Design of neuro-evolutionary model for solving nonlinear singularly perturbed boundary value problems

Raja, Muhammad Asif Zahoor; Abbas, Saleem; Syam, Muhammed I.; Wazwaz, Abdul‐Majid

doi:10.1016/j.asoc.2017.11.002

Cited by 25 publications

(2 citation statements)

References 47 publications

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“…These all are deterministic procedures with their own advantages, applications, and limitations while the stochastic techniques [29][30][31][32][33][34] are not extensively exploited for the parameter estimation of input nonlinear Hammerstein systems as yet. Few potential applications of these methodologies based on exploration and exploitation of artificial neural networks (ANNs), differential evolution (DE) and genetic algorithms (GAs) include fractional order systems [35][36], nonlinear singularly perturb systems [37], nonlinear pantograph systems [38], nonlinear prey-predator models [39], nonlinear chaotic systems [40][41], models of nonlinear optics [42], random matrix theory based application [43], thin film flow systems [44], thermal analysis of porous fin model [45], input nonlinear control autoregressive systems [46][47], active noise control systems [48][49] and control autoregressive moving average systems [50]. Beside these recently stochastic solvers are used to address viably the optimiza tio n problems arising in various domains such as astrophysics [51][52], atomic physics [53][54], plasma physics [55][56], thermodynamics [57], mechanics [58][59], nanotechnology [60][61], electric circuits [62][63], energy [64][65], power [66]…”

Section: Researchers Have Great Contributions To Develop Reliable Mec...mentioning

confidence: 99%

Design of meta-heuristic computing paradigms for Hammerstein identification systems in electrically stimulated muscle models

Mehmood

Zameer

Chaudhary

et al. 2020

Neural Comput & Applic

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In this study, a novel application of differential evolution (DE) based computatio na l heuristics is proposed for identification of Hammerstein structures representing the electrica lly stimulated muscle (ESM) models as a part of rehabilitation interventions for the stock patient to prevent the post spinal cord injury atrophy. The strength of approximation theory is incorporated for defining the fitness function for ESM system based on mean square deviation between actual and estimated responses. DE, genetic algorithms (GAs), particle swarm optimization (PSO), pattern search (PS) and simulated annealing (SA) are used as optimization mechanisms to identify the ESM models with input nonlinearities of sigmoidal, polynomial and spline kernels for noiseless and noisy environments. Comparative studies based on detailed statistics establish the worth of DE based heuristics over its counterparts GAs, PSO, PS and SA in terms of accuracy, convergence, robustness and efficiency for identification of ESM models arising in rehabilitation of the stock patients.

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Section: Researchers Have Great Contributions To Develop Reliable Mec...mentioning

confidence: 99%

Design of meta-heuristic computing paradigms for Hammerstein identification systems in electrically stimulated muscle models

Mehmood

Zameer

Chaudhary

et al. 2020

Neural Comput & Applic

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“…[1], [2], [3]. The radial basis function (RBF) method is a powerful method for solving differential equations related to many physical problems [4], [5], [6]. Radial basis functions are a type of function whose value depends only on the distance between a point and the origin.…”

Section: Introductionmentioning

confidence: 99%

Applying a New Trigonometric Radial Basis Function Approximation in Solving Nonlinear Vibration Problems

Talebirostami,

Najafabadi,

Ganji

2024

Int. J. Appl. Comput. Math

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This study introduces a semi-analytical New Trigonometric Radial Basis Function (NTRBF) method for solving strongly nonlinear differential equations in vibration problems. The method uses a particular trigonometric function to deal with differential equations in an extraordinary and original approach. It was compared to four different problems, including the Global Residue Harmonic Balance Method (GRHBM) in solving circular sector oscillator problem, the Continuous Piecewise Linearization method (CPLM) in solving strong nonlinear differential equation of a tapered beam, the Differential Transform Method (DTM) to solve centrifugal rotating frame motion, and Akbari-Ganji's Method (AGM) to solve Duffing-type nonlinear oscillator. These problems were solved in different conditions. The plots and tables represent both cumulative and maximum errors between the NTRBF and other methods, which use the numerical 4th-order Runge-Kutta method as a benchmark for accuracy. The outcomes prove the high accuracy and efficiency of the innovative technique and its unique capability in solving various nonlinear vibration problems.

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The Synthesis of the Switching Systems Optimal Parameters Search Algorithms

Druzhinina¹,

Masina

Petrov

2019

Communications in Computer and Information Science

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Design of neuro-evolutionary model for solving nonlinear singularly perturbed boundary value problems

Cited by 25 publications

References 47 publications

Design of meta-heuristic computing paradigms for Hammerstein identification systems in electrically stimulated muscle models

Design of meta-heuristic computing paradigms for Hammerstein identification systems in electrically stimulated muscle models

Applying a New Trigonometric Radial Basis Function Approximation in Solving Nonlinear Vibration Problems

The Synthesis of the Switching Systems Optimal Parameters Search Algorithms

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