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The water quality index has been universally accepted as an indicator to represent the water quality status of the surface water body comprehensively. The prevalent conventional Water Quality Indices (WQIs) suffer from limitations such as 'eclipsing' and 'ambiguity'. Artificial intelligence techniques such as artificial neural networks (ANNs) have gained importance to overcome the limitations of conventional WQIs. In the present study, the Levenberg Marquardt (LM) algorithm and the Scaled Conjugate Gradient (SCG) algorithm have been compared to develop WQI based on the ANN approach (i.e ANNWQI). It is observed that the LM algorithm outperforms the SCG algorithm for prediction of ANNWQI of Indian streams, while the Bayesian Regularization algorithm has not been found suitable for the same purpose in the present study. It is also observed that both LM and SCG algorithm gives robust predictions when the hidden layer contains ten neurons. The combination of data set partitioning of training (75%), Validation (15%), and testing (10%) have been found to give the robust performance of prediction of ANNWQI for Indian streams. The predicted ANNWQI model using the LM algorithm has a very high correlation with the measured WQI values and therefore recommended to be adopted as an effective alternative, to avoid lengthy calculations involved in prevalent conventional WQI.

In the artificial neural networks domain, the Levenberg-Marquardt technique is novel with convergent stability and generates a numerical solution of the wire coating system for Sisko fluid flow (WCS-SFF) through regression plots, histogram representations, state transition measures, and means squared errors. In this paper, the analysis of fluid flow problem based on WCS-SFF is studied with a new application of intelligent computing system via supervised learning mechanism using the efficacy of neural networks trained by Levenberg-Marquardt algorithm (NN-TLMA). The original mathematical formulation in terms of PDEs for WCS-SFF is converted into dimensionless nonlinear ODEs. The data collection for the projected NN-TLMA is produced for parameters associated with the system model WCS-SFF influencing the velocity using the explicit Runge-Kutta technique. The training, validation, and testing processes of NN-TLMA are utilized to evaluate the obtained results of WCS-SFF for various cases, and a comparison of the obtained results is performed with reference data set to check the accuracy and effectiveness of the proposed algorithm NN-TLMA for the analysis of non-Newtonian fluid problem-related WCS-SFF. The proposed NN-TLMA for solving the WCS-SFF is effectively confirmed through state transition dynamics, mean square error, regression analyses, and error histogram studies. The powerful consistency of suggested outcomes with reference solutions indicates the validity of the framework, and the accuracy of 10 - 8 to 10 - 6 is also achieved.

This paper studies the ability of the ANN to predict the pneumatic conveying performance of powders. At high air velocity, the flow is dilute. But at low air velocities it is fluidized dense. Fluidized dense flow involves several complex interactions among gas, particle and wall. But in dilute flow, the particle-particle interaction is less. Implementation of these interactions in a model is difficult. Experimental data available for pneumatic conveying were used to train the network and then predict the pressure drop. Three different training methods Levenberg Marquardt, Bayesian Regularization and Scaled Conjugate Gradient are used. The BR method takes more time for analysis, but it gives better results than others when sample size is small and noisy. For larger sample size the LM method gives better results than the other two methods. The model is also predicts the pressure drop within ±10% error margin under length scale-up conditions.

The present investigations are related to design an integrated computing numerical approach through Levenberg–Marquardt backpropagation (LMB) neural networks (NNs), i.e., LMB-NNs. The designed LMB-NNs approach is presented to solve the fourth-order nonlinear system of Emden–Fowler model (FO-SEFM). The solution of six different examples based on the FO-SEFM using the designed methodology LMB-NNs is numerically treated along with the discussion of singular point and shape factor. The comparison of the obtained results from the LMB-NNs and the exact solutions of each example has been presented. To evaluate the approximate results of the FO-SEFM for different problems, the testing, training, and authentication procedures are accompanied to adapt the NNs by reducing the functions of mean square error (MSE) through the LMB. The proportional investigations and performance studies based on the results of error histograms, MSE, regression, and correlation establish the effectiveness and correctness of the designed LMB-NNs approach.

It is essential to develop an accurate model of proton exchange membrane fuel cell (PEMFC) for a reliable operation and analysis, in which unknown parameters usually need to be determined. The inherent nonlinear, strong coupling, and diversification of PEMFC model seriously hinder traditional methods to identify the parameters. For the sake of overcoming these thorny obstacles, Levenberg-Marquardt backpropagation (LMBP) algorithm based on artificial neural networks (ANNs) is proposed for PEMFC parameter identification. Furthermore, the performance of LMBP is thoroughly evaluated and compared with four typical meta-heuristic algorithms under three cases. Simulation results indicate that LMBP performs a higher accuracy and faster speed for parameter identification. In particular, accuracy and convergence speed can achieve as much as 99.8% and 95.9% growth via LMBP, respectively.

The measurement of discharge plays an important role in the design of open channels. Direct measurements of discharges in large canals and rivers are not feasible because of high flow. Weirs are the most widely used discharge-measuring device for open channels. In this study, the experimental study along with the modeling of discharge through a sharp-crested triangular weir using ANN model has been conducted. The sharp-crested triangular weirs having apex angles 30°, 45°, 60°, 75°, 90° and weir heights 15 cm, 18 cm, and 20 cm have been used in this study. The experiments were conducted for each combination of weir angle and weir height. The head above the weir crest was measured for all such combinations of apex angles and weir heights for different discharges. These experimental data are then used to train the ANN model to predict the discharge over a sharp-crested triangular weir. The Levenberg–Marquardt algorithm has been used as training algorithm. The MSE and R have been used as statistical parameters to judge the performance of ANN model. The ANN model terminates after 18 epochs and the MSE obtained for training, validation and testing are 8.477e − 08, 1.471 e − 07 and 1.325 e − 07, respectively. The corresponding R values obtained for training, validation and testing are 0.9987, 0.9973 and 0.9962, respectively. It was also observed that the predicted discharge stays within the range of ± 5% of the experimental discharge value. The model performance results are encouraging and conclusive and the developed ANN model may be used to predict the discharge over sharp-crested triangular weir precisely.

A lot of neural network training algorithms on prediction exist and these algorithms are being used by researchers to solve evaluation, forecasting, clustering, function approximation etc. problems in traffic volume congestion. This study is aimed at analysing the performance of traffic congestion using some designated neural network training algorithms on traffic flow in some selected corridors within Akure, Ondo state, Nigeria. The selected corridors were Oba Adesida road, Oyemekun road and Oke Ijebu road all in Akure. The traffic flow data were collected manually with the help of field observers who monitored and record traffic movement along the corridors. To accomplish this, three common training algorithms were selected to train the traffic flow data. The data were trained using Bayesian Regularization (BR), Scaled Conjugate Gradient (SCG) and Levenberg-Marquardt (LM) training algorithms. The outputs/performances of these training functions were evaluated by using the Mean Square Error (MSE) and Coefficient of Regression (R) to find the best training algorithms. The results show that, the Bayesian regularization algorithm, performs better with MSE of 2.37e-13 and R of 0.9999 than SCG and LM algorithms.

We propose, in this paper, a novel technique for large Laplacian boundary deformations using estimated rotations. The introduced method is used in the domain of Region of Interest (ROI) to align features of mesh based on Multi Mother Wavelet Neural Network (MMWNN) structure found in several mother wavelet families. The wavelet network allows the alignment of the characteristic points of the original mesh towards the target mesh. The key component of our correspondence scheme is a deformation energy that penalizes geometric distortion, encourages structure preservation and simultaneously allows mesh topology changes. To ensure the design of wavelet neural network architecture, an optimization algorithm should be applied to estimate and optimize the network parameters. Therefore, we compare our approach of 3d mesh deformation using MMWNN architecture based on genetic algorithm and our approach relying on Levenberg-Marquardt Method. We also discuss the existing comparison metrics for static and deformed triangle meshes employing the two mentioned approaches. Besides, we enumerate their strengths, weaknesses and relative performance.

Fiber metal laminate constants of the metallic sheet and the fiber-reinforced composite sheet. FMLs can undergo delamination under transverse loads. Therefore, their nominal stress and energy relea...

Structured Tucker tensor decomposition models complete or incomplete multiway data sets (tensors), where the core tensor and the factor matrices can obey different constraints. The model includes block-term decomposition or canonical polyadic decomposition as special cases. We propose a very flexible optimization method for the structured Tucker decomposition problem, based on the second-order Levenberg-Marquardt optimization, using an approximation of the Hessian matrix by the Krylov subspace method. An algorithm with limited sensitivity of the decomposition is included. The proposed algorithm is shown to perform well in comparison to existing tensor decomposition methods.

The recent COVID-19 outbreak has severely affected people around the world. There is a need of an efficient decision making tool to improve awareness about the spread of COVID-19 infections among the common public. An accurate and reliable neural network based tool for predicting confirmed, recovered and death cases of COVID-19 can be very helpful to the health consultants for taking appropriate actions to control the outbreak. This paper proposes a novel Nonlinear Autoregressive (NAR) Neural Network Time Series (NAR-NNTS) model for forecasting COVID-19 cases. This NAR-NNTS model is trained with Scaled Conjugate Gradient (SCG), Levenberg Marquardt (LM) and Bayesian Regularization (BR) training algorithms. The performance of the proposed model has been compared by using Root Mean Square Error (RMSE), Mean Square Error (MSE) and correlation co-efficient i.e. R-value. The results show that NAR-NNTS model trained with LM training algorithm performs better than other models for COVID-19 epidemiological data prediction.

For the fractional-order Hammerstein system with white noise, the difficulty of identification is that the parameters of the linear and the nonlinear blocks and the fractional order are unknown and...

We show that there are infinitely many valid scaled gradients which can be used to train a neural network. A novel training method is proposed that finds the best scaled gradients in each training iteration. The method’s implementation uses first order derivatives which makes it scalable and suitable for deep learning and big data. In simulations, the proposed method has similar or less testing error than conjugate gradient and Levenberg Marquardt. The method reaches the final network utilizing fewer multiplies than the other two algorithms. It also works better than conjugate gradient in convolutional neural networks.

Existing generator parameterization methods, typically developed for large turbine generator units, are difficult to apply to small kW-level diesel generators in microgrid applications. This paper presents a model parameterization method that estimates a complete set of kW-level diesel generator parameters simultaneously using only load-step-change tests with limited measurement points. This method provides a more cost-efficient and robust approach to achieve high-fidelity modeling of diesel generators for microgrid dynamic simulation. A two-stage hybrid box-constrained Levenberg-Marquardt (H-BCLM) algorithm is developed to search the optimal parameter set given the parameter bounds. A heuristic algorithm, namely Generalized Opposition-based Learning Genetic Algorithm (GOL-GA), is applied to identify proper initial estimates at the first stage, followed by a modified Levenberg-Marquardt algorithm designed to fine tune the solution based on the first-stage result. The proposed method is validated against dynamic simulation of a diesel generator model and field measurements from a 16kW diesel generator unit., Comment: 9 pages, 9 figures, accepted by IEEE Transactions on Smart Grids

This paper considers the tensor split feasibility problem. Let C and Q be non-empty closed convex set and $${\mathcal {A}}$$ be a semi-symmetric tensor. The tensor split feasibility problem is to find $$x\in C $$ such that $${\mathcal {A}} x^{m-1} \in Q$$ . If we simply take this problem as a special case of the nonlinear split feasibility problem, then we can directly get a projection method to solve it. However, applying this kind of projection method to solve the tensor split feasibility problem is not so efficient. So we propose a Levenberg–Marquardt method to achieve higher efficiency. Theoretical analyses are conducted, and some preliminary numerical results show that the Levenberg–Marquardt method has advantage over the common projection method.

The main objective of the present research is to combine the effect of scale thickness on the flow pattern and characteristics of two-phase flow that is used in oil industry. In this regard, an intelligent nondestructive technique based on combination of gamma radiation attenuation and artificial intelligence is proposed to determine the type of flow pattern and gas volume percentage in two phase flow independent of petroleum pipeline’s scale layer thickness. The proposed system includes a dual energy gamma source, composed of Barium-133 and Cesium-137 radioisotopes, and two sodium iodide detectors for recording the transmitted and scattered photons. Support Vector Machine was implemented for regime identification and Multi-Layer Perceptron with Levenberg Marquardt algorithm was utilized for void fraction prediction. Total count in the scattering detector and counts under photo peaks of Barium-133 and Cesium-137 were assigned as the inputs of networks. The results show the ability of presented system to identify the annular regime and measure the void fraction independent of petroleum pipeline’s scale layer thickness.

A hybrid numerical-analytical solution to fluid flow in irregularly-shaped microchannels has been developed. The solution is based on the Generalized Integral Transform Technique (GITT) applied to a trapezoid-like duct to account for fabrication imperfections, as commonly found in commercially manufactured microchannels. With this approach, the eigenseries expansion is done using a 2D eigenfunction basis, constructed from a combination of simple 1D eigenfunctions defined within the original irregular domain. In order to improve convergence, a new filtering scheme based on an analytical solution to the problem in a rectangular channel, which is distorted to match the irregular domain, is employed. The solution is tested on a real microchannel geometry, obtained from a SEM image, and compared with micro-PIV measurements for the flow field in the same channel. In addition, the actual velocimetry data is input to an inverse problem implementation for recovering geometric parameters related to the irregular geometry using the GITT results as the forward solution. The numerical results obtained with the GITT presented a very satisfactory convergence, and the inverse solution was able to recover the channel geometric parameters with very reasonable accuracy.

Improving and increasing metal cutting process efficiency requires an in-depth knowledge of the cutting process, as well as the development/application of an efficient modeling technique, capable of forming the core tools for planning, scheduling, and integration of the machining processes. This study evaluates the application of Levenberg Marquardt (LM) and Scaled Conjugate Gradient (SCG) training algorithms of artificial neural networks in the modeling and prediction of metal removal rate (MRR) and average surface roughness (Ra) in the turning of cylindrical mild steel. The neural network models were trained using a set of experimental data consisting of the input parameters: cutting speed, depth of cut, and feed rate. Based on the graphical and statistical results, the LM offered the best accuracy in terms of the model fitting, RMSE and R2 obtained. For the LM algorithms, the least RMSE values of 1.7809 × 10−1, 2.6805 × 10−1, and 1.5815 × 10−1 were obtained for the training, validation, and test data respectively, and for the SCG algorithm, least RMSE values of 1.7809 × 10−1, 2.6805 × 10−1, and 1.5815 × 10−1 were recorded. Comparing both algorithms, the Levenberg Marquardt algorithm recorded the least average in terms of the number of the epoch, and RMSE value and at the same time the best performance in terms of good fitting.

Achieving accurate clock synchronization may not be feasible for distributed multiple-input multiple-output (MIMO) radar systems with non-ideal clocks of the sensors. In this paper, the problem of target localization and clock synchronization in distributed MIMO radar systems in presence of time synchronization errors is addressed by utilizing time delay measurements. Firstly, the necessity to consider time synchronization errors when locating a target is illustrated by analyzing the increase in Cramer-Rao lower bound (CRLB) of the target position due to the time synchronization error. Then, a self-synchronized localization framework based on the hybrid maximum likelihood and maximum a posteriori estimator is proposed to estimate the target position and time synchronization error sequentially. Specifically, a method based on the levenberg marquardt algorithm and an analytical solution are developed respectively to estimate the target position, and a combination strategy is recommended further based on the two methods to achieve a more accurate target position estimate. The time synchronization error is figured out then by utilizing the target position estimate. Meanwhile, the closed-form solution of estimating the target position and time synchronization error is analytically proved to be approximately unbiased and can attain the CRLB under weak noise conditions. It is demonstrated through numerical simulations that the combination strategy has better estimation performance than the two methods. Simultaneously, simulation results show that the proposed self-synchronized localization method outperforms the state-of-the-art algorithms in the target position and time synchronization error estimation accuracy.

Due to advances in computation, the computer system needs sufficient input data, and it allows it a better computer tool for efficient operation of the human-computer, such as the fast-moving Automatic Speech Recognition System. This paper aims in particular to provide an insight into the contact distance between humans and computers in unmanned aircraft vehicles. While there are several algorithms, a critical analysis of algorithms suitable for large-scale applications is still important. The aircraft without a human pilot on board is an unmanned aerial vehicle. Continuous Word Recognition systems for voice enhancement (commanding) based cockpit control are commonly used in unmanned aircraft. The goal is to evaluate the efficiency of the Levenberg Marquardt algorithm by using these recognition systems. To do this, optimal preparation can be selected using neural networks to increase the machine recognition effectiveness. MATLAB verify simulated findings and tests show that a high accuracy of recognition of over 87 percent is obtained.

The present paper investigates the influence of process parameters of friction stir welding (FSW) technique on the resulting microstructure and mechanical characteristics of the fabricated joints. The material considered for FSW is AA1100 aluminium rolled plates that are joined by using a square pin tool. In this research, parametric characterization of surface properties has been carried out by simulation using an artificial neural network (ANN) that is designed with multi layer, multi neuron and logistic sigmoid activation function. Levenberg-Marquardt algorithm including second-order error optimization has been selected to train the ANN. The ANN simulation has been done to estimate the tensile and yield strength, elongation, flexure stress and grain size with respect to tool rotational speed (RS), travel speed (TS) and plunge depth (PD), which are the process parameters of FSW process and also find an optimum condition which is essential to save energy and resources. This process finds its application in various automotive industries as there is a wide use of aluminium in the automobiles and aircrafts.

The management of the activities which characterize the lifecycle of a product could be challenging, hence, a well-structured Product Lifecycle Management System (PLMS) with Artificial Intelligence (AI) capability can offer a sustainable solution in this regard. This will promote data driven maintenance because AI and data analysis can drive the activities of the entire product’s lifecycle. The aim of this study is to demonstrate the use of AI for enhancing products’ performance during its use phase in the products’ life cycle and to develop a framework for the proposed PLMS and AI capability. The bearing component of a railcar was used as a case study. The temperature data of the bearing component employed were obtained from primary and secondary sources and were pre-processed in order to extract features and indicators for the training and predictive model development. The acquisition of the input data was followed by data pre-processing to remove noise and iterative training to obtain the predictive model. The training was done using the Levenberg Marquardt algorithm in a MATLAB 2018a environment in order to predict future temperature variations and the remaining useful life of the bearing. The results obtained indicated that the AI is suitable for condition based monitoring and prediction of the time to failure as well as the Remaining Useful Life (RUL) of the railcar bearing. It is envisaged that with the AI capability integrated into the PLMS will enhance components performance through effective monitoring during its use phase.

PurposeThe purpose of this paper is to realize an effective hybrid modeling (empirical-geometric) in order to describe the real behavior of the average roughness variation of the workpiece surface in turning with an elementary operation of superfinishing, using different analytic methodologies. The previous works are limited to describe the roughness for the usual elementary operations, citing the roughing and the semi-finishing, while this analysis builds technical rails for the industrialists in order to well conduct the operation of superfinishing in turning, by choosing the cutting parameters from the proposed model.Design/methodology/approachA statistical analysis of the average roughness measurements capability study, by the statistical process control method SPC and the ANN artificial neuron network, Levenberg–Marquardt's methods modified Monte Carlo SRM response surface.FindingsThe objective of this work was to describe the average roughness generated by the penetration of the cutting tool into a part in superfinishing turning. First, the authors used artificial colony analysis to determine optimal cutting conditions in order to have an average roughness lower than 0.8 µm. The cutting conditions selected: (1) the feed rate f ϵ [0.05; 0.2] mm/rev; (2) the pass depth ap ϵ [0.25; 1] mm; (3) the corner radius re = 0.2 mm and (4) cutting speed Vc ϵ [75; 100] m/min.Originality/valueThis work consists to realize an effective hybrid modeling (empirical-geometric) in order to describe the real behavior of the average roughness variation of the workpiece surface in turning with an elementary operation of superfinishing, using different analytic methodologies. The previous works are limited to describe the roughness for the usual elementary operations, citing the roughing and the semi-finishing, while this analysis builds technical rails for the industrialists in order to well conduct the operation of superfinishing in turning, by choosing the cutting parameters from the proposed model.

The precision of the camera calibration is one of the key factors that affect attitude measurement accuracy in many computer vision tasks. This study proposes a new calibration approach for binocular cameras. Firstly, based on singular value decomposition, the best transformation matrix to the essential matrix is approximated as the initial guess, which is solved in using the Frobenius norm. Secondly, the initial guess is refined through maximum likelihood estimation. A new calculating expression is derived for computing the relative position matrix of the binocular cameras. The Levenberg–Marquardt algorithm is then implemented to refine the initial guess. Large sets of synthesised and real point correspondences were tested to demonstrate the validity of the proposed method. Extensive experiments demonstrated that the proposed method outperforms the state-of-the-art methods. The error rate of the proposed method was 0.5% for the length test and about 1% for the angle test at a range of 1 m. This method can advance three-dimensional (3D) computer vision one additional step from laboratory environments to real-world use.

Recent developments in internal combustion engines have heightened the need for alternative biofuel. In the last five years, acetone-butanol-ethanol (ABE) has been extensively studied as a promisin...

To save the calculations of Jacobian, a multi-step Levenberg-Marquardt method named Shamanskii-like LM method for systems of nonlinear equations was proposed by Fan (2013). Its convergence properties have been proved by using a trust region technique under the local error bound condition. However, the authors wonder whether the similar convergence properties are still true with standard line searches since the direction may not be a descent direction. For this purpose, the authors present a new nonmonotone m-th order Armijo type line search to guarantee the global convergence. Under the same condition as trust region case, the convergence rate also has been shown to be m + 1 by using this line search technique. Numerical experiments show the new algorithm can save much running time for the large scale problems, so it is efficient and promising.

Backpropagation Neural Network (BPNN) is an artificial intelligence technique that has seen several applications in many fields of science and engineering. It is well-known that, the critical task in developing an effective and accurate BPNN model depends on an appropriate training algorithm, transfer function, number of hidden layers and number of hidden neurons. Despite the numerous contributing factors for the development of a BPNN model, training algorithm is key in achieving optimum BPNN model performance. This study is focused on evaluating and comparing the performance of 13 training algorithms in BPNN for the prediction of blast-induced ground vibration. The training algorithms considered include: Levenberg-Marquardt, Bayesian Regularisation, Broyden–Fletcher–Goldfarb–Shanno (BFGS) Quasi-Newton, Resilient Backpropagation, Scaled Conjugate Gradient, Conjugate Gradient with Powell/Beale Restarts, Fletcher-Powell Conjugate Gradient, Polak-Ribiére Conjugate Gradient, One Step Secant, Gradient Descent with Adaptive Learning Rate, Gradient Descent with Momentum, Gradient Descent, and Gradient Descent with Momentum and Adaptive Learning Rate. Using ranking values for the performance indicators of Mean Squared Error (MSE), correlation coefficient (R), number of training epoch (iteration) and the duration for convergence, the performance of the various training algorithms used to build the BPNN models were evaluated. The obtained overall ranking results showed that the BFGS Quasi-Newton algorithm outperformed the other training algorithms even though the Levenberg Marquardt algorithm was found to have the best computational speed and utilised the smallest number of epochs. Keywords: Artificial Intelligence, Blast-induced Ground Vibration, Backpropagation Training Algorithms

This paper presents a local modification of the Levenberg-Marquardt algorithm (LM). First, the mathematical basics of the classic LM method are shown. The classic LM algorithm is very efficient for learning small neural networks. For bigger neural networks, whose computational complexity grows significantly, it makes this method practically inefficient. In order to overcome this limitation, local modification of the LM is introduced in this paper. The main goal of this paper is to develop a more complexity efficient modification of the LM method by using a local computation. The introduced modification has been tested on the following benchmarks: the function approximation and classification problems. The obtained results have been compared to the classic LM method performance. The paper shows that the local modification of the LM method significantly improves the algorithm’s performance for bigger networks. Several possible proposals for future works are suggested.

The state of health (SOH) of lithium-ion (Li+) battery prediction plays significant roles in battery management and the determination of the durability of the battery in service. This study used segmentation-type anomaly detection, the Levenberg–Marquardt (LM) algorithm, and multiphase exponential regression (MER) model to determine SOH of the Li+ batteries. By determining the changepoint boundaries using the characteristic values such as voltage transition rate (VTR), temperature transition rate (TTR), and charge capacities of the Li+ battery at the changepoint timestamps, we determined the parametric values of the biphasic MER. The characteristic transition rate values, which depend on the transition probabilities of the rolling standard deviations of the measured voltage and temperature, were later utilized with the matching charge capacities to model various training–testing dataset combinations. This helped to estimate the SOH of the battery at different life-cycle phases. This study also developed a technique for real-time estimation of the remaining useful life of the battery by using the MER model parameters, VTR, and TTR which were previously unseen parametric values of the Li+ battery. The result obtained from the proposed model indicates that our technique will be effective for online SOH estimation of Li+ batteries.

An outstanding calibration algorithm is the most important factor that affects the precision of attitude measurement. This study proposes a non-linear optimisation algorithm to refine the solutions of the initial guess obtained using the Zhang's technique, the Bouget's technique, or the Hartley's algorithm. Large sets of point correspondences were adopted to test the validity of the proposed method. Extensive practical experiments demonstrated that the proposed method can significantly improve the accuracy of calibration and ultimately obtains higher measurement precision. The error of the reprojection in the proposed method was

Purpose As a result of the deregulations in the power system networks, diverse beneficial operations have been competing to optimize their operational costs and improve the consistency of their electrical infrastructure. Having certain and comprehensive state assessment of the electrical equipment helps the assortment of the suitable maintenance plan. Hence, the insulation condition monitoring and diagnostic techniques for the reliable and economic transformers are necessary to accomplish a comprehensive and proficient transformer condition assessment. Design/methodology/approach The main intent of this paper is to develop a new prediction model for the aging assessment of power transformer insulation oil. The data pertaining to power transformer insulation oil have been already collected using 20 working power transformers of 16-20 MVA operated at various substations in Punjab, India. It includes various parameters associated with the transformer such as breakdown voltage, moisture, resistivity, tan δ, interfacial tension and flashpoint. These data are given as input for predicting the age of the insulation oil. The proposed aging assessment model deploys a hybrid classifier model by merging the neural network (NN) and deep belief network (DBN). As the main contribution of this paper, the training algorithm of both NN and DBN is replaced by the modified lion algorithm (LA) named as a randomly modified lion algorithm (RM-LA) to reduce the error difference between the predicted and actual outcomes. Finally, the comparative analysis of different prediction models with respect to error measures proves the efficiency of the proposed model. Findings For the Transformer 2, root mean square error (RMSE) of the developed RM-LA-NN + DBN was 83.2, 92.5, 40.4, 57.4, 93.9 and 72 per cent improved than NN + DBN, PSO, FF, CSA, PS-CSA and LA-NN + DBN, respectively. Moreover, the RMSE of the suggested RM-LA-NN + DBN was 97.4 per cent superior to DBN + NN, 96.9 per cent superior to PSO, 81.4 per cent superior to FF, 93.2 per cent superior to CSA, 49.6 per cent superior to PS-CSA and 36.6 per cent superior to LA-based NN + DBN, respectively, for the Transformer 13. Originality/value This paper presents a new model for the aging assessment of transformer insulation oil using RM-LA-based DBN + NN. This is the first work uses RM-LA-based optimization for aging assessment in power transformation insulation oil.

In this study, a new method employing scattering parameters (SPs) method, genetic algorithm (GA) and Levenberg–Marquardt algorithm (LM) is proposed for modelling conducted electromagnetic interference (EMI) noise source impedance. On the basis of the impedance information extracted by traditional SP method, GA is adopted to optimise the impedance information by taking advantage of the fast convergence speed. The obtained values of the RCL parameter are used as a set of initial values. Then, by using the advantage of the high precision of the LM, the initial values obtained by the GA are iteratively calculated. Better results can be obtained by using this combination method. This method improves the processing accuracy while ensuring the processing speed and contributes to the design of conduction EMI filter.

A domestic cookie baking process was modeled using nonlinear forward and inverse models to predict surface temperature, moisture content and browning index that describe the baking quality of the end product. The baking processes were carried out at different oven temperatures (160, 180, 200 °C) and the changes in surface temperature, moisture content and browning index were determined to construct the identification models namely nonlinear polynomial models (PLN) and nonlinear artificial-neural network (ANN) model. The parameters of the artificial models were optimized using least-squares estimation and Levenberg-Marquardt optimization, respectively. The predicted baking characteristics in both forward and inverse phases were in good agreement with the measured ones even for the browning index which was difficult to model because of the its nonminimum-phase dynamics. The application results indicated that the developed intelligient models were very accurate, having low root mean-squared errors, the ANN model approximated the desired values better than the PLN models for all the state variables. Thus, the designed ANN models are applicable for the automatized industrial and domestic oven designs of the future.

Purpose Weather forecasting is the trending topic around the world as it is the way to predict the threats posed by extreme rainfall conditions that lead to damage the human life and properties. These issues can be managed only when the occurrence of the worse weather is predicted in advance, and sufficient warnings can be executed in time. Thus, keeping in mind the importance of the rainfall prediction system, the purpose of this paper is to propose an effective rainfall prediction model using the nonlinear auto-regressive with external input (NARX) model. Design/methodology/approach The paper proposes a rainfall prediction model using the time-series prediction that is enabled using the NARX model. The time-series prediction ensures the effective prediction of the rainfall in a particular area or the locality based on the rainfall data in the previous term or month or year. The proposed NARX model serves as an adaptive prediction model, for which the rainfall data of the previous period is the input, and the optimal computation is based on the proposed algorithm. The adaptive prediction using the proposed algorithm is exhibited in the NARX, and the proposed algorithm is developed based on the Grey Wolf Optimization and the Levenberg–Marqueret (LM) algorithm. The proposed algorithm inherits the advantages of both the algorithms with better computational time and accuracy. Findings The analysis using two databases enables the better understanding of the proposed rainfall detection methods and proves the effectiveness of the proposed prediction method. The effectiveness of the proposed method is enhanced and the accuracy is found to be better compared with the other existing methods and the mean square error and percentage root mean square difference of the proposed method are found to be around 0.0093 and 0.207. Originality/value The rainfall prediction is enabled adaptively using the proposed Grey Wolf Levenberg–Marquardt (GWLM)-based NARX, wherein an algorithm, named GWLM, is proposed by the integration of Grey Wolf Optimizer and LM algorithm.

Non-linear least squares problems arise from data fitting have received recently a lot of attention, particularly for the estimates of the model parameters over networked systems. Although the diffusion Gauss-Newton method offers many advantages for solving the non-linear least squares problem in wireless sensor network to estimate target position parameter, there are some key challenges when applying it to practice, including singularity of Gauss-Newton Hessian, selection to constant step sizes and steady state oscillation. These remaining issues lead to obvious performance degradation such as high computational cost, vulnerability to step size change and resulting instability on estimation.In this paper, to eliminate the singularity, we develop a diffusion Levenberg-Marquardt method such that the problem of constant step size is also addressed together. Then, to reach agreement on estimated vector, a consensus implementation is further proposed, thus eliminating the oscillation during steady state. Consequently, the proposed consensus-based diffusion Levenberg-Marquardt method provides a general solution for the non-linear least squares problems with an objective that takes the form of a sum of squared residual terms. By applying to collaborative localization and distributed optimization arise in large scale machine learning, simulation results confirm the effectiveness and wide applicability of proposed method in terms of convergence rate, accuracy and consistency of estimates.

Digital sun sensor is one of the most important sensors used in the Attitude Determination System (ADS) of the satellite. Due to the harsh environmental conditions that exist in the space, various distortions may occur in the sun sensor optical system that lead to the reduced accuracy of this equipment. So, it is necessary to recalibrate the optical parameters of the aforementioned sensors. For this purpose, first a novel attitude independent error model is proposed for the SS-411 sun sensor that includes the central point of the CCD array, installation error, filter thickness and sensor misalignment. So, the mutual interfaces between the sensor parameters are considered in the developed model. In order to extract the sensor parameters, a nonlinear optimization technique called the Levenberg–Marquardt is applied to the developed model as a batch algorithm. In addition, the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF) have been utilized as sequential strategies. It will be shown that by considering a worst case of variation amount for sensor parameters, an accuracy improvement of about 17° is achieved by the developed calibration algorithms. Comparison between the developed algorithms represents that UKF has higher accuracy, shorter time convergence but higher computational load. Keywords: Digital sun sensor, Extended Kalman filter, Levenberg–Marquardt, On-board calibration, Unscented Kalman filter

In this paper, we present an experimental test bench to implement various cooperative control strategies for multi-agent systems, and illustrate its use with experimental results for a source-seeking problem, where a group of small wheeled robots termed as Zooids should locate a source of a given spatial scalar field. This algorithm is implemented as a validation to demonstrate the capabilities of the test bench. We propose to achieve this by utilising an internal target-based position controller, under the assumptions of convexity of the scalar, continuous/discrete field and availability of local measurements of the field, so that agents can calculate its gradient and its Hessian. We then show in experiments, that using estimated gradients and Hessians (with data communicated from neighbours) in the presence of noisy measurements of the field strength provides satisfactory results for convex fields, under various algorithms such as Steepest Descent, Gauss-Newton, Levenberg Marquardt. These algorithms are analysed, and experimental results are discussed.

Although some scholars have established the calculation method of bolt head connection characteristics, the method contains fewer influence factors; the calculation accuracy is not high, and the general applicability is limited. Based on the Levenberg Marquardt optimization algorithms, a more accurate calculation model of bolt head connection stiffness is proposed in this article. The model includes many parameters such as bolt head thickness, equivalent diameter, bolt diameter, thickness of connected parts, elastic modulus of bolt and elastic modulus of connected parts. Through the finite-element verification and comparison with the results of the Fears Alkatan method, the calculation results of the bolt head connection stiffness calculation model in this article are effective and accurate, which provides a universal calculation model for calculating the bolt head connection stiffness of various parameters, and fills the shortage of inaccurate calculation of the current theoretical model of bolt head stiffness.

The learning factories are platform created to provide an effective learning environment that will bring about human capacity development in a bid to bridge the gap between learning and practice. In this study, the training modules involving the Artificial Intelligence (AI) system, which comprises of the Artificial Neural Network (ANN) with dynamic time series model was developed. This is to train maintenance personnel on how to constantly monitor and analyze data from the Internet of Things (IoT) and other sources in order to predict the state and potential failure of a railcar wheel bearing. The modules for training include the data acquisition, pre-processing, network training, features extraction and predictive model modules which are set up to acquaint the personnel in the maintenance section of the rail industry on the use of AI for condition based monitoring and prediction of wheel bearing failure. The demonstration of the training modules was carried out using the past data of the wheel-bearing temperature from a secondary source which was pre-processed and iteratively trained using the Levenberg Marquardt algorithm in a MATLAB 2018a environment in order to predict future temperature variations, the remaining useful life of the bearing and to obtain a predictive model. The result obtained indicates the feasibility of the AI in the diagnosis of the railcar wheel bearing condition, prediction of the Remaining Useful Life (RUL) of the bearing as well as the determination of the optimum time for maintenance.

Most parameter ID methods use least squares criterion to fit parameter values to observed behavior. However, the least squares criterion can be heavily influenced by outlying data or un-modelled effects. In such cases, least squares estimation can yield poor results. Outlying data is often manually removed to avoid inaccurate outcomes, but this process is complex, tedious and operator dependent. This research presents an adaptation of the Levenberg-Marquardt (L-M) parameter identification method that effectively ignores least-square contributions from outlying data. The adapted method (aL-M) is capable of ignoring outlier data in accordance with the coefficient of variation of the residuals and was thus, capable of operator independent omission of outlier data using the 3 standard deviation rule. The aL-M was compared to the original Levenberg-Marquardt (L-M) method in C-peptide, insulin and glucose data. In total three cases were tested: L-M in the full dataset, L-M in the same data where the points that were suspected to be affected by incomplete mixing at the depot site were removed, and the aL-M in the full data set. There were strong correlations between the aL-M and the reduced dataset from [0.85, 0.71] for the clinically valuable glucose parameters. In contrast, the unreduced data yielded poor residuals and poor correlations with the aL-M [0.44, 0.33]. The aL-M approach provided strong justification for consistent removal of data that was deemed to be affected by mixing.

The band interleaved data acquisition system (BI-DAS) is an attractive structure to improve the bandwidth of the acquisition system. However, the non-ideal characteristic of the spectrum analysis filter in BI-DAS results in an overlapping frequency band between two adjacent frequency sub-bands. Phase misalignment (PM) between two sub-bands in the overlapping band may cause those signals canceled or partially canceled to each other when sub-bands’ signal are merged. In this paper, a compensation module with a digital all-pass filter (APF) is proposed for the PM of the overlapping bands in BI-DASs. Based on this compensation module, a hybrid Particle Swarm Optimization (PSO) algorithm, along with the Levenberg-Marquardt (LM) algorithm is proposed to design coefficients of the compensation module. The compensation module and corresponding method proposed in this paper are verified in a BI-DAS with 20Gsps sampling rate and 5.5GHz bandwidth. The experimental results show that the proposed compensation module can effectively compensate the PM between the sub-bands in the overlapping band. The proposed hybrid PSO-LM (HPSOLM) algorithm combines the flexibility and reliability inherent in the PSO with the fast convergence and precision of the LM algorithm. It can effectively design the compensation module with stable APF while consuming less time and obtaining better compensation results than the conventional PSO method.

In this paper, the computational strength in terms of soft computing neural networks backpropagated with the efficacy of Levenberg-Marquard training (NN-BLMT) is presented to study the squeezing flow with the heat transfer model (SF-HTM). The governing system of PDEs is reduced to an equivalent system of nonlinear ODEs using similarity transformations. NN-BLMT dataset for all problem scenarios progresses through the standard Adam numerical method by the influence of Prandtl number, Eckert number, and thermal slip. The processing of NN-BLMT training, testing, and validation, is employed for various scenarios and cases to find and compare approximation solutions with reference results. For the fluidic system SF-HTM, convergence analysis based on mean square errors, histogram presentations, and statistical regression plots is considered for the proposed computing infrastructure’s performance in terms of NN-BLMT. Matching of the results for the fluid flow system SF-HTM based on proposed and reference results in terms of convergence up-to 10−07 to 10−03 proves the worth of proposed NN-BLMT.

This study aimed to develop a smart model prediction of strain calculation using fiber optic sensors and neural network. Optical parameters are obtained experimentally on a cantilever beam structure, under static loading conditions. Five variations are used by creating external damage to study strain variations on healthy, single damage and multiple damage beam structures. The strain values were correlated to the set of phase difference and change in intensities by using feed-forward back propagation neural network approach. The strain values using optical parameters were verified with conventional strain gauge measurement and finite element analysis. The neural network simulation provides advance and more accurate correlation results with strain gauge and FEA analysis.

In this paper, novel computing paradigm by exploiting the strength of feed-forward artificial neural networks (ANNs) with Levenberg-Marquardt Method (LMM), and Bayesian Regularization Method (BRM) based backpropagation is presented to find the solutions of initial value problems (IVBs) of linear/nonlinear pantograph delay differential equations (LP/NP-DDEs). The dataset for training, testing and validation is created with reference to known standard solutions of LP/NP-DDEs. ANNs are implemented using the said dataset for approximate modeling of the system on mean squared error based merit functions, while learning of the adjustable parameters is conducted with efficacy of LMM (ANN-LMM) and BRMs (ANN-BRM). The performance of the designed algorithms ANN-LMM and ANN-BRM on IVPs of first, second and third order NP-FDEs are verified by attaining a good agreement with the available solutions having accuracy in the range from 10-5 to 10-8 and are further endorsed through error histograms and regression measures.

Spectral distortion often occurs in spectral data due to the influence of the bandpass function of the spectrometer. Spectral deconvolution is an effective restoration method to solve this problem. Based on the theory of the maximum posteriori estimation, this paper transforms the spectral deconvolution problem into a multi-parameter optimization problem, and a novel spectral deconvolution method is proposed on the basis of Levenberg-Marquardt algorithm. Furthermore, a spectral adaptive operator is added to the method, which improves the effect of the regularization term. The proposed methods, Richardson-Lucy (R-L) method and Huber-Markov spectroscopic semi-blind deconvolution (HMSBD) method, are employed to deconvolute the white light-emitting diode (LED) spectra with two different color temperatures, respectively. The correction errors, root mean square errors, noise suppression ability, and the computation speed of above methods are compared. The experimental results prove the superiority of the proposed algorithm.

This paper deals with a robust complex-valued Levenberg-Marquardt algorithm specially developed for solving ill-conditioned power flow problems. Moreover, it can also be a useful tool for voltage instability and voltage collapse studies. Because power flow models are nonlinear, the Wirtinger calculus is applied to develop iterative algorithms based on Taylor series expansions of nonlinear functions of complex variables and their complex conjugates. Our proposal in complex plane is straightforward derived in rectangular coordinates. Consequently, its performance is compared to the well-known optimized multiplier based load flow method. Aiming this purpose, we show that few changes in the codes are required to transform the complex-valued Newton-Raphson power flow algorithm into the complex-valued Levenberg-Marquardt power flow one. Furthermore, we show that the latter lends itself well to modeling new smart grid technologies while exhibiting a bi-quadratic convergence rate and superior performance as compared to the former procedure. The performance of our proposal is demonstrated and analyzed on well-conditioned IEEE-14, −30, −57 and −118 bus systems and the Brazilian Southern-equivalent system termed SIN-1916 bus. Furthermore, its performance is also demonstrated on the ill-conditioned IEEE-11, −43 bus systems besides the SIN-1916 under stressed operating conditions or higher R / X ratios of transmission lines.

In this paper, we study the convergence rate of the Levenberg-Marquardt (LM) method under the Holderian local error bound condition and the Holderian continuity of the Jacobian, which are more gene...

The longitudinal vibrations of a rod weakened by transverse cracks are considered. Cracks are assumed to be open and modeled by translational springs. The stiffness of the springs corresponds to the size of the cracks. A method has been developed for identifying the number and position of transverse cracks, as well as the stiffness of the corresponding springs according to two spectra that correspond to two types of conditions at the ends of the rod: free—free and fixed—free. The developed method is based on minimizing the objective function that characterizes the difference between the given (measured) natural frequencies and natural frequencies calculated during the implementation of the algorithm. The objective function is minimized using the Levenberg—Marquardt algorithm. Numerical examples are considered. The stability of the obtained results with respect to noise in the initial data is investigated.

The material removal mechanism, submicrostructure of surface and subsurface layers, nanotransformations occurred in surface and subsurface layers during electrical discharge machining two structural materials such as anti-corrosion X10CrNiTi18-10 (12kH18N10T) steel of austenite class and 2024 (D16) duralumin in a deionized water medium were researched. The machining was conducted using a brass tool of 0.25 mm in diameter. The measured discharge gap is 45–60 µm for X10CrNiTi18-10 (12kH18N10T) steel and 105–120 µm for 2024 (D16) duralumin. Surface roughness parameters are arithmetic mean deviation (Ra) of 4.61 µm, 10-point height (Rz) of 28.73 µm, maximum peak-to-valley height (Rtm) of 29.50 µm, mean spacing between peaks (Sm) of 18.0 µm for steel; Ra of 5.41 µm, Rz of 35.29 µm, Rtm of 43.17 µm, Sm of 30.0 µm for duralumin. The recast layer with adsorbed components of the wire tool electrode and carbides was observed up to the depth of 4–6 µm for steel and 2.5–4 µm for duralumin. The Levenberg–Marquardt algorithm was used to mathematically interpolate the dependence of the interelectrode gap on the electrical resistance of the material. The observed microstructures provide grounding on the nature of electrical wear and nanomodification of the obtained surfaces.

The Mediterranean countries' coastal-karstic aquifer systems are facing increased pressure due to seawater intrusion and drought impacts. There is a need to understand better karstic systems' functional mechanisms for developing the most appropriate management scenario of water resources in these systems. In this study, the application of Non-Linear Autoregressive neural networks (NAR) on a dataset from mid-1968 to 1994 was deployed for predicting values of discharge flow rates and salinity of Almyros spring (Heraklion-Crete, Greece). Two neural networks were trained for the prediction of the discharge rates and the chloride concentration. The neural networks operated with the Levenberg–Marquardt algorithm's aid and attained a coefficient of determination R = 0.83, and R = 0.86, respectively, indicating a high degree of prediction capacity.