulation results have shown that the FOCNDSBADLE algorithm and FOCDSBADLE algorithm outperform the ALE algorithm and that the FOCNDSBADLE algorithm outperforms the FOCDSBADLE algorithm in the case of Gaussian noise.