Research Of Gaussian Process Regression Soft Sensor Modeling Based On Ensemble Learning

In the industrial process,some important quality variables are difficult to be measured real-time by online instruments,and laboratory offline analysis may have large time delay and high cost.Soft sensing technology online monitors quality variables by establishing the function relationship between the easy-to-measure variables and quality variables.For nonlinear and multi-stage industrial processes,global soft sensor models with single structure tends to have limitations,such as poor generalization ability and process interpretation.The ensemble learning based multi-model modeling methods,which construct several simple local models,and get the final prediction results by fusing the local model outputs.Based on the ensemble learning and the Gaussian Process Regression algorithm(GPR),this paper improves the existing soft sensing technologies.The main contents of this paper are organized as follows:1)Aiming at the fact that actual industrial processes are characterized by non-linearity,high dimensionality and time-variation,the kernel principal component analysis(KPCA)is used to nonlinearly reduce the data dimensions,and to reconstruct the input sample set based on the reduced principal component.Then,bagging algorithm is utilized to obtain several sample subsets from the original dataset.Sub GPR model can be constructed based on the sub dataset accordingly.Finally,the global model prediction output can be obtained by combining Bayesian posterior probabilities with prediction values of all sub-models.Simulation results for the real sewage treatment process dataset have indicated that the proposed algorithm has a good prediction accuracy as well as the generalization performance.2)Consider that the conventional ensemble learning methods without making full use of the two dimensional information contained in the samples,only based on single sample or variable dimension.Therefore,a soft sensor based on the hierarchical ensemble of Gaussian process regression models is proposed.The Gaussian mixture model(GMM)is used to divide the process data into different operation phases to capture the multi-phase characteristics of the process.Furthermore,the model data are divided into several subspaces,according to the contribution of each auxiliary variable in the principal component space,and the corresponding Gaussian process regression soft sensor model is build.The subspace model output is averaged to obtain the first level ensemble output,namely,the local prediction output in each mode.Finally,the posterior probability is used to fuse the model local model prediction to obtain the second level ensemble output.The debutanizer column process and the fermentation process of penicillin simulation results show that the proposed method has a high prediction accuracy and performance.3)There are many unlabeled samples in industrial processes.It is hard to obtain the ideal prediction result,if only the labeled samples are used for modeling.Therefore,a novel Gaussian process regression soft sensor modeling method is proposed based on semi-supervised Tri-training and ensemble learning method.First,the Bagging algorithm is run to partition the unlabeled dataset into three sub-datasets,and the labeled samples are used for model training.Second,the corresponding index values are calculated for unlabeled samples based on a confidence index,the satisfactory samples which are under the confidence degree are picked out,labeled and added into the corresponding labeled data samples.Finally,Gaussian process regression model is established for the three expanded labeled datasets,and the results are fused using the weighted method.The butane concentration of debutanizer the column process and the compressive strength of concrete simulation results show that the proposed method has a high prediction accuracy and performance.