A new method for detecting line spectrum of ship-radiated noise using Duffing oscillator

A detection scheme for line spectrum of ship-radiated noise is proposed using Duffing oscillator. The chaotic trajectory of Duffing oscillator is analyzed and the state equation of the system is improved to detect weak periodic signals in different frequencies. According to the simulation results, the phase transforms of Duffing oscillator are sensitive to periodic signals and immune to the random noise and the periodic interference signals which have larger angular frequency difference from the referential signal. By employing Lyapunov exponents in the field of detection as the criteria for chaos, the phase transforms of dynamic behaviors in quantity are successfully determined. Meanwhile, the threshold value in critical state has been evaluated more accurately. Based on the phase transforms of Duffing oscillator, a new method for detecting line spectrum of ship-radiated noise is given. Three types of ship-radiated noise signals are analyzed and the values of line spectrum are acquired successfully by this method. The experimental results show that this method has high sensitivity and high resolution.     

Dynamic Reconstruction-Based Fuzzy Neural Network Method for Fault Detection in Chaotic System

This paper presents a method for detecting weak fault signals in chaotic systems based on the chaotic dynamics reconstruction technique and the fuzzy neural system （FNS）. The Grassberger-Procaccia algorithm and least squares regression were used to calculate the correlation dimension for the model order estimate. Based on the model order, an appropriately structured FNS model was designed to predict system faults. Through reasonable analysis of predicted errors, the disturbed signal can be extracted efficiently and correctly from the chaotic background. Satisfactory results were obtained by using several kinds of simulative faults which were extracted from the practical chaotic fault systems. Experimental results demonstrate that the proposed approach has good prediction accuracy and can deal with data having a -40 dB signal to noise ratio （SNR）. The low SNR requirement makes the approach a powerful tool for early fault detection.     

The base-scale entropy analysis of short-term heart rate variability signal

The complexity of heart rate variability (HRV) signal can reflect physiological functions and healthy status of heart system. Detecting complexity of the short-term HRV signal has an important practical meaning. We introduce the base-scale entropy method to analyze the complexity of time series. The advantages of our method are its simplicity, extremely fast calculation for very short data and anti-noise characteristic. For the well-known chaotic dynamical system- logistic map, it is shown that our complexity behaves similarly to Lyapunov exponents, and is especially effective in the presence of random Gaussian noise. This paper addresses the use of base-scale entropy method to 3 low-dimensional nonlinear deterministic systems. At last, we apply this idea to short-term HRV signal, and the result shows the method could robustly identify patterns generated from healthy and pathologic states, as well as aging. The base-scale entropy can provide convenience in practically applications.     

Ability to detect weak effective seismic signals by utilizing chaotic vibrator system

Taking the advantage of CVS (Chaotic Vibrator System) sensitivity of large-scale periodic phase-state response to quasi-periodic or periodic signals,a series of numerical experiments were made to understand the ability of CVS to detect weak effective seismic signals in the common-shot seismic record distorted by strong stochastic noise. The re-sults demonstrate that the large-scale periodic phase-states of CVS are correlated with the signal composition of the quasi-periodic wavelet sequence constructing from horizontal moveout of seismic events,noise strength and the noise distortion de-gree to signal. For the same kind of events,the higher the noise distortion degree is,the lower the detectable SNR can be reached by CVS. For seismic data with the same noise distortion degree,the closer the scanning seismic velocity (the trial moveout ve-locity) approaches to the accurate velocity,the higher the detectable SNR can be reached by CVS. More-over,the truncating scanning velocities form an asymmetric belt,which indirectly makes CVS achieve a large-scale periodic phase-state and then the ratio of wavelet distortion coefficients in events can be a biggish variable scope.     

Extracting periodic driving signal from chaotic noise

After periodic signals pass through some nonlinear systems, they are usually transformed into noise-like and wide-band chaotic signals. The discrete spectrums of the original periodic signals are often covered by the chaotic spectrums. Recovering the periodic driving signals from the chaotic signals is important not only in theory but also in practical applications. Based on the modeling theory of nonlinear dynamic system, a "polynomial-simple harmonic drive" non-autonomous equation (P-S equation) to approximate the original system is proposed and the approximation error between P-S equation and the original system is obtained. By changing the drive frequency, we obtain the curve of the approximation error vs. drive frequency. Based on the relation between this curve and the spectrums of the original periodic signals, the spectrum of the original driving signal is extracted and the original signal is recovered.     

Using chaos to improve measurement precision

If the measuring signals wore input to the chaotic dynamic system as initial parameters, the system outputs might be in steady state, periodic state or chaos state. If the chaotic dynamic system outputs controlled in the periodic states, the periodic numbers would be changed most with the signals. Our novel method is to add chaotic dynamic vibration to the measurement or sensor system. The sensor sensitivity and precision of a measurement system would be improved with this method. Chaotic dynamics measurement algorithms are given and their sensitivity to parameters are analyzed in this paper. The effects of noises on the system are discussed,     

A new complex Duffing oscillator used in complex signal detection

In view of the fact that complex signals are often used in the digital processing of certain systems such as digital communication and radar systems,a new complex Duffing equation is proposed.In addition,the dynamical behaviors are analyzed.By calculating the maximal Lyapunov exponent and power spectrum,we prove that the proposed complex differential equation has a chaotic solution or a large-scale periodic one depending on different parameters.Based on the proposed equation,we present a complex chaotic oscillator detection system of the Duffing type.Such a dynamic system is sensitive to the initial conditions and highly immune to complex white Gaussian noise,so it can be used to detect a weak complex signal against a background of strong noise.Results of the Monte-Carlo simulation show that the proposed detection system can effectively detect complex single frequency signals and linear frequency modulation signals with a guaranteed low false alarm rate.     

Demodulator for Chaotic Secure Communication Based on proportional—litegral Feedback Design

A scheme of chaotic secure communication based on the parameter modulation and the inversion of a chaotic dynamical system is analyzed.According to this schems,information signal is modulated by a bifurcation parameter of the transmitter,which is in chaotic state.In the receiver,a proportional-integral feedback demodulator is used to demodulate the information signal,which only uses the available synchronizing error as well as stateness of receiver,The purpose of this demodulator is proposed to overscome the influence of differentiation operation,nonlinear part and singularities in chaotic system.Numerical simulation is proposed to show the effectiveness of this demodulator.     

A ballistocardiogram measurement system for home monitoring: design,performance, and evaluation

We present a ballistocardiogram （BCG） measurement system for obtaining the BCG signal. The performance of the BCG measurement system was tested, including the dynamic response frequency of the platform （32 Hz with a 75 kg load）, and the signal to noise ratio of the system （minimum 23 dB）. Factors that could influence BCG recording during measurement were investigated by collecting data from 48 healthy subjects （28 males and 20 females）. The basic features of the BCG signal, such as the amplitude and time interval, were extracted, and differences by gender were analyzed. A correlation between the IJ amplitude （amplitude difference between I-and J-peak） and the respiration phase was found （R2 = 0.49）. The BCG signals for both sitting （SiBCG） and standing （StBCG） postures were obtained using this system. These showed that the StBCG amplitudes were larger than those of SiB- CG but there was no significant difference in the time intervals. The robustness of our system was verified, and its potential for noninvasive cardiac activity monitoring was demonstrated.     

Extraction of Signal Frequency in Laser Ranging of Space Target Based on FPGA

Aiming at the problems in a linear frequency modulation continuous wave(LFMCW) ranging lidar system, such as low signal-to-noise in echo beat frequency and difficult extraction of the signal frequency, a method with high-speed and high accuracy based on field programmable gate array(FPGA) is proposed. Firstly, the laser echo beat signal is sampled by high-speed analog to digital converter(ADC) and then processed in FPGA for data preprocessing. After the signal is processed by the 8 192-point FPGA will obtain the frequency spectrum and then apply the frequency spectrum to data processing and adaptive noise signal peak detection. These two steps realize the real-time and accurate extraction process of the target echo beat signal frequency. Finally, the spectrum data is transmitted to the host computer and processed through the external data acquisition board for real-time spectrum display. Experimental results show that data preprocessing and spectrum data processing can effectively suppress DC bias and system modulation noise. Adaptive noise peak detection can accurately divide the threshold contour according to the dynamic noise of the system and realize the detection of target signal peak. When the sampling clock of the system is 100 MHz, the time needed for each calculation of the spectrum is 81.92 μs, and the refresh rate of the spectrum reaches 12.2 kHz, which meets the real-time requirements of the system.     

基于混沌理论和小波变换的微弱周期信号检测方法

根据小波变换具有多分辨率,混沌系统对噪声的强免疫力和对周期微弱信号的敏感性等特性,通过对小波阈值去噪方法和混沌Duffing振子方程的改进,提出小波阈值去噪和混沌系统相结合的微弱周期信号检测新方法.该方法利用小波变换的平滑作用对包含噪声的信号进行有限离散处理,并根据小波分解尺度确定阈值去噪深度,然后把重构的信号作为周期策动力的摄动并入混沌系统,采用混沌振子阵列实现在噪声背景下微弱信号的检测,并采用梅尔尼科夫方法作为混沌判据.该检测方法克服了以往小波分解对尺度确定的盲目性和阈值选择的不合理性以及对混沌临界状态与周期态区别的模糊性:同时能检测多种频率的信号.仿真测试表明:该方法直观、高效,检测精度高,检测的最低信噪比达到-100dB,频率误差为0.04％左右,改善了湮没在强噪声下的微弱信号检测技术.     

基于差分Poincaré映射的间歇混沌信号判别方法

针对混沌振子微弱信号检测中间歇混沌信号难以判别的问题,利用混沌系统的参数敏感特性,提出一种差分Poincar6映射判别方法,实现强噪声干扰下输出间歇混沌信号的判别.该方法选取周期激励幅值具有微小差异的两个混沌振子的Poincaré映射进行差值运算,利用周期状态下输出信号收敛,而混沌状态下输出信号分离的特点,降低了噪声对周期区域的影响,使可检测输入信号的信噪比达到了-87 dB.实验表明,在时域或Poincaré映射已经无法进行分辨的情况下,该方法仍然实现了检测系统输出间歇混沌信号的有效判别.     

基于混沌振子探测微弱动态周期测量信号

介绍了Duffing振子检测微弱信号的原理和过程以及利用混沌振子来检测淹没在强噪声背景中的微弱动态周期测量信号的方法．理论分析和仿真实验均表明混沌振子能有效地检测微弱动态周期信号．该检测方法既能形成一种独立的检测理论，也可以作为现行微弱信号检测理论的有效补充．     

基于双耦合混沌振子的未知频率弱信号检测

针对微弱信号检测的难点问题,提出了一种应用于未知频率微弱信号的分段测频检测方法.利用双耦合Duffing系统相轨迹状态的跃迁对于输入微弱信号的敏感特性实现了对淹没在强噪声中的微弱信号的检测,同时利用分段测频方法实现了对微弱信号的频率测量,有效地解决了单Duffing振子的微弱信号检测方法易受噪声影响产生误判的问题,突破了现有微弱信号混沌振子检测方法只能进行已知频率信号检测的局限性.仿真实验结果证明该方法确实能够较为准确地检测出输入微弱周期信号的频率,使微弱信号检测技术得到进一步完善.     

单结管电路中的随机共振过程

为考察二阶非线性电路响应中是否存在随机共振过程 ,用噪声信号和周期信号同时激励二阶非线性单结管电路 ,并观察其响应和测量输出响应信号的信噪比。结果表明 :在一定的条件下 ,增大输入噪声的值不仅不降低输出响应信噪比 ;反而迅速增加输出响应的信噪比 ,使输出响应中周期信号的分量反而加强 ,而且输出响应的信噪比对于输入噪声的变化具有“共振”形状的曲线。从而证明了二阶非线性单结管电路不仅是混沌系统 ,也是随机共振系统 ,且随机共振响应是混沌系统一种响应模态     

混沌干扰下的随机共振研究

利用随机共振现象可以实现弱信号检测,目前大量的研究是在白噪声或色噪声背景下进行的,对于混沌干扰下的随机共振的研究却很少。研究了混沌背景干扰下的信号检测,发现在混沌干扰下双稳系统也会发生随机共振现象,因此可以检测出淹没在混沌干扰中的信号;在混沌与噪声同时存在的混合背景下,随机共振现象仍然存在,混合背景可以发生与单一噪声背景类似的随机共振现象。     

一种基于改进替代数据法的图形化混沌判据

替代数据法是非线性系统分析的一种有效方法. 该方法不能直接判断信号是否处于混沌状态,而是基于排除法思路,提高混沌识别的置信度. 文中引入一种针对类周期信号混沌识别的伪周期替代数据法,在数值实验中发现了该算法的3个缺陷:一是相空间重构在实际信号分析中效果不佳;二是替代数据直线化;三是检验统计量容错性较差. 针对这些问题分别提出了改进方法. 使用改进算法对不同类别信号（包括由Logistic模型产生的周期信号和混沌信号以及其它典型混沌信号等）进行数据实验. 发现所有混沌信号在各噪声半径下的复杂度都呈线性增长趋势;而周期信号在噪声半径小于0.1时,复杂度的取值保持平稳,噪声半径大于0.1时,复杂度取值开始单调增长. 对数据实验的结果分析表明:在各噪声半径下复杂度的线性增长趋势是混沌信号的共同特征,可作为一种有效的图形化混沌判据.     

自治混沌系统中抗噪声干扰的频率检测模型

提出一种用自治混沌系统检测受到噪声干扰的信号频率的方法,将含有噪声干扰的信号加入到自治混沌系统的某一项,再给受扰系统施加一个状态负反馈,通过适当地调节反馈增益将受扰系统的轨道控制到系统的某一个极限环,然后利用循环相态技术,统计一定时间内轨道定向穿过某一个平面的次数,由固定的时间内得到周期的个数进而确定系统的振荡频率。由于系统的频率由待测信号的频率决定,而不受噪声的影响,所以待测信号的频率也就是系统的振荡频率。仿真实验结果进一步验证了该方法的有效性。     

一种保密通信系统混沌信号产生器的设计及仿真

提出了一种发送端与接收端混沌信号产生器“不对称”的保密通信方案．基于误差反馈同步原理,发送端与接收端各自设计带有不同特定辅助网络的混沌信号产生器;接收端获取了发送端混沌系统的参数、特定辅助网络的结构和传送信号的构成情况,才可以重构混沌系统并设计相应的辅助网络,从收到的信息中提取用于加密的混沌信号,解调出信息．仿真结果表明,发送端与接收端特定辅助网络的设计加强了保密通信系统的保密性,且系统具有较好的噪声鲁棒性。     

基于变尺度杜芬阵列的超声非线性输出信号检测

针对超声非线性输出信号中二次谐波信号比较弱、且是经过复杂传播的非线性时间序列,利用变尺度杜芬阵列对超声非线性输出信号进行检测评估材料的疲劳损伤。首先对杜芬振子进行频率变换、分析初始相位对检测结果的影响,构建检测实际工程信号的杜芬阵列模型,并对超声非线性输出信号进行变尺度变换,使杜芬阵列与超声非线性输出信号相匹配。当处理信号输入杜芬阵列模型时,第二个杜芬振子相轨迹由混沌状态过渡至大尺度周期状态,微弱二次谐波信号可以被有效的检测出来。根据杜芬振子总驱动力幅值和响应信号幅值之间的对应关系对二次谐波信号幅值进行有效估算。最后,探究随机噪声对检测模型的影响,当待测信号含有噪声时,杜芬振子相图仍变为大尺度周期状态,随着信噪比降低,相轨迹越来越粗糙,且稳定性变差。以上分析表明,利用构建的杜芬阵列模型能够有效检测超声非线性输出信号的二次谐波,对材料的疲劳损伤状态进行有效评估。