The Variational Inference-based ESN Ensemble Model For Intervals Prediction Of Industrial Data

For industrial data,due to the electromagnetic interference in the environment and the characteristics of the data,they often have heavy randomness.This has a certain influence on the prediction quality of the pure time series prediction.The pure time series can only give the change trend of the numerical value,and can not provide information about the randomness,but the interval prediction can provide more information.Therefore,it is worth studying and paying attention to.Previous studies and applications prove that neural networks have very good nonlinear processing capabilities,especially recurrent neural networks,which can reflect the temporal sequence characteristics of time series better,and the combination of statistical methods for interval forecasting has also been proved to be feasible and available.Pointing at interval prediction of industrial noisy time series,an interval prediction method based on an ESN ensemble optimized by variational inference is proposed.There are two main innovation points.First in the stage of model construction,the prior distribution variance of each ESN's output weight matrix is set to be independent,which could be more stable than the non-independent form;Second,in the stage of parameter solution,the paper uses variational inference to approximate posterior distribution of uncertain parameters,and get the parameters from the posterior distribution,thus the parameter estimation can be more accurate than the existing ESN ensemble optimized by marginal maximum likelihood estimation.In order to verify the effectiveness of the proposed method,the data set generated by trigonometric function is first used to carry out the parameter evaluation experiment.The accuracy and stability of the parameter estimation are evaluated by the noise distribution variance and the mean square root error.The experimental results show that the parameter estimation accuracy of the variational reasoning is more accurate,and the use of the multi group neural network are better to estimate the parameters;then using two real gas data sets from iron and steel enterprises to carry out actual interval prediction experiments,and compare this method with six mainstream and contrastive neural network based interval prediction methods,using the predictive value mean,mean square root error,interval coverage and time consumption.The result of the interval prediction.Experimental results show that our method performs well in prediction accuracy,interval quality,model stability and time consuming.