Recurrence Plots Research Articles

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.

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.

Spray swirling flame dynamic under combined modulation of air and fuel

Combustion instability is still a main challenge in developing advanced gas turbine combustors. It is essential to conduct instability control once it occurs. In this paper, liquid fuel modulation by a high-speed on/off valve is used to control flame oscillation generated by loudspeakers. Spray swirling flame dynamic under the combined modulation of air and fuel is experimentally studied. Flame dynamical characteristics and coherent structures at different excitation phase delays are discussed with nonlinear time-series analysis and proper orthogonal decomposition method. Experimental results show flame heat release rate fluctuation is decreased by 86% at 40° while flame instability is intensively enhanced at 220°. Phase portraits and recurrence plots show the flame is in a chaotic oscillation with low amplitude aperiodic oscillations at 40° while it suffers from the largest fluctuation at 220°. Difference in flame dynamic is caused by the destructive (out of phase) and constructive (in phase) interference of heat release rate fluctuations induced by air excitation and fuel modulation. Flame returns back to its nature dynamical behavior under out-of-phase modulation. Longitudinal modes of the spray flame are enhanced while the spiral modes are inhibited under in-phase modulation.

A Cross-Working Condition-Bearing Diagnosis Method Based on Image Fusion and a Residual Network Incorporating the Kolmogorov–Arnold Representation Theorem

With the optimization and advancement of industrial production and manufacturing, the application scenarios of bearings have become increasingly diverse and highly coupled. This complexity poses significant challenges for the extraction of bearing fault features, consequently affecting the accuracy of cross-condition fault diagnosis methods. To improve the extraction and recognition of fault features and enhance the diagnostic accuracy of models across different conditions, this paper proposes a cross-condition bearing diagnosis method. This method, named MCR-KAResNet-TLDAF, is based on image fusion and a residual network that incorporates the Kolmogorov–Arnold representation theorem. Firstly, the one-dimensional vibration signals of the bearing are processed using Markov transition field (MTF), continuous wavelet transform (CWT), and recurrence plot (RP) methods, converting the resulting images to grayscale. These grayscale images are then multiplied by corresponding coefficients and fed into the R, G, and B channels for image fusion. Subsequently, fault features are extracted using a residual network enhanced by the Kolmogorov–Arnold representation theorem. Additionally, a domain adaptation algorithm combining multiple kernel maximum mean discrepancy (MK-MMD ) and conditional domain adversarial network with entropy conditioning (CDAN+E ) is employed to align the source and target domains, thereby enhancing the model’s cross-condition diagnostic accuracy. The proposed method was experimentally validated on the Case Western Reserve University (CWRU) dataset and the Jiangnan University (JUN) dataset, which include the 6205-2RS JEM SKF, N205, and NU205 bearing models. The method achieved accuracy rates of 99.36% and 99.889% on the two datasets, respectively. Comparative experiments from various perspectives further confirm the superiority and effectiveness of the proposed model.

Recurrence quantification analysis of rs-fMRI data: A method to detect subtle changes in the TgF344-AD rat model

Background and objectiveAlzheimer's disease (AD) is one of the leading causes of dementia, affecting the world's population at a growing rate. The preclinical stage of AD lasts over a decade, hence understanding AD-related early neuropathological effects on brain function at this stage facilitates early detection of the disease. MethodsResting-state functional magnetic resonance imaging (rs-fMRI) has been a powerful tool for understanding brain function, and it has been widely used in AD research. In this study, we apply Recurrence Quantification Analysis (RQA) on rs-fMRI images of 4-months (4 m) and 6-months-old (6 m) TgF344-AD rats and WT littermates to identify changes related to the AD phenotype and aging. RQA has been focused on areas of the default mode-like network (DMLN) and was performed based on Recurrence Plots (RP). RP is a mathematical representation of any dynamical system that evolves over time as a set of its state recurrences. In this paper, RPs were extracted in order to identify the affected regions of the DMLN at very early stages of AD. ResultsUsing the RQA approach, we identified significant changes related to the AD phenotype at 4 m and/or 6 m in several areas of the rat DMLN including the BFB, Hippocampal fields CA1 and CA3, CG1, CG2, PrL, PtA, RSC, TeA, V1, V2. In addition, with age, brain activity of WT rats showed less predictability, while the AD rats presented reduced decline of predictability. ConclusionsThe results of this study demonstrate that RQA of rs-fMRI data is a potent approach that can detect subtle changes which might be missed by other methodologies due to the brain's non-linear dynamics. Moreover, this study provides helpful information about specific areas involved in AD pathology at very early stages of the disease in a very promising rat model of AD. Our results provide valuable information for the development of early detection methods and novel diagnosis tools for AD.

Exploring the recurrent states of football teams' tactical organization on the pitch during Brazilian official matches.

Football teams' tactical organization on the pitch is usually represented by the surface area. Considering the different shapes adopted by the teams during the match, the role of the tactical variability for success is lacking. The aim of this study was to explore and to evaluate the association between recurrent states of tactical organization and technical performance during football matches. A total of 28 teams of Brazilian First Division Championships were analysed. Teams' surface area shapes were represented by the maximum value of the Multiscale Fractal Dimension in each timestamp, producing a time series. Recurrences of states of tactical organization were determined via recurrence plots and recurrence quantitative analysis during attacking and defending phases, and considering the whole match. The outcomes were correlated with nine traditional technical performance indicators. The main results showed that structural recurrence or variability on tactical organization is associated with performance success during the defending and attacking actions. Recurrence plot and measures based on the recurrence density proved to be valuable tools to represent teams' dynamics.

Electrochemical Noise Analysis: An Approach to the Effectivity of Each Method in Different Materials.

Corrosion deterioration of materials is a major problem affecting economic, safety, and logistical issues, especially in the aeronautical sector. Detecting the correct corrosion type in metal alloys is very important to know how to mitigate the corrosion problem. Electrochemical noise (EN) is a corrosion technique used to characterize the behavior of different alloys and determine the type of corrosion in a system. The objective of this research is to characterize by EN technique different aeronautical alloys (Al, Ti, steels, and superalloys) using different analysis methods such as time domain (visual analysis, statistical), frequency domain (power spectral density (PSD)), and frequency-time domain (wavelet decomposition, Hilbert Huang analysis, and recurrence plots (RP)) related to the corrosion process. Optical microscopy (OM) is used to observe the surface of the tested samples. The alloys were exposed to 3.5 wt.% NaCl and H2SO4 solutions at room temperature. The results indicate that HHT and recurrence plots are the best options for determining the corrosion type compared with the other methods due to their ability to analyze dynamic and chaotic systems, such as corrosion. Corrosion processes such as passivation and localized corrosion can be differentiated when analyzed using HHT and RP methods when a passive system presents values of determinism between 0.5 and 0.8. Also, to differentiate the passive system from the localized system, it is necessary to see the recurrence plot due to the similarity of the determinism value. Noise impedance (Zn) is one of the best options for determining the corrosion kinetics of one system, showing that Ti CP2 and Ti-6Al-4V presented 742,824 and 939,575 Ω·cm2, while Rn presented 271,851 and 325,751 Ω·cm2, being the highest when exposed to H2SO4.

Involution symmetry quantification using recurrences.

Symmetries are ubiquitous in science, aiding theoretical comprehension by discerning patterns in mathematical models and natural phenomena. This work introduces a method for assessing the extent of symmetry within a time series. We explore both microscopic and macroscopic features extracted from a recurrence plot. By analyzing the statistics of small recurrence matrices, our approach delves into microscale dynamics, facilitating the identification of symmetric time series segments through diagonal macroscale structures on a recurrence plot. We validate our approach by successfully quantifying involution symmetries for three-dimensional dynamical models, specifically, order-2 rotational symmetry in the Lorenz '63 model, and inversion symmetry in the Chua circuit. Our quantifier also detects symmetry breaking in the modified Lorenz model for El Niño phenomenon. The method can be applied in a versatile manner, not only to three-dimensional trajectories but also to univariate time series. Symmetry quantification in time series is promising for enhancing dynamical system modeling and profiling.