In this study, a novel application of neurocomputing technique is presented for solving nonlinear heat transfer and natural convection porous fin problems arising in almost all areas of engineering and technology, especially in mechanical engineering. The mathematical models of the problems are exploited by the intelligent strength of Euler polynomials based Euler neural networks (ENN’s), optimized with a generalized normal distribution optimization (GNDO) algorithm and Interior point algorithm (IPA). In this scheme, ENN’s based differential equation models are constructed in an unsupervised manner, in which the neurons are trained by GNDO as an effective global search technique and IPA, which enhances the local search convergence. Moreover, a temperature distribution of heat transfer and natural convection porous fin are investigated by using an ENN-GNDO-IPA algorithm under the influence of variations in specific heat, thermal conductivity, internal heat generation, and heat transfer rate, respectively. A large number of executions are performed on the proposed technique for different cases to determine the reliability and effectiveness through various performance indicators including Nash–Sutcliffe efficiency (NSE), error in Nash–Sutcliffe efficiency (ENSE), mean absolute error (MAE), and Thiel’s inequality coefficient (TIC). Extensive graphical and statistical analysis shows the dominance of the proposed algorithm with state-of-the-art algorithms and numerical solver RK-4.

Application of Euler Neural Networks with Soft Computing Paradigm to Solve Nonlinear Problems Arising in Heat Transfer.

In this study, the intelligent computational strength of neural networks (NNs) based on the backpropagated Levenberg-Marquardt (BLM) algorithm is utilized to investigate the numerical solution of nonlinear multiorder fractional differential equations (FDEs). The reference data set for the design of the BLM-NN algorithm for different examples of FDEs are generated by using the exact solutions. To obtain the numerical solutions, multiple operations based on training, validation, and testing on the reference data set are carried out by the design scheme for various orders of FDEs. The approximate solutions by the BLM-NN algorithm are compared with analytical solutions and performance based on mean square error (MSE), error histogram (EH), regression, and curve fitting. This further validates the accuracy, robustness, and efficiency of the proposed algorithm.

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Application of Intelligent Paradigm through Neural Networks for Numerical Solution of Multiorder Fractional Differential Equations

In this paper, a novel soft computing algorithm is designed for the numerical solution of third-order nonlinear multi-singular Emden–Fowler equation (TONMS-EFE) using the strength of universal approximation capabilities of Legendre polynomials based Legendre neural networks supported with optimization power of the Whale Optimization Algorithm (WOA) and Nelder-Mead (NM) algorithm. Unsupervised error functions are constructed in terms of mean square error for governing TONMS-EF equations of first and second order. Unknown designed parameters in LeNN structure are optimized initially by WOA for global search while NM algorithm further enhances the rapid local search convergence. The proposed algorithm’s objective is to show the accuracy and robustness in solving challenging problems like TONMS-EFE. To study our designed scheme’s performance and effectiveness, LeNN-WOA-NM is implemented on four cases of TONMS-EFE. The results obtained by the proposed algorithm are compared with the Particle Swarm Optimization (PSO) algorithm, Cuckoo search algorithm (CSA), and WOA. Extensive graphical and statistical analysis for fitness value, absolute errors, and performance indicators in terms of mean, median, and standard deviations show the proposed algorithm’s efficiency and accuracy.

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Analysis of Third-Order Nonlinear Multi-Singular Emden–Fowler Equation by Using the LeNN-WOA-NM Algorithm

In this paper, we analyzed the mass transfer model with chemical reactions during the absorption of carbon dioxide (CO2) into phenyl glycidyl ether (PGE) solution. The mathematical model of the phenomenon is governed by a coupled nonlinear differential equation that corresponds to the reaction kinetics and diffusion. The system of differential equations is subjected to Dirichlet boundary conditions and a mixed set of Neumann and Dirichlet boundary conditions. Further, to calculate the concentration of CO2, PGE, and the flux in terms of reaction rate constants, we adopt the supervised learning strategy of a nonlinear autoregressive exogenous (NARX) neural network model with two activation functions (Log-sigmoid and Hyperbolic tangent). The reference data set for the possible outcomes of different scenarios based on variations in normalized parameters (α1, α2, β1, β2, k) are obtained using the MATLAB solver “pdex4”. The dataset is further interpreted by the Levenberg–Marquardt (LM) backpropagation algorithm for validation, testing, and training. The results obtained by the NARX-LM algorithm are compared with the Adomian decomposition method and residual method. The rapid convergence of solutions, smooth implementation, computational complexity, absolute errors, and statistics of the mean square error further validate the design scheme’s worth and efficiency.

Theoretical Analysis on Absorption of Carbon Dioxide (CO2) into Solutions of Phenyl Glycidyl Ether (PGE) Using Nonlinear Autoregressive Exogenous Neural Networks

In this paper, one dimensional mathematical model of convective-conductive-radiative fins is presented with thermal conductivity depending on temperature. The temperature field with insulated tip is determined for a fin in convective, conductive and radiative environments. Moreover, an intelligent soft computing paradigm named as the LeNN-WOA-NM algorithm is designed to analyze the mathematical model for the temperature field of convective-conductive-radiative fins. The proposed algorithm uses function approximating ability of Legendre polynomials based on artificial neural networks (ANN’s), global search optimization ability of Whale optimization algorithm (WOA), and local search convergence of Nelder-Mead algorithm. The proposed algorithm is applied to illustrate the effect of variations in coefficients of convection, radiation heat losses, and dimensionless parameter of thermal conductivity on temperature distribution of conductive-convective and radiative fins in convective and radiative environments. The experimental data establishes the effectiveness of the design scheme when compared with techniques in the latest literature. It can be observed that accuracy of approximate temperature increases with lower values of $N_{c}$ and $N_{r}$ while decreases with increase in $\lambda $ . The quality of solutions obtained by LeNN-WOA-NM algorithm are validated through performance indicators including absolute errors, MAD, TIC, and ENSE.

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Thermal Analysis of Conductive-Convective-Radiative Heat Exchangers With Temperature Dependent Thermal Conductivity

Design problems in structural engineering are often modeled as differential equations. These problems are posed as initial or boundary value problems with several possible variations in structural designs. In this paper, we have derived a mathematical model that represents different structures of beam-columns by varying axial load with or without internal forces including bending rigidity. We have also developed a novel solver, the LeNN-NM algorithm, which consists of weighted Legendre polynomials, and a single path following optimizer, the Nelder–Mead (NM) algorithm. To evaluate the performance of our solver, we have considered three design problems representing beam-columns. The values of performance indicators, MAD, TIC, NSE, and ENSE, are calculated for a hundred simulations. The outcome of our statistical analysis points to the superiority of the LeNN-NM algorithm. Graphical illustrations are presented to further elaborate on our claims.

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Wen Huang

Papers

Analysis of Beam-Column Designs by Varying Axial Load with Internal Forces and Bending Rigidity Using a New Soft Computing Technique

Comparative analysis of calculation methods for Cable Curve of Landscape Suspension Bridges

Shear Performance of Damaged Concrete Beams Reinforced by Penetrating FRP