Levenberg-Marquardt Research Articles

Intelligent neuron based interpretation of carreau trihybrid nanofluid model with streamline analysis: Configuration of distinct geometries

This current attempt develops a more efficient predictive model that can accurately simulate the behavior of Carreau trihybrid nanofluids in non-trivial configurations. This study interprets thermal behavior of Carreau trihybrid nanofluid model with streamline analysis considering the two geometries wedge and cone. Three nanoparticles are involved in base fluid (water) with physical effects of non-uniform heat sink source and nonlinear thermal radiation are assumed for heat transport and Lorentz forces are considered for velocity inspection. Furthermore, this study employs intelligent neural networks to interpret data for streamline and thermal transport analysis, focusing on the specific cases of wedge and cone geometries. Initial data fetched through bvp4c and further, obtained data trained through supervised neural scheme, Levenberg marquardt neural network (LM-NN) is applied and required predictions are made. Higher “Gc” indicates stronger solutal buoyancy forces, which promote upward fluid movement, thereby increasing the velocity gradient. With increasing (M), the velocity profile decreases. Fluid exhibits enhancing the velocity gradient with higher (n). Higher particle concentration enhances the fluid's viscosity and resistance.

Industrial robot calibration optimization method based on R-optimal criterion and improved IOOPS algorithm

Abstract In this paper, a novel kinematic parameter calibration method based on the R-optimal criterion and the improved iterative one-by-one pose search (IOOPS) algorithm is proposed to improve the end-effector positioning accuracy of industrial robots. First, a novel industrial robot error calibration model based on the product of exponential model and generalized error model is established, and the ideal pose transformation matrix from the robot base coordinate system to the laser tracker measurement coordinate system is obtained using the least-squares method, thereby obtaining the initial parameter vector of the robot calibration system. Second, various joint angle values at different positions within the robot’s workspace and the corresponding end-effector coordinate data, namely calibration sampling point data, are collected. Subsequently, the improved IOOPS algorithm combined with the observability index O R proposed by the R-optimal criterion is used to select the optimized calibration sampling points. Finally, the optimized sampling point data are combined with the Levenberg–Marquardt algorithm to optimize the parameters and obtain the optimal kinematic parameters. The experimental results show that the average end-effector error of the robot decreases from 0.5822 to 0.2492 mm after calibration using this method, demonstrating the effectiveness of the optimized sampling points in the calibration process achieved through the improved algorithm and the new observability index.

Artificial neural networking for computational assessment of ternary hybrid nanofluid flow caused by a stretching sheet: implications of machine-learning approach

Researchers are mainly interested in using soft computing artificial intelligence (AI) methods due to their broad applications in analysis, modelling and simulations. Backpropagation neural networks, one of the supervised learning algorithms, is commonly used to train data networks by optimizing the error between actual and predicted values. To optimize this process of training data, Levenberg-Marquardt algorithm is applied; particularly beneficial for solving nonlinear fluid flow problems. Little knowledge is known about the ternary-hybrid nanofluid flow caused by a stretching surface with heat generation, viscous dissipation, magnetic effect and porosity etc. This article presents a novel machine-learning approach using backpropagation neural networks augmented with the Levenberg-Marquardt procedure to figure out the ternary-hybrid nanofluid flow generated by a stretching sheet. It uniquely examines the mixture of copper, Iron oxide and silicon dioxide nanoparticles inside a single base fluid within a magnetic field, tackling the research gaps in the effects of heat generation, viscous dissipation, porosity, and magnetic effects on fluid flow system and heat transfer. Shooting numerical technique (RK-5th) is used for solving the governing ordinary equations. Graphical illustration, error analysis, mean squared error, histograms and regression analysis justify the proposed method, showing better performance for ternary nanofluids.

Optimization control strategy for diesel urea-selective catalytic reduction (SCR) urea injection based on the interior point method (IP) + higher order SCR model

In order to ensure that the NOx and NH3 emissions of diesel engines comply with the Euro VII emission standards, this paper optimizes the urea injection using a SCR model combined with the interior point method. First, the equations of the higher-order SCR model were simplified by the variable substitution method and the line method and solved by the backward difference formula to improve computational accuracy. The Levenberg-Marquardt algorithm was used to calibrate the chemical reaction rate parameters to optimize model performance. Second, an optimization cost function was designed to optimize the upstream NH3 concentration in combination with the interior point method and the higher-order SCR model to meet the requirements of Euro VII emission standards. Third, the model effect was verified by performing WHTC hot-start testing on an engine complying with the National VI emission standard. The results show that the average error between the measured NOx concentration and the calculated is 1.49 ppm, which verifies the high accuracy of the model. Finally, the effects of the interior point method, NSGA-II, and MOPSO algorithms in optimizing the upstream NH3 concentration were compared. The results showed that the interior point method outperformed the other algorithms in terms of optimization time and effect, with an optimization time of 149 s, a NOx conversion rate of 97.36 %, and an average downstream NH3 concentration of 4.65 ppm. This achieved a high NOx conversion rate and low NH3 slip in accordance with the requirements of the Euro VII regulation.

Application of Markov Chains and Artificial Neural Networks in the prediction of Hepatitis Cases in the southern states of Brazil

Viral hepatitis is a disease caused by five known types of virus and can be chronic or acute. This study collected historical data on hepatitis in the southern states of Brazil and applied Markov Chains as an input parameter for predicting cases, using Artificial Neural Networks (ANN). A comparison was then made between the method that includes the two methodologies and the prediction made by ANN using only the data from the historical series. The mean absolute error (MAE) and mean absolute percentage error (MAPE) were calculated to determine the best forecasting model for each state. It was not possible to determine a configuration that simultaneously presented the best MAE and MAPE values for each state, but it was found that the lowest errors were obtained by using Markov Chains as an information generator for the ANN models, with a MAPE of 4.45% using the Levenberg-Marquardt training algorithm, with a delay equal to 3 and a number of neurons equal to 60.

Paradigm on Levenberg–Marquardt neural algorithm analysis of heat conduction optimization for ternary hybrid nanofluid with entropy generation

AbstractThe significance of the present article is to enhance the thermal management and energy efficiency of complex engineering infrastructures such as energy storage systems, modern electric vehicles, thermal insulations, heavy‐duty machinery, and production units. This research aims to understand the intricate relationship between the thermal conductivity performance of ternary () hybrid nanomaterial and entropy generation to optimize material design and efficacy. A synergetic combination of three distinct nanomaterials silicon dioxide, ferric oxide, and titanium oxide with ethylene glycol and water in the ratio 3:2 as a base solvent is comprised of contributing unique thermophysical properties. To elucidate the impact of this hybrid composition on thermal conductivity, various factors are analyzed. The advanced computational technique of Artificial intelligent feed‐forward neural network (AIFFNN) is utilized. The problem governed the system of PDEs, which is transformed into ODEs by dimensionless similarity. Adams method provided the dataset which is filtered and embedded into Marquardt–Levenberg Algorithm (LMA). The study examines the role of nanomaterial constituents, morphology, and boundary conditions on thermal performance and entropy generation. Graphical analysis of velocity, temperature, and entropy is provided with respect to varying parameters, including surface absorption (λ), magnetic strength (Tesla M), radiation parameter (Rd), Brownian motion (Br), and Eckert number (Ec). The findings have practical significance for optimizing material design in engineering and industrial applications.

Exploring artificial neural networks for the forward kinematics of a SCARA robotic manipulator using varied datasets and training optimizers

Abstract Although analytical methods are traditionally employed, the solution to the Forward Kinematics (FK) problem for Selective Compliance Assembly Robot Arm (SCARA) manipulator robots can prove intricate and computationally demanding. Recognizing this challenge, this study endeavors to introduce an intelligent approach by leveraging Artificial Neural Networks (ANNs) to address the FK problem specifically tailored for a four-degree-of-freedom (4-DoF) SCARA robot. To train the ANNs, we employ three distinct datasets, one with a fixed step size, one with a random step size, and one based on a sinusoidal signal. Moreover, the objective is to scrutinize the ANNs performance under the influence of three distinct training algorithms: Levenberg-Marquardt (LM), Bayesian Regularization (BR), and Scaled Conjugate Gradient (SCG). Through a systematic comparison of various ANN models, diverse training algorithms, and the three chosen datasets, the investigation reveals that optimal Mean Squared Error (MSE) results are achieved with random step size datasets for models with two hidden layers using the LM algorithm (MSE = 8.6099e-05). For the BR algorithm, the best MSE (8.0535e-05) was obtained with sinusoidal datasets and three hidden layers. For the SCG algorithm, the optimal MSE (1.1144e-04) was achieved with fixed step size datasets and one hidden layer. The accuracy of the ANN model is significantly influenced by the dataset, the choice of training optimizer, and the configuration of hidden layers. Consequently, further research could explore hybrid approaches that integrate evolutionary algorithms to leverage their respective strengths and improve overall ANN model performance.

Artificial neural network models for forecasting the extracted yield of essential oils from Curcuma longa L. by hydro-distillation

Abstract Turmeric is commonly acknowledged in traditional medical practices for its strong healing properties. In the present work, hydro-distillation was employed to extract essential oils from turmeric powder. The response surface methodology (RSM) was applied to investigate the effects of various parameters, including evaporation rate (0.23, 0.5, 0.8, 0.97, 1.36, 2 ml/min), solid/liquid ratio (4:100, 6:100, 8:100, 1:10, 11:100 g/ml), and extraction duration (13–250 min) on the yield of essential oils. The central composite design (CCD) proved to be an effective tool for evaluating the extraction yield of essential oils. A three-layer artificial neural network (ANN) was utilized to develop the extraction model, employing the Levenberg–Marquardt (LM) optimization algorithm. The neural network’s input layer comprised the solid/liquid ratio, evaporation rate, and extraction time, while the output layer indicated the yield of essential oil extraction. The most appropriate model included a hidden layer with 16 neurons, achieving R 2 and MSE values of 0.9989 and 0.0013, respectively. This investigation indicates that an artificial neural network prediction model serves as an effective method for estimating essential oil yield.

Real-Time Nonlinear Image Reconstruction in Electrical Capacitance Tomography Using the Generative Adversarial Network

This study investigated the potential of the generative adversarial neural network (cGAN) image reconstruction in industrial electrical capacitance tomography. The image reconstruction quality was examined using image patterns typical for a two-phase flow. The training dataset was prepared by generating images of random test objects and simulating the corresponding capacitance measurements. Numerical simulations were performed using the ECTsim toolkit for MATLAB. A cylindrical sixteen-electrode ECT sensor was used in the experiments. Real measurements were obtained using the EVT4 data acquisition system. The reconstructed images were evaluated using selected image quality metrics. The results obtained using cGAN are better than those obtained using the Landweber iteration and simplified Levenberg–Marquardt algorithm. The suggested method offers a promising solution for a fast reconstruction algorithm suitable for real-time monitoring and the control of a two-phase flow using ECT.

Speed and accuracy investigations of neural network algorithms for ionospheric modelling at an equatorial region

Neural networks are very efficient tools for modeling, including ionospheric modeling. The training algorithm is important for achieving the optimum performance of the trained network. This research is therefore meant to evaluate and compare the performances of ten neural network training algorithms based on their prediction accuracies, and the duration/times taken by each of the algorithms to establish the optimum result. The neural networks were trained using electron density measurements by Radio Occultation (RO) technique from the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) satellites. Data for the period 2006 through 2021 was used. The networks were trained using about 2.9 million data points collected from the Kano region, Nigeria (5-degree rectangular region around geographic: 12.00° N, 8.59° E) after performing data quality control. The training algorithms considered in the work include: Bayesian Regularization (BR); Broyden-Fletcher-Goldfarb-Shanno Quasi-Newton (BFG); Conjugate Gradient with Powell/Beale (CGB); Fletcher-Reeves Conjugate Gradient (CGF); Gradient descent with momentum and adaptive learning rate (GDX); Levenberg Marquardt (LM); One Step Secant (OSS); Polak-Ribiére Conjugate Gradient (CGP); Resilient Backpropagation (RP); and Scaled Conjugate Gradient (SCG). The results showed that the BR and the LM algorithms gave the best performances in minimizing the errors of prediction (the mean RMSEs are respectively 112 and 114 ×103 electrons/cm3), but the RP algorithm, which came third in terms of accuracy, was significantly faster than both the LM and BR algorithms. The worst-performing algorithm in terms of accuracy was the GDX algorithm, although it was the fastest algorithm. The BFG algorithm was the worst-performing algorithm in terms of a combination of speed and accuracy. The developed neural network model was validated using ionosonde electron density measurements obtained from Ilorin, Nigeria (geographic: 8.5° N, 4.5° E; geomagnetic: 1.8° S). A comparison of the neural network, the NeQuick, and the IRI model predictions relative to the ionosonde measurements indicate that the neural network model was the best-performing model; the NN model predictions minimized the mean absolute errors (MAEs) in ∼44% of 399 ionosonde profiles investigated, the IRI model did so in ∼32%, and the NeQuick did so in ∼24%. The MAEs of the NeQuick however exhibited the best (least) variance. In overall, the NN model gave the least (best) mean of the MAEs (∼73 × 103 cm−3), compared to ∼82 × 103 cm−3 given by both the NeQuick and the IRI models, further supporting the idea that neural networks are excellent for present-day ionospheric modeling.

A spectrum correlation matrix-based rapid damage identification method for joints in hinged slab bridges by sparse measurement

Hinged slab bridges are widely used in the medium and small-span bridges on highways and the joints are highly susceptible to damage under the action of the increasing traffic. However, current methods for damage identification of hinged joints, whether rely on static or dynamic testing, typically require substantial manpower, resources and time, which presents challenges for the rapid evaluation of numerous bridges. In view of this, a novel damage index named spectrum correlation matrix (SCM) is proposed and its feature extraction technology is established as well as the potential for sparse measurement is theoretically explained. Furthermore, a rapid, robust, and convenient damage identification methodology using SCM and Levenberg-Marquardt algorithm is proposed. An optimal strategy for the layout of sparse measuring points has been explored, the sensitivity and the effectiveness of the proposed method is validated through both numerical simulations and the in-situ test of a bridge in service. The results indicate that the SCM contains abundant vibration information and shows a high sensitivity to damage. The strategy for the layout of measuring points is highly efficient and the proposed methodology greatly reduces the number of measuring points compared to previous vibration-based methods, which eases rapid identification of damage for joints in hinged slab bridges.

Development and characterization of carboxylated copper oxide conjugated polymeric nanocomposites and correlating with computational techniques

The quality and effectiveness of composite-based components are influenced by their mechanical characteristics. Hence, a structured approach is essential to identify the key factors that contribute to achieving superior mechanical characteristics. This study investigates the utilization of an artificial neural network (ANN) to predict the mechanical characteristics, explicitly density, and hardness, of carboxyl copper oxide nanoparticle (CCONP)/DL-lactide and glycolide copolymer (PDLG) nanocomposites fabricated through microwave-assisted sintering. The research explores the effects of numerous microwave sintering conditions on the microstructure and mechanical properties of the nanocomposites. Physical characterization techniques including FTIR and TEM analysis are employed to confirm physical interactions and nanocomposite size. A back-propagation neural network with a 2–10-2 architecture was developed to predict density and hardness. The network was trained using the Levenberg-Marquardt algorithm and the Scaled Conjugate Gradient method. The predicted values are compared with experimental results, showing good agreement with correlation coefficients (R) of 0.883 for density and 0.9737 for hardness. This demonstrates the effectiveness of the ANN approach in evaluating the mechanical properties of CCONP/PDLG nanocomposites, providing a reliable tool for decision-making and potentially reducing experimental characterization costs.

Optimization of temperature prediction algorithms and simulation of future neighborhood-scale thermal environments in Chongqing

With climate change and urbanization, predicting the outdoor thermal environment of residential areas has become increasingly crucial, particularly during extreme weather conditions. Existing studies lack a comprehensive approach to optimizing temperature prediction algorithms for Chongqing and simulating extreme thermal environments at the neighborhood scale for future decades. This study employed various algorithms, including Levenberg-Marquardt optimization, Monte Carlo simulation, ARIMA modeling, and SARIMA prediction, to simulate and forecast temperature data for the central urban area of Chongqing from 2014 to 2023. By assessing metrics such as root mean square error (RMSE), R-squared (R2), and mean absolute percentage error (MAPE), the most effective prediction algorithm was identified. Results indicate that the Levenberg-Marquardt optimization algorithm, known for its nonlinear curve fitting capabilities, demonstrated superior performance in both the test and training sets, achieving an RMSE of 0.82 °C, MAPE of 1.81 %, and R2 of 0.75. This algorithm was subsequently used to forecast the outdoor temperature trend in Chongqing from 2024 to 2050, while also simulating the outdoor wind field, temperature distribution, building surface temperatures, and wind speeds in a residential district at neighborhood scale for 2030, 2040, and 2050 at a building density of 40 %. Findings reveal that peak pedestrian-level temperatures could reach 45.62 °C, and peak roof surface temperatures could reach 93.93 °C under extreme conditions. Furthermore, the study proposes practical recommendations for building layouts and cooling strategies. These findings are expected to improve residential planning in Chongqing, enhance residents' quality of life, and provide insights for other regions facing future temperature changes.

The novel methods of insulation detection based on Adaptive Levenberg–Marquardt algorithm and Third-Order Variable Forgetting Factor Recursive Least Squares-Decouple algorithm

Electric vehicles (EVs) are central to the future of automotive development, with high-voltage insulation performance critical for operational safety. Existing insulation detection methods face challenges such as limited scope, low accuracy, poor interference resistance, and slow response. This study introduces two insulation detection models based on the unbalanced bridge method and low-frequency signal injection, analyzing their theoretical effectiveness and confirming superior detection capability in the unbalanced bridge method. Furthermore, to address feedback voltage waveform issues in this method, an adaptive Levenberg–Marquardt (ALM) algorithm is proposed to prevent the divergence typically seen in traditional approaches. Additionally, a decoupling algorithm utilizing a Third-order Variable Forgetting Factor Recursive Least Squares (TVFF-Decouple) simplifies algorithm complexity significantly while enabling anomaly detection. Finally, AEKF and SRCKF algorithms were used for observation, identifying an optimal combination that reduces noise interference effectively. Simulations and bench tests demonstrate that the proposed methods swiftly and accurately detect positive and negative insulation resistances and equivalent Y capacitance under various conditions.

Thermophysical properties, and figures-of-merit analyses of nanodiamond/CuO ionanofluids: Experimental and artificial neural network predictions

The nanodiamond/copper oxide (ND/CuO) nanoparticles were dispersed into 1-ethyl-3-methylimidazolium chloride [EMiM]Cl to create ionanofluids. The experiments were performed to analyse the thermophysical properties under particle volume loadings from 0.2 % to 1.0 %, and temperature ranging from 30 to 60 °C. Theoretical approach was made to understand the Figures-of-Merit (FoM) of the prepared ionanofluids, while they flow in a tube, and helical coil through the evaluated thermophysical properties. The lower thermal conductivity augment of 14.27 % was noticed at 0.2% vol. and larger thermal conductivity enhancement of 35.20 % was noticed at 1.0% vol. and at a temperature of 60 °C, against the base fluid. Moreover, the viscosity of 1.0% vol. of ionanofluid was enhanced by 61.66 % at a temperature of 30 °C, over the base fluid. The other properties like density was increased with an increase of volume loadings, and specific heat was decreased with an increase of volume loadings. The FoM results indicated that, all the prepared volume concentrations of ionanofluids flow in a tube was benefited fluid when the fluid operating temperature was exceeds to 35 °C, on the other side, the prepared ionanofluids flow in a helical coil was benefited fluid when its operating temperature was above 30 °C for 0.8 %, and 1.0% vol. loadings. The estimated thermophysical properties were also used as input and output data for an artificial neural network of Levenberg-Marquardt (LM) algorithm. It is noticed from the LM algorithm results, the predicted data is well agreed with an experimental data. For all the data, the correlation coefficient (R2) of thermal conductivity is 0.99283, viscosity is 0.9971, density is 0.99887, and specific heat is 0.99817, was observed, respectively.

An artificial neural network approach to characterizing the behavior of bioconvective nanofluid model using backpropagation of Levenberg–Marquardt algorithm

The study of the behavior of bioconvective nanofluid model (BC-NFM) was explored using bioconvection properties in the computational analysis of magnetized nanofluid flow that was convectively heated, which is critical for applications in energy systems and biomedical devices. We implemented a backpropagated Levenberg–Marquardt neural network approach (BLMNNA) to enhance the analysis and prediction accuracy of such fluid flows. Using the Adams numerical technique, we generated a comprehensive dataset for eight distinct scenarios by variation of thermophoresis parameter, Rayleigh number, Deborah parameter, Hartman number, Prandtl number, bioconvection Lewis number, and Schmidt number to train and test our model. The results demonstrate significant improvements in prediction accuracy and computational efficiency compared to traditional numerical solvers. The steps of training, testing, and validating the developed BLMNNA are used to get the desired numerical solutions of BC-NFM for various instances. The worth and accuracy of the stochastic numerical solutions of BC-NFM are established and authenticated by the outputs of the designed methodology BLMNNA through Adaptation graphs of Mean Square Error, regression studies, plots of error histogram and index of state transition. Excellent measurements of performance in terms of MEAN SQUARE ERROR are achieved at level 9.76E[Formula: see text], 1.41E[Formula: see text], 1.79E[Formula: see text], 1.22E[Formula: see text], 8.49E[Formula: see text], 7.19E[Formula: see text], 9.72E[Formula: see text], and 9.35E[Formula: see text] against 69, 73, 96, 76, 237, 86, 120, and 33 epochs. The significant connection between the proposed and reference findings demonstrates the validity of the BLMNNA based on error analysis, which ranges from E[Formula: see text] to E[Formula: see text] for all situations. The results show that the proposed neural network approach achieves a high level of accuracy, closely matching the outcomes obtained from the numerical solver. The method provides an efficient and precise solution for the analysis of complex fluid flow problems, representing a significant advancement over traditional numerical techniques.

A combined Markov Chain Monte Carlo and Levenberg–Marquardt inversion method for heterogeneous subsurface reservoir modeling

In this study, we systematically investigate an inverse method for heterogeneous porous media to obtain porosity and permeability fields considering only production well data. The forward modeling of the input data, namely pressure and saturation fields, is based on the motion equations of a coupled Darcy flow system involving two phases of isothermal fluid flow. We discretize these equations using a multiscale finite volume simulation technique in the spatial domain, and the backward Euler method in time domain. In the inversion procedure, we combine a global optimization method, the Markov Chain Monte Carlo (MCMC) method, with a local optimization method, the Levenberg–Marquardt (LM) method. The MCMC was implemented as the Random Walk algorithm, and to generate the samples of the porosity and permeability fields, we employed Karhunen–Loève (KL) expansion of second-order stationary fields with Gaussian covariance. The coefficients of the KL expansion are estimated by minimizing the norm of the residual dependent on these fields. At the end of the MCMC iterations, we refine the KL coefficients associated with the porosity and permeability fields using the LM method. We verify in the numerical experiments that the accuracy of the porosity and permeability fields is improved by the LM refinement step.

Fast Two-dimensional Positioning Method of Crab Pulsar Based on Multiple Optimization Algorithms

In the two-dimensional positioning method of pulsars, the grid method is used to provide non-sensitive direction and positional estimates. However, the grid method has a high computational load and low accuracy due to the interval of the grid. To improve estimation accuracy and reduce the computational load, we propose a fast two-dimensional positioning method for the crab pulsar based on multiple optimization algorithms (FTPCO). The FTPCO uses the Levenberg–Marquardt (LM) algorithm, three-point orientation (TPO) method, particle swarm optimization (PSO) and Newton–Raphson-based optimizer (NRBO) to substitute the grid method. First, to avoid the influence of the non-sensitive direction on positioning, we take an orbital error and the distortion of the pulsar profile as optimization objectives and combine the grid method with the LM algorithm or PSO to search for the non-sensitive direction. Then, on the sensitive plane perpendicular to the non-sensitive direction, the TPO method is proposed to fast search the sensitive direction and sub-sensitive direction. Finally, the NRBO is employed on the sensitive and sub-sensitive directions to achieve two-dimensional positioning of the Crab pulsar. The simulation results show that the computational load of the FTPCO is reduced by 89.4% and the positioning accuracy of the FTPCO is improved by approximately 38% compared with the grid method. The FTPCO has the advantage of high real-time accuracy and does not fall into the local optimum.

Flow data forecasting for the junction flow using artificial neural network

The present study aims to predict the flow characteristics downstream of a cylinder, which is the result of junction flow using an Artificial Neural Network (ANN) algorithm. The training and test datasets were obtained through Particle Image Velocimetry (PIV) experiments. The experiments were conducted at Reynolds numbers Re = 1.5 x 103 and 4 x 103 based on the cylinder diameter (D) at dimensionless measurement heights (Z = h/D) of Z1 = 0.06, Z2 = 0.4, Z3 = 0.8, and Z4 = 1.6 respectively. While the X- and Y-coordinate and dimensionless measurement location (Z) variables are employed as inputs to the ANN model, the output variables are vorticity ⟨ω⟩, streamwise velocity ⟨u⟩, and transverse velocity ⟨v⟩, which are derived from the time-averaged flow data. Modeling flow characteristics with easily obtainable independent variables without flow and physical properties was considered. Three various training algorithms such as Levenberg Marquardt (LM), Resilient Backpropagation (RP), and Scaled Conjugate Gradient (SCG) were employed to assess and compare their prediction performance. The results indicate that the LM learning algorithm outperforms the RP and SCG algorithms, especially at low Reynolds (Re) numbers. The ANN model, trained with the LM algorithm, exhibits significant success, achieving R = 0.9816 correlation coefficient (R), MAE = 2.4250 m/s Mean Absolute Error (MAE), and RMSE = 3.3541 m/s Root Mean Square Error (RMSE) for streamwise velocity ⟨u⟩ data. Notably, the LM algorithm for the testing process demonstrates the best predictions at Re = 1.5x103, yielding R = 0.9779, MAE = 2.7417 m/s, and RMSE = 3.7493 m/s. The ANN-LM model's patterns closely align with experimental results, affirming its accuracy, which proves that the prediction of time-averaged velocity data solely based on spatial coordinates as input can be achieved successfully.

An improved generalized Prandtl–Ishlinskii model for the hysteresis modeling of pneumatic artificial muscles

Due to the merits of high flexibility, large driving force, and light weight, the pneumatic artificial muscle (PAM) has been widely applied in robot. However, the inherent asymmetric hysteresis nonlinear characteristics affect the control performance of PAM seriously. This paper presents an improved generalized Prandtl–Ishlinskii (GPI-M) model for the asymmetric hysteresis characterization of PAM, which adopts the simplified Magic Formula (SMF) as the envelop function instead of hyperbolic tangent function (GPI) or arc tangent function (GPI-A). With regard to the effect of parameters identification, the Levenberg-Marquardt (LM) algorithm, genetic algorithm (GA), particle swarm optimization (PSO) algorithm, and differential evolution (DE) algorithm are studied, which shows the LM algorithm is far superior to the other three intelligent algorithms in terms of computational efficiency and identification accuracy. Furthermore, a crosswise comparative study on three models and two envelop functions investigating modeling accuracy reveals that the newly introduced GPI-M model exhibits better performance than the modified symmetric generalized Prandtl-Ishlinskii (MSGPI) model and the GPI-A model presented previously. Meanwhile, the influence of the operator numbers on the modeling accuracy of three models is discussed, which finds that the GPI-M model possess the best accuracy with the least operator numbers.