Recurrent Plot Research Articles

Fault diagnosis method of automobile rolling bearing based on transfer learning and improved DenseNet

Aiming at the problems caused by ignoring the time series characteristics, the scarcity of labeled data and the long diagnosis time in the fault diagnosis of one-dimensional vibration signals of automobile bearings, a new method combining improved DenseNet and transfer learning is proposed in this study. This method uses Recurrent Plot (RP) technology to convert one-dimensional vibration data into two-dimensional images to fully tap the potential value of time series. By optimizing the DenseNet network structure, the fault features are extracted effectively. Lightweight network design and MobileViT Attention mechanism are used to reduce the number of parameters and improve computing efficiency. With the help of transfer learning technology, the fault features in the source domain are transferred to the target domain, which solves the problem of cross-condition diagnosis and greatly reduces the diagnosis time. The experimental results show that the proposed method can improve the accuracy of fault identification and diagnosis efficiency, and achieve accurate classification.

3DECG-Net: ECG fusion network for multi-label cardiac arrhythmia detection

Cardiovascular diseases represent the leading global cause of death, typically diagnosed and addressed through electrocardiograms (ECG), which record the heart's electrical activity. In recent years, there has been a notable surge in ECG recordings, driven by the widespread use of wearable devices. However, the limited availability of medical experts to analyze these recordings underscores the necessity for automated ECG analysis using computer-aided methods. In this study, we introduced 3DECG-Net, a deep learning model designed to detect and classify seven distinct heart states through the analysis of data fusion from 12-lead ECG in a multi-label framework. Our model leverages a residual architecture with a multi-head attention mechanism, undergoing training within a five-fold cross-validation scheme. By transforming 12-lead ECG signals into 3D data with the help of Recurrent Plot technique, 3DECG-Net achieves a noteworthy micro F1-score of 80.3 %, surpassing the performance of other state-of-the-art deep learning models developed for this specific task. Also, we present an ECG preprocessing framework to generate compact, high-quality ECG signals for potential application in future studies within this domain. We conduct an explainable AI experiment using Local Interpretable Model-agnostic Explanations (LIME) to elucidate the significance of each lead in accurately diagnosing specific arrhythmias, ensuring the logical processing of ECG data by 3DECG-Net. The findings of this study suggest that the proposed model is trustworthy and has the potential to be used as an effective diagnostic toolset for identifying heart arrhythmias. Its effectiveness can improve the diagnostic process, facilitate early treatment, and enhance overall efficiency in medical settings.

Precision prediction in grinding processes based on displacement signal conversion into recurrent plot

The processing of grinding data and the prediction of accuracy are extremely complex; this paper proposes a novel prediction method to ensure the machining accuracy of computer numerical control (CNC) grinding machines. It consists of two components, namely the filter decomposition recurrence plot (RP) transformation (FDRP) and the deep inverted residual attention network (DIRAN). A pipeline named FDRP has been designed to address the issues in the processing of data and the shortcomings of RP. Firstly, the displacement signals undergo filtering to preserve essential grinding information while effectively removing noise. Secondly, long-time series signals are decomposed and augmented based on the characteristics of the machining process. Lastly, an RP transformation is applied to one-dimensional time series data, resulting in the generation of images that accurately represent the grinding process. Furthermore, this paper proposes a novel machining accuracy prediction model. The DIRAN uses a multi-layer inverse residual network structure combined with attention mechanism to extract the features of two-dimensional RP, and its performance is better than other typical prediction methods. It can be applied to predict the polar angle of the workpiece in industrial processing and reduce the defect rate.

Recurrence plot embeddings as short segment nonlinear features for multimodal speaker identification using air, bone and throat microphones

Speech is produced by a nonlinear, dynamical Vocal Tract (VT) system, and is transmitted through multiple (air, bone and skin conduction) modes, as captured by the air, bone and throat microphones respectively. Speaker specific characteristics that capture this nonlinearity are rarely used as stand-alone features for speaker modeling, and at best have been used in tandem with well known linear spectral features to produce tangible results. This paper proposes Recurrent Plot (RP) embeddings as stand-alone, non-linear speaker-discriminating features. Two datasets, the continuous multimodal TIMIT speech corpus and the consonant-vowel unimodal syllable dataset, are used in this study for conducting closed-set speaker identification experiments. Experiments with unimodal speaker recognition systems show that RP embeddings capture the nonlinear dynamics of the VT system which are unique to every speaker, in all the modes of speech. The Air (A), Bone (B) and Throat (T) microphone systems, trained purely on RP embeddings perform with an accuracy of 95.81%, 98.18% and 99.74%, respectively. Experiments using the joint feature space of combined RP embeddings for bimodal (A–T, A–B, B–T) and trimodal (A–B–T) systems show that the best trimodal system (99.84% accuracy) performs on par with trimodal systems using spectrogram (99.45%) and MFCC (99.98%). The 98.84% performance of the B–T bimodal system shows the efficacy of a speaker recognition system based entirely on alternate (bone and throat) speech, in the absence of the standard (air) speech. The results underscore the significance of the RP embedding, as a nonlinear feature representation of the dynamical VT system that can act independently for speaker recognition. It is envisaged that speech recognition too will benefit from this nonlinear feature.

Biometric Recognition Based on Recurrence Plot and InceptionV3 Model Using Eye Movements.

The ability to use eye movement signals as a feature in biometric recognition is a novel characteristic of biometric recognition technology. However, present technologies have not fully exploited the correlation features between eye movement signals. To address this, we propose an eye movement biometric recognition model that is based on recurrence plot encoding and the InceptionV3 model. We first encode the original eye movement signal using the recurrence plot to obtain a two-dimensional image that is then used as input for the InceptionV3 model to perform biometric recognition. Our experimental results using the GazeBaseV2.0 eye movement dataset demonstrate that our proposed model achieved a high biometric recognition accuracy of 96.58% ± 0.66% using the recurrence plot transformation of the horizontal gaze position signals and the InceptionV3 model, surpassing the accuracy achieved by other models. The use of horizontal gaze position eye movement signals for biometric recognition outperforms the use of vertical gaze position signals when using our proposed methods. Furthermore, the biometric recognition that is achieved through recurrent plot encoding is superior to that achieved using Markov transition fields and Gramian angular field transformations.

Recognizing Chaos by Deep Learning and Transfer Learning on Recurrence Plots

Chaos recognition is necessary to determine the prediction possibility for specific time series. In this paper, we attempt to seek a novel chaos recognition method based on the recurrent plot (RP) and the convolutional neural network (CNN). The RP can transform the time series into a two-dimensional image, which intuitively reflects the inherent nature of the time series. On the other hand, the CNN is powerful in pattern classification. In this way, the existing chaos recognition results can be unified in a general framework to form accumulated knowledge, which can be used to recognize novel dynamics. First, three major time series classes, namely chaotic, periodic and random ones generated from the classical dynamics, are represented by the RPs respectively. Then, these RPs are used as the dataset to train the residual neural network (ResNet). In this process, the transfer learning is used to speed up convergence. The chaos recognition precision can be up to 97.6%. Finally, different encoding methods and classification networks are used for comparative experiments, and the resultant ResNet is applied to the time series from a supercavitating vehicle motion and two hyperchaotic systems. The experimental results demonstrate the effectiveness of the proposed method.

Imaging feature-based clustering of financial time series.

Timeseries representation underpin our ability to understand and predict the change of natural system. Series are often predicated on our choice of highly redundant factors, and in fact, the system is driven by a much smaller set of latent intrinsic keys. It means that a better representation of data makes points in phase space clearly for researchers. Specially, a 2D structure of timeseries could combine the trend and correlation characters of different periods in timeseries together, which provides more clear information for top tasks. In this work, the effectiveness of 2D structure of timeseries is investigated in clustering tasks. There are 4 kinds of methods that the Recurrent Plot (RP), the Gramian Angular Summation Field (GASF), the Gramian Angular Differential Field (GADF) and the Markov Transition Field (MTF) have been adopted in the analysis. By classifying the CSI300 and S&P500 indexes, we found that the RP imaging series are valid in recognizing abnormal fluctuations of financial timeseries, as the silhouette values of clusters are over 0.6 to 1. Compared with segment methods, the 2D models have the lowest instability value of 0. It verifies that the SIFT features of RP images take advantage of the volatility of financial series for clustering tasks.

Atrial fibrillation classification based on the 2D representation of minimal subset ECG and a non-deep neural network.

Atrial fibrillation (AF) is the most common cardiac arrhythmia, and its early detection is critical for preventing complications and optimizing treatment. In this study, a novel AF prediction method is proposed, which is based on investigating a subset of the 12-lead ECG data using a recurrent plot and ParNet-adv model. The minimal subset of ECG leads (II &V1) is determined via a forward stepwise selection procedure, and the selected 1D ECG data is transformed into 2D recurrence plot (RP) images as an input to train a shallow ParNet-adv Network for AF prediction. In this study, the proposed method achieved F1 score of 0.9763, Precision of 0.9654, Recall of 0.9875, Specificity of 0.9646, and Accuracy of 0.9760, which significantly outperformed solutions based on single leads and complete 12 leads. When studying several ECG datasets, including the CPSC and Georgia ECG databases of the PhysioNet/Computing in Cardiology Challenge 2020, the new method achieved F1 score of 0.9693 and 0.8660, respectively. The results suggested a good generalization of the proposed method. Compared with several state-of-art frameworks, the proposed model with a shallow network of only 12 depths and asymmetric convolutions achieved the highest average F1 score. Extensive experimental studies proved that the proposed method has a high potential for AF prediction in clinical and particularly wearable applications.

VMD–RP–CSRN Based Fault Diagnosis Method for Rolling Bearings

In response to the problems of low accuracy and poor noise immunity of the traditional fault diagnosis method for rolling bearing fault diagnosis due to the complex and variable operating conditions of rolling bearings and the large noise interference during bearing signal acquisition, a rolling bearing fault diagnosis model based on VMD–RP–CSRN is proposed. Firstly, the initial feature extraction of the bearing signal is carried out by variational modal decomposition (VMD), which is then converted into a two-dimensional image with fault features by recurrent plot (RP) coding, and then the feature images are input to a channel split residual network (CSRN) for feature extraction and fault classification. In order to verify the accuracy and noise immunity of the proposed method for the diagnosis of bearing faults under complex working conditions, experiments on the selection of parameters in the CSRN model were conducted on the bearing dataset of Jiangnan University, and experiments on the diagnosis of bearing faults under complex working conditions and noise immunity of CSRN were carried out and compared with other commonly used methods. The proposed bearing fault diagnosis method based on VMD–RP–CSRN combines VMD and RP to retain the fault features in the original signal to the maximum extent and stress the hidden features in the signal. The proposed channel split operation realizes the extraction of hidden features by selecting the main operating channel of the three-channel feature image, and makes more fault features participate in the feature extraction of the diagnosis model. The experimental results demonstrate that the proposed method is at least 1.2% better than the comparison method, and has better noise immunity. In addition, experiments on the fault diagnosis capability of the model with different data set sizes and the diagnosis of variable speed bearing data by the model show that the proposed method has better generalization performance and diagnosis capability.

Electrocardiogram Signal Classification Based on Mix Time-Series Imaging

Arrhythmia is a significant cause of death, and it is essential to analyze the electrocardiogram (ECG) signals as this is usually used to diagnose arrhythmia. However, the traditional time series classification methods based on ECG ignore the nonlinearity, temporality, or other characteristics inside these signals. This paper proposes an electrocardiogram classification method that encodes one-dimensional ECG signals into the three-channel images, named ECG classification based on Mix Time-series Imaging (EC-MTSI). Specifically, this hybrid transformation method combines Gramian angular field (GAF), recurrent plot (RP), and tiling, preserving the original ECG time series’ time dependence and correlation. We use a variety of neural networks to extract features and perform feature fusion and classification. This retains sufficient details while emphasizing local information. To demonstrate the effectiveness of the EC-MTSI, we conduct abundant experiments in a commonly-used dataset. In our experiments, the general accuracy reached 93.23%, and the accuracy of identifying high-risk arrhythmias of ventricular beats and supraventricular beats alone are as high as 97.4% and 96.3%, respectively. The results reveal that the proposed method significantly outperforms the existing approaches.

THE SQUARE AS SYMBOLIC SPACE IN A.S. PUSHKIN’s WRITING

Repetition and variation of some baseline motives and images are a hallmark of A. Pushkin’s poetic system. A comprehensive system of A. Pushkin’s writing arises due to complex and contradictory relationships of specific elements. A principle of ‘resourceful contradiction’ forms the basis for the system. The square is one of the key space images which not only unites a wide range of works (from ‘Boris Godunov’ tragedy to ‘The Captain’s Daughter’ novel) but forms a recurrent plot as well. The author of the paper demonstrates the functioning of this image and elicits its semantics by means of numerous texts. The square space in Pushkin’s works is both a death site and a place of salvation; both a place of historic resolutions and a place of historic dead end. Special attention is paid to the allusive principle which is constitutive in Pushkin’s fiction system. The image of the square is inseparable from the events of December, 14, 1825 and July, 25, 1826 in a number of works (‘The Bronze Horseman’, ‘The Captain’s Daughter’ and others).

Open-Set Events Identification Based on Deep Metric-Learning for DMZI Perimeter System

Intrusion monitoring based on optical fiber distributed sensing is a pattern recognition problem of target events. Due to the addition of uncontrollable unknown events in practical applications, the open-set problem brought about greatly reduces the accuracy of traditional events recognition methods. In order to solve this problem, this paper design a deep metric-learning network, combined with Recurrent Plot (RP) coding to improve the accuracy of target events recognition in an open environment. In this paper, the RP algorithm is used to encode the intrusion signals into images that reflect the signal’s motion. The deep metric-learning network is used to project the image into the feature space. And feature centers of each class can be calculated rely on the training samples. So, the network identifies the intrusion event according to the distance between the test sample and the feature center. By setting the appropriate threshold, the samples whose distance exceeds the threshold are identified as unknown class to solve the open-set problem. In the experiments, the dual Mach-Zehnder interferometry (DMZI) distributed optical fiber perimeter system is built to collect event signals. For 7 known event classes the highest identification accuracy can reach 99.7%. After adding 3 unknown event classes, the accuracy rate can exceed 93.3% with appropriate threshold. And the total response time is only 0.4 s. This novel method guarantees the accuracy of target identification under the introduction of unknown events and improves the robustness of the distributed optical fiber perimeter security system.

Recurrence Quantification Analysis of Glottal Signal as non Linear Tool for Pathological Voice Assessment and Classification

Automatic detection and assessment of Vocal Folds pathologies using signal processing techniques knows an extensively challenge use in the voice or speech research community. This paper contributes the application of the Recurrence Quantification Analysis (RQA) to a glottal signal waveform in order to evaluate the dynamic process of Vocal Folds (VFs) for diagnosis and classify the voice disorders. The proposed solution starts by extracting the glottal signal waveform from the voice signal through an inverse filtering algorithm. In the next step, the parameters of RQA are determined via the Recurrent Plot (RP) structure of the glottal signal where the normal voice is considered as a reference. Finally, these parameters are used as input features set of a hybrid Particle Swarm Optimization-Support Vector Machines (PSO-SVM) algorithms to segregate between normal and pathological voices. For the test validation, we have adopted the collection of Saarbrucken Voice Database (SVD) where we have selected the long vowel /a:/ of 133 normal samples and 260 pathological samples uttered by four groups of subjects : persons having suffered from vocal folds paralysis, persons having vocal folds polyps, persons having spasmodic dysphonia and normal voices. The obtained results show the effectiveness of RQA applied to the glottal signal as a features extraction technique. Indeed, the PSO-SVM as a classification method presented an effective tool for assessment and diagnosis of pathological voices with an accuracy of 97.41%

A recurrent plot based stochastic nonlinear ray propagation model for underwater signal propagation

A stochastic nonlinear ray propagation model is proposed to carry out an exploration of the nonlinear ray theory in underwater signal propagation. The recurrence plot method is proposed to quantify the ray chaos and stochastics to optimize the model. Based on this method, the distribution function of the control parameter δ is derived. Experiments and simulations indicate that this stochastic nonlinear ray propagation model provides a good explanation and description on the stochastic frequency shift in underwater signal propagation.

A Robust Approach for Securing Audio Classification Against Adversarial Attacks

Adversarial audio attacks can be considered as a small perturbation unperceptive to human ears that is intentionally added to an audio signal and causes a machine learning model to make mistakes. This poses a security concern about the safety of machine learning models since the adversarial attacks can fool such models toward the wrong predictions. In this paper we first review some strong adversarial attacks that may affect both audio signals and their 2D representations and evaluate the resiliency of deep learning models and support vector machines (SVM) trained on 2D audio representations such as short time Fourier transform, discrete wavelet transform (DWT) and cross recurrent plot against several state-of-the-art adversarial attacks. Next, we propose a novel approach based on pre-processed DWT representation of audio signals and SVM to secure audio systems against adversarial attacks. The proposed architecture has several preprocessing modules for generating and enhancing spectrograms including dimension reduction and smoothing. We extract features from small patches of the spectrograms using the speeded up robust feature (SURF) algorithm which are further used to transform into cluster distance distribution using the K-Means++ algorithm. Finally, SURF-generated vectors are encoded by this codebook and the resulting codewords are used for training a SVM. All these steps yield to a novel approach for audio classification that provides a good tradeoff between accuracy and resilience. Experimental results on three environmental sound datasets show the competitive performance of the proposed approach compared to the deep neural networks both in terms of accuracy and robustness against strong adversarial attacks.

Analysis of detection of ecological hazard based on computing the measures of current recurrence of ecosystem states

Analysis of the early detection of an environmental hazard in ecosystems was performed. New measures of the current recurrence of states that allow their use for the early detection of an environmental hazard in ecosystems were proposed. Calculations of the measures under consideration are based on the distribution of the known measure of global recurrence for the case of the calculation of measures of current recurrence in moving square windows. In this case, one of the measures under consideration is based on the implementation of a moving square window along the main diagonal of the recurrent plot of state. Another measure is based on the use of a moving window of the specified size along the horizontal (vertical) axis of recurrence plots. The latter made it possible to obtain a constructive current measure for calculation of recurrence to identify dangerous states in ecosystems based on the temporal localization of zero recurrence of states at minimum sizes of a moving window. In accordance with the proposed measures of current recurrence, the possibilities of using the measures for the early identification of an environmental hazard for gas medium with the ignition center of combustible material, such as alcohol, were analyzed. It was shown that the window measure of current recurrence at a horizontal moving small­size window is the most suitable of the considered measures. It was found that for such a measure, window sizes must be in the range from 5×5 to 15×15 counts. In this case, the values of region e of neighborhood for the considered states must be selected in the range from 0.01 to 0.15. It was determined theoretically and experimentally that the specified measure of current recurrence of states with a horizontally moving window can be considered as a structural current measure of recurrence to ensure a reliable early detection of hazardous states in different ecosystems

Interpretation of surface degradation on polymeric insulators

Abstract Silicone rubber based polymeric insulators are being used widely used as outdoor insulation for high voltage applications. However, their long-term service life performance is highly dependent on local environmental conditions that cause deterioration of material properties of the insulators. In the present work, tracking and erosion studies are conducted on silicone rubber samples using. Inclined Plane Tracking (IPT) and Erosion method based on IEC 60587. The contaminants used to simulate different environmental conditions are as per standard and in addition acidic rain composition is used. Leakage current flowing through samples was continuously monitored and recorded over the experimental duration. The consequence of leakage current variation is analyzed using. Recurrent Plot (RP) Analysis and this resulted in variation of quantitative parameters Recurrence Rate (RR), Determinism (DET), Entropy (ENT) and Length (L) these are used to interpret the tracking and erosion performance of silicone rubber samples. Further, physico-chemical analysis is conducted using Scanning Electron Microscopy (SEM), Energy Dispersive X-Ray (EDAX) and Fourier Transform Infra-Red (FTIR) spectroscopy to observe surface morphology and chemical changes happened in the samples. Thermo-Gravimetric Analysis (TGA) is performed to observe thermal stability and presence of Aluminum Tri-hydrate (ATH) fillers before and after experiments. The investigations show RP method as a potential tool for detection and diagnostic of polymeric insulators.

Extracting clinically relevant information from pulse oximetry traces

Cardiovascular assessment is necessary, yet unafordable for large population groups worlwide. Here we illustrate how signals obtained from standard oximeters can provide reliable estimates for transit time, a measure associated to vascular stiffness, as well as complexity measures derived from Recursive plot analysis. The salient features of our research were: 1) The possibility to use of photoplethysmographic (PPG) signals as a surrogate for transit time estimation; 2)The use of PPG signals for HRV analysis; 3)The possibility to use 2-min PPG recordings for cardiovascular estimation; 4)The proposal of a new vascular age estimator. An automated algorithm for estimating transit time from the PPG waveform yielded a strong association with age (r=0.80). All indices obtained from Recurrent Plot analysis of tachograms with PPG signals exhibited a high correlation with subject´s age. On the basis of the estimated indices a new estimator for cardiovascular age has been introduced, which exhibited a high correlation with age (r=0.97). Thus we concluded that PPG signals do retain information about cardiovascular age. This is evidenced from changes with age of different indices obtained from 2-min duration PPG traces. These result might be relevant for boosting cardiovascular diagnosis in settings with limited resources. Keywords: Pulse Oximetry, Heart Rate Variability, Transit Time Estimation, Recurrent Plot Analysis, Cardio Vascular Age.

Temporal Variation of the Rotation of the Solar Mean Magnetic Field

Abstract Based on continuous wavelet transformation analysis, the daily solar mean magnetic field (SMMF) from 1975 May 16 to 2014 July 31 is analyzed to reveal its rotational behavior. Both the recurrent plot in Bartels form and the continuous wavelet transformation analysis show the existence of rotational modulation in the variation of the daily SMMF. The dependence of the rotational cycle lengths on solar cycle phase is also studied, which indicates that the yearly mean rotational cycle lengths generally seem to be longer during the rising phase of solar cycles and shorter during the declining phase. The mean rotational cycle length for the rising phase of all of the solar cycles in the considered time is 28.28 ± 0.67 days, while for the declining phase it is 27.32 ± 0.64 days. The difference of the mean rotational cycle lengths between the rising phase and the declining phase is 0.96 days. The periodicity analysis, through the use of an auto-correlation function, indicates that the rotational cycle lengths have a significant period of about 10.1 years. Furthermore, the cross-correlation analysis indicates that there exists a phase difference between the rotational cycle lengths and solar activity.

Understanding the influence of water droplet initiated discharges on damage caused to corona-aged silicone rubber

Corona activity on the surface of silicone rubber has high impact on variation in hydrophobicity of the material, and on corona inception voltage (CIV) of water droplet sitting on the corona degraded surface. The CIV is high under negative DC as compared to positive DC/AC voltages. Increase in conductivity of water droplet reduces CIV. Surface charge accumulation studies indicate that the charge retention capability of the insulating material gets reduced drastically with silicone rubber damaged due to corona causing degradation of surface. Irrespective of the number of cycles of corona discharge activities carried out, the time constant of charge decay, after the removal of charge injection, remains the same. The water droplet initiated discharges under AC and DC voltages radiate UHF signal in the bandwidth 0.3–1.2 GHz. With single droplet sitting on top of the corona damaged silicone rubber, the amount of charge retained by the water droplet is low when the droplet is placed and charged immediately after corona discharge activity to surface of the insulating material. When the water droplet is placed after a certain time period, the charge accumulation characteristics of silicone rubber are regained. Leakage current measured during water droplet discharge studies through recurrent plot (RP) analysis reveals that, under AC voltage, it is possible to classify corona inception, arcing and bridging of water droplet between high voltage and ground electrode. The RP obtained for the current signals generated due to water droplet discharges under positive and negative DC voltages are different. The amount of damage caused to silicone rubber due to water droplet is high under negative DC voltage as compared to positive/AC voltages. While correlating the level of damage to the insulating material due to water droplet and the RQA parameters of RP, it is observed that higher the recurrence rate along with high determinism can cause severe damage to the insulating material. Structural analysis using ATR-FTIR and pyrolysis-GC/MS studies reveal significant functional group variation on surface of silicone rubber, especially when the number of cycles of corona ageing is more.