Recurrence Plots Research Articles

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.

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.

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.

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.

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.

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.

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.

Chaotic systems based on higher-order oscillatory equations

This paper discusses the design process toward new lumped chaotic systems that originates in higher-order ordinary differential equations commonly used as description of ideal oscillators. In investigated third-order case, two chaotic oscillators were constructed. These systems are dual in the sense of vector field geometry local to fixed points. The existence of robust chaos was proved by both standard routines of numerical analysis and practical measurement. For the fourth-order oscillatory equation, the concept based on interaction between superinductor and supercapacitor was examined in detail. Since both “superelements” are active, the nonlinearity essential to the evolution of chaos is fully passive. It is demonstrated that complex motion is robust and does not represent long transient behavior or numerical artefact. The existence of chaos was verified using standard quantifiers of the flow, such as the largest Lyapunov exponents, recurrence plots, approximate entropy and sensitivity calculation. A good final agreement between theoretical assumptions and practical results will be concluded, on a visual comparison basis.

Gearbox fault diagnosis based on RGT-MFFIN and multi-sensor fusion image generation

Abstract In gearbox fault diagnosis based on vibration and torque state data, traditional one-dimensional time-frequency domain analysis methods often suffer from insufficient feature expression and mining, and require complex noise reduction and filtering preprocessing. To address this issue, this paper proposes a fusion image generation method that integrates the advantages of recurrence plot (RP) and Gramian angular summation field (GASF) to generate recurrence Gramian transformed (RGT) images. This approach integrates both global and local fault information, making the fault characteristics more intuitive and easier to analyze. Given that multi-sensor collaboration can enhance feature representation, feature-level fusion increases the computational burden, and decision-level fusion is prone to losing inter-sensor correlation information, this paper adopts data-level fusion for image sample enhancement. In the diagnostic method, the challenge of traditional convolutional neural networks (CNNs) in extracting diverse geometric linear structures from fused images is addressed by introducing deformable convolutional blocks for initial feature extraction. Additionally, a multi-scale feature fusion interaction network (MFFIN) is constructed. This network incorporates a channel-space interactive attention mechanism on top of multi-scale feature extraction, assigning weights to features according to their importance while facilitating the interaction of feature information. Finally, validation is carried out using public datasets, and the experimental results show that the proposed method demonstrates significant advantages in classification accuracy and robustness under variable operating conditions and noise, thereby proving its effectiveness and practicality.

An algorithm for simplified recurrence analysis.

Recurrence analysis applications are hindered by several issues including the selection of critical parameters, noise sensitivity, computational complexity, or the analysis of non-stationary systems. Great progresses have been made by the community to address these issues individually, yet the diversity of resulting techniques with often additional parameters as well as a lack of consensus still impedes its use by nonspecialists. We present a procedure for simplified recurrence analysis based on compact recurrence plots with automatized parameter selection and enhanced noise robustness, and that are suited to the analysis of complex non-stationary systems. This approach aims at supporting the expansion of recurrence analysis for currently challenging or future applications such as for large systems, on-site studies, or using machine learning. The method is demonstrated on both synthetic and real data showing promising results.

Identifying chaotic dynamics in noisy time series through multimodal deep neural networks

Abstract Chaos detection is the problem of identifying whether a series of measurements is being sampled from an underlying set of chaotic dynamics. The unavoidable presence of measurement noise significantly affects the performance of chaos detectors, as discerning chaotic dynamics from stochastic signals becomes more challenging. This paper presents a computationally efficient multi-modal deep neural network tailored for chaos detection by combining information coming from the analysis of time series, recurrence plots and spectrograms. The proposed approach is the first one suitable for multi-class classification of chaotic systems while being robust with respect to measurement noise, and is validated on a dataset of 15 different chaotic and non-chaotic dynamics subject to white, pink or brown coloured noise.

Exploring Price Patterns of Vegetables with Recurrence Quantification Analysis

This study investigates the time-series behavior of vegetable prices in the Central Market of Thessaloniki, Greece, using Recurrence Plot (RP) analysis and Recurrence Quantification Analysis (RQA), which considers non-linearities and does not necessitate stationarity of time series. The period of study was 1999–2016 for practical and research reasons. In the present work, we focus on vegetables available throughout the year, exploring the dynamics and interrelationships between their prices to avoid missing data. The study applies RP visual inspection classification, a clustering based on RQA parameters, and a classification based on the RQA analysis graphs with epochs for the first time. The aim of the paper was to investigate the grouping of products based on their price dynamical behavior. The results show that the formed groups present similarities related to their use as dishes and their way of cultivation, which apparently affect the price dynamics. The results offer insights into market behaviors, helping to inform better management strategies and policymaking and offer a possibility to predict variability of prices. This information can interest government policies in various directions, such as what products to develop for greater stability, identity for fluctuating prices, etc. In future work, a larger dataset including missing data could be included, as well as a machine-learning algorithm to classify the products based on the RQA with epochs graphs.