Research On Echo State Networks Prediction Algorithm Of Time Series And Application

A time series is the data set obtained in the order of time.People get most of the data sets which are in the form of time series.One of the most important research contents in time series analysis is time series prediction,which predicts future values based on current and past observations.Accurate time series prediction has a very large practical significance on human production and life.The characteristics of time series in the real world are very complex,so time series prediction is a very difficult problem.At present,time series prediction has become an important research field of machine learning.Time series prediction using echo state network(ESN)has achieved good results in some respects.Echo state network is a simplified recurrent neural network,which belongs to the important research contents in reservoir computing.The greatest advantage of echo state network is that training is simple and requires only training output weights.By introducing the probability method,the prediction performance of echo state network can be improved.That is,the Bayesian method is used to train echo state network.The Bayesian method of training echo state network needs to be based on the assumed probability distribution,but the data feature of the real time series is very complex.In order to predict the time series of the real world,this dissertation studies the time series prediction method and application based on echo state network.The main work and innovation of the dissertation are summarized as follows:(1)The Kalman filter(KF)is the effective method of training echo state network when the theoretical distribution from model is consistent with the distribution from the real system.The KF is usually based on the Gaussian distribution assumption.But in practical application,this assumption is always violated in the real-world system.In order to overcome the problem that the probability distribution of the model hypothesis is inconsistent with the true probability distribution of the system,the Kalman filter with inflation factor was proposed to train the echo state network by using the covariance matrix which could reflect the accuracy of the parameter estimation and the degree of trust on the previous training data.In echo state networks,the proposed method solved the problem that the Gaussian distribution assumed in Kalman filter did not conform to the actual data and was noted as KFWIF-ESN in this dissertation.Furthermore,the convergence of the KFWIF-ESN was analyzed by means of Lyapunov stability theory.Our proposed method improves the prediction accuracy of ESN and extends its applications.Experimental investigations using well-known benchmark datasets and real-world applications show that the proposed KFWIF-ESN can model different types of dynamical systems and is superior to other Methods.(2)Recurrent neural network(RNN)can model complex system with high accuracy.As a type of RNN design approach,echo state network is used for temperature forecasting in this study.Temperature prediction is a challenging problem and a concern in energy,environment,industry and agriculture etc.Climate models and statistical time-series forecasting methods are the ineffective forecasting tools of the long-range temperature prediction.Based on analysis of monthly maximum,monthly mean and monthly minimum temperatures data sets,a novel recursive Bayesian linear regression(RBLR)algorithm based on ESN was presented in this study.The algorithm consists of two main components: an ESN and a RBLR algorithm with an adaptive inflation factor that can modify the covariance matrix in order to change the confidence level of the prior data.The adaptive inflation factor is calculated using the prediction error.Our proposed method improves the prediction accuracy of the long-range temperature forecasting.Experimental investigations using Central England temperature time series show that the proposed method can forecast monthly maximum,mean and minimum temperatures for the next 12 months and produce good prediction.(3)In the Bayesian method,it is very common to assume the priori probability distribution as the Gaussian distribution.There are two reasons why the hypothesis is Gaussian distribution.On the one hand,Gaussian distribution has very good mathematical properties,it is easy to achieve Bayesian reasoning;the other is the central limit theorem as a theoretical basis,when there are many unknown causes of mixed noise that can be considered to obey Gaussian distribution.However,the data from the actual system can not be described by the Gaussian distribution because of the presence of outliers and complex noise in these data.In view of the fact that there may be outliers and complex noise in the actual time series,the data containing the outliers are described by the heavy tail feature of the student t distribution.The Bayesian recursive learning method based on student t distribution was deduced and a Bayesian method based on student t distribution to train echo state network was proposed,which solves the problem that echo state network based on Gaussian distribution can not effectively predict the time series containing outliers.The experimental results show that the method is robust when there are the outliers in the time series and is superior to the existing method.