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Search Results (2,644)

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Keywords = nonlinear networked systems

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21 pages, 1142 KiB  
Article
Advancing Air Quality Monitoring: Deep Learning-Based CNN-RNN Hybrid Model for PM2.5 Forecasting
by Anıl Utku, Umit Can, Mustafa Alpsülün, Hasan Celal Balıkçı, Azadeh Amoozegar, Abdulmuttalip Pilatin and Abdulkadir Barut
Atmosphere 2025, 16(9), 1003; https://doi.org/10.3390/atmos16091003 (registering DOI) - 24 Aug 2025
Abstract
Particulate matter, particularly PM2.5, poses a significant threat to public health due to its ability to disperse widely and its detrimental impact on the respiratory and circulatory systems upon inhalation. Consequently, it is imperative to maintain regular monitoring and assessment of [...] Read more.
Particulate matter, particularly PM2.5, poses a significant threat to public health due to its ability to disperse widely and its detrimental impact on the respiratory and circulatory systems upon inhalation. Consequently, it is imperative to maintain regular monitoring and assessment of particulate matter levels to anticipate air pollution events and promptly mitigate their adverse effects. However, predicting air quality is inherently complex, given the multitude of variables that influence it. Deep learning models, renowned for their ability to capture nonlinear relationships, offer a promising approach to address this challenge, with hybrid architectures demonstrating enhanced performance. This study aims to develop and evaluate a hybrid model integrating Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs) for forecasting PM2.5 levels in India, Milan, and Frankfurt. A comparative analysis with established deep learning and machine learning techniques substantiates the superior predictive capabilities of the proposed CNN-RNN model. The findings underscore its potential as an effective tool for air quality prediction, with implications for informed decision-making and proactive intervention strategies to safeguard public health. Full article
(This article belongs to the Section Air Quality)
48 pages, 1710 KiB  
Article
Optimal Placement of a Unified Power Quality Conditioner (UPQC) in Distribution Systems Using Exhaustive Search to Improve Voltage Profiles and Harmonic Distortion
by Juan S. Espinosa Gutiérrez and Alexander Aguila Téllez
Energies 2025, 18(17), 4499; https://doi.org/10.3390/en18174499 (registering DOI) - 24 Aug 2025
Abstract
This paper presents an exhaustive search approach to determine the optimal placement of a Unified Power Quality Conditioner (UPQC) in a distribution system that integrates a distributed generation (DG) unit based on photovoltaic (PV) panels. The main objective is to enhance voltage profiles [...] Read more.
This paper presents an exhaustive search approach to determine the optimal placement of a Unified Power Quality Conditioner (UPQC) in a distribution system that integrates a distributed generation (DG) unit based on photovoltaic (PV) panels. The main objective is to enhance voltage profiles and reduce total harmonic distortion (THD) in the presence of nonlinear loads. A multi-objective optimization model is formulated, combining THD minimization and voltage deviation reduction through a weighted cost function. Two case studies are conducted using the IEEE 33-bus test system modeled in MATLAB Simulink, considering different scenarios: one with nonlinear loads and another with additional DG integration. The UPQC is tested at critical nodes to assess its impact on power quality indicators. Results show that placing the UPQC at node 14 yields the lowest cost function value in both cases, with THD reductions exceeding 90% at the installation node and notable improvements across the system. These findings confirm that brute-force optimization is a reliable and effective strategy for UPQC siting, especially in distribution networks subjected to nonlinear disturbances and renewable-based DG. The proposed methodology provides a practical framework for power quality enhancement and supports decision-making in modern smart grid environments. Full article
(This article belongs to the Special Issue Advances in Electrical Power System Quality)
19 pages, 1633 KiB  
Article
Temporal-Alignment Cluster Identification and Relevance-Driven Feature Refinement for Ultra-Short-Term Wind Power Forecasting
by Yan Yan and Yan Zhou
Energies 2025, 18(17), 4477; https://doi.org/10.3390/en18174477 - 22 Aug 2025
Abstract
Ultra-short-term wind power forecasting is challenged by high volatility and complex temporal patterns, with traditional single-model approaches often failing to provide stable and accurate predictions under diverse operational scenarios. To address this issue, a framework based on the TCN-ELM hybrid model with temporal [...] Read more.
Ultra-short-term wind power forecasting is challenged by high volatility and complex temporal patterns, with traditional single-model approaches often failing to provide stable and accurate predictions under diverse operational scenarios. To address this issue, a framework based on the TCN-ELM hybrid model with temporal alignment clustering and feature refinement is proposed for ultra-short-term wind power forecasting. First, dynamic time warping (DTW)–K-means is applied to cluster historical power curves in the temporal alignment space, identifying consistent operational patterns and providing prior information for subsequent predictions. Then, a correlation-driven feature refinement method is introduced to weight and select the most representative meteorological and power sequence features within each cluster, optimizing the feature set for improved prediction accuracy. Next, a TCN-ELM hybrid model is constructed, combining the advantages of temporal convolutional networks (TCNs) in capturing sequential features and an extreme learning machine (ELM) in efficient nonlinear modelling. This hybrid approach enhances forecasting performance through their synergistic capabilities. Traditional ultra-short-term forecasting often focuses solely on historical power as input, especially with a 15 min resolution, but this study emphasizes reducing the time scale of meteorological forecasts and power samples to within one hour, aiming to improve the reliability of the forecasting model in handling sudden meteorological changes within the ultra-short-term time horizon. To validate the proposed framework, comparisons are made with several benchmark models, including traditional TCN, ELM, and long short-term memory (LSTM) networks. Experimental results demonstrate that the proposed framework achieves higher prediction accuracy and better robustness across various operational modes, particularly under high-variability scenarios, out-performing conventional models like TCN and ELM. The method provides a reliable technical solution for ultra-short-term wind power forecasting, grid scheduling, and power system stability. Full article
19 pages, 738 KiB  
Article
Short-Term Multi-Energy Load Forecasting Method Based on Transformer Spatio-Temporal Graph Neural Network
by Heng Zhou, Qing Ai and Ruiting Li
Energies 2025, 18(17), 4466; https://doi.org/10.3390/en18174466 - 22 Aug 2025
Viewed by 40
Abstract
To tackle the limitations in simultaneously modeling long-term dependencies in the time dimension and nonlinear interactions in the feature dimension, as well as their inability to fully reflect the impact of real-time load changes on spatial dependencies, a short-term multi-energy load forecasting method [...] Read more.
To tackle the limitations in simultaneously modeling long-term dependencies in the time dimension and nonlinear interactions in the feature dimension, as well as their inability to fully reflect the impact of real-time load changes on spatial dependencies, a short-term multi-energy load forecasting method based on Transformer Spatio-Temporal Graph neural network (TSTG) is proposed. This method employs a multi-head spatio-temporal attention module to model long-term dependencies in the time dimension and nonlinear interactions in the feature dimension in parallel across multiple subspaces. Additionally, a dynamic adaptive graph convolution module is designed to construct adaptive adjacency matrices by combining physical topology and feature similarity, dynamically adjusting node connection weights based on real-time load characteristics to more accurately characterize the spatial dynamics of multi-energy interactions. Furthermore, TSTG adopts an end-to-end spatio-temporal joint optimization framework, achieving synchronous extraction and fusion of spatio-temporal features through an encoder–decoder architecture. Experimental results show that TSTG significantly outperforms existing methods in short-term load forecasting tasks, providing an effective solution for refined forecasting in integrated energy systems. Full article
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19 pages, 2900 KiB  
Article
A Transformer-Based Approach for Joint Interference Cancellation and Signal Detection in FTN-RIS MIMO Systems
by Seong-Gyun Choi, Seung-Hwan Seo, Ji-Hee Yu, Yoon-Ju Choi, Ki-Chang Tong, Min-Hyeok Choi, Yeong-Gyun Jung, Myung-Sun Baek and Hyoung-Kyu Song
Mathematics 2025, 13(17), 2699; https://doi.org/10.3390/math13172699 - 22 Aug 2025
Viewed by 36
Abstract
Next-generation communication systems demand extreme spectral efficiency to handle ever-increasing data traffic. The combination of faster-than-Nyquist (FTN) signaling and reconfigurable intelligent surfaces (RISs) presents a promising solution to meet this demand. However, the aggressive time compression inherent to FTN signaling introduces severe and [...] Read more.
Next-generation communication systems demand extreme spectral efficiency to handle ever-increasing data traffic. The combination of faster-than-Nyquist (FTN) signaling and reconfigurable intelligent surfaces (RISs) presents a promising solution to meet this demand. However, the aggressive time compression inherent to FTN signaling introduces severe and highly non-linear inter-symbol interference (ISI). This complex distortion is challenging for conventional linear equalizers and even for recurrent neural network (RNN)-based detectors, which can struggle to model long-range dependencies within the signal sequence. To overcome this limitation, this paper proposes a novel signal detection framework based on the transformer model. By leveraging its core multi-head self-attention mechanism, the transformer globally analyzes the entire received signal sequence at once. This enables it to effectively model and reverse complex ISI patterns by identifying the most significant interfering symbols, regardless of their position, leading to superior signal recovery. The simulation results validate the outstanding performance of the proposed approach. To achieve a target bit error rate (BER) of 104, the transformer-based detector shows a significant signal-to-noise ratio (SNR) gain of approximately 1.5 dB over a Bi-LSTM detector over 4 dB compared to the conventional FTN-RIS system, while maintaining a high spectral efficiency of nearly 2 bps/s/Hz. Full article
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16 pages, 5540 KiB  
Article
Sensor-Driven RSSI Prediction via Adaptive Machine Learning and Environmental Sensing
by Anya Apavatjrut
Sensors 2025, 25(16), 5199; https://doi.org/10.3390/s25165199 - 21 Aug 2025
Viewed by 208
Abstract
Received Signal Strength Indicator (RSSI) prediction is valuable for network planning and optimization as it helps determine the optimal placements of wireless access points and enables better coverage planning. It is also crucial for efficient handover management between cells or access points, reducing [...] Read more.
Received Signal Strength Indicator (RSSI) prediction is valuable for network planning and optimization as it helps determine the optimal placements of wireless access points and enables better coverage planning. It is also crucial for efficient handover management between cells or access points, reducing dropped connections and improving service quality. Additionally, RSSI prediction supports indoor positioning systems, power management optimization, and cost-efficient network deployment. Path loss models have historically served as the foundation for RSSI prediction, providing a theoretical framework for estimating signal strength degradation. However, modern machine learning approaches have emerged as a revolutionary solution for network optimization, providing more versatile and data-driven methods to enhance wireless network performance. In this paper, an adaptive machine learning framework integrating environmental sensing parameters such as temperature, relative humidity, barometric pressure, and particulate matter for RSSI prediction is proposed. Performance analysis reveals that RSSI values are influenced by environmental factors through complex, non-linear interactions, thereby challenging the conventional linear assumptions of traditional path loss models. The proposed model demonstrates improved predictive accuracy over the baseline, with relative increases in variance explained of 6.02% and 2.04% compared to the baseline model excluding and including environmental parameters, respectively. Additionally, the root mean squared error is reduced to 1.40 dB. These results demonstrate that cognitive methods incorporating environmental data can substantially enhance RSSI prediction accuracy in wireless communications. Full article
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21 pages, 3373 KiB  
Article
RBF Neural Network-Based Anti-Disturbance Trajectory Tracking Control for Wafer Transfer Robot Under Variable Payload Conditions
by Bo Xu, Luyao Yuan and Hao Yu
Appl. Sci. 2025, 15(16), 9193; https://doi.org/10.3390/app15169193 - 21 Aug 2025
Viewed by 196
Abstract
Variations in the drive motor’s load inertia during wafer transfer robot arm motion critically degrade end-effector trajectory accuracy. To address this challenge, this study proposes an anti-disturbance control strategy integrating Radial Basis Function Neural Network (RBFNN) and event-triggered mechanisms. Firstly, dynamic simulations reveal [...] Read more.
Variations in the drive motor’s load inertia during wafer transfer robot arm motion critically degrade end-effector trajectory accuracy. To address this challenge, this study proposes an anti-disturbance control strategy integrating Radial Basis Function Neural Network (RBFNN) and event-triggered mechanisms. Firstly, dynamic simulations reveal that nonlinear load inertia growth increases joint reaction forces and diminishes trajectory precision. The RBFNN dynamically approximates system nonlinearities, while an adaptive law updates its weights online to compensate for load variations and external disturbances. Secondly, an event-triggered mechanism is introduced, updating the controller only when specific conditions are met, thereby reducing communication burden and actuator wear. Subsequently, Lyapunov stability analysis proves the closed-loop system is Uniformly Ultimately Bounded (UUB) and prevents Zeno behavior. Finally, simulations on a planar 2-DOF manipulator demonstrate significantly enhanced trajectory tracking accuracy under variable loads. Critically, the adaptive neural network control method reduces trajectory tracking error by 50% and decreases controller update frequency by 84.7%. This work thus provides both theoretical foundations and engineering references for high-precision wafer transfer robot control. Full article
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23 pages, 3243 KiB  
Article
Research on Dynamic Measurement and Early Warning of Systemic Financial Risk in China Based on TVP-FAVAR and Deep Learning Model
by Hufang Yang, Luyi Liu, Jieyang Cui, Wenbin Wu and Yuyang Gao
Systems 2025, 13(8), 720; https://doi.org/10.3390/systems13080720 - 21 Aug 2025
Viewed by 416
Abstract
With the accelerated development of economic globalization, it is of great significance to strengthen the ability to measure, evaluate, and warn of systemic financial risks for preventing and defusing financial risks. Thus, this research established the Time-Varying Parameter Factor-Augmented Vector Autoregression model (TVP-FAVAR), [...] Read more.
With the accelerated development of economic globalization, it is of great significance to strengthen the ability to measure, evaluate, and warn of systemic financial risks for preventing and defusing financial risks. Thus, this research established the Time-Varying Parameter Factor-Augmented Vector Autoregression model (TVP-FAVAR), combined with the Markov Regime Switching Autoregressive Model, to dynamically measure China’s systemic financial risk. The network public opinion index is constructed and introduced into the financial risk early warning system to capture the dynamic impact of market sentiment on financial risks. After testing the nonlinear causal relationship between financial indicators based on the transfer entropy method, the Transformer deep learning model is applied to build a financial risk early warning system, and the performance is compared to traditional methods. The experimental results showed that (1) the trend of the systemic financial risk index based on the dynamic measurement of the TVP-FAVAR model fitted the actual situation well and that (2) the Transformer model public opinion index could fully and effectively mine the nonlinear relationship between data. Compared to traditional machine learning methods, the Transformer model has significant advantages in stronger prediction accuracy and generalization ability. This study provided a new technical path for financial risk early warning and has important reference value for improving the financial regulatory system. Full article
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19 pages, 2887 KiB  
Article
Disturbance Observer-Based Saturation-Tolerant Prescribed Performance Control for Nonlinear Multi-Agent Systems
by Shijie Chang, Jiayu Bai, Haoxiang Wen and Shuokai Wei
Electronics 2025, 14(16), 3310; https://doi.org/10.3390/electronics14163310 - 20 Aug 2025
Viewed by 206
Abstract
This study focuses on the adaptive tracking control issue for nonlinear multi-agent systems (MASs) under the influence of asymmetric input constraints and external disturbances. Firstly, an auxiliary system is proposed, which can ensure flexible prescribed performance under input saturation conditions. Meanwhile, by introducing [...] Read more.
This study focuses on the adaptive tracking control issue for nonlinear multi-agent systems (MASs) under the influence of asymmetric input constraints and external disturbances. Firstly, an auxiliary system is proposed, which can ensure flexible prescribed performance under input saturation conditions. Meanwhile, by introducing a transformation function, the distributed errors are freed from initial constraints. Employing the backstepping method, the adaptive technique, and a neural network approximation technology, a finite-time prescribed performance adaptive tracking control algorithm is designed, enabling the tracking errors to stably converge within the prescribed performance bounds. Secondly, a composite disturbance observer is developed to estimate and mitigate the combined disturbances, which include external perturbations and approximation errors from radial basis function neural networks (RBF NNs). It not only achieves effective disturbance compensation but also further suppresses the approximation errors of RBF NNs. Finally, stability analysis using the Lyapunov function demonstrates that all closed-loop signals remain uniformly ultimately bounded (UUB), with adaptive tracking errors converging to a compact region within a finite time. Simulation results and comparative studies confirm the proposed method’s effectiveness and advantages, providing a basis for its practical use in distributed control applications. Full article
(This article belongs to the Section Systems & Control Engineering)
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22 pages, 2382 KiB  
Article
Spatiotemporal Anomaly Detection in Distributed Acoustic Sensing Using a GraphDiffusion Model
by Seunghun Jeong, Huioon Kim, Young Ho Kim, Chang-Soo Park, Hyoyoung Jung and Hong Kook Kim
Sensors 2025, 25(16), 5157; https://doi.org/10.3390/s25165157 - 19 Aug 2025
Viewed by 261
Abstract
Distributed acoustic sensing (DAS), which can provide dense spatial and temporal measurements using optical fibers, is quickly becoming critical for large-scale infrastructure monitoring. However, anomaly detection in DAS data is still challenging owing to the spatial correlations between sensing channels and nonlinear temporal [...] Read more.
Distributed acoustic sensing (DAS), which can provide dense spatial and temporal measurements using optical fibers, is quickly becoming critical for large-scale infrastructure monitoring. However, anomaly detection in DAS data is still challenging owing to the spatial correlations between sensing channels and nonlinear temporal dynamics. Recent approaches often disregard the explicit sensor layout and instead handle DAS data as two-dimensional images or flattened sequences, eliminating the spatial topology. This work proposes GraphDiffusion, a novel generative anomaly-detection model that combines a conditional denoising diffusion probabilistic model (DDPM) and a graph neural network (GNN) to overcome these limitations. By treating each channel as a graph node and building edges based on Euclidean proximity, the GNN explicitly models the spatial arrangement of DAS sensors, allowing the network to capture local interchannel dependencies. The conditional DDPM uses iterative denoising to model the temporal dynamics of standard signals, enabling the system to detect deviations without the need for anomalies. The performance evaluations based on real-world DAS datasets reveal that GraphDiffusion achieves 98.2% and 98.0% based on the area under the curve (AUC) of the F1-score at K different levels (F1K-AUC), an AUC of receiver operating characteristic (ROC) at K different levels (ROCK-AUC), outperforming other comparative models. Full article
(This article belongs to the Section Intelligent Sensors)
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38 pages, 5063 KiB  
Article
Sensor-Driven Surrogate Modeling and Control of Nonlinear Dynamical Systems Using FAE-CAE-LSTM and Deep Reinforcement Learning
by Mahdi Kherad, Mohammad Kazem Moayyedi, Faranak Fotouhi-Ghazvini, Maryam Vahabi and Hossein Fotouhi
Sensors 2025, 25(16), 5149; https://doi.org/10.3390/s25165149 - 19 Aug 2025
Viewed by 243
Abstract
In cyber-physical systems governed by nonlinear partial differential equations (PDEs), real-time control is often limited by sparse sensor data and high-dimensional system dynamics. Deep reinforcement learning (DRL) has shown promise for controlling such systems, but training DRL agents directly on full-order simulations is [...] Read more.
In cyber-physical systems governed by nonlinear partial differential equations (PDEs), real-time control is often limited by sparse sensor data and high-dimensional system dynamics. Deep reinforcement learning (DRL) has shown promise for controlling such systems, but training DRL agents directly on full-order simulations is computationally intensive. This paper presents a sensor-driven, non-intrusive reduced-order modeling (NIROM) framework called FAE-CAE-LSTM, which combines convolutional and fully connected autoencoders with a long short-term memory (LSTM) network. The model compresses high-dimensional states into a latent space and captures their temporal evolution. A DRL agent is trained entirely in this reduced space, interacting with the surrogate built from sensor-like spatiotemporal measurements, such as pressure and velocity fields. A CNN-MLP reward estimator provides data-driven feedback without requiring access to governing equations. The method is tested on benchmark systems including Burgers’ equation, the Kuramoto–Sivashinsky equation, and flow past a circular cylinder; accuracy is further validated on flow past a square cylinder. Experimental results show that the proposed approach achieves accurate reconstruction, robust control, and significant computational speedup over traditional simulation-based training. These findings confirm the effectiveness of the FAE-CAE-LSTM surrogate in enabling real-time, sensor-informed, scalable DRL-based control of nonlinear dynamical systems. Full article
(This article belongs to the Special Issue Sensor-Enhanced Machine Learning for Complex System Optimization)
26 pages, 3443 KiB  
Article
Intelligent Soft Sensors for Inferential Monitoring of Hydrodesulfurization Process Analyzers
by Željka Ujević Andrijić, Srečko Herceg, Magdalena Šimić and Nenad Bolf
Actuators 2025, 14(8), 410; https://doi.org/10.3390/act14080410 - 19 Aug 2025
Viewed by 165
Abstract
This work presents the development of soft sensor models for monitoring the operation of online process analyzers used to measure the sulfur content in the product of the refinery hydrodesulfurization process. Since sulfur content often fluctuates over time, soft sensor models must account [...] Read more.
This work presents the development of soft sensor models for monitoring the operation of online process analyzers used to measure the sulfur content in the product of the refinery hydrodesulfurization process. Since sulfur content often fluctuates over time, soft sensor models must account for these frequency fluctuations. We have therefore developed dynamic data-driven models based on linear and nonlinear system identification techniques (finite impulse response—FIR, autoregressive with exogenous inputs—ARX, output error—OE, nonlinear ARX—NARX, Hammerstein–Wiener—HW) and machine learning techniques, including models based on long short-term memory (LSTM) and gated recurrent unit (GRU) networks, as well as artificial neural networks (ANNs). The core steps in model development included the selection and preprocessing of continuously measured plant process data, collected from a full-scale industrial hydrodesulfurization unit under normal operating conditions. The developed soft sensor models are intended to support or replace process analyzers during maintenance periods or equipment failures. Moreover, these models enable the application of inferential control strategies, where unmeasured process variables—such as sulfur content—can be estimated in real time and used as feedback for advanced process control. Full article
(This article belongs to the Special Issue Analysis and Design of Linear/Nonlinear Control System)
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15 pages, 2317 KiB  
Article
Evolution of Mechanical Properties, Mineral Crystallization, and Micro-Gel Formation in Alkali-Activated Carbide Slag Cementitious Materials
by Yonghao Huang, Guodong Huang, Zhenghu Han, Fengan Zhang, Meng Liu and Jinyu Hao
Crystals 2025, 15(8), 731; https://doi.org/10.3390/cryst15080731 - 19 Aug 2025
Viewed by 221
Abstract
For efficient utilization of carbide slag (CS) waste to high-value building materials, in this study, CS and ground granulated blast furnace slag (GBFS) were used as primary raw materials to prepare alkali-activated cementitious systems under strong alkaline excitation. Multiscale mechanisms involving macroscopic mechanical [...] Read more.
For efficient utilization of carbide slag (CS) waste to high-value building materials, in this study, CS and ground granulated blast furnace slag (GBFS) were used as primary raw materials to prepare alkali-activated cementitious systems under strong alkaline excitation. Multiscale mechanisms involving macroscopic mechanical property development were investigated. Microstructural characterization elucidated how raw material composition affected mineral crystal formation and transformation while revealing enhancement mechanisms governing micro-gel network structure formation and evolution dynamics. The results indicate that excessive calcium components coupled with deficient Si–Al sources in CS severely inhibit the formation of C-S-H and C-A-S-H gel phases, consequently impeding mechanical performance development. Also, GBFS incorporation offsets inherent silicon–aluminum deficiencies. Active [SiO4]4− and [AlO4]5− released from GBFS drive polycondensation reactions toward advanced polymerization states. Compressive strength has a nonlinear growth kinetics characterized by rapid initial ascent, followed by asymptotic plateauing as GBFS content increases. Optimal comprehensive performance emerges at a 5:5 GBFS-to-CS mass ratio, where 28d compressive strength reaches 47.5 MPa. Full article
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17 pages, 7815 KiB  
Article
Design and Analysis of Memristive Electromagnetic Radiation in a Hopfield Neural Network
by Zhimin Gu, Bin Hu, Hongxin Zhang, Xiaodan Wang, Yaning Qi and Min Yang
Symmetry 2025, 17(8), 1352; https://doi.org/10.3390/sym17081352 - 19 Aug 2025
Viewed by 241
Abstract
This study introduces a memristive Hopfield neural network (M-HNN) model to investigate electromagnetic radiation impacts on neural dynamics in complex electromagnetic environments. The proposed framework integrates a magnetic flux-controlled memristor into a three-neuron Hopfield architecture, revealing significant alterations in network dynamics through comprehensive [...] Read more.
This study introduces a memristive Hopfield neural network (M-HNN) model to investigate electromagnetic radiation impacts on neural dynamics in complex electromagnetic environments. The proposed framework integrates a magnetic flux-controlled memristor into a three-neuron Hopfield architecture, revealing significant alterations in network dynamics through comprehensive nonlinear analysis. Numerical investigations demonstrate that memristor-induced electromagnetic effects induce distinctive phenomena, including coexisting attractors, transient chaotic states, symmetric bifurcation diagrams and attractor structures, and constant chaos. The proposed system can generate more than 12 different attractors and extends the chaotic region. Compared with the chaotic range of the baseline Hopfield neural network (HNN), the expansion amplitude reaches 933%. Dynamic characteristics are systematically examined using phase trajectory analysis, bifurcation mapping, and Lyapunov exponent quantification. Experimental validation via a DSP-based hardware implementation confirms the model’s operational feasibility and consistency with numerical predictions, establishing a reliable platform for electromagnetic–neural interaction studies. Full article
(This article belongs to the Topic A Real-World Application of Chaos Theory)
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20 pages, 1548 KiB  
Article
A Credibility-Based Self-Evolution Algorithm for Equipment Digital Twins Based on Multi-Layer Deep Koopman Operator
by Hongbo Cheng, Lin Zhang, Kunyu Wang, Han Lu and Yihan Guo
Appl. Sci. 2025, 15(16), 9082; https://doi.org/10.3390/app15169082 - 18 Aug 2025
Viewed by 188
Abstract
In the context of Industry 4.0 and intelligent manufacturing, the scale and complexity of complex equipment systems are continuously increasing, making effective high-precision modeling, simulation, and prediction in the engineering field significant challenges. Digital twin technology, by establishing real-time connections between virtual models [...] Read more.
In the context of Industry 4.0 and intelligent manufacturing, the scale and complexity of complex equipment systems are continuously increasing, making effective high-precision modeling, simulation, and prediction in the engineering field significant challenges. Digital twin technology, by establishing real-time connections between virtual models and physical systems, provides strong support for the real-time monitoring, optimization, and prediction of complex systems. However, traditional digital twin models face significant limitations when synchronizing with high-dimensional nonlinear and non-stationary dynamical systems due to the latter’s dynamic characteristics. To address this issue, we propose a multi-layer deep Koopman operator-based (MDK) credibility-based self-evolution algorithm for equipment digital twins. By constructing multiple time-scale embedding layers and combining deep neural networks for observability function learning, the algorithm effectively captures the dynamic features of complex nonlinear systems at different time scales, enabling their global dynamic modeling and precise analysis. Furthermore, to enhance the model’s adaptability, a trustworthiness-based evolution-triggering mechanism and an adaptive model fine-tuning algorithm are designed. When the digital twin model’s trustworthiness assessment indicates a decline in prediction accuracy, the evolution mechanism is automatically triggered to optimize and update the model with the fine-tuning algorithm to maintain its stability and robustness during dynamic evolution. The experimental results demonstrate that the proposed method achieves significant improvements in prediction accuracy within unmanned aerial vehicle (UAV) systems, showcasing its broad application potential in intelligent manufacturing and complex equipment systems. Full article
(This article belongs to the Special Issue Integration of Digital Simulation Models in Smart Manufacturing)
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