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Neural Computing and Applications

, Volume 31, Issue 10, pp 5819–5842 | Cite as

Nature-inspired heuristic paradigms for parameter estimation of control autoregressive moving average systems

  • Ammara Mehmood
  • Aneela Zameer
  • Muhammad Asif Zahoor Raja
  • Rabia Bibi
  • Naveed Ishtiaq Chaudhary
  • Muhammad Saeed AslamEmail author
Original Article

Abstract

Aim of this research is to explore the strength of evolutionary and swarm intelligence techniques for parameter identification of control autoregressive moving average (CARMA) systems. The fitness function for CARMA system identification problem is formulated through error function created in mean square sense, and learning of unknown parameters of the system model is carried out with an effective global search techniques based on genetic algorithms and particle swarm optimization algorithm. Comparative study of the design methodology is conducted from actual parameters of the systems for different values of noise variance and degree of freedom in CARMA identification model. The correctness of the proposed scheme is validated through the results of various performance measures based on mean absolute error, mean weight deviation, variance account for and Theil’s inequality coefficient, and their global variants for sufficiently large number of independent runs.

Keywords

System identification Parameter estimation Evolutionary computing Genetic algorithms CARMA model 

Notes

Compliance with ethical standards

Conflict of interest

All the authors of the manuscript declared that there are no potential conflicts of interest.

Human and animal rights statements

All the authors of the manuscript declared that there is no research involving human participants and/or animal.

Informed consent

All the authors of the manuscript declared that there is no material that required informed consent.

References

  1. 1.
    Li H, Xu L, Zhang Z (2017) Parameter estimation of maneuvering target using maximum likelihood estimation for MIMO radar with colocated antennas. J Comput Commun 5(03):69CrossRefGoogle Scholar
  2. 2.
    Ding F (2014) State filtering and parameter estimation for state space systems with scarce measurements. Signal Process 104:369–380CrossRefGoogle Scholar
  3. 3.
    Ugalde HMR, Carmona JC, Reyes-Reyes J, Alvarado VM, Corbier C (2015) Balanced simplicity–accuracy neural network model families for system identification. Neural Comput Appl 26(1):171–186CrossRefGoogle Scholar
  4. 4.
    Wang Y, Ding F (2016) Recursive parameter estimation algorithms and convergence for a class of nonlinear systems with colored noise. Circuits Syst Signal Process 35(10):3461–3481MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Shen Q, Ding F (2016) Least squares identification for Hammerstein multi-input multi-output systems based on the key-term separation technique. Circuits Syst Signal Process 35(10):3745–3758MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Ding F, Liu PX, Liu G (2010) Gradient based and least-squares based iterative identification methods for OE and OEMA systems. Digit Signal Process 20(3):664–677CrossRefGoogle Scholar
  7. 7.
    Wang C, Tang T (2014) Several gradient-based iterative estimation algorithms for a class of nonlinear systems using the filtering technique. Nonlinear Dyn 77(3):769–780MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Wang X, Ding F, Alsaadi FE, Hayat T (2016) Convergence analysis of the hierarchical least squares algorithm for bilinear-in-parameter systems. Circuits Syst Signal Process 35(12):4307–4330MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Shen Q, Ding F (2016) Hierarchical multi-innovation extended stochastic gradient algorithms for input nonlinear multivariable OEMA systems by the key-term separation principle. Nonlinear Dyn 85(1):499–507MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Wang X, Ding F (2015) Recursive parameter and state estimation for an input nonlinear state space system using the hierarchical identification principle. Signal Process 117:208–218CrossRefGoogle Scholar
  11. 11.
    Chen H, Ding F (2015) Hierarchical least squares identification for Hammerstein nonlinear controlled autoregressive systems. Circuits Syst Signal Process 34(1):61–75MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Mao Y, Ding F (2015) Multi-innovation stochastic gradient identification for Hammerstein controlled autoregressive autoregressive systems based on the filtering technique. Nonlinear Dyn 79(3):1745–1755zbMATHCrossRefGoogle Scholar
  13. 13.
    Chaudhary NI, Raja MAZ, Aslam MS, Ahmed N (2016) Novel generalization of Volterra LMS algorithm to fractional order with application to system identification. Neural Comput Appl.  https://doi.org/10.1007/s00521-016-2548-5 CrossRefGoogle Scholar
  14. 14.
    Raja MAZ, Chaudhary NI (2014) Adaptive strategies for parameter estimation of Box-Jenkins systems. IET Signal Process 8(9):968–980CrossRefGoogle Scholar
  15. 15.
    Chaudhary NI, Raja MAZ (2015) Design of fractional adaptive strategy for input nonlinear Box-Jenkins systems. Signal Process 116:141–151CrossRefGoogle Scholar
  16. 16.
    Chaudhary NI, Raja MAZ (2015) Identification of Hammerstein nonlinear ARMAX systems using nonlinear adaptive algorithms. Nonlinear Dyn 79(2):1385–1397MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Chaudhary NI, Raja MAZ, Khan AUR (2015) Design of modified fractional adaptive strategies for Hammerstein nonlinear control autoregressive systems. Nonlinear Dyn 82(4):1811–1830CrossRefGoogle Scholar
  18. 18.
    Bao B, Xu Y, Sheng J, Ding R (2011) Least squares based iterative parameter estimation algorithm for multivariable controlled ARMA system modelling with finite measurement data. Math Comput Model 53(9):1664–1669MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Yao G, Ding R (2012) Two-stage least squares based iterative identification algorithm for controlled autoregressive moving average (CARMA) systems. Comput Math Appl 63(5):975–984MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Li J, Ding F (2015) Filtering-based recursive least-squares identification algorithm for controlled autoregressive moving average systems using the maximum likelihood principle. J Vib Control 21(15):3098–3106MathSciNetCrossRefGoogle Scholar
  21. 21.
    Raja MAZ, Chaudhary NI (2015) Two-stage fractional least mean square identification algorithm for parameter estimation of CARMA systems. Signal Process 107:327–339CrossRefGoogle Scholar
  22. 22.
    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):474–489CrossRefGoogle Scholar
  23. 23.
    Chiroma H, Khan A, Abubakar AI, Saadi Y, Hamza MF, Shuib L, Gital AY, Herawan T (2016) A new approach for forecasting OPEC petroleum consumption based on neural network train by using flower pollination algorithm. Appl Soft Comput 48:50–58CrossRefGoogle Scholar
  24. 24.
    Abubakar AI, Khan A, Nawi NM, Rehman MZ, Wah TY, Chiroma H, Herawan T (2016) Studying the effect of training levenberg marquardt neural network by using hybrid meta-heuristic algorithms. J Comput Theor Nanosci 13(1):450–460CrossRefGoogle Scholar
  25. 25.
    Mall S, Chakraverty S (2015) Numerical solution of nonlinear singular initial value problems of Emden–Fowler type using Chebyshev Neural Network method. Neurocomputing 149:975–982CrossRefGoogle Scholar
  26. 26.
    Draa A, Benayad Z, Djenna FZ (2015) An opposition-based firefly algorithm for medical image contrast enhancement. Int J Inf Commun Technol 7(4–5):385–405Google Scholar
  27. 27.
    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 38:617–636CrossRefGoogle Scholar
  28. 28.
    Draa A, Bouaziz A (2014) An artificial bee colony algorithm for image contrast enhancement. Swarm Evol Comput 16:69–84CrossRefGoogle Scholar
  29. 29.
    Raja MAZ, Samar R, Haroon T, Shah SM (2015) Unsupervised neural network model optimized with evolutionary computations for solving variants of nonlinear MHD Jeffery–Hamel problem. Appl Math Mech 36(12):1611–1638MathSciNetCrossRefGoogle Scholar
  30. 30.
    Dahi ZAEM, Mezioud C, Draa A (2016) On the efficiency of the binary flower pollination algorithm: application on the antenna positioning problem. Appl Soft Comput 47:395–414CrossRefGoogle Scholar
  31. 31.
    Raja MAZ, Samar R, Alaidarous ES, Shivanian E (2016) Bio-inspired computing platform for reliable solution of Bratu-type equations arising in the modeling of electrically conducting solids. Appl Math Model 40(11):5964–5977MathSciNetCrossRefGoogle Scholar
  32. 32.
    Abubakar AI, Shuib L, Chiroma H (2015) Optimization of neural network using cuckoo search for the classification of diabetes. J Comput Theor Nanosci 12(12):5755–5758CrossRefGoogle Scholar
  33. 33.
    Baymani M, Effati S, Niazmand H, Kerayechian A (2015) Artificial neural network method for solving the Navier–Stokes equations. Neural Comput Appl 26(4):765–773CrossRefGoogle Scholar
  34. 34.
    Draa A, Bouzoubia S, Boukhalfa I (2015) A sinusoidal differential evolution algorithm for numerical optimisation. Appl Soft Comput 27:99–126CrossRefGoogle Scholar
  35. 35.
    Effati S, Mansoori A, Eshaghnezhad M (2015) An efficient projection neural network for solving bilinear programming problems. Neurocomputing 168:1188–1197CrossRefGoogle Scholar
  36. 36.
    Raja MAZ (2014) Stochastic numerical treatment for solving Troesch’s problem. Inf Sci 279:860–873MathSciNetzbMATHCrossRefGoogle Scholar
  37. 37.
    Raja MAZ, Shah FH, Alaidarous ES, Syam MI (2017) Design of bio-inspired heuristic technique integrated with interior-point algorithm to analyze the dynamics of heartbeat model. Appl Soft Comput 52:605–629CrossRefGoogle Scholar
  38. 38.
    Raja MAZ, Shah FH, Syam MI (2017) Intelligent computing approach to solve the nonlinear Van der Pol system for heartbeat model. Neural Comput Appl.  https://doi.org/10.1007/s00521-017-2949-0 CrossRefGoogle Scholar
  39. 39.
    Raja MAZ, Asma K, Aslam MS (2018) Bio-inspired computational heuristics to study models of hiv infection of CD4+ T-cell. Int J Biomath.  https://doi.org/10.1142/S1793524518500195 MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    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):1866CrossRefGoogle Scholar
  41. 41.
    Raja MAZ, Abbas S, Syam MI, Wazwaz AM (2018) Design of neuro-evolutionary model for solving nonlinear singularly perturbed boundary value problems. Appl Soft Comput 62:373–394CrossRefGoogle Scholar
  42. 42.
    Raja MAZ, Manzar MA, Shah FH, Shah FH (2018) Intelligent computing for Mathieu’s systems for parameter excitation, vertically driven pendulum and dusty plasma models. Appl Soft Comput 62:359–372CrossRefGoogle Scholar
  43. 43.
    Raja MAZ, Aslam MS, Chaudhary NI, Nawaz M, Shah SM (2017) Design of hybrid nature-inspired heuristics with application to active noise control systems. Neural Comput Appl.  https://doi.org/10.1007/s00521-017-3214-2 CrossRefGoogle Scholar
  44. 44.
    Akbar S, Raja MAZ, Zaman F, Mehmood T, Khan MAR (2017) Design of bio-inspired heuristic techniques hybridized with sequential quadratic programming for joint parameters estimation of electromagnetic plane waves. Wirel Pers Commun 96(1):1475–1494CrossRefGoogle Scholar
  45. 45.
    Raja MAZ, Azad S, Shah SM (2017) Bio-inspired computational heuristics to study the boundary layer flow of the Falkner–Scan system with mass transfer and wall stretching. Appl Soft Comput 57:293–314CrossRefGoogle Scholar
  46. 46.
    Lodhi S, Manzar MA, Raja MAZ (2017) Fractional neural network models for nonlinear Riccati systems. Neural Comput Appl.  https://doi.org/10.1007/s00521-017-2991-y CrossRefGoogle Scholar
  47. 47.
    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 132:139–158MathSciNetCrossRefGoogle Scholar
  48. 48.
    Sabouri J, Effati S, Pakdaman M (2017) A neural network approach for solving a class of fractional optimal control problems. Neural Process Lett 45(1):59–74CrossRefGoogle Scholar
  49. 49.
    Pasolli E, Melgani F (2015) Genetic algorithm-based method for mitigating label noise issue in ECG signal classification. Biomed Signal Process Control 19:130–136CrossRefGoogle Scholar
  50. 50.
    Raja MAZ, Mehmood A, Niazi SA, Shah SM (2016) Computational intelligence methodology for the analysis of RC circuit modelled with nonlinear differential order system. Neural Comput Appl.  https://doi.org/10.1007/s00521-016-2806-6 CrossRefGoogle Scholar
  51. 51.
    Valarmathi K, Devaraj D, Radhakrishnan TK (2009) Real-coded genetic algorithm for system identification and controller tuning. Appl Math Model 33(8):3392–3401CrossRefGoogle Scholar
  52. 52.
    Boudjelaba K, Ros F, Chikouche D (2014) Potential of particle swarm optimization and genetic algorithms for FIR filter design. Circuits Syst Signal Process 33(10):3195–3222CrossRefGoogle Scholar
  53. 53.
    Arabali A, Ghofrani M, Etezadi-Amoli M, Fadali MS, Baghzouz Y (2013) Genetic-algorithm-based optimization approach for energy management. IEEE Trans Power Deliv 28(1):162–170CrossRefGoogle Scholar
  54. 54.
    Nikolos IK, Valavanis KP, Tsourveloudis NC, Kostaras AN (2003) Evolutionary algorithm based offline/online path planner for UAV navigation. IEEE Trans Syst Man Cybern B (Cybern) 33(6):898–912CrossRefGoogle Scholar
  55. 55.
    Dahi ZAEM, Mezioud C, Draa A (2016) A quantum-inspired genetic algorithm for solving the antenna positioning problem. Swarm Evol Comput 31:24–63CrossRefGoogle Scholar
  56. 56.
    Raja MAZ, Shah AA, Mehmood A, Chaudhary NI, Aslam MS (2016) Bio-inspired computational heuristics for parameter estimation of nonlinear Hammerstein controlled autoregressive system. Neural Comput Appl.  https://doi.org/10.1007/s00521-016-2677-x CrossRefGoogle Scholar
  57. 57.
    Raja MAZ, Sabir Z, Mehmood N, Al-Aidarous ES, Khan JA (2015) Design of stochastic solvers based on genetic algorithms for solving nonlinear equations. Neural Comput Appl 26(1):1–23.  https://doi.org/10.1007/s00521-014-1676-z CrossRefGoogle Scholar
  58. 58.
    Raja MAZ, Kiani AK, Shehzad A, Zameer A (2016) Memetic computing through bio-inspired heuristics integration with sequential quadratic programming for nonlinear systems arising in different physical models. SpringerPlus 5(1):2063.  https://doi.org/10.1186/s40064-016-3750-8 CrossRefGoogle Scholar
  59. 59.
    Raja MAZ, Niazi SA, Butt SA (2017) An intelligent computing technique to analyze the vibrational dynamics of rotating electrical machine. Neurocomputing 219:280–299.  https://doi.org/10.1016/j.neucom.2016.09.032 CrossRefGoogle Scholar
  60. 60.
    Masood Z, Majeed K, Samar R, Raja MAZ (2017) Design of Mexican Hat Wavelet neural networks for solving Bratu type nonlinear systems. Neurocomputing 221:1–14CrossRefGoogle Scholar
  61. 61.
    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):1400CrossRefGoogle Scholar
  62. 62.
    Raja MAZ, Farooq U, Chaudhary NI, Wazwaz AM (2016) Stochastic numerical solver for nanofluidic problems containing multi-walled carbon nanotubes. Appl Soft Comput 38:561–586CrossRefGoogle Scholar
  63. 63.
    Özmen A, Weber GW (2014) RMARS: robustification of multivariate adaptive regression spline under polyhedral uncertainty. J Comput Appl Math 259:914–924MathSciNetzbMATHCrossRefGoogle Scholar
  64. 64.
    Özmen A, Kropat E, Weber GW (2017) Robust optimization in spline regression models for multi-model regulatory networks under polyhedral uncertainty. Optimization 66(12):2135–2155MathSciNetzbMATHCrossRefGoogle Scholar
  65. 65.
    Özmen A (2016) Robust optimization of spline models and complex regulatory networks: theory methods and applications. Springer, New York.  https://doi.org/10.1007/978-3-319-30800-5 CrossRefGoogle Scholar
  66. 66.
    Kara G, Özmen A, Weber GW (2017) Stability advances in robust portfolio optimization under parallelepiped uncertainty. Cent Eur J Oper Res.  https://doi.org/10.1007/s10100-017-0508-5 CrossRefzbMATHGoogle Scholar
  67. 67.
    Taylan P, Weber GW, Yerlikaya F (2008) May. Continuous optimization applied in MARS for modern applications in finance, science and technology. In: ISI Proceedings of 20th mini-EURO conference continuous optimization and knowledge-based technologies, pp 317–322Google Scholar
  68. 68.
    Weber GW, Batmaz İ, Köksal G, Taylan P, Yerlikaya-Özkurt F (2012) CMARS: a new contribution to nonparametric regression with multivariate adaptive regression splines supported by continuous optimization. Inverse Probl Sci Eng 20(3):371–400MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2018

Authors and Affiliations

  1. 1.Department of Electrical EngineeringPakistan Institute of Engineering and Applied Sciences (PIEAS)NilorePakistan
  2. 2.Department of Computer and Information SciencesPakistan Institute of Engineering and Applied Sciences (PIEAS)NilorePakistan
  3. 3.Department of Electrical EngineeringCOMSATS Institute of Information TechnologyAttockPakistan
  4. 4.Department of Electrical EngineeringInternational Islamic UniversityIslamabadPakistan
  5. 5.School of Electrical and Electronic EngineeringUniversity of AdelaideAdelaideAustralia

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