基于ELMAN网络的非线性混沌微弱信号检测

为了快速和实时地从具有强噪声的较低信噪比的原始信号中检测出有用信息,设计了一种混沌相空间重构理论和ELMAN神经网络的信号检测方法;首先,描述了采用混沌相空间重构理论对原始信号进行重构的原理和方法,在获取重构的时间序列的基础上,采用ELMAN网络来近似表示用于检测信号的函数型,然后,设计了ELMAN网络中各层之间连接权值的计算方式,并提出了采用ELMAN网络进行信号检测的具体过程,最后给出了采用混沌相空间重构理论和ELMAN网络的信号检测模型;对Lorenz混沌系统模型进行仿真实验,结果证明了文章方法能有效地对瞬时信号和周期性信息进行检测,在具有高斯白噪声的情况下,仍然具有降噪效果好的优点,是一种用于信号检测的可行性方法。     

基于独立成分分析和经验模态分解的混沌信号降噪

基于经验模态分解和独立成分分析去噪的特点,提出了一种联合独立成分分析和经验模态分解的混沌信号降噪方法. 利用经验模态分解对混沌信号进行分解,根据平移不变经验模态分解的思想构造多维输入向量, 通过所构造的多维输入向量和独立成分分析对混沌信号的各层内蕴模态函数进行自适应去噪处理; 将处理后的所有内蕴模态函数进行累加重构,从而得到降噪后的混沌信号. 仿真实验中分别对叠加不同强度高斯噪声的Lorenz混沌信号及实际观测的月太阳黑子混沌序列进行了研究, 结果表明本文方法能够对混沌信号进行有效的降噪,而且能够较好地校正相空间中点的位置, 逼近真实的混沌吸引子轨迹. 关键词： 独立成分分析 经验模态分解 混沌信号 降噪     

变分模态分量降噪后重构的水声弱信号检测

针对能量检测法在低信噪比下对非合作水声探测信号的检测性能显著下降的问题,提出了一种组合变分模态分解和小波变换降噪重构的信号检测方法。以信号分解出的各个本征模态函数的近似熵与互相关系数比值作为分量分类参数,将所得分量分为信号分量、含噪信号分量与噪声分量,然后利用第二代小波变换对含噪信号分量降噪后与信号分量组成重构信号,最后对重构信号进行检测。数值仿真结果表明该方法可以在无先验信息的情况下对CW和LFM信号自适应降噪,信噪比0 dB以下时CW信号重构后信噪比提升约12 dB,宽带LFM信号信噪比提升约8～9 dB,有效提升了低虚警概率下信号的检测概率。湖试结果表明,虚警概率为0.1时检测概率可提升至0.9以上,验证了该方法的有效性。     

二次谐波的变分模态分解和小波阈值函数降噪

针对利用可调谐半导体激光器吸收光谱学(TDLAS)技术测量气体浓度过程中二次谐波谱线存在的外界噪声干扰问题,提出一种基于变分模态分解和小波阈值函数复合算法的二次谐波降噪方法。首先对二次谐波含噪信号进行分解,得到有用固有模态函数(IMF)并进行重构,再对重构信号进行小波阈值函数降噪处理。讨论了变分模态分解中最佳平衡参数的选取,得出最佳平衡参数与含噪信号中噪声成正比的结论。通过改变小波变换的阈值函数改变高频小波系数,以更好地抑制噪声。对实际测量曲线的降噪结果表明,所提出的降噪方法可以在信噪比较低的情况下有效抑制噪声,提取有用的二次谐波信号。     

基于滑动窗口子空间的混沌信号降噪算法

基于子空间投影理论，利用混沌信号特性，提出了一种基于滑动窗口子空间投影的混沌信号降噪算法，通过相空间重构和多次迭代运算，较好地解决了低信噪比下的混沌信号降噪问题。对算法的复杂性作了研究，并对重构维数、延迟时间、迭代次数等参数的选择进行了讨论。利用Lorenz模型进行仿真得到了比较好的效果，与传统算法相比，新算法具有降噪效果较好、局部特性损失较少、精度较高等优点。     

离散时间序列的网络模体分析

时间序列可以被转换成网络的形式,复杂网络理论也因此可以用于刻画时间序列的时域和相空间特性.本文针对可视图算法和相空间重构算法这两种时间序列的转换算法,研究了它们的伴生网络在倍周期分岔和混沌等各种类型时间序列的模体分布特征,分析了这两种算法各自的优点.     

混沌时间序列重构相空间参数选取研究

基于重构相空间的延迟时间和嵌入维数这两个参数的选取不相关的观点,提出用互信息函数法确定延迟时间后,用CAO方法来确定嵌入维数的新思路.通过对几种典型的混沌动力学系统的数值验证,结果表明该方案能够确定出相空间重构的有效延迟时间和最佳嵌入维数.该方法能够从时间序列中有效地重构原系统的相空间,是混沌信号识别的一种有效途径.     

一种强噪声背景下微弱超声信号提取方法研究

为解决在强噪声背景下获取超声信号的难题,基于粒子群优化算法和稀疏分解理论提出一种强噪声背景下微弱超声信号提取方法.该方法将降噪问题转换为在无穷大参数集上对函数进行优化的问题,首先以稀疏分解理论和超声信号的结构特点为依据构建了粒子群优化算法运行所需要的目标函数及去噪后信号的重构函数,从而将粒子群优化算法和超声信号降噪联系在一起;然后根据粒子群优化算法可以在连续参数空间寻优的特点建立了用于匹配超声信号的连续超完备字典,并采用改进的自适应粒子群优化算法在该字典中对目标函数进行优化;最后根据对目标函数在字典上的优化结果确定最优原子,并利用最优原子按照重构函数重构出降噪后的超声信号.通过对仿真超声信号和实测超声信号的处理,结果表明本文提出的方法可以有效提取信噪比低至-4 dB的强噪声背景下的微弱超声信号,且和基于自适应阈值的小波方法相比本文方法表现出更好的降噪性能.     

基于广义窗函数和最小二乘支持向量机的混沌背景下微弱信号检测

为了从混沌背景中检测微弱信号,研究分析了复杂非线性系统的相空间重构理论,提出了一种基于广义窗函数的最小二乘支持向量机的预测法. 该方法以广义嵌入窗为基础,利用自关联函数法确定Lorenz系统的嵌入维数和时间延迟, 实现相空间重构,结合最小二乘支持向量机建立Lorenz系统的误差预测模型, 检测微弱目标信号(瞬态和周期信号).仿真实验表明,该方法的预测模型具有较小的误差, 能够有效地从混沌背景噪声中检测出微弱目标信号,减小噪声对目标信号的影响. 与传统方法相比,在降低检测门限的同时,能够有效地提高预测的精度, 在混沌噪声下信噪比为-87.41 dB的情况下,相对于传统支持向量机方法所得的均方根误差0.049(-54.60 dB时)降低近两个数量级至0.000036123(-87.41 dB时).     

基于数据融合的多变量相空间重构方法

针对单变量时间序列和多变量时间序列相空间重构所存在的问题,提出一种新的多变量融合的相空间重构方法. 通过Bayes估计理论,将多变量在同一相空间中进行相点的最优融合,得到了更为理想的融合相空间. 应用所提出的方法对Lorenz系统及耦合Rssler系统进行了多变量融合的相空间重构. 通过多变量重构图与单变量重构图的比较,发现基于数据融合的多变量相空间重构图包含了所有单变量相空间重构图的重要信息,使重构的相空间更加完备,较全面地反映出吸引子的全貌信息. 最后应用该方法对转子油膜涡动故障得到的多变量时间序列 关键词： 多变量时间序列 相空间重构 数据融合 Bayes估计     

Phase reconstruction in lensless digital in-line holographic microscopy

The phase reconstruction in a digital in-line holographic microscopy is compared using two numerical reconstruction methods. The first method uses one Fourier transform and second one uses three Fourier transforms. It is shown that the latter method gives improved object phase reconstruction as compared to the former.     

基于小波变换的混沌信号相空间重构研究

应用小波变换和非线性动力学方法研究了混沌信号在相空间中的行为，指出混沌时间序 列的小波变换实质上是在重构的相空间中，混沌吸引子向小波滤波器向量所张的空间中的投 影，与Packard等人提出的相空间重构方法本质上是一致的.实验结果表明，混沌信号经过 小波变换后，吸引子轨迹与原有轨迹具有相似的结构，同时，系统的关联维数、Kolmogorov 熵等非线性不变量仍然得到保留.这些结果表明，利用小波变换研究混沌信号是有效的. 关键词： 小波变换 相空间重构 混沌信号 脑电信号     

Phase space reconstruction of chaotic dynamical system based on wavelet decomposition

In view of the disadvantages of the traditional phase space reconstruction method,this paper presents the method of phase space reconstruction based on the wavelet decomposition and indicates that the wavelet decomposition of chaotic dynamical system is essentially a projection of chaotic attractor on the axes of space opened by the wavelet filter vectors,which corresponds to the time-delayed embedding method of phase space reconstruction proposed by Packard and Takens.The experimental results show that,the structure of dynamical trajectory of chaotic system on the wavelet space is much similar to the original system,and the nonlinear invariants such as correlation dimension,Lyapunov exponent and Kolmogorov entropy are still reserved.It demonstrates that wavelet decomposition is effective for characterizing chaotic dynamical system.     

Revisiting black hole thermodynamics in massive gravity: charged particle absorption and infalling shell of dust

In this study, we apply two methods to consider the variation of massive black holes in both normal and extended thermodynamic phase spaces. The first method considers a charged particle being absorbed by the black hole, whereas the second considers a shell of dust falling into it. With the former method, the first and second laws of thermodynamics are always satisfied in the normal phase space; however, in the extended phase space, the first law is satisfied but the validity of the second law?of?thermodynamics depends upon the model parameters. With the latter method, both laws are valid. We argue that the former method's violation of the second law of thermodynamics may be attributable to the assumption that the change of internal energy of the black hole is equal to the energy of the particle. Finally, we demonstrate that the event horizon always ensures the validity of weak cosmic censorship in both phase spaces; this means that the violation of the second law of thermodynamics, arising under the aforementioned assumption, does not affect the weak cosmic censorship conjecture. This further supports our argument that the assumption in the first method is responsible for the violation and requires deeper treatment.     

Equations of motion from chaotic data: A driven optical fiber ring resonator

We apply a recently proposed method for the reconstruction of equations of motion from a time series to experimental chaotic optical data and find the theoretically expected Ikeda model. In contrast to phase space reconstruction methods, it is based on nonlinear regression and maximal correlation, and the resulting model can be investigated further. We demonstrate the retrieval of physical parameters by calculating the experimentally not accessible phase evolution of a non-stationary data set.     

Uniform distribution of projection data for improved reconstruction quality of 4D EPR imaging

In continuous wave (CW) electron paramagnetic resonance imaging (EPRI), high quality of reconstruction in a limited acquisition time is a high priority. It has been shown for the case of 3D EPRI, that a uniform distribution of the projection data generally enhances reconstruction quality. In this work, we have suggested two data acquisition techniques for which the gradient orientations are more evenly distributed over the 4D acquisition space as compared to the existing methods. The first sampling technique is based on equal solid angle partitioning of 4D space, while the second technique is based on Fekete points estimation in 4D to generate a more uniform distribution of data. After acquisition, filtered backprojection (FBP) is applied to carry out the reconstruction in a single stage. The single-stage reconstruction improves the spatial resolution by eliminating the necessity of data interpolation in multi-stage reconstructions. For the proposed data distributions, the simulations and experimental results indicate a higher fidelity to the true object configuration. Using the uniform distribution, we expect about 50% reduction in the acquisition time over the traditional method of equal linear angle acquisition.     

Methods of Wavebeam Phase Front Reconstruction Using Intensity Measurements

Two methods for phase front reconstruction of paraxial linear polarized wavebeams are presented. Both of them are based on wavebeam field intensity measurements. The first method requires a reference wavebeam with known characteristics. The second one allows phase reconstruction using only wavebeam intensity measurements in a few cross sections. The methods described are successfully applied in the millimeter range for wavebeam diagnostics in mode converters, transmission lines and antenna elements. Since the methods are based on general principles they may be used not only for microwaves investigation.     

On Hamiltonian Formulations of the Schrödinger System

We review and compare different variational formulations for the Schrödinger field. Some of them rely on the addition of a conveniently chosen total time derivative to the hermitic Lagrangian. Alternatively, the Dirac-Bergmann algorithm yields the Schrödinger equation first as a consistency condition in the full phase space, second as canonical equation in the reduced phase space. The two methods lead to the same (reduced) Hamiltonian. As a third possibility, the Faddeev-Jackiw method is shown to be a shortcut of the Dirac method. By implementing the quantization scheme for systems with second class constraints, inconsistencies of previous treatments are eliminated.     

Sound absorption coefficient measurements by phase-conjugate ultrasonic waves

Measurements of the sound absorption coefficient in test objects containing solid microparticles randomly distributed over the object volumes are carried out. Two methods are used for this purpose: the standard echo-pulse insert-substitution method and a modified method using phase conjugation of ultrasound. The test objects are made from gelatin, and the size of the particles introduced in it is chosen to allow measurements in both the long- and medium-wavelength scattering modes of the probing beam. It is shown that, in the first scattering mode, in which the presence of particles causes additional viscous and temperature losses, the two aforementioned methods give identical results. In the second scattering mode, in which the dominant mechanism of additional loss is elastic scattering, the use of phase conjugation allows an almost complete reconstruction of the scattered field and, hence, a more reliable upper estimate for the coefficient of ultrasonic absorption in the test objects.