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Keywords = echo state networks

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25 pages, 3586 KB  
Article
A Classification Algorithm of UAV and Bird Target Based on L/K Dual-Band Micro-Doppler and Mamba
by Tao Zhang and Xiaoru Song
Drones 2026, 10(4), 265; https://doi.org/10.3390/drones10040265 - 6 Apr 2026
Viewed by 144
Abstract
To address the challenge of accurately distinguishing UAVs and birds in a low-altitude detection field, this paper proposes a classification algorithm of UAVs and birds based on L/K dual-band micro-Doppler spectrograms and Mamba. We establish a dual-band radar detection model for unmanned aerial [...] Read more.
To address the challenge of accurately distinguishing UAVs and birds in a low-altitude detection field, this paper proposes a classification algorithm of UAVs and birds based on L/K dual-band micro-Doppler spectrograms and Mamba. We establish a dual-band radar detection model for unmanned aerial vehicles (UAVs) and birds, provide a method for characterizing the Doppler parameters of the echo signals, and research a UAV and bird target classification network model that integrates micro-Doppler and Mamba. Based on a dual-branch encoding framework, we use Patch block decomposition to design a classification model to serialize the two-dimensional spectrogram of the echo signal, and introduce the Mamba state-space backbone network to extract the long-term sequence features of the target’s micro-motion. The main breakthrough of the proposed classification algorithm lies in the feature fusion stage, where a late fusion strategy is adopted to integrate the dual-path high-level representation measures, fully leveraging the sensitivity of the K-band to high-frequency textures and the scale complementarity of the L-band. Then, according to the joint loss function of mutual learning and contrastive learning, we improve the model’s prediction consistency and representation discriminability. Through experimental testing, the results show that the proposed method can effectively classify UAVs and birds, and compared with other algorithms, the accuracy rate reaches 97.5%. Full article
(This article belongs to the Section Drone Communications)
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17 pages, 467 KB  
Article
Staying Young at the Edge: A Software Aging Perspective for Foundation Models as a Service
by Benedetta Picano and Romano Fantacci
Computers 2026, 15(3), 158; https://doi.org/10.3390/computers15030158 - 3 Mar 2026
Viewed by 360
Abstract
Nowadays, the emergence of Foundation Models as a Service enables mobile users to access powerful capabilities such as inference and fine-tuning on demand and without incurring local computational overhead. This paper introduces a software-aware offloading framework for FMaaS that allows edge nodes to [...] Read more.
Nowadays, the emergence of Foundation Models as a Service enables mobile users to access powerful capabilities such as inference and fine-tuning on demand and without incurring local computational overhead. This paper introduces a software-aware offloading framework for FMaaS that allows edge nodes to forecast software aging and prevent service degradation. Each node employs a lightweight Echo State Network to predict its software age, with tasks dynamically assigned based on communication cost, inference delay, and forecast reliability. Simulation results including ablation studies confirm the effectiveness of software age forecasting in reducing task failures and improving session continuity. Full article
(This article belongs to the Special Issue Best Practices, Challenges and Opportunities in Software Engineering)
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25 pages, 2611 KB  
Article
Noise-Robust Wafer Map Defect Classification via CNN-ESN Hybrid Architecture
by Hayeon Choi, Dasom Im, Sangeun Oh and Jonghwan Lee
Micromachines 2026, 17(3), 309; https://doi.org/10.3390/mi17030309 - 28 Feb 2026
Viewed by 390
Abstract
Wafer map defect classification plays a critical role in yield monitoring and root-cause analysis in semiconductor manufacturing. Although recent convolutional neural network (CNN)-based approaches have achieved high classification accuracy, most existing models are evaluated primarily on clean datasets and remain vulnerable to unseen [...] Read more.
Wafer map defect classification plays a critical role in yield monitoring and root-cause analysis in semiconductor manufacturing. Although recent convolutional neural network (CNN)-based approaches have achieved high classification accuracy, most existing models are evaluated primarily on clean datasets and remain vulnerable to unseen perturbations and representation-level variability at test time. In this paper, we propose a hybrid CNN–echo state network (ESN) architecture that integrates spatial feature extraction with sequential aggregation to enhance robustness under input perturbations. The CNN backbone extracts two-dimensional feature maps, which are converted into ordered sequences using a multidirectional scanline strategy and processed by an ESN reservoir. The resulting sequential representations are combined with CNN features through a class-specific adaptive fusion mechanism. Using the defect-only eight-class version of the WM-811K dataset, we systematically evaluate robustness under multiple perturbation scenarios, with particular focus on the clean train/noisy test (CT-NT) setting. To ensure a controlled robustness evaluation aligned with the binary nature of wafer map data, we introduce binary-consistent die-flip perturbations and additionally employ additive Gaussian perturbations as a representation-level stress test. Under clean-data conditions, the proposed model showed a 0.61 pp improvement in test accuracy compared to the ResNet34-based CNN, with notably larger gains for rare classes and defect types exhibiting strong structural patterns. In the clean train/noisy test scenario, where the model was trained on clean wafer map data and evaluated under controlled test-time perturbations, the accuracy of the CNN baseline dropped to 77.59% at σ = 0.10, whereas the proposed hybrid model maintained an accuracy of 87.30%, resulting in an absolute improvement of 9.71 pp. Per-class analysis reveals that the robustness gain is class-dependent, with pronounced improvements for defect types exhibiting clear and repetitive structural patterns, such as Loc and Edge-Ring. Further mechanistic analysis demonstrates that the robustness improvement arises from enhanced representation stability and bounded reservoir dynamics, rather than from changes in CNN feature extraction or training regularization. These results demonstrate that the proposed CNN-ESN hybrid architecture provides meaningful advantages in terms of robustness under noisy evaluation conditions without requiring noise-aware training or prior knowledge of perturbation characteristics. Full article
(This article belongs to the Special Issue Emerging Technologies and Applications for Semiconductor Industry)
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22 pages, 13052 KB  
Article
Enhanced Migratory Biological Echo Extrapolation from Weather Radar Using ISA-LSTM
by Dou Meng, Yunping Liu, Dongli Wu, Zhiliang Deng, Yifu Chen and Chunzhi Wang
Atmosphere 2026, 17(3), 257; https://doi.org/10.3390/atmos17030257 - 28 Feb 2026
Viewed by 271
Abstract
Weather radar provides continuous, large-scale observations of aerial biological activity. However, biological echoes typically exhibit weak signals, sparse distributions, and non-stationary abrupt variations, causing existing extrapolation models to suffer from over-smoothing and loss of detail and making it difficult to capture their short-term [...] Read more.
Weather radar provides continuous, large-scale observations of aerial biological activity. However, biological echoes typically exhibit weak signals, sparse distributions, and non-stationary abrupt variations, causing existing extrapolation models to suffer from over-smoothing and loss of detail and making it difficult to capture their short-term evolution effectively. To address this issue, we propose an Integrated Self-Attention Long Short-Term Memory (ISA-LSTM) model that integrates a self-attention mechanism within the Predictive Recurrent Neural Network (PredRNN) framework. Coupled convolutional modules are introduced to enhance feature interactions between inputs and hidden states, while a spatiotemporal self-attention mechanism improves long-term dependency modeling and local detail preservation. Experiments conducted on 6000 biological echo samples from three weather radars in the Poyang Lake region demonstrate that the proposed model achieves superior extrapolation accuracy and stability compared with existing methods, maintaining a low false-alarm rate for lead times of up to 50 min. The results suggest that ISA-LSTM offers an effective deep learning approach for biological echo extrapolation, with applications in aviation safety and agricultural pest and disease early warning. Full article
(This article belongs to the Section Atmospheric Techniques, Instruments, and Modeling)
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15 pages, 18903 KB  
Article
An Operational Framework for Affect-Adjacent Structure in Plant–Environment Interaction
by Benjamin Calvert, Luc Caspar and Olaf Witkowski
Bioengineering 2026, 13(3), 287; https://doi.org/10.3390/bioengineering13030287 - 28 Feb 2026
Viewed by 512
Abstract
Plants exhibit complex internal dynamics in response to environmental conditions, yet whether these dynamics reflect structured affective regimes remains unclear. This study investigates whether internal plant signals encode information about affective states defined relationally by sustained environmental conditions. Valence and arousal were operationalised [...] Read more.
Plants exhibit complex internal dynamics in response to environmental conditions, yet whether these dynamics reflect structured affective regimes remains unclear. This study investigates whether internal plant signals encode information about affective states defined relationally by sustained environmental conditions. Valence and arousal were operationalised using temperature, humidity, and residual light. Using only internal plant measurements—including bioelectrical activity and volatile gas emissions—we evaluated whether machine learning models could decode affective structure without access to environmental variables. Binary classification revealed that valence was reliably decoded over longer temporal windows, whereas arousal required shorter windows, suggesting distinct underlying timescales. Direct multi-class quadrant classification proved unstable, but an Echo State Network capturing temporal dependencies achieved improved performance. These results indicate that the recorded plants internal dynamics carry a learnable, temporally extended signature of environmentally defined affective regimes, supporting an interpretation of plant affect as embodied environmental engagement. Full article
(This article belongs to the Section Biochemical Engineering)
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24 pages, 8654 KB  
Article
Machine Learning-Based Lifetime Prediction of Lithium Batteries: A Comparative Assessment for Electric Vehicle Applications
by Abdelilah Hammou, Raffaele Petrone, Demba Diallo, Boubekeur Tala-Ighil, Philippe Makany Boussiengue, Hicham Chaoui and Hamid Gualous
Energies 2026, 19(5), 1203; https://doi.org/10.3390/en19051203 - 27 Feb 2026
Viewed by 480
Abstract
This paper evaluates and compares four data-driven methods (Gaussian Process Regression (GPR), echo state network (ESN), gated recurrent unit (GRU), and long short-term memory (LSTM)) for lithium-ion capacity prognostics adapted to electric vehicle conditions. This comparison aims to find the most efficient prognosis [...] Read more.
This paper evaluates and compares four data-driven methods (Gaussian Process Regression (GPR), echo state network (ESN), gated recurrent unit (GRU), and long short-term memory (LSTM)) for lithium-ion capacity prognostics adapted to electric vehicle conditions. This comparison aims to find the most efficient prognosis method considering two constraints: the limitation of computational power and the unavailability of on-board capacity measurement that requires full charge and discharge conditions. The machine learning models are trained using capacity values estimated under vehicle conditions. The ageing data is collected from cycling tests of two battery chemistries, Lithium Fer Phosphate (LFP) and Nickel Manganese Cobalt (NMC), with different ageing trends. The prognosis algorithms are tuned with three different percentages of the data, allowing for the evaluation of the methods at different ageing stages. The comparison and analysis of the results show that ESN outperforms other methods; it has the lowest prediction error (mean absolute percentage error less than 1.4% at initial ageing of the cells) and the shortest training time, making it the most appropriate method for automotive applications. Full article
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16 pages, 1467 KB  
Article
ECG Heartbeat Classification Using Echo State Networks with Noisy Reservoirs and Variable Activation Function
by Ioannis P. Antoniades, Anastasios N. Tsiftsis, Christos K. Volos, Andreas D. Tsigopoulos, Konstantia G. Kyritsi and Hector E. Nistazakis
Computation 2026, 14(2), 49; https://doi.org/10.3390/computation14020049 - 13 Feb 2026
Viewed by 383
Abstract
In this work, we use an Echo State Network (ESN) model, which is essentially a recurrent neural network (RNN) operating according to the reservoir computing (RC) paradigm, to classify individual ECG heartbeats using the MIT-BIH arrhythmia database. The aim is to evaluate the [...] Read more.
In this work, we use an Echo State Network (ESN) model, which is essentially a recurrent neural network (RNN) operating according to the reservoir computing (RC) paradigm, to classify individual ECG heartbeats using the MIT-BIH arrhythmia database. The aim is to evaluate the performance of ESN in a challenging task that involves classification of complex, unprocessed one-dimensional signals, distributed into five classes. Moreover, we investigate the performance of the ESN in the presence of (i) noise in the dynamics of the internal variables of the hidden (reservoir) layer and (ii) random variability in the activation functions of the hidden layer cells (neurons). The overall accuracy of the best-performing ESN, without noise and variability, exceeded 96% with per-class accuracies ranging from 90.2% to 99.1%, which is higher than previous studies using CNNs and more complex machine learning approaches. The top-performing ESN required only 40 min of training on a CPU (Intel i5-1235U@1.3 GHz) HP laptop. Notably, an alternative ESN configuration that matched the accuracy of a prior CNN-based study (93.4%) required only 6 min of training, whereas a CNN would typically require an estimated training time of 2–3 days. Surprisingly, ESN performance proved to be very robust when Gaussian noise was added to the dynamics of the reservoir hidden variables, even for high noise amplitudes. Moreover, the success rates remained essentially the same when random variability was imposed in the activation functions of the hidden layer cells. The stability of ESN performance under noisy conditions and random variability in the hidden layer (reservoir) cells demonstrates the potential of analog hardware implementations of ESNs to be robust in time-series classification tasks. Full article
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18 pages, 3314 KB  
Article
Reservoir Computing: Foundations, Advances, and Challenges Toward Neuromorphic Intelligence
by Andrew Liu, Muhammad Farhan Azmine, Chunxiao Lin and Yang Yi
AI 2026, 7(2), 70; https://doi.org/10.3390/ai7020070 - 13 Feb 2026
Viewed by 1196
Abstract
Reservoir computing (RC) has emerged as an energy-efficient paradigm for temporal information processing, offering reduced training complexity by fixing recurrent dynamics and training only a simple readout layer. Among RC models, Echo State Networks (ESNs) and Liquid State Machines (LSMs) represent two distinct [...] Read more.
Reservoir computing (RC) has emerged as an energy-efficient paradigm for temporal information processing, offering reduced training complexity by fixing recurrent dynamics and training only a simple readout layer. Among RC models, Echo State Networks (ESNs) and Liquid State Machines (LSMs) represent two distinct approaches based on continuous-valued and spiking neural dynamics, respectively. In this work, we present a comparative evaluation of ESNs and LSMs on the Mackey–Glass chaotic time-series prediction task, with emphasis on scalability, overfitting behavior, and robustness to reduced numerical error precision. Experimental results show that ESNs achieve lower prediction error with relatively small reservoirs but exhibit early performance saturation and signs of overfitting as reservoir size increases. In contrast, LSMs demonstrate more consistent generalization with increasing reservoir size and maintain stable performance under aggressive reservoir quantization. These findings highlight fundamental trade-offs between accuracy and hardware efficiency, and suggest that spiking RC models are well suited for energy-constrained and neuromorphic computing applications. Full article
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25 pages, 4974 KB  
Article
Physics-Constrained Deep Learning with Adaptive Z-R Relationship for Accurate and Interpretable Quantitative Precipitation Estimation
by Ting Shu, Huan Zhao, Kanglong Cai and Zexuan Zhu
Remote Sens. 2026, 18(1), 156; https://doi.org/10.3390/rs18010156 - 3 Jan 2026
Viewed by 586
Abstract
Quantitative precipitation estimation (QPE) from radar reflectivity is fundamental for weather nowcasting and water resource management. Conventional Z-R relationship formulas, derived from Rayleigh scattering theory, rely heavily on empirical parameter fitting, which limits the estimation accuracy and generalization across different precipitation regimes. Recent [...] Read more.
Quantitative precipitation estimation (QPE) from radar reflectivity is fundamental for weather nowcasting and water resource management. Conventional Z-R relationship formulas, derived from Rayleigh scattering theory, rely heavily on empirical parameter fitting, which limits the estimation accuracy and generalization across different precipitation regimes. Recent deep learning (DL)-based QPE methods can capture the complex nonlinear relationships between radar reflectivity and rainfall. However, most of them overlook fundamental physical constraints, resulting in reduced robustness and interpretability. To address these issues, this paper proposes FusionQPE, a novel Physics-Constrained DL framework that integrates an adaptive Z-R formula. Specifically, FusionQPE employs a Dense convolutional neural network (DenseNet) backbone to extract multi-scale spatial features from radar echoes, while a modified squeeze-and-excitation (SE) network adaptively learns the parameters of the Z-R relationship. The final rainfall estimate is obtained through a linear combination of outputs from both the DenseNet backbone and the adaptive Z-R branch, where the trained linear weight and Z-R parameters provide interpretable insights into the model’s physical reasoning. Moreover, a physical-based constraint derived from the Z-R branch output is incorporated into the loss function to further strengthen physical consistency. Comprehensive experiments on real radar and rain gauge observations from Guangzhou, China, demonstrate that FusionQPE consistently outperforms both traditional and state-of-the-art DL-based QPE models across multiple evaluation metrics. The ablation and interpretability analysis further confirms that the adaptive Z-R branch improves both the physical consistency and credibility of the model’s precipitation estimation. Full article
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14 pages, 917 KB  
Article
Is Economic Connectedness Likely to Raise the Environmental Footprint?
by Anna Auza and José Alberto Fuinhas
Biosphere 2025, 1(1), 7; https://doi.org/10.3390/biosphere1010007 - 18 Dec 2025
Viewed by 453
Abstract
Economic connectedness has been recently found to lower income inequality by rising intergenerational mobility, yet its environmental impacts are less well known. More well-known is the fact that the non-carbon footprint is easier to reach via regulations because its production is domestic. These [...] Read more.
Economic connectedness has been recently found to lower income inequality by rising intergenerational mobility, yet its environmental impacts are less well known. More well-known is the fact that the non-carbon footprint is easier to reach via regulations because its production is domestic. These two problems of income inequality and environmental pollution have echoed in public opinion polls as one of the major current problems in developed countries. We thereby look at the United States on the state level during the last two decades (2010–2020) with a Hausman–Taylor estimator for panel data. The choice of the estimator stems from its appropriateness for panel datasets with constant variables. We find that in the United States, economic connectedness between friends, whereby friendships were formed within the same group, may be blamed for the rising environmental (non-carbon) footprint. The non-carbon footprint is, therefore, explained by the bonding of social capital, which may restrict innovation. We document the case where social capital in the form of economic connectedness may be harmful to the public good, such as the environment, our main contribution. The negative effect of bonding social capital on environmental outcomes due to rigid social networks and particular network technology use is a novel addition to the prior research. The policy implications are discussed in more detail, and a call is made to distinguish social capital types and promote bridging social capital where bonding social capital is relatively strong. Full article
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22 pages, 23477 KB  
Article
FPGA-Accelerated ESN with Chaos Training for Financial Time Series Prediction
by Zeinab A. Hassaan, Mohammed H. Yacoub and Lobna A. Said
Mach. Learn. Knowl. Extr. 2025, 7(4), 160; https://doi.org/10.3390/make7040160 - 3 Dec 2025
Cited by 1 | Viewed by 1110
Abstract
Improving financial time series forecasting presents challenges because models often struggle to identify diverse fault patterns in unseen data. This issue is critical in fintech, where accurate and reliable forecasting of financial data is essential for effective risk management and informed investment strategies. [...] Read more.
Improving financial time series forecasting presents challenges because models often struggle to identify diverse fault patterns in unseen data. This issue is critical in fintech, where accurate and reliable forecasting of financial data is essential for effective risk management and informed investment strategies. This work addresses these challenges by initializing the weights and biases of two proposed models, Gated Recurrent Units (GRUs) and the Echo State Network (ESN), with different chaotic sequences to enhance prediction accuracy and capabilities. We compare reservoir computing (RC) and recurrent neural network (RNN) models with and without the integration of chaotic systems, utilizing standard initialization. The models are validated on six different datasets, including the 500 largest publicly traded companies in the US (S&P500), the Irish Stock Exchange Quotient (ISEQ) dataset, the XAU and USD forex pair (XAU/USD), the USD and JPY forex pair with respect to the currency exchange rate (USD/JPY), Chinese daily stock prices, and the top 100 index of UK companies (FTSE 100). The ESN model, combined with the Lorenz system, achieves the lowest error among other models, reinforcing the effectiveness of chaos-trained models for prediction. The proposed ESN model, accelerated by the Kintex-Ultrascale KCU105 FPGA board, achieves a maximum frequency of 83.5 MHz and a power consumption of 0.677 W. The results of the hardware simulation align with MATLAB R2025b fixed-point analysis. Full article
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21 pages, 6349 KB  
Article
PLPGR-Net: Photon-Level Physically Guided Restoration Network for Underwater Laser Range-Gated Image
by Qing Tian, Longfei Hu, Zheng Zhang and Qiang Yang
J. Mar. Sci. Eng. 2025, 13(12), 2217; https://doi.org/10.3390/jmse13122217 - 21 Nov 2025
Viewed by 656
Abstract
Underwater laser range-gated imaging (ULRGI) effectively suppresses backscatter from water bodies through a time-gated photon capture mechanism, significantly extending underwater detection ranges compared to conventional imaging techniques. However, as imaging distance increases, rapid laser power attenuation causes localized pixel loss in captured images. [...] Read more.
Underwater laser range-gated imaging (ULRGI) effectively suppresses backscatter from water bodies through a time-gated photon capture mechanism, significantly extending underwater detection ranges compared to conventional imaging techniques. However, as imaging distance increases, rapid laser power attenuation causes localized pixel loss in captured images. To address ULRGI’s limitations in multi-frame stacking—particularly poor real-time performance and artifact generation—this paper proposes the Photon-Level Physically Guided Underwater Laser-Gated Image Restoration Network (PLPGR-Net). To overcome image degradation caused by water scattering and address the challenge of strong coupling between target echo signals and scattering noise, we designed a three-branch architecture driven by photon-level physical priors. This architecture comprises: scattering background suppression module, sparse photon perception module, and enhanced U-Net high-frequency information recovery module. By establishing a multidimensional physical constraint loss system, we guide image reconstruction across three dimensions—pixels, features, and physical laws—ensuring the restored results align with underwater photon distribution characteristics. This approach significantly enhances operational efficiency in critical applications such as underwater infrastructure inspection and cultural relic detection. Comparative experiments using proprietary datasets and state-of-the-art denoising and underwater image restoration algorithms validate the method’s outstanding performance in deeply integrating physical interpretability with deep learning generalization capabilities. Full article
(This article belongs to the Special Issue Advancements in Deep-Sea Equipment and Technology, 3rd Edition)
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17 pages, 2138 KB  
Article
Surface Electromyography-Based Wrist Angle Estimation and Robotic Arm Control with Echo State Networks
by Toshihiro Kawase and Hiroki Ikeda
Actuators 2025, 14(11), 548; https://doi.org/10.3390/act14110548 - 9 Nov 2025
Cited by 1 | Viewed by 1079
Abstract
Continuous estimation of joint angles based on surface electromyography (sEMG) signals is a promising method for naturally controlling prosthetic limbs and assistive devices. However, conventional methods based on neural networks have limitations such as long training times and calibration burdens. This study investigates [...] Read more.
Continuous estimation of joint angles based on surface electromyography (sEMG) signals is a promising method for naturally controlling prosthetic limbs and assistive devices. However, conventional methods based on neural networks have limitations such as long training times and calibration burdens. This study investigates the use of an echo state network (ESN), which enables fast training, to estimate wrist joint angles from sEMG. Five participants mimicked the motion of a 1-degree-of-freedom robotic arm by flexing and extending their wrist, while sEMG signals from the wrist flexor and extensor muscles and the robotic arm’s angle were recorded. The ESN was trained to take two sEMG channels as input and the robotic joint angle as output. High-accuracy estimation with a median coefficient of determination R2 = 0.835 was achieved for representative ESN parameters. Additionally, the effects of the reservoir size, spectral radius, and time constant on estimation accuracy were evaluated using data from a single participant. Furthermore, online estimation of joint angles based on sEMG signals enabled successful control of the robotic arm. These results suggest that sEMG-based ESN estimation offers fast, accurate joint control and could be useful for prosthetics and fundamental studies on body perception. Full article
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41 pages, 12462 KB  
Article
Real-Time Efficient Approximation of Nonlinear Fractional-Order PDE Systems via Selective Heterogeneous Ensemble Learning
by Biao Ma and Shimin Dong
Fractal Fract. 2025, 9(10), 660; https://doi.org/10.3390/fractalfract9100660 - 13 Oct 2025
Viewed by 776
Abstract
Rod-pumping systems represent complex nonlinear systems. Traditional soft-sensing methods used for efficiency prediction in such systems typically rely on complicated fractional-order partial differential equations, severely limiting the real-time capability of efficiency estimation. To address this limitation, we propose an approximate efficiency prediction model [...] Read more.
Rod-pumping systems represent complex nonlinear systems. Traditional soft-sensing methods used for efficiency prediction in such systems typically rely on complicated fractional-order partial differential equations, severely limiting the real-time capability of efficiency estimation. To address this limitation, we propose an approximate efficiency prediction model for nonlinear fractional-order differential systems based on selective heterogeneous ensemble learning. This method integrates electrical power time-series data with fundamental operational parameters to enhance real-time predictive capability. Initially, we extract critical parameters influencing system efficiency using statistical principles. These primary influencing factors are identified through Pearson correlation coefficients and validated using p-value significance analysis. Subsequently, we introduce three foundational approximate system efficiency models: Convolutional Neural Network-Echo State Network-Bidirectional Long Short-Term Memory (CNN-ESN-BiLSTM), Bidirectional Long Short-Term Memory-Bidirectional Gated Recurrent Unit-Transformer (BiLSTM-BiGRU-Transformer), and Convolutional Neural Network-Echo State Network-Bidirectional Gated Recurrent Unit (CNN-ESN-BiGRU). Finally, to balance diversity among basic approximation models and predictive accuracy, we develop a selective heterogeneous ensemble-based approximate efficiency model for nonlinear fractional-order differential systems. Experimental validation utilizing actual oil-well parameters demonstrates that the proposed approach effectively and accurately predicts the efficiency of rod-pumping systems. Full article
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14 pages, 3611 KB  
Article
Performance Comparison of LSTM and ESN Models in Time-Series Prediction of Solar Power Generation
by Yehan Joo, Dogyoon Kim, Youngmin Noh, Jaewon Choi and Jonghwan Lee
Sustainability 2025, 17(19), 8538; https://doi.org/10.3390/su17198538 - 23 Sep 2025
Cited by 3 | Viewed by 1374
Abstract
Improving the prediction accuracy of solar power generation is a critical challenge in promoting sustainable energy solutions. While machine learning models like long short-term memory (LSTM) have gained attention, they face practical limitations such as their complex structure, long training time, and susceptibility [...] Read more.
Improving the prediction accuracy of solar power generation is a critical challenge in promoting sustainable energy solutions. While machine learning models like long short-term memory (LSTM) have gained attention, they face practical limitations such as their complex structure, long training time, and susceptibility to overfitting. Echo state networks (ESNs) have attracted attention for their small number of trainable parameters and fast training speed, but their sensitivity to hyperparameter settings makes performance improvement difficult. In this study, the key hyperparameters of an ESN (spectral radius, input noise, and leakage rate) were optimized to maximize performance. The ESN achieved a Root Mean Square Error (RMSE) of 0.0069 for power prediction, demonstrating a significant improvement in accuracy over a tuned LSTM model. ESNs are also well-suited for real-time prediction and large-scale data processing, owing to their low computational cost and fast training speed. By providing a more accurate and efficient forecasting tool, this study supports grid operators in managing the intermittency of renewable energy, thereby fostering a more stable and reliable sustainable energy infrastructure. Full article
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