Weak Fault Feature Extraction of the Rotating Machinery Using Flexible Analytic Wavelet Transform and Nonlinear Quantum Permutation Entropy

Addressing the challenges posed by the nonlinear and non-stationary vibrations in rotating machinery,where weak fault characteristic signals hinder accurate fault state representation,we propose a novel feature extraction method that combines the Flexible Analytic Wavelet Transform(FAWT)with Nonlinear Quantum Permutation Entropy.FAWT,leveraging fractional orders and arbitrary scaling and translation factors,exhibits superior translational invariance and adjustable fundamental oscillatory characteristics.This flexibility enables FAWT to provide well-suited wavelet shapes,effectively matching subtle fault components and avoiding performance degradation associated with fixed frequency partitioning and low-oscillation bases in detecting weak faults.In our approach,gearbox vibration signals undergo FAWT to obtain sub-bands.Quantum theory is then introduced into permutation entropy to propose Nonlinear Quantum Permutation Entropy,a feature that more accurately characterizes the operational state of vibration simulation signals.The nonlinear quantum permutation entropy extracted from sub-bands is utilized to characterize the operating state of rotating machinery.A comprehensive analysis of vibration signals from rolling bearings and gearboxes validates the feasibility of the proposed method.Comparative assessments with parameters derived from traditional permutation entropy,sample entropy,wavelet transform(WT),and empirical mode decomposition(EMD)underscore the superior effectiveness of this approach in fault detection and classification for rotating machinery.

Microseismic signal denoising by combining variational mode decomposition with permutation entropy

Remarkable progress has been achieved on microseismic signal denoising in recent years,which is the basic component for rock-burst detection.However,its denoising effectiveness remains unsatisfactory.To extract the effective microseismic signal from polluted noisy signals,a novel microseismic signal denoising method that combines the variational mode decomposition(VMD)and permutation entropy(PE),which we denote as VMD–PE,is proposed in this paper.VMD is a recently introduced technique for adaptive signal decomposition,where K is an important decomposing parameter that determines the number of modes.VMD provides a predictable eff ect on the nature of detected modes.In this work,we present a method that addresses the problem of selecting an appropriate K value by constructing a simulation signal whose spectrum is similar to that of a mine microseismic signal and apply this value to the VMD–PE method.In addition,PE is developed to identify the relevant effective microseismic signal modes,which are reconstructed to realize signal filtering.The experimental results show that the VMD–PE method remarkably outperforms the empirical mode decomposition(EMD)–VMD filtering and detrended fl uctuation analysis(DFA)–VMD denoising methods of the simulated and real microseismic signals.We expect that this novel method can inspire and help evaluate new ideas in this field.

Morphology Similarity Distance for Bearing Fault Diagnosis Based on Multi-Scale Permutation Entropy

Bearings are crucial components in rotating machines,which have direct effects on industrial productivity and safety.To fast and accurately identify the operating condition of bearings,a novel method based on multi⁃scale permutation entropy(MPE)and morphology similarity distance(MSD)is proposed in this paper.Firstly,the MPE values of the original signals were calculated to characterize the complexity in different scales and they constructed feature vectors after normalization.Then,the MSD was employed to measure the distance among test samples from different fault types and the reference samples,and achieved classification with the minimum MSD.Finally,the proposed method was verified with two experiments concerning artificially seeded damage bearings and run⁃to⁃failure bearings,respectively.Different categories were considered for the two experiments and high classification accuracies were obtained.The experimental results indicate that the proposed method is effective and feasible in bearing fault diagnosis.

INVESTIGATION OF THE SPATIAL AND TEMPORAL DISTRIBUTION OF EXTREME HIGH TEMPERATURE IN CHINA WITH DETRENDED FLUCTUATION AND PERMUTATION ENTROPY

With temperatures increasing as a result of global warming,extreme high temperatures are becoming more intense and more frequent on larger scale during summer in China.In recent years,a variety of researches have examined the high temperature distribution in China.However,it hardly considers the variation of temperature data and systems when defining the threshold of extreme high temperature.In order to discern the spatio-temporal distribution of extreme heat in China,we examined the daily maximum temperature data of 83 observation stations in China from 1950 to 2008.The objective of this study was to understand the distribution characteristics of extreme high temperature events defined by Detrended Fluctuation Analysis(DFA).The statistical methods of Permutation Entropy(PE)were also used in this study to analyze the temporal distribution.The results showed that the frequency of extreme high temperature events in China presented 3 periods of 7,10—13 and 16—20 years,respectively.The abrupt changes generally happened in the 1960s,the end of 1970s and early 1980s.It was also found that the maximum frequency occurred in the early 1950s,and the frequency decreased sharply until the late 1980s when an evidently increasing trend emerged.Furthermore,the annual averaged frequency of extreme high temperature events reveals a decreasing-increasing-decreasing trend from southwest to northeast China,but an increasing-decreasing trend from southeast to northwest China.And the frequency was higher in southern region than that in northern region.Besides,the maximum and minimum of frequencies were relatively concentrated spatially.Our results also shed light on the reasons for the periods and abrupt changes of the frequency of extreme high temperature events in China.

Adaptive Bearing Fault Diagnosis based on Wavelet Packet Decomposition and LMD Permutation Entropy

Bearing fault signal is nonlinear and non-stationary, therefore proposed a fault feature extraction method based on wavelet packet decomposition （WPD） and local mean decomposition （LMD） permutation entropy, which is based on the support vector machine （SVM） as the feature vector pattern recognition device Firstly, the wavelet packet analysis method is used to denoise the original vibration signal, and the frequency band division and signal reconstruction are carried out according to the characteristic frequency. Then the decomposition of the reconstructed signal is decomposed into a number of product functions （PE） by the local mean decomposition （LMD） , and the permutation entropy of the PF component which contains the main fault information is calculated to realize the feature quantization of the PF component. Finally, the entropy feature vector input multi-classification SVM, which is used to determine the type of fault and fault degree of bearing The experimental results show that the recognition rate of rolling bearing fault diagnosis is 95%. Comparing with other methods, the present this method can effectively extract the features of bearing fault and has a higher recognition accuracy

Cloud Resource Integrated Prediction Model Based on Variational Modal Decomposition-Permutation Entropy and LSTM

Predicting the usage of container cloud resources has always been an important and challenging problem in improving the performance of cloud resource clusters.We proposed an integrated prediction method of stacking container cloud resources based on variational modal decomposition(VMD)-Permutation entropy(PE)and long short-term memory(LSTM)neural network to solve the prediction difficulties caused by the non-stationarity and volatility of resource data.The variational modal decomposition algorithm decomposes the time series data of cloud resources to obtain intrinsic mode function and residual components,which solves the signal decomposition algorithm’s end-effect and modal confusion problems.The permutation entropy is used to evaluate the complexity of the intrinsic mode function,and the reconstruction based on similar entropy and low complexity is used to reduce the difficulty of modeling.Finally,we use the LSTM and stacking fusion models to predict and superimpose;the stacking integration model integrates Gradient boosting regression(GBR),Kernel ridge regression(KRR),and Elastic net regression(ENet)as primary learners,and the secondary learner adopts the kernel ridge regression method with solid generalization ability.The Amazon public data set experiment shows that compared with Holt-winters,LSTM,and Neuralprophet models,we can see that the optimization range of multiple evaluation indicators is 0.338∼1.913,0.057∼0.940,0.000∼0.017 and 1.038∼8.481 in root means square error(RMSE),mean absolute error(MAE),mean absolute percentage error(MAPE)and variance(VAR),showing its stability and better prediction accuracy.

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.

基于PE-HMM的渡槽结构运行状态评价

随着远距离、高流量、大跨度渡槽工程的不断发展,渡槽运行状态监测与评价日益重要。以广东省罗定市长岗坡渡槽工程为例,基于渡槽泄流振动位移数据,提出一种基于排列熵算法(PE)和隐马尔可夫模型(HMM)的渡槽运行状态评价方法。首先,运用排列熵算法和K-means法提取振动位移数据基本特征,形成HMM模型的观测状态序列。其次,运用HMM算法训练模型参数,以平均误差百分比为指标,筛选出最佳模型参数,并以该参数为初值再次训练得到渡槽运行期隐状态的概率分布。最后,结合渡槽运行期隐状态对应的分值等级及概率值,求得渡槽运行状态期望值,从而量化评价渡槽运行状态。结果表明,基于PE-HMM法的渡槽运行状态评价结果与实地勘察结论一致,可见PE-HMM法能够从渡槽振动位移数据角度出发,真实反映渡槽结构运行状态,具有较高的评判精度与工程指导意义。

基于GMPE和GWO-MKELM算法的往复压缩机轴承故障诊断

针对往复压缩机内部结构复杂,轴承间隙故障特征提取困难和识别准确率不高等问题,提出了多尺度排列熵和多核极限学习机混合算法的智能诊断新方法。首先,针对多尺度排列熵在多尺度过程中,利用均值粗粒化的方式在一定程度上“中和”了原始信号的动力学突变行为,降低了熵值分析的准确性,提出了一种广义多尺度排列熵算法;然后,为解决核极限学习机处理复杂数据样本分类存在的局限性,将高斯核函数、多项式核函数和感知器核函数进行线性叠加,构建混合核函数,提出了多核极限学习机模型。仿真实验结果表明,该故障诊断方法识别准确率高达98%,高效地实现了轴承不同种类故障的智能诊断。

基于PE-CEEMD-SVD的Φ-OTDR信号降噪方法

为实现相位敏感光时域反射仪中相位信号的精确测量,提出了一种基于排列熵算法的互补集合经验模态分解联合奇异值分解的新型降噪方法(PE-CEEMD-SVD)。首先,对含有噪声的相位信号进行CEEMD分解,得到一系列频率不同的IMF分量;然后,将PE算法和相关系数机制相结合,保留较大相关的有用分量,对较小相关的噪声分量使用SVD算法进行二次降噪;最后将两次降噪后保留下来的有用分量进行重构。仿真和实验结果表明,相较于EMD、EEMD和CEEMD降噪方法,该方法可获得更高信噪比的信号,有利于相位信号的精确测量。

CEEMDAN-WPE-CLSA超短期风电功率预测方法研究

提出了一种结合自适应噪声完全集合经验模态分解、加权排列熵、卷积神经网络、长短期记忆网络和自注意力机制的超短期风电功率预测方法。首先,利用自适应噪声完全集合经验模态分解将原始风电功率时间序列自适应分解为一系列的模态分量,降低原始序列的非线性和波动性;其次,根据加权排列熵计算各模态分量间的相似性并对相似的分量进行重组,以修正自适应噪声完全集合经验模态分解的过度分解问题,使得修正后的模态分量更具规律性;最后,将重组后的分量输入卷积长短期记忆网络进行时序建模,并利用自注意力机制对卷积长短期记忆网络的神经元权重进行重新分配,提高了卷积长短期记忆网络对输入特征不确定性的适应能力。在此基础上,明确了自注意力机制和自适应噪声完全集合经验模态分解、加权排列熵在风电功率预测中的作用机制,以及风电功率信号包含的重要物理信息,证明了自适应噪声完全集合经验模态分解、加权排列熵以及自注意力机制在风电功率信号模态分解和长短期记忆网络隐层输出权重分配中的有效性。

A novel signal feature extraction technology based on empirical wavelet transform and reverse dispersion entropy

Feature extraction is an important part of signal processing,which is significant for signal detection,classification,and recognition.The nonlinear dynamic analysis method can extract the nonlinear characteristics of signals and is widely used in different fields.Reverse dispersion entropy(RDE)proposed by us recently,as a nonlinear dynamic analysis method,has the advantages of fast computing speed and strong anti-noise ability,which is more suitable for measuring the complexity of signal than traditional permutation entropy(PE)and dispersion entropy(DE).Empirical wavelet transform(EWT),based on the theory of wavelet analysis,can decompose a complex non-stationary signal into a number of empirical wavelet functions(EWFs)with compact support set spectrum,which has better decomposition performance than empirical mode decomposition(EMD)and its improved algorithms.Considering the advantages of RDE and EWT,on the one hand,we introduce EWT into the field of underwater acoustic signal processing and fault diagnosis to improve the signal decomposition accuracy;on the other hand,we use RDE as the features of EWFs to improve the signal separability and stability.Finally,we propose a novel signal feature extraction technology based on EWT and RDE in this paper.Experimental results show that the proposed feature extraction technology can effectively extract the complexity features of actual signals.Moreover,it also has higher distinguishing ability for different types of signals than five latest feature extraction technologies.

RCMNAAPE在旋转机械故障诊断中的应用

针对精细复合多尺度排列熵(RCMPE)无法充分提取旋转机械振动信号中的故障信息,从而导致旋转机械故障识别准确率不稳定这一缺陷,提出了一种基于精细复合多尺度归一化幅值感知排列熵(RCMNAAPE)、拉普拉斯分数(LS)和灰狼算法优化支持向量机(GWO-SVM)的旋转机械故障诊断方法。首先,利用幅值感知排列熵替换了RCMPE中的排列熵,提出了RCMNAAPE,并将其用于提取旋转机械振动信号的故障特征生成特征样本;随后,采用了LS从原始的高维故障特征向量中筛选出较少的能够更准确描述故障状态的特征,构造敏感特征样本;最后,将低维的故障特征向量输入由灰狼算法优化的支持向量机中进行了训练和测试,完成了旋转机械样本的故障识别和分类,利用滚动轴承和齿轮箱故障数据集将RCMNAAPE-LS-GWO-SVM与其他故障诊断方法进行了对比分析,并开展了评估。研究结果表明:基于RCMNAAPE-LS-GWO-SVM的故障诊断方法能够有效识别旋转机械的各类故障,其识别准确率高于其他对比的故障诊断方法,其中滚动轴承故障的识别准确率达到99.33%,齿轮箱故障的识别准确率达到98.67%。虽然,该方法的特征提取效率不佳,平均特征提取时间分别为153.02 s和163.98 s,仅优于精细复合多尺度模糊熵(RCMFE),但其综合性能更加优异。

基于VMD-PE-MulitiBiLSTM的超短期风电功率预测

为减少超短期风电功率预测的误差,提出基于变分模态分解(variational mode decomposition,VMD)-排列熵(permutation entropy,PE)和多层双向长短时记忆(multilayer bidirectional long short-term memory,MultiBiLSTM)组合的超短期风电功率预测模型。首先,利用VMD分解算法将历史风电功率序列分解成若干个子模态分量,根据计算的PE值重构分解的子模态风电分量;然后,使用特征注意力(feature attention,FA)机制和深度残差级联网络(deep residual cascade network,DRCnet)构建MulitiBiLSTM预测模型,预测重构后的子序列;最后,重构子序列预测值,得到最终风电功率预测结果。使用贵州某风场的数据集对所提出的方法进行验证,并和其他预测模型进行对比。结果表明,使用VMD-PE-MultiBiLSTM模型能显著降低风电功率预测误差。

基于参数优化的VMD和PE的变频负载漏电信号提取方法

针对在室内建筑电气火灾风险管理中变频负载发生漏电故障时,线路中故障剩余电流包含大量噪声干扰容易造成误报警的问题,提出了一种基于参数优化的变分模态分解和排列熵的变频负载漏电信号提取方法。首先,对原始信号根据粒子群算法优化得到的分解个数和惩罚因子进行变分模态分解;然后,利用排列熵筛选出包含故障信息的本征模态分量,并重构得到故障剩余电流信号;最后,与完全集合经验模态分解算法结合排列熵进行比较。结果表明,所提算法能快速准确地提取出变频负载漏电时产生的故障剩余电流信号,为变频负载漏电信号提取提供了新的思路。

基于DIGWO-VMD-CMPE的轴承故障识别方法

针对滚动轴承故障信号特征提取困难和识别准确率低的问题,提出了一种基于维度学习的改进灰狼优化算法(DIGWO)优化变分模态分解(VMD)和复合多尺度排列熵(CMPE)的轴承故障识别方法。首先,采用基于维度学习的狩猎(DLH)搜索策略、余弦收敛因子a和个体狼ω位置更新的方法将灰狼优化算法(GWO)改进为DIGWO,并利用DIGWO算法的自适应性优化VMD分解,得到了多个本征模态函数(IMFs);然后,利用复合多尺度排列熵计算IMFs的特征值,选取适当维数的特征,构建了故障特征向量;最后,利用DIGWO算法优化支持向量机(SVM)的惩罚系数C和径向基函数g,建立了DIGWO-SVM滚动轴承故障诊断分类器,并利用滚动轴承的振动数据验证了算法的有效性。研究结果表明:基于CMPE的DIGWO-SVM滚动轴承故障诊断方法能够有效地识别轴承的运行状况,识别准确率达到了99.42%,相较于PSO-SVM、SSA-SVM方法提高了7.75%、1.68%,证明了该方法的分类性能在滚动轴承故障诊断中更具优势。

基于ICEEMDAN-MPE和GWO-SVM的滚动轴承故障诊断方法

针对滚动轴承故障状态难以准确且快速的识别,提出了一种基于改进自适应噪声完备集成经验模态分解(Improved Complementary Ensemble Empirical Mode Decomposition with Adaptive Noise,ICEEMDAN)-多尺度排列熵(Multi-Scale Permutation Entropy,MPE)和灰狼算法优化支持向量机(Grey Wolf Optimization Algorithm-Support Vector Machine,GWO-SVM)结合的故障诊断方法。首先将轴承信号进行ICEEMDAN分解,然后选取其中相关性较大的IMF(Intrinsic Mode Function)分量计算多尺度排列熵构成特征集合,最后通过GWO-SVM算法进行故障状态识别。通过滚动轴承数据集和不同算法的对比实验,验证了ICEEMDAN-MPE-GWO-SVM方法的有效性,表明该方法可以准确且快速的诊断滚动轴承的故障情况。

基于EEMD-SVD-PE的轨道波磨趋势项提取

钢轨波磨检测是保障行车安全的重要手段,针对复杂钢轨线路波磨数据中的轨道起伏趋势提取问题,提出了一种基于排列组合熵(Permutation Entropy, PE)选取低复杂度奇异值分量重构趋势的EEMD-SVD信号去趋方法.相比已有的经验模式分解去趋算法,该方法考虑到原始IMF可能存在的信号成分混杂问题(如含有白噪声与信号的低频成分),首次提出通过奇异值分解来精确提取隐藏在多维IMF矩阵中的趋势项成分作为奇异值分量.由于协方差矩阵构建的奇异值分量排列时只考虑了能量的分布而未考虑趋势项信号低复杂度、高幅的特点,使用排列组合熵来选出符合趋势项特征的奇异值分量,最后对满足要求的奇异值分量进行重建得到最终的趋势项.为验证本文方法的有效性,分别进行了数字仿真和实际钢轨波磨数据去趋实验.数字仿真实验结果表明该方法整体去趋性能优于低通滤波法、与EMD结合的线性规划法和小波分解法,尤其在多信噪比的仿真实验中,当信噪比较低时,提趋准确率最大提高约30%.同时,实际钢轨波磨数据去趋实验说明本文方法能够适用于钢轨波磨检测.

基于VMD-PE和优化相关向量机的短期风电功率预测

针对风电功率序列非线性、非平稳性等特点,提出一种基于变分模态分解(VMD).排列熵(PE)和混沌布谷鸟搜索算法(CCS)优化相关向量机的短期风电功率预测新方法。为降低风电功率序列非平稳性和减小计算规模,首先采用变分模态分解技术(VMD),将原始风电功率序列分解成一系列不同的子模态,利用排列熵(PE)分析其复杂度并重组得到子序列;然后采用CCS优化后的相关向量机(CCS.RVM)对各子序列进行提前24h预测;最后将预测结果叠加得到最终预测值,并利用某风电场实际采集数据进行仿真验证。结果表明,所提预测模型能有效提高风电功率预测的准确性。

基于CEEMDAN-PE的心冲击信号降噪方法研究

心冲击信号(BCG)是反应心脏力学特征的生理信号,能实现无电极束缚条件下的连续采集测量,然而BCG信号微弱且极易受到干扰,测量时经常会淹没在噪声中。为了有效识别BCG信号,提出一种基于自适应噪声的完全集合经验模态分解(CEEMDAN)联合排列熵(PE)的BCG降噪方法。首先,将采集到的BCG信号通过CEEMDAN分解得到一系列按频率由高到低的固有模态函数(IMF)。其次,通过PE计算各个IMF分量的值并确定有效信号的阈值范围,从而滤除信号中的高频噪声和基线漂移。最后实验结果显示,降噪后信号的幅频特性得到明显改善且信噪比较传统方法有明显提高,证明了本文降噪方法效果显著,能够有效还原BCG信号特征。