A comparative analysis of particle swarm optimization and differential evolution algorithms for parameter estimation in nonlinear dynamic systems

Abstract The use of evolutionary algorithms has been popular in recent years for solving the inverse problem of identifying system parameters given the chaotic response of a dynamical system. The inverse problem is reformulated as a minimization problem and population-based optimizers such as evolutionary algorithms have been shown to be efficient solvers of the minimization problem. However, to the best of our knowledge, there has been no published work that evaluates the efficacy of using the two most popular evolutionary techniques – particle swarm optimization and differential evolution algorithm, on a wide range of parameter estimation problems. In this paper, the two methods along with their variants (for a total of seven algorithms) are applied to fifteen different parameter estimation problems of varying degrees of complexity. Estimation results are analyzed using nonparametric statistical methods to identify if an algorithm is statistically superior to others over the class of problems analyzed. Results based on parameter estimation quality suggest that there are significant differences between the algorithms with the newer, more sophisticated algorithms performing better than their canonical versions. More importantly, significant differences were also found among variants of the particle swarm optimizer and the best performing differential evolution algorithm.

[1]  Francisco Herrera,et al.  A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms , 2011, Swarm Evol. Comput..

[2]  Ling Wang,et al.  Parameter estimation for chaotic systems by particle swarm optimization , 2007 .

[3]  Guanrong Chen,et al.  Bifurcation Analysis of Chen's equation , 2000, Int. J. Bifurc. Chaos.

[4]  Huanwen Tang,et al.  Application of chaos in simulated annealing , 2004 .

[5]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[6]  Govind P. Agrawal,et al.  Absolute instabilities in lasers with host-induced nonlinearities and dispersion , 1998 .

[7]  G. Marano,et al.  Genetic-Algorithm-Based Strategies for Dynamic Identification of Nonlinear Systems with Noise-Corrupted Response , 2010 .

[8]  Keith Worden,et al.  IDENTIFICATION OF HYSTERETIC SYSTEMS USING THE DIFFERENTIAL EVOLUTION ALGORITHM , 2001 .

[9]  Amit Konar,et al.  Two improved differential evolution schemes for faster global search , 2005, GECCO '05.

[10]  Jun-Juh Yan,et al.  Parameter identification of chaotic systems using evolutionary programming approach , 2008, Expert Syst. Appl..

[11]  W. W. Daniel.  Applied Nonparametric Statistics , 1979 .

[12]  Wei-Der Chang,et al.  An improved real-coded genetic algorithm for parameters estimation of nonlinear systems , 2006 .

[13]  Daizhan Cheng,et al.  Bridge the Gap between the Lorenz System and the Chen System , 2002, Int. J. Bifurc. Chaos.

[14]  Mohd Azlan Hussain,et al.  Application of memetic algorithm in modelling discrete-time multivariable dynamics systems , 2008 .

[15]  Bo Peng,et al.  Differential evolution algorithm-based parameter estimation for chaotic systems , 2009 .

[16]  Rong-Fong Fung,et al.  Using the modified PSO method to identify a Scott-Russell mechanism actuated by a piezoelectric element , 2009 .

[17]  Bijan Samali,et al.  A novel hysteretic model for magnetorheological fluid dampers and parameter identification using particle swarm optimization , 2006 .

[18]  V. K. Koumousis,et al.  Identification of Bouc-Wen hysteretic systems by a hybrid evolutionary algorithm , 2008 .

[19]  Xiangdong Wang,et al.  Parameters identification of chaotic systems via chaotic ant swarm , 2006 .

[20]  Xin-She Yang,et al.  Firefly algorithm, stochastic test functions and design optimisation , 2010, Int. J. Bio Inspired Comput..

[21]  Santo Banerjee,et al.  Global optimization of an optical chaotic system by Chaotic Multi Swarm Particle Swarm Optimization , 2012, Expert Syst. Appl..

[22]  Nopdanai Ajavakom,et al.  On system identification and response prediction of degrading structures , 2006 .

[23]  Giuseppe Quaranta,et al.  Parameters identification of Van der Pol–Duffing oscillators via particle swarm optimization and differential evolution , 2010 .

[24]  Hamidreza Modares,et al.  Parameter identification of chaotic dynamic systems through an improved particle swarm optimization , 2010, Expert Syst. Appl..

[25]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[26]  Jinhu Lu,et al.  Synchronization of an uncertain unified chaotic system via adaptive control , 2002 .

[27]  Han Xiao,et al.  Parameters identification of chaotic system by chaotic gravitational search algorithm , 2012, Chaos, Solitons & Fractals.

[28]  Sami F. Masri,et al.  Identification of structural systems by neural networks , 1996 .

[29]  A. Roy Chowdhury,et al.  Chaotic aspects of lasers with host-induced nonlinearity and its control , 2001 .

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

[31]  Shing-Tai Pan,et al.  Identification of Chaotic Systems by Neural Network with Hybrid Learning Algorithm , 2008, IMECS.

[32]  J R Saunders,et al.  A particle swarm optimizer with passive congregation. , 2004, Bio Systems.