Research On Chaotic Time Series Forecasting Based On Particle Swarm Optimization Algorithm

Chaos refers to the long-term unpredictable and random motion of the deterministic system due to its sensitivity to the initial value,which widely exists in complex systems such as meteorology,medicine and finance system.Time series is a series of variables existing in natural and social sciences,the values are arranged at regular intervals in a certain interval.Chaotic time series is a kind of time series with chaotic characteristics.The model based on statistical theory is a kind of effective forecasting method.It is widely used in the forecasting of chaotic time series by mining and analyzing data information to build a black box model,which greatly improves the prediction accuracy.This kind of prediction model still has some optimization problems,such as model training,hyper-parameter setting,input variable redundancy and so on.Aiming at the different optimization problems in the process of prediction modeling,this paper improves the particle swarm optimization algorithm,and synthesizes the advantages of prediction model and particle swarm optimization algorithm,proposes several different prediction methods to improve the forecasting effect.In order to solve the problem of ill conditioned solution in the training process of chaotic time series prediction model,this chapter transforms the training problem of output weight of prediction model into nonlinear constrained optimization problem,and uses the improved particle swarm optimization algorithm to solve the optimal weight parameters.The least square method is a kind of simple and fast prediction model training method,which is widely used in machine learning model research,such as extreme learning machine,echo state network and so on.However,when the training method based on the least square idea solves the practical problems,the output weights often have ill conditioned solutions and the amplitude of the output weights is large,which leads to the ill posed phenomenon,making the generalization ability of the prediction model poor.In this chapter,aiming at the above problems,the particle swarm optimization and the multiobjective particle swarm optimization algorithm are improved respectively.Two improved algorithms are used to train the echo state network and the extreme learning machine prediction model respectively.Two prediction methods,IPSO-ESN method and IMOPSO-ELM method,are proposed.The two methods constrain the output weight in the training process through regularization method and multi-objective functions respectively.The value of the weight value can strengthen the generalization ability and improve the overall prediction effect.Finally,the simulation results on different chaotic time series are compared with multi group comparison methods to verify the effectiveness and practicability of the proposed method in the prediction problem.Aiming at the problem of parameter selection in chaotic time series modeling,this paper proposes a PSO-PSR-ESN combined model based on particle swarm optimization algorithm,which can be applied to the prediction of chaotic time series.The selection of embedding dimension and delay time in phase space reconstruction,and four key parameters in the echo state network is very important for the improvement of prediction accuracy.The traditional method to determine the delay time and embedding dimension of phase space reconstruction is independent of the modeling and prediction section,and the calculated parameters are not necessarily optimal in the prediction problem.The hyper-parameter setting of echo state network model greatly affects the prediction accuracy.At present,the selection method of hyper-parameters has great contingency,which affects the prediction accuracy.In this chapter,the phase space reconstruction and prediction model are taken as a whole,the parameter selection problem is regarded as an optimization problem,and the prediction accuracy is taken as the objective function.Particle swarm optimization algorithm is utilized to optimize the phase space reconstruction parameters and echo state network parameters simultaneously.Finally,the prediction simulation is carried out on the PM_2.5 concentration data measured in different cities in Beijing-Tianjin-Hebei region,which verifies the validity and practicability of the proposed model in the prediction of PM_2.5 concentration time series.