Time Series Analysis Based On Improved Gauss Bare-bones Differential Evolution Algorithm And Echo State Network

Time series widespread in scientific and social activities and it has great scientific research value to make reasonable and accurate predictions on it.Recent years,the Echo state networks(ESN)has been widely recognized by many researchers with its advantages of simple and efficient training algorithm and strong dynamic properties of the reserve pool,and has gradually become the mainstream of time series predictive modeling.In view of the problems that the reserve pool in the ESN has poor adaptability,and it contains a large number of nodes,and the parameters are difficult to adjust,etc.This paper will use the Differential Evolution(DE)algorithm to select the parameter settings that best match the current time series for the reserve pool.In order to improve the optimization performance that the DE algorithm brings to parameter,the following two improvement methods are proposed for the DE algorithm: The one,a new strategy selection factor ZZ is proposed,which makes the individual dynamically select the mutation strategy that conforms to the current evolutionary state as evolution progresses,so as to improve the optimization performance of the DE algorithm;The other one,replace the Gaussian mutation strategy in the strategy selection mechanism with a Gaussian triangle mutation strategy to further enhance the exploration ability of DE algorithm in the early stage of evolution.There will be a new DE algorithm through the improvement of the above two points,which is called the improved Gaussian skeleton differential evolution algorithm(IGBDE)in this paper.Finally,IGBDE is compared with the same type of skeleton algorithm GBDE,MGBDE,t BBDE,SMGBDE,CABDE under 18 test functions consisting of 13 benchmark functions and 5advanced offset functions in CEC2005.The results show that the improved Gaussian Skeleton Differential Evolution(IGBDE)proposed in this paper has great advantages over the previous five skeleton algorithms of the same type when dealing with unimodal functions,complex test functions with rotation or offset..Then,utilizing the IGBDE proposed in this paper to optimize the ESN performing time series prediction analysis.In addition,the initialization storage pool parameter is newly added to the reserve pool parameter,which combined with the other four basic parameters of the reserve pool(pool size,spectral radius,sparsity,input conversion factor)to form the network parameters that the IGBDE algorithm needs to optimize.Through the analysis of simulation experiment results about Model IGBDE-ESN on the time series Mackey-Glass and on the monthly average temperature in Ganzhou,it is concluded that the model proposed in this paper has higher accuracy and better stability in the prediction of time series than other prediction models of the same type.