Levenberg-Marquardt Research Articles

Numerical analysis of thermophoretic particle deposition on 3D Casson nanofluid: Artificial neural networks-based Levenberg–Marquardt algorithm

Abstract The aim of this research is to provide a new computer-assisted approach for predicting thermophoresis particle decomposition on three-dimensional Casson nanofluid flow that passed over a stretched surface (thermophoresis particle decomposition on three-dimensional Casson nanofluid flow; TPD-CNF). In order to understand the flow behavior of nanofluid flow model, an optimized Levenberg–Marquardt learning algorithm with backpropagation neural network (LMLA-BPNN) has been designed. The mathematical model of TPD-CNF framed with appropriate assumptions and turned into ordinary differential equations via suitable similarity transformations are used. The bvp4c approach is used to collect the data for the LMLA-BPNN, which is used for parameters related with the TPD-CNF model controlling the velocity, temperature, and nanofluid concentration profiles. The proposed algorithm LMLA-BPNN is used to evaluate the obtained TDP-CNF model performance in various instances, and a correlation of the findings with a reference dataset is performed to check the validity and efficacy of the proposed algorithm for the analysis of nanofluids flow composed of sodium alginate nanoparticles dispersed in base fluid water. Statistical tools such as Mean square error, State transition dynamics, regression analysis, and error dynamic histogram investigations all successfully validate the suggested LMLA-BPNN for solving the TPD-CNF model. LMLA-BPNN networks have been used to numerically study the impact of different parameters of interest, such as Casson parameter, power-law index, thermophoretic parameter, and Schmidt number on flow profiles (axial and transverse), and energy and nanofluid concentration profiles. The range, i.e., 10−4–10−5 of absolute error of the reference and target data demonstrates the optimal accuracy performance of LMLA-BPNN networks.

A Levenberg–Marquardt algorithm‐based line parameters identification method for distribution network considering multisource measurement

AbstractThe uncertainty brought by the integration of distributed generations in distribution networks poses a higher demand for situation awareness in the distribution network. Accurate identification of distribution network line parameters is of great significance for the operation and control of the distribution network. This paper proposes a method for identifying distribution network line parameters considering multisource measurement. Firstly, the initial values of conductivity and susceptance are obtained through linear regression and converted into resistance and reactance, respectively. Then, based on the series parallel connection of the network end branches, a non‐linear function about resistance reactance is derived. By combining the measurement data of micro phasor measurement unit and advanced metering infrastructure at multiple times, the non‐linear measurement equation of the line is established, and the Levenberg–Marquardt algorithm is used to solve the non‐linear function, thus achieving the identification of distribution line parameters. The case study demonstrates the accuracy and effectiveness of the proposed method.

Magnetic target nonlinear positioning method based on planar regular octagon tensor system

The magnetic target location technology based on the principle of magnetic gradient tensor has broad engineering application prospects. However, commonly used target positioning methods are easily interfered with by the geomagnetic environment. We proposed a magnetic target nonlinear positioning method to achieve precise localization of magnetic objects. An ellipsoid fitting method based on the total least square algorithm is proposed to correct the measurement system’s magnetic interference and array error. The results show that the algorithm can reduce the root mean square error of the total magnetic field strength by 93.05% to 0.1007 uT. The tensor components are all limited to 100 nT m−1. Then, a target positioning function is constructed with the magnetic moment information introduced as a constraint term, and the location of the magnetic target is optimally calculated using the Levenberg–Marquardt algorithm. The field experimental results indicate when the magnetic targets are located at (5,0,0) and (10,−5,0), the positioning errors are 5.11% and 6.62%. This technology can also achieve high-precision path tracking of magnetic targets.

UNFIS: A Novel Neuro-Fuzzy Inference System with Unstructured fuzzy rules

An important constraint of Fuzzy Inference Systems (FIS) is their structured rules. Indeed, each rule should evaluate all input variables in its antecedent part. Thus, the length of all fuzzy rules and the number of input variables are equal. However, in many decision-making problems evaluating some conditions on a limited set of input variables is sufficient to decide properly (unstructured rules). Consequently, the FIS’s performance, generalizability, and interpretability are restricted by the aforementioned limitation. This study provides a neuro-fuzzy inference system that can create each fuzzy rule taking into account various sets of input variables in order to handle this problem. To realize this capability, a new fuzzy selector neuron with an adaptive parameter is proposed that can select input variables in the antecedent part of each fuzzy rule. Moreover, the consequent part of the Takagi–Sugeno–Kang FIS is properly changed to consider only the selected set of input variables. To learn the parameters of the proposed architecture, the Levenberg–Marquardt (LM) method is used for regression problems. For classification applications, a trust-region-based learning method (General quasi-Levenberg–Marquardt (GqLM)) is proposed to minimize cross-entropy in multiclass problems. The performance of the proposed method is compared with some related previous approaches in some real-world classification and regression problems. Based on these comparisons, the proposed method has better or very close performance with a parsimonious structure consisting of unstructured fuzzy rules.

Prediction of monthly evapotranspiration by artificial neural network model development with Levenberg–Marquardt method in Elazig, Turkey

The phenomenon of evapotranspiration (ET) is closely linked to the issue of water scarcity, as it involves water loss through both evaporation and plant transpiration. Accurate prediction of evapotranspiration is of utmost importance in the strategic planning of agricultural irrigation, effective management of water resources, and precise hydrological modeling. The current investigation aims to predict the monthly ET values in the Elazig province by developing an artificial neural network (ANN) model utilizing the Levenberg–Marquardt method. Consequently, the values of temperature, precipitation, relative humidity, solar hour, and mean wind speed were utilized in forecasting evapotranspiration values by implementing ANN algorithms. This research makes a valuable contribution to the existing body of literature by utilizing an ANN model developed with the Levenberg–Marquardt method to estimate evapotranspiration. It has been discovered that evapotranspiration values are impacted by various factors such as temperature (minimum, average, maximum), relative humidity (minimum, average, maximum), wind speed, solar hour, and precipitation values, which are taken into consideration for prediction. The findings indicated that Elazig, Keban, Baskil, and Agin sites had R values of 0.9995, 0.9948, 0.9898, and 0.9994 in the proposed model. It was found that Elazig’s MAPE ranged from 0 to 0.2288, Keban’s was 0.0001 to 0.3703, Baskil’s was between 0 and 0.4453, and Agin’s was both 0 and 0.2784. The findings obtained from the proposed model are compatible with evapotranspiration values computed from the Hargreaves method (R2 = 0.996). The study’s findings provide significant insights for planners and decision-makers involved in the planning and managing water resources and agricultural irrigation.

Form-finding for tensegrity structures based on the equilibrium equation

Finding form is a critical step in designing tensegrity structures. On the condition that the partial node coordinates, topology, and a bar/cable attribute (the force density of bar is -1 and the force density of cable is 1.) are known, a form-finding method, which is used to find the remaining node coordinates and the force density relation between elements, is proposed in this paper. Firstly, the equilibrium conditions of the tensegrity system are analyzed, and the equilibrium equation is established. Secondly, the variables that must be solved are set and substituted into the equilibrium equation, and the target equation with the variables is built. The Levenberg-Marquardt method with a damping parameter updating strategy is introduced to solve the least squares problem by transforming the equilibrium equation problem into the least squares problem. The form-finding process is performed by solving the least squares formula. Three examples demonstrate the efficiency and accuracy of searching for self-equilibrium configurations.

StarShip: Mitigating I/O Bottlenecks in Serverless Computing for Scientific Workflows

This work highlights the significance of I/O bottlenecks that data-intensive HPC workflows face in serverless environments - an issue that has been largely overlooked by prior works. To address this challenge, we propose a novel framework, StarShip, which effectively addresses I/O bottlenecks for HPC workflows executing in serverless environments by leveraging different storage options and multi-tier functions, co-optimizing for service time and service cost. StarShip exploits the Levenberg-Marquardt optimization method to find an effective solution in a large, complex search space. StarShip achieves significantly better performance and cost compared to competing techniques, improving service time by 45% and service cost by 37.6% on average over state-of-the-art solutions.

Thermal relaxation parameters estimation of non-Fourier heat transfer in laser-irradiated living tissue using the Levenberg-Marquardt algorithm

The present work is concerned with solving the inverse heat transfer problem (IHTP) to estimate the thermal relaxation parameters corresponding to the dual phase lag (DPL) model-based bio-heat transfer in laser-irradiated living tissue. This problem is divided into two parts: direct and inverse problems. The solution of the inverse problem has been obtained using the Levenberg–Marquardt algorithm. On the other hand, the solution to the direct problem is obtained by solving the DPL model-based bio-heat transfer equation (BHTE) with the transient radiative transfer equation (TRTE). So, the TRTE has been numerically solved by the modified discrete ordinate method (DOM) to find the intensity field in the living tissue subjected to short-pulsed laser radiation, and it acts as a heat source in the DPL model-based BHTE. So, the DPL model-based BHTE has been analytically solved by employing the finite integral transform technique to get the temperature variation inside the laser-irradiated living tissue. First, the computer code developed for estimating unknown thermal relaxation parameters using the Levenberg–Marquardt algorithm has been verified against the data given in the literature, and found good agreement between them. Then, the thermal response of laser-irradiated living tissue has been investigated. After that, the influence of sensor position on the sensitivity of the IHTP solution has been discussed. The impact of the total transient readings and the measurement error on estimating the unknown parameters have been investigated. The present study’s findings can significantly contribute to various parameter estimation problems where the conventional methods for direct measurements of parameters are impossible or very difficult. Furthermore, the current results may considerably impact the study of the thermic response of living tissue during laser-based photothermal therapy.

Prediction of Student’s Academic Performance through Data Mining Approach

The universities and institutes produce a large amount of student data that can be used in a disciplinary way and useful information can be extracted by using an automated approach. Educational Data Mining (EDM) is an emerging discipline used in the educational environment to deal with big student data and extract useful information. The data mining of students’ data can help the At-risk students as well as the stakeholders by the early warning. This study aims to predict the performance of the students based on student-related data to increase the overall performance. In existing studies, insufficient attributes and complexity of network models is a problem. The student’s current records and grades need to be analyzed. In this approach, the Levenberg Marquardt Algorithm (MLA) deep learning algorithm is used. The data consists of the class test, attendance, assignment and midterm scores. The neural network model consists of four input variables, three hidden and one output layer. The performance of the deep neural network is evaluated by accuracy, precision, recall and F1 score. The proposed model gained a higher accuracy of 88.6% than existing studies. The study successfully predicts the student's final grades using current academic records. This research will be beneficial to the students, educators and educational authorities as a whole.

Prediction of Student’s Academic Performance through Data Mining Approach

The universities and institutes produce a large amount of student data that can be used in a disciplinary way and useful information can be extracted by using an automated approach. Educational Data Mining (EDM) is an emerging discipline used in the educational environment to deal with big student data and extract useful information. The data mining of students’ data can help the At-risk students as well as the stakeholders by the early warning. This study aims to predict the performance of the students based on student-related data to increase the overall performance. In existing studies, insufficient attributes and complexity of network models is a problem. The student’s current records and grades need to be analyzed. In this approach, the Levenberg Marquardt Algorithm (MLA) deep learning algorithm is used. The data consists of the class test, attendance, assignment and midterm scores. The neural network model consists of four input variables, three hidden and one output layer. The performance of the deep neural network is evaluated by accuracy, precision, recall and F1 score. The proposed model gained a higher accuracy of 88.6% than existing studies. The study successfully predicts the student's final grades using current academic records. This research will be beneficial to the students, educators and educational authorities as a whole.

The evaluation of course teaching effect based on improved RBF neural network

As basic education is increasingly digitized, the need for better teaching and learning quality also rises. Teaching reform is crucial to achieve this, and incorporating the Levenberg-Marquardt (L-M) into the Radial Basis Function (RBF) can help establish a fair online teaching evaluation system. The experimental results showed that the convergence ability of the model was significantly improved compared with the traditional RBF neural network. The overall mean square error of the improved model was 10°. The actual value prediction accuracy of the improved model is higher than that of the Backpropagation (BP). When the actual value was at its peak, the accuracy reached 98 %, the overall fluctuation range of absolute error was low, the highest absolute error value reached 0.78, and the average absolute error was below 0.5. With targeted improvements, teachers and students could better understand and change their own learning situations, as reflected in empirical evaluations.

Characterize fracture geometry and propagation with low frequency distributed acoustic sensing strain data

Low-frequency distributed acoustic sensing (LF-DAS) strain data from offset wells are widely used to characterize hydraulic fracture geometry. In this paper, we propose a new optimization model for DAS interpretation. The model quantifies the fracture propagation trajectory and fracture geometry variation with time from low-frequency DAS strain data of offset wells. First, the optimization model is developed by combining the Green function and the Sneddon fracture width function to correlate parameters such as fracture width distribution, fracture length and fracture location with the far-field strain distribution. Second, the optimization model is solved by the Levenberg-Marquardt nonlinear least squares algorithm. The model was validated by generating cases. In addition, the model was applied to the interpretation of fracture propagation characteristics for the fiber optic well case of HFTS-2 offset wells. The interpretation results can visually determine the fracture modification effect and help to improve the production efficiency.

A fresh look at nonsmooth Levenberg–Marquardt methods with applications to bilevel optimization

In this paper, we revisit the classical problem of solving over-determined systems of nonsmooth equations numerically. We suggest a nonsmooth Levenberg–Marquardt method for its solution which, in contrast to the existing literature, does not require local Lipschitzness of the data functions. This is possible when using Newton-differentiability instead of semismoothness as the underlying tool of generalized differentiation. Conditions for local fast convergence of the method are given. Afterwards, in the context of over-determined mixed nonlinear complementarity systems, our findings are applied, and globalized solution methods, based on a residual induced by the maximum and the Fischer–Burmeister function, respectively, are constructed. The assumptions for local fast convergence are worked out and compared. Finally, these methods are applied for the numerical solution of bilevel optimization problems. We recall the derivation of a stationarity condition taking the shape of an over-determined mixed nonlinear complementarity system involving a penalty parameter, formulate assumptions for local fast convergence of our solution methods explicitly, and present results of numerical experiments. Particularly, we investigate whether the treatment of the appearing penalty parameter as an additional variable is beneficial or not.

Hygroscopic behavior of noni leaf powder (Morinda citrifolia L.) obtained by drying in foam layer

Studies on the ethnicbotanical aspect and properties of noni (Morinda citrifolia L.) reveal that noni leaves contain chemical compounds that are related to antibacterial, antioxidant, antiviral, antifungal, antitumor, anthelmintic, analgesic, inflammatory, hypotensive and immunostimulating, among these compounds are, for example, flavanoid glycosides. The drying process is, in turn, used as a way of preserving perishable products, such as plants, due to the removal of water available for microbial deterioration, keeping the properties of the material preserved. For proper storage and increasing the shelf life of the powder obtained after the drying process, it is important to know the adsorption isotherms. This study aims to survey the adsorption isotherms of powders obtained from noni leaves. The powders to be analyzed were obtained through the foam layer drying process in the maximum, minimum and central factorials of the complete experimental planning of previously carried out studies. For the mathematical adjustment of the obtained isotherms, three different mathematical models from the literature were tested, based on experimental moisture adsorption data, for non-linear regression analysis, using the Gauss-Newton and Levenberg-Marquardt methods. The isosteric heat of the powders was also calculated to understand the behavior of the adsorbed phase with temperature variation, in addition to the affinity between adsorbate and adsorbent. The noni leaf powder showed high hygroscopicity, ranging from 0.098 to 0.969 and the Oswin model was the one that best represented empirical adjustments describing the process. The isotherms were classified as Brunauer Type III. It was also possible to infer that the energy required to remove water present in the noni leaf powder decreases with increasing equilibrium humidity.

Numeric Validation of the Inversion Model of Electrical Resistivity Imaging Method using the Levenberg-Marquardt Algorithm

This paper introduces a new application of the Electrical Resistivity Imaging (ERI) method within the realm of structural assessment, deviating from its conventional use in geology. The study presents an innovative inversion model that incorporates the Levenberg-Marquardt algorithm, representing a notable leap in seamlessly integrating ERI into structural analysis. Rigorous validation of the inversion methodology is conducted through extensive benchmarking against simulated reference data, focusing on 1D and 2D resistivity distributions within timber specimens. By utilizing known resistivity fields, the paper quantitatively validates the accuracy of reconstructed models obtained through numerical simulations. Notably, both longitudinal and transverse surveys exhibit exceptional outcomes, showcasing a high correlation with the actual resistivity profiles, achieved within a concise 10-13 iterations. This meticulous validation process conclusively underscores the effectiveness and precision of the proposed inversion approach. Beyond its scientific contribution, this research expands the conventional boundaries of ERI application and establishes it as an invaluable tool for structural monitoring.

Adaptive time-step unscented kalman filtering (ATS-UKF) based observer design for urea selective catalytic reduction (SCR) performance of diesel engines

To reduce the number of sensors in the SCR catalyst, state feedback and fault diagnosis information are provided. Firstly, a model based on the coupling of flow, heat transfer, and gas-solid phase catalytic reaction in the SCR system is investigated in this paper. The parabolic partial differential equations are simplified by the variable substitution method and the method of lines approach (MOL). The simplified system of equations is solved by backward differentiation formulas (BDF) with adaptive adjustment time step strategy. Meanwhile, the chemical reaction parameters are accurately calibrated per second using the Levenberg-Marquardt method. Secondly, the ATS-UKF is designed in this paper, and to ensure the synchronisation between the ATS-UKF and the SCR model calculations, the time step of solving the BDF by the SCR model is taken as the time step of propagating the sigma points. Two observation scenarios are assumed: (1) no downstream NH3 concentration sensor, ammonia coverage and downstream NH3 concentration are observed by ATS-UKF; (2) no downstream NOx sensor, ammonia coverage and downstream NOx concentration are observed by ATS-UKF. Finally, the paper carries out bench tests. In the first case, the ammonia coverage obtained by the ATS-UKF reached 0.99 with respect to the model-calculated value R². The mean absolute error (MAE) between the observed and experimental values of the ATS-UKF for the downstream NH3 concentration was 2.76 ppm. In the second case, the ammonia coverage obtained by the ATS-UKF reached 0.99 with respect to the model-calculated value R², and the MAE between the observed and experimental values of the ATS-UKF for the downstream NOx concentration was 1.53 ppm. Environmental ImplicationThe Adaptive Time-Step Unscented Kalman Filtering (ATS-UKF) enhances urea Selective Catalytic Reduction (SCR) in diesel engines, improving environmental outcomes. This method minimizes sensor dependence, enabling more precise SCR system management and effective emission reduction. By advancing emission control technologies, ATS-UKF contributes to global air pollution mitigation efforts, supporting cleaner air and environmental sustainability. Its innovative approach in monitoring and predicting SCR performance marks a significant step towards eco-friendly diesel engine operation.

Toward Cancer Chemoprevention: Mathematical Modeling of Chemically Induced Carcinogenesis and Chemoprevention

Cancer, which is currently rated as the second-leading cause of mortality across the globe, is one of the most hazardous disease groups that has plagued humanity for centuries. The experiments presented here span over two decades and were conducted on a specific species of mice, aiming to neutralize a highly carcinogenic agent by altering its chemical structure when combined with certain compounds. A plethora of growth models, each of which makes use of distinctive qualities, are utilized in the investigation and explanation of the phenomena of chemically induced oncogenesis and prevention. The analysis ultimately results in the formalization of the process of locating the growth model that provides the best descriptive power based on predefined criteria. This is accomplished through a methodological workflow that adopts a computational pipeline based on the Levenberg–Marquardt algorithm with pioneering and conventional metrics as well as a ruleset. The developed process simplifies the investigated phenomena as the parameter space of growth models is reduced. The predictability is proven strong in the near future (i.e., a 0.61% difference between the predicted and actual values). The parameters differentiate between active compounds (i.e., classification results reach up to 96% in sensitivity and other performance metrics). The distribution of parameter contribution complements the findings that the logistic growth model is the most appropriate (i.e., 44.47%). In addition, the dosage of chemicals is increased by a factor of two for the next round of trials, which exposes parallel behavior between the two dosages. As a consequence, the study reveals important information on chemoprevention and the cycles of cancer proliferation. If developed further, it might lead to the development of nutritional supplements that completely inhibit the expansion of cancerous tumors. The methodology provided can be used to describe other phenomena that progress over time and it has the power to estimate future results.

Simultaneous spectrophotometric determination of Co (II) and Co (III) in acidic medium with partial least squares regression and artificial neural networks

This study aims at the application of two chemometric techniques to visible spectra of acetic acid solutions of Co (II) and Co (III) for simultaneous determination thereof. Spectral data of 145 samples in the range of 400–700 nm were used to build the models. Partial least squares regression models were developed for which latent variables were determined using internal cross-validation with a leave-one-out strategy and 3 and 2 latent variables were selected for Co(II) and Co(III) based on root mean square error of cross-validation. For these models, root mean square errors of prediction were 1.16 and 0.536 mM and coefficients of determination were 0.975 and 0.892 for Co (II) and Co (III). As an alternate method, artificial neural networks consisting of three layers, with 10 neurons in hidden layer, were trained to model spectra and concentrations of cobalt species. Levenberg-Marquardt algorithm with feed-forward back-propagation learning resulted root mean square errors of prediction of 0.316 and 0.346 mM for Co (II) and Co (III) respectively and coefficients of determination were 0.996 and 0.988.

Application programming interface for electron beam welding of Inconel 718 thin plates

In this paper the simulation of electron beam welding of Inconel 718 thin plates by a moving linear heat source is considered. Neural network models are developed and used for the description of the dependence of the molten pool geometry characteristics on the process parameters - electron beam power, welding velocity, and the plate thickness. Neural network models, based on a multi-layered feedforward neural network, trained with Levenberg-Marquardt error backpropagation algorithm are compared with estimated regression models. The neural networks are trained, tested and validated using a set of experimental data. The resulting models are implemented for developing of an application programming interface for electron beam welding of Inconel 718 thin plates, which is used for prediction, investigation and graphical optimization of the molten pool geometry characteristics of the obtained electron beam welds.

Discrepancies between reported knuckleball spin rates and dynamics

Major League Baseball tracks every pitch of every game and provides the public with access to a significant amount of data for each pitch. This level of data availability is not seen in many other sports and offers substantial opportunities to provide analysis on the sport. Major League Baseball does not provide the raw data but provides refined data. While the algorithms for transforming the raw data are robust, the algorithms are not perfect. This study investigates the specific case of knuckleball pitches and shows that the equations of motion and reported spin rates do not align. This study uses the modified shooting method combined with the Levenberg–Marquardt algorithm to determine the trajectories of the pitches based on the provided data and known equations of motion. This study investigates three scenarios: 1) the reported data are correct; 2) the pitches are correctly identified, but the spin rates are incorrect; and 3) the spin rates are correct, but the pitches are incorrectly identified as knuckleballs. We show that the reported data are inconsistent with the equations of motion and that, based on statistical analysis, the pitch identification is likely incorrect.