International Scientific Journal

Thermal Science - Online First

online first only

Investigations of nonlinear induction motor model using the Gudermannian neural networks

This study aims to solve the nonlinear fifth-order induction motor model (FO-IMM) using the Gudermannian neural networks (GNNs) 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). GNNs are executed to discretize the nonlinear 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 nonlinear 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.
PAPER REVISED: 2021-08-16
PAPER ACCEPTED: 2021-08-21
  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. Agarwal, R.P., 1986. Boundary value problems from higher order differential equations. World Scientific.
  6. 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.
  7. 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.
  8. 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.
  9. Siddiqi, S.S. et al., 2007. Sextic spline solutions of fifth order boundary value problems. Applied Mathematics Letters, 20(5), pp.591-597.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. Umar, M., 2019. Intelligent computing for numerical treatment of nonlinear prey-predator models. Applied Soft Computing, 80, pp.506-524.
  19. 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.
  20. Sabir, Z. et al., 2018. Neuro-heuristics for nonlinear singular Thomas-Fermi systems. Applied Soft Computing, 65, pp.152-169.
  21. Sabir, Z. et al., 2019. Stochastic numerical approach for solving second order nonlinear singular functional differential equation. Applied Mathematics and Computation, 363, p.124605.
  22. 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.
  23. 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).
  24. 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).
  25. 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.
  26. 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.
  27. Wen-Xiu Ma, Mohamed R. Ali, R. Sadat, "Analytical Solutions for Nonlinear Dispersive Physical Model", Complexity, vol. 2020, Article D 3714832, 8 pages, 2020.
  28. 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).
  29. 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..
  30. Sridhar, 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
  31. Chang, F. S., 2016. Greedy-Search-based Multi-Objective Genetic Algorithm for Emergency Humanitarian Logistics Scheduling.
  32. 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.
  33. Vaishnav, P. et al., 2017. Traveling Salesman Problem Using Genetic Algorithm: A Survey.
  34. 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.
  35. 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.
  36. 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.
  37. Alharbi, al., 2017. A genetic algorithm based approach for solving the minimum dominating set of queens problem. Journal of Optimization, 2017.
  38. 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.
  39. 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.
  40. Hager, W.W. et al., 2020. A Newton-type Active Set Method for Nonlinear Optimization with Polyhedral Constraints. arXiv preprint arXiv:2011.01201.
  41. 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.
  42. 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.
  43. 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.
  44. 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.