Recurrence Plots Research Articles

Design of an epidemic prevention and control bracelet system integrated with convolutional neural networks: Promote real-time physiological feedback and adaptive training in remote physical education

This study aims to design an epidemic prevention and control bracelet system that integrates convolutional neural network (CNN). This system can collect and process the user’s physiological index data in real time, especially in the remote physical education scene, and provide learners with immediate physiological index feedback and personalized adaptive training suggestions through accurate human action recognition (HAR) technology. One-dimensional acceleration signal is converted into two-dimensional image, and CNN’s powerful feature extraction and classification ability is used to effectively solve the problem that manual feature extraction is complex and nonlinear features are difficult to capture. By considering the joint action trajectory in the time window, a dynamic Recurrence Plot (RP) is constructed to capture the dynamic changes among joints. To input recursive graph data into CNN, it needs to be converted into image form. In the task of HAR, CNN can automatically learn useful features from images without manually designing features. It can not only effectively extract features from images, but also be directly used in classification tasks. Experimental results show that compared with other algorithms, the proposed RP + CNN model has the best performance in action recognition, with an accuracy of 96.89% and a F1 value of 86.76%. RP captures the dynamic patterns and periodic behaviors in time series by visualizing the repeated appearance of system states over time. The RP + CNN model is used to extract and classify human action features, which significantly improves the accuracy and efficiency of HAR. This innovative method not only simplifies the complex process of traditional manual feature extraction, but also enhances the system’s ability to identify nonlinear and complex action patterns, which provides strong technical support for remote physical education.

Soliton Solutions and Chaotic Dynamics of the Ion-Acoustic Plasma Governed by a (3+1)-Dimensional Generalized Korteweg–de Vries–Zakharov–Kuznetsov Equation

This study explores the novel dynamics of the (3+1)-dimensional generalized Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation. A Galilean transformation is employed to derive the associated system of equations. Perturbing this system allows us to investigate the presence and characteristics of chaotic behavior, including return maps, fractal dimension, power spectrum, recurrence plots, and strange attractors, supported by 2D and time-dependent phase portraits. A sensitivity analysis is demonstrated to show how the system behaves when there are small changes in initial values. Finally, the planar dynamical system method is used to derive anti-kink, dark soliton, and kink soliton solutions, advancing our understanding of the range of solutions admitted by the model.

Understanding Electric Current Effects on Tribological Behaviors of Instantaneous Current-Carrying Pair With Recurrence Plot

Abstract Armature–rail instantaneous current-carrying friction in electromagnetic launchers refers to a sliding electric-mechanical impact friction and transition-induced arc erosion on a millisecond time scale. To reveal the electric current (50–300 A) effects on friction behavior and wear mechanism, the instantaneous current-carrying friction tests were performed with Al 1060 and Brass H62. Given the short nonlinear friction-induced signals, the friction behavior, including the time-domain information and system state, was comprehensively analyzed via frictional sound pressure (FSP), recurrence plot (RP), and recurrence quantification analysis (RQA). The wear topography was observed and characterized by the multifractal spectrum. Recurrence analyses demonstrate that as the current increases, the nonstationarity of the system state weakens, and the complexity and unpredictability enhance. Higher currents reduce the FSP amplitude, i.e., enhance the interfacial lubrication effect, but intensify electrical wear and surface roughness. This signifies a wear mechanism transition from abrasive wear and slight adhesive wear to arc ablation, fatigue wear, and severe adhesive wear. The widening spectrum width implies that the irregularity and fluctuation of the topography are enhanced with the current. RP patterns and RQA quantifiers correlate with the wear damage state. The results provide a reference for antiwear design and online degradation tracking of the rail.

Feature-fused residual network for time series classification

In various fields such as healthcare and transportation, accurately classifying time series data can provide important support for decision-making. To further improve the accuracy of time series classification, we propose a Feature-fused Residual Network based on Multi-scale Signed Recurrence Plot (MSRP-FFRN). This method transforms one-dimensional time series into two-dimensional images, representing the temporal correlation of time series in a two-dimensional space and revealing hidden details within the data. To enhance these details further, we extract multi-scale features by setting receptive fields of different sizes and using adaptive network depths, which improves image quality. To evaluate the performance of this method, we conducted experiments on 43 UCR datasets and compared it with nine state-of-the-art baseline methods. The experimental results show that MSRP-FFRN ranks first on critical difference diagram, achieving the highest accuracy on 18 datasets with an average accuracy of 89.9%, making it the best-performing method overall. Additionally, the effectiveness of this method is further validated through metrics such as Precision, Recall, and F1 score. Results from ablation experiments also highlight the efficacy of the improvements made by MSRP-FFRN.

The Application of the Recurrence Plot to Analyze Rubbing in An Unbalance Rotating Disk

The Application of the Recurrence Plot to Analyze Rubbing in An Unbalance Rotating Disk

Mesoscale eddy in situ observation and characterization via underwater glider and complex network theory.

Mesoscale eddies have attracted increased attention due to their central role in ocean energy and mass transport. The observations of their three-dimensional structure will facilitate the understanding of nonlinear eddy dynamics. In this paper, we propose a novel framework, the mesoscale eddy characterization from ordinal modalities recurrence networks method (MeC-OMRN), that utilizes a Petrel-II underwater glider for in situ observations and vertical structure characterization of a moving mesoscale eddy in the northern South China Sea. First, higher resolution continuous observation profile data collected throughout the traversal by the underwater glider are acquired and preprocessed. Subsequently, we analyze and compute these nonlinear data. To further amplify the hidden structural features of the mesoscale eddy, we construct ordinal modalities sequences rich in spatiotemporal characteristics based on the measured vertical density of the mesoscale eddy. Based on this, we employ ordinal modalities recurrence plots (OMRPs) to depict the vertical structure inside and outside the eddy, revealing significant differences in the OMRPs and the unevenness of density stratification within the eddy. To validate our intriguing findings from the perspective of complex network theory, we build the multivariate weighted ordinal modalities recurrence networks, through which network measures exhibit a more random distribution of vertical density stratification within the eddy, possibly due to more intense vertical convection and oscillations within the eddy's seawater micelles. These framework and intriguing findings are anticipated to be applied to more data-driven in situ observation tasks of oceanic phenomena.

Denoising diffusion probabilistic model enhanced tool condition monitoring method under imbalanced conditions

Abstract In recent years, tool condition monitoring (TCM) based on deep learning has been widely considered and achieved remarkable success. However, these methods typically require relatively large training samples to produce significant results, which are both imbalanced and rather troublesome to obtain in the practical application of TCM. To address this issue, a novel TCM method combined with multiscale permutation entropy (MPE), denoising diffusion probabilistic model (DDPM) and a residual network (ResNet) is proposed under conditions of sample imbalance. First, the one-dimensional sensing signal data is converted to a grayscale recurrence plot (RP) by minimizing the MPE of the signals in each channel. Second, combine and splice these grayscale RPs from different channels in each sample into color RPs. After that, the generated RP images using DDPM are added to the imbalanced dataset to augment the data to achieve a balanced state of the dataset. Finally, the balanced mixed data set of real and fake samples is input into a ResNet for recognition and monitoring tool conditions. TCM experiments are conducted to verify the performance of the proposed method with imbalanced dataset, and the results of experimental investigation demonstrate that the accuracy of the proposed method improved by 2%–18.8% compared to that of the other four sample augmentation methods using ResNet18 when the imbalance rate is 1:200.

Enhanced CAD Detection Using Novel Multi-Modal Learning: Integration of ECG, PCG, and Coupling Signals.

Early and highly precise detection is essential for delaying the progression of coronary artery disease (CAD). Previous methods primarily based on single-modal data inherently lack sufficient information that compromises detection precision. This paper proposes a novel multi-modal learning method aimed to enhance CAD detection by integrating ECG, PCG, and coupling signals. A novel coupling signal is initially generated by operating the deconvolution of ECG and PCG. Then, various entropy features are extracted from ECG, PCG, and its coupling signals, as well as recurrence deep features also encoded by integrating recurrence plots and a parallel-input 2-D CNN. After feature reduction and selection, final classification is performed by combining optimal multi-modal features and support vector machine. This method was validated on simultaneously recorded standard lead-II ECG and PCG signals from 199 subjects. The experimental results demonstrate that the proposed multi-modal method by integrating all signals achieved a notable enhancement in detection performance with best accuracy of 95.96%, notably outperforming results of single-modal and joint analysis with accuracies of 80.41%, 86.51%, 91.44%, and 90.42% using ECG, PCG, coupling signal, and joint ECG and PCG, respectively. This indicates that our multi-modal method provides more sufficient information for CAD detection, with the coupling information playing an important role in classification.

Coronary Artery Disease Detection Based on a Novel Multi-Modal Deep-Coding Method Using ECG and PCG Signals.

Coronary artery disease (CAD) is an irreversible and fatal disease. It necessitates timely and precise diagnosis to slow CAD progression. Electrocardiogram (ECG) and phonocardiogram (PCG), conveying abundant disease-related information, are prevalent clinical techniques for early CAD diagnosis. Nevertheless, most previous methods have relied on single-modal data, restricting their diagnosis precision due to suffering from information shortages. To address this issue and capture adequate information, the development of a multi-modal method becomes imperative. In this study, a novel multi-modal learning method is proposed to integrate both ECG and PCG for CAD detection. Along with deconvolution operation, a novel ECG-PCG coupling signal is evaluated initially to enrich the diagnosis information. After constructing a modified recurrence plot, we build a parallel CNN network to encode multi-modal information, involving ECG, PCG and ECG-PCG coupling deep-coding features. To remove irrelevant information while preserving discriminative features, we add an autoencoder network to compress feature dimension. Final CAD classification is conducted by combining support vector machine and optimal multi-modal features. The experiment is validated on 199 simultaneously recorded ECG and PCG signals from non-CAD and CAD subjects, and achieves high performance with accuracy, sensitivity, specificity and f1-score of 98.49%, 98.57%,98.57% and 98.89%, respectively. The result demonstrates the superiority of the proposed multi-modal method in overcoming information shortages of single-modal signals and outperforming existing models in CAD detection. This study highlights the potential of multi-modal deep-coding information, and offers a wider insight to enhance CAD diagnosis.

Enhanced probabilistic damage localization for composite plate based on joint recurrence plots

Localizing damage is a key aspect of monitoring composite laminate structural health. To address the problem of generating the damage index (DI) of composite laminates using Lamb waves, a reconstruction approach for probabilistic damage inspection (RAPID) based on joint recurrence plots (JRP) was proposed. First, the dynamics of the Lamb wave signals are analyzed using phase space reconstruction. Second, the damage information in each sensing path is represented using JRP, and the DI based on the JRP is built with variational auto-encoder (VAE). Finally, the relative magnitude of the DI was employed to modify RAPID’s weight distribution function, allowing for composite plate damage localization detection. The findings of finite element modeling and experiment data reveal that the approach can achieve accurate localization imaging of the composite plate’s interior damage while also properly identifying the damage under 20 dB and 10 dB noise interference. The approach does not require an understanding of Lamb wave dispersion characteristics and involve the extraction of complicated wave packet signals, making it promising for structural health monitoring based on damage index.

Frequency–Time Domain Analysis Based on Electrochemical Noise of Dual-Phase (DP) and Ferrite–Bainite (FB) Steels in Chloride Solutions for Automotive Applications

The automotive industry uses high-strength (HS), low-alloy (HSLA) steels and advanced high-strength steels (AHSSs) to manufacture front and rear rails and safety posts, as well as the car body, suspension, and chassis components of cars. These steels can be exposed to corrosive environments, such as in countries where de-icing salts are used. This research aims to characterize the corrosion behavior of AHSSs based on electrochemical noise (EN) [dual-phase (DP) and ferrite–bainite (FB)]. At room temperature, the steels were immersed in NaCl, CaCl2, and MgCl2 solutions and were studied by frequency–time domain analysis using wavelet decomposition, Hilbert–Huang analysis, and recurrence plots (RPs) related to the corrosion process and noise impedance (Zn). Optical microscopy (OM) was used to observe the microstructure of the tested samples. The results generally indicated that the main corrosion process is related to uniform corrosion. The corrosion behavior of AHSSs exposed to a NaCl solution could be related to the morphology of the phase constituents that are exposed to solutions with chlorides. The Zn results showed that DP780 presented a higher corrosion resistance with 918 Ω·cm2; meanwhile, FB780 presented 409 Ω·cm2 when exposed to NaCl. Also, the corrosion mechanism of materials begins with a localized corrosion process spreading to all the surfaces, generating a uniform corrosion process after some exposition time.

Influence of momentum ratio on heat release rate and noise of co/counter-swirl non-premixed diluted CO/H2 flames

Understanding co/counter-swirl or twin-swirl flames remains challenging due to the complex interaction of two swirling streams. In the present study, we investigate the heat release features of non-premixed co/counter-swirl syngas/air flames and their’ influence on combustor noise in a ∼20 kW combustor using simultaneous high-speed OH*-chemiluminescence (5 kHz) and microphone measurement (50 kHz) by varying the momentum ratio (M) from 0.4 to 0.95. Furthermore, the velocity field is examined using a low-speed two-dimensional particle image velocimetry (2D-PIV, frequency = 7 Hz). For all studied momentum ratios, the frequency spectra of noise measurements for both co/counter-swirl flames consistently exhibit a dominant frequency (∼285 Hz), close to the fundamental axial mode of the combustor. A further analysis using spectrograms, phase spaces, and recurrence plots reveals intermittent patterns in noise measurements, featuring periodic (P) and aperiodic regions (A). In periodic regions (P), noise synchronizes with the global fluctuation of the heat release rate as observed in chemiluminescence. Along with global fluctuation, the chemiluminescence also reveals a rotational component of heat release rate with distinct frequencies for co and counter-swirl configurations. This rotational motion possibly originated from a precessing vortex core (PVC) as indicated by the zig-zag arrangements of vortices in the inner shear layer. Furthermore, the impact of M on global fluctuation and rotational motion has been investigated using the frequency spectrum of OH*-intensity and the distribution of peaks in noise measurement. The global fluctuation is found to be suppressed when M increases while the rotational component becomes prominent at higher M. Therefore, the study elucidates the co-existence of global fluctuation and rotational motion and how these motions evolve with the varying momentum ratio (M), thus enhancing the understanding of combustion characteristics of the complex twin-swirl (co/counter-swirl) flames.

A fault diagnosis method for bearings and gears in rotating machinery based on data fusion and transfer learning

Abstract Rotating machinery is a crucial component of industrial equipment, and the fault diagnosis of bearings and gears, as vital elements of rotating machinery, is essential since they often fail under harsh working conditions, leading to significant property losses and serious personal safety problems. However, fault data for gears and bearings are often sparse in actual condition, and it is a challenge to ensure the reliability and stability of fault diagnosis results by extracting the features of a single data. To solve the above problems, this paper proposes a fault diagnosis method that combines Transfer Learning and data fusion techniques. Firstly, in this method, two kinds of fault signals are transformed into Gramian Angular Difference Fields and Recurrence Plot. Next, a U-shaped feature fusion dual discriminator generative adversarial network is used to fuse two-dimensional images from multiple sensor data. Its feature fusion module deeply integrates the features of the two images, thereby solving the impact of single data on the reliability and stability of fault diagnosis. Moreover, open-source datasets are used for Transfer Learning training to tackle the small sample problem. Finally, a decision-level information fusion classifier, the Dual-Branch Dempster-Shafer Classifier (DB-DSC), classifies the fused images. This classifier incorporates an improved soft threshold function and D-S evidence theory to achieve adaptive gradient changes and improve the robustness and accuracy of classification results. The experimental results show the effectiveness and stability of the proposed method, and the generated images get high score in several metrics. The average classification accuracy of the classification network reaches 93% and 92.5% on the two datasets, Therefore, the proposed method exhibits strong fault diagnosis capabilities under the small sample conditions of bearings and gears.

Image representation of vibration signals and its application on fault diagnosis of rotating machinery with convolutional neural network: A benchmark study

Intelligent fault diagnosis methods on the basis of two-dimensional (2D) image representation of vibration signals (IRVS) and the convolutional neural network (CNN) have been extensively applied in rotating machinery. However, as a large number of IRVS methods are being used, their performance has not been fairly and comprehensively evaluated, which leads to difficulties for researchers to make choices. To address this issue, this paper conducted a benchmark study aimed at comparing the comprehensive performance of different IRVS methods, including computation time, fault diagnosis accuracy, and noise resistance performance. Firstly, the IRVS methods and the fault diagnosis method combining IRVS and CNN were summarized. Then, the general process of the IRVS-CNN method was proposed. Finally, 17 types of IRVS methods were selected, and the performance of the IRVS method was compared based on three datasets and two classic CNN models. The results indicate that the computing time taken to generate 2D images using unthresholded recurrence plot (UTRP), and frequency-domain unthresholded recurrence plot (FDUTRP) methods is relatively longer. The vast majority of frequency-domain methods and time-frequency domain methods can achieve or approach a high accuracy rate in all experiments, demonstrating their outstanding performance. Frequency-domain color vibration image (FDCVI), FDUTRP, and continuous wavelet transform (CWT) have good noise resistance. These results provide a reference for future researchers in selecting IRVS methods.

Lie-bäcklund symmetry, soliton solutions, chaotic structure and its characteristics of the extended (3 + 1) dimensional Kairat-II model

AbstractThis study investigates the (3 + 1)-dimensional extended Kairat-II model using Lie-Bäcklund symmetry (LBS) and the improved modified extended tanh-function approach (IMETFA). The bifurcation and sensitivity analyses are conducted to understand the stability and chaotic behavior of the model. Through graphical visualizations of phase diagrams, Lyapunov exponents, power spectra, fractal dimension and recurrence plots, the complex dynamics and stability characteristics of the model are elucidated. Additionally, the research focuses on the derivation of dark soliton and various combo soliton solutions of the Kairat-II model. The derived soliton solutions are graphically displayed in 3D and 2D plots. The obtained results are new and have never been reported in the literature for the considered equation.

Fusion of Image Transformation Techniques for IoT-based Multivariate Time-Series

The emergence of the Internet of Things (IoT) has ushered in a new era of data generation, with the opportunity for data to become a key element of connected devices. This study investigates new methods to bridge the realms of multivariate time-series data and image analysis, paying special attention to Gramian Angular Summation Field (GASF), Gramian Angular Difference Field (GADF), Markov Transition Field (MTF), and Recurrence Plot (RP) transformation techniques. These techniques serve to convert raw time-series data into visual representations, laying the foundation for deeper analysis and predictive modeling. The study introduces a novel paradigm by not only employing individual image transformation techniques but also fusing them in both horizontal and square orientations. By leveraging Convolutional Neural Networks (CNNs), this study demonstrates the efficiency of innovative fused oriented image transformation techniques in predicting complex patterns within a multivariate time-series dataset related to electricity distribution and transformer oil temperature. Experimental results demonstrate that the fusion of image transformation techniques yields notably enhanced performance compared to employing each technique individually. Fused-Horizontal techniques exhibit the highest performance, while Fused-Square techniques show the second best performance among all fused oriented and individual techniques. This emphasizes the importance of fused oriented image transformation techniques in prediction tasks.

Experimental study of oil-water two-phase flow patterns in a vertical large diameter pipe

The flow structure and the phase inversion have great influence on the flow measurement in vertical upward oil-water two-phase flow. This paper attempts to investigate the flow patterns in oil-water flows through a vertical upward large pipe with the designed mini-conductance array probes measurement system and the vertical multi-electrode array (VMEA) measurement system. According to the output waveform of the mini-conductance array probes, the oil-in-water flow, transition flow and water-in-oil flow can be identified effectively. The fluctuating signals of the VMEA is processed by the recurrence plot and the time-frequency representation, the results show that the VMEA conductance signal with average measurement characteristics can realize an effective identification of the above three flow patterns, which has a good agreement with the results of the mini-conductance array probes. Finally, via comparing with previous published flow pattern transition boundary models in different pipe diameters, it is founded that the boundary line of the transition to oil-in-water based on the kinematic wave-based model and the observation-based model in the same diameter pipe are consistent with our experimental data. And the pipe diameter affects the flow pattern transition, compared with the boundary in small diameter pipe, the phase inversion requires a larger oil velocity, and the transition zone becomes narrower in large diameter pipe.

Parameter inference from a non-stationary unknown process.

Non-stationary systems are found throughout the world, from climate patterns under the influence of variation in carbon dioxide concentration to brain dynamics driven by ascending neuromodulation. Accordingly, there is a need for methods to analyze non-stationary processes, and yet, most time-series analysis methods that are used in practice on important problems across science and industry make the simplifying assumption of stationarity. One important problem in the analysis of non-stationary systems is the problem class that we refer to as parameter inference from a non-stationary unknown process (PINUP). Given an observed time series, this involves inferring the parameters that drive non-stationarity of the time series, without requiring knowledge or inference of a mathematical model of the underlying system. Here, we review and unify a diverse literature of algorithms for PINUP. We formulate the problem and categorize the various algorithmic contributions into those based on (1) dimension reduction, (2) statistical time-series features, (3) prediction error, (4) phase-space partitioning, (5) recurrence plots, and (6) Bayesian inference. This synthesis will allow researchers to identify gaps in the literature and will enable systematic comparisons of different methods. We also demonstrate that the most common systems that existing methods are tested on-notably, the non-stationary Lorenz process and logistic map-are surprisingly easy to perform well on using simple statistical features like windowed mean and variance, undermining the practice of using good performance on these systems as evidence of algorithmic performance. We then identify more challenging problems that many existing methods perform poorly on and which can be used to drive methodological advances in the field. Our results unify disjoint scientific contributions to analyzing the non-stationary systems and suggest new directions for progress on the PINUP problem and the broader study of non-stationary phenomena.

Exploring nonlinear dynamics in brain functionality through phase portraits and fuzzy recurrence plots.

Much of the complexity and diversity found in nature is driven by nonlinear phenomena, and this holds true for the brain. Nonlinear dynamics theory has been successfully utilized in explaining brain functions from a biophysics standpoint, and the field of statistical physics continues to make substantial progress in understanding brain connectivity and function. This study delves into complex brain functional connectivity using biophysical nonlinear dynamics approaches. We aim to uncover hidden information in high-dimensional and nonlinear neural signals, with the hope of providing a useful tool for analyzing information transitions in functionally complex networks. By utilizing phase portraits and fuzzy recurrence plots, we investigated the latent information in the functional connectivity of complex brain networks. Our numerical experiments, which include synthetic linear dynamics neural time series and a biophysically realistic neural mass model, showed that phase portraits and fuzzy recurrence plots are highly sensitive to changes in neural dynamics and can also be used to predict functional connectivity based on structural connectivity. Furthermore, the results showed that phase trajectories of neuronal activity encode low-dimensional dynamics, and the geometric properties of the limit-cycle attractor formed by the phase portraits can be used to explain the neurodynamics. Additionally, our results showed that the phase portrait and fuzzy recurrence plots can be used as functional connectivity descriptors, and both metrics were able to capture and explain nonlinear dynamics behavior during specific cognitive tasks. In conclusion, our findings suggest that phase portraits and fuzzy recurrence plots could be highly effective as functional connectivity descriptors, providing valuable insights into nonlinear dynamics in the brain.

Exploring Nonlinear Dynamics In Brain Functionality Through Phase Portraits And Fuzzy Recurrence Plots.

Much of the complexity and diversity found in nature is driven by nonlinear phenomena, and this holds true for the brain. Nonlinear dynamics theory has been successfully utilized in explaining brain functions from a biophysics standpoint, and the field of statistical physics continues to make substantial progress in understanding brain connectivity and function. This study delves into complex brain functional connectivity using biophysical nonlinear dynamics approaches. We aim to uncover hidden information in high-dimensional and nonlinear neural signals, with the hope of providing a useful tool for analyzing information transitions in functionally complex networks. By utilizing phase portraits and fuzzy recurrence plots, we investigated the latent information in the functional connectivity of complex brain networks. Our numerical experiments, which include synthetic linear dynamics neural time series and a biophysically realistic neural mass model, showed that phase portraits and fuzzy recurrence plots are highly sensitive to changes in neural dynamics and can also be used to predict functional connectivity based on structural connectivity. Furthermore, the results showed that phase trajectories of neuronal activity encode low-dimensional dynamics, and the geometric properties of the limit-cycle attractor formed by the phase portraits can be used to explain the neurodynamics. Additionally, our results showed that the phase portrait and fuzzy recurrence plots can be used as functional connectivity descriptors, and both metrics were able to capture and explain nonlinear dynamics behavior during specific cognitive tasks. In conclusion, our findings suggest that phase portraits and fuzzy recurrence plots could be highly effective as functional connectivity descriptors, providing valuable insights into nonlinear dynamics in the brain.