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Radial basis function (RBF) neural network training presents a challenging optimization task, necessitating the utilization of advanced algorithms that can fully train the network so as to produce accurate and computationally efficient models. To achieve this goal, this work introduces a new framework where the original RBF training problem is divided into two simpler subproblems; the linear parameters, namely the network weights, are projected out of the problem using variable projection (VP), thus leaving a reduced functional, which depends only on nonlinear parameters, i.e., the RBF centers. The centers are updated using the Levenberg–Marquardt (LM) algorithm, while the optimal values of the synaptic weights are calculated in each iteration of the LM algorithm using linear regression. The proposed VP-LM scheme is coupled with the fuzzy means (FM) algorithm, which helps to select the number of RBF centers and enhances the overall search procedure, thus resulting to a framework that produces parsimonious models with enhanced accuracy in shorter training times. The proposed training scheme is evaluated on 12 both real-world and synthetic benchmark datasets and tested against various RBF training algorithms, as well as different neural network architectures. The experimental results underscore the effectiveness of the VP-FM algorithm in producing neural network models that outperform those generated by alternative methods in many aspects; to be more specific, the proposed approach achieves very competitive model accuracy, while resulting to smaller network sizes and thus lower complexity, which leads to shorter training times. [ABSTRACT FROM AUTHOR]

Accurate analysis of creep effects in finite element analysis depends on whether the exponential form of the creep coefficient can accurately reproduce the creep coefficient curve. This paper aims to develop a high-precision fitting method for arbitrary creep coefficient curves to achieve accurate finite element creep analysis. The core issue was examined, and an optimization algorithm was proposed. First, the simulated annealing algorithm was used to search for the global optimal solution, followed by the application of the Levenberg-Marquardt algorithm for precise calculations. Two examples were employed to verify the method. The results showed that: (1) The proposed creep coefficient curve fitting method could accurately fit the creep coefficient curve. (2) The case studies showed that the algorithm achieved a correlation coefficient ( R) above 0. 999 9 when fitting the creep coefficient curves according to highway and railway standards, indicating high fitting accuracy and strong general applicability. (3) The proposed algorithm featured a simple structure and clear hierarchy, allowing for easy implementation using common programming languages. This method provides valuable insights for the development of finite element program creep analysis modules or related scientific research on concrete creep behavior. [ABSTRACT FROM AUTHOR]

The increasing adoption of batteries in a variety of applications has highlighted the necessity of accurate parameter identification and effective modeling, especially for lithium-ion batteries, which are preferred due to their high power and energy densities. This paper proposes a comprehensive framework using the Levenberg–Marquardt algorithm (LMA) for validating and identifying lithium-ion battery model parameters to improve the accuracy of state of charge (SOC) estimations, using only discharging measurements in the N-order Thevenin equivalent circuit model, thereby increasing computational efficiency. The framework encompasses two key stages: model parameter identification and model verification. This framework is validated using experimental measurements on the INR 18650-20R battery, produced by Samsung SDI Co., Ltd. (Suwon, Republic of Korea), conducted by the Center for Advanced Life Cycle Engineering (CALCE) battery group at the University of Maryland. The proposed framework demonstrates robustness and accuracy. The results indicate that optimization using only the discharging data suffices for accurate parameter estimation. In addition, it demonstrates excellent agreement with the experimental measurements. The research underscores the effectiveness of the proposed framework in enhancing SOC estimation accuracy, thus contributing significantly to the reliable performance and longevity of lithium-ion batteries in practical applications. [ABSTRACT FROM AUTHOR]

При решении задач математического моделирования часто приходится обращаться к теории интегрально-дифференциального исчисления. С ее помощью можно описывать динамические процессы самой разной природы. Использование аппарата дробных производных позволяет уточнить некоторые из этих моделей за счет учета в уравнениях эффекта памяти. Данный эффект выражается в зависимости текущего состояния динамической системы от предыдущих состояний, то есть нелокальности. Интенсивность этого эффекта будет определяться значением показателя степени дробной производной. Классически это некое значение αα является нецелым и постоянным. Однако существуют обобщения дробных производных на случай переменной во времени нелокальности α(t) и других функциональных зависимостей. Подобные дробно-дифференциальные модели все чаще находят свое применение в теории и практике физико-математических, а также технических наук. Однако, учитывая понимание природы моделируемого процесса, подбор различных параметров таких моделей приходится осуществлять эмпирически. Например, модельные параметры уточняются путем перебора значений и сопоставления временных рядов: результатов моделирования и экспериментальных данных, представляющих процесс. Это продолжается до тех пор, пока результаты моделирования не начнут качественно аппроксимировать данные. Такой подход трудоемок, что неизбежно приводит нас к идеям о решении обратных задач. Цель данной работы – показать, что с помощью методов безусловной оптимизации возможно решение обратных задач для определения вида функциональной зависимости α(t). Прямая задача определяется как задача Коши для дробного уравнения, где производная понимается в смысле Герасимова-Капуто с переменным показателем степени дробной производной α(t). Прямая задача решается численно с помощью нелокальной неявной конечно-разностной схемы. Обратная задача определяется как задача дискретной минимизации функции α(t) на основе экспериментальных данных. В качестве метода для решения был выбран итерационный метод Левенберга-Марквардта. На тестовых примерах было показано, что метод Левенберга-Марквардта действительно может быть использован для безусловной оптимизации с целью определения вида функции α(t) и её оптимальных значений в конкретных моделях.

Abstract In the present work, a simple intelligence-based computation of artificial neural networks with the Levenberg-Marquardt backpropagation algorithm is developed to analyze the new ferromagnetic hybrid nanofluid flow model in the presence of a magnetic dipole within the context of flow over a stretching sheet. A combination of cobalt and iron (III) oxide (Co-Fe2O3) is strategically selected as ferromagnetic hybrid nanoparticles within the base fluid, water. The initial representation of the developed ferromagnetic hybrid nanofluid flow model, which is a system of highly nonlinear partial differential equations, is transformed into a system of nonlinear ordinary differential equations using appropriate similarity transformations. The reference data set of the possible outcomes is obtained from bvp4c for varying the parameters of the ferromagnetic hybrid nanofluid flow model. The estimated solutions of the proposed model are described during the testing, training, and validation phases of the backpropagated neural network. The performance evaluation and comparative study of the algorithm are carried out by regression analysis, error histograms, function fitting graphs, and mean squared error results. The findings of our study analyze the increasing effect of the ferrohydrodynamic interaction parameter $$\beta$$ β to enhance the temperature and velocity profiles, while increasing the thermal relaxation parameter $$\alpha$$ α decreases the temperature profile. The performance on MSE was shown for the temperature and velocity profiles of the developed model about 9.1703e−10, 7.1313ee−10, 3.1462e−10, and 4.8747e−10. The accuracy of the artificial neural networks with the Levenberg-Marquardt algorithm method is confirmed through various analyses and comparative results with the reference data. The purpose of this study is to enhance understanding of ferromagnetic hybrid nanofluid flow models using artificial neural networks with the Levenberg-Marquardt algorithm, offering precise analysis of key parameter effects on temperature and velocity profiles. Future studies will provide novel soft computing methods that leverage artificial neural networks to effectively solve problems in fluid mechanics and expand to engineering applications, improving their usefulness in tackling real-world problems.

‎This study suggests a novel approach for calibrating European option pricing model by a hybrid model based on the optimized artificial neural network and Black-Scholes model‎. ‎In this model‎, ‎the inputs of the artificial neural network are the Black-Scholes equations with different maturity dates and strike prices‎. ‎The presented calibration process involves training the neural network on historical option prices and adjusting its parameters using the Levenberg-Marquardt optimization algorithm‎. ‎The resulting hybrid model shows superior accuracy and efficiency in option pricing on both in sample and out of sample dataset‎.

Almost every year, earthquakes threaten many lives, so not only do developing countries suffer negative effects from earthquakes on their economies but also developed ones that lose significant economic resources, suffer massive fatalities, and have to suspend businesses and occupancy. Existing buildings in earthquake-prone areas need structural safety assessments or seismic vulnerability assessments. It is crucial to assess earthquake damage before an earthquake to prevent further losses, and to assess building damage after an earthquake to aid emergency responders. Many models do not take into account the surveyor's subjectivity, which causes observational vagueness and uncertainty. Additionally, a lack of experience or knowledge, engineering errors, and inconspicuous parameters could affect the assessment. Thus, a consensus-based Likert–LMBP (the Levenberg–Marquardt backpropagation algorithm) model was developed to rapidly assess the seismic performance of buildings based on post-earthquake visual images in the devastating Kahramanmaraş earthquake, which occurred on 6 February 2023 and had magnitudes of 7.7 and 7.6 and severely affected 11 districts in Türkiye. Vulnerability variables for buildings are assessed using linguistic variables on a five-point Likert scale based on expert consensus values derived from post-earthquake visual images. The building vulnerability parameters required for the proposed model are determined as the top hill–slope effect, weak story effect, soft story effect, short column effect, plan irregularity, pounding effect, heavy overhang effect, number of stories, construction year, structural system state, and apparent building quality. Structural analyses categorized buildings as no damage, slight damage, moderate damage, or severe damage/collapse. Training the model resulted in quite good performance (mse = 7.26306 × 10−5). Based on the statistical analysis of the entire data set, the mean and the standard deviation of the errors were 0.00068 and 0.00852, respectively. [ABSTRACT FROM AUTHOR]

Various faults of photovoltaic (PV) modules inevitably occur in the work process, since PV modules are installed in hostile situation. To obtain the types of failure, a novel fault diagnosis method based on back propagation (BP) neural network with Levenberg-Marquardt (L-M) algorithm for PV modules is proposed. Through the in-depth analysis the output of PV modules under normal and fault conditions, the input variables of the diagnosis model are acquired. The high-speed and real-time fault diagnosis model for PV modules is first designed based on TMS320VC5402 DSP and long-distance wireless fault diagnosis is realized by Zigbee technology. The simulation and experimental results show that the fault diagnosis method for PV modules based on BP network with L-M algorithm can effectively detect four types of fault for PV modules such as open circuit, short circuit, partial shading and abnormal degradation. The numerical results verify the effectiveness and correctness of the proposed method, which can provide a great educational benefit of PV operation technology. [ABSTRACT FROM AUTHOR]

Water bodies can offer local microclimates that have the potential to attenuate the effects of urban heat islands by reducing local temperature. This capability is shaded when the river is channelized. In such cases, the river temperature rises during hot periods, leading to negative impacts on the water quality. The main aim of this paper is to develop a local simple model to predict the temperature of the Dâmbovița River at its exit from Bucharest City, the capital of Romania. The location is chosen based on the historical critical impacts, in terms of extreme heatwaves that took place during hot summers, as well as future possible risks due to climate change. The water temperature prediction model is based on an artificial neural network that uses the Levenberg–Marquardt algorithm, due to its stability and rapid convergence capabilities. The model forecasts, with an accuracy of ±1 °C, the water temperature in an ungauged, downstream location, as a function of measured air and upstream water temperatures. The proposed model represents a first attempt to provide water managers in Bucharest City with a useful tool that will allow them to take timely measures to counteract the unwanted effects that can be generated by high water temperatures. [ABSTRACT FROM AUTHOR]

Currently, magnetic gradient tensor-based localization methods face challenges such as significant errors in geomagnetic field estimation, susceptibility to local optima in optimization algorithms, and inefficient performance. In addressing these issues, this article propose a two-point localization method under the constraint of overlaying geometric invariants. This method initially establishes the relationship between the target position and the magnetic gradient tensor by substituting an intermediate variable for the magnetic moment. Exploiting the property of the eigenvector corresponding to the minimum absolute eigenvalue being perpendicular to the target position vector, this constraint is superimposed to formulate a nonlinear system of equations of the target's position. In the process of determining the target position, the Nara method is employed for obtaining the initial values, followed by the utilization of the Levenberg–Marquardt algorithm to derive a precise solution. Experimental validation through both simulations and experiments confirms the effectiveness of the proposed method. The results demonstrate its capability to overcome the challenges faced by a single-point localization method in the presence of some errors in geomagnetic field estimation. In comparison to traditional two-point localization methods, the proposed method exhibits the highest precision. The localization outcomes under different noise conditions underscore the robust noise resistance and resilience of the proposed method. [ABSTRACT FROM AUTHOR]

This study addresses the challenge of utilizing incomplete long-term discharge data when using gridded precipitation datasets and data-driven modeling in Iran's Karkheh basin. The Multilayer Perceptron Neural Network (MLPNN), a rainfall-runoff (R-R) model, was applied, leveraging precipitation data from the Asian Precipitation—Highly Resolved Observational Data Integration Toward Evaluation (APHRODITE), Global Precipitation Climatology Center (GPCC), and Climatic Research Unit (CRU). The MLPNN was trained using the Levenberg–Marquardt algorithm and optimized with the Non-dominated Sorting Genetic Algorithm-II (NSGA-II). Input data were pre-processed through principal component analysis (PCA) and singular value decomposition (SVD). This study explored two scenarios: Scenario 1 (S1) used in situ data for calibration and gridded dataset data for testing, while Scenario 2 (S2) involved separate calibrations and tests for each dataset. The findings reveal that APHRODITE outperformed in S1, with all datasets showing improved results in S2. The best results were achieved with hybrid applications of the S2-PCA-NSGA-II for APHRODITE and S2-SVD-NSGA-II for GPCC and CRU. This study concludes that gridded precipitation datasets, when properly calibrated, significantly enhance runoff simulation accuracy, highlighting the importance of bias correction in rainfall-runoff modeling. It is important to emphasize that this modeling approach may not be suitable in situations where a catchment is undergoing significant changes, whether due to development interventions or the impacts of anthropogenic climate change. This limitation highlights the need for dynamic modeling approaches that can adapt to changing catchment conditions. [ABSTRACT FROM AUTHOR]

This paper proposes an inverse dynamics solution for two cooperative robots in a low depth milling application, by using the Levenberg-Marquardt algorithm. The objective is to achieve precise and coordinated control of the motions of the two robots working cooperatively to perform a milling task on a part. The proposed solution involves modeling the dynamics of the robots and their interactions, and formulating an optimization problem to obtain the forces on the workpiece. The proposed approach takes into account the kinematic and the dynamic constraints of the robots, as well as their interactions, in order to ensure smooth and coordinated motion. The Levenberg-Marquardt algorithm's effectiveness in achieving precise and synchronized motion and force control for a pair of collaborative robots during low-effort milling is validated through simulations conducted in MATLAB/SimMechanics. The simulation results confirm the robust performance of the proposed solution. This proposed approach shows potential for boosting the efficiency and the precision of collaborative milling tasks within industrial environments, ultimately resulting in improved manufacturing capabilities and increased productivity. Further experimental validation on a real robotic system is planned for future work. [ABSTRACT FROM AUTHOR]

This article explores the enhancement of thermal exchange in a dissipative Triple-nanoparticle (Al2O3+CuO+Cu) hybrid fluid over a stretchable wavy cylindrical surface with slip effect, incorporating Python bvp algorithm with artificial intelligence AI analysis of numerical results. The stochastic AI analysis gives the enhanced and optimized results with predictive modeling, incorporating randomness of influencing parameters and nonlinear turbulent behavior of model. The model has significant importance and application in noise reducing and drag reduction devices or structures. Moreover, the presented geometrical structure is useful in enhancing thermal conduction characteristic. The intricate interplay of constituent nanoparticles and their effect on complex heat transfer in drag optimization devices is the main focus of this study. Mathematical Model of PDEs of this flow problem is converted into system of ODEs by similarity transformations with introducing dimensionless parameters. Numerical solutions of the emerged system are obtained by Python bvp solver algorithm and graphical solutions by Python are presented. To expedite the solution process and enhance the accuracy of prediction, advanced AI algorithm, such as neural network and machine learning technique is adopted. Numerical dataset obtained from Python is embedded for further AI analysis by using Levenberg Marquardt Feed-forward Algorithm (LMFA) with 10 computing neurons and 4 output layers representing results for 4 parametric variations.A rise in the fluid flow speed is observed with higher of value yield stress or Newtonian-behavior i.e. of Casson parameter a1 and stretching parameter λ for the sheet, but shows a decline with enhancing turbulence s2. Temperature profile show a descending behavior with inclination of Eckert ratio Ec, and Prandtl ratio of momentum-thermal diffusivity.

In vehicular networks, diverse safety information can be shared among vehicles through internet connections. In vehicle-to-internet communications, vehicles on the road are wirelessly connected to different cloud networks, thereby accelerating safety information exchange. Onboard sensors acquire traffic-related information, and reliable intermediate nodes and network services, such as navigational facilities, allow to transmit safety information to distant target vehicles and stations. Using vehicle-to-network communications, we minimize delays and achieve high accuracy through consistent connectivity links. Our proposed approach uses intermediate nodes with two-hop separation to forward information. Target vehicle detection and routing of safety information are performed using machine learning algorithms. Compared with existing vehicle-to-internet solutions, our approach provides substantial improvements by reducing latency, packet drop, and overhead.

Intelligent reflecting surfaces (IRS) can effectively improve the system performance of non-orthogonal multiple access (NOMA) systems. In this paper, we propose a Levenberg–Marquardt algorithm-based supervised learning network (LMA-SLN) to maximize the sum-rate of an IRS-assisted NOMA system. By decoupling the sum-rate maximization problem into the active and passive beamforming optimization sub-problems, we design an alternating optimization scheme to optimize the active and passive beamformings. Then, the LMA-SLN is trained with ideal channel state information (CSI) to obtain the optimized network parameters. Finally, the trained LMA-SLN is applied to optimize the active and passive beamformings without requiring CSI. The experimental results show that the proposed LMA-SLN scheme achieves the superior performance on improving the sum-rate.

The increasing adoption of batteries in a variety of applications has highlighted the necessity of accurate parameter identification and effective modeling, especially for lithium-ion batteries, which are preferred due to their high power and energy densities. This paper proposes a comprehensive framework using the Levenberg–Marquardt algorithm (LMA) for validating and identifying lithium-ion battery model parameters to improve the accuracy of state of charge (SOC) estimations, using only discharging measurements in the N-order Thevenin equivalent circuit model, thereby increasing computational efficiency. The framework encompasses two key stages: model parameter identification and model verification. This framework is validated using experimental measurements on the INR 18650-20R battery, produced by Samsung SDI Co., Ltd. (Suwon, Republic of Korea), conducted by the Center for Advanced Life Cycle Engineering (CALCE) battery group at the University of Maryland. The proposed framework demonstrates robustness and accuracy. The results indicate that optimization using only the discharging data suffices for accurate parameter estimation. In addition, it demonstrates excellent agreement with the experimental measurements. The research underscores the effectiveness of the proposed framework in enhancing SOC estimation accuracy, thus contributing significantly to the reliable performance and longevity of lithium-ion batteries in practical applications.

The accurate measurement of time-of-flight (TOF) is essential in ultrasonic testing. Further, noise interference is the key factor affecting the measurement accuracy. Therefore, to develop a reliable computational method of TOF for test pieces working in noisy environments, an integration method of a hybrid genetic algorithm and the Levenberg-Marquardt algorithm (GA-LM) for ultrasonic thickness measurement is proposed in the present research. A Gaussian model is first established for an echo signal. Further, the model-based parameter estimation is converted into a nonlinear optimization problem by applying the least square method. As the parameter estimation methods are easily affected by the initial value, an integrating innovation of the GA-LM algorithm is proposed. The initial values of the model parameters are selected by GA to obtain an approximate global optimal solution. Subsequently, this approximate solution is used as the initial value for the LM algorithm to perform iterations. The accurate global optimal solution of the Gaussian model is obtained through these iterations. Finally, the measuring accuracy and robustness of the GA-LM algorithm for TOF computation are verified by both numerical simulation and experiment data. [ABSTRACT FROM AUTHOR]

In this study, we concentrate on solving the problem of non-Lipschitz absolute value equations (NAVE). A new Bezier curve based smoothing technique is introduced and a new Levenberg–Marquardt type algorithm is developed depending on the smoothing technique. The numerical performance of the algorithm is analysed by considering some well-known and randomly generated test problems. Finally, the comparison with other methods is illustrated to demonstrate the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The study was designed to re-examine and calibrate the Blaney-Morin-Nigeria (BMN) evapotranspiration (ET) model for two specific locations, Asaba and Uyo in South-south of Nigeria. This was achieved using a non-linear iterative technique based on Levenberg-Marquardt algorithm, making use of climatic variables. The newly developed model constants were H = 288.0, m = 0.96; H = 285.8, m = 0.91 and H = 287.0, m = 1.00 for South-south Nigeria, Asaba and Uyo respectively compared to the H = 520.0, m = 1.31 for the original BMN ET model. Data were analysed using different statistical indices (RMSE, MAE, S²d, MBE and r). The three newly developed BMN models when compared with FAO-56 PM model gave a more satisfactory reference evapotranspiration ETo estimates than the original BMN ET model when compared with FAO-56 PM model. In Asaba, result showed that the original BMN, the BMN for Asaba and the BMN for South-south underestimated FAO-56 PM ET by 9.87%, 2.70% and 7.14% respectively, while in Uyo, the original BMN model and South-south model overestimated FAO-56 PM ET by 4.19% and 3.99% respectively, whereas that for Asaba was underestimated by 1.83%. The comparative analysis using statistical indices showed that the new BMN models gave a better prediction of ETo with s, c, S²d, MAE, RMSE and r values as 0.90, 0.54, 0.15 mm² day-2, 0.32, 0.41 mm day-1 and 0.85 respectively as against 0.46, 2.42, 0.70 mm² day-2, 0.80, 0.91 mm day-1 and 0.81, which were obtained from the original BMN model. The location specific models for Asaba and Uyo predicted ETo best among the evapotranspiration models followed by the South-south model and the original BMN model gave the worst prediction. [ABSTRACT FROM AUTHOR]

In vehicular networks, diverse safety information can be shared among vehicles through internet connections. In vehicle‐to‐internet communications, vehicles on the road are wirelessly connected to different cloud networks, thereby accelerating safety information exchange. Onboard sensors acquire traffic‐related information, and reliable intermediate nodes and network services, such as navigational facilities, allow to transmit safety information to distant target vehicles and stations. Using vehicle‐to‐network communications, we minimize delays and achieve high accuracy through consistent connectivity links. Our proposed approach uses intermediate nodes with two‐hop separation to forward information. Target vehicle detection and routing of safety information are performed using machine learning algorithms. Compared with existing vehicle‐to‐internet solutions, our approach provides substantial improvements by reducing latency, packet drop, and overhead. [ABSTRACT FROM AUTHOR]

SBAS InSAR has long been used to monitor the mining surface deformation, and its research has been of great interest to researchers worldwide. For the unsatisfactory accuracy of SBAS InSAR-monitored mining surface deformation results, a new corrected model is proposed by integrating SBAS InSAR and Logistic Function. Firstly, the time series deformation results of the mining area were obtained by SBAS InSAR, and the variation law of the differences between SBAS InSAR- and leveling-monitored deformation values was statistically analyzed. Subsequently, the corrected model was constructed using the logistic linear regression analysis function and solved using the Levenberg-Marquardt algorithm. Finally, the corrected high-precision time series deformation results in the mining area were obtained. A mining area in Shandong Province of China was taken as the research object, and the practical application effect of the proposed corrected model was verified. Results showed that the Logistic Function could describe the variation law of the differences relatively accurately, and the corrected results were significantly better than the SBAS InSAR-monitored results, and the RMSEs of the corrected results were improved by 33–58%. The accuracy of SBAS InSAR-monitored mining surface deformation was effectively improved. [ABSTRACT FROM AUTHOR]

Various engineering applications lead to the appearance of partial differential equations resulting in boundary value problems (BVPs). Orthogonal collocation method based Haar wavelets has gained significant attention in solving these problems. The Haar wavelets have several properties like vanishing moment, compact effect, and orthogonality. These properties prioritize being used as base functions for solving BVPs. However, the approximation leads to a relatively high number of unknown coefficients, which needs an efficient and reliable nonlinear solver to reach their values. The Levenberg–Marquardt algorithm (LM) is one of the most efficient nonlinear solvers. However, it may diverge in case of too far initial guesses, especially in many unknowns. The reptile search algorithm (RSA) is a recent reliable, nature-inspired optimization technique that has a noticeable capability in dealing with high-dimensional issues. Therefore, this paper proposes a hybrid optimization algorithm that integrates the RSA and LM algorithms using Haar wavelets as bases, named RSA–LM–Haar algorithm, to solve regular and singular natures of the BVPs more efficiently. To evaluate the performance of the proposed RSA–LM–Haar algorithm, it is tested on twelve case studies of BVPs including the singular and regular problems. The results are compared with those based on the LM alone, named LM–Haar algorithm. Finally, the applicability of the proposed algorithm is verified using two practical chemical applications to prove its ability to solve real-time applications effectively. All the results affirmed the capability of the proposed algorithm in solving both regular and singular BVPs. All results and comparisons illustrated that the proposed hybridization algorithm provides remarkable performance. [ABSTRACT FROM AUTHOR]

The Weibull distribution function is essential for planning and designing wind-farm implementation projects and wind-resource assessments. However, the Weibull distribution is limited for those areas with high frequencies of calm winds. One solution is to use the hybrid Weibull distribution. In fact, when the wind speed data present heterogeneous structures, it makes sense to group them into classes that describe the different wind regimes. However, the single use of the Weibull distribution presents fitting errors that should be minimized. In this context, mixture distributions represent an appropriate alternative for modelling wind-speed data. This approach was used to combine the distributions associated with different wind-speed classes by weighting the contribution of each of them. This study proposes an approach based on mixtures of Weibull distributions for modelling wind-speed data in the West Africa region. The study focused on mixture Weibull (WW-BAY) and mixture hybrid Weibull (WWH-BAY) distributions using Bayes' theorem to characterize the wind speed distribution over twelve years of recorded data at the Abuja, Accra, Cotonou, Lome, and Tambacounda sites in West Africa. The parameters of the models were computed using the expectation-maximization (E-M) algorithm. The parameters of the models were estimated using the expectation-maximization (E-M) algorithm. The initial values were provided by the Levenberg-Marquardt algorithm. The results obtained from the proposed models were compared with those from the classical Weibull distribution whose parameters are estimated by some numerical method such as the energy pattern factor, maximum likelihood, and the empirical Justus methods based on statistical criteria. It is found that the WWH-BAY model gives the best prediction of power density at the Cotonou and Lome sites, with relative percentage error values of 0.00351 and 0.01084. The energy pattern factor method presents the lowest errors at the Abuja site with a relative percentage error value of -0.54752, Accra with -0.55774, and WW-BAY performs well for the Tambacounda site with 0.19232. It is recommended that these models are useful for wind energy applications in the West African region.

Almost every year, earthquakes threaten many lives, so not only do developing countries suffer negative effects from earthquakes on their economies but also developed ones that lose significant economic resources, suffer massive fatalities, and have to suspend businesses and occupancy. Existing buildings in earthquake-prone areas need structural safety assessments or seismic vulnerability assessments. It is crucial to assess earthquake damage before an earthquake to prevent further losses, and to assess building damage after an earthquake to aid emergency responders. Many models do not take into account the surveyor’s subjectivity, which causes observational vagueness and uncertainty. Additionally, a lack of experience or knowledge, engineering errors, and inconspicuous parameters could affect the assessment. Thus, a consensus-based Likert–LMBP (the Levenberg–Marquardt backpropagation algorithm) model was developed to rapidly assess the seismic performance of buildings based on post-earthquake visual images in the devastating Kahramanmaraş earthquake, which occurred on 6 February 2023 and had magnitudes of 7.7 and 7.6 and severely affected 11 districts in Türkiye. Vulnerability variables for buildings are assessed using linguistic variables on a five-point Likert scale based on expert consensus values derived from post-earthquake visual images. The building vulnerability parameters required for the proposed model are determined as the top hill–slope effect, weak story effect, soft story effect, short column effect, plan irregularity, pounding effect, heavy overhang effect, number of stories, construction year, structural system state, and apparent building quality. Structural analyses categorized buildings as no damage, slight damage, moderate damage, or severe damage/collapse. Training the model resulted in quite good performance (mse = 7.26306 × 10−5). Based on the statistical analysis of the entire data set, the mean and the standard deviation of the errors were 0.00068 and 0.00852, respectively.

This study is designed to analyze the fuzzy dynamical model of vibrating mass system by using neural networks (NNs). Stochastic numerical solvers are implemented with Levenberg–Marquardt backpropagation (LMB) algorithm. The proposed solvers handle the uncertainties of fuzzy differential system and minimize the error consistently. Validation, constancy and verification of NNs with LMB algorithm are endorsed by attaining reasonable accuracy through statistical measures in terms of error histograms, regression and mean squared errors for different values of fuzzy parameters. [ABSTRACT FROM AUTHOR]

In this article, we propose an approach for system identification for a class of discrete-time fractional-order Hammerstein systems using only input–output data. Using a combined state and parameter estimation approach, we develop an algorithm serving to estimate simultaneously, the system parameters, the system orders, and the system states. By minimizing the defining criterion, which is non-convex and nonlinear in the parameters, the model parameters are estimated using the recursive least squares and the Levenberg–Marquardt algorithms. Next, the system states are estimated using the Luenberger observer. Then, the convergence analysis of the proposed algorithm is proved. Finally, the Monte Carlo simulation analysis and an application to Ultracapacitor system are used to demonstrate the effectiveness of the suggested method. [ABSTRACT FROM AUTHOR]

With its flexibility of a collaboration robot and demands for maintaining virtual model's fidelity in cyber-physical system of robotic manufacturing, frequent calibration is required. This paper proposes a cost-effective calibration method of a collaborative robot using a single wire encoder. First, DH (Denavit-Hartenberg) convention-based kinematics of the robot are analyzed. Then, a mathematical relation between distance errors between robot's end effector and wire encoder and the kinematic parameters are presented. In the experiment, turning-in-place-based measurement methodology is applied. Also, in order to reduce error caused by wire bending at the point where a wire is hooked in previous studies, a rotatable wire hanger which has 2-DoF (Degree of Freedom) rotary joint is fabricated and applied. Next, identifiable parameters are analyzed through SVD (Singular value decomposition), then 21 parameters are calculated via Levenberg–Marquardt algorithm. The estimated parameters were validated by comparing fidelity of the calibrated and nominal model against actual physical system measured by a robot arm type measurement device. As a result, feasibility of the proposed method was checked by confirming 64.3% better fidelity of the calibrated model using the proposed method. Furthermore, the performance of the method also shows better results than camera-based robot's internal calibration function provided by manufacturer. [ABSTRACT FROM AUTHOR]

Industrial robots have become key components for manufacturing automations due to their larger workspaces and flexibility. However, low stiffness and high compliance of industrial robots may inevitably lead to vibration by self‐excitation or periodic force dependent on workspace configuration. Therefore, the knowledge of the robot's modal properties should be accurately required to enhance the operation accuracy of industrial robots. To improve the identification accuracy of experimental modal parameters of field industrial robots, an improved subspace identification method is proposed to perform nonlinear iterative optimization for updating the state parameters of industrial robots. Experimental response measurement of a six‐degrees‐of‐freedom industrial robot is carried out to obtain modal parameters under various poses. The identification results of the improved subspace modal method are preferable to that of the traditional method. Moreover, the reconstructed three‐dimension working frequency space is presented to exactly characterize experimental modal frequencies throughout its workspace. The proposed method effectively improves the identification accuracy of modal parameters when compared with the traditional algorithms and the influence of robots' pose change on modal parameters is also investigated by experimental modal measurements. [ABSTRACT FROM AUTHOR]

The Weibull distribution function is essential for planning and designing wind-farm implementation projects and wind-resource assessments. However, the Weibull distribution is limited for those areas with high frequencies of calm winds. One solution is to use the hybrid Weibull distribution. In fact, when the wind speed data present heterogeneous structures, it makes sense to group them into classes that describe the different wind regimes. However, the single use of the Weibull distribution presents fitting errors that should be minimized. In this context, mixture distributions represent an appropriate alternative for modelling wind-speed data. This approach was used to combine the distributions associated with different wind-speed classes by weighting the contribution of each of them. This study proposes an approach based on mixtures of Weibull distributions for modelling wind-speed data in the West Africa region. The study focused on mixture Weibull (WW-BAY) and mixture hybrid Weibull (WWH-BAY) distributions using Bayes' theorem to characterize the wind speed distribution over twelve years of recorded data at the Abuja, Accra, Cotonou, Lome, and Tambacounda sites in West Africa. The parameters of the models were computed using the expectation-maximization (E-M) algorithm. The parameters of the models were estimated using the expectation-maximization (E-M) algorithm. The initial values were provided by the Levenberg-Marquardt algorithm. The results obtained from the proposed models were compared with those from the classical Weibull distribution whose parameters are estimated by some numerical method such as the energy pattern factor, maximum likelihood, and the empirical Justus methods based on statistical criteria. It is found that the WWH-BAY model gives the best prediction of power density at the Cotonou and Lome sites, with relative percentage error values of 0.00351 and 0.01084. The energy pattern factor method presents the lowest errors at the Abuja site with a relative percentage error value of -0.54752, Accra with -0.55774, and WW-BAY performs well for the Tambacounda site with 0.19232. It is recommended that these models are useful for wind energy applications in the West African region. [ABSTRACT FROM AUTHOR]

The heat and mass transfer within non-Newtonian fluid flow results in complex mathematical equations and solution in this regard remains a challenging task for researchers. The present paper offers a numerical solution for the non-Newtonian flow field by using Artificial neural networking (ANN) model with the Levenberg Marquardt training technique. To be more specific, we considered thermally magnetized non-Newtonian flow headed for inclined heated surfaces. The flow is carried with viscous dissipation, stagnation point, heat generation, mixed convection, and thermal radiation effects. The concentration aspects are entertained by the owing concentration equation. The shooting method is used to solve the mathematical flow equations. The quantity of interest includes the temperature and heat transfer coefficient. Two different artificial neural networking models have been built. The training of networks is done by use of the Levenberg Marquardt technique. The values of the coefficient of determination suggest artificial neural networks as the best method for predicting the Nusselt number at both surfaces. The thermal radiation parameter and Prandtl number admit a direct relationship to the Nusselt number while the differing is the case for variable thermal conductivity and Casson parameters. Further, by using Nusselt number (NN)-ANN models, we found that for cylindrical surface, the strength of the NN is greater than the flat surface.

Water bodies can offer local microclimates that have the potential to attenuate the effects of urban heat islands by reducing local temperature. This capability is shaded when the river is channelized. In such cases, the river temperature rises during hot periods, leading to negative impacts on the water quality. The main aim of this paper is to develop a local simple model to predict the temperature of the Dâmbovița River at its exit from Bucharest City, the capital of Romania. The location is chosen based on the historical critical impacts, in terms of extreme heatwaves that took place during hot summers, as well as future possible risks due to climate change. The water temperature prediction model is based on an artificial neural network that uses the Levenberg–Marquardt algorithm, due to its stability and rapid convergence capabilities. The model forecasts, with an accuracy of ±1 °C, the water temperature in an ungauged, downstream location, as a function of measured air and upstream water temperatures. The proposed model represents a first attempt to provide water managers in Bucharest City with a useful tool that will allow them to take timely measures to counteract the unwanted effects that can be generated by high water temperatures.

This study addresses the challenge of utilizing incomplete long-term discharge data when using gridded precipitation datasets and data-driven modeling in Iran’s Karkheh basin. The Multilayer Perceptron Neural Network (MLPNN), a rainfall-runoff (R-R) model, was applied, leveraging precipitation data from the Asian Precipitation—Highly Resolved Observational Data Integration Toward Evaluation (APHRODITE), Global Precipitation Climatology Center (GPCC), and Climatic Research Unit (CRU). The MLPNN was trained using the Levenberg–Marquardt algorithm and optimized with the Non-dominated Sorting Genetic Algorithm-II (NSGA-II). Input data were pre-processed through principal component analysis (PCA) and singular value decomposition (SVD). This study explored two scenarios: Scenario 1 (S1) used in situ data for calibration and gridded dataset data for testing, while Scenario 2 (S2) involved separate calibrations and tests for each dataset. The findings reveal that APHRODITE outperformed in S1, with all datasets showing improved results in S2. The best results were achieved with hybrid applications of the S2-PCA-NSGA-II for APHRODITE and S2-SVD-NSGA-II for GPCC and CRU. This study concludes that gridded precipitation datasets, when properly calibrated, significantly enhance runoff simulation accuracy, highlighting the importance of bias correction in rainfall-runoff modeling. It is important to emphasize that this modeling approach may not be suitable in situations where a catchment is undergoing significant changes, whether due to development interventions or the impacts of anthropogenic climate change. This limitation highlights the need for dynamic modeling approaches that can adapt to changing catchment conditions.

Currently, magnetic gradient tensor-based localization methods face challenges such as significant errors in geomagnetic field estimation, susceptibility to local optima in optimization algorithms, and inefficient performance. In addressing these issues, this article propose a two-point localization method under the constraint of overlaying geometric invariants. This method initially establishes the relationship between the target position and the magnetic gradient tensor by substituting an intermediate variable for the magnetic moment. Exploiting the property of the eigenvector corresponding to the minimum absolute eigenvalue being perpendicular to the target position vector, this constraint is superimposed to formulate a nonlinear system of equations of the target’s position. In the process of determining the target position, the Nara method is employed for obtaining the initial values, followed by the utilization of the Levenberg–Marquardt algorithm to derive a precise solution. Experimental validation through both simulations and experiments confirms the effectiveness of the proposed method. The results demonstrate its capability to overcome the challenges faced by a single-point localization method in the presence of some errors in geomagnetic field estimation. In comparison to traditional two-point localization methods, the proposed method exhibits the highest precision. The localization outcomes under different noise conditions underscore the robust noise resistance and resilience of the proposed method.

The main motive of this paper is to control a nonlinear process tank system using an intelligent neuro-controller-based Artificial Neural Network (ANN). To reduce the mean squared error Proportional–Integral–Derivative (PID) and fuzzy controllers were evaluated with Bayesian Regularisation. Moreover, Bayesian regularization can also disclose potentially complex relationships, where it finds its application in quantitative research resulting in robust structure, thereby justifying its usage in the proposed system. Here the network training was based on the Levenberg–Marquardt algorithm. Two neural controllers were employed to emphasize the plant’s output response during step and nonlinear responses.The output of the neuro-controller was found to have a decreased overshoot time and undershoot time. The results of the proposed method’s settling time, overshoot, and undershoot were compared. The comparative results indicate a better performance of the proposed model. The MATLAB platform was used to complete the entire project.

A solar air heater (SAH) is a unique form of solar thermal collector that utilizes solar energy emitted from the sun to produce heated air. Various experimental and theoretical investigations have been undertaken to improve the poor thermal performance of SAHs. The difficulties related to these studies drew attention toward a reliable soft computing technique exemplified by the Artificial Neural Network (ANN) technique. The current work applied actual meteorological data from Miskolc City, Hungary, to an ANN model with the structure of a Multi-layer Perceptron (MLP) to forecast the energy performance of a V-corrugated solar-powered air heater. Seven input parameters and one output parameter make up the ANN structure, with a single hidden layer. For the purpose of selecting the most effective network for predicting output parameters, ten neurons have been assessed. The suggested ANN model was trained with 336 data sets using the Levenberg-Marquardt (LM) learning technique. The comparison of anticipated and real thermal performance values shows a very good agreement. The statistical error analysis showed that the optimal ANN model structure of 7-8-1 can reliably and accurately predict SAH's thermal performance and thus it can save both time and cost. [ABSTRACT FROM AUTHOR]

The application of the method of phase-amplitude functions to the calculation of neutron-transmission processes in layered media containing highly absorbent elements is described. This method allows us to simultaneously calculate the reflection, transmission and absorption coefficients for neutrons. It requires less computing resources than other algorithms. A generalization of the method to matrix equations used in polarized neutron reflectometry is also presented. Examples of calculations of various characteristics of neutron transmission for layered resonator-type systems with a potential well are given. [ABSTRACT FROM AUTHOR]

The heat and mass transfer within non-Newtonian fluid flow results in complex mathematical equations and solution in this regard remains a challenging task for researchers. The present paper offers a numerical solution for the non-Newtonian flow field by using Artificial neural networking (ANN) model with the Levenberg Marquardt training technique. To be more specific, we considered thermally magnetized non-Newtonian flow headed for inclined heated surfaces. The flow is carried with viscous dissipation, stagnation point, heat generation, mixed convection, and thermal radiation effects. The concentration aspects are entertained by the owing concentration equation. The shooting method is used to solve the mathematical flow equations. The quantity of interest includes the temperature and heat transfer coefficient. Two different artificial neural networking models have been built. The training of networks is done by use of the Levenberg Marquardt technique. The values of the coefficient of determination suggest artificial neural networks as the best method for predicting the Nusselt number at both surfaces. The thermal radiation parameter and Prandtl number admit a direct relationship to the Nusselt number while the differing is the case for variable thermal conductivity and Casson parameters. Further, by using Nusselt number (NN)-ANN models, we found that for cylindrical surface, the strength of the NN is greater than the flat surface. [ABSTRACT FROM AUTHOR]

In this study, an artificial neural network (ANN) and an adaptive neuro-fuzzy inference system (ANFIS) were used to predict the adsorption potential of an adsorbent for the removal of chromium (VI) from an aqueous solution. Four operational variables were studied to assess their impact on the adsorption study in the ANFIS model: initial Ni (II) concentration (mg/L), pH, contact duration (min), and adsorbent dose (mg/L). To build the ANN model, 70% of the data was used for training and 15% for testing and validation. The network was trained using feedforward propagation and the Levenberg–Marquardt algorithm. The regression coefficients (R2) for the ANFIS and ANN models were 0.99 and 0.98, respectively. The results show good agreement between the model-predicted and experimental data, indicating that the models are appropriate and compatible. The RMSE between the predicted and observed removal percentage values for the ANFIS model was 0.008, whereas the RMSE for the ANN model was 0.06. The AARE values between the predicted and experimental removal percentage values for the ANFIS and ANN models were determined to be 0.009 and 0.045, respectively. The MSE vales between the predicted and experimental removal percentages for the ANFIS and ANN models were found to be 0.002 and 0.035, respectively. The optimum conditions were as follows: pH 6, an initial concentration of 275 mg/L, a contact time of 60 min, and a dosage of 12.5 mg/L; the absorption was 91.00%. [ABSTRACT FROM AUTHOR]

Purpose: It is very important to identify the material parameters of composites efficiently and accurately for the dynamic analysis and response prediction of composite structures. In this paper, a high-precision and efficient multi parameter synchronous identification method is proposed for fiber reinforced laminates. Methods: Based on the first-order shear theory and considering the influence of fiber angle, the constitutive model of fiber reinforced laminated composite in any direction is established by using energy method. The model includes four mechanical parameters in a single plane to accurately obtain the anisotropic material parameters. To ensure the accuracy of identification and further accelerate the convergence speed, the Levenberg Marquardt optimization algorithm is innovatively improved, that is, the decision principles of the iterative step and search range are proposed. A detailed parameter identification procedure is proposed, which can identify the four anisotropic parameters once from the modal data of composite plates. Results: Based on experimental tests, the identification method proposed in this paper is used to identify the anisotropic material parameters of laminated composite plates with orthogonal laminated structure and needle structure. Then, the identification process and results of this method are compared with those of the Genetic Algorithm, which verify the accuracy and efficiency of this identification method. Finally, the influences of fiber angle and boundary conditions on the natural frequency are analyzed theoretically. Conclusion: The identification efficiency was doubled that compared with the Genetic Algorithm. The parameter identification method proposed has a good application prospect for other types of composite materials. [ABSTRACT FROM AUTHOR]