Levenberg-Marquardt Research Articles

A novel method for aero-engine map calibration using adaptation factor surface

High-fidelity component-level models (CLMs) are essential for aero-engine performance modeling, monitoring, and diagnosis, relying heavily on precise component maps. Inaccuracies in these maps can cause significant deviations between predicted and actual measurements. This study introduces a novel wide-range performance adaptation method (WPAM) utilizing adaptation factor surfaces, enabling precise adjustment of speed line operating points. The adaptation factors for the component maps are calculated based on both steady-state and transient measurements using the Levenberg-Marquardt method, with transient adaptation calculations converted into a steady-state solution. Adaptation factor surfaces are constructed using the moving least squares method to modify component maps in both spool speed and β-value directions. Validated on two engines with distinct maps, WPAM significantly enhances CLM accuracy under steady-state and transient conditions, considering multidimensional engine and CLM map discrepancies. It is applicable to degraded and variable geometry engines, exhibiting robustness in handling noisy measurement data.

Fatigue cracking prediction of RIOHTrack full-scale test track based on variable-order fractional Burgers model

We propose a modified thermal cracking (MTC) model in this paper, which utilizes the evolution of crack propagation to predict the number and density of cracks that will form on the RIOHTrack full-scale test track. We incorporate the variable-order fractional Burgers model as an important component of the thermal cracking (TC) model, for calculating the creep compliance. Furthermore, we apply the Levenberg–Marquardt (LM) algorithm as a data-driven approach, for parameter fitting. The MTC model is constructed technically through creep compliance approximation compute and parameter fitting as follows. First, we employ the variable-order fractional Burgers model to calculate the asymptotic creep compliance of each pavement segment within the RIOHTrack full-scale test track. More precisely, we derive the explicit asymptotic expansion of creep compliance based on the variable-order fractional Burgers model. Such an asymptotic expansion represented by the Gamma function is a simplified representation of the creep compliance, and it ensures that the fitting accuracy R2 is greater than 0.87. Parameter fitting of the creep compliance is based on the RIOHTrack full-scale pavement test data, using the LM algorithm. Then, the creep compliance in the original TC model is mathematically upgraded to the above variable-order fractional approximation form, and parameters in the MTC model are numerically estimated using the LM algorithm based on prior knowledge from the RIOHTrack test data. Our prediction analyses based on the RIOHTrack data demonstrate the superior performance of the proposed MTC model.

Predicting hospital admissions for upper respiratory tract complaints: An artificial neural network approach integrating air pollution and meteorological factors.

This study uses artificial neural networks (ANNs) to examine the intricate relationship between air pollutants, meteorological factors, and respiratory disorders. The study investigates the correlation between hospital admissions for respiratory diseases and the levels of PM10 and SO2 pollutants, as well as local meteorological conditions, using data from 2017 to 2019. The objective of this study is to clarify the impact of air pollution on the well-being of the general population, specifically focusing on respiratory ailments. An ANN called a multilayer perceptron (MLP) was used. The network was trained using the Levenberg-Marquardt (LM) backpropagation algorithm. The data revealed a substantial increase in hospital admissions for upper respiratory tract diseases, amounting to a total of 11,746 cases. There were clear seasonal fluctuations, with fall having the highest number of cases of bronchitis (N = 181), sinusitis (N = 83), and upper respiratory infections (N = 194). The study also found demographic differences, with females and people aged 18 to 65years having greater admission rates. The performance of the ANN model, measured using R2 values, demonstrated a high level of predictive accuracy. Specifically, the R2 value was 0.91675 during training, 0.99182 during testing, and 0.95287 for validating the prediction of asthma. The comparative analysis revealed that the ANN-MLP model provided the most optimal result. The results emphasize the effectiveness of ANNs in representing the complex relationships between air quality, climatic conditions, and respiratory health. The results offer crucial insights for formulating focused healthcare policies and treatments to alleviate the detrimental impact of air pollution and meteorological factors.

Pose Selection Based on a Hybrid Observation Index for Robotic Accuracy Improvement

The problem of the insufficient accuracy performance of industrial robots in high-precision manufacturing is addressed in this paper. Firstly, a kinematic error model based on an M-DH model was presented. Secondly, a hybrid observability index O6 was proposed to select the optimal poses for parameter identification. O6 is the combination of O1 and O3. The optimal poses were obtained by using the IOOPS algorithm. Thirdly, the fitness function for parameter identification was established, and the Levenberg–Marquardt (LM) algorithm was applied for the accurate identification of kinematic parameter errors. Finally, several experiments were conducted to evaluate the performance of the proposed hybrid observability index O6. The average position error and average attitude error of Staubli TX60 robot were reduced by 89% and 49%. The results show that the proposed hybrid observability index O6 has great stability and effectiveness for robot calibration.

A modified Levenberg–Marquardt algorithm for low order-value optimization problem

AbstractIn this paper, we consider a modified Levenberg–Marquardt algorithm for Low Order Value Optimization problems(LOVO). In the algorithm, we obtain the search direction by a combination of LM steps and approximate LM steps, and solve the subproblems therein by QR decomposition or cholesky decomposition. We prove the global convergence of the algorithm theoretically and discuss the worst-case complexity of the algorithm. Numerical results show that the algorithm in this paper is superior in terms of number of iterations and computation time compared to both LM-LOVO and GN-LOVO algorithm.

The whole-process tracking method of stable state transformation for multistable tensegrity based on Levenberg-Marquardt method

The tensegrity structure is prestressed spatial structure composed of rods and cables. Its multistable phenomenon brings great research potential in energy storage and robotic. In order to completely analyze the changes of configurations and mechanical property in stable state transformation (SST) processes of multistable tensegrity structures, a whole-process tracking (WPT) method based on Levenberg-Marquardt method is proposed. Three numerical examples are calculated, and the WPT is successfully realized, which proves the feasibility and universality of proposed WPT method. According to the calculation results, the variation of the driving force and elastic strain energy during SST are further summarized. Alternatively, different types of driving-paths are investigated, the results show that mechanical property during SST could be adjusted effectively by modifying the driving-path. The proposed WPT method and analysis results provides insights for designing and implementing multistable tensegrity structures.

Insight into the thermal transport by considering the modified Buongiorno model during the silicon oil-based hybrid nanofluid flow: probed by artificial intelligence

This work aims to analyze the impacts of the magnetic field, activation of energy, thermal radiation, thermophoresis, and Brownian effects on the hybrid nanofluid (HNF) (Ag++silicon oil) flow past a porous spinning disk. The pressure loss due to porosity is constituted by the Darcy–Forchheimer relation. The modified Buongiorno model is considered for simulating the flow field into a mathematical form. The modeled problem is further simplified with the new group of dimensionless variables and further transformed into a first-order system of equations. The reduced system is further analyzed with the Levenberg–Marquardt algorithm using a trained artificial neural network (ANN) with a tolerance, step size of 0.001, and 1,000 epochs. The state variables under the impacts of the pertinent parameters are assessed with graphs and tables. It has been observed that when the magnetic parameter increases, the velocity gradient of mono and hybrid nanofluids (NFs) decreases. As the input of the Darcy–Forchheimer parameter increases, the velocity profiles decrease. The result shows that as the thermophoresis parameter increases, temperature and concentration increase as well. When the activation energy parameter increases, the concentration profile becomes higher. For a deep insight into the analysis of the problem, a statistical approach for data fitting in the form of regression lines and error histograms for NF and HNF is presented. The regression lines show that 100% of the data is used in curve fitting, while the error histograms depict the minimal zero error −7.1e6 for the increasing values of Nt. Furthermore, the mean square error and performance validation for each varying parameter are presented. For validation, the present results are compared with the available literature in the form of a table, where the current results show great agreement with the existing one.

Magnetic field, radiation, and Joule heating effects on natural convection Williamson fluid flow through a vertical channel using Levenberg–Marquardt algorithm

The study examined the natural convection flow of Williamson fluid through a vertical channel under the influence of the magnetic field, radiation, and joule heating effects. The governing partial differential equations are turned into ordinary differential equations using suitable transformations and solved by using the spectral quasi-linearization method (SQLM). The study explained a neural network algorithm called feed-forward back-propagation using the Levenberg–Marquardt technique (BPFF-LMT). Furthermore, a reference dataset is created for several parameters, including the magnetic parameter, Hall parameter, radiation parameter, Weissenberg number, Biot number, and Joule heating parameter. This dataset encompasses velocity and temperature profiles for different scenarios, employing the SQLM. The BPFF-LMT method’s accuracy was evaluated through a comprehensive analysis involving training, validation, and testing phases, along with mean squared error, error histograms, and performance and regression graphs. The artificial neural network’s result shows good accuracy when compared to the SQLM solution numerically. The results are presented visually through graphical representation and further analyzed quantitatively concerning the active parameters featured in the mathematical formulations. The result indicates that increasing values of the magnetic parameter result in decreased velocity and temperature profiles. Additionally, the heat transfer rate increases in the left channel. Both the radiation parameter and Weissenberg number contribute to higher velocity and temperature profiles, leading to increased skin friction in the left channel. The accuracy of the BPFF-LMT method is illustrated through graphs displaying the absolute error falling within the range of [Formula: see text] to [Formula: see text].

Mathematical modeling and machine learning-based optimization for enhancing biofiltration efficiency of volatile organic compounds

Biofiltration is a method of pollution management that utilizes a bioreactor containing live material to absorb and destroy pollutants biologically. In this paper, we investigate mathematical models of biofiltration for mixing volatile organic compounds (VOCs) for instance hydrophilic (methanol) and hydrophobic (α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document}-pinene). The system of nonlinear diffusion equations describes the Michaelis-Menten kinetics of the enzymic chemical reaction. These models represent the chemical oxidation in the gas phase and mass transmission within the air-biofilm junction. Furthermore, for the numerical study of the saturation of α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document}-pinene and methanol in the biofilm and gas state, we have developed an efficient supervised machine learning algorithm based on the architecture of Elman neural networks (ENN). Moreover, the Levenberg-Marquardt (LM) optimization paradigm is used to find the parameters/ neurons involved in the ENN architecture. The approximation to a solutions found by the ENN-LM technique for methanol saturation and α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document}-pinene under variations in different physical parameters are allegorized with the numerical results computed by state-of-the-art techniques. The graphical and statistical illustration of indications of performance relative to the terms of absolute errors, mean absolute deviations, computational complexity, and mean square error validates that our results perfectly describe the real-life situation and can further be used for problems arising in chemical engineering.

Study on the Application of Error Back-Propagation Algorithm Applied to the Student Status Management in Higher Education Institutions

The objective of this work is to predict the employment rate of students based on the information in the SSM (student status management) in colleges and universities. Firstly, the relevant content of SSM is introduced. Secondly, the BP (Back Propagation) neural network, the LM (Levenberg Marquardt) algorithm, and the BR (Bayesian Regularization) algorithm are introduced. In addition, the LM algorithm is combined with the BR algorithm to optimize the BP neural network, so as to establish a prediction model of the employment rate of college graduates based on the LM-BP neural network (the established prediction model). Finally, the established prediction model is verified after the historical data of college students in the SSM are managed and processed using the big data analysis technology. It suggests that the established prediction model shows higher prediction accuracy, more stable prediction performance, more ideal prediction effect, and higher practical application value.

Complexity bound of a Levenberg–Marquardt algorithm based on probabilistic Jacobian models

Complexity bound of a Levenberg–Marquardt algorithm based on probabilistic Jacobian models

A neuro‐computational study of viscous dissipation and nonlinear Arrhenius chemical kinetics during the hypodicarbonous acid‐based hybrid nanofluid flow past a Riga plate

AbstractWe examine the flow of Casson hybrid nanofluid (Cu+/) through a Riga plate sensor with perforations that act as an electromagnetic actuator. The hypodicarbonous acid is considered a base fluid. The impact of Arrhenius chemical kinetics and viscous dissipation are taken into account during the dynamics. The problem is formulated by considering the heat and mass transfer. An appropriate scaling is used to reduce the complexity of the problem, and further transform it into a system of ordinary differential equations (ODEs). The reduced system is further set for the first‐order system of equations that are analyzed with the Artificial Neural Network (ANN) which is trained with the Levenberg–Marquardt algorithm. The results for the state variables are displayed through graphs and tables by performing 1000 independent iterations with tolerance and . The Hartman, Casson, and Richardson numbers with their increasing values enhance the velocity profile. The chemical reaction parameter and the Prandtl number decline the thermal and concentration profiles, respectively. The Statistical analysis in the form of regression and histograms is also carried out in each case. The absolute error (AE) ranges up to and validations that range up to are presented for the varying values of each parameter. A comparative analysis of the nanofluid (NF) and hybrid nanofluid (HNF) is performed in each case study. The results for skin friction and Nusselt number are displayed numerically in the form of tables and are compared with the available literature, where the accuracy and performance of ANN are proved.

A COMPARATIVE MODELING AND OPTIMIZATION OF SURFACE ROUGHNESS IN THE END MILLING OF Al 3003 SUBJECTED TO NON-EQUAL CHANNEL ANGULAR PRESSING (NECAP)

This paper highlights the surface roughness optimization of a specific material, Al 3003, which has been subjected to the non-equal channel angular pressing (NECAP) process. Considering spindle speed, feed rate, and depth of cut as input variables and surface roughness as an output variable, experiments have been conducted based on the L27 orthogonal array of the Taguchi method. Four prediction models, namely exponential and response surface methodology (RSM) as mathematical models, and artificial neural networks (ANNs) prediction models with different training algorithms (Bayesian Regularization (BR) and Levenberg–Marquardt (LM)), are proposed. Applying effectiveness and performance criteria, the prediction accuracy of the exponential model (90.35%), RSM (93.07%), BR (97.83%), and LM (97.54%) shows that all proposed prediction models are efficient enough. The ANN model trained with BR is found to be the best fit for predicting surface roughness. In order to optimize surface roughness, a newly introduced optimization method called the Intelligible-in-time Logics Algorithm (ILA) is employed. High spindle speed (1000[Formula: see text]rev/min), low feed rate (100[Formula: see text]mm/min) and depth of cut (0.5[Formula: see text]mm) have been the optimum cutting parameter combinations to obtain minimum surface roughness (0.4956[Formula: see text][Formula: see text]m). The results have been verified by confirmation tests and Particle Swarm Optimization (PSO) method. ILA and PSO predict the same optimum parameter combinations and minimum surface roughness, while ILA performs optimization in less time (114.4[Formula: see text]s), about 3.5 times faster than PSO. The paper’s findings strongly advocate the application of ILA in machining data optimization.

Advanced method for estimating the volumetric intensity along tunnels using ANN

ABSTRACT Simulating realistic scenarios with numerical models often demands substantial computational resources, which can be excessively time-consuming. In complex Discrete Fracture Network (DFN) simulations where mutual influence among fracture parameters is crucial, efficient Artificial Intelligence (AI) algorithms offer a promising solution. This study focuses on the Monte Seco tunnel in Brazil, employing Artificial Neural Networks (ANN) with the Levenberg-Marquardt Algorithm (ANN-LM) to estimate Volumetric discontinuity intensity (P32). Comparative analysis with traditional DFN-based methods reveals superior predictive performance of the ANN model over Multiple Linear Regression (MLR). MATLAB was utilized for implementation, considering the interdependence of geometric parameters across fracture sets to estimate P32 values. Sensitivity analysis identified correlations between F1 parameters (density and trace length) and P32 estimates for F2, aiding in predicting potential tunnel instability. A Graphical User Interface (GUI) was developed to streamline calculations, replacing cumbersome spreadsheet methods.

Fabrication of molecular-scale logic devices and implication of artificial neural networks for analysis of anion-responsive behaviors of luminescent ruthenium-terpyridine complex

Anion responsive spectral characteristics of a homoleptic luminescent Ru(II)-terpyridine complex derived from 4′-(p-triphenylphosphoniummethylphenyl)-2,2′:6′,2″-terpyridine bromide (tpy-PhCH2PPh3Br) ligand has been utilized here to mimic the operation of several advanced logic functions. The complex displays remarkable change in absorption and emission spectral profiles in presence of selected anions due to concerted hydrogen bonding followed by anion-induced proton abstraction. Importantly, deprotonation by specific anions followed by restoration to the initial form of the complex is feasible in presence of acid and the process could be recycled. The spectral responsiveness of the complex is employed to mimic various advanced Boolean logic functions, such as IMPLICATION, INHIBIT and combinational logic gates. Execution of exhaustive sensing investigations is often labor-intensive and time-consuming. To address the gap, we employed herein artificial neural network (ANN) models employing three different training algorithms, viz. Bayesian Regularization (BR), Scaled Conjugate Gradient (SCG), and Levenberg-Marquardt (LM) for comprehensive analysis and prediction of the experimental observations. We also compared the outcomes of these models with one another as well as with the experimental data to enable an accurate modeling of the complex’s anion-sensing behavior.

Artificial neural network for predicting the performance of waste polypropylene plastic-derived carbon nanotubes

AbstractIn this study, an artificial neural network model using function fitting neural networks was developed to describe the yield and quality of multi-walled carbon nanotubes deposited over NiMo/CaTiO3 catalyst using waste polypropylene plastics as cheap hydrocarbon feedstock using a single-stage chemical vapour deposition technique. The experimental dataset was developed using a user-specific design with four numeric factors (input variable): synthesis temperature, furnace heating rate, residence time, and carrier gas (nitrogen) flow rate to control the performance (yield and quality) of produced carbon nanotubes. Levenberg–Marquardt algorithm was utilized in training, validating, and testing the experimental dataset. The predicted model gave a considerable correlation coefficient (R) value close to 1. The presented model would be of remarkable benefit to successfully describe and predict the performance of polypropylene-derived carbon nanotubes and show how the predictive variables could affect the response variables (quality and yield) of carbon nanotubes.

Intelligent computing for the electro-osmotically modulated peristaltic pumping of blood-based nanofluid

The study delves into a novel application of artificial neural networks within the biomedical realm, specifically focusing on the peristaltic pumping of ionized blood-infused nanofluid using the Casson model. The investigation takes into account the impacts of electrokinetic forces, chemical reaction, thermal radiation and variable thermal conductivity. The endorsed nanofluid model encompasses both thermophoretic and Brownian diffusions. The Nernst-Planck and Poisson equations are used to characterize electroosmotic process. The mathematical model is then numerically solved using NDSolve in Mathematica. The variation in relevant hemodynamic characteristics concerning key flow parameters is explored through numerous graphical representations. Two distinct artificial neural networks have been developed to estimate values for rates of mass and heat transfer. The Levenberg-Marquardt algorithm is used as the training algorithm in network models with multi-layer perceptron architecture. Graphical inspection of the results demonstrates a decrease in blood flow with an elevated Helmholtz-Smoluchowski velocity. A lower pressure gradient is recorded with a higher electroosmotic parameter. Furthermore, an augmentation in the thermal conductivity parameter leads to a reduction in heat transfer rate at the wall. The concentration profile demonstrates an increase with a rise in the chemical reaction parameter. The results obtained from the neural network models exhibit an ideal harmony with the target values. The developed neural network models demonstrated the ability to predict rates of heat and mass transfer values with average deviations of −0.01% and 0.004%, respectively.

Recovering induced polarization effects from 1-D coupled inversion of transient electromagnetic data

SUMMARY Induced polarization (IP) effects can significantly affect and superimpose the inductive earth response, leading to heavily distorted data and, if overlooked, false geological interpretation. In this paper, we implemented the Levenberg–Marquardt (LM) and very fast simulated annealing (VFSA) algorithms to recover IP effects from central loop transient electromagnetic (TEM) data. To incorporate the IP effect in the TEM response, we used the Cole–Cole parametrization, maximum phase angle (MPA), maximum imaginary conductivity (MIC) and Jeffrey transform of Cole–Cole parameters. The result of 1-D forward calculation and inversion of synthetic TEM data revealed that the Cole–Cole parametrization is more robust and reliable than MPA, MIC and Jeffrey transform, and that the synthetic data were well fitted and IP parameters well recovered using this model. However, the incorporation of the IP effect leads to a highly nonlinear and non-unique inverse problem which requires an accurate starting model, especially for LM inversion. To evaluate the performance of our algorithm using field data, we carried out a 1-D inversion of TEM data acquired along a profile that traverses a waste site located near Cologne, Germany. Furthermore, to obtain a priori information and validate the result of TEM data modelling, we conducted an electrical resistivity tomography (ERT) and time-domain IP (TDIP) survey along the TEM profile. A 2-D inversion was used to retrieve the Cole–Cole parameters as input for TEM interpretation. By including the IP information, the TEM field data can be explained quantitively, and a consistent and improved interpretation of the waste body is achieved.

Dynamics modeling and nonlinear attitude controller design for a rocket-type unmanned aerial vehicle

This paper presents an altitude and attitude control system for a newly designed rocket-type unmanned aerial vehicle (UAV) propelled by a gimbal-based coaxial rotor system (GCRS) enabling thrust vector control (TVC). The GCRS is the only means of actuation available to control the UAV’s orientation, and the flight dynamics identify the primary control difficulty as the highly nonlinear and tightly coupled control distribution problem. To address this, the study presents detailed derivations of attitude flight dynamics and a control strategy to track the desired attitude trajectory. First, a Proportional-Integral-Derivative (PID) control algorithm is developed based on the formulation of linear matrix inequality (LMI) to ensure robust stability and performance. Second, an optimization algorithm using the Levenberg–Marquardt (LM) method is introduced to solve the nonlinear inverse mapping problem between the control law and the actual actuator outputs, addressing the nonlinear coupled control input distribution problem of the GCRS. In summary, the main contribution is the proposal of a new TVC UAV system based on GCRS. The PID control algorithm and LM algorithm were designed to solve the distribution problem of the actuation model and confirm altitude and attitude tracking missions. Finally, to validate the flight properties of the rocket-type UAV and the performance of the proposed control algorithm, several numerical simulations were conducted. The results indicate that the tightly coupled control input nonlinear inverse problem was successfully solved, and the proposed control algorithm achieved effective attitude stabilization even in the presence of disturbances.

Maximum displacement prediction model for steel beams with hexagonal web openings under impact loading based on artificial neural networks

The estimation of the maximum displacement of steel beams with hexagonal web openings under impact loads is crucial for the anti-impact design of structures. The dynamic characteristics are complex, and the maximum displacement can be obtained experimentally, although the time cost, and expense of such experiments are high. In this context, a 6-5-1 artificial neural network model based on the Levenberg-Marquardt backpropagation algorithm was developed, incorporating 5-fold cross-validation techniques. Due to limited experimental data, 324 high-precision finite element models were created in bulk using Python-based ABAQUS software scripts to provide additional numerical data, and 26 specimens were designed for drop hammer tests to validate the finite element models. The artificial neural network model on the test data yielded a mean squared error of 0.0268, a mean absolute error of 0.0014, and a coefficient of determination value of 0.9806, with samples having an error of less than 10% comprising 77.16% of the total samples. Using Garson’s algorithm, the contribution of input features was estimated, and a full parameter analysis of the proposed model was conducted. The results indicate that the most significant factor is the impact mass, which accounts for 37.58%. When the impact mass increased from 530 kg to 630 kg, the maximum displacement of Q235 surged by 93.75%. The factor with the least impact is the opening spacing, accounting for 2%, with an average increase in maximum displacement of only 3.45%. Finally, ANN-based equations that can be used as design tools are established.