Nothing Special   »   [go: up one dir, main page]
Skip to main content

Advertisement

Springer Nature Link
Log in

Computational intelligence methodology for the analysis of RC circuit modelled with nonlinear differential order system

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

In this study, we solve nonlinear initial value problems arising in circuit analysis by applying bio-inspired computational intelligence technique using feed-forward artificial neural networks (ANNs) optimized with genetic algorithms (GAs), sequential quadratic programming (SQP), and their combined scheme. The system of resister–capacitor (RC) circuit having nonlinear capacitance is mathematically modelled with unsupervised ANNs by defining an energy function in mean-square error (MSE) sense. The objectives are to minimize the MSE for which the parameters of the networks are estimated initially with GA-based global search and in steady state with SQP algorithm for efficient local search. We consider a set of scenarios to evaluate the performance of the proposed scheme for different resistance and capacitance values along with current variations in the nonlinear RC circuit system. The results are compared with well-established fully explicit Runge–Kutta numerical solver in order to verify the accuracy of the applied bio-inspired heuristics. To prove the worth of the scheme, a comprehensive statistical analysis is provided for the performance metrics based on root MSE, mean absolute error, Theil’s inequality coefficient, Nash–Sutcliffe efficiency, variance account for, and the coefficient of determination (R 2).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Agarwal A, Lang JH (2005) Foundations of analog and digital electronic circuits. Morgan Kaufmann, San Francisco. ISBN 1-55860-735-8

    MATH  Google Scholar 

  2. Acton QA (2013) Silicon compounds—advances in research and application. Scholarly Editions, Atlanta. ISBN 9781481680172

    Google Scholar 

  3. Irwin JD (2006) Basic engineering circuit analysis. Wiley, Hoboken. ISBN 7-302-13021-3

    Google Scholar 

  4. Sul SK (2011) Control of electric machine drive systems. Wiley, Hoboken, ISBN 978-0- 47059079-9

  5. Nilsson JW, Riedel SA (2008) Electric circuits. Prentice Hall, Englewood Cliffs. ISBN 0-13-198925-1

    Google Scholar 

  6. Wolf DM, Sanders SR (1996) Multiparameter homotopy methods for finding DC operating points of nonlinear circuits. IEEE Trans Circuits Syst I Fundam Theory Appl 43(10):824–838

    Article  MathSciNet  Google Scholar 

  7. Wang T, Chiang HD (2014) On the global convergence of a class of homotopy methods for nonlinear circuits and systems. IEEE Trans Circuits Syst II Express Br 61(11):900–904

    Article  Google Scholar 

  8. Song WZ, Liu XL, Zhang L (2014) Waveform relaxation approach to solution of nonlinear circuit. Appl Mech Mater 459(2014):183–188

    Google Scholar 

  9. Vazquez-Leal H, Boubaker K, Hernández-Martínez L, Huerta-Chua J (2013) Approximation for transient of nonlinear circuits using RHPM and BPES methods. J Electr Compt Eng. doi:10.1155/2013/973813

    Google Scholar 

  10. Zhou D, Cai W, Zhang Wu (1999) An adaptive wavelet method for nonlinear circuit simulation. IEEE Trans Circuits Syst I Fundam Theory Appl 46(8):931–938

    Article  MATH  Google Scholar 

  11. Filobello-Nino U, Vazquez-Leal H, Khan Y et al (2012) HPM applied to solved nonlinear circuits: a study case. Appl Math Sci 6(85–88):4331–4344

    MathSciNet  MATH  Google Scholar 

  12. Koksal M, Herdem S (2002) Analysis of nonlinear circuits by using differential Taylor transform. Comput Electr Eng 28(6):513–525

    Article  MATH  Google Scholar 

  13. Herdem S, Köksal M (2002) A fast algorithm to compute the steady-state solution of nonlinear circuits by piecewise linearization. Comput Electr Eng 28(2):91–101

    Article  MATH  Google Scholar 

  14. Tohyama Y et al (2010) Equivalent circuits for implicit Runge–Kutta methods in circuit simulators for nonlinear circuits. Nonlinear Theory Its Appl IEICE 1(1):176–185

    Article  Google Scholar 

  15. Hantila FI et al (2011) A new method for time domain computation of the steady state in nonlinear circuits. In: 2011 IEEE international conference on microwaves, communications, antennas and electronics systems (COMCAS). IEEE

  16. Abu Arqub O, Al-Smadi M, Momani S, Hayat T (2016) Application of reproducing kernel algorithm for solving second-order, two-point fuzzy boundary value problems. Soft Comput. doi:10.1007/s00500-016-2262-3

    MATH  Google Scholar 

  17. Akdagli A, Kayabasi A (2014) An accurate computation method based on artificial neural networks with different learning algorithms for resonant frequency of annular ring microstrip antennas. J Comput Electron 13(4):1014–1019

    Article  Google Scholar 

  18. Kassem AM, Abdelaziz AY (2015) BFA optimization for voltage and frequency control of a stand-alone wind generation unit. Electr Eng 97(4):313–325

    Article  Google Scholar 

  19. Das G, Pattnaik PK, Padhy SK (2014) Artificial neural network trained by particle swarm optimization for non-linear channel equalization. Expert Syst Appl 41(7):3491–3496

    Article  Google Scholar 

  20. Gokozan H, Taskin S, Seker S, Ekiz H (2015) A neural network based approach to estimate of power system harmonics for an induction furnace under the different load conditions. Electr Eng 97(2):111–117

    Article  Google Scholar 

  21. Mohammed AA, Neilson RD, Deans WF, MacConnell P (2014) Crack detection in a rotating shaft using artificial neural networks and PSD characterisation. Meccanica 49(2):255–266

    Article  MATH  Google Scholar 

  22. Khan Y (2016) Partial discharge pattern analysis using PCA and back-propagation artificial neural network for the estimation of size and position of metallic particle adhering to spacer in GIS. Electr Eng 98(1):29–42

    Article  Google Scholar 

  23. Polat M, Oksuztepe E, Kurum H (2016) Switched reluctance motor control without position sensor by using data obtained from finite element method in artificial neural network. Electr Eng 98(1):43–54

    Article  Google Scholar 

  24. Mall S, Chakraverty S (2015) Numerical solution of nonlinear singular initial value problems of Emden–Fowler type using Chebyshev Neural Network method. Neurocomputing 149:975–982

    Article  Google Scholar 

  25. Chakraverty S, Mall S (2014) Regression-based weight generation algorithm in neural network for solution of initial and boundary value problems. Neural Comput Appl 25(3–4):585–594

    Article  Google Scholar 

  26. Mall S, Chakraverty S (2014) Chebyshev Neural Network based model for solving Lane–Emden type equations. Appl Math Comput 247:100–114

    MathSciNet  MATH  Google Scholar 

  27. Abu Arqub O, Abo-Hammour Z (2014) Numerical solution of systems of second-order boundary value problems using continuous genetic algorithm. Inf Sci 279:396–415

    Article  MathSciNet  MATH  Google Scholar 

  28. Khan JA, Raja MAZ, Syam MI, Tanoli SAK, Awan SE (2015) Design and application of nature inspired computing approach for nonlinear stiff oscillatory problems. Neural Comput Appl 26(7):1763–1780

    Article  Google Scholar 

  29. Raja MAZ, Khan JA, Chaudhary NI, Shivanian E (2016) Reliable numerical treatment of nonlinear singular Flierl–Petviashivili equations for unbounded domain using ANN, GAs, and SQP. Appl Soft Comput 38:617–636

    Article  Google Scholar 

  30. Raja MAZ, Samar R (2014) Numerical treatment of nonlinear MHD Jeffery–Hamel problems using stochastic algorithms. Comput Fluids 91:28–46

    Article  MathSciNet  MATH  Google Scholar 

  31. Raja MAZ, Samar R (2014) Numerical Treatment for nonlinear MHD Jeffery–Hamel problem using Neural Networks Optimized with Interior Point Algorithm. Neurocomputing 124:178–193. doi:10.1016/j.neucom.2013.07.013

    Article  Google Scholar 

  32. Raja MAZ, Khan JA, Shah SM, Bhahoal D, Samar R (2015) Comparison of three unsupervised neural network models for first Painlevé Transcendent. Neural Comput Appl 26(5):1055–1071. doi:10.1007/s00521-014-1774-y

    Article  Google Scholar 

  33. Raja MAZ, Khan JA, Behloul D, Haroon T, Siddiqui AM, Samar R (2015) Exactly satisfying initial conditions neural network models for numerical treatment of first Painlevé equation. Appl Soft Comput 26:244–256. doi:10.1016/j.asoc.2014.10.009

    Article  Google Scholar 

  34. Abu O (2015) Arqub, Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations. Neural Comput Appl. doi:10.1007/s00521-015-2110-x

    Google Scholar 

  35. Raja MAZ (2014) Stochastic numerical techniques for solving Troesch’s Problem. Inf Sci 279:860–873. doi:10.1016/j.ins.2014.04.036

    Article  MATH  Google Scholar 

  36. Raja MAZ (2014) Unsupervised neural networks for solving Troesch’s problem. Chin Phys B 23(1):018903

    Article  Google Scholar 

  37. Raja MAZ (2014) Solution of the one-dimensional Bratu equation arising in the fuel ignition model using ANN optimised with PSO and SQP. Connect Sci 26(3):195–214. doi:10.1080/09540091.2014.907555

    Article  Google Scholar 

  38. Raja MAZ, Ahmad SI (2014) Numerical treatment for solving one-dimensional Bratu problem using neural networks. Neural Comput Appl 24(3–4):549–561. doi:10.1007/s00521-012-1261-2

    Article  Google Scholar 

  39. Raja MAZ, Ahmad SI, Samar R (2013) Neural network optimized with evolutionary computing technique for solving the 2-dimensional bratu problem. Neural Comput Appl 23(7–8):2199–2210. doi:10.1007/s00521-012-1170-4

    Article  Google Scholar 

  40. Raja MAZ, Samar R, Rashidi MM (2014) Application of three unsupervised neural network models to singular nonlinear BVP of transformed 2D Bratu equation. Neural Comput Appl 25:1585–1601. doi:10.1007/s00521-014-1641-x

    Article  Google Scholar 

  41. Raja MAZ, Ahmad SI, Samar R (2014) Solution of the 2-dimensional Bratu problem using neural network, swarm intelligence and sequential quadratic programming. Neural Comput Appl 25:1723–1739. doi:10.1007/s00521-014-1664-3

    Article  Google Scholar 

  42. Raja MAZ, Khan JA, Qureshi IM (2010) A new Stochastic approach for solution of Riccati differential equation of fractional order. Ann Math Artif Intell 60(3–4):229–250

    Article  MathSciNet  MATH  Google Scholar 

  43. Raja MAZ, Manzar MA, Samar R (2015) An efficient computational intelligence approach for solving fractional order Riccati equations using ANN and SQP. Appl Math Model 39(10):3075–3093. doi:10.1016/j.apm.2014.11.024

    Article  MathSciNet  Google Scholar 

  44. Raja MAZ, Samar R, Manzar MA, Shah SM (2017) Design of unsupervised fractional neural network model optimized with interior point algorithm for solving Bagley–Torvik equation. Math Comput Simul 132:139–158

    Article  MathSciNet  Google Scholar 

  45. Raja MAZ (2014) Numerical treatment for boundary value problems of pantograph functional differential equation using computational intelligence algorithms. Appl Soft Comput 24:806–821. doi:10.1016/j.asoc.2014.08.055

    Article  Google Scholar 

  46. Raja MAZ, Sabir Z, Mahmood N, Alaidarous ES, Khan JA (2015) Design of Stochastic solvers based on variants of genetic algorithms for solving nonlinear equations. Neural Comput Appl 26(1):1–23. doi:10.1007/s00521-014-1676-z

    Article  Google Scholar 

  47. Raja MAZ, Khan JA, Haroon T (2014) Stochastic numerical treatment for thin film flow of third grade fluid using unsupervised neural networks. J Chem Inst Taiwan. doi:10.1016/j.jtice.2014.10.018

    Google Scholar 

  48. Fatoorehchi H, Abolghasemi H, Zarghami R (2015) Analytical approximate solutions for a general nonlinear resistor–nonlinear capacitor circuit model. Appl Math Model 39(19):6021–6031

    Article  MathSciNet  Google Scholar 

  49. Holland JH (1975) Adaptation in natural and artificial systems. MI, University of Michigan press, Ann arbor

    Google Scholar 

  50. Haupt RL, Haupt SE (2004) Practical genetic algorithms. Wiley, New York

    MATH  Google Scholar 

  51. Dan J et al (2015) Frequency-dependent friction in pipelines. Chin Phys B 24(3):4701

    Google Scholar 

  52. Zhou C et al (2015) Identification of isomers and control of ionization and dissociation processes using dual-mass-spectrometer scheme and genetic algorithm optimization. Chin Phys B 24(4):043303

    Article  MathSciNet  Google Scholar 

  53. Sun Z, Wang N, Bi Y (2015) Type-1/type-2 fuzzy logic systems optimization with RNA genetic algorithm for double inverted pendulum. Appl Math Model 39(1):70–85

    Article  MathSciNet  Google Scholar 

  54. Jammoussi AY, Ghribi SF, Masmoudi DS (2014) Adaboost face detector based on Joint Integral Histogram and Genetic Algorithms for feature extraction process. SpringerPlus 3(1):355

    Article  Google Scholar 

  55. Katiyar G, Mehfuz S (2016) A hybrid recognition system for off-line handwritten characters. SpringerPlus 5(1):1

    Article  Google Scholar 

  56. Raja MAZ, Zameer A, Khan AU, Wazwaz AM (2016) A new numerical approach to solve Thomas–Fermi model of an atom using bio-inspired heuristics integrated with sequential quadratic programming. SpringerPlus 5(1):1400

    Article  Google Scholar 

  57. Ahmad I, Raja MAZ, Bilal M, Ashraf F (2016) Bio-inspired computational heuristics to study Lane–Emden systems arising in astrophysics model. SpringerPlus 5(1):1866

    Article  Google Scholar 

  58. Raja MAZ, Khan MAR, Mahmood T, Farooq U, Chaudhary NI (2016) Design of bio-inspired computing technique for nanofluidics based on nonlinear Jeffery–Hamel flow equations. Can J Phys 94(5):474–489

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, COMSATS Institute of Information Technology, Attock, Pakistan

    Muhammad Asif Zahoor Raja & Ammara Mehmood

  2. Department of Computer Systems Engineering, UCE&T, Islamia University Bahawalpur, Bahawalpur, Pakistan

    Shahab Ahmad Niazi

  3. Department of Electrical Engineering, Capital University of Science and Technology, Islamabad, Pakistan

    Syed Muslim Shah

Authors
  1. Muhammad Asif Zahoor Raja
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ammara Mehmood
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shahab Ahmad Niazi
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Syed Muslim Shah
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Syed Muslim Shah.

Ethics declarations

Conflict of interest

All the authors of the manuscript declared that there is no potential conflict of interest, research involving human participants and/or animal and material that required informed consent.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Raja, M.A.Z., Mehmood, A., Niazi, S.A. et al. Computational intelligence methodology for the analysis of RC circuit modelled with nonlinear differential order system. Neural Comput & Applic 30, 1905–1924 (2018). https://doi.org/10.1007/s00521-016-2806-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-016-2806-6

Keywords

Search

Navigation