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Search Results (396)

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Keywords = autoregressive exogenous model

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25 pages, 33109 KB  
Article
Spatio-Temporal Shoreline Changes and AI-Based Predictions for Sustainable Management of the Damietta–Port Said Coast, Nile Delta, Egypt
by Hesham M. El-Asmar, Mahmoud Sh. Felfla and Amal A. Mokhtar
Sustainability 2026, 18(3), 1557; https://doi.org/10.3390/su18031557 - 3 Feb 2026
Abstract
The Damietta–Port Said coast, Nile Delta, has experienced extreme morphological change over the past four decades due to sediment reduction due to Aswan High Dam and continued anthropogenic pressures. Using multi-temporal Landsat (1985–2025) and high-resolution RapidEye and PlanetScope imagery with 50 m-spaced transects, [...] Read more.
The Damietta–Port Said coast, Nile Delta, has experienced extreme morphological change over the past four decades due to sediment reduction due to Aswan High Dam and continued anthropogenic pressures. Using multi-temporal Landsat (1985–2025) and high-resolution RapidEye and PlanetScope imagery with 50 m-spaced transects, the study documents major shoreline shifts: the Damietta sand spit retreated by >1 km at its proximal apex while its distal tip advanced by ≈3.1 km southeastward under persistent longshore drift. Sectoral analyses reveal typical structure-induced patterns of updrift accretion (+180 to +210 m) and downdrift erosion (−50 to −330 m). To improve predictive capability beyond linear DSAS extrapolation, Nonlinear Autoregressive Exogenous (NARX) and Bidirectional Long Short-Term Memory (BiLSTM) neural networks were applied to forecast the 2050 shoreline. BiLSTM demonstrated superior stability, capturing nonlinear sediment transport patterns where NARX produced unstable over-predictions. Furthermore, coupled wave–flow modeling validates a sustainable management strategy employing successive short groins (45–50 m length, 150 m spacing). Simulations indicate that this configuration reduces longshore current velocities by 40–60% and suppresses rip-current eddies, offering a sediment-compatible alternative to conventional breakwaters and seawalls. This integrated remote sensing, hydrodynamic, and AI-based framework provides a robust scientific basis for adaptive, sediment-compatible shoreline management, supporting the long-term resilience of one of Egypt’s most vulnerable deltaic coasts under accelerating climatic and anthropogenic pressures. Full article
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23 pages, 6191 KB  
Article
Restoring Pugin: Toward Predictive Conservation of Historical Buildings Using a Digital Twin Approach
by Benachir Medjdoub, Bubaker Shakmak, Moulay Chalal, Mohammadreza Khosravi, Rihana Sajad, Nacer Bezai and Ayesha Illangakoon
Sustainability 2026, 18(3), 1516; https://doi.org/10.3390/su18031516 - 3 Feb 2026
Viewed by 101
Abstract
Conservation of historic buildings has long relied on traditional, reactive methods that address deterioration only after it occurs, often leading to irreversible damage. This study introduces an innovative approach that integrates Digital Twin (DT) technology with advanced machine learning algorithms to enable predictive [...] Read more.
Conservation of historic buildings has long relied on traditional, reactive methods that address deterioration only after it occurs, often leading to irreversible damage. This study introduces an innovative approach that integrates Digital Twin (DT) technology with advanced machine learning algorithms to enable predictive and data-driven conservation. Focusing on Nottingham Cathedral, a Grade II listed Gothic Revival building, this research developed a 3D Historic Building Information Model (HBIM) enhanced with real-time environmental monitoring of temperature, humidity, and air quality. The collected data were analysed using MATLABR2024a to train and evaluate several predictive algorithms, including Long Short-Term Memory (LSTM), Backpropagation Neural Network (BPNN), Adaptive Neuro-Fuzzy Inference System (ANFIS), and Nonlinear Autoregressive Exogenous (NARX) models. The NARX model achieved the highest accuracy (Root Mean Square Error (RMSE) = 0.19) in forecasting indoor environmental conditions. Findings indicate that maintaining an indoor temperature increase of 4–6 °C can effectively reduce relative humidity below 60%, minimising deterioration risks. The study demonstrates how integrating DT and machine learning offers a proactive framework for environmental optimisation and long-term preservation of heritage assets, moving conservation practice from reactive restoration toward predictive conservation. Full article
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20 pages, 1071 KB  
Article
Modeling for Data Efficiency: System Identification as a Precursor to Reinforcement Learning for Nonlinear Systems
by Nusrat Farheen, Golam Gause Jaman and Marco P. Schoen
Machines 2026, 14(2), 157; https://doi.org/10.3390/machines14020157 - 30 Jan 2026
Viewed by 229
Abstract
Safe and sample-conscious controller synthesis for nonlinear dynamics benefits from reinforcement learning that exploits an explicit plant model. A nonlinear mass–spring–damper with hardening effects and hard stops is studied, and off-plant Q-learning is enabled using two data-driven surrogates: (i) a piecewise linear model [...] Read more.
Safe and sample-conscious controller synthesis for nonlinear dynamics benefits from reinforcement learning that exploits an explicit plant model. A nonlinear mass–spring–damper with hardening effects and hard stops is studied, and off-plant Q-learning is enabled using two data-driven surrogates: (i) a piecewise linear model assembled from operating region transfer function estimates and blended by triangular memberships and (ii) a global nonlinear autoregressive model with exogenous input constructed from past inputs and outputs. In unit step reference tracking on the true plant, the piecewise linear route yields lower error and reduced steady-state bias (MAE = 0.03; SSE = 3%) compared with the NLARX route (MAE = 0.31; SSE = 30%) in the reported configuration. The improved regulation is obtained at a higher identification cost (60,000 samples versus 12,000 samples), reflecting a fidelity–knowledge–data trade-off between localized linearization and global nonlinear regression. All reported performance metrics correspond to deterministic validation runs using fixed surrogate models and trained policies and are intended to support methodological comparison rather than statistical performance characterization. These results indicate that model-based Q-learning with identified surrogates enables off-plant policy training while containing experimental risk and that performance depends on modeling choices, state discretization, and reward shaping. Full article
(This article belongs to the Special Issue Advances in Dynamics and Vibration Control in Mechanical Engineering)
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23 pages, 9799 KB  
Article
Inertia Estimation of Regional Power Systems Using Band-Pass Filtering of PMU Ambient Data
by Kyeong-Yeong Lee, Sung-Guk Yoon and Jin Kwon Hwang
Energies 2026, 19(2), 424; https://doi.org/10.3390/en19020424 - 15 Jan 2026
Viewed by 303
Abstract
This paper proposes a regional inertia estimation method in power systems using ambient data measured by phasor measurement units (PMUs). The proposed method employs band-pass filtering to suppress the low-frequency influence of mechanical power and to attenuate high-frequency noise and discrepancies between rotor [...] Read more.
This paper proposes a regional inertia estimation method in power systems using ambient data measured by phasor measurement units (PMUs). The proposed method employs band-pass filtering to suppress the low-frequency influence of mechanical power and to attenuate high-frequency noise and discrepancies between rotor speed and electrical frequency. By utilizing a simple first-order AutoRegressive Moving Average with eXogenous input (ARMAX) model, this process allows the inertia constant to be directly identified. This method requires no prior model order selection, rotor speed estimation, or computation of the rate of change of frequency (RoCoF). The proposed method was validated through simulation on three benchmark systems: the Kundur two-area system, the IEEE Australian simplified 14-generator system, and the IEEE 39-bus system. The method achieved area-level inertia estimates within approximately ±5% error across all test cases, exhibiting consistent performance despite variations in disturbance models and system configurations. The estimation also maintained stable performance with short data windows of a few minutes, demonstrating its suitability for near real-time monitoring applications. Full article
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21 pages, 30287 KB  
Article
Online Estimation of Lithium-Ion Battery State of Charge Using Multilayer Perceptron Applied to an Instrumented Robot
by Kawe Monteiro de Souza, José Rodolfo Galvão, Jorge Augusto Pessatto Mondadori, Maria Bernadete de Morais França, Paulo Broniera Junior and Fernanda Cristina Corrêa
Batteries 2026, 12(1), 25; https://doi.org/10.3390/batteries12010025 - 10 Jan 2026
Viewed by 289
Abstract
Electric vehicles (EVs) rely on a battery pack as their primary energy source, making it a critical component for their operation. To guarantee safe and correct functioning, a Battery Management System (BMS) is employed, which uses variables such as State of Charge (SOC) [...] Read more.
Electric vehicles (EVs) rely on a battery pack as their primary energy source, making it a critical component for their operation. To guarantee safe and correct functioning, a Battery Management System (BMS) is employed, which uses variables such as State of Charge (SOC) to set charge/discharge limits and to monitor pack health. In this article, we propose a Multilayer Perceptron (MLP) network to estimate the SOC of a 14.8 V battery pack installed in a robotic vacuum cleaner. Both offline and online (real-time) tests were conducted under continuous load and with rest intervals. The MLP’s output is compared against two commonly used approaches: NARX (Nonlinear Autoregressive Exogenous) and CNN (Convolutional Neural Network). Performance is evaluated via statistical metrics, Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE), and we also assess computational cost using Operational Intensity. Finally, we map these results onto a Roofline Model to predict how the MLP would perform on an automotive-grade microcontroller unit (MCU). A generalization analysis is performed using Transfer Learning and optimization using MLP–Kalman. The best performers are the MLP–Kalman network, which achieved an RMSE of approximately 13% relative to the true SOC, and NARX, which achieved approximately 12%. The computational cost of both is very close, making it particularly suitable for use in BMS. Full article
(This article belongs to the Section Battery Performance, Ageing, Reliability and Safety)
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38 pages, 1480 KB  
Article
Forecasting Office Construction Price Indices for Cost Planning in Germany Using Regularized VARX Models
by Matthias Passek and Konrad Nübel
Buildings 2026, 16(1), 103; https://doi.org/10.3390/buildings16010103 - 25 Dec 2025
Viewed by 296
Abstract
Construction price indices play a critical role in shaping construction activity and determining the economic success of building projects in Germany, where they can serve as central inputs to cost planning and to updating trade-level project budgets over the planning and construction horizon. [...] Read more.
Construction price indices play a critical role in shaping construction activity and determining the economic success of building projects in Germany, where they can serve as central inputs to cost planning and to updating trade-level project budgets over the planning and construction horizon. This paper develops a forecasting framework for 35 sub-construction price indices for office buildings, providing granular inputs for cost escalation and risk assessment. We employ regularized vector autoregressive models with exogenous variables (VARX) implemented via the BigVAR package and estimate them in a model-vintage design for an unbalanced panel. These high-dimensional models are benchmarked against compact VARX and vector error-correction models (VECM) that jointly forecast each target index with a small macroeconomic block consisting of the gross domestic product (GDP) and the three-month interbank rate. Candidate specifications are evaluated using mean absolute percentage error (MAPE) and out-of-sample root mean square error (RMSE), and the final forecasting model for each index is selected based on ex post MAPE. The results show that regularized VARX models capture dynamic interdependencies among the sub-indices and, for most series, outperform the VARX and VECM benchmarks. The resulting forecasts provide practitioners with trade-specific escalation factors that can support budgeting, contract design, and the mitigation of cost risk in office-building projects. Full article
(This article belongs to the Section Architectural Design, Urban Science, and Real Estate)
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20 pages, 8145 KB  
Article
State of Health Estimation of Lithium Cobalt Oxide Batteries Based on ARX Identification Across Different Temperatures
by Simone Barcellona, Mattia Ribera, Emanuele Fedele, Pasquale Franzese, Luigi Piegari, Lorenzo Codecasa and Diego Iannuzzi
Batteries 2026, 12(1), 2; https://doi.org/10.3390/batteries12010002 - 20 Dec 2025
Viewed by 427
Abstract
Lithium-ion batteries (LiBs) undergo degradation influenced by storage and cycling conditions. Accurate state of health (SOH) assessment is crucial for predicting battery aging, which is generally marked by a decline in capacity (energy fade) or an increase in internal resistance (power fade). This [...] Read more.
Lithium-ion batteries (LiBs) undergo degradation influenced by storage and cycling conditions. Accurate state of health (SOH) assessment is crucial for predicting battery aging, which is generally marked by a decline in capacity (energy fade) or an increase in internal resistance (power fade). This study investigates the impulse response (IR) technique for assessing the SOH of lithium cobalt oxide batteries, addressing both capacity fade and rising internal resistance. The IR method relies on a predefined dataset that records the voltage response of the LiB to pulse current inputs across various states of charge (SOC), temperatures, and aging conditions to train a series of linear auto-regressive exogenous (ARX) models. This dataset is then used as a look-up table for subsequent SOH estimation under new operating conditions. The results demonstrate that the method can capture trends in capacity fade and resistance increase only when multiple battery temperatures are incorporated into the look-up table. In contrast, estimations based on ARX models trained at a single fixed temperature fail to provide reliable predictions of battery SOH. Full article
(This article belongs to the Special Issue Towards a Smarter Battery Management System: 3rd Edition)
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22 pages, 2279 KB  
Article
Ship Model Identification Using Interpretable 4-DOF Maneuverability Models for River Combat Boat
by Juan Contreras Montes, Aldo Lovo Ayala, Daniela Ospino-Balcázar, Kevin Velasquez Gutierrez, Carlos Soto Montaño, Roosvel Soto-Diaz, Javier Jiménez-Cabas, José Oñate López and José Escorcia-Gutierrez
Computation 2025, 13(12), 296; https://doi.org/10.3390/computation13120296 - 18 Dec 2025
Viewed by 280
Abstract
Ship maneuverability models are typically defined by three degrees of freedom: surge, sway, and yaw. However, patrol vessels operating in riverine environments often exhibit significant roll motion during course changes, necessitating the inclusion of this dynamic. This study develops interpretable machine learning models [...] Read more.
Ship maneuverability models are typically defined by three degrees of freedom: surge, sway, and yaw. However, patrol vessels operating in riverine environments often exhibit significant roll motion during course changes, necessitating the inclusion of this dynamic. This study develops interpretable machine learning models capable of predicting vessel behavior in four degrees of freedom (4-DoF): surge, sway, yaw, and roll. A dataset of 125 h of simulated maneuvers was employed, including 29 h of out-of-distribution (OOD) conditions to test model generalization. Four models were implemented and compared over a 15-step prediction horizon: linear regression, third-order polynomial regression, a state-space model obtained via the N4SID algorithm, and an AutoRegressive model with eXogenous inputs (ARX). Results demonstrate that all models captured the essential vessel dynamics, with the state-space model achieving the best overall performance (e.g., NMSE = 0.0246 for surge velocity on test data and 0.0499 under OOD conditions). Variable-wise, surge and sway showed the lowest errors, roll rate remained stable, and yaw rate was the most sensitive to distribution shifts. Model-wise, the ARX model achieved the lowest NMSE for surge prediction (0.0149), while regression-based models provided interpretable yet less accurate alternatives. Multi-horizon evaluation (1-, 5-, 15-, and 30-step) under OOD conditions confirmed a consistent monotonic degradation across models. These findings validate the feasibility of using interpretable machine learning models for predictive control, autonomous navigation, and combat scenario simulation in riverine operations. Full article
(This article belongs to the Section Computational Engineering)
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16 pages, 3166 KB  
Article
Prophet-Based Artificial Intelligence Versus Seasonal Auto-Regressive Models for Flood Forecasting with Exogenous Variables
by Adya Aiswarya Dash and Edward McBean
Water 2025, 17(24), 3551; https://doi.org/10.3390/w17243551 - 15 Dec 2025
Viewed by 479
Abstract
Accurate stream flow forecasting is essential for flood risk management and preparedness. This study compares two forecasting approaches: (a) the Seasonal Auto-Regressive Integrated Moving Average with Exogenous Regressors (SARIMAX), a classical statistical model, and (b) Prophet, a decomposable time-series forecasting model that incorporates [...] Read more.
Accurate stream flow forecasting is essential for flood risk management and preparedness. This study compares two forecasting approaches: (a) the Seasonal Auto-Regressive Integrated Moving Average with Exogenous Regressors (SARIMAX), a classical statistical model, and (b) Prophet, a decomposable time-series forecasting model that incorporates seasonality and exogenous predictors. Forecasts were generated for 15-day and 3-day horizons and evaluated using uncertainty bounds, Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and the coefficient of determination (R2). Results indicate that SARIMAX was less effective at capturing the observed variability, producing wide uncertainty (177.7%) and high errors (MAE = 153.73; RMSE = 207.10) with a negative R2 (–4.42). At shorter horizons, its performance remained limited (uncertainty = 28.04%; MAE = 61.52; RMSE = 94.88; R2 = –0.14). In contrast, Prophet achieved significantly lower uncertainty (16%), high accuracy (R2 = 0.95), and exceptional performance on short-term forecasts (R2 = 0.99). Conventional procedures such as SARIMAX have long been relied upon by engineers for their interpretability, and remain important as part of a strategy; however, they fail to represent nonlinear dynamics and exogenous influences now captured effectively by AI-based models. These findings highlight Prophet’s superiority across horizons and its promise for enhancing operational flood forecasting through its ability to effectively capture non-linear dynamics and exogenous influences. Full article
(This article belongs to the Special Issue "Watershed–Urban" Flooding and Waterlogging Disasters)
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24 pages, 2233 KB  
Article
Development of a Digital Twin of a DC Motor Using NARX Artificial Neural Networks
by Victor Busher, Valeriy Kuznetsov, Zbigniew Ciekanowski, Artur Rojek, Tomasz Grudniewski, Natalya Druzhinina, Vitalii Kuznetsov, Mykola Tryputen, Petro Hubskyi and Alibek Batyrbek
Energies 2025, 18(24), 6502; https://doi.org/10.3390/en18246502 - 11 Dec 2025
Viewed by 415
Abstract
This study presents the development process of a digital twin for a complex dynamic object using Artificial Neural Networks. A separately excited DC motor is considered as an example, which, despite its well-known electromechanical properties, remains a non-trivial object for neural network modeling. [...] Read more.
This study presents the development process of a digital twin for a complex dynamic object using Artificial Neural Networks. A separately excited DC motor is considered as an example, which, despite its well-known electromechanical properties, remains a non-trivial object for neural network modeling. It is shown that describing the motor using a generalized neural network with various configurations does not yield satisfactory results. The optimal solution was based on a separation into two distinct nonlinear autoregressive with exogenous inputs (NARX) artificial neural networks with cross-connections for the two main machine variables: one for modeling the armature current with exogenous inputs of voltage and armature speed, and another for modeling the angular speed with inputs of voltage and armature current. Both neural networks are characterized by a relatively small number of neurons in the hidden layer and a time delay of no more than 3 time steps. This solution, consistent with the physical understanding of the motor as an object where electromagnetic energy is converted into thermal and mechanical energy (and vice versa), allows the model to be calibrated for the ideal no-load mode and subsequently account for the influence of torque loads of various natures and changes in the control object parameters over a wide range. The study demonstrates that even for modeling an object such as a DC electric drive with cascaded control, reducing errors at the boundaries of the known operating range requires generating test signals covering approximately 120% of the nominal speed range and 250–400% of the nominal current. Analysis of various test signals revealed that training with a sequence of step changes and linear variations across the entire operating range of armature current and speed provides higher accuracy compared to training with random or uniform signals. Furthermore, to ensure the neural network model’s functionality under varying load torque, a mechanical load observer was developed, and a model architecture incorporating an additional input for disturbance was proposed. The SEDCM_NARX_LOAD neural network model demonstrates a theoretically justified response to load application, although dynamic and static errors arise. In the experiment, the current error was 7.4%, and the speed error was 0.5%. The practical significance of the research lies in the potential use of the proposed model for simulating dynamic and static operational modes of electromechanical systems, tuning controllers, and testing control strategies without employing a physical motor. Full article
(This article belongs to the Section F5: Artificial Intelligence and Smart Energy)
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26 pages, 2704 KB  
Article
Statistical Quantification of the COVID-19 Pandemic’s Continuing Lingering Effect on Economic Losses in the Tourism Sector
by Amos Mohau Mphanya, Sandile Charles Shongwe, Thabiso Ernest Masena and Frans Frederick Koning
Economies 2025, 13(12), 362; https://doi.org/10.3390/economies13120362 - 9 Dec 2025
Viewed by 353
Abstract
The impact of the COVID-19 pandemic on the number of international tourist arrivals in the Republic of South Africa (RSA) is studied in this paper using the seasonal autoregressive integrated moving average (SARIMA) model comprising a pulse function covariate vector evaluated via trial [...] Read more.
The impact of the COVID-19 pandemic on the number of international tourist arrivals in the Republic of South Africa (RSA) is studied in this paper using the seasonal autoregressive integrated moving average (SARIMA) model comprising a pulse function covariate vector evaluated via trial and error as an exogenous variable (SARIMAX). This paper provides a methodological innovation that combines outlier detection with intervention quantification so that tourism academics and practitioners can correctly capture estimated economic losses caused by the COVID-19 pandemic and the response to it. In the pre-intervention modelling, four additive outliers and innovative outliers were detected and incorporated into the SARIMAX(1,1,1)(0,1,2)12 model, which significantly lowered the model’s evaluation metrics, making it the best fitting pre-intervention model. Next, from March 2020 to June 2025 (end of dataset), it is shown that the estimated total losses amount to 7,328,919 tourists compared to if there been no pandemic. This means that the number of tourist arrivals in the RSA has not yet returned to the pre-COVID-19 forecasted path as of June 2025, indicating that the COVID-19 pandemic continues to have long-term negative effects on the RSA’s number of tourist arrivals. Therefore, more efforts must be focused on developing innovative and advanced statistical models to assist the RSA government and private entities in creating incentives for investment, planning more effectively, providing societies reliant on tourism with more resources, and creating suitable regulations that boost the economy through the tourism sector. Full article
(This article belongs to the Section Economic Development)
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40 pages, 9179 KB  
Article
Cloud-Enabled Hybrid, Accurate and Robust Short-Term Electric Load Forecasting Framework for Smart Residential Buildings: Evaluation of Aggregate vs. Appliance-Level Forecasting
by Kamran Hassanpouri Baesmat, Emma E. Regentova and Yahia Baghzouz
Smart Cities 2025, 8(6), 199; https://doi.org/10.3390/smartcities8060199 - 27 Nov 2025
Viewed by 738
Abstract
Accurate short-term load forecasting is vital for smart-city energy management, enabling real-time grid stability and sustainable demand response. This study introduces a cloud-enabled hybrid forecasting framework that integrates Seasonal Autoregressive Integrated Moving Average with Exogenous variables (SARIMAX), Random Forest (RF), and Long Short-Term [...] Read more.
Accurate short-term load forecasting is vital for smart-city energy management, enabling real-time grid stability and sustainable demand response. This study introduces a cloud-enabled hybrid forecasting framework that integrates Seasonal Autoregressive Integrated Moving Average with Exogenous variables (SARIMAX), Random Forest (RF), and Long Short-Term Memory (LSTM) models, unified through a residual-correction mechanism to capture both linear seasonal and nonlinear temporal dynamics. The framework performs fine-grained 5 min forecasting at both appliance and aggregate levels, revealing that the aggregate forecast achieves higher stability and accuracy than the sum of appliance-level predictions. To ensure operational resilience, three independent hybrid models are deployed across distinct cloud platforms with a two-out-of-three voting scheme, that guarantees continuity if a single-cloud interruption occurs. Using a real residential dataset from a house in Summerlin, Las Vegas (2022), the proposed system achieved a Root Mean Squared Logarithmic Error (RMSLE) of 0.0431 for aggregated load prediction representing a 35% improvement over the next-best model (Random Forest) and maintained consistent prediction accuracy during simulated cloud outages. These results demonstrate that the proposed framework provides a scalable, fault-tolerant, and accurate energy forecasting. Full article
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14 pages, 6156 KB  
Article
Hysteresis Modeling of a Magnetic Shape Memory Alloy Actuator Using a NARMAX Model and a Long Short-Term Memory Neural Network
by Haoran Wu and Miaolei Zhou
Actuators 2025, 14(12), 573; https://doi.org/10.3390/act14120573 - 26 Nov 2025
Viewed by 413
Abstract
Hysteresis primarily affects the positioning accuracy of the magnetic shape memory alloy-based actuator (M-SMAA). This paper proposes the use of the nonlinear autoregressive moving average with an exogenous input (NARMAX) model to describe the complex dynamic hysteresis of M-SMAA. First, an improved Prandtl–Ishlinskii [...] Read more.
Hysteresis primarily affects the positioning accuracy of the magnetic shape memory alloy-based actuator (M-SMAA). This paper proposes the use of the nonlinear autoregressive moving average with an exogenous input (NARMAX) model to describe the complex dynamic hysteresis of M-SMAA. First, an improved Prandtl–Ishlinskii operator is proposed as the exogenous variable function for the NARMAX model, using a hyperbolic tangent function as the input to the exogenous variable function, to better capture and represent the multivalued mapping hysteresis in M-SMAA. Then, a long short-term memory neural network is introduced to construct the NARMAX model, further optimizing its performance. Finally, the experimental results verify the effectiveness of the model. Full article
(This article belongs to the Special Issue Advances in Smart Materials-Based Actuators)
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19 pages, 4157 KB  
Article
Robustness Analysis of a Fast Virtual Temperature Sensor Using a Recurrent Neural Network Model Sensitivity
by Patryk Chaber and Bartosz Chaber
Sensors 2025, 25(23), 7193; https://doi.org/10.3390/s25237193 - 25 Nov 2025
Viewed by 588
Abstract
Virtual sensing is an emerging field of research that has garnered increasing attention in recent years. In this paper, we focus our attention on recurrent neural networks for time-series forecasting, namely, the Nonlinear AutoRegressive eXogenous model (NARX). The NARX is utilized as a [...] Read more.
Virtual sensing is an emerging field of research that has garnered increasing attention in recent years. In this paper, we focus our attention on recurrent neural networks for time-series forecasting, namely, the Nonlinear AutoRegressive eXogenous model (NARX). The NARX is utilized as a surrogate neural network for simulating heat flow. Our research has investigated the sensitivity of NARX models of varying complexity. The presented results show that the loss function value alone does not indicate the model’s sensitivity. We have demonstrated that undertrained models exhibit visible artifacts in their sensitivity, highlighting the model’s weak points. From observing how the sensitivity changes over training epochs, we can conclude that the sensitivity increases with more epochs, while its overall shape remains relatively unchanged. Full article
(This article belongs to the Section Sensors Development)
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20 pages, 873 KB  
Article
Multi-Sensor Recursive EM Algorithm for Robust Identification of ARX Models
by Xin Chen and Jiale Li
Sensors 2025, 25(22), 7060; https://doi.org/10.3390/s25227060 - 19 Nov 2025
Viewed by 520
Abstract
A robust multi-sensor recursive Expectation-Maximization (RMSREM) algorithm is proposed in this paper for autoregressive eXogenous (ARX) models, addressing the challenges of heavy-tailed noise, as well as the difficulty in simultaneously processing multi-sensor information. First, for the potential outliers in industrial processes, the Student’s [...] Read more.
A robust multi-sensor recursive Expectation-Maximization (RMSREM) algorithm is proposed in this paper for autoregressive eXogenous (ARX) models, addressing the challenges of heavy-tailed noise, as well as the difficulty in simultaneously processing multi-sensor information. First, for the potential outliers in industrial processes, the Student’s t-distribution is introduced to model the statistical characteristics of measurement noise, whose heavy-tailed property enhances the algorithm’s robustness. Second, a recursive framework is integrated into the Expectation-Maximization (EM) algorithm to satisfy the real-time requirement of dynamic system identification. Through a recursive scheme of the Q-function and sufficient statistics, model parameters are updated in real-time, allowing them to adapt to time-varying system characteristics. Finally, by exploiting the redundancy and complementarity of multi-sensor data, a multi-sensor information fusion mechanism is designed that adaptively calculates the weight of each sensor based on the noise variances. This mechanism effectively fuses multi-source observation information and mitigates the impact of single-sensor failure or inaccuracy on identification performance. Numerical examples and simulations of the continuous stirred-tank reactor (CSTR) demonstrate the validity of the proposed RMSREM algorithm. Full article
(This article belongs to the Section Industrial Sensors)
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