Time Series Information Research Articles

Research on Joint Forecasting Technology of Cold, Heat, and Electricity Loads Based on Multi-Task Learning

The cooperative optimization and dispatch operation of the integrated energy system (IES) depends on accurate load forecasts. A multivariate load, joint prediction model, based on the combination of multi-task learning (MTL) and dynamic time warping (DTW), is proposed to address the issue of the prediction model’s limited accuracy caused by the fragmentation of the multivariate load coupling relationship and the absence of future time series information. Firstly, the MTL model, based on the bidirectional long short-term memory (BiLSTM) neural network, extracts the coupling information among the multivariate loads and performs the preliminary prediction; secondly, the DTW algorithm clusters and splices the load data that are similar to the target value as the input features of the model; finally, the BiLSTM-attention model is used for secondary prediction, and the improved Bayesian optimization algorithm is applied for adaptive selection of optimal hyperparameters. Based on the game-theoretic view of Shapley’s additive interpretation (SHAP), a model interpretation technique is introduced to determine the validity of the liquidity indicator and the asynchronous relationship between the significance of the indicator and its actual contribution. The prediction results show that the joint prediction model proposed in this paper has higher training speed and prediction accuracy than the traditional single-load prediction model.

Time-Series Forecasting and Sequence Learning Using Memristor-based Reservoir System

Pushing the frontiers of time-series information processing in the ever-growing domain of edge devices with stringent resources has been impeded by the systems’ ability to process information and learn locally on the device. Local processing and learning of time-series information typically demand intensive computations and massive storage as the process involves retrieving information and tuning hundreds of parameters back in time. In this work, we developed a memristor-based echo state network accelerator that features efficient temporal data processing and in-situ online learning. The proposed design is benchmarked using various datasets involving real-world tasks, such as forecasting the load energy consumption and weather conditions. The experimental results illustrate that the hardware model experiences a marginal degradation in performance as compared to the software counterpart. This is mainly attributed to the limited precision and dynamic range of network parameters when emulated using memristor devices. The proposed system is evaluated for lifespan, robustness, and energy-delay product. It is observed that the system demonstrates reasonable robustness for device failure below 10%, which may occur due to stuck-at faults. Furthermore, 247 × reduction in energy consumption is achieved when compared to a custom CMOS digital design implemented at the same technology node.

A Method for Filling Missing Values in Multivariate Sequence Bidirectional Recurrent Neural Networks Based on Feature Correlations

Multivariate real-life time series data often contain missing values. These missing values often affect subsequent prediction tasks. Traditional imputation methods generally consider only some of the characteristics of multivariate time series data. This can easily lead to inaccurate filling results. In this paper, a feature correlation-based bidirectional recurrent network (BRNN-FR) is proposed to solve the problem of missing values in multivariate sequence data. First, this method involves the design of a bidirectional prediction network based on time intervals and the use of forward and reverse time series information between data points to obtain the characteristics of data changes with time to the greatest extent. Second, considering the correlation between features, a combined feature selection strategy based on the Pearson correlation coefficient and mutual information was proposed. A multiple regression model was established to predict between features. Finally, a bidirectional network ensemble filling algorithm based on the relationships between features is established to predict missing values. Comprehensive experiments on four public datasets show that the mean absolute error (MAE), root mean square error (RMSE) and maximum R2 value (R2_score) of the BRNN-FR algorithm in the direct imputation test are better than those of the other comparison methods in most cases. BRNN-FR also achieved a better area under the curve (AUC) in the indirect comparison experiment of two classifications of in-hospital death after filling the medical dataset. Using the AIR air quality dataset and the power transformer temperature dataset from the ETTH1 interpolation regression to predict the next 3hours and 6hours of average numerical results, most of the optimal regression results are obtained.

The STAP-Net: A new health perception and prediction framework for bearing-rotor systems under special working conditions

The health perception of bearing-rotor systems and their remaining useful life prediction has been a critical and challenging theme in the field of Prognostic and Health Management (PHM). Deep learning has become a prominent area of PHM research. However, current models have difficulty in adequately extracting the deep degradation characteristics of bearings and effectively capturing time-series information during the failure process. Also, most remaining useful life (RUL) prediction methods focus on point estimation, limiting their ability to quantify prediction uncertainty. To address these shortcomings, this study proposes a novel health perception and prediction framework, the Spatiotemporal Self-Attention Mechanism Probabilistic model (STAP-Net). The framework embodies the principles of lightweight design, focusing, and probabilistic approaches, and is tailored for bearing rotor systems operating under unique conditions. The key innovation of STAP-Net is the integration of a modified gate recurrent unit, known as the Weight Diminish Recurrent Unit (WDRU). It greatly reduces the training parameters of the proposed STAP-Net framework and improves the convergence speed of the framework while ensuring the prediction accuracy. Through analyzing the bearing-rotor system degradation data, the efficacy of STAP-Net is validated under special operating conditions such as misalignment and abrasive wear. The superior performance of the proposed framework is evaluated and confirmed based on 3 key metrics: high-precision point prediction, suitable prediction intervals, and reliable probabilistic prediction results.

Household energy consumption forecasting based on adaptive signal decomposition enhanced iTransformer network

With the presence of volatility and noise in the energy consumption data, existing energy consumption forecasting methods have difficulties in achieving satisfactory forecasting results from multiple perspectives, including accuracy, robustness, generalization, and efficiency. This study introduces a novel energy consumption forecasting framework that combines the adaptive signal decomposition method and iTransformer (ASSA-iTransformer) to tackle the above-mentioned difficulties. Each subsequence obtained by ASSA decomposition was fed into the iTransformer framework, and deep-level time series information was extracted. Compared to state-of-the-art methods across various evaluation dimensions, ASSA-iTransformer has improved the average mean absolute error (MAE) by 23.7%, root mean square error (RMSE) by 27.6%, and mean absolute percentage error (MAPE) by 16.4%. Moreover, the R2 values on five real-world household energy consumption datasets are close to 1, demonstrating overall outstanding performance.

Gaspery: Optimized Scheduling of Radial Velocity Follow-up Observations for Active Host Stars

Radial velocity (RV) follow-up is a critical complement of transiting exoplanet surveys like the Transiting Exoplanet Survey Satellite, both for validating discoveries of exoplanets and measuring their masses. Stellar activity introduces challenges to interpreting these measurements because the noise from the host star, which is often correlated in time, can result in high RV uncertainty. A robust understanding of stellar activity and how its timescales interact with the observing cadence can optimize limited RV resources. For this reason, in the era of oversubscribed, high-precision RV measurements, folding stellar activity timescales into the scheduling of observation campaigns is ideal. We present gaspery, an open-source code implementation to enable the optimization of RV observing strategies. Gaspery employs a generalized formulation of the Fisher information for RV time series, which also incorporates information about stellar correlated noise. We show that the information contained in an observing strategy can be significantly affected by beat frequencies between the orbital period of the planet, the stellar rotation period, and the observation epochs. We investigate how the follow-up observing strategy will affect the resulting RV uncertainty, as a function of stellar properties such as the spot decay timescale and rotation period. We then describe two example use cases for gaspery: (1) calculating the minimum number of observations to reach an uncertainty tolerance in a correlated noise regime and (2) finding an optimal strategy given a fixed observing budget. Finally, we outline a prescription for selecting an observing strategy that is generalizable to different targets.

RFNet: Multivariate long sequence time-series forecasting based on recurrent representation and feature enhancement

Multivariate time series exhibit complex patterns and structures involving interactions among multiple variables and long-term temporal dependencies, making multivariate long sequence time series forecasting (MLSTF) exceptionally challenging. Despite significant progress in Transformer-based methods in the MLSTF domain, many models still rely on stacked encoder–decoder architectures to capture complex time series patterns. This leads to increased computational complexity and overlooks spatial pattern information in multivariate time series, thereby limiting the model’s performance. To address these challenges, we propose RFNet, a lightweight model based on recurrent representation and feature enhancement. We partition the time series into fixed-size subsequences to retain local contextual temporal pattern information and cross-variable spatial pattern information. The recurrent representation module employs gate attention mechanisms and memory units to capture local information of the subsequences and obtain long-term correlation information of the input sequence by integrating information from different memory units. Meanwhile, we utilize a shared multi-layer perceptron (MLP) to capture global pattern information of the input sequence. The feature enhancement module explicitly extracts complex spatial patterns in the time series by transforming the input sequence. We validate the performance of RFNet on ten real-world datasets. The results demonstrate an improvement of approximately 55.3% over state-of-the-art MLSTF models, highlighting its significant advantage in addressing multivariate long sequence time series forecasting problems.

Two-stage Day-ahead Multi-step Prediction of Wind Power Considering Time-series Information Interaction

With the large-scale development of wind power, high penetration wind power grid connection poses serious challenges to the safe and stable operation of the power system. However, the current accuracy of wind power forecasting is facing bottlenecks due to the limitations of Numerical Weather Prediction (NWP) data. Therefore, this article proposes a two-stage day-ahead multi-step wind power prediction (WPP) scheme that considers temporal information interaction. In the first stage, the next day prediction of wind power is based on historical power and 0∼24 hours NWP data. Then, an embedded deep decomposition module is used to extract predictable components and multi-scale information fusion is performed. In the second stage, the result of day-ahead WPP is obtained based on the extracted predictable components and combined with 24∼48 hours of NWP data. The wind farms in Jilin and Inner Mongolia of China are used to experimental analysis. The results show that the scheme proposed in the article has a better prediction effect compared with other schemes in the paper, which can effectively improve the multi-step prediction accuracy of day-ahead wind power.

Enhancing Recommendation Diversity and Novelty with Bi-LSTM and Mean Shift Clustering

In the digital age, personalized recommendation systems have become crucial for information dissemination and user experience. While traditional systems focus on accuracy, they often overlook diversity, novelty, and serendipity. This study introduces an innovative recommendation system model, Time-based Outlier Aware Recommender (TOAR), designed to address the challenges of content homogenization and information bubbles in personalized recommendations. TOAR integrates Neural Matrix Factorization (NeuMF), Bidirectional Long Short-Term Memory Networks (Bi-LSTM), and Mean Shift clustering to enhance recommendation accuracy, novelty, and diversity. The model analyzes temporal dynamics of user behavior and facilitates cross-domain knowledge exchange through feature sharing and transfer learning mechanisms. By incorporating an attention mechanism and unsupervised clustering, TOAR effectively captures important time-series information and ensures recommendation diversity. Experimental results on a news recommendation dataset demonstrate TOAR’s superior performance across multiple metrics, including AUC, precision, NDCG, and novelty, compared to traditional and deep learning-based recommendation models. This research provides a foundation for developing more intelligent and personalized recommendation services that balance accuracy with content diversity.

Spatiotemporal understanding of behaviors of laying hens using wearable inertial sensors

Automatic detection of behaviors and locations has been increasingly needed in the management of non-cage systems where hen behaviors are highly diverse and active. Here we show a technology to spatiotemporally understand behaviors using a wearable inertial sensor, containing a three-axis accelerometer and three-axis angular velocity sensor (i.e., gyroscope), and a marker. Using supervised machine learning, we first developed a tool that automatically classified and counted 11 behaviors, including comfort behaviors such as head scratching and tail-wagging with small movements as well as dust-bathing with dynamic movements. As expected, these behaviors were observed more frequently in floor pens than in conventional cages (all P < 0.01). We also spatially mapped the behaviors in floor pens and visualized the behavioral frequency in each resource by detecting the colored markers on the sensor. Furthermore, using the time-series information included in the sensor data, we analyzed the behavioral transition from one behavior to another. The behavioral transitions were more complex in floor pens, and the number was higher in body shaking, tail-wagging, resting, litter scratching, dust-bathing, preening, and moving in floor pens than in conventional cages (all P < 0.05). Our tools presented deeper insights into where and what hens behaved and also suggested that connectivity between behaviors, as well as observing the frequency of a behavior, can be an important indicator for welfare assessment in laying hens.

Mathematical Analysis of Neural Networks for Signal Processing

In flag preparing, neural systems have gotten to be exceptionally valuable since they give adaptable ways to see at and get it complicated information patterns. A full scientific ponder of neural systems utilized for flag preparing errands is given in this paper. The most objective of the consider is to figure out the fundamental thoughts, structures, and numerical equations that make neural networks work well in preparing information from distinctive regions. The fundamental thoughts of neural systems are looked at, beginning with neurons, layers, and actuation capacities, which are the network's building squares. Scientific models appear how these parts work together within the arrange and how they offer assistance turn input signals into valuable yields through rehashed learning forms. The numerical modeling of feedforward and repetitive neural systems is emphasized, appearing how well they work with both consecutive and time-series information. The think about moreover talks approximately more progressed points, such as optimization strategies like slope plummet and its varieties, which are exceptionally critical for educating neural systems to create forecasts with less botch. The science system incorporates looking into regularization strategies such as L1 and L2 regularization, which are vital for maintaining a strategic distance from overfitting and making generalization way better. Neural systems are utilized in flag handling in a wide run of real-world circumstances, counting discourse and voice acknowledgment, picture handling, organic flag examination, and broadcast communications. Case considers appear how neural systems offer assistance illuminate issues within the genuine world by finding highlights, lowering noise, and making strides flag acknowledgment in situations that alter.

A New Accurate Aircraft Trajectory Prediction in Terminal Airspace Based on Spatio-Temporal Attention Mechanism

Trajectory prediction serves as a prerequisite for future trajectory-based operation, significantly reducing the uncertainty of aircraft movement information within airspace by scientifically forecasting the three-dimensional positions of aircraft over a certain period. As convergence points in the aviation network, airport terminal airspace exhibits the most complex traffic conditions in the entire air route network. It has stronger mutual influences and interactions among aircraft compared to the en-route phase. Current research typically uses the trajectory time series information of a single aircraft as input for subsequent predictions. However, it often lacks consideration of the close-range spatial interactions between multiple aircraft in the terminal airspace. This results in a gap in the study of aircraft trajectory prediction that couples spatiotemporal features. This paper aims to predict the four-dimensional trajectories of aircraft in terminal airspace, constructing a Spatio-Temporal Transformer (ST-Transformer) prediction model based on temporal and spatial attention mechanisms. Using radar aircraft trajectory data from the Guangzhou Baiyun Airport terminal airspace, the results indicate that the proposed ST-Transformer model has a smaller prediction error compared to mainstream deep learning prediction models. This demonstrates that the model can better integrate the temporal sequence correlation of trajectory features and the potential spatial interaction information among trajectories for accurate prediction.

Forecasting of Inland Fish Production: Case of Catla (&lt;em&gt;Catla catla&lt;/em&gt;) and Gift Tilapia (&lt;em&gt;Oreochromis niloticus&lt;/em&gt;) Production in Udawalawa Reservoir in Sabaragamuwa Province, Sri Lanka

This study focused on assessing and forecasting Catla (Catla catla) and Tilapia (Oreochromis niloticus) production in the Udawalawe reservoir in Sri Lanka using an 11-year time series data from 2010 to 2021. The relevant secondary data were collected from the National Aquaculture Development Authority of Sri Lanka (NAQDA). Unit root tests, Dickey-Fuller tests, and Seasonal Auto Regressive Integrated Moving Average (SARIMA) models and trend analysis were applied for the data analyses. According to the results, stationarity behaviour was observed in both Catla and Tilapia production information series. Hence, SARIMA (2,2,1) (1,0,1)12 is the appropriate empirical model for forecasting Catla production. Furthermore, the maximum average landings of Catla production were observed in the March-June time period. SARIMA (1,0,1) (1,1,1)12 was indicated as the most suitable model to forecast Tilapia production in the reservoir. The maximum average of Tilapia production was also observed in the March-June period. Both the SARIMA model and trend analysis gave approximately equal production information regarding Catla and Tilapia. Thus, these findings showed that the SARIMA model has more accuracy than trend analysis when analysing the time series information for short durations. However, when the duration becomes larger, forecasting is not suitable using the SARIMA model, and trend analysis gives a clear view up to a certain level. Both Catla and Tilapia production exhibited significant changing patterns and multiple seasonalities. Thus, trend analysis gives valuable insights than SARIMA model in long term predictions in case of this study. These findings are highly important for enhancing fish production in this reservoir, as they predict future fish catches under the current reservoir conditions.

Dynamic obstacle avoidance model of autonomous driving with attention mechanism and temporal residual block

Dynamic obstacle avoidance is crucial in autonomous driving, ensuring vehicle safety by preventing collisions and enhancing driving efficiency. Dynamic obstacle avoidance algorithms have made significant progress due to deep learning. However, video-based target detection methods can suffer from missed or false detections when processing consecutive frames, especially for high-speed moving targets or in complex dynamic scenes. Multi-target tracking methods require intricate algorithm designs for target initialization and occluded object recovery, which can be compromised by tracker performance, leading to unstable tracking or target loss. To address the issue of target loss in multi-target tracking, we designed the novel YTCN model that infuses time series information through temporal convolution and enhances the sensitivity of the receptive field with Spatial Pyramid Pooling, Feature Concatenate and Spatial Convolution(SPPFCSPC), enhancing the model’s feature extraction capability. Simultaneously, we developed the novel Global Attention Mechanism(GAM) and Double Attention(DA) mechanisms that merge channel and spatial features to enhance feature representation. Finally we design the Temporal Residual Block(TRB) to model the temporal obstacles. Experimental results show that our method achieves 82.4 % of mAP_0.5 on the BDD 100 K dataset, which gets 1.3 % higher than the previous methods.

New Insights on the Information Content of the Normalized Difference Vegetation Index Sentinel-2 Time Series for Assessing Vegetation Dynamics

The Sentinel-2 NDVI time series information content from 2017 to 2023 at a 10 m spatial resolution was evaluated based on the NDVI temporal dependency in five scenarios in central Spain. First, time series were interpolated and then filtered using the Savitzky–Golay, Fast Fourier Transform, Whittaker, and Maximum Value filters. Temporal dependency was assessed using the Q-Ljung-Box and Fisher’s Kappa tests, and similarity between raw and filtered time series was assessed using Correlation Coefficient and Root Mean Square Error. An Interpolating Efficiency Indicator (IEI) was proposed to summarize the number and temporal distribution of low-quality observations. Type of climate, atmospheric disturbances, land cover dynamics, and management were the main sources of variability in five scenarios: (1) rainfed wheat and barley presented high short-term variability due to clouds (lower IEI in winter and spring) during the growing cycle and high interannual variability due to precipitation; (2) maize showed stable summer cycles (high IEI) and low interannual variability due to irrigation; (3) irrigated alfalfa was cut five to six times during summer, resulting in specific intra-annual variability; (4) beech forest showed a strong and stable summer cycle, despite the short-term variability due to clouds (low IEI); and (5) evergreen pine forest had a highly variable growing cycle due to fast responses to temperature and precipitation through the year and medium IEI values. Interpolation after removing non-valid observations resulted in an increase in temporal dependency (Q-test), particularly a short term in areas with low IEI values. The information improvement made it possible to identify hidden periodicities and trends using the Fisher’s Kappa test. The SG filter showed high similarity values and weak influence on dynamics, while the MVF showed an overestimation of the NDVI values.

Ultra-short-term photovoltaic power prediction based on similar day clustering and temporal convolutional network with bidirectional long short-term memory model: A case study using DKASC data

Due to its strong dependence on weather conditions, photovoltaic (PV) power is highly intermittent in nature. In light of this, this paper introduces a PV power prediction model based on similar-day clustering and temporal convolutional network (TCN) with bidirectional long short-term memory (BiLSTM) model. Firstly, in the data preprocessing stage, improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) method is used to decompose and denoise the original PV power data to obtain subsequences of different frequencies. Subsequently, the sample entropy (SE) method is incorporated to reconstruct the subsequences and generate low-frequency and high-frequency subsequences with more pronounced temporal features. In addition, a self-organizing map (SOM) with the K-means algorithm is used to categorize historical days into four weather types: sunny, cloudy, rainy, and intermittent. Through grey relational analysis (GRA), meteorological factors significantly affecting PV power prediction are identified to construct a multidimensional feature set. During the model prediction phase, historical PV power data and related meteorological impact factors are input into the TCN-BiLSTM model to perform multi-data-driven PV power prediction. Finally, the predicted results of each subsequence are linearly combined to obtain the ultimate PV power prediction. The proposed model is compared with convolutional neural network (CNN)-LSTM, LSTM, and TCN models, achieving a reduction in the root mean square error (RMSE) of 0.129 kW, 0.238 kW, and 0.257 kW, respectively. This demonstrates that the proposed model exhibits superior overall performance in time series modeling and information capture, enhancing the understanding of seasonal, periodic, and irregular patterns in PV power generation data.

Metadata-enhanced contrastive learning from retinal optical coherence tomography images

Deep learning has potential to automate screening, monitoring and grading of disease in medical images. Pretraining with contrastive learning enables models to extract robust and generalisable features from natural image datasets, facilitating label-efficient downstream image analysis. However, the direct application of conventional contrastive methods to medical datasets introduces two domain-specific issues. Firstly, several image transformations which have been shown to be crucial for effective contrastive learning do not translate from the natural image to the medical image domain. Secondly, the assumption made by conventional methods, that any two images are dissimilar, is systematically misleading in medical datasets depicting the same anatomy and disease. This is exacerbated in longitudinal image datasets that repeatedly image the same patient cohort to monitor their disease progression over time. In this paper we tackle these issues by extending conventional contrastive frameworks with a novel metadata-enhanced strategy. Our approach employs widely available patient metadata to approximate the true set of inter-image contrastive relationships. To this end we employ records for patient identity, eye position (i.e. left or right) and time series information. In experiments using two large longitudinal datasets containing 170,427 retinal optical coherence tomography (OCT) images of 7912 patients with age-related macular degeneration (AMD), we evaluate the utility of using metadata to incorporate the temporal dynamics of disease progression into pretraining. Our metadata-enhanced approach outperforms both standard contrastive methods and a retinal image foundation model in five out of six image-level downstream tasks related to AMD. We find benefits in both a low-data and high-data regime across tasks ranging from AMD stage and type classification to prediction of visual acuity. Due to its modularity, our method can be quickly and cost-effectively tested to establish the potential benefits of including available metadata in contrastive pretraining.

Optimizing CNN-LSTM for the Localization of False Data Injection Attacks in Power Systems

As the informatization of power systems advances, the secure operation of power systems faces various potential network attacks and threats. The false data injection attack (FDIA) is a common attack mode that can lead to abnormal system operations and serious economic losses by injecting abnormal data into terminal links or devices. The current research on FDIA primarily focuses on detecting its existence, but there is relatively little research on the localization of the attacks. To address this challenge, this study proposes a novel FDIA localization method (GA-CNN-LSTM) that combines convolutional neural networks (CNNs), long short-term memory (LSTM), and a genetic algorithm (GA) and can accurately locate the attacked bus or line. This method utilizes a CNN to extract local features and combines LSTM with time series information to extract global features. It integrates a CNN and LSTM to deeply explore complex patterns and dynamic changes in the data, effectively extract FDIA features in the data, and optimize the hyperparameters of the neural network using the GA to ensure an optimal performance of the model. Simulation experiments were conducted on the IEEE 14-bus and 118-bus test systems. The results indicate that the GA-CNN-LSTM method achieved F1 scores for location identification of 99.71% and 99.10%, respectively, demonstrating superior localization performance compared to other methods.

High-fidelity phase-field simulation of solid-state sintering enabled by Bayesian data assimilation using in situ electron tomography data

Experimental observation methods for understanding industrially important solid-state sintering are essential for the development of new materials and devices. To experimentally characterize solid-state sintering, the limitations posed by the complexity of target materials, experimental equipment, and observation conditions must be overcome. Therefore, hybrid techniques for predicting sintering behavior based on experimental datasets and physics-based simulation models are highly sought after. Herein, we propose a new technique for combining a physics-based model and experimental observation results from solid-state sintering using a nonsequential Bayesian data assimilation (DA) method. The proposed technique assimilates experimental data—obtained using in situ electron tomography/scanning transmission electron microscopy—into the corresponding phase-field (PF) model to enable high-fidelity PF simulations by estimating multiple material parameters included in the PF model. This study demonstrates the inverse estimation of seven parameters, including temperature-dependent diffusion coefficients, from the time-series information on the morphology of sintered nanoparticles observed in situ. The estimated parameters provide the high-fidelity PF simulation to capture the observed solid-state sintering of copper nanoparticles. Thus, this study contributes to the construction of digital twins for solid-state sintering based on DA-integrated PF simulations and in situ observation datasets and deepens our understanding of the sintering process.

Multi-scale hierarchical model for long-term time series forecasting

Long-term time series forecasting (LTSF) has become an urgent requirement in many applications, such as wind power supply planning. This is a highly challenging task because it requires considering both the complex frequency-domain and time-domain information in long-term time series simultaneously. However, existing work only considers potential patterns in a single domain (e.g., time or frequency domain), whereas a large amount of time-frequency domain information exists in real-world LTSFs. In this paper, we propose a multi-scale hierarchical network (MHNet) based on time-frequency decomposition to solve the above problem. MHNet first introduces a multi-scale hierarchical representation, extracting and learning features of time series in the time domain, and gradually builds up a global understanding and representation of the time series at different time scales, enabling the model to process time series over lengthy periods of time with lower computational complexity. Then, the robustness to noise is enhanced by employing a transformer that leverages frequency-enhanced decomposition to model global dependencies and integrates attention mechanisms in the frequency domain. Meanwhile, forecasting accuracy is further improved by designing a periodic trend decomposition module for multiple decompositions to reduce input-output fluctuations. Experiments on five real benchmark datasets show that the forecasting accuracy and computational efficiency of MHNet outperform state-of-the-art methods.