Multi‐layer features ensemble soft sensor regression model based on stacked autoencoder and vine copula

Abstract

It is crucial in industrial processes to consider key variables to ensure safe operation and high product quality. Moreover, these variables are difficult to obtain using traditional measurement methods; hence, it makes sense to develop soft sensor regression models to process the variable prediction. However, there are numerous variables integrating noisy and redundant information in complex industrial processes. Using such variables in traditional regression models may result in reducing the model's efficiency and performance. Thus, this paper proposes a multi-layer feature ensemble soft sensor regression method using a stacked auto-encoder (SAE) and vine copula (ESAE-VCR) to address these problems. To do so, the number of neurons in the hidden layer of the SAE is determined by the principal component analysis (PCA). The multi-layer features of the process variables are extracted using a stacked AE, and the regression models are established for each feature layer. A linear regression ensemble method is used to combine the regression models with the multi-layer features to obtain the final predictive model that will estimate the values of the key variables. The effectiveness and practicality of the ESAE-VCR are validated by comparing them with several common soft measurement methods in two examples. In the numerical example, the ESAE-VCR yields an accuracy of prediction (R 2 ) of 0.9898 and a root mean square error (RMSE) of 0.1804. In the industrial example, the ESAE-VCR yields an R 2 of 0.9908 and an RMSE of 0.1205.