Research On Particle Swarm Optimization And Its Application To Fractional Order System Identification

Particle swarm optimization(PSO)algorithm is an intelligence optimization algorithm based on swarm behavior.PSO has the characteristics of simple calculation,easy programming and strong adaptability.But it suffers from falling into local optima.And its performance is influenced by adjustable parameters.The theoretical analysis of PSO is not complete enough so far.On the other hand,the improvements of PSO often tend to make the algorithm more complex to use.This dissertation makes some efforts on theoretical analysis and improvements of PSO.Furthermore,PSO algorithm is applied to frequency domain identification of fractional order system.The main work of this dissertation is as follows.(1)The issue of convergence analysis of stochastic particle trajectory in PSO algorithm is addressed using the stability theory of time varying discrete system.Based on the theoretical study,Monte Carlo method is applied to obtain the convergence properties of particle trajectories with different parameters upon the interesting parameter region.Different from most existing works,what we get are the convergence probabilities rather than convergence regions.Experiments on particle trajectories with different parameters show that it is more accurate to describe the particle trajectory using"convergence probability".(2)A set of fixed parameters and a set of time-varying parameters are recommended in this pater.Inertia weight and acceleration factors have significant impact on the performance of PSO algorithm.First the fixed model is considered.Through simulation experiments on twelve classical benchmark functions,this paper studies the exploitation ability and optimization performance with different parameters.Based on the experimental results,we recommend a setting for fixed parameters.Furthermore,in view of the limitations of fixed parameters,we study the situation when inertia weight remains unchanged and acceleration factors change with iterations.Then a setting for varying parameters is recommended.(3)An improved algorithm which is easy to use is proposed.In order to further improve the performance of PSO and simplify its application,this dissertation proposes an improved algorithm based on bare bones particle swarm optimization(BBPSO)which is easier to understand and use.In proposed algorithm,the mean of Gaussian distribution of each particle is controlled adaptively.This strategy can increase the dispersal of distribution center and reduce the concentration of particle around the center.Moreover,a new boundary condition which is likes a mirror wall is employed.Furthermore,the population topology is changed during the evolutionary process.The improved algorithm is proved to be guaranteed to converge to global optimum solution with probability one.The algorithm is compared with other improved variations of PSO and BBPSO on CEC2013 benchmark functions.Non-parametric test is carried on experimental data.Results show that the proposed algorithm has a better overall performance on the test functions.(4)The PSO algorithm is applied to frequency domain identification of fractional order system.First PSO is combined with recursive least-squares method to estimate the fractional derivative order and the coefficients of denominator and numerator simultaneously.PSO is applied to estimating the order and RIV is applied to the identification of multinomial coefficients.The proposed method not only overcomes the shortcoming of not precise enough when using PSO alone,but also overcomes the shortcoming of helplessness for order parameter estimation when using the least square method alone.Since the least squares method cannot obtain satisfactory results in noisy environment,PSO is combined with instrumental variable method,getting another identification method which is able to estimate system parameters well in the case of small signal noise ratio.The proposed identification methods are validated through simulations.