THERMAL SCIENCE
International Scientific Journal
INVESTIGATIONS OF NON-LINEAR INDUCTION MOTOR MODEL USING THE GUDERMANNIAN NEURAL NETWORKS
ABSTRACT
This study aims to solve the non-linear fifth-order induction motor model (FO-IMM) using the Gudermannian neural networks (GNN) along with the optimization procedures of global search as a genetic algorithm together with the quick local search process as active-set technique (GNN-GA-AST). The GNN are executed to discretize the non-linear FO-IMM to prompt the fitness function in the procedure of mean square error. The exactness of the GNN-GA-AST is observed by comparing the obtained results with the reference results. The numerical performances of the stochastic GNN-GA-AST are provided to tackle three different variants based on the non-linear FO-IMM to authenticate the consistency, significance and efficacy of the designed stochastic GNN-GA-AST. Additionally, statistical illustrations are available to authenticate the precision, accuracy and convergence of the designed stochastic GNN-GA-AST.
KEYWORDS
PAPER SUBMITTED: 2021-05-08
PAPER REVISED: 2021-08-16
PAPER ACCEPTED: 2021-08-21
PUBLISHED ONLINE: 2021-09-04
THERMAL SCIENCE YEAR
2022, VOLUME
26, ISSUE
Issue 4, PAGES [3399 - 3412]
- Richards, G. et al., 1994. Reduced order models for induction motors with two rotor circuits. IEEE Transactions on Energy Conversion, 9(4), pp.673-678.
- Davies, A.R., et al., 1988. Spectral Galerkin methods for the primary two‐point boundary value problem in modelling viscoelastic flows. International Journal for Numerical Methods in Engineering, 26(3), pp.647-662.
- Karageorghis, A., et al., 1988. Spectral collocation methods for the primary two‐point boundary value problem in modelling viscoelastic flows. International Journal for Numerical Methods in Engineering, 26(4), pp.805-813.
- Caglar, H.N., et al., 1999. The numerical solution of fifth-order boundary value problems with sixth-degree B-spline functions. Applied Mathematics Letters, 12(5), pp.25-30.
- Agarwal, R.P., 1986. Boundary value problems from higher order differential equations. World Scientific.
- Noor, M.A. et al., 2009. A new approach to fifth-order boundary value problems. International Journal of Nonlinear Science, 7(2), pp.143-148.
- Siddiqi, S.S., et al., 1996. 1. Spline Solutions of Linear Sixth-order Boundary-value Problems. Computer Methods in Applied Mechanics and Engineering, 31, pp.309-325.
- Siddiqi, S.S. et al., 1996. Spline solutions of linear sixth-order boundary-value problems. International Journal of Computer Mathematics, 60(3-4), pp.295-304.
- Siddiqi, S.S. et al., 2007. Sextic spline solutions of fifth order boundary value problems. Applied Mathematics Letters, 20(5), pp.591-597.
- Akram, G. et al 2017. Application of homotopy analysis method to the solution of ninth order boundary value problems in AFTI-F16 fighters. Journal of the Association of Arab Universities for Basic and Applied Sciences, 24, pp.149-155.
- Viswanadham, K.K., et al 2010. Numerical solution of fifth order boundary value problems by collocation method with sixth order B-splines. International Journal of Applied Science and Engineering, 8(2), pp.119-125.
- Akram, G. et al., 2011. Solution of fifth order boundary value problems in reproducing kernel space. Middle-East Journal of Scientific Research, 10(2), pp.191-195.
- Sabir, Z., et al, O., 2020. Numerical investigations to design a novel model based on the fifth order system of Emden-Fowler equations. Theoretical and Applied Mechanics Letters, 10(5), pp.333-342.
- NS KasiViswanadham, K. et al., 2012. Quartic B-spline collocation method for fifth order boundary value problems. International Journal of Computer Applications, 43(13), pp.1-6.
- Siddiqi, S.S., et al, A., 2011. Solution of fifth-order singularly perturbed boundary value problems using non-polynomial spline technique Euro. J Sci Res, 56, pp.415-425.
- Siddiqi, S.S. et al, M., 2015. Application of non-polynomial spline to the solution of fifth-order boundary value problems in induction motor. Journal of the Egyptian Mathematical Society, 23(1), pp.20-26.
- Raja, M.A.Z. et al., 2019. Numerical solution of doubly singular nonlinear systems using neural networks-based integrated intelligent computing. Neural Computing and Applications, 31(3), pp.793-812.
- Umar, M., 2019. Intelligent computing for numerical treatment of nonlinear prey-predator models. Applied Soft Computing, 80, pp.506-524.
- Umar, M. et al., 2020. A stochastic computational intelligent solver for numerical treatment of mosquito dispersal model in a heterogeneous environment. The European Physical Journal Plus, 135(7), pp.1-23.
- Sabir, Z. et al., 2018. Neuro-heuristics for nonlinear singular Thomas-Fermi systems. Applied Soft Computing, 65, pp.152-169.
- Sabir, Z. et al., 2019. Stochastic numerical approach for solving second order nonlinear singular functional differential equation. Applied Mathematics and Computation, 363, p.124605.
- Sabir, Z et al., 2020. Neuro-swarm intelligent computing to solve the second-order singular functional differential model. The European Physical Journal Plus, 135(6), p.474.
- Sabir, Z., Ali, M.R., Raja, M.A.Z. et al. Computational intelligence approach using Levenberg-Marquardt backpropagation neural networks to solve the fourth-order nonlinear system of Emden-Fowler model. Engineering with Computers (2021). doi.org/10.1007/s00366-021-01427-2.
- Ayub, A., Sabir, Z., Altamirano, G.C. et al. Characteristics of melting heat transport of blood with time-dependent cross-nanofluid model using Keller-Box and BVP4C method. Engineering with Computers (2021). doi.org/10.1007/s00366-021-01406-7.
- Sabir, Z. et al., 2020. Design of stochastic numerical solver for the solution of singular three-point second-order boundary value problems. Neural Computing and Applications, pp.1-17.
- Raja, M.A.Z., et al, 2018. A new stochastic computing paradigm for the dynamics of nonlinear singular heat conduction model of the human head. The European Physical Journal Plus, 133(9), p.364.
- Wen-Xiu Ma, Mohamed R. Ali, R. Sadat, "Analytical Solutions for Nonlinear Dispersive Physical Model", Complexity, vol. 2020, Article D 3714832, 8 pages, 2020. doi.org/10.1155/2020/3714832.
- Mohamed R. Ali , Dumitru Baleanu, New wavelet method for solving boundary value problems arising from an adiabatic tubular chemical reactor theory, International Journal of BiomathematicsVol. 13, No. 07, 2050059 (2020).
- Mohamed M. Mousa, Mohamed R. Ali & Wen-Xiu Ma, A combined method for simulating MHD convection in square cavities through localized heating by method of line and penalty-artificial compressibility, Journal of Taibah University for Science, 15:1, 208-217, (2021). DOI: 10.1080/16583655.2021.1951503..
- Sridhar, R.et al. "Optimization of heterogeneous Bin packing using adaptive genetic algorithm." In IOP Conference Series: Materials Science and Engineering, vol. 183, no. 1, p. 012026. IOP Publishing, 2017
- Chang, F. S., 2016. Greedy-Search-based Multi-Objective Genetic Algorithm for Emergency Humanitarian Logistics Scheduling.
- An, P. Q. et al., 2016, August. One-day-ahead cost optimisation for a multi-energy source building using a genetic algorithm. In Control (CONTROL), 2016 UKACC 11th International Conference on (pp. 1-6). IEEE.
- Vaishnav, P. et al., 2017. Traveling Salesman Problem Using Genetic Algorithm: A Survey.
- Tuhus-Dubrow, D. et al., 2010. Genetic-algorithm based approach to optimize building envelope design for residential buildings. Building and environment, 45(7), pp. 1574-1581.
- Das, S. et al., 2017, February. Optimal Set of Overlapping Clusters Using Multi-objective Genetic Algorithm. In Proceedings of the ninth International Conference on Machine Learning and computing (pp. 232-237). ACM.
- Tan, J. et al., 2017. Determination of glass transitions in boiled candies by capacitance based thermal analysis (CTA) and genetic algorithm (GA). Journal of Food Engineering, 193, pp. 68-75.
- Alharbi, S.et al., 2017. A genetic algorithm based approach for solving the minimum dominating set of queens problem. Journal of Optimization, 2017.
- Sabir, Z. et al., 2020. Integrated neuro‐evolution heuristic with sequential quadratic programming for second‐order prediction differential models. Numerical Methods for Partial Differential Equations.
- Gao, Y., et al., 2020. Primal-dual active set method for pricing American better-of option on two assets. Communications in Nonlinear Science and Numerical Simulation, 80, p.104976.
- Hager, W.W. et al., 2020. A Newton-type Active Set Method for Nonlinear Optimization with Polyhedral Constraints. arXiv preprint arXiv:2011.01201.
- Piller, O., et al., 2020. A Content-Based Active-Set Method for Pressure-Dependent Models of Water Distribution Systems with Flow Controls. Journal of Water Resources Planning and Management, 146(4), p.04020009.
- Azizi, M., et al., 2020. A fuzzy system based active set algorithm for the numerical solution of the optimal control problem governed by partial differential equation. European Journal of Control, 54, pp.99-110.
- Shen, C., et al., 2020. An accelerated active-set algorithm for a quadratic semidefinite program with general constraints. Computational Optimization and Applications, pp.1-42.
- Abide, S., et al., 2021. Inexact primal-dual active set method for solving elastodynamic frictional contact problems. Computers & Mathematics with Applications, 82, pp.36-59.