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33 pages, 3902 KiB  
Article
A Predictive Method for Temperature Based on Ensemble EMD with Linear Regression
by Yujun Yang, Yimei Yang and Huijuan Liao
Algorithms 2025, 18(8), 458; https://doi.org/10.3390/a18080458 - 23 Jul 2025
Viewed by 166
Abstract
Temperature prediction plays a crucial role across various sectors, including agriculture and climate research. Understanding weather patterns, seasonal shifts, and climate dynamics heavily relies on accurate temperature forecasts. This paper presents an innovative hybrid method, EEMD-LR, that combines ensemble empirical mode decomposition (EEMD) [...] Read more.
Temperature prediction plays a crucial role across various sectors, including agriculture and climate research. Understanding weather patterns, seasonal shifts, and climate dynamics heavily relies on accurate temperature forecasts. This paper presents an innovative hybrid method, EEMD-LR, that combines ensemble empirical mode decomposition (EEMD) with linear regression (LR) for temperature prediction. EEMD is used to decompose temperature signals into stable sub-signals, enhancing their predictability. LR is then applied to forecast each sub-signal, and the resulting predictions are integrated to obtain the final temperature forecast. The proposed EEMD-LR model achieved RMSE, MAE, and R2 values of 0.000027, 0.000021, and 1.000000, respectively, on the sine simulation time-series data used in this study. For actual temperature time-series data, the model achieved RMSE, MAE, and R2 values of 0.713150, 0.512700, and 0.994749, respectively. The experimental results on these two datasets indicate that the EEMD-LR model demonstrates superior predictive performance compared to alternative methods. Full article
(This article belongs to the Section Algorithms for Multidisciplinary Applications)
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20 pages, 5571 KiB  
Proceeding Paper
A Forecasting Method Based on a Dynamical Approach and Time Series Data for Vehicle Service Parts Demand
by Vinh Long Phan, Makoto Taniguchi and Hidenori Yabushita
Eng. Proc. 2025, 101(1), 3; https://doi.org/10.3390/engproc2025101003 - 21 Jul 2025
Viewed by 178
Abstract
In the automotive industry, the supply of service parts—such as bumpers, batteries, and aero parts—is required even after the end of vehicle production, as customers need them for maintenance and repairs. To earn customer confidence, manufacturers must ensure timely availability of these parts [...] Read more.
In the automotive industry, the supply of service parts—such as bumpers, batteries, and aero parts—is required even after the end of vehicle production, as customers need them for maintenance and repairs. To earn customer confidence, manufacturers must ensure timely availability of these parts while managing inventory efficiently. An excess of inventory can increase warehousing costs, while stock shortages can lead to supply delays. Accurate demand forecasting is essential to balance these factors, considering the changing demand characteristics over time, such as long-term trends, seasonal fluctuations, and irregular variations. This paper introduces a novel method for time series forecasting that employs Ensemble Empirical Mode Decomposition (EEMD) and Dynamic Mode Decomposition (DMD) to analyze service part demand. EEMD decomposes historical order data into multiple modes, and DMD is used to predict transitions within these modes. The proposed method demonstrated an approximately 30% reduction in forecasting error compared to comparative methods, showcasing its effectiveness in accurately predicting service parts demand across various patterns. Full article
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43 pages, 6462 KiB  
Article
An Integrated Mechanical Fault Diagnosis Framework Using Improved GOOSE-VMD, RobustICA, and CYCBD
by Jingzong Yang and Xuefeng Li
Machines 2025, 13(7), 631; https://doi.org/10.3390/machines13070631 - 21 Jul 2025
Viewed by 255
Abstract
Rolling element bearings serve as critical transmission components in industrial automation systems, yet their fault signatures are susceptible to interference from strong background noise, complex operating conditions, and nonlinear impact characteristics. Addressing the limitations of conventional methods in adaptive parameter optimization and weak [...] Read more.
Rolling element bearings serve as critical transmission components in industrial automation systems, yet their fault signatures are susceptible to interference from strong background noise, complex operating conditions, and nonlinear impact characteristics. Addressing the limitations of conventional methods in adaptive parameter optimization and weak feature enhancement, this paper proposes an innovative diagnostic framework integrating Improved Goose optimized Variational Mode Decomposition (IGOOSE-VMD), RobustICA, and CYCBD. First, to mitigate modal aliasing issues caused by empirical parameter dependency in VMD, we fuse a refraction-guided reverse learning mechanism with a dynamic mutation strategy to develop the IGOOSE. By employing an energy-feature-driven fitness function, this approach achieves synergistic optimization of the mode number and penalty factor. Subsequently, a multi-channel observation model is constructed based on optimal component selection. Noise interference is suppressed through the robust separation capabilities of RobustICA, while CYCBD introduces cyclostationarity-based prior constraints to formulate a blind deconvolution operator with periodic impact enhancement properties. This significantly improves the temporal sparsity of fault-induced impact components. Experimental results demonstrate that, compared to traditional time–frequency analysis techniques (e.g., EMD, EEMD, LMD, ITD) and deconvolution methods (including MCKD, MED, OMEDA), the proposed approach exhibits superior noise immunity and higher fault feature extraction accuracy under high background noise conditions. Full article
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21 pages, 3698 KiB  
Article
Research on Bearing Fault Diagnosis Method Based on MESO-TCN
by Ruibin Gao, Jing Zhu, Yifan Wu, Kaiwen Xiao and Yang Shen
Machines 2025, 13(7), 558; https://doi.org/10.3390/machines13070558 - 27 Jun 2025
Viewed by 258
Abstract
To address the issues of information redundancy, limited feature representation, and empirically set parameters in rolling bearing fault diagnosis, this paper proposes a Multi-Entropy Screening and Optimization Temporal Convolutional Network (MESO-TCN). The method integrates feature filtering, network modeling, and parameter optimization into a [...] Read more.
To address the issues of information redundancy, limited feature representation, and empirically set parameters in rolling bearing fault diagnosis, this paper proposes a Multi-Entropy Screening and Optimization Temporal Convolutional Network (MESO-TCN). The method integrates feature filtering, network modeling, and parameter optimization into a unified diagnostic framework. Specifically, ensemble empirical mode decomposition (EEMD) is combined with a hybrid entropy criterion to preprocess the raw vibration signals and suppress redundant noise. A kernel-extended temporal convolutional network (ETCN) is designed with multi-scale dilated convolution to extract diverse temporal fault patterns. Furthermore, an improved whale optimization algorithm incorporating a firefly-inspired mechanism is introduced to adaptively optimize key hyperparameters. Experimental results on datasets from Xi’an Jiaotong University and Southeast University demonstrate that MESO-TCN achieves average accuracies of 99.78% and 95.82%, respectively, outperforming mainstream baseline methods. These findings indicate the method’s strong generalization ability, feature discriminability, and engineering applicability in intelligent fault diagnosis of rotating machinery. Full article
(This article belongs to the Section Machines Testing and Maintenance)
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17 pages, 6587 KiB  
Article
EEMD Energy Spectrum Decoupling: An Efficient Hilbert–Huang Fusion Approach for Intelligent Bearing Fault Diagnosis
by Lianyou Lai, Weijian Xu and Zhongzhe Song
Appl. Sci. 2025, 15(12), 6458; https://doi.org/10.3390/app15126458 - 8 Jun 2025
Viewed by 437
Abstract
As a critical component of rotating machinery, the operational status of rolling bearings is considered to directly determine the reliability of rail traffic systems. To address the complex modulation effects existing between multiple bearing components and the non-linear, non-stationary characteristics exhibited by vibration [...] Read more.
As a critical component of rotating machinery, the operational status of rolling bearings is considered to directly determine the reliability of rail traffic systems. To address the complex modulation effects existing between multiple bearing components and the non-linear, non-stationary characteristics exhibited by vibration acceleration signals, an intelligent fault diagnosis method for bearings based on Hilbert envelope demodulation and Ensemble Empirical Mode Decomposition energy distribution features is proposed. First, the original vibration signal is subjected to envelope demodulation processing by the Hilbert transform, thereby effectively separating the envelope signal containing fault characteristics. Subsequently, the demodulated envelope signal is decomposed by EEMD to extract Intrinsic Mode Functions (IMFs), where each IMF component is calculated layer by layer using a normalization method based on the EEMD decomposition sequence. Finally, the proposed algorithm is validated by the standard bearing fault dataset from Case Western Reserve University. Experimental results show that the proposed method achieves 100% accuracy in fault identification, and its superiority is proven to exceed conventional diagnostic approaches significantly. Full article
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37 pages, 6517 KiB  
Article
Forecast Natural Gas Price by an Extreme Learning Machine Framework Based on Multi-Strategy Grey Wolf Optimizer and Signal Decomposition
by Zhuolin Wu, Jiaqi Zhou and Xiaobing Yu
Sustainability 2025, 17(12), 5249; https://doi.org/10.3390/su17125249 - 6 Jun 2025
Viewed by 674
Abstract
Natural gas is one of the most important sources of energy in modern society. However, its strong volatility highlights the importance of accurately forecasting natural gas price trends and movements. The nonlinear nature of the natural gas price series makes it difficult to [...] Read more.
Natural gas is one of the most important sources of energy in modern society. However, its strong volatility highlights the importance of accurately forecasting natural gas price trends and movements. The nonlinear nature of the natural gas price series makes it difficult to capture. Therefore, we propose a forecasting framework based on signal decomposition and intelligent optimization algorithms to predict natural gas prices. In this forecasting framework, we implement point, probability interval, and quantile interval forecasting. First, the natural gas price sequence is decomposed into multiple Intrinsic Mode Functions (IMFs) using the Ensemble Empirical Mode Decomposition (EEMD) technique. Each decomposed sequence is then predicted using an optimized Extreme Learning Machine (ELM), and the individual results are aggregated as the final result. To improve the efficiency of the intelligent algorithm, a Multi-Strategy Grey Wolf Optimizer (MSGWO) is developed to optimize the hidden layer matrices of the ELM. The experimental results prove that the proposed framework not only provides more reliable point forecasts with good nonlinear adaptability but also describes the uncertainty of natural gas price series more accurately and completely. Full article
(This article belongs to the Special Issue Energy Price Forecasting and Sustainability on Energy Transition)
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48 pages, 1559 KiB  
Review
A Review of Key Signal Processing Techniques for Structural Health Monitoring: Highlighting Non-Parametric Time-Frequency Analysis, Adaptive Decomposition, and Deconvolution
by Yixin Zhou, Zepeng Ma and Lei Fu
Algorithms 2025, 18(6), 318; https://doi.org/10.3390/a18060318 - 27 May 2025
Cited by 1 | Viewed by 1523
Abstract
This paper reviews key signal processing techniques in structural health monitoring (SHM), focusing on non-parametric time–frequency analysis, adaptive decomposition, and deconvolution methods. It examines the short-time Fourier transform (STFT), wavelet transform (WT), and Wigner–Ville distribution (WVD), highlighting their applications, advantages, and limitations in [...] Read more.
This paper reviews key signal processing techniques in structural health monitoring (SHM), focusing on non-parametric time–frequency analysis, adaptive decomposition, and deconvolution methods. It examines the short-time Fourier transform (STFT), wavelet transform (WT), and Wigner–Ville distribution (WVD), highlighting their applications, advantages, and limitations in SHM. The review also explores adaptive techniques like empirical mode decomposition (EMD) and its variants (EEMD, MEEMD), as well as variational mode decomposition (VMD) and its improved versions (SVMD, AVMD), emphasizing their effectiveness in handling nonlinear and non-stationary signals. Additionally, deconvolution methods such as minimum entropy deconvolution (MED) and maximum correlated kurtosis deconvolution (MCKD) are discussed for mechanical fault diagnosis. The paper aims to provide a comprehensive overview of these techniques, offering insights for future research into SHM signal processing. Full article
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19 pages, 2212 KiB  
Article
Optimal Forecast Combination for Japanese Tourism Demand
by Yongmei Fang, Emmanuel Sirimal Silva, Bo Guan, Hossein Hassani and Saeed Heravi
Tour. Hosp. 2025, 6(2), 79; https://doi.org/10.3390/tourhosp6020079 - 7 May 2025
Viewed by 861
Abstract
This study introduces a novel forecast combination method for monthly Japanese tourism demand, analyzed at both aggregated and disaggregated levels, including tourist, business, and other travel purposes. The sample period spans from January 1996 to December 2018. Initially, the time series data were [...] Read more.
This study introduces a novel forecast combination method for monthly Japanese tourism demand, analyzed at both aggregated and disaggregated levels, including tourist, business, and other travel purposes. The sample period spans from January 1996 to December 2018. Initially, the time series data were decomposed into high and low frequencies using the Ensemble Empirical Mode Decomposition (EEMD) technique. Following this, Autoregressive Integrated Moving Average (ARIMA), Neural Network (NN), and Support Vector Machine (SVM) forecasting models were applied to each decomposed component individually. The forecasts from these models were then combined to produce the final predictions. Our findings indicate that the two-stage forecast combination method significantly enhances forecasting accuracy in most cases. Consequently, the combined forecasts utilizing EEMD outperform those generated by individual models. Full article
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16 pages, 4867 KiB  
Article
Characterization of Muscle Fatigue Degree in Cyclical Movements Based on the High-Frequency Components of sEMG
by Kexiang Li, Ye Sun, Jiayi Li, Hui Li, Jianhua Zhang and Li Wang
Biomimetics 2025, 10(5), 291; https://doi.org/10.3390/biomimetics10050291 - 6 May 2025
Viewed by 535
Abstract
Prolonged and high-intensity human–robot interaction can cause muscle fatigue. This fatigue leads to changes in both the time domain and frequency domain of the surface electromyography (sEMG) signals, which are closely related to human body movements. Consequently, these changes affect the accuracy and [...] Read more.
Prolonged and high-intensity human–robot interaction can cause muscle fatigue. This fatigue leads to changes in both the time domain and frequency domain of the surface electromyography (sEMG) signals, which are closely related to human body movements. Consequently, these changes affect the accuracy and stability of using sEMG signals to recognize human body movements. Although numerous studies have confirmed that the median frequency of sEMG signals decreases as the degree of muscle fatigue increases—and this has been used for classifying fatigue and non-fatigue states— there is still a lack of quantitative characterization of the degree of muscle fatigue. Therefore, this paper proposes a method for quantitatively characterizing the degree of muscle fatigue during periodic exercise, based on the high-frequency components obtained through ensemble empirical mode decomposition (EEMD). Firstly, the sEMG signals of the estimated individuals are subjected to EEMD to obtain the high-frequency components, and the short-time Fourier transform is used to calculate the median frequency (MF) of these high-frequency components. Secondly, the obtained median frequencies are linearly fitted, and based on this, a standardized median frequency distribution range (SMFDR) of sEMG signals under muscle fatigue is established. Finally, a muscle fatigue estimator is proposed to achieve the quantification of the degree of muscle fatigue based on the SMFDR. Experimental validation across five subjects demonstrated that this method effectively quantifies cyclical muscle fatigue, with results revealing the methodology exhibits superiority in identifying multiple fatigue states during cyclical movements under consistent loading conditions. Full article
(This article belongs to the Special Issue Computational Biology Simulation, Agent-Based Modelling and AI)
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13 pages, 10859 KiB  
Article
A Lightning Very-High-Frequency Mapping DOA Method Based on L Array and 2D-MUSIC
by Chuansheng Wang, Nianwen Xiang, Zhaokun Li, Zengwei Lyu, Yu Yang and Huaifei Chen
Atmosphere 2025, 16(5), 486; https://doi.org/10.3390/atmos16050486 - 22 Apr 2025
Viewed by 480
Abstract
Lightning Very-High-Frequency (VHF) radiation source mapping technology represents a pivotal advancement in the study of lightning discharge processes and their underlying physical mechanisms. This paper introduces a novel methodology for reconstructing lightning discharge channels by employing the Multiple Signal Classification (MUSIC) algorithm to [...] Read more.
Lightning Very-High-Frequency (VHF) radiation source mapping technology represents a pivotal advancement in the study of lightning discharge processes and their underlying physical mechanisms. This paper introduces a novel methodology for reconstructing lightning discharge channels by employing the Multiple Signal Classification (MUSIC) algorithm to estimate the Direction of Arrival (DOA) of lightning VHF radiation sources, specifically tailored for both non-uniform and uniform L-shaped arrays (2D-MUSIC). The proposed approach integrates the Random Sample Consensus (RANSAC) algorithm with 2D-MUSIC, thereby enhancing the precision and robustness of the reconstruction process. Initially, the array data are subjected to denoising via the Ensemble Empirical Mode Decomposition (EEMD) algorithm. Following this, the covariance matrix of the processed array data is decomposed to isolate the signal subspace, which corresponds to the signal components, and the noise subspace, which is orthogonal to the signal components. By exploiting the orthogonality between these subspaces, the method achieves an accurate estimation of the signal incidence direction, thereby facilitating the precise reconstruction of the lightning channel. To validate the feasibility of this method, comprehensive numerical simulations were conducted, revealing remarkable accuracy with elevation and azimuth angle errors both maintained below 1 degree. Furthermore, VHF non-uniform and uniform L-shaped lightning observation systems were established and deployed to analyze real lightning events occurring in 2021 and 2023. The empirical results demonstrate that the proposed method effectively reconstructs lightning channel structures across diverse L-shaped array configurations. This innovative approach significantly augments the capabilities of various broadband VHF arrays in radiation source imaging and makes a substantial contribution to the study of lightning development processes. The findings of this study underscore the potential of the proposed methodology to advance our understanding of lightning dynamics and enhance the accuracy of lightning channel reconstruction. Full article
(This article belongs to the Section Atmospheric Techniques, Instruments, and Modeling)
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25 pages, 7475 KiB  
Article
A Sensor Data-Driven Fault Diagnosis Method for Automotive Transmission Gearboxes Based on Improved EEMD and CNN-BiLSTM
by Youhong Xu, Hui Wang, Feng Xu, Shaoping Bi and Jiangang Ye
Processes 2025, 13(4), 1200; https://doi.org/10.3390/pr13041200 - 16 Apr 2025
Cited by 1 | Viewed by 586
Abstract
With the rapid development of new energy vehicle technologies, higher demands have been placed on fault diagnosis for automotive transmission gearboxes. To address the poor adaptability of traditional methods under complex operating conditions, this paper proposes a sensor data-driven fault diagnosis method based [...] Read more.
With the rapid development of new energy vehicle technologies, higher demands have been placed on fault diagnosis for automotive transmission gearboxes. To address the poor adaptability of traditional methods under complex operating conditions, this paper proposes a sensor data-driven fault diagnosis method based on improved ensemble empirical mode decomposition (EEMD) combined with convolutional neural networks (CNNs) and Bidirectional Long Short-Term Memory (BiLSTM) networks. The method incorporates a dynamic noise adjustment mechanism, allowing the noise amplitude to adapt to the characteristics of the signal. This improves the stability and accuracy of signal decomposition, effectively reducing the instability and error accumulation associated with fixed-amplitude white noise in traditional EEMD. By combining the CNN and BiLSTM modules, the approach achieves efficient feature extraction and dynamic modeling. First, vibration signals of the transmission gearbox under different operating states are collected via sensors, and an improved EEMD method is employed to decompose the signals, removing background noise and nonstationary components to extract diagnostically significant intrinsic mode functions (IMFs). Then, the CNN is utilized to extract features from the IMFs, deeply mining their spatiotemporal characteristics, while the BiLSTM captures the temporal sequence dependencies of the signals, enhancing the comprehensive modeling of nonlinear and dynamic fault features. The combination of these two networks enables efficient adaptation to complex conditions, achieving accurate classification and identification of multiple gearbox fault modes. Results indicate that the proposed approach is highly accurate and robust for identifying gearbox fault modes, significantly exceeding the performance of conventional methods and isolated network models. This provides an efficient and intelligent solution for fault diagnosis of automotive transmission gearboxes. Full article
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24 pages, 2416 KiB  
Article
Explainable Spatio-Temporal Inference Network for Car-Sharing Demand Prediction
by Nihad Brahimi, Huaping Zhang and Zahid Razzaq
ISPRS Int. J. Geo-Inf. 2025, 14(4), 163; https://doi.org/10.3390/ijgi14040163 - 9 Apr 2025
Cited by 1 | Viewed by 772
Abstract
Efficient resource allocation in car-sharing systems relies on precise predictions of demand. Predicting vehicle demand is challenging due to the interconnections of temporal, spatial, and spatio-temporal features. This paper presents the Explainable Spatio-Temporal Inference Network (eX-STIN), a new approach that improves upon our [...] Read more.
Efficient resource allocation in car-sharing systems relies on precise predictions of demand. Predicting vehicle demand is challenging due to the interconnections of temporal, spatial, and spatio-temporal features. This paper presents the Explainable Spatio-Temporal Inference Network (eX-STIN), a new approach that improves upon our prior Unified Spatio-Temporal Inference Prediction Network (USTIN) model. It offers a comprehensive framework for the integration of various data. The eX-STIN model enhances the previous one by utilizing Ensemble Empirical Mode Decomposition (EEMD), which results in refined feature extraction. It uses Minimum Redundancy Maximum Relevance (mRMR) to find features that are relevant and not redundant, and Shapley Additive Explanations (SHAP) to show how each feature affects the model’s predictions. We conducted extensive experiments that use real car-sharing data to thoroughly evaluate the efficacy of the eX-STIN model. The studies revealed the model’s ability to accurately represent the relationships among temporal, spatial, and spatio-temporal features, outperforming the state-of-the-art models. Moreover, the experiments revealed that eX-STIN exhibits enhanced predictive accuracy compared to the USTIN model. This proposed approach enhances both the accuracy of demand prediction and the transparency of resource allocation decisions in car-sharing services. Full article
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36 pages, 18532 KiB  
Article
A Heavy Metal Ion Water Quality Detection Model Based on Spectral Analysis: New Methods for Enhancing Detection Speed and Visible Spectral Denoising
by Bingyang Sun, Shunsheng Yang and Xu Cheng
Sensors 2025, 25(7), 2318; https://doi.org/10.3390/s25072318 - 5 Apr 2025
Viewed by 507
Abstract
This paper analyzes the current state of water quality detection equipment and, based on the demand for portable water quality detection systems that are on-site, rapid, accurate, cost-effective, and capable of multi-parameter measurements using spectral analysis, represents the future development direction of water [...] Read more.
This paper analyzes the current state of water quality detection equipment and, based on the demand for portable water quality detection systems that are on-site, rapid, accurate, cost-effective, and capable of multi-parameter measurements using spectral analysis, represents the future development direction of water quality detection. By focusing on indicators of heavy metal ion water pollution, this study aims to achieve the “rapid and accurate detection of water quality using spectral analysis” and emphasizes key technologies such as “visible absorption spectroscopy in photoelectric detection technology and spectral analysis”, “spectral denoising methods”, and “Convolutional Neural Network (CNN) modeling and deployment”. A novel combined denoising method integrating Ensemble Empirical Mode Decomposition (EEMD) and Singular Value Decomposition (SVD) is developed and applied for the first time in spectral water quality detection to improve accuracy. The system uses a ZYNQ-based spectral analysis platform to detect heavy metal ion concentrations, enhancing detection speed. Comparative tests with copper ion standard solutions against Chinese national standards show good accuracy and reproducibility. The developed EEMD-SVD method demonstrates superior denoising effectiveness in processing actual spectral data within the water quality detection system. Full article
(This article belongs to the Section Environmental Sensing)
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19 pages, 2858 KiB  
Article
Mode Decomposition Bi-Directional Long Short-Term Memory (BiLSTM) Attention Mechanism and Transformer (AMT) Model for Ozone (O3) Prediction in Johannesburg, South Africa
by Israel Edem Agbehadji and Ibidun Christiana Obagbuwa
Forecasting 2025, 7(2), 15; https://doi.org/10.3390/forecast7020015 - 2 Apr 2025
Cited by 1 | Viewed by 1114
Abstract
This paper presents a model that combines mode decomposition approaches with a bi-directional long short-term memory (BiLSTM) attention mechanism and a transformer (AMT) to predict the concentration level of ozone (O3) in Johannesburg, South Africa. Johannesburg is a densely populated city [...] Read more.
This paper presents a model that combines mode decomposition approaches with a bi-directional long short-term memory (BiLSTM) attention mechanism and a transformer (AMT) to predict the concentration level of ozone (O3) in Johannesburg, South Africa. Johannesburg is a densely populated city and the industrial and economic hub of South Africa. Being the industrial hub, air pollution is a major concern as it affects human health. Using air pollutants and meteorological datasets, a model was proposed that uses a mode decomposition approach to address the nonlinear nature of O3 concentration. This nonlinearity is one of the most challenging issues in air quality prediction, and this study proposed a model to decompose input data and identify the most relevant features and leverage attention mechanisms to produce weighted parameters that can enhance the model’s performance. The model’s performance enhancement approach was aimed at ensuring an effective model that easily adapts to frequently changing pollutant data in air quality prediction. The performance was evaluated statistically with root mean squared error (RMSE), mean absolute error (MAE), and mean square error (MSE). The proposed EEMD-CEEMDAN-BiLSTM-AMT model produced the most optimal result with MSE (4.80 × 10−6), RMSE (0.002), and MAE (0.001). When compared with the other similar models, the proposed model was best in terms of MSE value. Future work seeks to enhance the proposed model to fine-tune its performance on different air pollutant concentrations in South Africa. Full article
(This article belongs to the Section Environmental Forecasting)
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30 pages, 6184 KiB  
Article
A New Hybrid Deep Sequence Model for Decomposing, Interpreting, and Predicting Sulfur Dioxide Decline in Coastal Cities of Northern China
by Guoju Wang, Rongjie Zhu, Xiang Gong, Xiaoling Li, Yuanzheng Gao, Wenming Yin, Renzheng Wang, Huan Li, Huiwang Gao and Tao Zou
Sustainability 2025, 17(6), 2546; https://doi.org/10.3390/su17062546 - 14 Mar 2025
Viewed by 694
Abstract
The recent success of emission reduction policies in China has significantly lowered sulfur dioxide (SO2) levels. However, accurately forecasting these concentrations remains challenging due to their inherent non-stationary tendency. This study introduces an innovative hybrid deep learning model, RF-VMD-Seq2Seq, combining the [...] Read more.
The recent success of emission reduction policies in China has significantly lowered sulfur dioxide (SO2) levels. However, accurately forecasting these concentrations remains challenging due to their inherent non-stationary tendency. This study introduces an innovative hybrid deep learning model, RF-VMD-Seq2Seq, combining the Random Forest (RF) algorithm, Variational Mode Decomposition (VMD), and the Sequence-to-Sequence (Seq2Seq) framework to improve SO2 concentration forecasting in five coastal cities of northern China. Our results show that the predicted SO2 concentrations closely align with observed values, effectively capturing fluctuations, outliers, and extreme events—such as sharp declines the Novel Coronavirus Pneumonia (COVID-19) pandemic in 2020—along with the upper 5% of SO2 levels. The model achieved high coefficients of determination (>0.91) and Pearson’s correlation (>0.96), with low prediction errors (RMSE < 1.35 μg/m3, MAE < 0.94 μg/m3, MAPE < 15%). The low-frequency band decomposing from VMD showed a notable long-term decrease in SO2 concentrations from 2013 to 2020, with a sharp decline since 2018 during heating seasons, probably due to the ‘Coal-to-Natural Gas’ policy in northern China. The input sequence length of seven steps was recommended for the prediction model, based on high-frequency periodicities extracted through VMD, which significantly improved our model performance. This highlights the critical role of weekly-cycle variations in SO2 levels, driven by anthropogenic activities, in enhancing the accuracy of one-day-ahead SO2 predictions across northern China’s coastal regions. The results of the RF model further reveal that CO and NO2, sharing common anthropogenic sources with SO2, contribute over 50% to predicting SO2 concentrations, while meteorological factors—relative humidity (RH) and air temperature—contribute less than 20%. Additionally, the integration of VMD outperformed both the standard Seq2Seq and Ensemble Empirical Mode Decomposition (EEMD)-enhanced Seq2Seq models, showcasing the advantages of VMD in predicting SO2 decline. This research highlights the potential of the RF-VMD-Seq2Seq model for non-stationary SO2 prediction and its relevance for environmental protection and public health management. Full article
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