Dilated Causal Convolutions Research Articles

Pruned tree-structured temporal convolutional networks for quality variable prediction of industrial process

In real industrial processes, the rapid and accurate acquisition of quality variables is essential. Therefore, this paper proposes a pruned tree-structured temporal convolutional network (PT-TCN) for efficient and accurate variables prediction. First, a novel tree network is developed, utilizing dilated causal convolution blocks as nodes to avoid the loss of local information. Each node extracts distinct local information, and by concatenating all tree nodes, the network can capture a comprehensive range of temporal scales. Then, to avoid the increased complexity caused by the tree structure, we design an online two-stage pruning strategy to compress the tree network without introducing additional computations. During the training process, blocks are initially pruned based on the correlation assessment between quality variables and tree nodes. Subsequently, weight normalization layers are employed to evaluate the importance of output channels in blocks, thereby enabling intra-block channel pruning. The effectiveness of PT-TCN is verified on Tennessee Eastman benchmark process. In addition, experiments on the real zinc flotation process demonstrate that the proposed PT-TCN improves in R2 and MAE by 1.32% and 1.26% respectively in predicting quality variables, and it can reduce 91.8% parameters of the initial tree-structured TCN without sacrificing accuracy.

Feature-Level Fusion Multi-Sensor Aggregation Temporal Network for Smartphone-Based Human Activity Recognition

Smartphone-based Human Activity Recognition (HAR) identifies human movements using inertial signals gathered from multiple smartphone sensors. Generally, these signals are stacked as one (data-level fusion) and fed into deep learning algorithms for feature extractions. This research studies feature-level fusion, individually processing inertial signals from each sensor, and proposes a lightweight deep temporal learning model, Feature-Level Fusion Multi-Sensor Aggregation Temporal Network (FLF-MSATN), that performs feature extraction on inertial signals from each sensor separately. The raw signals, segmented into equally sized time windows, are passed into individual Dilated-Pooled Convolutional Heads (DPC Heads) for temporal feature analysis. Each DPC Head has a spatiotemporal block containing dilated causal convolutions and average pooling, to extract underlying patterns. The DPC Heads’ outputs are concatenated and passed into a Global Average Pooling layer to generate a condensed confidence map before activity classification. FLF-MSATN is assessed using a subject-independent protocol on a publicly available HAR dataset, UCI HAR, and a self-collected HAR dataset, achieving 96.67% and 82.70% accuracies, respectively. A Data-Level Fusion MSATN is built to compare and verify the model performance attained by the proposed FLF-MSATN. The empirical results show that implementing FLF-MSATN enhances the accuracy by ~3.4% for UCI HAR and ~9.68% for self-collected datasets.

Temporal convolutional network with soft threshold and contractile self-attention mechanism for remaining useful life prediction of rolling bearings

Abstract RUL prediction is an effective approach to prevent system failures and cut maintenance expenditures. Due to the wide receptive field and the avoidance of future information leakage, temporal convolutional neural network (TCN) is widely applied for RUL estimation of bearings. However, the predictive performance of TCN is limited by the loss of degradation features and the breakdown of continuity of timing information. To overcome the above defects, hybrid temporal convolutional neural network with soft threshold and contractile self-attention mechanism (HTCN-SC) is presented. Firstly, the adaptive threshold is determined by the contraction self-attention mechanism with higher interpretability, which captures the contribution of different features to the estimation of RUL. Then, the soft threshold is employed to activate the degraded features. On the one hand, the degeneracy features endowed by the dilated causal convolution with obvious negative values are fully preserved. On the other hand, the noise components that are given low weights are completely suppressed compared to the original TCN. Finally, parallel branch composed of one-dimensional convolutional networks are used to supplement the continuity of time series. Degradation signals from different working conditions and bearings are employed to verify the performance of the HTCN-SC. The results indicate that HTCN-SC with accurate RUL estimation and generalization ability is an effective tool for rolling bearing health monitoring.

AdpSTGCN: Adaptive spatial–temporal graph convolutional network for traffic forecasting

Traffic flow forecasting plays a crucial role in applications such as intelligent transportation systems. Despite significant research in this field, the current methods have limitations that hinder the realization of highly accurate predictions. Existing GCN-based approaches typically rely on a definite graph structure derived from a physical topology or learned from node features, which is insufficient for building intricate spatial relationships among nodes. To address this challenge, we propose an adaptive spatial–temporal graph convolutional network for traffic forecasting. Our approach exploits a multi-head attention mechanism to construct multi-view feature graphs. We then introduce an adaptive graph convolution method to dynamically aggregate and propagate information from both the topology graph and multi-view feature graphs, which are capable of capturing complex spatial correlations across diverse proximity ranges. Furthermore, we designed a cascaded structural framework that combines temporal information with node features using gated dilated causal convolution to ensure the integrated modeling of spatial–temporal dynamics in traffic flow. Experiments on real-world datasets demonstrate that our proposed method outperforms the current mainstream methods, achieving better performance in traffic flow forecasting. The code is available at https://github.com/dhxdla/AdpSTGCN.git.

TVGCN: Time-varying graph convolutional networks for multivariate and multifeature spatiotemporal series prediction.

Spatiotemporal (ST) graph modeling has garnered increasing attention recently. Most existing methods rely on a predefined graph structure or construct a single learnable graph throughout training. However, it is challenging to use a predefined graph structure to capture dynamic ST changes effectively due to evolving node relationships over time. Furthermore, these methods typically utilize only the original data, neglecting external temporal factors. Therefore, we put forward a novel time-varying graph convolutional network model that integrates external factors for multifeature ST series prediction. Firstly, we construct a time-varying adjacency matrix using attention to capture dynamic spatial relationships among nodes. The graph structure adapts over time during training, validation, and testing phases. Then, we model temporal dependence by dilated causal convolution, leveraging gated activation unit and residual connection. Notably, the prediction accuracy is enhanced through the incorporation of embedding absolute time and the fusion of multifeature. This model has been applied to three real-world multifeature datasets, achieving state-of-the-art performance in all cases. Experiments show that the method has high accuracy and robustness when applied to multifeature and multivariate ST series problems.

Fault detection and classification in overhead transmission lines through comprehensive feature extraction using temporal convolution neural network

AbstractFaults in transmission lines cause instability of power system and result in degrading end users sophisticated equipment. Therefore, in case of fault and for the quick restoration of problematic phases, reliable and accurate fault detection and classification techniques are required to categorize the faults in a minimum time. In this work, 500 kV transmission line (Jamshoro‐New Karachi), Sindh, Pakistan has been modeled in MATLAB. The discrete wavelet transform (DWT) has been used to extract features from the transient current signal for different faults in 500 kV transmission line under various parameters such as fault location, fault inception angle, ground resistance and fault resistance and time series data has been obtained for fault classification. Moreover, the temporal convolutional neural network (TCN) is used for fault classification in 500 kV transmission network due to its robust framework. From simulation results, it is found that faults in 500 kV transmission line are classified with 99.9% accuracy. Furthermore, the simulation results of the TCN model compared to bidirectional long short‐term memory (BiLSTM) and Gated Recurrent Unit (GRU) and it has been found that TCN model is capable of classifying faults in 500 kV transmission line with high accuracy due to its ability to handle long receptive field size, less memory requirement and parallel processing due to dilated causal convolutions. Through this work, the meantime to repair of 500 kV transmission line can be reduced.

Fully automatic quantification for hand synovitis in rheumatoid arthritis using pixel-classification-based segmentation network in DCE-MRI.

A classification-based segmentation method is proposed to quantify synovium in rheumatoid arthritis (RA) patients using a deep learning (DL) method based on time-intensity curve (TIC) analysis in dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). This retrospective study analyzed a hand MR dataset of 28 RA patients (six males, mean age 53.7years). A researcher, under expert guidance, used in-house software to delineate regions of interest (ROIs) for hand muscles, bones, and synovitis, generating a dataset with 27,255 pixels with corresponding TICs (muscle: 11,413, bone: 8502, synovitis: 7340). One experienced musculoskeletal radiologist performed ground truth segmentation of enhanced pannus in the joint bounding box on the 10th DCE phase, or around 5min after contrast injection. Data preprocessing included median filtering for noise reduction, phase-only correlation algorithm for motion correction, and contrast-limited adaptive histogram equalization for improved image contrast and noise suppression. TIC intensity values were normalized using zero-mean normalization. A DL model with dilated causal convolution and SELU activation function was developed for enhanced pannus segmentation, tested using leave-one-out cross-validation. 407 joint bounding boxes were manually segmented, with 129 synovitis masks. On the pixel-based level, the DL model achieved sensitivity of 85%, specificity of 98%, accuracy of 99% and precision of 84% for enhanced pannus segmentation, with a mean Dice score of 0.73. The false-positive rate for predicting cases without synovitis was 0.8%. DL-measured enhanced pannus volume strongly correlated with ground truth at both pixel-based (r = 0.87, p < 0.001) and patient-based levels (r = 0.84, p < 0.001). Bland-Altman analysis showed the mean difference for hand joints at the pixel-based and patient-based levels were -9.46 mm3 and -50.87 mm3, respectively. Our DL-based DCE-MRI TIC shape analysis has the potential for automatic segmentation and quantification of enhanced synovium in the hands of RA patients.

Load Prediction in Double-Channel Residual Self-Attention Temporal Convolutional Network with Weight Adaptive Updating in Cloud Computing.

When resource demand increases and decreases rapidly, container clusters in the cloud environment need to respond to the number of containers in a timely manner to ensure service quality. Resource load prediction is a prominent challenge issue with the widespread adoption of cloud computing. A novel cloud computing load prediction method has been proposed, the Double-channel residual Self-attention Temporal convolutional Network with Weight adaptive updating (DSTNW), in order to make the response of the container cluster more rapid and accurate. A Double-channel Temporal Convolution Network model (DTN) has been developed to capture long-term sequence dependencies and enhance feature extraction capabilities when the model handles long load sequences. Double-channel dilated causal convolution has been adopted to replace the single-channel dilated causal convolution in the DTN. A residual temporal self-attention mechanism (SM) has been proposed to improve the performance of the network and focus on features with significant contributions from the DTN. DTN and SM jointly constitute a dual-channel residual self-attention temporal convolutional network (DSTN). In addition, by evaluating the accuracy aspects of single and stacked DSTNs, an adaptive weight strategy has been proposed to assign corresponding weights for the single and stacked DSTNs, respectively. The experimental results highlight that the developed method has outstanding prediction performance for cloud computing in comparison with some state-of-the-art methods. The proposed method achieved an average improvement of 24.16% and 30.48% on the Container dataset and Google dataset, respectively.

Efficient shrinkage temporal convolutional network model for photovoltaic power prediction

Power stations operating on PhotoVoltaic (PV) power generation are challenged by demand forecasting as PV power generation is random and intermittent. This paper presents an Efficient Shrinkage Temporal Convolutional Network (ESTCN) model, which combines the Temporal Convolutional Network (TCN) and an improved Deep Residual Shrinkage Network (DRSN) to forecast PV power output. First, the attention sub-network of the DRSN is improved, the fully connected layer of the sub-network is canceled, and feature extraction is done directly on the model features following global average pooling using a one-dimensional convolution to obtain cross-channel interaction and increased model efficiency. Next, an improved attention mechanism and adaptive soft thresholding are introduced into TCN to automatically determine the noise threshold to address the issue of information weight dispersion caused by redundant information in the input samples. By incorporating dilated causal convolution, attention module, soft thresholding, and residual connection, the ESTCN model is formed and is shown to enhance PV power output prediction with only a minimal increase in the number of parameters. The power station in Ningxia, China is adopted as a validation example with data taken from the year 2020. The fitting and prediction results of the ESTCN model are compared against the Convolutional Neural Network, Long Short-Term Memory, and TCN models. The ESTCN model yielded the following values of the evaluation metrics: Root Mean Square Error (RMSE) of 1.47 kW, Mean Absolute Error (MAE) of 0.79 kW, and coefficient of determination of 0.999. Compared to the TCN model, the prediction errors based on RMSE and MAE improved by 0.39 kW and 0.18 kW, respectively. Applying the ESTCN model to predict PV power generation of power stations in two regions in China, Ningxia and Xinjiang, shows the ESTCN model to be superior, scalable, and universal over other deep learning models.

A novel approach based on spatio-temporal attention and multi-scale modeling for mechanical failure prediction

Accurately predicting the remaining useful life (RUL) of equipment is crucial for planning production and eliminating unplanned downtime events. Specifically, the application of effective RUL prediction methods can detect potential equipment failures in advance to provide timely maintenance measures, which can help enterprises better plan and manage resources, optimize production plans, and provide strong support for subsequent maintenance decisions. The data-driven approaches have achieved great success in the field of RUL prediction by fully exploiting mechanical degradation information from historical operation data. However, these approaches have certain limitations, for instance, (1) they always fail to precisely extract spatial and temporal features in noisy environments simultaneously; (2) they often fail to effectively capture local features and global degradation trends simultaneously. To overcome the above limitations, we design an end-to-end model, termed ASATCN-TABGRU, for mechanical failure prediction, which contains an automatic shrinking attention temporal convolutional network (ASATCN) and a temporal attention bidirectional gated recurrent unit (TABGRU). In ASATCN module, to extract spatio-temporal information from historical operation data, we first perform a multi-scale modeling of historical operation data through a deliberately designed dilated causal convolution subnetwork (DCCS) to obtain local features. Then, we propose a novel soft thresholding subnetwork (STS) based on the normalization-based attention module (NAM), to capture useful temporal features through the automatic shrinking soft thresholding mechanism from the local features sequence; in addition, we design a hybrid attention subnetwork (HAS) to capture spatial features with flexible and different importance by the spatial-channel attention mechanism from historical operation data. The precise extraction of spatio-temporal features is then achieved through a connection operation. With the above encoded spatio-temporary features sequence, a TABGRU module is further proposed to capture global degradation trends by simultaneously extracting contextual information and historical influence information, thereby effectively modeling the local and global features. The experiments show that our approach has better performance and robustness, compared with other state-of-the-art approaches, particularly on the small sample dataset.

High-Order Temporal Convolutional Network for Improving Classification Performance of SSVEP-EEG

Background and objectiveSteady-state visual evoked potential (SSVEP)-based brain-computer interfaces (BCIs) aim to detect target frequencies corresponding to specific commands in electroencephalographic (EEG) signals by classification algorithms to achieve the desired control. However, SSVEP signals suffer from low signal-to-noise ratio and large differences in brain activity. Moreover, the existing CNN models have small receptive fields, which make it difficult to receive large range of feature information and limit the effectiveness of classification algorithms. MethodsTo this end, we proposed a high-order temporal convolutional neural network (HOT-CNN) model for enhancing the performance of SSVEP target recognition. Specifically, the SSVEP-EEG signals was divided into equal-length time segments and a time-slice attention module was designed to capture the correlation between time slices. The module improves the local characterization of signals and reduces biological noise interference by automatically assigning high weights to locally relevant temporal sampling cues and lower weights to other temporal cues. Moreover, for global features, a temporal convolutional network module was designed to increases the receptive field of the network and to extract more comprehensive time domain features by using dilated causal convolution. Finally, the fusion and analysis of local and global features are achieved by designing a feature fusion and classification module to accomplish accurate classification of SSVEP signals. ResultsOur method was evaluated on large publicly available datasets containing 35 subjects and 40 categories. Experimental results indicated that HOT-CNN achieved encouraging performance compared with other advanced methods: the highest information transfer rate of 241.01bits/min was obtained using 0.5s stimuli, and the highest average accuracy of 96.39% was obtained using 1.0s stimuli. ConclusionsThe method effectively reinforced the global and local time-domain information and improved the classification performance of SSVEP, which has wide application prospects.

Error prediction of a capacitor voltage transformer using dilated causal convolution and LSTM

To timely and accurately complete the error prediction of capacitor voltage transformers, this paper proposes an error prediction algorithm for capacitor voltage transformers that combines dilated causal convolution and LSTM. The algorithm is divided into two parts: one part updates the state of the input sequence using LSTM, while the other part extracts features through dilated causal convolution, maintaining data causality about the original sequence. Finally, the outputs of these two parts are combined to make the obtained sequence feature information more accurate and enriched. Experiments show that the MSE between the error prediction results obtained by this method and the actual error samples of capacitor voltage transformers is only 0.0003, which can accurately and efficiently complete the error prediction of capacitor voltage transformers.

Remaining useful life estimation of bearing using spatio-temporal convolutional transformer

The maintenance costs, productivity, health, and safety of mechanical equipment all heavily rely on the remaining usable life (RUL) of the bearings. Recently, the transformer has been widely used in the RUL field due to its ability to capture some of the degradation information of the bearing. However, the transformer is weak in acquiring local information and fails to extract temporal features from the degradation process. To solve the above problems, this paper proposes a spatio-temporal convolutional transformer (STCT) model, which mainly consists of the dual convolutional spatio-temporal network (DCSTN) and multi-scale transformer (MST). It not only captures the degradation features of the bearings from the temporal and spatial perspectives but also enhances the ability of the transformer to acquire local information. We propose DCSTN as a feature extraction module, and the proposed spatio-temporal attention as the core of the DCSTN can capture the relevant degradation state features at different moments. In addition, MST uses a new module of multi-scale dilated causal convolution combined with multi-head attention to realize the combination of global degradation information and local contextual information capturing ability. We demonstrate the effectiveness and sophistication of the STCT model by conducting comparative experiments with ablation experiments on publicly available datasets.

Hybrid-FHR: a multi-modal AI approach for automated fetal acidosis diagnosis

BackgroundIn clinical medicine, fetal heart rate (FHR) monitoring using cardiotocography (CTG) is one of the most commonly used methods for assessing fetal acidosis. However, as the visual interpretation of CTG depends on the subjective judgment of the clinician, this has led to high inter-observer and intra-observer variability, making it necessary to introduce automated diagnostic techniques.MethodsIn this study, we propose a computer-aided diagnostic algorithm (Hybrid-FHR) for fetal acidosis to assist physicians in making objective decisions and taking timely interventions. Hybrid-FHR uses multi-modal features, including one-dimensional FHR signals and three types of expert features designed based on prior knowledge (morphological time domain, frequency domain, and nonlinear). To extract the spatiotemporal feature representation of one-dimensional FHR signals, we designed a multi-scale squeeze and excitation temporal convolutional network (SE-TCN) backbone model based on dilated causal convolution, which can effectively capture the long-term dependence of FHR signals by expanding the receptive field of each layer’s convolution kernel while maintaining a relatively small parameter size. In addition, we proposed a cross-modal feature fusion (CMFF) method that uses multi-head attention mechanisms to explore the relationships between different modalities, obtaining more informative feature representations and improving diagnostic accuracy.ResultsOur ablation experiments show that the Hybrid-FHR outperforms traditional previous methods, with average accuracy, specificity, sensitivity, precision, and F1 score of 96.8, 97.5, 96, 97.5, and 96.7%, respectively.ConclusionsOur algorithm enables automated CTG analysis, assisting healthcare professionals in the early identification of fetal acidosis and the prompt implementation of interventions.

Semantic segmentation of anomalous diffusion using deep convolutional networks

Heterogeneous dynamics commonly emerges in anomalous diffusion with intermittent transitions of diffusion states but proves challenging to identify using conventional statistical methods. To effectively capture these transient changes of diffusion states, we propose a deep learning model (U-AnDi) for the semantic segmentation of anomalous diffusion trajectories. This model is developed with the dilated causal convolution (DCC), gated activation unit (GAU), and U-Net architecture. The study addresses two key subtasks related to trajectory segmentation and changepoint detection, concentrating on variations in diffusion exponents and dynamic models. Additionally, extended analyses are conducted on the segmentation of single-model trajectories, multistate biological trajectories, and anomalous diffusion with added correlation functions. By rationally designing comparative models and evaluating the performance of U-AnDi against these models, we discover that U-AnDi consistently outperforms other models across all segmentation tasks, thereby affirming its superiority in the field. This performance edge also sheds light on the interpretability of U-AnDi's core components: DCC, GAU, and U-Net. The clarity with which these components contribute to U-AnDi's success underscores their congruence with the intrinsic physics underlying anomalous diffusion. Furthermore, our model is examined using real-world anomalous diffusion data: the diffusion of transmembrane proteins on cell membrane surfaces, and the segmentation results are highly consistent with experimental observations. Our findings could offer a heuristic deep learning solution for the detection of heterogeneous dynamics in single-molecule/particle tracking experiments, and have the potential to be generalized as a universal scheme for time-series segmentation. Published by the American Physical Society 2024

Enhancing rock and soil hazard monitoring in open-pit mining operations through ultra-short-term wind speed prediction

Wind speed exacerbates challenges associated with rock stability, introducing factors such as heightened erosion and the possibility of particle loosening. This increased sensitivity to erosion can result in material displacement, thereby compromising the overall stability of rock layers within the open-pit mining site. Therefore, accurate wind speed predictions are crucial for understanding the impact on rock stability, ensuring the safety and efficiency of open-pit mining operations. While most existing studies on wind speed prediction primarily focus on making overall predictions from the entire wind speed sequence, with limited consideration for the stationarity characteristics of the sequence, This paper introduces a novel approach for effective monitoring and early warning of geotechnical hazards. Our proposed method involves dividing wind speed data into stationary and non-stationary segments using the sliding window average method within the threshold method, validated by the Augmented Dickey-Fuller test. Subsequently, we use temporal convolutional networks (TCN) with dilated causal convolution and long short-term memory to predict the stationary segment of wind speed, effectively improving prediction accuracy for this segment. For the non-stationary segment, we implement complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) to reduce sequence complexity, followed by TCN with an attention mechanism (ATTENTION) to forecast wind speed one step ahead. Finally, we overlay the predictions of these two segments to obtain the final prediction. Our proposed model, tested with data from an open-pit mining area in western China, achieved promising results with an average absolute error of 0.14 knots, mean squared error of 0.05 knots2, and root mean squared error of 0.20 knots. These findings signify a significant advancement in the accuracy of short-term wind speed prediction. This advancement not only enables the rapid assessment and proactive response to imminent risks but also contributes to geotechnical hazard monitoring in open-pit mining operations.

Multi-Spatio-Temporal Convolutional Neural Network for Short-Term Metro Passenger Flow Prediction

Accurate short-term prediction of metro passenger flow can offer significant assistance in optimizing train schedules, reducing congestion during peak times, and improving the service level of the metro system. Currently, most models do not fully utilize the high-resolution data aggregated by automatic fare collection systems. Therefore, we propose a model, called MST-GRT, that aggregates multi-time granularity data and considers multi-graph structures. Firstly, we analyze the correlation between metro passenger flow sequences at different time granularities and establish a principle for extracting the spatiotemporal correlation of data at different time granularities using the multi-graph neural network. Subsequently, we use residual blocks to construct a deep convolutional neural network to aggregate the data of different time granularities from small to large, obtaining multi-channel feature maps of multi-time granularity. To process the multi-channel feature maps, we use 2D dilated causal convolution to reconstruct the TCN (Temporal Convolutional Network) to compress the channel number of the feature maps and extract the time dependency of the data, and finally output the results through a fully connected layer. The experimental results demonstrate that our model outperforms the baseline models on the Hangzhou Metro smart-card data set.

GraphSAGE-Based Dynamic Spatial–Temporal Graph Convolutional Network for Traffic Prediction

Traffic networks exhibit complex spatial-temporal dependencies, and accurately capturing such dependencies is critical to improving prediction accuracy. Recently, many deep learning models have been proposed for spatial-temporal dependency modeling. While numerous deep learning models have been developed for spatial-temporal dependency modeling, most rely on different types of convolutions to extract spatial and temporal correlations separately. To address this limitation, we propose a novel deep learning framework for traffic prediction called GraphSAGE-based Dynamic Spatial-Temporal Graph Convolutional Network (DST-GraphSAGE), which can capture dynamic spatial and temporal dependencies simultaneously. Our model utilizes a spatial-temporal GraphSAGE module to extract localized spatial-temporal correlations from past observations of a node’s spatial neighbors. Meanwhile, the attention mechanism is incorporated to dynamically learn weights between traffic nodes based on graph features. Additionally, to capture long-term trends in traffic data, we employ dilated causal convolution as the temporal convolution layer. A series of numerical experiments are conducted on five real-world datasets, which demonstrates the effectiveness of our model for spatial-temporal dependency modeling.

Long-term multivariate time series forecasting in data centers based on multi-factor separation evolutionary spatial–temporal graph neural networks

Data center infrastructures require constant monitoring to ensure stable and reliable operation and time-series forecasting plays an indispensable role in intelligent operations and maintenance in data centers. However, the potential for accurate time-series predictions is often limited due to the overlooked relationships between data records from independent sensors. Inferring relationships for a potential graph representation of a data center is challenging due to complex relationships between nodes and multiple factors that may cause connections between them. Moreover, graphs change dynamically in long-term predictions, but current methods do not account for future graph changes. To address these challenges, we propose a long-term time-series forecasting framework called Multi-factor Separation Evolutionary Spatial–Temporal Graph Neural Networks (MSE-STGNN). Our framework considers edge diversity, graph changes and spatial–temporal architecture in long-term prediction processes and proposes three modules. Specifically, we propose a Multi-factor Separation (MS) module to separate the factors influencing node connectivity, enabling the acquisition of a graph more closely aligned with actual circumstances; then we propose a Graph Prediction (GP) module to incorporate future graphs to correct errors in the graph on which multi-step predictions depend. Moreover, we propose an Attention-enhanced Spatial–temporal dilated causal convolution module (AS-Conv) to more effectively leverage information pertaining to spatial and historical events. Our experimental results on datasets comprising of temperature and IT power data collected from real-world data centers show that the proposed method outperforms other advanced prediction methods in terms of prediction accuracy, and the learned latent graphs are explainable.

Significant wave height prediction based on the local-EMD-WaveNet model

This research constructed the innovative Local-EMD-WaveNet, a multi-channel neural network model, specifically designed for the prediction of significant wave height (SWH) at a singular point. It leverages Local Empirical Mode Decomposition (EMD) on significant wave heights in Ghanaian waters, integrating the derived decomposition results with wind speed data. This compiled data is then channeled into the model, which exploits the capabilities of dilated causal convolution to capture and analyze the time-series characteristics integral to future SWH predictions. The model ingeniously embeds EMD within the training process, treating the decomposed sub-waves and wind speed sequences as unique channels along the “depth” dimension. Following the application of dilated causal convolution, these channels are systematically “stacked”. Compared to conventional LSTM and direct data incorporation methods, Local-EMD-WaveNet consistently outperforms, especially in long-term predictions. The model exhibited significant improvements in Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) during 48 and 56 time-step predictions, marking increases of 27.3% and 23.5%, respectively, outshining both WaveNet and LSTM. Particularly in situations with larger wave height variations, Local-EMD-WaveNet accurately captures waveforms' peaks and troughs. These results validate Local-EMD-WaveNet as a reliable wave forecasting tool with considerable potential in ocean engineering and maritime applications.