Open accessJournal Article

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

05 Mar 2021-Complexity (Hindawi Limited)-Vol. 2021, pp 1-19
Abstract: 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.

Topics: Solver (56%), , Flexural rigidity (50%)
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Yin Zhang, Jianqiang Lin1, Zhenhuan Hu1, Naveed Ahmad Khan2  +1 moreInstitutions (2)
10 May 2021-IEEE Access
Abstract: 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.

Topics: , Cuckoo search (53%),  ... read more

10 Citations

Open accessJournal Article
16 Aug 2021-Entropy
Abstract: 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.

Topics: Heat transfer (54%), Euler's formula (52%),  ... read more

5 Citations

Open accessJournal Article
05 Oct 2021-Molecules
Abstract: 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.

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2 Citations

Open accessJournal Article
Abstract: In this paper, the problem of temperature distribution for convective straight fins with constant and temperature-dependent thermal conductivity is solved by using artificial neural networks trained by the biogeography-based heterogeneous cuckoo search (BHCS) algorithm. We have solved the integer and noninteger order energy balance equation in order to analyse the temperature distribution in convective straight fins. We have compared our results with homotopy perturbation method (HPM), variational iteration method (VIM), and homotopy perturbation Sumudu transform method (HPSTM). The results show that the ANN–BHCS algorithm gives better results than other analytical techniques. We have further checked the efficiency of the ANN–BHCS algorithm by using the performance metrics MAD, TIC, and ENSE. We have calculated the values of MAD, TIC, and ENSE for case 1 of the problem, and histograms of these metrics show the efficiency of our algorithm.

Topics: ,

2 Citations

Open accessJournal Article
Ashfaq Ahmad1, Muhammad Sulaiman1, Poom Kumam2, Maharani Abu Bakar3  +1 moreInstitutions (4)
01 Jan 2021-IEEE Access
Abstract: In the present article, mathematical analysis of drilling system with reverse air circulation is presented by a novel hybrid technique of feedforward artificial neural network (ANN) and biogeography based cuckoo search (BHCS) algorithm. A series solution is constructed with unknown weights for the differential equations representing the drilling problem. Five numerical cases are analysed to show the effectiveness of our method for the solution of differential equations. From the experimental outcomes, it is investigated that our soft computing procedure has a better rate of convergence to the best solution as compared to state-of-the-art techniques. From solution graphs, it is established that our results are in agreement with the reference solutions. It is noted that our technique is easy to implement and can be used for any mathematical model containing nonlinear differential equations. The graphical abstract of this article is given in Figure (1) . FIGURE 1. Graphical illustration of the soft computing procedure followed in this paper.

Topics: Soft computing (55%), Rate of convergence (52%),  ... read more

2 Citations

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34 results found

Journal Article
Abdul-Majid Wazwaz1Institutions (1)
Abstract: In this paper, a reliable technique for calculating Adomian polynomials for nonlinear operators will be developed. The new algorithm offers a promising approach for calculating Adomian polynomials for all forms of nonlinearity. The algorithm will be illustrated by studying suitable forms of nonlinearity. A nonlinear evolution model will be investigated.

Topics: , Taylor series (55%),  ... read more

575 Citations

Open accessJournal Article
Abstract: We apply the homotopy perturbation method for solving the fourth-order boundary value problems. The analytical results of the boundary value problems have been obtained in terms of convergent series with easily computable components. Several examples are given to illustrate the efficiency and implementation of the homotopy perturbation method. Comparisons are made to confirm the reliability of the method. Homotopy method can be considered an alternative method to Adomian decomposition method and its variant forms.

Topics: , n-connected (68%),  ... read more

140 Citations

Journal Article
Abdul-Majid Wazwaz1Institutions (1)
Abstract: A fast and accurate algorithm is developed for the solution of sixth-order boundary value problems (BVPs) with two-point boundary conditions. A modified form of the Adomian decomposition method is applied to construct the numerical solution for such problems. The scheme is tested on one linear and two nonlinear problems. The results demonstrate reliability and efficiency of the algorithm developed.

Topics: , , Boundary knot method (62%) ... read more

140 Citations

Journal Article
Abstract: In this paper, we have shown that higher order boundary value problems can be written as a system of integral equations, which can be solved by using the variational iteration technique. The analytical results of the equations have been obtained in terms of convergent series with easily computable components. Several examples are given to illustrate the efficiency and implementation of the method. Comparisons are made to confirm the reliability of the technique. Variational iteration technique may be considered as alternative and efficient for finding the approximate solutions of the boundary values problems.

Topics: , , Numerical analysis (51%) ... read more

138 Citations

Open accessJournal Article
Nehad Ali Shah1, Ilyas Khan2Institutions (2)
Abstract: This paper presents a Caputo–Fabrizio fractional derivatives approach to the thermal analysis of a second grade fluid over an infinite oscillating vertical flat plate. Together with an oscillating boundary motion, the heat transfer is caused by the buoyancy force induced by temperature differences between the plate and the fluid. Closed form solutions of the fluid velocity and temperature are obtained by means of the Laplace transform. The solutions of ordinary second grade and Newtonian fluids corresponding to time derivatives of integer and fractional orders are obtained as particular cases of the present solutions. Numerical computations and graphical illustrations are used in order to study the effects of the Caputo–Fabrizio time-fractional parameter $$\upalpha$$, the material parameter $$\alpha _2$$, and the Prandtl and Grashof numbers on the velocity field. A comparison for time derivative of integer order versus fractional order is shown graphically for both Newtonian and second grade fluids. It is found that fractional fluids (second grade and Newtonian) have highest velocities. This shows that the fractional parameter enhances the fluid flow.