Soft sensor design using domain-adversarial Gaussian processes—A transfer learning framework

The main objective of this paper is to develop a soft sensor for prediction of quality variables when training and test data come from similar but different distributions. The challenge is to develop a soft sensor when only limited labeled data are available, which requires transferring knowledge from a related source operating condition to improve the performance of the soft sensor on the target task. To realize this, we present a novel transfer learning approach which we refer to as the Domain-Adversarial Gaussian Process (DAGP). In this framework, a feature extractor and a domain classifier are incorporated to learn a feature representation that is invariant across domains. Furthermore, a predictor is developed to minimize the fitting error between inputs and their corresponding outputs from both source domain dataset and limited target dataset. Thus, feature extraction and prediction knowledge learned from both the source operating condition with sufficient data and the target operating condition with limited data can be transferred to improve the performance of the target soft sensor. The overall framework is jointly trained and its parameters are estimated using a variational inference approach, in an adversarial fashion to align the feature extractor and regression model across domains. We demonstrate the efficacy of the proposed method on a simulated study, on a continuous stirred tank reactor benchmark subject to sensor miscalibration, and on an industrial steam-assisted gravity drainage example, indicating that the DAGP can improve prediction performance of the soft sensor when limited labeled training data are available.