Application Researches On Interval Prediction Method Based On Bootstrap Method And Relevance Vector Machine

In the actual industrial process,some key process variables are closely related to the safety assurance of the production process and even the quality of the products.Therefore,accurate prediction of process variables is very important for process control,production decision making and other applications.Generally speaking,prediction results are usually given by point estimation results.However,point estimation results are more and more difficult to meet the precision requirements due to the characteristics of high-dimension,high nonlinearity,and containing noise of process data.At the same time,the uncertainty of the prediction results cannot be estimated when the real value cannot be obtained.Therefore,this paper focuses on the interval prediction method and its application in process industry.The main research contents are as follows:(1)In order to estimate the uncertainty and trend of the prediction results,an interval prediction method based on Bootstrap and RVM(Bootstrapped RVM)is proposed in this paper.In this method,Bootstrap is used to resampling and obtaining prediction intervals,and RVM is used as a regression algorithm.After combining the two methods,a reliable prediction interval can be constructed,and the prediction results can be quickly obtained.When the dataset is not large,the training speed of proposed method is also fast enough.(2)Because Bootstrap method needs multiple sampling and training RVM models for each group of resampling data,the training and testing time increases linearly.In this regard,a parallel computing method is introduced,and the existing training and testing algorithms are improved by parallel algorithm(Parallel Bootstrapped RVM).The training and testing process of multiple groups of samples are concurrently and independently carried out by each core of processor in the computer,thus reducing the impact of the multiple training and testing problems of the Bootstrap method to a certain extent.It also improves the speed of training and testing process,and the utilization ratio of computer computing resources.(3)Combined with Double Sparse Relevance Vector Machine and Bootstrap method,this paper proposes another interval prediction method:Parallel Bootstrapped DSRVM.This method can deal with data that containing more complex features,and the approximation of noise variance is closer to the real value.(4)Considering the relative value calculation method of the cumulative deviation indicator,a new Interval Mean Error indicator is proposed for dealing with the error magnification effect that caused by data near the zero value in the dataset.In addition,because of the timeliness of the data in the actual application,this paper proposed an improvement and expression method named time-window evaluation indicators.(5)The proposed methods are validated by using artificial data that generated by a standard function and actual High Density Polyethylene data.Among them,artificial data are mixed with multiple types of noise separately.The simulation experiments use the Bootstrap based RVM,DSRVM,SVM and ELM methods to construct prediction intervals.In addition,the influence on interval prediction results of Pairs-Bootstrap,Residual-Bootstrap and Wild-Bootstrap methods are also compared in the simulation experiments.Compared with other methods,the simulation results show that the two proposed methods can achieve better performance in terms of prediction accuracy,variance estimation,real value approximation ability,training time and testing time.