Soft sensor modeling with a selective updating strategy for Gaussian process regression based on probabilistic principle component analysis

Considering the deviation of the working condition and the high updating frequency of the traditional moving window methods, this paper proposes a selective strategy of moving window for the Gaussian process regression in the latent probabilistic component space. First, the probabilistic principle component analysis (PPCA) is employed to deal with the multi-dimensional issue and extract essential information of the process data. Because the latent probabilistic components are more sensitive to the deviation of the working condition in the industrial process than the original data, the regression performance is improved under the PPCA framework. Under the proposed strategy, the soft sensor is able to detect the change of the working condition, and the updating is activated only when the predicted error exceeds the preset threshold, otherwise the model is kept unchanged. Furthermore, the promotion of both predicted accuracy and efficiency can be obtained by regulating the threshold. To test the effectiveness of the proposed method, a wastewater case study is provided, and the result shows that the proposed strategy works better under the probabilistic than other conventional methods.