Chaotic signal detection and estimation based on attractor sets: applications to secure communications

We consider the problem of detection and estimation of chaotic signals in the presence of white Gaussian noise. Traditionally this has been a difficult problem since generalized likelihood ratio tests are difficult to implement due to the chaotic nature of the signals of interest. Based on Poincare's recurrence theorem we derive an algorithm for approximating a chaotic time series with unknown initial conditions. The algorithm approximates signals using elements carefully chosen from a dictionary constructed based on the chaotic signal's attractor. We derive a detection approach based on the signal estimation algorithm and show, with simulated data, that the new approach can outperform other methods for chaotic signal detection. Finally, we describe how the attractor based detection scheme can be used in a secure binary digital communications protocol.     

电力系统故障的微弱信号检测方法的研究

为了确保电力系统能够安全稳定的运行,实时检测故障中的微弱信号。通过噪声干扰情况下微弱信号的不同变化进行研究,得到了一种微弱信号的DUFFING混沌检测模型。系统发生故障时会产生相应的微弱信号,运用DUFFING混沌振子法分析不同情况下微弱信号的时域波形和相平面轨迹变化规律,并建立数学检测模型,对其幅值进行混沌检测仿真。结果表明,当r=0.8264V,w=1rad/s时将白噪声和微弱正弦信号同时加入后,此时,混沌状态、大尺度周期状态的相平面运行轨迹依然在进行有规律的运行,可以清晰的观察出需要检测的微弱信号。在强噪声存在于系统中时,该方法明显克服了噪声对信号稳定性的干扰,能精确有效检测微弱信号。系统在应对不同工作环境、仪器设备老化等情况时,提高了检测效率,保证系统的稳定运行。     

Parameters identification and adaptive full state hybrid projective synchronization of chaotic (hyper-chaotic) systems

Based on the active control idea and the invariance principle of differential equations, a general scheme of adaptive full state hybrid projective synchronization (FSHPS) and parameters identification of a class of chaotic (hyper-chaotic) systems with linearly dependent uncertain parameters is proposed in this Letter. With this effective scheme parameters identification and FSHPS of chaotic and hyper-chaotic systems can be realized simultaneously. Numerical simulations on the chaotic Chen system and the hyper-chaotic Chen system are presented to verify the effectiveness of the proposed scheme.     

Model-based detector and extraction of weak signal frequencies from chaotic data

Detecting a weak signal from chaotic time series is of general interest in science and engineering. In this work we introduce and investigate a signal detection algorithm for which chaos theory, nonlinear dynamical reconstruction techniques, neural networks, and time-frequency analysis are put together in a synergistic manner. By applying the scheme to numerical simulation and different experimental measurement data sets (Henon map, chaotic circuit, and NH(3) laser data sets), we demonstrate that weak signals hidden beneath the noise floor can be detected by using a model-based detector. Particularly, the signal frequencies can be extracted accurately in the time-frequency space. By comparing the model-based method with the standard denoising wavelet technique as well as supervised principal components analysis detector, we further show that the nonlinear dynamics and neural network-based approach performs better in extracting frequencies of weak signals hidden in chaotic time series.     

Optimizing chaos-based signals for complex radar targets

There has been interest in the use of chaotic signals for radar, but most researchers consider only a few chaotic systems and how these signals perform for the detection of point targets. The range of possible chaotic signals is far greater than what most of these researchers consider, so to demonstrate this, I use a chaotic map whose parameters may be adjusted by a numerical optimization routine, producing different chaotic signals that are modulated onto a carrier and optimized for different situations. It is also suggested that any advantage for these chaos-based signals may come in the detection of complex targets, not point targets, and I compare the performance of chaos-based signals to a standard radar signal, the linear frequency modulated chirp. I find that I can optimize a chaos-based signal to increase the cross-correlation with the reflection from one complex target compared to the cross-correlation with the reflection from a different target, thus allowing the identification of a complex target. I am also able to increase the cross-correlation of the reflection from a complex target compared with the cross-correlation with the reflection from spatially extended clutter. I show that a larger output signal-to-noise ratio is possible if I cross-correlate with a reference signal that is different from the transmitted signal, and I justify my results by showing how the ambiguity diagram for a chaos-based signal can be different than the ambiguity diagram for a noise signal.     

基于Duffing振子的微弱周期信号混沌检测性能研究

不同的混沌振子具有不同的混沌检测性能. 本文围绕Duffing振子的混沌检测方法, 从混沌系统临界点相图的突变性、混沌区间保持性以及混沌临界点的容噪性等三个方面的检测性能做了进一步研究, 并分别分析了影响这些性能的因素, 最后围绕这三个方面对两个不同混沌振子的混沌检测性能做了分析和比较. 关键词： 混沌检测 微弱信号检测 Duffing方程 检测性能     

一种基于新型间歇混沌振子的舰船线谱检测方法

为了实现低信噪比下未知频率的舰船辐射线谱的检测,对常规型间歇混沌振子列检测方法进行了改进,提出了一种基于适应步长型间歇混沌振子的信号检测方法.该方法可以只用一个Duffing振子,通过设定一组能够覆盖待测信号所在频段的求解步长序列,实现对未知频率、具有任意初相位的微弱周期信号的搜索检测.为进一步提高系统的弱信号检测性能,分析了Holmes型Duffing方程在不同频率内置策动力下对弱信号灵敏度的差异.综合理论分析和仿真研究结果给出了Duffing振子在内置策动力角频率为0.4 rad/s时对弱信号检测性能最佳,并据此对所采用的Duffing振子进行了优化;仿真结果表明,改进后的Duffing振子的弱信号检测性能提高了12 dB.最后将此方法应用于一组含有舰船辐射线谱的实船数据,结果表明此方法可以实现低信噪比下的未知频率微弱线谱检测.     

混沌超宽带系统的广义负熵盲检测机理研究

本文提出了利用广义负熵盲检测机理对混沌超宽带系统的进行非相干盲检测的研究方法, 在传输信道状态未知的情况下即可检测出混沌脉冲信号. 该方法能够克服用于超宽带无线电通信的直接混沌通信方案存在的实际应用问题, 能够有效解决未知复杂多径信道问题. 通过仿真结果分析表明, 采用非相干盲检测方法的直接混沌通信超宽带方案, 不需要信道状态信息, 具有很好的分离检测效果. 为未知非理想信道下, 非相干盲检测的混沌超宽带系统提出了新思路.     

Envelope order tracking for fault detection in rolling element bearings

An envelope order tracking analysis scheme is proposed in the paper for the fault detection of rolling element bearing (REB) under varying-speed running condition. The developed method takes the advantages of order tracking, envelope analysis and spectral kurtosis. The fast kurtogram algorithm is utilized to obtain both optimal center frequency and bandwidth of the band-pass filter based on the maximum spectral kurtosis. The envelope containing vibration features of the incipient REB fault can be extracted adaptively. The envelope is re-sampled by the even-angle sampling scheme, and thus the non-stationary signal in the time domain is represented as a quasi-stationary signal in the angular domain. As a result, the frequency-smear problem can be eliminated in order spectrum and the fault diagnosis of REB in the varying-speed running condition of the rotating machinery is achieved. Experiments are conducted to verify the validity of the proposed method.     

基于混沌和随机共振的微弱信号检测

推导了分数阶线性振子系统响应的一阶稳态矩的频率不变性和相移特性, 并通过理论分析得出, 在随机共振机制下, 分数阶线性振子对系统响应一阶稳态矩的幅值具有放大作用. 构造Duffing混沌振子检测器, 利用混沌系统对参数摄动的敏感性以及对噪声的免疫能力实现弱信号检测. 数值模拟证实, 该方法可以有效地从噪声背景中将微弱正弦信号检测出来, 并且相对传统的混沌检测方法能显著降低信噪比检测门限.     

基于分数阶可停振动系统的周期未知微弱信号检测方法

本文建立了分数阶可停振动系统, 其可停振动状态的改变对周期策动力敏感, 对零均值随机微小扰动不敏感, 这事实上为周期未知微弱信号检测提供了一种新的高效检测方法和判别标准. 与现有的利用混沌系统的大尺度周期状态变化检测周期未知弱信号的方法 需逐一尝试设置不同频率内置信号以便期望与待检周期信号发生共振不同, 利用分数阶可停振动系统的可停振动状态变化检测周期未知微弱信号的方法, 除了同样具有因为状态变化对周期信号的敏感性而能够实现极低检测门限的特点外, 还具有混沌系统信号检测所不具有的优点: 1)无需预先估计待检信号的周期; 2)无需计算系统状态的临界阈值; 3)可停振动状态可由本文设计的指数波动函数可靠地进行判断; 4)通过系统微分阶数的变化, 将检测系统层次化, 从而可得到比整数阶检测系统更低的检测门限, 特别是在色噪声环境下, 通过选取合适的微分阶数, 基于分数阶可停振动系统的微弱周期信号检测法能够大幅度的降低检测门限, 在本文的仿真试验中, 检测门限可达-182 dB. 关键词： 分数阶非线性系统 Duffing振子 弱信号检测     

类Liu系统在水声微弱信号检测中的应用研究

利用三阶混沌系统构造了一种新的微弱信号检测系统——类Liu系统, 对类Liu 系统进行了深度的理论分析. 类Liu系统中, 当输入待测信号幅值大于某临界值时, 系统可达到平衡点S₀, S₀中系统变量x平衡于摄动力信号, 系统变量y, z收敛于零态, 且S₀ 对应的Lyapunov指数小于零. 通过Matlab仿真、Multisim电路仿真以及实际电路证明了类Liu系统的周期态收敛性及广域检测性, 解决了传统Duffing系统进行微弱信号检测时周期态不收敛、只能进行窄域检测等问题, 同时谱级信噪比范围仍可达-46.57 dB. 类Liu系统采用了全新的设计理念, 具有较高的实用价值, 对未来海洋物联网中的水声通信有一定参考价值.     

A Rolling Bearing Fault Classification Scheme Based on k-Optimized Adaptive Local Iterative Filtering and Improved Multiscale Permutation Entropy

The health condition of the rolling bearing seriously affects the operation of the whole mechanical system. When the rolling bearing parts fail, the time series collected in the field generally shows strong nonlinearity and non-stationarity. To obtain the faulty characteristics of mechanical equipment accurately, a rolling bearing fault detection technique based on k-optimized adaptive local iterative filtering (ALIF), improved multiscale permutation entropy (improved MPE), and BP neural network was proposed. In the ALIF algorithm, a k-optimized ALIF method based on permutation entropy (PE) is presented to select the number of ALIF decomposition layers adaptively. The completely average coarse-graining method was proposed to excavate more hidden information. The performance analysis of the simulation signal shows that the improved MPE can more accurately dig out the depth information of the time series, and the entropy value obtained is more consistent and stable. In the research application, rolling bearing time series are decomposed by k-optimized ALIF to obtain a certain number of intrinsic mode functions (IMFs). Then the improved MPE value of effective IMF is calculated and input into backpropagation (BP) neural network as the feature vector for automatic fault identification. The comparative analysis of simulation signals shows that this method can extract fault information effectively. At the same time, the experimental part shows that this scheme not only effectively extracts the fault features, but also realizes the classification and identification of different fault modes and faults of different degrees, which has a certain application prospect in the research and application direction of rolling bearing fault identification.     

基于Hilbert变换及间歇混沌的水声微弱信号检测方法研究

利用Duffing振 子从混沌到间歇混沌的相变及其对策动力和待检测信号频差较小的周期信号的敏感性, 研究了强海洋背景噪声下微弱周期信号的检测. 通过构造混沌振子列的方法对频率未知信号进行扫频, 从而提取待检测信号的频率范围, 最后利用希尔伯特变换, 实现对间歇混沌的包络检测, 并计算出待检测信号的频率. 计算机仿真与实测水声信号处理结果表明, 利用基于希尔伯特变换的间歇混沌振子对水声微弱信号检测, 其检测信噪比比一般的间歇混沌振子提高了至少4.4 dB, 验证了所提方法的有效性.     

A new chaotic secure communication scheme

A new chaotic secure communication scheme is constructed. Unified chaotic system is used to encrypt the emitted signal. Different from the existing chaotic secure communication methods, the useful information is embodied in the parameter of chaotic systems in this Letter. The receiver is designed which can succeed in recovering the former signal. Finally computer simulations are done to verify the proposed methods, and the results show that the obtained theoretic results are feasible and efficient.     

基于最优滤波器的强混沌背景中谐波信号检测方法研究

强混沌背景中的微弱谐波信号检测有重要的工程研究意义. 目前的检测方法主要是基于Takens理论的混沌相空间重构方法, 然而这些方法往往对信干噪比要求高, 且对高斯白噪声敏感等. 本文注意到混沌信号的二阶统计特性是不变的, 根据这个特点提出了一种基于最优滤波器的强混沌背景中的微弱谐波信号检测方法. 该方法首先构建一个数据矩阵, 在频域上对每个频率通道分别检测谐波信号, 从而将信号检测问题转化为最优化问题, 然后利用最优化理论设计滤波器, 使待检测频率通道的信号增益保持不变, 而尽量抑制其他频率通道的信号, 最后通过判断每一频率通道的输出信干噪比来检测谐波信号. 与传统方法相比, 本文方法有如下优点: 1)可以检测更低信干噪比下的微弱谐波信号; 2)可检测的信号幅度范围更大; 3)抗白噪声性能更强. 仿真结果证明了本文方法的有效性.     

混沌噪声背景下微弱脉冲信号的检测及恢复

构建了一种在混沌噪声背景下检测并恢复微弱脉冲信号的模型.首先,基于混沌信号的短期可预测性及其对微小扰动的敏感性,对观测信号进行相空间重构、建立局域线性自回归模型进行单步预测,得到预测误差,并利用假设检验方法从预测误差中检测观测信号中是否含有微弱脉冲信号.然后,对微弱脉冲信号建立单点跳跃模型,并融合局域线性自回归模型,构成双局域线性(DLL)模型,以极小化DLL模型的均方预测误差为目标进行优化,采用向后拟合算法估计模型的参数,并最终恢复出混沌噪声背景下的微弱脉冲信号.仿真实验结果表明本文所建的模型能够有效地检测并恢复出混沌噪声背景中的微弱脉冲信号.     

A new adaptive observer-based synchronization scheme for private communication

The problem of secure communication via parameter modulation in a class of uncertain chaotic systems is considered. For a given uncertain master chaotic system, a robust adaptive observer-based response can be constructed to synchronize the drive system. The information signal is used to modulate one parameter of a given chaotic system. The resulting chaotic signal is later demodulated and the information signal is recovered using an adaptive demodulator. The convergence of the demodulator is established. Theoretical analysis and numerical simulation on Chua's circuit show the effectiveness and efficiency of the proposed scheme.     

An adaptive chaotic secure communication scheme with channel noises

In this Letter, an adaptive secure communication scheme with channel noises is proposed. Based on the idea of chaotic masking-modulation, the message is encrypted by a chaotic signal. By using adaptive feedback control techniques, the transmitter and the receiver are synchronized, so the masked signal can be perfectly recovered by the receiver in the presence of channel noises. In light of the Lyapunov stability theory for stochastic differential equations, several theoretical results are rigorously established. Finally, the famous Chua's circuits is used to illustrate the possible applications of the obtained theoretical results, and the computer simulations show that the proposed scheme is feasible and efficient.     

光学双稳系统混沌驱动保密通讯原理研究

根据声光双稳系统混沌驱动下的动力学行为，提出利用系统的相位特性实现信息的混沌加密，并且由接收端混沌驱动产生的混沌信号完成信息提取的原理。发现在较大的噪声覆盖下仍然可以实现信息的安全传送，由于信息解密不需要与载波安全同步的混信号而只利用传输信号与接收端被驱动系统输出信号的相位关系，因此这种方法具有实际应用价值。