Comparison study of typical algorithms for reconstructing time series from the recurrence plot of dynamical systems

The three most widely used methods for reconstructing the underlying time series via the recurrence plots （RPs） of a dynamical system are compared with each other in this paper. We aim to reconstruct a toy series, a periodical series, a random series, and a chaotic series to compare the effectiveness of the most widely used typical methods in terms of signal correlation analysis. The application of the most effective algorithm to the typical chaotic Lorenz system verifies the correctness of such an effective algorithm. It is verified that, based on the unthresholded RPs, one can reconstruct the original attractor by choosing different RP thresholds based on the Hirata algorithm. It is shown that, in real applications, it is possible to reconstruct the underlying dynamics by using quite little information from observations of real dynamical systems. Moreover, rules of the threshold chosen in the algorithm are also suggested.

Classification of Short Time Series in Early Parkinson’s Disease With Deep Learning of Fuzzy Recurrence Plots

There are many techniques using sensors and wearable devices for detecting and monitoring patients with Parkinson’s disease(PD).A recent development is the utilization of human interaction with computer keyboards for analyzing and identifying motor signs in the early stages of the disease.Current designs for classification of time series of computer-key hold durations recorded from healthy control and PD subjects require the time series of length to be considerably long.With an attempt to avoid discomfort to participants in performing long physical tasks for data recording,this paper introduces the use of fuzzy recurrence plots of very short time series as input data for the machine training and classification with long short-term memory(LSTM)neural networks.Being an original approach that is able to both significantly increase the feature dimensions and provides the property of deterministic dynamical systems of very short time series for information processing carried out by an LSTM layer architecture,fuzzy recurrence plots provide promising results and outperform the direct input of the time series for the classification of healthy control and early PD subjects.

Recognition of dynamically varying PRI modulation via deep learning and recurrence plot

Recognition of pulse repetition interval(PRI)modulation is a fundamental task in the interpretation of radar intentions.However,the existing PRI modulation recognition methods mainly focus on single-label classification of PRI sequences.The prerequisite for the effectiveness of these methods is that the PRI sequences are perfectly divided according to different modulation types before identification,while the actual situation is that radar pulses reach the receiver continuously,and there is no completely reliable method to achieve this division in the case of non-cooperative reception.Based on the above actual needs,this paper implements an algorithm based on the recurrence plot technique and the multi-target detection model,which does not need to divide the PRI sequence in advance.Compared with the sliding window method,it can more effectively realize the recognition of the dynamically varying PRI mo dulation.

Middle ear reconstruction estimated by recurrence plot technique

Middle ear surgery techniques have enabled to improve hearing destroyed by a disease. Despite huge improvement in instrumentation and techniques the results of hearing improvement surgery are still difficult to predict. This paper presents the results of vibrations measurements in a human middle ear obtained at the Medical University of Lublin. Vibrations of the stapes in the case of the intact ossicular chain, after cement incus rebuilding and incus interpositions are compared each other. In this aim a new approach of ossicles vibrations observation is introduced in order to complete information obtained from classical approach which bases on the transfer function. Measurements of ossicular chain vibrations are performed on fresh human temporal bone specimen using the laser doppler vibrometer. Next, after classical research, the extended analysis with the recurrence plots technique is performed.

Analysis of Key Features of Non-Linear Behavior Using Recurrence Plots. Case Study: Urban Pollution at Mexico City

The use of Recurrence plots have been extensively used in various fields. In this work, Recurrence Plots (RPs) investigates the changes in the non-linear behaviour of urban air pollution using large datasets of raw data (hourly). This analysis has not been used before to extract information from large datasets for this type non-linear problem. Two different approaches have been used to tackle this problem. The first approach is to show results according to monitoring network. The second approach is to show the results by particle type. This analysis shows the feasibility of using Recurrence Analysis for pollution monitoring and control.

Nonlinear dynamics in Divisia monetary aggregates:an application of recurrence quantification analysis

We construct recurrence plots(RPs)and conduct recurrence quantification analysis(RQA)to investigate the dynamic properties of the new Center for Financial Stability(CFS)Divisia monetary aggregates for the United States.In this study,we use the lat-est vintage of Divisia aggregates,maintained within CFS.We use monthly data,from January 1967 to December 2020,which is a sample period that includes the extreme economic events of the 2007–2009 global financial crisis.We then make comparisons between narrow and broad Divisia money measures and find evidence of a nonlinear but reserved possible chaotic explanation of their origin.The application of RPs to broad Divisia monetary aggregates encompasses an additional drift structure around the global financial crisis in 2008.Applying the moving window RQA to the growth rates of narrow and broad Divisia monetary aggregates,we identify periods of changes in data-generating processes and associate such changes to monetary policy regimes and financial innovations that occurred during those times.

Recurrence Quantification Analysis of Rough Surfaces Applied to Optical and Speckle Profiles

In this paper, Recurrence Quantification Analysis (RQA) is set as a practical nonlinear data tool to establish and compare surface roughness (Ra) through percentage parameters of a dynamical system: Recurrence (%REC), Determinism (%DET) and Laminarity (%LAM). Variations in surface roughness of different machining procedures from a typical metallic casting comparator are obtained from scattering intensity of a laser beam and expressed as changes in the statistics of speckle patterns and profiles optical properties. The application of the analysis (RQA) by Recurrence Plots (RPs), allowed to distinguish between machining procedures, highlighting features that other methods are unable to detect.

基于CRP和RQA的变压器绕组压紧状态检测

为了掌握绕组压紧力状况,通过分析变压器表面振动变化情况,提出了基于交叉递归图(Cross Recurrence Plot,CRP)和递归定量分析(Recurrence Quantification Analysis,RQA)的绕组压紧状态检测方法。首先,从振动信号的递归特性出发,对多元和一元振动信号进行相空间重构。然后,分别采用CRP和RQA对相轨迹进行定性和定量分析,据此对绕组压紧状态进行检测。实验数据的分析结果表明,CRP中对角线结构的变化能定性反映出绕组压紧状态的变化,多元与一元振动信号的RQA度量能够分别从整体和局部角度对绕组压紧状态进行定量检测。研究结果为从非线性动力学角度监测绕组松动故障提供了理论依据。

基于RP-CNN的柴油机故障识别

为了在故障诊断的过程中充分利用数据间存在的时间信息,提出一种递归图-卷积神经网络(RP-CNN)的柴油机故障识别模型。将一维振动信号通过递归图原理编码成为图像作为卷积神经网络的训练样本,完成柴油机的故障特征提取与分类。通过不同的编码方式以及不同的诊断模型进行对比试验。结果表明,卷积神经网络在识别图像上的优势与递归图编码相结合的诊断方式优于其他的智能算法。

基于知识蒸馏与RP-MobileNetV3的电能质量复合扰动识别

针对复合电能质量扰动(power quality disturbance,PQD)识别中特征提取复杂、识别正确率低和模型难以轻量化等问题,提出一种利用递归图(recurrence plot,RP)对PQD信号可视化方法和基于知识蒸馏的模型训练方法。首先,基于RP挖掘PQD信号隐含特征并构建图像数据集,并利用深度残差收缩网络(deep residual shrinkage network,DRSN)对图像数据集进行更深层次特征提取并完成自主分类。然后,基于知识蒸馏(knowledge distillation,KD)让已训练的DRSN指导轻量化网络MobileNetV3进行训练,通过蒸馏实现知识的跨网络传输。最后,仿真实验和硬件实验表明,利用知识蒸馏训练的MobileNetV3能实现高精度且轻量化的复合扰动识别,同时在30 dB噪声环境下正确率能提升1.06%,对实际扰动信号识别效果良好,具有良好的噪声鲁棒性。

基于CRP和RQA的高压并联电抗器振动信号分析

并联电抗器油箱表面的振动信号与电抗器绕组和铁心的状态密切相关。因此,可以通过振动信号来监测并联电抗器绕组和铁心状态。本文针对电抗器振动信号的非线性特征,提出了一种基于交叉递归图(CRP)与递归量化分析(RQA)相结合的信号处理方法,对铁心饼上表面振动信号与油箱表面多个测点信号的相关性进行研究。实验结果表明,该方法不仅能定性描述电抗器不同测点信号的相关性,还可利用提取的RQA参量对递归现象定量表述。研究结果从非线性动力学角度为高压并联电抗器振动敏感区域确定及振动测点选取提供了依据。

A pre-warning system of abnormal energy consumption in lead smelting based on LSSVR-RP-CI

The pre-warning of abnormal energy consumption is important for energy conservation of industrial engineering. However, related studies on the lead smelting industries which usually have a huge energy consumption are rarely reported. Therefore, a pre-warning system was established in this study based on the intelligent prediction of energy consumption and the identification of abnormal energy consumption. A least square support vector regression (LSSVR) model optimized by the adaptive genetic algorithm was developed to predict the energy consumption in the process of lead smelting. A recurrence plots (RP) analysis and a confidence intervals (CI) analysis were conducted to quantitatively confirm the stationary degree of energy consumption and the normal range of energy consumption, respectively, to realize the identification of abnormal energy consumption. It is found the prediction accuracy of LSSVR model can exceed 90% based on the comparison between the actual and predicted data. The energy consumption is considered to be non-stationary if the correlation coefficient between the time series of periodicity and energy consumption is larger than that between the time series of periodicity and Lorenz. Additionally, the lower limit and upper limit of normal energy consumption are obtained.

基于VAE预处理和RP-2D CNN的不平衡负荷数据类型辨识方法

针对负荷数据类型辨识中存在的类别不平衡及特征提取不足的问题,提出一种基于变分自编码器预处理和递归图-二维卷积神经网络的不平衡负荷数据类型辨识方法。首先,利用变分自编码器的过采样方法对少数类样本进行平衡化处理。然后,使用递归图算法将负荷曲线图像化。最后,根据二维卷积神经网络求取分类结果。算例分析表明,变分自编码器能有效地改善负荷数据中存在的类别不平衡问题,提高少数类的召回率;同时,相比于序列输入的分类器模型,经过递归图编码后,其图像输入的二维卷积神经网络模型有更高的分类准确度。

基于RP与NMF的内燃机气阀故障诊断方法

针对传统的内燃机故障振动诊断方法,难以有效提取故障特征,诊断精度较低的缺点,提出一种基于递归图(recurrence plots,RP)与非负矩阵分解(non-negative matrix factorization,NMF)的内燃机故障诊断新方法。该方法是利用图像的方法来进行故障诊断:首先通过递归图将采集到的内燃机缸盖表面振动信号生成图像,然后用非负矩阵对得到递归图进行特征参数提取,最后用分类器进行分类识别完成故障诊断。将该方法应用于气阀机构8种工况下振动信号诊断实例中,结果表明:该方法克服了传统的振动诊断方法从时域或频域进行分析时参数选取和故障特征提取的难题,直接将信号生成图像,对图像进行自适应特征参数提取、分类识别,能有效诊断出内燃机气阀机构故障,故障识别精度高,为内燃机振动诊断探索了一条新途径。

基于IRP和TD2DPCA的轴承故障诊断方法

针对轴承振动信号的非平稳特征和现实中难以提取故障参数的情况,提出了一种基于图像的轴承故障诊断方法即基于递归灰度图(Improved Recurrence Plots,IRP)和双向二维主成分分析(Two directional,Two dimensional Principal Component Analysis,TD2DPCA)的轴承故障诊断法。该方法对递归图(Recurrence Plots,RP)中阈值选取的问题进行了优化,提出了IRP算法,对采集到的轴承振动信号进行IRP分析,生成递归灰度图;然后用TD2DPCA对生成的递归灰度图进行特征参数提取,得到系数编码矩阵;最后采用分类器对上述编码矩阵直接进行模式识别,以实现轴承故障的自动化诊断。将该方法应用在轴承4种典型工况的故障诊断实例中,识别率高达99.8%,结果表明:基于IRP和TD2DPCA的轴承故障诊断方法能够自适应的对轴承进行故障诊断,具有故障识别精度高、噪声鲁棒性好等优点,为轴承振动诊断探索了一条新途径。

基于电容传感器的CO_(2)气液两相流流型识别

为了实现碳捕捉与封存(CCS)管道内CO_(2)流量的精确测量,需要对CO_(2)的流型进行辨识。基于递归定量分析和模糊C均值(FCM)聚类算法,建立了CO_(2)气液两相流的流型识别模型。提出利用小波变换在多尺度下分析CO_(2)气液两相流电容信号递归图结构特性的方法,对各个尺度下的递归图分别进行定量分析,提取出不同流型下CO_(2)流动的电容传感器递归特征参数。采用FCM算法,对特征参数进行流型聚类,完成了对CO_(2)气液两相流的分层流、气泡流和雾状流3种流型的识别。

基于递归图和增强残差网络的轴承故障诊断

针对噪声干扰情况下轴承振动信号特征难以充分提取,故障识别精度低的问题,提出将递归图与增强深度残差网络相结合的RP-EResNet模型并应用于轴承故障诊断。将非线性的振动信号嵌入到具有可变时滞的延迟坐标空间中生成二维的递归图,并将压缩-激励模块、多尺度卷积、分组卷积网络模块融合到残差网络结构中得到增强的RP-EResNet模型,最终将递归图输入RP-EResNet模型中进行轴承故障诊断。使用不同的轴承数据集验证了RP-EResNet模型的性能,消融试验和对比试验的结果表明:与不同的深度学习方法相比,RP-EResNet模型能够在强噪声下增强特征提取能力,提升轴承故障的识别精度,具有良好的泛化性能和抗噪性能。

基于尺度递归分析的恶性室性心律失常检测

为及时准确地检测恶性室性心律失常,本研究提出了一种结合心电多尺度分析与递归量化分析(recurrence quantification analysis, RQA)的方法。首先,通过固定频率经验小波变换滤波器组将心电信号(electrocardiogram, ECG)分解为两个子信号(0.5~10 Hz、10~30 Hz),并分别映射为递归图;然后基于0.5~10 Hz频段子信号与原信号构建交叉递归图,从三张递归图中提取RQA特征;最后将特征输入XGBoost分类器进行特征排序与筛选,实现ECG的准确分类。本研究使用MIT-BIT恶性室性心律失常数据库和Creighton大学室性快速性心律失常数据库进行实验。在10折交叉验证下,该方法对5 s心电的恶性室性心律失常检测的灵敏度、特异性、准确率分别为97.40%、99.01%和98.69%。本研究方法在检测恶性室性心律失常方面具有一定的可靠性。

基于ISAM-Drsnet的故障识别模型及其应用

针对滚动轴承故障诊断时网络模型在复杂环境下有效特征提取困难,无法充分挖掘具有周期性的滚动轴承故障数据时序特征的问题,提出了一种基于改进条纹注意力机制与深度残差收缩网络的滚动轴承故障诊断模型(ISAM-Drsnet)。首先,采用递归图(RP)编码方式生成了二维图像,使用ISAM和改进软阈值算法加强了Drsnet;然后,采取重叠采样的方式对数据集进行了增强处理,并将数据输入到ISAM-Drsnet中,实现了对不同故障类型的识别目的;最后,利用凯斯西储大学滚动轴承数据集进行了实验,选取了最佳数据截取长度,研究了改进软阈值、数据集规模、噪声对模型的影响;同时,将该模型与支持向量机(SVM)、反向传播神经网络(BPNN)、卷积神经网络(CNN)等进行了对比分析,并采用混淆矩阵等可视化方法对该模型进行了性能评估。实验结果表明:该模型(方法)的故障诊断性能明显优于SVM、BPNN、CNN等模型,其故障诊断精度可达99.79%,相比原始的Drsnet上升了1.60%;且在数据集规模有限和信号添加噪声的情况下,模型仍具有较高的故障诊断精度。研究结果表明:该轴承故障诊断模型不仅具有优秀的诊断性能,同时还具有较强的鲁棒性。

极端事件冲击下原油期货市场有效性的演变特征

原油期货市场极易受到地缘政治冲突和金融危机等极端事件冲击的影响,基于多重分形降趋波动分析和递归图方法构建了4种指标,量化分析了上海原油期货市场的有效性,并以国际原油Brent和WTI期货市场作为对比,系统地研究了极端事件冲击下市场有效性的动态演变特征。最后,对WTI原油期货市场的长历史数据进行了分析。研究发现:在相同的样本期间内,由于中国原油期货的制度优势、审慎适时的风控政策和具有强大韧性的经济基本面,极端事件冲击对国际原油期货市场有效性的负面影响要大于国内市场,从而使得上海原油期货市场的有效性在不同时间尺度下都高于Brent和WTI原油期货市场;原油期货市场的有效性不是固定不变的,具有显著的均值回复特征,极端突发事件会对原油期货市场的有效性造成严重的负面冲击,由于原油期货市场系统具有自我修复的能力,外生冲击造成的短暂动荡会被逐渐吸收化解,以维持自身市场有效性的相对稳定。所构建的市场有效性指标对预警原油期货市场风险具有一定的效果。