Study of Rolling Motion of Ships in Random Beam Seas with Nonlinear Restoring Moment and Damping Effects Using Neuroevolutionary Technique

Quantitative Study of Non-Linear Convection Diffusion Equations for a Rotating-Disc Electrode

Rotating-disc electrodes (RDEs) are favored technologies for analyzing electrochemical processes in electrically charged cells and other revolving machines, such as engines, compressors, gearboxes, and generators. The model is based on the concept of the nonlinear entropy convection-diffusion equations, which are constructed using semi-boundaries as an infinite notion. In this model, the surrogate solutions with different parameter values for the mathematical characterization of non-dimensional OH- and H+ ion concentrations at a rotating-disc electrode (RDE) are investigated using an intelligent hybrid technique by utilizing neural networks (NN) and the Levenberg-Marquardt algorithm (LMA). Reference solutions were calculated using the RK-4 numerical method. Through the training, validation, and testing sampling of reference solutions, the NN-BLMA approximations were recorded. Error histograms, absolute error, curve fitting graphs, and regression graphs validated the NN-BLMA's resilience and accuracy for the problem. Additionally, the comparison graphs between the reference solution and the NN-BLMA procedure established that our paradigm is reliable and accurate.

Application of a Machine Learning Algorithm for Evaluation of Stiff Fractional Modeling of Polytropic Gas Spheres and Electric Circuits

Fractional polytropic gas sphere problems and electrical engineering models typically simulated with interconnected circuits have numerous applications in physical, astrophysical phenomena, and thermionic currents. Generally, most of these models are singular-nonlinear, symmetric, and include time delay, which has increased attention to them among researchers. In this work, we explored deep neural networks (DNNs) with an optimization algorithm to calculate the approximate solutions for nonlinear fractional differential equations (NFDEs). The target data-driven design of the DNN-LM algorithm was further implemented on the fractional models to study the rigorous impact and symmetry of different parameters on RL, RC circuits, and polytropic gas spheres. The targeted data generated from the analytical and numerical approaches in the literature for different cases were utilized by the deep neural networks to predict the numerical solutions by minimizing the differences in mean square error using the Levenberg–Marquardt algorithm. The numerical solutions obtained by the designed technique were contrasted with the multi-step reproducing kernel Hilbert space method (MS-RKM), Laplace transformation method (LTM), and Padé approximations. The results demonstrate the accuracy of the design technique as the DNN-LM algorithm overlaps with the actual results with minimum percentage absolute errors that lie between 10−8 and 10−12. The extensive graphical and statistical analysis of the designed technique showed that the DNN-LM algorithm is dependable and facilitates the examination of higher-order nonlinear complex problems due to the flexibility of the DNN architecture and the effectiveness of the optimization procedure.

On the Computational Study of a Fully Wetted Longitudinal Porous Heat Exchanger Using a Machine Learning Approach

The present study concerns the modeling of the thermal behavior of a porous longitudinal fin under fully wetted conditions with linear, quadratic, and exponential thermal conductivities surrounded by environments that are convective, conductive, and radiative. Porous fins are widely used in various engineering and everyday life applications. The Darcy model was used to formulate the governing non-linear singular differential equation for the heat transfer phenomenon in the fin. The universal approximation power of multilayer perceptron artificial neural networks (ANN) was applied to establish a model of approximate solutions for the singular non-linear boundary value problem. The optimization strategy of a sports-inspired meta-heuristic paradigm, the Tiki-Taka algorithm (TTA) with sequential quadratic programming (SQP), was utilized to determine the thermal performance and the effective use of fins for diverse values of physical parameters, such as parameter for the moist porous medium, dimensionless ambient temperature, radiation coefficient, power index, in-homogeneity index, convection coefficient, and dimensionless temperature. The results of the designed ANN-TTA-SQP algorithm were validated by comparison with state-of-the-art techniques, including the whale optimization algorithm (WOA), cuckoo search algorithm (CSA), grey wolf optimization (GWO) algorithm, particle swarm optimization (PSO) algorithm, and machine learning algorithms. The percentage of absolute errors and the mean square error in the solutions of the proposed technique were found to lie between 10-4 to 10-5 and 10-8 to 10-10, respectively. A comprehensive study of graphs, statistics of the solutions, and errors demonstrated that the proposed scheme's results were accurate, stable, and reliable. It was concluded that the pace at which heat is transferred from the surface of the fin to the surrounding environment increases in proportion to the degree to which the wet porosity parameter is increased. At the same time, inverse behavior was observed for increase in the power index. The results obtained may support the structural design of thermally effective cooling methods for various electronic consumer devices.

Analysis of Nanofluid Particles in a Duct with Thermal Radiation by Using an Efficient Metaheuristic-Driven Approach

This study investigated the steady two-phase flow of a nanofluid in a permeable duct with thermal radiation, a magnetic field, and external forces. The basic continuity and momentum equations were considered along with the Buongiorno model to formulate the governing mathematical model of the problem. Furthermore, the intelligent computational strength of artificial neural networks (ANNs) was utilized to construct the approximate solution for the problem. The unsupervised objective functions of the governing equations in terms of mean square error were optimized by hybridizing the global search ability of an arithmetic optimization algorithm (AOA) with the local search capability of an interior point algorithm (IPA). The proposed ANN-AOA-IPA technique was implemented to study the effect of variations in the thermophoretic parameter (Nt), Hartmann number (Ha), Brownian (Nb) and radiation (Rd) motion parameters, Eckert number (Ec), Reynolds number (Re) and Schmidt number (Sc) on the velocity profile, thermal profile, Nusselt number and skin friction coefficient of the nanofluid. The results obtained by the designed metaheuristic algorithm were compared with the numerical solutions obtained by the Runge–Kutta method of order 4 (RK-4) and machine learning algorithms based on a nonlinear autoregressive network with exogenous inputs (NARX) and backpropagated Levenberg–Marquardt algorithm. The mean percentage errors in approximate solutions obtained by ANN-AOA-IPA are around 10−6 to 10−7. The graphical analysis illustrates that the velocity, temperature, and concentration profiles of the nanofluid increase with an increase in the suction parameter, Eckert number and Schmidt number, respectively. Solutions and the results of performance indicators such as mean absolute deviation, Theil’s inequality coefficient and error in Nash–Sutcliffe efficiency further validate the proposed algorithm’s utility and efficiency.