Deep Gaussian mixture adaptive network for robust soft sensor modeling with a closed-loop calibration mechanism

Abstract

Process drift leads to an out-of-distribution problem between historical training data and online deployment data, which deteriorates the performance of soft sensors. Unfortunately, few existing deep learning soft sensors have calibration mechanisms to deal with the process drift. To this end, this article proposes a robust Deep Gaussian Mixture Adaptive Network (DGMAN)-based soft sensor with a closed-loop calibration mechanism. First, a Gaussian Mixture Conditional Variational Autoencoder (GMCVAE) is presented, with the ability to capture the multimodality in industrial data. Afterwards, we propose a novel semi-supervised Gaussian mixture domain adaptation to perform conditional and marginal probability distribution alignment in the Gaussian mixture probabilistic latent space created by GMCVAE, using both labeled and unlabeled target samples. Theoretically, two kinds of process drift, including concept drift and virtual drift, could be alleviated by conditional distribution adaptation and marginal distribution adaptation, respectively. In addition, a new closed-loop calibration mechanism is deployed in a pre-training and fine-tuning fashion. Finally, robust analysis in theory and experimental results on the gas turbine dataset demonstrate that the proposed DGMAN-based soft sensor with robustness against process drift can maintain long-term validity in real industrial processes. Calibrated by only 100 labeled samples per year, the RMSE of DGMAN is 5.55 ± 0.32 after three years of deployment in the power plant, outperforming all comparison methods.