Denoising Nonlinear Time Series Using Singular Spectrum Analysis and Fuzzy Entropy

We present a hybrid singular spectrum analysis （SSA） and fuzzy entropy method to filter noisy nonlinear time series. With this approach, SSA decomposes the noisy time series into its constituent components including both the deterministic behavior and noise, while fuzzy entropy automatically differentiates the optimal dominant components from the noise based on the complexity of each component. We demonstrate the effectiveness of the hybrid approach in reconstructing the Lorenz and Mackey--Class attractors, as well as improving the multi-step prediction quality of these two series in noisy environments.

Wavelet packet decomposition entropy threshold method for discrete spectrum interferences rejection of on-line partial discharge monitoring

The frequency domain division theory of dyadic wavelet decomposition and wavelet packet decomposition (WPD) with orthogonal wavelet base frame are presented. The WPD coefficients of signals are treated as the outputs of equivalent bandwidth filters with different center frequency. The corresponding WPD entropy values of coefficients increase sharply when the discrete spectrum interferences (DSIs), frequency spectrum of which is centered at several frequency points existing in some frequency region. Based on WPD, an entropy threshold method (ETM) is put forward, in which entropy is used to determine whether partial discharge (PD) signals are interfered by DSIs. Simulation and real data processing demonstrate that ETM works with good efficiency, without pre-knowing DSI information. ETM extracts the phase of PD pulses accurately and can calibrate the quantity of single type discharge.

Short-Term Prediction of Photovoltaic Power Generation Based on LMD Permutation Entropy and Singular Spectrum Analysis

The power output state of photovoltaic power generation is affected by the earth’s rotation and solar radiation intensity.On the one hand,its output sequence has daily periodicity;on the other hand,it has discrete randomness.With the development of new energy economy,the proportion of photovoltaic energy increased accordingly.In order to solve the problem of improving the energy conversion efficiency in the grid-connected optical network and ensure the stability of photovoltaic power generation,this paper proposes the short-termprediction of photovoltaic power generation based on the improvedmulti-scale permutation entropy,localmean decomposition and singular spectrum analysis algorithm.Firstly,taking the power output per unit day as the research object,the multi-scale permutation entropy is used to calculate the eigenvectors under different weather conditions,and the cluster analysis is used to reconstruct the historical power generation under typical weather rainy and snowy,sunny,abrupt,cloudy.Then,local mean decomposition(LMD)is used to decompose the output sequence,so as to extract more detail components of the reconstructed output sequence.Finally,combined with the weather forecast of the Meteorological Bureau for the next day,the singular spectrumanalysis algorithm is used to predict the photovoltaic classification of the recombination decomposition sequence under typical weather.Through the verification and analysis of examples,the hierarchical prediction experiments of reconstructed and non-reconstructed output sequences are compared.The results show that the algorithm proposed in this paper is effective in realizing the short-term prediction of photovoltaic generator,and has the advantages of simple structure and high prediction accuracy.

Research on a deconvolution algorithm for laser-induced fluorescence diagnosis based on the maximum entropy principle

Laser-induced fluorescence(LIF)spectroscopy is employed for plasma diagnosis,necessitating the utilization of deconvolution algorithms to isolate the Doppler effect from the raw spectral signal.However,direct deconvolution becomes invalid in the presence of noise as it leads to infinite amplification of high-frequency noise components.To address this issue,we propose a deconvolution algorithm based on the maximum entropy principle.We validate the effectiveness of the proposed algorithm by utilizing simulated LIF spectra at various noise levels(signal-to-noise ratio,SNR=20–80 d B)and measured LIF spectra with Xe as the working fluid.In the typical measured spectrum(SNR=26.23 d B)experiment,compared with the Gaussian filter and the Richardson–Lucy(R-L)algorithm,the proposed algorithm demonstrates an increase in SNR of 1.39 d B and 4.66 d B,respectively,along with a reduction in the root-meansquare error(RMSE)of 35%and 64%,respectively.Additionally,there is a decrease in the spectral angle(SA)of 0.05 and 0.11,respectively.In the high-quality spectrum(SNR=43.96 d B)experiment,the results show that the running time of the proposed algorithm is reduced by about98%compared with the R-L iterative algorithm.Moreover,the maximum entropy algorithm avoids parameter optimization settings and is more suitable for automatic implementation.In conclusion,the proposed algorithm can accurately resolve Doppler spectrum details while effectively suppressing noise,thus highlighting its advantage in LIF spectral deconvolution applications.

New Individual Identification Method of Radiation Source Signal Based on Entropy Feature and SVM

In this paper,according to the defect of methods which have low identification rate in low SNR,a new individual identification method of radiation source based on information entropy feature and SVM is presented. Firstly,based on the theory of multi-resolution wavelet analysis,the wavelet power spectrum of noncooperative signal can be gotten. Secondly,according to the information entropy theory,the wavelet power spectrum entropy is defined in this paper. Therefore,the database of signal's wavelet power spectrum entropy can be built in different SNR and signal parameters. Finally,the sorting and identification model based on SVM is built for the individual identification of radiation source signal. The simulation result indicates that this method has a high individual's identification rate in low SNR,when the SNR is greater than 4 dB,the identification rate can reach 100%. Under unstable SNR conditions,when the range of SNR is between 0 dB and 24 dB,the average identification rate is more than 92. 67%. Therefore,this method has a great application value in the complex electromagnetic environment.

An algorithm based on evidence theory and fuzzy entropy to defend against SSDF

In cognitive radio networks, spectrum sensing is one of the most important functions to identify available spectrum for improving the spectrum utilization. Due to the open characteristic of the wireless electromagnetic environment, the wireless network is vulnerable to be attacked by malicious users(MUs), and spectrum sensing data falsification(SSDF) attack is one of the most harmful attacks on spectrum sensing performance. In this article,an algorithm based on the evidence theory and fuzzy entropy is proposed to resist SSDF attacks. In this algorithm, secondary users(SUs) obtain the corresponding degree of membership function and basic probability assignment function based on the local energy detection result. The new conflicting coefficient is calculated based on the evidence distance and classical conflicting coefficient, and the conflicting weight of the evidence is obtained.The fuzzy weight is calculated by the fuzzy entropy. The credibility weight is obtained by updating the credibility. On this basis, the probability assignment function of the evidence is corrected, and the final result is obtained by using the fusion formula. Simulation results show that the proposed algorithm has a higher detection probability and lower false alarm probability than other algorithms.It can effectively defend against SSDF attacks and improve the performance of spectrum sensing.

Maximum entropy spectral characteristics of seismic activity for great earthquakes in China

The maximum entropy spectral characteristics of seismicity in the seismic enhanced region of 11 great earthquakes is analysed in this paper to seek the difference of seismic period spectral structure between the normal and the abnormal stage of seismic activity in this paper. The results show that, during decades or even one hundred years before great earthquakes, only short periods with 6.5～24.3 years appear, and long ones disappear. Otherwise, long periods with 18.5～38.5 years exist chiefly within the normal stages. Decades years after great earthquakes, the period spectra of seismicity are generally about several or ten years. Then the characteristics of great earthquakes is explained physically by applying the strong body seismogenic model, so a method of studying and predicting great earthquakes is offered.

Area and entropy spectra of black holes via an adiabatic invariant

By considering and using an adiabatic invariant for black holes, the area and entropy spectra of static spherically- symmetric black holes are investigated. Without using quasi-normal modes of black holes, equally-spaced area and entropy spectra are derived by only utilizing the adiabatic invariant. The spectra for non-charged and charged black holes are calculated, respectively. All these results are consistent with the original Bekenstein spectra.

Polarimetric entropy of the ocean surface with a two-scale scattering model

The relationships among an ocean wave spectrum,a fully polarimetric coherence matrix,and radar parameters are deduced with an electromagnetic wave theory.Furthermore,the relationship between the polarimetric entropy and ocean wave spectrum is established based on the definition of entropy and a twoscale scattering model of the ocean surface.It is the first time that the polarimetric entropy of the ocean surface is presented in theory.Meanwhile,the relationships among the fully polarimetric entropy and the parameters related to radar and ocean are discussed.The study is the basis of further monitoring targets on the ocean surface and deriving oceanic information with the entropy from the ocean surface.The contrast enhancement between human-made targets and the ocean surface with the entropy is presented with quad-pol airborne synthetic aperture radar（AIRSAR） data.

Area Spectrum of D-Dimensional Large Schwarzschild-AdS Black Hole from Asymptotic Quasinormal Modes

We investigate the area and entropy spectra of D-dimensional large Schwarzschild black holes. By utilizing the new physical interpretation of quasinormal mode frequency we find that a large Schwarzschild-AdS black hole has an equally spaced area spectrum and an equidistant entropy spectrum; both are dependent on the spacetime dimension.

MAXIMUM ENTROPY DECONVOLUTION OF XPS PEAK

Necessity of XPS spectrum deconvolution, disadvantages of the traditional Fast Fourier Transform decon-volution method (FFT) , principle, method and advantages of Maximum Entropy Deconvolution Method (MEM) are de-scribed. Criteria for determing the number of data points sam-pled in MEM are the main point disccussed in the paper,some XPS deconvolution applications of our MEM software show that the MEM makes XPS deconvolution much easier than the traditional FFT method.

基于邦纳多球谱仪探测的中子能谱解谱研究

在中子辐射领域,中子解谱问题备受关注。邦纳多球谱仪常用于中子能谱探测,最大熵法可针对多球谱仪探测数据进行中子解谱。基于此原理,建立包含邦纳多球谱仪的仿真模型,以蒙特卡罗方法的模拟结果作为先验谱,使用基于最大熵原理的最大熵反卷积(MAXED)方法进行中子解谱,结果证明了方法的有效性和准确性。通过增加蒙特卡罗方法的随机粒子数,获得了精确度不同的多组先验谱,对于不同的先验谱,最终解谱结果均可获得统计学显著性,解谱结果有效。经过对比,先验谱越精准,最终解谱结果准确度越高,说明通过合适的降方差方法获得准确的蒙特卡罗计算结果至关重要,可为后续研究和实验提供参考。同步使用了基于迭代算法的GRAVEL方法进行中子解谱,两种解谱方法计算结果对比进一步证明了MAXED方法解谱的优越性能。

Area and entropy spectra of black holes via an adiabatic invariant

By considering and using an adiabatic invariant for black holes, the area and entropy spectra of static spherically-symmetric black holes are investigated. Without using quasi-normal modes of black holes, equally-spaced area and entropy spectra are derived by only utilizing the adiabatic invariant. The spectra for non-charged and charged black holes are calculated, respectively. All these results are consistent with the original Bekenstein spectra.

基于双重分解和双向长短时记忆网络的中长期负荷预测模型

针对中长期电力负荷序列噪声含量高、难以直接提取序列周期规律从而影响预测精度的问题,提出了一种基于完全自适应噪声集合经验模态分解(complete ensemble empirical mode decomposition with adaptive noise,CEEMDAN)和奇异谱分析(singular spectrum analysis,SSA)双重分解的双向长短时记忆网络(bidirectional long and short time memory,BiLSTM)预测模型。首先,采用CEEMDAN对历史负荷进行分解,以得到若干个周期规律更为清晰的子序列;再利用多尺度熵(multiscale entropy,MSE)计算所有子序列的复杂程度,根据不同时间尺度上的样本熵值将相似的子序列重构聚合;然后,利用SSA去噪的功能,对高度复杂的新序列进行二次分解,去除序列中的噪声并提取更为主要的规律,从而进一步提高中长序列预测精度;再将得到的最终一组子序列输入BiLSTM进行预测;最后,考虑到天气、节假日等外部因素对电力负荷的影响,提出了一种误差修正技术。选取了巴拿马某地区的用电负荷进行实验,实验结果表明,经过双重分解可以将均方根误差降低87.4%;预测未来一年的负荷序列时,采用的BiLSTM模型将拟合系数最高提高2.5%;所提出的误差修正技术可将均方根误差降低9.7%。

基于ICEEMDAN和PSO-LSSVM的石油机械滚动轴承故障诊断方法研究

针对滚动轴承疲劳故障振动信号具有能量弱、特征稀疏等特点,提出了一种通过改进自适应噪声完备经验模态分解方法与粒子群优化的最小二乘支持向量机结合的故障识别方法;对轴承不同故障信号利用改进的自适应噪声完备经验模态算法分解为一系列固有模态函数分量;根据相关系数-方差贡献率准则筛选出最能表征原始信号状态的分量,并计算重构分量的奇异谱熵值构成特征向量;将提取的特征向量集合输入到基于粒子群优化的最小二乘支持向量机分类器中,进行模型的训练和故障模式的识别,与SVM和LSSVM分类器模型进行准确率和效率比较;试验结果表明,该方法在滚动轴承故障信号中能有效提取故障特征,准确率达98.75%,具有一定可靠性和实用性。

基于功率谱熵的无线电引信目标与干扰信号分类方法

无线电调频引信在战场环境容易受到干扰信号的干扰导致早炸,丧失打击能力。为提升无线电调频引信抗干扰能力,准确识别引信目标与干扰信号,提出一种基于功率谱熵特征的无线电调频引信目标与干扰信号分类识别方法。利用实测采集的无线电引信检波端输出信号,通过提取目标和干扰信号的功率谱指数熵和Renyi熵特征构成特征向量,作为K邻近(KNN)分类器的输入进行目标和干扰信号分类识别,并利用5-折交叉检验方法对其进行验证。结果表明:目标和干扰信号的功率指数熵和Renyi熵具有显著差异性,使用KNN分类器对其进行分类识别时,最高的识别准确率可达99.47%。

一种基于类小波变换的无线电频谱监测数据无损压缩方法

无线电频谱监测海量数据存储和分析是无线电监管工作的重要组成部分。频谱数据具有时间相关性以及不同频点间的相关冗余,对此本文设计了一种基于类小波变换的无线电频谱监测数据无损压缩方法。该方法首先基于时间相关性将一维频谱信号转换成二维矩阵;转换成二维矩阵后数据在水平方向以及垂直方向都存在冗余,算法采用卷积神经网络来代替传统小波中的预测和更新模块,并引入了自适应压缩块来处理不同维度的特征,从而获得更紧凑的频谱数据表示。研究进一步设计了一种基于上下文的深度熵模型,利用类小波变换不同子带系数获得熵编码参数,以此估计累积概率,从而实现频谱数据的压缩。实验结果表明,与已有的Deflate等传统频谱监测数据无损压缩方法相比,本文算法有进一步的性能提升,与典型的JPEG2000、PNG、JPEG-LS等二维图像无损压缩方法相比,本文所提出的方法的压缩效果也提高了20%以上。

ITD结合参数优化MOMEDA的滚动轴承故障特征提取

针对固有时间尺度分解(Intrinsic time scale decomposition,ITD)方法在强背景噪声影响下难以提取轴承故障特征的问题,提出了一种ITD与参数优化的多点最优最小熵解卷积(Multipoint optimal minimum entropy deconvolution adjusted,MOMEDA)相结合的滚动轴承故障特征提取方法。首先根据包络谱峰值因子最大原则提取包含丰富故障信息的ITD分量,其次对该分量进行MOMEDA降噪处理。对影响MOMEDA滤波效果的两个参数——故障周期T与滤波器长度L分别以多点峭度和平方包络谱的基尼指数进行优化,最后进行包络谱分析提取故障特征频率。通过仿真信号与实测信号分析表明该方法能在强噪声干扰下有效提取故障特征。

坡谱信息熵与区域水土流失关系研究

坡谱信息熵可以在宏观上反映地形起伏特征和地貌组合差异,且计算相对便捷。为探索坡谱信息熵与区域水土流失之间的关系,文章以西北黄土高原水土保持区为例,基于ALOS数字高程模型(空间分辨率12.5 m)计算研究区内的坡谱信息熵、土壤侵蚀模数,构建坡谱信息熵与土壤侵蚀模数之间的函数关系。研究结果表明:研究区内坡谱曲线主要为“L”形、“S”形,坡谱信息熵值在0.67~1.72nat之间;平均土壤侵蚀模数为1940t/(km^(2)·a)。在流域尺度、二级尺度和三级尺度上,构建坡谱信息熵与土壤侵蚀模数的函数模型,均呈极显著的多项式函数关系,但在流域尺度上,坡谱信息熵与土壤侵蚀模数的关系存在较大不确定性。

基于传感信号采集的电控发动机振动故障监测方法

通过调理振动信号可以更高效地监测振动故障。为此,提出基于传感信号采集的电控发动机振动故障监测方法。首先,搭建电控发电机传感信号采集与处理架构,通过放大传感信号增益、滤波和转换信号模数的方式处理待监测信号,为提高监测准确性奠定可靠的数据基础。通过小波包分解与重构,获取信号的时域参数和小波能谱熵,并构建三维特征量。然后,利用“一对一”分解策略优化孪生支持向量机,构造多元分类器,使其更适用于振动故障监测这一多类别分类问题,再输入待监测信号的特征量,通过确定故障类别实现持续性监测。仿真结果表明:该方法训练耗时的最大值仅为897 ms,对于转子摩擦振动、不平衡振动等5种类型故障的监测准确率始终在97%以上,在缩减训练样本后准确率仍保持在90%以上。