Levenberg-Marquardt Research Articles

Application of artificial neuronal networks for the prediction of monthly photovoltaic power using tilt angle as input in Rabat city, Morocco

The use of artificial neural networks (ANNs) is attracting interest in the field of renewable energies, particularly for predicting operational parameters of photovoltaic (PV) systems. Thus, the present study aims to develop an ANN model for predicting the output power of a photovoltaic module. In this context, two ANN models with two and three hidden layers, respectively, were trained and validated to predict the average monthly photovoltaic power Pp produced by a 0. 325 kW photovoltaic module by varying the tilt angle from 0° to 90° of Rabat city, Morocco. The training data used in this study include longitude, latitude, calculated photovoltaic power, tilt angle, and months as inputs, while the predicted Pp is the target. These two proposed models are trained using the Levenberg-Marquardt (LM) optimiser. Furthermore, to confirm the reliability of each of these two proposed ANN models, existing photovoltaic power data were used to validate the two proposed models by predicting the average monthly power of the photovoltaic module. For the tilt angle of 34°, which corresponds to the latitude of the city of Rabat, the ANN model with three hidden layers performed better with an R2 value of 0.9997.

Error estimates for simplified Levenberg–Marquardt method for nonlinear ill-posed operator equations in Hilbert Spaces

Abstract In this paper, we consider the simplified Levenberg–Marquardt method for nonlinear ill-posed inverse problems in Hilbert spaces for obtaining stable approximations of solutions to the ill-posed nonlinear equations of the form F ⁢ ( u ) = y {F(u)=y} , where F : 𝒟 ⁢ ( F ) ⊂ 𝖴 → 𝖸 {F:\mathcal{D}(F)\subset\mathsf{U}\to\mathsf{Y}} is a nonlinear operator between Hilbert spaces 𝖴 {\mathsf{U}} and 𝖸 {\mathsf{Y}} . The method is defined as follows: u n + 1 δ = u n δ - ( T 0 ∗ ⁢ T 0 + α n ⁢ I ) - 1 ⁢ T 0 ∗ ⁢ ( F ⁢ ( u n δ ) - y δ ) , u_{n+1}^{\delta}=u_{n}^{\delta}-(T_{0}^{\ast}T_{0}+\alpha_{n}I)^{-1}T_{0}^{% \ast}(F(u_{n}^{\delta})-y^{\delta}), where T 0 = F ′ ⁢ ( u 0 ) {T_{0}=F^{\prime}(u_{0})} and T 0 ∗ = F ′ ⁢ ( u 0 ) ∗ {T_{0}^{\ast}=F^{\prime}(u_{0})^{\ast}} . Here F ′ ⁢ ( u 0 ) {F^{\prime}(u_{0})} denotes the Frèchet derivative of F at an initial guess u 0 ∈ 𝒟 ⁢ ( F ) {u_{0}\in\mathcal{D}(F)} for the exact solution u † {u^{\dagger}} , F ′ ⁢ ( u 0 ) ∗ {F^{\prime}(u_{0})^{\ast}} is the adjoint of F ′ ⁢ ( u 0 ) {F^{\prime}(u_{0})} and { α n } {\{\alpha_{n}\}} is an a priori chosen sequence of non-negative real numbers satisfying suitable properties. We use Morozov-type stopping rule to terminate the iterations. Under suitable non-linearity conditions on operator F, we show convergence of the method and also obtain a convergence rate result under a Hölder-type source condition on the element u 0 - u † {u_{0}-u^{\dagger}} . Furthermore, we derive convergence of the method for the case when no source conditions are used and the study concludes with numerical examples which validate the theoretical conclusions.

Artificial intelligence-based neural network modeling of adsorptive removal of phenol from aquatic environment

In this study, adsorptive uptake of phenol from aqueous system using Arachis hypogaea (groundnut) shell-based adsorbent was experimentally investigated and modelled using artificial intelligence-based neural network approach. Artificial neural networks with different number of neurons were designed using Levenberg-Marquardt algorithm to find the best model for phenol adsorption. The feedforward back propagation neural network comprising TRAINLM, LARNGDM and TANSIG as training, adaptation learning and transfer functions, respectively, with ten neurons in the hidden layer exhibited the optimal architecture with the strongest correlation R2=0.9901 and the smallest mean square error MSE=0.045. The studies indicated a maximum adsorptive uptake of phenol to be 37.31 mg/g onto the activated shell powder. The kinetic analysis favored pseudo second order R2=0.9999and the equilibrium data was best represented by Freundlich isotherm modelR2=0.9976. Phenolic remediation phenomenon ensued in a spontaneous manner, was exothermic ∆H0=−34.25kJ/moland involved physisorption. The experimental results are agreement with model.

Novel traveling wave fault location method for HVDC transmission line based on wavefront frequency

The key of traveling wave (TW) fault location (FL) method is the calculation of TW velocity and the calibration of TW wave head. In order to achieve high-precision FL, detailed transmission line (TL) parameters are needed to accurately calculate the TW velocity. In view of the problem that the existing high-precision TWFL methods are highly dependent on the calculation of TW velocity, the paper contributes to following aspects: (i) the mapping relationship between wavefront frequency and fault distance/fault pole is constructed; (ii) a neural network model suitable for FL and fault pole identification is designed, which is optimized by Particle Swarm Optimization (PSO) algorithm and Levenberg–Marquardt (L-M) algorithm; (iii) a complete FL scheme is proposed. In order to verify the FL accuracy of proposed method, an ±800 kV bipolar high-voltage direct-current (HVDC) transmission system model is constructed using PSCAD/EMTDC. According to the simulation results, the errors of FL is less than 0.2 km and the accuracy of fault pole identification is 100%. For the problems of fault type, fault resistance and noise, the proposed method shows high robustness.

Comprehensive calibration and laboratory validation of a micro electromechanical system sensor-based flexible inclinometer

Abstract Real-time monitoring of slopes, tunnels, and dams is important for ensuring the long-term stability and reliability of such structures. Despite the successes of current technologies in many applications, a gap still exists in certain areas such as precision in steep slopes and complex soil conditions. This study has designed a flexible inclinometer based on an array of Micro Electromechanical System (MEMS) sensors to enhance the accuracy and flexibility of existing monitoring techniques. The inclination angle of each flexible inclinometer measurement unit was measured to monitor the horizontal or vertical displacement of the target structural body. We used the Levenberg–Marquardt (LM) algorithm for optimizing the MEMS sensors based calibration and designed multiple experiments to test the accuracy of the proposed method. Experimental results show that the calibrated flexible inclinometer measurement unit has an inclination angle of less than 0.04° and the accuracy of the flexible inclinometer lies within ±0.4 mm in the horizontal attitude and 1.6 mm in the vertical attitude. Our research has developed a novel tool for geotechnical engineering monitoring that can aid in increasing the precision of real-time assessment and prediction of structural stability.

Dairy factory milk product processing and sustainable of the shelf-life extension with artificial intelligence: a model study

This study models milk product processing and sustainable of the shelf-life extension in a dairy factory using artificial intelligence. The Cappadocia dairy factory was used to study chemical processes and computational system modeling and simulation. Levenberg–Marquardt algorithm was used to create an artificial neural network model from real-time data. An AI-based method utilizing a Multilayer Perceptron (MLP) Artificial Neural Network (ANN) model was employed to precisely analyze productivity data in dairy factories. There are 9 product types and production quantities used as input parameters, and 90 datasets of actual dairy products used as output values. The model was trained using the Levenberg–Marquardt algorithm on 62 datasets for training, 14 for validation, and 14 for testing. The accuracy of the model is affected by the optimal data segmentation. The model showed how AI algorithms can improve processes and industrial production by increasing dairy production efficiency from 20 to 40%. Model efficiency values were compared to observed values to determine prediction accuracy. Model mean squared error was 4.02E-06, and coefficient of determination was 0.99984. Model efficiency predictions and observed values differed by −0.04% on average. This study investigated using artificial intelligence to optimize salvage processes and systems to increase energy efficiency and reduce environmental impact. The results show that a neural network model trained with real data can predict dairy plant productivity.

Forecasting and Comparison of Nonlinear Statistical Growth Models for Fish Seed Production in Eastern Coastal States of India

The study was carried out to compare the goodness of fit of three non–linear growth models viz., Monomolecular, Logistic and Gompertz growth models and analysing the instability index among the collected fish seed Production data from the eastern costal states of Indian for the period from 1994–1995 to 2019–2020. The parameters of each model were estimated using Levenberg–Marquardt (LM) iterative method. The ‘independence’ and ‘normality’ of error terms were examined by using ‘Run–test’ and ‘Shapiro–Wilk test’. Among the three models tested, monomolecular model was found as best model to describe variation in fish seed production in all Eastern Costal States of India. The values of CDI for fish seed production were 146.94 %, 79.30 % and 63.41% respectively which revealed that fish seed production had high instability in Odisha, Tamil Nadu and Andhra Pradesh while low instability (14.93 % and 13.13%) in West Bengal and India.

Sequential Data-Based Fault Location for Single-Line-to-Ground Fault in a T-Connection Power Line

Due to the demand for temporary rapid grid connection in renewable energy power plants, the topology structure of T-connected power lines has been widely used in the power grid. In this three-terminal system, fault localization is difficult because of traditional impedance-based or traveling wave-based fault localization methods; the three-terminal data should be synchronized and communicated. Since different terminal assets belong to different enterprises, it is actually difficult to maintain good synchronization between them. Therefore, in practical applications, the fault location of T-connected power lines often fails. This article proposes a single terminal fault location method for a T-connection power line to address this issue. It is based on the fact that the local topology of the T-connected power line in the healthy phase remains unchanged during the fault-clearing process. It utilizes the sequential current and voltage data changes generated by the sequential tripping ping emitted by the circuit breaker from different terminals to describe the constant topology of the healthy phase as an equation and calculates the accurate fault location after solving the equation. The Levenberg–Marquardt algorithm was used to calculate fault distance and transition resistance, and the effectiveness of this method was verified through simulation.

Refined InSAR Mapping Based on Improved Tropospheric Delay Correction Method for Automatic Identification of Wide-Area Potential Landslides

Slow-moving landslides often occur in areas of high relief, which are significantly affected by tropospheric delay. In general, tropospheric delay correction methods in the synthetic-aperture radar interferometry (InSAR) field can be broadly divided into those based on external auxiliary information and those based on traditional empirical models. External auxiliary information is hindered by the low spatial–temporal resolution. Traditional empirical models can be adaptable for the spatial heterogeneity of tropospheric delay, but are limited by preset window sizes and models. In this regard, this paper proposes an improved tropospheric delay correction method based on the multivariable move-window variation model (MMVM) to adaptively determine the window size and the empirical model. Considering topography and surface deformation, the MMVM uses multivariate variogram models with iterative weight to determine the window size and model, and uses the Levenberg–Marquardt (LM) algorithm to enhance convergence speed and robustness. The high-precision surface deformation is then derived. Combined with hotspot analysis (HSA), wide-area potential landslides can be automatically identified. The reservoir area of the Baihetan hydropower station in the lower reaches of the Jinsha River was selected as the study area, using 118 Sentinel-1A images to compare with four methods in three aspects: corrected interferograms, derived deformation rate, and stability of time-series deformation. In terms of mean standard deviation, the MMVM achieved the lowest value for the unwrapped phase in the non-deformed areas, representing a reduction of 56.4% compared to the original value. Finally, 32 landslides were identified, 16 of which posed a threat to nearby villages. The experimental results demonstrate the superiority of the proposed method and provide support to disaster investigation departments.

INTELLIGENT NUMERICAL METHOD FOR STUDYING MAXWELL WILLIAMSON NANOFLUID FLOW WITH ACTIVATION ENERGY

The use of artificial intelligence and its techniques has become increasingly widespread in recent times. It is being used to solve stiff non-linear equations. Additionally, nanofluids play a pivotal role in studying heat transfer. All of this was the motivation for doing this work. This work investigates a two-dimensional magnetohydrodynamic stretched flow (2D-MHDSF) of Maxwell Williamson nanofluid (MWNF) affected by bioconvection and activation energy numerically through Levenberg-Marquardt backpropagation method (LMBM)-based artificial neural network approach. The mathematical formulation for the problem was obtained through non-linear partial differential equations (PDEs). The leading PDEs were transmitted into non-linear ordinary differential equations by similarity transformation variables. The reference results for the 2D-MHDSF-MWNF model are produced by the Lobatto IIIA method through different scenarios of specific parameters for the flow velocity, fluid temperature, nanoparticle concentration, and motile density profiles. Using obtained results as a dataset to apply the testing, training, and validation steps of the suggested LMBM for the 2D-MHDSF-MWNF model. The mean squared error, analysis of regression, and error histograms are presented to prove the efficiency and precision of the proposed method. The numerical results of LMBM are displayed as a study of the effects of different physical factors on flow dynamics for 2D-MHDSF-MWNF.

Contrast-Enhanced Magnetic Resonance Imaging Based T1 Mapping and Extracellular Volume Fractions Are Associated with Peripheral Artery Disease.

Extracellular volume fraction (ECV), measured with contrast-enhanced magnetic resonance imaging (CE-MRI), has been utilized to study myocardial fibrosis, but its role in peripheral artery disease (PAD) remains unknown. We hypothesized that T1 mapping and ECV differ between PAD patients and matched controls. A total of 37 individuals (18 PAD patients and 19 matched controls) underwent 3.0T CE-MRI. Skeletal calf muscle T1 mapping was performed before and after gadolinium contrast with a motion-corrected modified look-locker inversion recovery (MOLLI) pulse sequence. T1 values were calculated with a three-parameter Levenberg-Marquardt curve fitting algorithm. ECV and T1 maps were quantified in five calf muscle compartments (anterior [AM], lateral [LM], and deep posterior [DM] muscle groups; soleus [SM] and gastrocnemius [GM] muscles). Averaged peak blood pool T1 values were obtained from the posterior and anterior tibialis and peroneal arteries. T1 values and ECV are heterogeneous across calf muscle compartments. Native peak T1 values of the AM, LM, and DM were significantly higher in PAD patients compared to controls (all p < 0.028). ECVs of the AM and SM were significantly higher in PAD patients compared to controls (AM: 26.4% (21.2, 31.6) vs. 17.3% (10.2, 25.1), p = 0.046; SM: 22.7% (19.5, 27.8) vs. 13.8% (10.2, 19.1), p = 0.020). Native peak T1 values across all five calf muscle compartments, and ECV fractions of the anterior muscle group and the soleus muscle were significantly elevated in PAD patients compared with matched controls. Non-invasive T1 mapping and ECV quantification may be of interest for the study of PAD.

A closed-loop calibration method for serial robots based on position constraints and local area measurement

This paper presents a cost-effective and efficient closed-loop calibration method to enhance the absolute positioning accuracy of industrial robots. The method utilizes an economical and highly accurate set of simple measurement devices, including a device mounted on the robot's end effector and a spherical constraint device positioned within the robot's workspace. A novel local area measurement method is employed for the spherical constraint device, effectively converting position errors into the errors in the sphere center position of the constraint device. Furthermore, the error model considers both kinematic parameter deviations of the robot itself as well as those of the measurement device, along with non-kinematic errors caused by link self-weight. The closed-loop calibration model relies on position constraints, enabling identification and compensation of all error parameters using Levenberg Marquardt method after substituting measured data. The effectiveness of this proposed method is demonstrated through simulation and experimentation. In simulations, average position error reduces from 8.249 mm to 0.8384 mm, while absolute mean difference in sphere center positions obtained using our measurement equipment decreases from 1.206 mm to 0.1027 mm. Significant reductions in both position error and difference in sphere center position are indicated after calibration. This proves that the absolute mean value of the sphere center position difference can be used as the basis for judging the size of the robot's end position error. Experimental results show that absolute mean difference in sphere center position decreases from 0.4319 mm to 0.02869 mm, leading to substantial improvement in overall positioning accuracy.

An efficient approach for solving a class of fractional anomalous diffusion equation with convergence

This article presents a study on Fractional Anomalous Diffusion (FAD) and proposes a novel numerical algorithm for solving Caputo’s type fractional sub-diffusion equations to convert the fractional model into a set of nonlinear algebraic equations. These equations are efficiently solved using the Levenberg-Marquardt algorithm. The study provides the error analysis to validate the proposed method. The effectiveness and accuracy of the method are demonstrated through several test problems, and its performance and reliability are compared with other existing methods in the literature. The results indicate that the proposed method is a reliable and efficient technique for solving fractional sub-diffusion equations, with better accuracy and computational efficiency than other existing methods. The study’s findings could provide a valuable tool for solving FAD in various applications, including physics, chemistry, biology, and engineering.

Modeling of artificial neural network to analyze heat and mass transfer of ternary hybrid nanofluid between two parallel plates with inclined magnetic field

The applications of the artificial neural network (ANN) have become the focus of interest of researchers due to their convenience for accurate modeling, simulation, and efficiency of evaluation. The primary objective of this study is to investigate the characteristics of heat and mass transfer of the ternary hybrid nanofluid flow (THNF), which is squeezed between two parallel plates, using ANN. The plate which lies on x-axis is stretching while the upper plate (UP) can move in upward and downward direction. An inclined magnetic field (MF) is also applied to the lower plate (LP). A system of partial differential equations of flow, energy, and mass transfer is used to simulate the THNF, which is then condensed using similarity substitution to a collection of ordinary differential equations (ODEs). Using the differential transform method (DTM), the resultant nonlinear ODEs in dimensionless form are further solved. The influence of the different varying physical parameters on velocity, temperature, and concentration is graphically presented and discussed. It becomes apparent that the velocity, heat, and mass transfer in squeezing flows are significantly impacted by the inclination angle of the applied MF. To demonstrate the validity of the study, the numerical findings of the Nusselt and the Sherwood numbers are provided. For the accuracy of the used approach, DTM results are compared with results from the numerical approach. The novelty of the current work is to train the neural network with the Levenberg–Marquardt algorithm in the model. To get the estimated output of the model, different scenarios are set for training, testing, and validation. The analysis is done by mean square error (MSE), histogram, fitness curve, and regression (RG). The created ANN model is shown to be reliable due to its exceptional accuracy throughout the training, validation, and testing stages.

Predictive modelling of allowable storage time for pearl millet using multilayer perception neural network

Biotic and abiotic factors interact to damage grains in the storage ecosystem. Monitoring temperature fluctuations and moisture migration is crucial to control their impact on grain quality. Grains with high temperature and moisture content have limited time for post-harvest activities. Hence, it is important to determine the time before spoilage for different grain moisture contents and storage temperatures. The study evaluated the impact of storage variables, specifically moisture content, storage temperature, and storage period, on the parameters associated with grain quality and seed deterioration in pearl millet. A model for predicting the allowable storage time was developed using a feed-forward-back propagation multilayer perception (MLP) neural network. The effectiveness of Levenberg–Marquardt (LM), Bayesian Regularization (BR), and Scaled Conjugated Gradient (SCG) algorithms in predicting the safe storage time was evaluated and compared. The BR neural network model showed higher predictability with an R2 value greater than 0.98 and low error values. The safe storage guidelines chart and model developed for allowable storage time will be helpful for farmers and grain processing industries including storage hubs to schedule different post-harvest operations of pearl millet with minimal changes in grain quality.

The Levenberg–Marquardt method: an overview of modern convergence theories and more

The Levenberg–Marquardt method: an overview of modern convergence theories and more

Prediction of boundary heat flux in mold by inverse problem method

This study utilizes inverse heat transfer techniques to analyze heat flux distribution within a mold. By collecting temperature data from thermocouples, a two-dimensional heat transfer model of the mold’s cross section is developed to investigate the transverse heat flux behavior, temperature distribution, relationship between heat flux and height, and three-dimensional heat flux within the mold. The direct problem model is solved using the finite volume method, while the inverse problem is tackled with the Levenberg-Marquardt Method (LMM) in conjunction with the Broyden method (BM). The model’s validity is confirmed through experimentation, which includes assessing the impact of initial parameter estimations, thermocouple placements and quantities, and measurement inaccuracies.

Computational intelligence for empirical modelling and optimization of methylene blue adsorption phenomena utilizing an activated carbon‐supported [Co(NH3)6]Cl3 complex

AbstractThe study focuses on the efficiency of hexaamminecobalt (III) chloride (HACo, [Co(NH3)6]Cl3) immobilized on activated carbon for removing methylene blue (MB) from water solutions. The primary objective of this study was to assess the sorption performance of HACo immobilized on activated carbon in removing MB from water solutions. Additionally, predictive models were developed to optimize the MB removal percentage. Lastly, the study aimed to determine the optimal conditions for achieving maximum MB removal. Samples were characterized using scanning electron microscopy. Batch sorption experiments were conducted to analyze the impact of MB concentration, adsorbent mass, pH, temperature, and contact time. Predictive models were built using multiple linear regression and neural network techniques, specifically artificial neural networks (ANN) and hybrid ANN–particle swarm optimization (ANN‐PSO). The PSO‐ANN model with a single hidden layer of eight neurons trained using the Levenberg–Marquardt algorithm demonstrated high accuracy in predicting MB removal percentage, with mean absolute percentage error (MAPE) = 0.083788, root mean square error (RMSE) = 0.11441, and R2 = 0.99693. The MB adsorption process followed a mono‐layer with one energy model and a pseudo‐first‐order kinetic model. Optimization using the genetic algorithm revealed that the maximum MB removal percentage of 99.56% is achievable at an MB concentration of 9.36 mg/L, adsorbent mass of 15.72 mg, and temperature of 311.2 K. The study confirms the effectiveness of HACo immobilized on activated carbon for MB removal. The PSO‐ANN predictive model proved superior in accuracy compared to empirical models. Optimization results provide the optimal conditions for maximizing MB removal, offering valuable insights for practical applications.

Assessment of heat transfer characteristics of a corrugated heat exchanger based on various corrugation parameters using artificial neural network approach

The complexity of the fluid flow process involved makes it difficult to estimate the characteristics of corrugated tubes. Heat exchangers are often designed to be more efficient by using numerical techniques. Recently, machine learning algorithms have become a viable method for assessing the behaviors of flow and heat transfer in corrugated tubes. Based on a set of data, machine learning algorithms can better estimate how efficient a heat exchanger is. In the present study, an artificial neural network is conducted to figure out the Nusselt number, friction factor, and performance evaluation criteria for heat transfer in straight corrugated tubes based on flow rate and corrugation parameters. The Reynolds number varies between 480 and 6100, spanning various flow regimes in the corrugated tubes, while the corrugation pitch and corrugation depth change between 6 mm and 18 mm and 0.6 and 1.0 mm, respectively. After totaling 220 data points, the network structure with a multilayer perceptron structure is trained. The Levenberg-Marquardt algorithm is performed for training with 17 neurons in the hidden layer. The established neural network structure forecasts Nusselt number, friction factor, and performance evaluation criteria parameters with deviation rates of 0.11 %, −0.63 %, and 0.17 %, respectively. The neural network exhibits higher performance when compared to related correlations from the literature. This study is a novel one in open sources due to using artificial neural networks to estimate the flow and thermal behaviors in corrugated tubes operating at low flow rates. The current recommended approach may be regarded as a beneficial tool particularly for thermal systems as it aids designers in enhancing the system efficiency with accurate estimations.

Kinetic modeling of dual-stage oxidative extractive denitrogenation of model fuel

The petroleum fraction of crude oil is laden with notorious nitrogen compounds, whose removal facilitates fuel oil transport and enhances the longevity of hydrodesulfurization catalysts. Petroleum refining operation thus demands the adoption of unconventional techniques, such as coupled oxidative–extractive denitrogenation. Kinetic models can provide insights into the reaction mechanism and the design and performance of reactors. In this work, nine different kinetic models were developed by applying the Langmuir–Hinshelwood and Eley–Rideal approaches to various reaction pathways. The screening of the kinetic models was done based on the values of the rate law parameters and corresponding R 2 and adjusted R 2 values calculated through a multi-parametric, non-linear regression based on the Levenberg–Marquardt algorithm. Out of all the models, the Eley–Rideal model corresponding to the rate expression rs9 was found to be the best fit, reflecting that hydrogen peroxide remained in bulk while pyridine alone was adsorbed on the catalyst. The selection of suitable extractants for the extractive removal of oxidation products was made based on their extraction efficiency and partition coefficients. The ternary liquid–liquid equilibrium (LLE) data for the (acidulated water-pyridine-isooctane) and (acidulated water-pyridine N-oxide-isooctane) systems were plotted, and Othmer–Tobias, Hand, and Bachman correlations explained the consistency of the experimental LLE data.