Block-Wise Parallel Semisupervised Linear Dynamical System for Massive and Inconsecutive Time-Series Data With Application to Soft Sensing

Linear dynamical system (LDS) has established itself as a powerful tool for soft sensing dynamic industrial processes, which, however, still faces some practically pivotal issues. First, traditional LDS-based soft sensors require training samples to be labeled and ignore time delays (TDs) between explanatory variables (EVs) and primary variables (PVs), whereas labeled samples are usually scarce and the TDs could have appreciable impacts on the predictive accuracy. Second, LDS models are trained in a serial way, rendering significant computational deficiency when dealing with massive data that imply a wealth of information on process dynamics. What is worse, such learning paradigm may fail to take full advantage of all available data because the time-series data chain is often broken due to malfunctions of data communication system or measurement sensors. These issues lead the LDS-based soft sensors to degraded performance such as low accuracy, computational deficiency, and poor interpretability. To this end, this article first proposes a semisupervised training framework for the LDS with optimized TDs (TD-SsLDS), so as to make up for the deficiencies of supervised learning and overlooking of TDs. Furthermore, a block-wise parallel TD-SsLDS (BwP-TD-SsLDS) is proposed, where a highly efficient learning algorithm is designed to extract patterns from multiple data blocks in a parallel way such that the LDS is enabled to learn from massive and inconsecutive time-series data. Case studies are conducted on both artificial example and real-life industrial process for evaluating the performance of the TD-SsLDS and BwP-TD-SsLDS. The results demonstrate that the proposed schemes could significantly improve the predictive and computational performance for the LDS-based soft sensors.