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Integrated computational intelligent paradigm for nonlinear electric circuit models using neural networks, genetic algorithms and sequential quadratic programming

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Abstract

In this paper, a novel application of biologically inspired computing paradigm is presented for solving initial value problem (IVP) of electric circuits based on nonlinear RL model by exploiting the competency of accurate modeling with feed forward artificial neural network (FF-ANN), global search efficacy of genetic algorithms (GA) and rapid local search with sequential quadratic programming (SQP). The fitness function for IVP of associated nonlinear RL circuit is developed by exploiting the approximation theory in mean squared error sense using an approximate FF-ANN model. Training of the networks is conducted by integrated computational heuristic based on GA-aided with SQP, i.e., GA-SQP. The designed methodology is evaluated to variants of nonlinear RL systems based on both AC and DC excitations for number of scenarios with different voltages, resistances and inductance parameters. The comparative studies of the proposed results with Adam’s numerical solutions in terms of various performance measures verify the accuracy of the scheme. Results of statistics based on Monte-Carlo simulations validate the accuracy, convergence, stability and robustness of the designed scheme for solving problem in nonlinear circuit theory.

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Abbreviations

AE:

Absolute error

ANS:

Adam’s numerical solver

DC/AC:

Direct current/alternating current

EGNSE :

Error function of NSE

E VAF :

Error function of VAF

FF-ANN:

Forward artificial neural network

GA:

Genetic algorithms

G MAE :

Global MAE

G NSE :

Global NSE

G VAF :

Global VAF

IVP:

Initial value problem

MAE:

Mean absolute error

MIN:

Minimum

NNDEM:

Neural network-based differential equations models

NSE:

Nash–Sutcliffe efficiency

ODE:

Ordinary differential equations

RL:

Resistor inductor

SQP:

Sequential quadratic programming

SS:

Stochastic solvers

STD:

Standard deviation

VAF:

Variance account for

i :

Current

Ψ :

Flux-linkage of the inductor

α :

A constant

δ :

Unknown vector

w :

Unknown vector

β :

Unknown vector

ε :

Objective function

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Authors and Affiliations

  1. Department of Electrical Engineering, Pakistan Institute of Engineering and Applied Sciences, Nilore, Islamabad, Pakistan

    Ammara Mehmood

  2. Department of Computer and Information Sciences, Pakistan Institute of Engineering and Applied Sciences, Nilore, Islamabad, Pakistan

    Aneela Zameer

  3. School of Biomedical Engineering, Centre for Health Technologies, Department of Engineering and IT, University of Technology, Sydney, NSW, Australia

    Sai Ho Ling

  4. Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus, Attock, Pakistan

    Ata ur Rehman & Muhammad Asif Zahoor Raja

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  1. Ammara Mehmood
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  2. Aneela Zameer
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  3. Sai Ho Ling
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Correspondence to Sai Ho Ling.

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The numerical illustrations of results in the case of AC excitation are given in Tables A1 and A2, while the graphics are presented in Figs. A1 to A5 (DOCX 190 kb)

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Mehmood, A., Zameer, A., Ling, S.H. et al. Integrated computational intelligent paradigm for nonlinear electric circuit models using neural networks, genetic algorithms and sequential quadratic programming. Neural Comput & Applic 32, 10337–10357 (2020). https://doi.org/10.1007/s00521-019-04573-3

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