Developing Variational Autoencoders with Differential Entropy Soft Sensor Models for Nonlinear Processes

Abstract

Developing a good soft sensor for prediction has been a major interest, given the time lag to obtain quality data. Deep learning based variational autoencoders (VAE) have been implemented in industrial plants because of their capacities in dealing with the complex stochastic nonlinearity with better probabilistic interpretation. However, unsupervised VAE is inapplicable to the prediction. This article proposes a nonlinear soft sensor, which is an extension of the VAE framework with differential entropy (VAE_DE) loss function to construct a prediction model. The proposed VAE_DE model structure allows all the available data to be used for training although the data consist of process-quality data pairs and/or solely process data. Also, VAE DE enhances the prediction performance and its robustness through capturing the inter-correlations between process data and quality data in the nonlinear probabilistic model. Under the proposed framework, VAE DE model can be used for quick quality estimates of process data with unavailable quality data. The prediction quality of the proposed method is testified through a numerical case and an industrial case.