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Brushless DC (BLDC) motors are widely used in industrial applications due to their high efficiency and performance. However, accurately predicting key parameters such as torque and speed remains a challenge because of the motor’s inherently nonlinear dynamics. This study presents a data-driven modeling approach using a Nonlinear Autoregressive Neural Network with Exogenous Inputs (NARX-NN) to predict the torque and speed of a BLDC motor. Input-Output data were obtained from a Simulink-based BLDC motor model under varying input voltages and load conditions. The proposed NARX-NN architecture was trained on this data, effectively learning the nonlinear Multi-Input Multi-Output (MIMO) system dynamics. The model achieved high prediction accuracy, with a Mean Squared Error (MSE) of 3.4162e-04 (training), 3.0296e-04 (validation) and 8.4225e-04 (testing) while R-values of 1 in each in case of speed. While the model also achieved high prediction accuracy, with a Mean Squared Error (MSE) of 0.0062 (training and validation), and 0.0065 (testing) while R-values of 0.9997 (training and validation) and 0.9998 (testing) in case of torque. These statistical results are compared with the work already carried out for prediction of speed of BLDC motor, dominating the superiority of the proposed approach. Hence, it confirms the model’s robustness in capturing complex motor behavior. The proposed approach offers a reliable predictive tool suitable for integration into real-time control systems, enabling enhanced motor efficiency, early fault detection, and torque ripple mitigation.

This paper proposes a hybrid methodology for one-step-ahead torsional torque estimation in an electric drive with an elastic connection. The approach integrates Nonlinear Autoregressive Neural Networks with Exogenous Inputs (NARX NNs) and model-based feedback. The NARX model uses real-time and historical motor speed and torque signals as inputs while leveraging physics-derived torsional torque as a feedback input to refine estimation accuracy and robustness. While model-based methods provide insight into system dynamics, they lack predictive capability—an essential feature for proactive control. Conversely, standalone NARX NNs often suffer from error accumulation and overfitting. The proposed hybrid architecture synergises the adaptive learning of NARX NNs with the fidelity of physics-based feedback, enabling proactive vibration damping. The method was implemented and evaluated on a two-mass drive system using an IP controller and additional torsional torque feedback. Results demonstrate high accuracy and reliability in one-step-ahead torsional torque estimation, enabling effective proactive vibration damping. MATLAB 2024a/Simulink and dSPACE 1103 were used for simulation and hardware-in-the-loop testing.

Due to the increasing demand for consumable water, groundwater management is critical, especially in arid and semi-arid regions. Effective management strategies are crucial for maintaining a sustainable water supply and promoting environmental health. Machine learning models can identify patterns and trends that help forecast fluctuations in groundwater levels. These predictions are essential for sustainable water resource management, thereby preventing water shortages. In this study, a machine learning model based on a time series neural network “Nonlinear Autoregressive Exogenous Neural Network (NARX–NN)” was made to predict the groundwater levels in Tazerbo, Al Kufra Basin, southeast Libya. The proposed model uses annual data of the groundwater levels for the last two decades (2004–2024) collected from 14 piezometric wells in the study area. The model was trained and validated using statistical performance metrics, including R 2 , MSE, and RMSE, achieving high predictive accuracy across all wells. The model performed excellently during training and testing. Using NARX-NN, scenario-based forecasts for 2030 and 2040 were generated for 14 wells under two pumping rates 255,000 m³/day and 400,000 m³/day. At the current rate, groundwater is projected to decline by ~ 2 m by 2030 and ~ 1.6 m by 2040. Under higher pumping rates, drawdowns could exceed 50 m by 2030 and 2040. The results reveal spatially variable trends in groundwater decline, with significant drops projected in the northern and eastern zones under increased extraction. These findings offer valuable insights into sustainable groundwater management and long-term planning in water-stressed basins.

The extensive use of renewable energy sources (RESs) in energy sectors plays a vital role in meeting the present energy demand. The widespread utilization of allocated resources leads to multiple usages of converters for synchronization with the power grid, introducing poor power quality. The integration of distributed energy resources produces uncertainties which are reflected in the distribution system. The major power quality problems such as voltage sag/swell, voltage unbalancing, poor power factor, harmonics distortion (THD), and power transients appear during the transition of micro-grids (MGs). In this research, a single micro-grid is designed with PVs, wind generators, and fuel cells as distributed energy resources (DERs). A nonlinear auto regressive exogenous input neural network (NARX-NN) controller has been investigated in this micro-grid in order to maintain the above power quality issues within the specific standard range (IEEE/IEC standards). The performance of the NARX-NN controller is compared with PID and fuzzy-PID controllers. The single micro-grid is extended to design a three-phase large-scale realistic micro-grid structure to test the feasibility of the proposed controller. The realistic micro-grid is verified through addition of line-impedance, communication delay, demand response, and off-nominal situations. The proposed controller is also validated by simulating different test scenarios using MATLAB/Simulink and TMS320-based processor-in-loop (PIL) for real-time implementation.

One of the issues associated with the supply of electricity is its generation capacity, and this has led to prevalent power cuts and high costs of usage experienced in many developing nations, including South Africa. Historical research has shown that the annual rate of increase for electricity has grown at an alarming rate since 2008 and, in some years, has grown as much as 16%. The objectives of this study are to estimate the cost analysis of electricity usage at the twenty-nine residences of the University of Johannesburg (UJ-Res) and propose a model for our university, as well as other South African universities, to become more energy-efficient. This was achieved by analyzing the tariffs between 2015 and 2021. A forecast was made for a period of five years (2021 to 2026) using a non-linear autoregressive exogenous neural network (NARX-NN) time-series model. From the results obtained, the better NARX-NN model studied has a root mean squared error (RMSE) of 2.47 × 105 and a determination coefficient (R2) of 0.9661. The projection result also shows that the annual cost of energy consumed will increase for the projected years, with the year 2022 being the peak with an estimated annual cost of over ZAR 30 million (USD 2,076,268).

In this paper, we aimed to identify the dynamics of a crude distillation unit (CDU) using closed-loop data with NARX−NN and the Koopman operator in both linear (KL) and bilinear (KB) forms. A comparative analysis was conducted to assess the performance of each method under different experimental conditions, such as the gain, a delay and time constant mismatch, tight constraints, nonlinearities, and poor tuning. Although NARX−NN showed good training performance with the lowest Mean Squared Error (MSE), the KB demonstrated better generalization and robustness, outperforming the other methods. The KL observed a significant decline in performance in the presence of nonlinearities in inputs, yet it remained competitive with the KB under other circumstances. The use of the bilinear form proved to be crucial, as it offered a more accurate representation of CDU dynamics, resulting in enhanced performance.

The city of Bandung, as the capital city of West Java, is one of several areas in Indonesia with high rainfall. This situation can cause disasters, such as floods and landslides, that can harm many parties. Rainfall in Indonesia, particularly on the island of Java itself, is closely related to the global phenomenon of Niño 3.4. In the period from January 2001–November 2021, the rainfall and Niño 3.4 showed some extreme values. In order to foresee the disasters, an accurate rainfall forecast should be performed. For this reason, we try to construct a model of rainfall forecast and its relation to the global phenomenon of Niño 3.4 using the nonlinear autoregressive exogenous neural network (NARX NN). The result shows that NARX NN (13-7-1) with a Mean Absolute Percentage Error (MAPE) value of 6.26% and R2 of 85.37% is best suited for the prediction of this phenomenon. In addition, this study provides forecast results for the next six periods, which can be used as a reference for the relevant authorities to foresee the possibility of flooding in Bandung city. From the forecast results, it can be concluded that the highest rainfall forecasts in the city of Bandung are in February 2022, and will slowly decrease in March 2022. To prevent hydro-meteorological disasters, such as floods in Bandung city, the community can clear waterways, such as clogged drains, rivers, and dams, as well as prepare tools for evacuation.

In this study, the stator phase flux linkage of a switched reluctance motor was estimated using a nonlinear autoregressive network with external input (NARX) neural network (NN). The application of artificial neural network (ANN) technique for phase flux linkage estimation yielded satisfactory results and the online phase resistance variation compensation requirement, which is an important problem in classical flux linkage calculation methodology, was eliminated. Using the NARX neural network model, which was trained with a set of experimental data, the phase flux linkage value was estimated by the NN from the phase current measurements during real-time operation. The stator phase current values measured under different speed and load conditions together with offline calculated flux linkage values composed the training dataset. The training data preparation methodology was explained in section 2. It was followed by an explanation of the NN training process and the training results were given. The NN based phase flux linkage estimation technique was compared with other techniques such as finite element analysis, torque balance method, voltage balance method in section 7 experimentally.