A Novel Order Reduction Method Using Cuckoo Search Algorithm

ABSTRACT In this paper, a novel method is presented to obtain stable reduced-order model of higher order linear time invariant continuous systems using optimization technique. In order to perform optimization, a new meta-heuristic search algorithm, called Cuckoo Search (CS) is applied which is inspired by the natural behaviour of cuckoo species including the Lévy flight behaviour of some birds and fruit flies. The effectiveness of the proposed method is supported by some numerical examples of single input single output (SISO) systems and the results are compared with other well-known methods available in the literature in terms of most popular performance indices like integral square error, integral absolute error, and integral time absolute error. The method is extended for multi input multi output (MIMO) systems also.

[1]  S. R. Desai,et al.  A novel order diminution of LTI systems using Big Bang Big Crunch optimization and Routh Approximation , 2013 .

[2]  Ali Kaveh,et al.  Optimum design of steel frames using Cuckoo Search algorithm with Lévy flights , 2013 .

[3]  Nicolas E. Humphries,et al.  Foraging success of biological Lévy flights recorded in situ , 2012, Proceedings of the National Academy of Sciences.

[4]  Maamar Bettayeb,et al.  H2 and H∞ optimal model reduction using genetic algorithms , 2011, J. Frankl. Inst..

[5]  Dia I. Abu-Al-Nadi,et al.  Reduced Order Modeling of Linear MIMO Systems Using Particle Swarm Optimization , 2011 .

[6]  Gandhimohan M. Viswanathan,et al.  Ecology: Fish in Lévy-flight foraging , 2010, Nature.

[7]  Xin-She Yang,et al.  Engineering optimisation by cuckoo search , 2010, Int. J. Math. Model. Numer. Optimisation.

[8]  Sidhartha Panda,et al.  Evolutionary Techniques for Model Order Reduction of Large Scale Linear Systems , 2009 .

[9]  Siamak Talatahari,et al.  A particle swarm ant colony optimization for truss structures with discrete variables , 2009 .

[10]  Siamak Talatahari,et al.  Particle swarm optimizer, ant colony strategy and harmony search scheme hybridized for optimization of truss structures , 2009 .

[11]  M. K. Pandey,et al.  System order reduction using GA for unit impulse input and a comparative study using ISE & IRE , 2009, ICAC3 '09.

[12]  Xin-She Yang,et al.  Nature-Inspired Metaheuristic Algorithms , 2008 .

[13]  G. Parmar,et al.  System reduction using factor division algorithm and eigen spectrum analysis , 2007 .

[14]  Frederic Bartumeus,et al.  LÉVY PROCESSES IN ANIMAL MOVEMENT: AN EVOLUTIONARY HYPOTHESIS , 2007 .

[15]  S. Mukherjee,et al.  Order Reduction of Linear Dynamic Systems using Stability Equation Method and GA , 2007 .

[16]  Clifford T. Brown,et al.  Lévy Flights in Dobe Ju/’hoansi Foraging Patterns , 2007 .

[17]  G. Parmar,et al.  Reduced Order Modelling of Linear Dynamic Systems using Particle Swarm Optimized Eigen Spectrum Analysis , 2007 .

[18]  Ibrahim Eksin,et al.  A new optimization method: Big Bang-Big Crunch , 2006, Adv. Eng. Softw..

[19]  K. Lee,et al.  A new structural optimization method based on the harmony search algorithm , 2004 .

[20]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[21]  T. N. Lucas Factor division: a useful algorithm in model reduction , 1983 .

[22]  K. Han,et al.  Reduction of Transfer Functions by the Stability-Equation Method , 1979 .

[23]  Y. Bistritz,et al.  Model reduction by Chebyshev polynomial techniques , 1979 .

[24]  E. Eitelberg Interactive Model Reduction by Minimizing the Weighted Equation Error , 1979 .

[25]  Mathukumalli Vidyasagar,et al.  Order reduction by ℓ 1- and ℓ ∞ -norm minimization , 1978 .

[26]  B. Friedland,et al.  Routh approximations for reducing order of linear, time-invariant systems , 1975 .

[27]  Y. Shamash Stable reduced-order models using Padé-type approximations , 1974 .

[28]  D. Wilson,et al.  Model reduction for multivariable systems , 1974 .

[29]  D. Wilson Optimum solution of model-reduction problem , 1970 .

[30]  M. Chidambara,et al.  Further comments on "A method for simplifying linear dynamic systems" , 1967 .

[31]  G. Marchesini,et al.  On obtaining transfer functions from gain-function derivatives , 1967, IEEE Transactions on Automatic Control.

[32]  R. Stephenson A and V , 1962, The British journal of ophthalmology.

[33]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[34]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[35]  G. Obinata,et al.  Authors' reply to "Comments on model reduction by minimizing the equation error" , 1983 .

[36]  M. Chidambara,et al.  Two simple techniques for the simplification of large dynamic systems , 1969 .

[37]  E. Davison,et al.  On "A method for simplifying linear dynamic systems" , 1966 .