One-dimensional Time Series Research Articles

A Mechanical Fault Identification Method for On-Load Tap Changers Based on Hybrid Time—Frequency Graphs of Vibration Signals and DSCNN-SVM with Small Sample Sizes

In engineering applications, the accuracy of on-load tap changer (OLTC) mechanical fault identification methods based on vibration signals is constrained by the quantity and quality of the samples. Therefore, a novel small-sample-size OLTC mechanical fault identification method incorporating short-time Fourier transform (STFT), synchrosqueezed wavelet transform (SWT), a dual-stream convolutional neural network (DSCNN), and support vector machine (SVM) is proposed. Firstly, the one-dimensional time-series vibration signals are transformed using STFT and SWT to obtain time–frequency graphs. STFT time–frequency graphs capture the global features of the OLTC vibration signals, while SWT time–frequency graphs capture the local features of the OLTC vibration signals. Secondly, these time–frequency graphs are input into the CNN to extract key features. In the fusion layer, the feature vectors from the STFT and SWT graphs are combined to form a fusion vector that encompasses both global and local time–frequency features. Finally, the softmax classifier of the traditional CNN is replaced with an SVM classifier, and the fusion vector is input into this classifier. Compared to the traditional fault identification methods, the proposed method demonstrates higher identification accuracy and stronger generalization ability under the conditions of small sample sizes and noise interference.

Research on power battery anomaly detection method based on improved TimesNet

Health monitoring and abnormality detection of power batteries for new energy vehicles has been one of the hot topics in recent years. Accurate and efficient power battery anomaly detection is crucial to ensure stable operation of the battery system and energy saving. However, power battery data are often non-linear and unstable due to external factors, such as temperature conditions, which pose challenges for anomaly detection. Existing methods for collecting battery data’s temporal and spatial features are available, but many of them yield suboptimal detection accuracy and feature extraction efficiency due to their disregard for the multi-periodicity of the data. This paper proposes a novel network structure for power battery anomaly detection based on an improved TimesNet. Firstly, the original battery data undergo preprocessing, and the feature correlation coefficient matrix is established using the MIC algorithm. Secondly, the improved TimesNet network is employed to convert the one-dimensional time feature sequence into a two-dimensional tensor, enabling the extraction of temporal features and dependencies at various cycle scales. Finally, the two-dimensional tensor is transformed into a one-dimensional time series, which undergoes information-weighted aggregation to obtain the final anomaly detection results. To assess the effectiveness and generalization of the proposed model, experiments are conducted using Battery and four public datasets for anomaly detection. The experimental results demonstrate that the proposed model outperforms the transformer, autoformer, TimesNet, and Dlinear models, achieving an improvement of 1%–19% in the F1 value and 1%–3% in the ACC compared to the other models.

CTCTime: A New Model for Unidimensional Time Series Classification

One-dimensional time series classification has always been an important research direction, playing an irreplaceable role in various fields. With the rapid development of deep learning, most traditional time series classification methods have gradually been replaced by neural network-based classification methods. At present, in the field of time series classification, models that perform well are mostly based on Convolutional Neural Networks (CNNs), while models with the Transformer architecture, which have shown outstanding performance in natural language processing and computer vision, do not stand out. In order to change this situation, We have investigated the feasibility of training models based on a single Transformer architecture directly on small datasets without additional data processing. Furthermore, we propose a new model called CTCTime, which combines the Transformer architecture with CNNs to address one-dimensional time series classification problems. We compared CTCTime with 13 traditional algorithms on 44 datasets from the UCR archive and with 7 advanced methods on 85 datasets. The UCR datasets are classic datasets for one-dimensional time series classification tasks. The experimental results demonstrate its feasibility, accuracy, and scalability.

Solar wind data analysis aided by synthetic modeling: A better understanding of plasma frame variations from temporal data

Context. In situ measurements of the solar wind, a turbulent and anisotropic plasma flow originating at the Sun, are mostly carried out by single spacecraft, resulting in one-dimensional time series. Aims. The conversion of these measurements to the spatial frame of the plasma is a great challenge, but it is required for direct comparison of the measurements with magnetohydrodynamic turbulence theories. Methods. We present a tool kit based on the synthetic modeling of solar wind fluctuations as two-dimensional noise maps with adjustable spectral and power anisotropy that can help with the temporal-spatial conversion of real data. Specifically, by following the spacecraft trajectory through a noise map (relative velocity and angle relative to some mean magnetic field) with properties tuned to mimic those of the solar wind, the likelihood that the temporal data fluctuations represent parallel or perpendicular fluctuations in the plasma frame can be quantified by correlating structure functions of the noise map. Synthetic temporal data can also be generated, which can provide a testing ground for analysis applied to the solar wind data. Results. We demonstrate this tool by investigating Parker Solar Probe’s seventh encounter trajectory and data, and we showcase several possible ways in which it can be used. We find that whether temporal variations in the spacecraft frame come from parallel or perpendicular variations in the plasma frame strongly depends on the spectral and power anisotropy of the measured wind. Conclusions. Data analysis assisted by such underlying synthetic models as presented here could open up new ways to interpret measurements in the future, specifically in the more reliable determination of plasma frame quantities from temporal measurements.

Student Motivation Analysis Based on Raising-Hand Videos.

In current smart classroom research, numerous studies focus on recognizing hand-raising, but few analyze the movements to interpret students' intentions. This limitation hinders teachers from utilizing this information to enhance the effectiveness of smart classroom teaching. Assistive teaching methods, including robotic and artificial intelligence teaching, require smart classroom systems to both recognize and thoroughly analyze hand-raising movements. This detailed analysis enables systems to provide targeted guidance based on students' hand-raising behavior. This study proposes a morphology-based analysis method to innovatively convert students' skeleton key point data into several one-dimensional time series. By analyzing these time series, this method offers a more detailed analysis of student hand-raising behavior, addressing the limitations of deep learning methods that cannot compare classroom hand-raising enthusiasm or establish a detailed database of such behavior. This method primarily utilizes a neural network to obtain students' skeleton estimation results, which are then converted into time series of several variables using the morphology-based analysis method. The YOLOX and HrNet models were employed to obtain the skeleton estimation results; YOLOX is an object detection model, while HrNet is a skeleton estimation model. This method successfully recognizes hand-raising actions and provides a detailed analysis of their speed and amplitude, effectively supplementing the coarse recognition capabilities of neural networks. The effectiveness of this method has been validated through experiments.

Two-dimensional Hilbert-Huang transform-based thermographic data processing for non-destructive material defect detection

ABSTRACT Previous research has established the Hilbert-Huang transform (HHT) as a powerful tool for processing and analysing one-dimensional time series signals. Its extension into multi-dimensional Euclidean spaces further demonstrates its versatility. In this study, we leverage a two-dimensional (2D) HHT to enhance non-destructive testing, utilising active infrared thermographic data to improve the detection of material defects. The proposed methodology incorporates a 2D HHT, which synergises multidimensional ensemble empirical mode decomposition with the Riesz transform (RT). This combination is adept at uncovering both global (i.e. intrinsic mode functions) and local (i.e. phase angle and spatial frequency) information. In particular, RT is integrated with a Gaussian filter, which allows for a more thorough analysis of the inherent characteristics of defects through the monogenic signal produced by RT. The experimental application of this method on a mosaic sample, intentionally embedded with defects, has yielded promising results. The approach effectively distinguishes critical defect signals from the surroundings, leading to more accurate and clearer results.

Carbon price forecasting using leaky integrator echo state networks with the framework of decomposition-reconstruction-integration

Carbon trading is one of the strategies to achieve the goal of dual carbon. However, carbon prices exhibit non-stationary and nonlinear characteristics, posing significant challenges for accurate forecasting. Inspired by the ideas of “division and conquest” and “granularity reconstruction”, a decomposition-reconstruction-integration framework is built for carbon price forecasting. The proposed model leverages a comprehensive ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and sample entropy (SE) to extract features from two perspectives of time and complexity, and thus the one-dimensional time series of carbon price is reconstructed into different items. Subsequently, leaky integrator echo state networks (LiESNs) are utilized to forecast each of these items individually. These individual forecasts are then integrated to generate the final point forecast. To evaluate the uncertainty of the point forecast, a Gaussian process model is applied to interval forecast. The proposed model comprehensively considers the time series features of carbon price including the temporal modal features in the decomposition stage, the entropy probability features in the reconstruction stage, and the essential temporal dependencies via dynamic reservoir of interconnected neurons in the integration forecasting stage. Experimental results demonstrate the model's exceptional forecasting performance, surpassing the effectiveness of alternative approaches.

Fault Diagnosis of Hydropower Units Based on Gramian Angular Summation Field and Parallel CNN

To enhance the operational efficiency and fault detection accuracy of hydroelectric units, this paper proposes a parallel convolutional neural network model that integrates the Gramian angular summation field (GASF) with an Improved coati optimization algorithm–parallel convolutional neural network (ICOA-PCNN). Additionally, to further improve the model’s accuracy in fault identification, a multi-head self-attention mechanism (MSA) and support vector machine (SVM) are introduced for a secondary optimization of the model. Initially, the GASF technique converts one-dimensional time series signals into two-dimensional images, and a COA-CNN dual-branch model is established for feature extraction. To address the issues of uneven population distribution and susceptibility to local optima in the COA algorithm, various optimization strategies are implemented to improve its global search capability. Experimental results indicate that the accuracy of this model reaches 100%, significantly surpassing other nonoptimized models. This research provides a valuable addition to fault diagnosis technology for modern hydroelectric units.

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.

Time series diffusion method: A denoising diffusion probabilistic model for vibration signal generation

Diffusion models have demonstrated powerful data generation capabilities in various research fields such as image generation. However, in the field of vibration signal generation, the criteria for evaluating the quality of the generated signal are different from that of image generation and there is a fundamental difference between them. At present, there is no research on the ability of diffusion model to generate vibration signal. In this paper, a Time Series Diffusion Method (TSDM) is proposed for vibration signal generation, leveraging the foundational principles of diffusion models. The TSDM uses an improved U-net architecture with attention block, ResBlock and TimeEmbedding to effectively segment and extract features from one-dimensional time series data. It operates based on forward diffusion and reverse denoising processes for time-series generation. Experimental validation is conducted using single-frequency, multi-frequency datasets, and bearing fault datasets. The results show that TSDM can accurately generate the single-frequency and multi-frequency features in the time series and retain the basic frequency features for the diffusion generation results of the bearing fault series. It is also found that the original DDPM could not generate high quality vibration signals, but the improved U-net in TSDM, which applied the combination of attention block and ResBlock, could effectively improve the quality of vibration signal generation. Finally, TSDM is applied to the small sample fault diagnosis of three public bearing fault datasets, and the results show that the accuracy of small sample fault diagnosis of the three datasets is improved by 32.380%, 18.355% and 9.298% at most, respectively.

Monitoring the Dynamic Networks of Stock Returns with an Application to the Swedish Stock Market

AbstractIn this paper, two approaches for measuring the distance between stock returns and the network connectedness are presented that are based on the Pearson correlation coefficient dissimilarity and the generalized variance decomposition dissimilarity. Using these two procedures, the center of the network is determined. Also, hierarchical clustering methods are used to divide the dense networks into sparse trees, which provide us with information about how the companies of a financial market are related to each other. We implement the derived theoretical results to study the dynamic connectedness between the companies in the Swedish capital market by considering 28 companies included in the determination of the market index OMX30. The network structure of the market is constructed using different methods to determine the distance between the companies. We use hierarchical clustering methods to find the relation among the companies in each window. Next, we obtain a one-dimensional time series of the distances between the clustering trees that reflect the changes in the relationship between the companies in the market over time. The method from statistical process control, namely the Shewhart control chart, is applied to those time series to detect abnormal changes in the financial market.

Multi-scale attention network (MSAN) for track circuits fault diagnosis

As one of the three major outdoor components of the railroad signal system, the track circuit plays an important role in ensuring the safety and efficiency of train operation. Therefore, when a fault occurs, the cause of the fault needs to be found quickly and accurately and dealt with in a timely manner to avoid affecting the efficiency of train operation and the occurrence of safety accidents. This article proposes a fault diagnosis method based on multi-scale attention network, which uses Gramian Angular Field (GAF) to transform one-dimensional time series into two-dimensional images, making full use of the advantages of convolutional networks in processing image data. A new feature fusion training structure is designed to effectively train the model, fully extract features at different scales, and fusing spatial feature information through spatial attention mechanisms. Finally, experiments are conducted using real track circuit fault datasets, and the accuracy of fault diagnosis reaches 99.36%, and our model demonstrates better performance compared to classical and state-of-the-art models. And the ablation experiments verified that each module in the designed model plays a key role.

Anomaly Identification for Photovoltaic Power Stations Using a Dual Classification System and Gramian Angular Field Visualization

With the increasing scale of photovoltaic (PV) power stations, timely anomaly detection through analyzing the PV output power curve is crucial. However, overlooking the impact of external factors on the expected power output would lead to inaccurate identification of PV station anomalies. This study focuses on the discrepancy between measured and expected PV power generation values, using a dual classification system. The system leverages two-dimensional Gramian angular field (GAF) data and curve features extracted from one-dimensional time series, along with attention weights from a CNN network. This approach effectively classifies anomalies, including normal operation, aging pollution, and arc faults, achieving an overall classification accuracy of 95.83%.

Delegated quantum neural networks for encrypted data

Quantum machine learning is expected to utilize the potential advantages of quantum computing to advance the efficiency of machine learning. However, with the help of quantum cloud servers, ordinary users may confront the threat of privacy leakage of input data and models when performing the training or inference of quantum neural networks (QNNs). To address this problem, we present a new framework that allows the training and inference of delegated QNNs to be performed on encrypted data to protect the privacy of users’ data and models. This framework contains two models that are alternately trained: an encryptor and a predictor. The classical client first trains the encryptor defined by a classical neural network to map plaintext input data to vastly different ciphertext data. The ciphertext data is sent to the quantum cloud server to train the predictor defined by a QNN, which can indirectly predict the labels of plaintext data. With the trained encryptor and predictor, the client can send the encrypted data to the server for prediction and obtain almost equivalent prediction results. The proposed framework is applied to three types of QNN models, each dealing with low-dimensional tabular data, image data, and one-dimensional time series data, respectively. Experimental results show that the privacy protection method based on our framework can protect data and model privacy without degrading the performance of QNNs. The framework does not require users to have quantum capabilities and is suitable for protecting data and model privacy for various QNN models.

A small sample bearing fault diagnosis method based on novel Zernike moment feature attention convolutional neural network

Bearings are one of the core components of rotating machine machinery. Monitoring their health status can ensure the safe and stable operation of rotating machine equipment. The limited nature of bearing fault samples makes it difficult to meet the demand for sufficient samples based on deep learning methods. Therefore, how to solve the problem of small- samples is the key to achieving intelligent fault diagnosis. In bearing failures based on vibration signals, the complex operating environment causes the vibration signals to inevitably mix with noise. The mixing of fault signature features and noise intensifies the strong spatial coupling of different types of fault features. In addition, diagnosing bearing failures under different loads is challenging because of the complex working conditions of bearings. Given the above problems, a small sample-bearing fault diagnosis method based on a high and low-frequency layered algorithm (HLFLA) and a novel Zernike moment feature attention convolutional neural network (ZMFA-CNN) is proposed. First, the proposed HLFLA converts one-dimensional time series signals into two-dimensional signals distributed rectangularly according to different frequency bands, and is used to simplify network feature screening, reduce the impact of noise, and retain adjacent signal constraint information. In addition, a new ZMFA-CNN is proposed to further extract multi-order moment features and attention weights, and can significantly improve the model generalization ability without increasing model parameters. At the same time, it is combined with FilterResponseNorm2d and thresholded linear unit to further improve model performance. Finally, sufficient experiments verified that the algorithm proposed in this paper can solve the above problems and has excellent transfer generalization ability and noise robustness. In addition, the experimental results of applying the algorithm proposed in this article to gas turbine main bearing fault diagnosis prove the reliability of the algorithm proposed in this article.

Алгоритм динамического распределения и балансировки нагрузки в распределенных облачных вычислениях

A mathematical model and algorithm of a two-level load management system for virtual clusters of a data processing center (data center) have been developed. At the first management level, virtual machines (VMs) are assigned to physical servers. At the same time, a greedy algorithm is used with restrictions on the time of searching for acceptable load distribution alternatives. The second level of management is implemented taking into account the chaotic structure of network traffic between the data center and users. Checking for the randomness of a time series of information traffic is carried out using Lyapunov exponents. The predictive model of the load intensity is implemented using the method of phase space reconstruction based on a set of values of a one-dimensional time series. When constructing a reconstructed phase space attractor, the time delay value is selected from the condition of reaching the zero value of the autocorrelation function, and the dimension of the embedding is determined by the angle of inclination of the straight line approximating the dependence of the value of the correlation integral on the radius of a given threshold point. The Tayler window is used to exclude correlated points in the numerical series. The criterion for evaluating the effectiveness of the developed algorithm is an integral indicator of the deviation of the load of each server from a given level. The proposed model can be used to build a data center load balancing system in conditions of its nonlinear nature.

Battery health prediction using two-dimensional multi-channel ensemble models

The accurate assessment of battery health is crucial for maximizing the performance and lifespan of lithium-ion batteries. In this paper, an ensemble model based on a two-dimensional multi-channel convolutional neural network is proposed to predict the maximum usable capacity of lithium-ion batteries. First, based on the charge–discharge process, the characteristic-derived lines of the capacity–voltage (Q–V) curve are extracted. Next, the Gramian angular summation field (GASF) is employed to convert one-dimensional time series data into image matrices, with the aim of preserving temporal characteristics. Finally, the paper discusses the impact of 2D matrix size on prediction results and introduces the use of a 2D multi-channel ensemble model for the unsupervised recognition and extraction of battery decline information from images, marking the first time this approach has been utilized. The experimental results demonstrate that the proposed method effectively captures battery degradation patterns from multiple perspectives. The average mean absolute percentage error of 1.95% and root mean square error of 1.41% on the verified batteries indicate the robustness and generalizability of the approach.

Bearing Fault Diagnosis Based on VMD-WPT-ViT for Wind Turbine

As an important part of wind turbine, the fault diagnosis of rolling bearings is helpful to maintain the stable operation of the fan. However, most of the existing fault diagnosis methods focus on one-dimensional time series data, which is not only difficult to extract multi-level feature information, but also fails to consider the noise problem in the signal. Therefore, to solve the above problems, a noise reduction algorithm combining variational mode decomposition (VMD) and wavelet packet threshold noise reduction (WPT) is proposed, and Vision-Transformer (ViT) model is combined to realize the fault diagnosis of rolling bearings of wind turbines. VMD is used to decompose the original signal and find out the noisy component. WPT is used to de-noise the component, and the de-noised component and other components are reconstructed to form a pure signal and converted into a two-dimensional image. Finally, a diagnostic model is built based on Vision-transformer. The experimental results show that the proposed method can effectively improve the diagnostic accuracy by extracting the advanced global features of the signal.

Compound fault diagnosis of rolling bearings with few-shot based on DCGAN-RepLKNet

To guarantee the security of personnel on-site, diagnosing the malfunction of mechanical apparatus is imperative. The accomplishments within the domain of fault diagnosis have been partly attributed to the advancements in deep learning technology, which excels in feature extraction through extensive datasets. However, it is difficult to collect sufficient data to train high-precision fault diagnosis models in practice. A novel method called deep convolution generative adversarial network (DCGAN)-RepLKNet is proposed to address the challenge of gathering enough data to train high-precision fault diagnosis models in practice. This technique involves transforming a one-dimensional time series vibration signal into a two-dimensional (2D) time-frequency map via wavelet transform technology. Subsequently, DCGAN expands the 2D time–frequency map samples produced. Finally, RepLKNet is used to classify the fault samples. The proposed method has been verified in the PU compound fault data set and bearing real damage data set. The results show that the accuracy of this method has been improved by 5.70%, 6.34%, 9.08%, and 16.35% compared to 2D-CNN under different sizes datasets in case 1, and by 24.5% compared to 2D-CNN in case 2.

High-resolution short-term prediction of the COVID-19 epidemic based on spatial-temporal model modified by historical meteorological data

In the global challenge of Coronavirus disease 2019 (COVID-19) pandemic, accurate prediction of daily new cases is crucial for epidemic prevention and socioeconomic planning. In contrast to traditional local, one-dimensional time-series data-based infection models, the study introduces an innovative approach by formulating the short-term prediction problem of new cases in a region as multidimensional, gridded time series for both input and prediction targets. A spatial-temporal depth prediction model for COVID-19 (ConvLSTM) is presented, and further ConvLSTM by integrating historical meteorological factors (Meteor-ConvLSTM) is refined, considering the influence of meteorological factors on the propagation of COVID-19. The correlation between 10 meteorological factors and the dynamic progression of COVID-19 was evaluated, employing spatial analysis techniques (spatial autocorrelation analysis, trend surface analysis, etc.) to describe the spatial and temporal characteristics of the epidemic. Leveraging the original ConvLSTM, an artificial neural network layer is introduced to learn how meteorological factors impact the infection spread, providing a 5-day forecast at a 0.01° × 0.01° pixel resolution. Simulation results using real dataset from the 3.15 outbreak in Shanghai demonstrate the efficacy of Meteor-ConvLSTM, with reduced RMSE of 0.110 and increased R2 of 0.125 (original ConvLSTM: RMSE = 0.702, R2 = 0.567; Meteor-ConvLSTM: RMSE = 0.592, R2 = 0.692), showcasing its utility for investigating the epidemiological characteristics, transmission dynamics, and epidemic development.