One-dimensional Time Series Research Articles

Intraflow temporal correlation-based network traffic prediction

Traditional network traffic prediction methods often rely on complex models that extract features by spatiotemporal dependency analysis in network traffic matrices. However, these methods are limited by specific network topologies and lack generalization ability. Furthermore, it is difficult for traditional time series models to capture multiperiod features. In this study, we propose a network traffic prediction method to address the aforementioned issues, where we combine the flow-by-flow mechanism with an improved TimesNet model. The proposed method transforms the original network traffic matrix into origin-destination sequences using a flow-by-flow mechanism and then uses the improved TimesNet model to transform one-dimensional time series into multiperiod two-dimensional tensors. These transformations not only overcome the limitations of network topologies and the lack of one-dimensional time series representation ability but also focus the analysis on the temporal correlations within the flow. The CoTAttention module is introduced to extract the deep features of periodically changing network traffic, thus improving the accuracy of network traffic prediction. We conduct experiments on the Abilene and GÉANT datasets to verify the effectiveness of the proposed network traffic prediction model based on intraflow temporal correlations. Moreover, we compare its performance with other advanced methods. The experimental results show that the proposed method exhibits superior performance in network traffic prediction tasks, providing powerful guidance for network bandwidth allocation and resource optimization.

Bus Schedule Time Prediction Based on LSTM-SVR Model

With the acceleration of urbanization, urban bus scheduling systems are facing unprecedented challenges. Traditional bus scheduling provides the original schedule time and the planned time of arrival at the destination, where the schedule time is the departure time of the bus. However, various factors encountered during the drive result in significant differences in the driving time of the bus. To ensure timely arrivals, the bus scheduling system has to rely on manual adjustments to optimize the schedule time to determine the actual departure time. In order to reduce the scheduling cost and align the schedule time closer to the actual departure time, this paper proposes a dynamic scheduling model, LSTM-SVR, which leverages the advantages of LSTM in capturing the time series features and the ability of SVR in dealing with nonlinear problems, especially its generalization ability in small datasets. Firstly, LSTM is used to efficiently capture features of multidimensional time series data and convert them into one-dimensional effective feature outputs. Secondly, SVR is used to train the nonlinear relationship between these one-dimensional features and the target variables. Thirdly, the one-dimensional time series features extracted from the test set are put into the generated nonlinear model for prediction to obtain the predicted schedule time. Finally, we validate the model using real data from an urban bus scheduling system. The experimental results show that the proposed hybrid LSTM-SVR model outperforms LSTM-BOA, SVR-BOA, and BiLSTM-SOA models in the accuracy of predicting bus schedule time, thus confirming the effectiveness and superior prediction performance of the model.

Feature-fused residual network for time series classification

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

Anomaly detection in sensor data via encoding time series into images

Detecting anomalies in multivariate time series data is crucial for maintaining the optimal functionality of control system equipment. While existing research has made significant strides in this area, the increasing complexity of industrial environments poses challenges in accurately capturing the interactions between variables. Therefore, this paper introduces an innovative anomaly detection approach that extends one-dimensional time series into two-dimensions to capture the spatial correlations within the data. Unlike traditional approaches, we utilize the Gramian Angular Field to encode the correlations between different sensors at specific time points into images, enabling precise learning of spatial information across multiple variables. Subsequently, we construct an adversarial generative model to accurately identify anomalies at the pixel level, facilitating precise localization of abnormal points. We evaluate our method using five open-source datasets from various fields. Our method outperforms state-of-the-art anomaly detection techniques across all datasets, showcasing its superior performance. Particularly, our method achieves a 11.5% increase in F1 score on the high-dimensional WADI dataset compared to the baseline method. Additionally, we conduct thorough effectiveness analysis, parameter impact experiments, significant statistical analysis, and burden analysis, confirming the efficacy of our approach in capturing both the temporal dynamics and spatial relationships inherent in multivariate time series data.

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.

Comparative analysis of speaker identification performance using deep learning, machine learning, and novel subspace classifiers with multiple feature extraction techniques

Speaker identification is vital in various application domains, such as automation, security, and enhancing user experience. In the literature, convolutional neural network (CNN) or recurrent neural network (RNN) classifiers are generally used due to the one-dimensional time series of speech signals. However, new approaches using subspace classifiers are also crucial in speaker identification. In this study, in addition to the newly developed subspace classifiers for speaker identification, traditional classification algorithms, and various hybrid algorithms are analyzed in terms of performance. Stacked Features-Common Vector Approach (SF-CVA) and Hybrid CVA-Fisher Linear Discriminant Analysis (HCF) subspace classifiers are used for speaker identification for the first time in the literature. In addition, CVA is evaluated for the first time for speaker identification using hybrid deep learning algorithms. The study includes Recurrent Neural Network-Long Short-Term Memory (RNN-LSTM), i-vector + Probabilistic Linear Discriminant Analysis (i-vector+PLDA), Time Delayed Neural Network (TDNN), AutoEncoder+Softmax (AE+Softmax), K-Nearest Neighbors (KNN), Support Vector Machine (SVM), Common Vector Approach (CVA), SF-CVA, HCF, and Alexnet classifiers for speaker identification. This study uses MNIST, TIMIT and Voxceleb1 databases for clean and noisy speech signals. Six different feature structures are tested in the study. The six different feature extraction approaches consist of Mel Frequency Cepstral Coefficients (MFCC)+Pitch, Gammatone Filter Bank Cepstral Coefficients (GTCC)+Pitch, MFCC+GTCC+Pitch+seven spectral features, spectrograms,i-vectors, and Alexnet feature vectors. High accuracy rates were obtained, especially in tests using SF-CVA. RNN-LSTM, i-vector+KNN, AE+Softmax, TDNN, and i-vector+HCF classifiers also gave high test accuracy rates.

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.