Levenberg-Marquardt Research Articles

A Degradation Model of Electrical Contact Performance for Copper Alloy Contacts with Tin Coatings Under Power Current-Carrying Fretting Conditions

The fretting degradation of coating materials is complicated when the Joule heating effect of the load current is non-negligible. In this work, the fretting degradation behavior of tin-coated copper alloy contacts was examined across the current range from 5 A to 30 A and the fretting amplitude range from 200 μm to 400 μm. The uniform degradation process and associated mechanisms, including the wear-dominated stage, softening-dominated stage, and oxidation-dominated stage were recognized and interpreted explicitly. An innovative fusion model for the degradation of electrical contact performance, data-driven and based on physics mechanism, was proposed. The contact voltage was selected as the characterization variable and pre-processed by the threshold-crossing filter method and the Levenberg–Marquardt algorithm. The optimal degradation model, considering the coupled effects of current and fretting amplitude, was presented with the use of the support vector regression method. Finally, the prediction accuracy of the model was validated by experiment results.

Prediction on mechanical properties of engineered cementitious composites: An experimental and machine learning approach

AbstractThe adoption of engineered cementitious composites (ECC) has witnessed a notable surge in recent years, primarily because of their remarkable strain‐hardening behavior and other hardened properties. On the other hand, machine learning (ML) approaches have been widely employed to predict various properties in engineering applications by incorporating an ‘n’ number of inputs and target data. An ML aids in understanding the selection, properties, and blending ability of materials, thereby reducing the cost and duration of research. In this study, an ML technique based on an artificial neural network (ANN) is utilized to predict the mechanical properties of ECC with different binders. For this purpose, several parameters are collected from the present investigation and various literature sources, and the collected data are trained using three algorithms, namely, scaled conjugate gradient (SCG), Bayesian regularization (BR), and Levenberg–Marquardt (LM). The correlations and variations between the experimental and predicted outputs are analyzed. In addition, a comparison between the experimental results obtained by each investigator and the corresponding outputs predicted by the individual algorithms is highlighted. The LM algorithm achieved a mean regression value of 0.910 for the prediction of compressive strength, whereas the BR showed values of 0.908 and 0.852 for predicting the direct tensile and flexural properties of ECC, respectively. Furthermore, considering the standard benchmark, the proposed model exhibited a high correlation with the coefficient of determination (R2).

Real-time wheel-rail adhesion anti-skid control model for high-speed articulated trains on long downhill slopes during braking

To improve the braking efficiency of articulated trains on long-steep downhill gradients under different wheel-rail adhesion levels, this paper develops a real-time train braking control system equipped with an optimal adhesion anti-slip controller. Simulation validation is conducted under both dry and wet wheel-rail contact conditions with different braking torques applied on a steep downhill slope. The anti-slip adhesion control system comprises two modules: an adhesion optimization module using a forgetting factor recursive least squares (FFRLS) method to determine creep force function slopes for enhancing wheel-rail adhesion utilization, and a controller employing a neural network with a Levenberg–Marquardt (L-M) algorithm. Through the co-simulation of the train-track coupling dynamic model and the anti-skid control system, the real-time adjustment of the braking torque of the train can be quickly corrected. The results indicate that the anti-skid control system demonstrates excellent self-adjustment capabilities under various operating conditions. It effectively controls wheel slip, achieving optimal wheel-rail adhesion. This ensures the shortest possible braking distance while maintaining train stability and improving train transmission efficiency.

Specific Heat Analysis of Water and Ethylene Glycol Based rGO-ND Hybrid Nanofluids: Experimental and Artificial Neural Network Predictions

The isobaric specific heat was measured experimentally for two kind of hybrid nanofluids like water and ethylene glycol based reduced graphene oxide-nanodiamond (rGO-ND) hybrid nanofluids at different particle volume loadings of 0.2%, 0.4%, 0.6%, 0.8% and 1.0%, and in the temperature range from 293 K to 333 K, respectively. The obtained experimental specific heat data was used for the artificial neural network (ANN) algorithms of Support Vector Regression (SVR), and Levenberg-Marquardt (LM) models for the predictions. Results indicated that, the specific heat of water, and ethylene glycol-based hybrid nanofluids at 1.0% vol. of hybrid nanofluid is lowered by 1.09% and 1.10% at a temperature of 333 K, compared to their own base fluids. The SVR and LM models for the specific heat of water-based hybrid nanofluids predict accurately with a correlation coefficient of 0.99849, and 0.99957, similarly, the SVR and LM models for the specific heat of ethylene glycol-based hybrid nanofluids predict accurately with a correlation coefficient of 0.99998, and 0.99906, respectively. The obtained data was compared with other kind of nanofluids data. The polynomial regression equation was proposed for the water and ethylene glycol-based hybrid nanofluids through the SVR model.

Advanced Neural Network-Based Load Frequency Regulation in Two-Area Power Systems

In this paper, enhancing dynamic performance in power systems through load frequency control (LFC) is explored across diverse operating scenarios. A new Neural Network Model Predictive Controller (NN-MPC) specifically tailored for two-zone load frequency power systems is presented. ” Make your paper more scientific. The NN-MPC marries the predictive accuracy of neural networks with the robust capabilities of model predictive control, employing the nonlinear Levenberg-Marquardt method for optimization. Utilizing local area error deviation as feedback, the proposed controller's efficacy is tested against a spectrum of operational conditions and systemic variations. Comparative simulations with a Fuzzy Logic Controller (FLC) reveal the proposed NN-MPC's superior performance, underscoring its potential as a formidable solution in power system regulation.

A generalization of the M5 Tree model and artificial neural network model for estimating daily reference evapotranspiration under minimal climatic data conditions

ABSTRACT To enhance water use efficiency in agriculture, accurately estimating plant water consumption is essential. This study examines the ability of artificial neural networks (ANNs) and decision tree models to calculate reference evapotranspiration (ET0). Data from Shahrekord, Farokhshahr, and Saman stations (2004–2013), including temperature, humidity, wind speed at 2 m, and sunshine hours, were used. The FAO Penman–Monteith model evaluated the models. In the first phase, eight scenarios were designed to estimate evapotranspiration under different climatic data. Evaluation metrics like root mean square error (RMSE), mean absolute error (MAE), and correlation coefficient (R) were calculated. Results showed that the ANN model, with a feedforward network and Levenberg–Marquardt algorithm, outperformed the M5 decision tree model at all stations: (RMSE = 0.3, MAE = 0.23, R = 0.99) at the Shahrekord airport (RMSE = 0.34, MAE = 0.26, R = 0.99) at Farokhshahr, and (RMSE = 0.31, MAE = 0.24, R = 0.99) at Saman. In the second phase, both models were trained with Farokhshahr data and tested with data from the other stations. Results again showed the superior performance of the ANN model. Overall, the study concluded that the ANN model outperforms the M5 model in data-scarce conditions, making it a better tool for water resource management.

A Feed-Forward Back-Propagation Neural Network Approach for Integration of Electric Vehicles into Vehicle-to-Grid (V2G) to Predict State of Charge for Lithium-Ion Batteries

The accurate prediction and efficient management of the State of Charge (SoC) of electric vehicle (EV) batteries are critical challenges in the integration of vehicle-to-grid (V2G) systems within multi-energy microgrid (MMO) models. Inaccurate SoC estimation can lead to inefficiencies, increased costs, and potential disruptions in power generation. This paper addresses the problem of optimizing SoC estimation to enhance the reliability and efficiency of V2G scheduling and MMO coordination. In this work, we develop a Feed-Forward Back-Propagation Network (FFBPN) using MATLAB 2024 software, employing the Levenberg–Marquardt algorithm and varying the number of hidden neurons to achieve better performance; performance was measured by the maximum coefficient of determination (R2) and the minimum mean squared error (MSE). Utilizing the NASA Prognostics Center of Excellence (PCoE) dataset, we validate the model’s capability to accurately predict the life cycle of EV batteries. Our proposed FFBPN model demonstrates superior performance compared to existing methods from the literature, offering significant implications for future V2G system developments. The comparison between training, validation, and testing phases underscores the model’s validity and precisely identifies the characteristic curves of FFBPN, showcasing its potential to enhance profitability, efficiency, production, energy savings, and minimize environmental impact.

A Neural Controller Design for Enhancing Stability of a Single Machine Infinite Bus Power System

This paper examines the formulation and implementation of a neuro-controller for the excitation system of synchronous generators in a Single-Machine Infinite Bus (SMIB) power system. The SMIB model is employed as a fundamental model of a power system, thereby facilitating the assessment and comparison of disparate control strategies with the objective of enhancing system stability. The goal of this study is to enhance the stability of the SMIB power system through the implementation of an Artificial Neural Network (ANN) neuro-controller, providing a comparison of its performance to that of a Power System Stabilizer (PSS) and a Proportional-Integral-Derivative (PID) controller. The proposed neuro-controller will be integrated into the generator's excitation system and will be designed to regulate the excitation voltage in response to fluctuations in the system's operational parameters. To this end, an ANN is calibrated to account for the singularity of the generator's excitation level and terminal voltage. The Levenberg-Marquardt algorithm is employed to ascertain the optimal weight coefficients for the ANN. To assess the performance of the neuro-controller, simulations were conducted using MATLAB/Simulink. The simulations encompass a comprehensive range of operational scenarios, including diverse disturbances and alterations in the reference voltage level. Subsequently, the neuro-controller's outputs are evaluated in comparison to the PSS and PID controllers, as these are the prevailing controllers used to enhance voltage regulation and transient stability in power systems. This paper presents the results of an analysis of the neuro-controller's impact on the system's robustness, voltage variation amplitude, and generator dynamic performance during faults. Simulation results demonstrate that the application of an ANN-based neuro-controller yields superior outcomes in voltage regulation and transient stability compared to the conventional controllers PSS and PID. Furthermore, the neuro-controller is distinguished by accelerated response times and enhanced precision in voltage level regulation. The neuro-controller represents a superior approach to the control of a power system, particularly in the context of SMIB, which would ultimately result in enhanced performance and stability.

Advanced neural network modeling with Levenberg–Marquardt algorithm for optimizing tri-hybrid nanofluid dynamics in solar HVAC systems

Advanced neural network modeling with Levenberg–Marquardt algorithm for optimizing tri-hybrid nanofluid dynamics in solar HVAC systems

NNHMC: An Efficient Stokes Inversion Method Using a Neural Network (NN) Model Combined with the Hamiltonian Monte Carlo (HMC) Algorithm

The Milne–Eddington (M-E) atmosphere model is commonly adopted in the inversion of the magnetic fields in the solar photosphere. By applying the Levenberg–Marquardt algorithm or training a neural network (NN) model, the magnetic field vector can be quickly inferred from the Stokes profile but lacks reliable and statistically well-defined confidence intervals for parameters. To address this, we present an efficient Bayesian inference method called NNHMC, combining the NN model with the Hamiltonian Monte Carlo (HMC) algorithm. The NN model is used to speedily synthesize batches of synthetic Stokes profiles, accelerating the inference process. The HMC algorithm significantly improves sampling efficiency in high-dimensional parameter spaces and can handle large-scale data sets in batches. The spectropolarimetric observation of an active region obtained by the Hinode/spectropolarimeter (SP) is used to demonstrate the capability of the NNHMC method. The strength, inclination, and azimuth of the magnetic field and the line-of-sight velocity inferred with the NNHMC method are very similar to those derived with the MERLIN code. Furthermore, this study provided posterior distributions and uncertainties for these parameters. A test on the same hardware and software platform shows a speed increase of up to 2.5 orders of magnitude with respect to the traditional Markov Chain Monte Carlo method (without the NN, using the M-E atmosphere model), establishing the NNHMC method as a highly effective tool for Stokes inversion based on Bayesian inference.

Physics-based and data-driven modelling and simulation of Solid Oxide Fuel Cells

This paper presents a comprehensive approach to multiscale and multiphysics modelling of Solid Oxide Fuel Cells (SOFCs) by combining physics-based simulations with data-driven techniques. The modelling approach is tailored to specific end-use scenarios, ensuring that parameter selection aligns with operational requirements for accurate and efficient SOFC design. The study begins by constructing Representative Volume Elements (RVEs) from reconstructed microstructures, applying first-order homogenisation to upscale material properties, which are then incorporated into a macroscopic SOFC model. A major contribution is the structured model definition based on physical process entities, using a graphical representation of model topology. This approach simplifies complex system interactions by representing capacities (such as reservoirs, distributed systems, and interfaces) and transport processes (e.g., diffusion, convection, thermal diffusion), thereby enhancing clarity and improving the accuracy of SOFC performance simulations.A machine learning framework complements the physics-based modelling by training Artificial Neural Networks (ANNs) on simulation-generated datasets, delivering fast and reliable performance predictions. The study compares two optimisation techniques — Levenberg–Marquardt (LM) and Adam optimiser — demonstrating that LM is more effective for sparse datasets and smaller networks, whereas Adam performs better with large datasets and higher learning capacities. This hybrid modelling approach not only boosts predictive accuracy for SOFC performance but also lowers computational costs. By integrating physics-based simulations, machine learning, and a knowledge-driven simulation platform, this work advances SOFC design and optimisation, contributing to more efficient and cost-effective clean energy solutions.Additionally, the paper introduces a knowledge-driven simulation platform to enhance data management and integrate multiscale, multiphysics models. The platform leverages structured data models and ontological mappings to improve semantic interoperability, allowing for dataset reuse and validation across different simulation stages. This ensures a robust, reusable, and well-organised workflow, facilitating large-scale simulations and improving overall modelling accuracy.

Assessment of mass transfer performance using the two-film theory and surrogate models for intensified CO2 capture process by amine solutions in rotating packed beds

CO2 capture is a crucial aspect of attempts to mitigate climate change. The purpose of this study is to investigate the impacts of essential operating parameters on the mass transfer performance of absorbing CO2 in rotating packed beds (RPBs). A multilayer perceptron neural network (MLPNN) model with the Levenberg-Marquardt learning algorithm, a mass transfer model using the two-film theory, and an empirical correlation model were developed to predict the overall gas-phase volumetric mass-transfer coefficient (KGaV) for RPB-based CO2 absorption. The developed MLPNN model showed excellent agreement with the actual data, with an MSE of 0.0357, an AARD of 7.4%, and an R2 of 0.9839. A sensitivity analysis was conducted using Taguchi orthogonal array design on distinct mass transfer correlations. The results of the two-film theory and surrogate models for the diethylenetriamine (DETA) solvent were compared. The MLPNN model provided better predictions than other developed models with an AARD of 13% for CO2H2O-DETA system. Therefore, the effects of operating parameters such as concentration, temperature, solvent flow rate, and rotational speed on KGaVand CO2 removal efficiency were evaluated using the MLPNN model. Finally, an empirical correlation was proposed to predict KGaVas a function of operational parameters.

Quasi-periodic breathers and their dynamics to the Fokas system in nonlinear optics

The Fokas system is widely applied in nonlinear optics which can be used to describe the propagation behavior of optical solitons. An effective method for constructing the quasi-periodic breathers of the Fokas system is presented by combining the Hirota’s bilinear method with the theta function. The solvable problem of the quasi-periodic breathers is successfully transformed into a least squares problem whose numerical solutions ultimately are obtained through the Gauss–Newton method and the Levenberg–Marquardt method. Theoretical inference and numerical results show that when the real part of the diagonal elements of the Riemann matrix tends to positive infinity, the quasi-periodic breathers can be reduced to regular breathers. By analyzing the propagation characteristics of the quasi-periodic breathers, these quasi-periodic breathers are divided into three categories, general quasi-periodic breathers, quasi-periodic approximate Kuznetsov–Ma breathers and quasi-periodic Akhmediev breathers. Furthermore, by using an analytical method related to the characteristic lines for the quasi-periodic breathers, the dynamic characteristics including the periods and wave velocities of the quasi-periodic breathers are analyzed.

Static security assessment of renewable integrated power systems using ensemble of modified ELM with unsupervised feature learning technique

The integration of renewable energy sources into power systems poses various challenges for static security assessment, including intermittency and variability of renewable generation, uncertainty in forecasting and impact on grid stability. Overcoming these challenges involves utilizing advanced modelling methods, refining forecasting algorithms, enhancing monitoring and control systems for the grid, and developing robust static security assessment approaches specifically designed for power systems integrated with renewable energy generation. A modified Extreme learning machine (ELM) based ensemble approach is proposed in this study, where ELM is combined with Levenberg-Marquardt (LM) backpropagation technique to improve the accuracy and robustness of prediction. Further, computational efficiency is improved through an unsupervised feature learning technique in the form of autoencoder to reduce the curse of dimensionality. The ensemble technique provides a comprehensive solution for evaluating the static security of power systems in the presence of uncertainties introduced by renewable energy sources. The uncertainties are incorporated into the test systems by simulating random solar and wind scenarios using a well-established Monte Carlo (MC) simulation method. The effectiveness of this approach is demonstrated through numerical testing on modified IEEE 14-bus, 30-bus, 118-bus, and an Indian practical 75-bus systems. Results show that the proposed model outperforms base learners in terms of reliability and efficiency.

Levenberg-Marquardt algorithm to examine thermal third grade non-Newtonian fluid using as a polymer for wire covering with variable viscosity

To ensure protection against harsh environmental conditions and to enhance mechanical durability, the application of a coating is essential. The present research delves a unique approach aimed at assessing the impact of nonlinear radiation and heat transmission (HT) phenomena on wire coating (WC) exhausting a third-grade viscoelastic fluid (VETF) used as a melting polymer underneath the impact of Joule heating through the utilization of a multilayer perceptron (MLP) feed-forward back-propagation, an Artificial Neural Network (ANN) under the control of the Levenberg-Marquardt Algorithm (ANN-LMA). The suggested Neural Network based ANN-LMA is substantiated efficiently by analyzing state transition dynamics (STD), mean square error (MSE), and regression analyses (RA). The fundamental differential equation governing TGVF is distorted into a dimensionless set of nonlinear ordinary differential equations (ODEs). Utilizing the bvp4c approach, a benchmark dataset of TGVF is generated, considering the effects of parameters linked to the wire covering system. It is noteworthy that the temperature parameter significantly influences the distribution of temperature and HT features within the die's stream zone. The phenomenon of fluid velocity reduction within the die is noted to be inversely proportional to the magnetic factor escalation, whereas the magnetic factor exhibits a stimulating influence on temperature dispersion. In the vicinity of the wire surface, the speed of the coating substance experiences enhancement as the temperature and radiation parameters escalate. Examination further reveals a decrement in the temperature as the magnitudes of radiation and temperature factors are enhanced. The robust coherence between the proposed results and established solutions highlights the soundness of the framework with an accuracy level from 10−8 to 10−6.

Prediction acrylamide contents in fried dough twist based on the application of artificial neural network

Acrylamide forms through the reaction between reducing sugars and asparagine in the thermal processing of food. Detection measures like LC-MS, HPLC are time-consuming and costly, which inspired us to use back propagation-artificial neural networks (BP-ANN) based on a genetic algorithm to establish an acrylamide prediction model in fried dough twist. The effects of frying time and temperature on acrylamide contents, as well as the color difference and acid value at different time and temperature were determined. Acrylamide content was found significantly correlated with temperature (P < 0.01) and was correlated with acid value and color difference (P < 0.05). Thus, temperature, acid value, and the color difference were set as input layers, and acrylamide content was set as an output layer to establish a BP-ANN network prediction model. The weight and threshold values in the BP-ANN network prediction model were optimized with a multi-population genetic algorithm and the test data were set to obtain an optimized BP neural network predicting model. The results showed that the Levenberg-Marquardt back-propagation training algorithm of the BP-ANN model with 5 hidden layer neurons and 0.005 learning rate was the best predictive performance, which the correlation coefficients (R) of test and validation were 0.9640 and 0.8999, suggesting a good fitting and strong approximation ability. The BP-ANN model is expected to accurately predict the content of acrylamide in fried dough twist.

ANN prediction of mode I fracture energy in epoxy adhesive joints: Adherend, adhesive, and strain rate effects

In this investigation, the mode I fracture behavior of an epoxy adhesive joint has been investigated to probe the combined effects of adherend Young's modulus and thickness, strain rate, and adhesive length. Experimental fracture testing was conducted on double-cantilever beam (DCB) specimens under three various strain rate thresholds, namely, quasi-static (0.0005 s−1), low (0.015 s−1), and intermediate (0.5 s−1). The specimens were constructed with varying adherend materials (i.e., copper, aluminum), thickness (12–20 mm), and adhesive lengths (25–75 mm). The fracture load was measured in each experiment, and the critical strain energy release rate, JCi, was calculated via a finite element analysis (FEA) in each case. Results with a 95 % confidence interval showed adherend thickness had a negligible effect within the investigated range (p-value = 0.462). JCi was significantly impacted by adhesive length (p-value = 0.009) and two other investigated parameters (p-values = 0.000). The development of artificial neural networks (ANNs) with Levenberg-Marquardt (LM) led to the prediction of JCi based on the examined parameters. With a mean absolute percentage error (MAPE) of 8.9 % and a mean squared error (MSE) of 683 J2/m4 on unseen test data, the ANN model built in this study was able to predict the JCi in epoxy adhesive joints, indicating its potential to produce an accurate prediction for JCi in epoxy adhesive joints. This work offers insights for precise fracture behavior prediction under mode I stress conditions as well as some helpful information that can be utilized to optimize adhesive joint design.

Improved Kalman Filtering Algorithm Based on Levenberg-Marquart Algorithm in Ultra-Wideband Indoor Positioning.

To improve the current indoor positioning algorithms, which have insufficient positioning accuracy, an ultra-wideband (UWB) positioning algorithm based on the Levenberg-Marquardt algorithm with improved Kalman filtering is proposed. An alternative double-sided two-way ranging (ADS-TWR) algorithm is used to obtain the distance from the UWB tag to each base station and calculate the initial position of the tag by the least squares method. The Levenberg-Marquardt algorithm is used to correct the covariance matrix of the Kalman filter, and the improved Kalman filtering algorithm is used to filter the initial position to obtain the final position of the tag. The feasibility and effectiveness of the algorithm are verified by MATLAB simulation. Finally, the UWB positioning system is constructed, and the improved Kalman filter algorithm is experimentally verified in LOS and NLOS environments. The average X-axis and the Y-axis positioning errors in the LOS environment are 6.9 mm and 5.4 mm, respectively, with a root mean square error of 10.8 mm. The average positioning errors for the X-axis and Y-axis in the NLOS environment are 20.8 mm and 18.0 mm, respectively, while the root mean square error is 28.9 mm. The experimental results show that the improved algorithm has high accuracy and good stability. At the same time, it can effectively improve the convergence speed of the Kalman filter.

Advancing Parameter Estimation in Differential Equations: A Hybrid Approach Integrating Levenberg–Marquardt and Luus–Jaakola Algorithms

This study presents an integrated approach that combines the Levenberg–Marquardt (LM) and Luus–Jaakola (LJ) algorithms to enhance parameter estimation for various applications. The LM algorithm, known for its precision in solving non-linear least squares problems, is effectively paired with the LJ algorithm, a robust stochastic optimization method, to improve accuracy and computational efficiency. This hybrid LM-LJ methodology is demonstrated through several case studies, including the optimization of MESH equations in distillation processes, modeling controlled diffusion in biopolymer films, and analyzing heat and mass transfer during the drying of cylindrical quince slices. By overcoming the convergence issues typical of gradient-based methods and performing global searches without initial parameter bounds, this approach effectively handles complex models and closely aligns simulation results with experimental data. These capabilities highlight the versatility of this approach in engineering and environmental modeling, significantly enhancing parameter estimation in systems governed by differential equations.

A solving new method for the urea-selective catalytic reduction (SCR) system in a diesel engine using coupled hyperbolic-parabolic partial differential equations (PDEs)

To control the diesel engine urea SCR system with high accuracy, firstly, the partial differential equations of the SCR system are simplified through variable substitution and the method of characteristic lines to eliminate the partial derivative terms of the hyperbolic partial differential equations in the flow direction. The backward difference method is used to solve the problem, and the adaptive time step is adjusted to improve computational efficiency. Secondly, the Levenberg-Marquardt algorithm is applied to identify the model parameters per second based on the 1800-s test bench data. By combining the experimental data with the parameter identification results, this paper calculated the downstream NOx concentration with 99.5 % accuracy. Finally, the 1800s transient test data was applied to a commonly used single-state SCR control model, and cell numbers 1–4 of the cases were numerically simulated. It was found that the reduced-order model had a computation time of 1 s but was less accurate. When the test data was applied to the model presented in this study, the calculation time was 27s, and the model's calculation results show that the average error of the downstream NOx concentration is 16.95 ppm, which is 14.3 ppm lower than that of the two-cell one-state model.