A Multi-rate Probabilistic Slow Feature Regression Model for Dynamic Feature Learning and Industrial Soft Sensor Development

In practical process industries, the measurements coming from different sources are collected at different sampling rates, thereby soft sensors developed using uniformly sampled measurements may result in poor prediction performance. Besides, industrial processes are inherently stochastic and most of them present dynamic characteristic. To cope with these issues, a multi-rate probabilistic slow feature regression (MR-PSFR) model is proposed in this paper for dynamic feature learning and soft sensor development in industrial processes. In the MR-PSFR, both input and output observation datasets with different sampling rates are used to extract the slow features, which can separate slowly and fast changing features and have a better interpretation of the outputs. Then, the expectation-maximization algorithm is modified to derive the model parameters of MR-PSFR and the quality prediction strategy for multi-rate processes is constructed. Finally, the proposed method is investigated through a numerical example and a real industrial process. The simulation results show that the extracted slow features better represent the intrinsic characteristics of the processes and the proposed model has better prediction performance for multi-rate dynamic processes than other methods.