Low-Rank Joint Embedding and Its Application for Robust Process Monitoring

Industrial data are in general corrupted by noises and outliers. In this context, robustness to the contaminated data is a challenging issue in process monitoring. In this article, a novel method named low-rank joint embedding is proposed for robust process monitoring. By learning a low-rank coefficient matrix, low-rank joint embedding can capture the global structure of the original data and alleviate the negative effect of outliers, making the monitoring results more reliable. Moreover, a manifold regularization is introduced to preserve the local geometric structure of data, which enables the extracted low-dimensional representation of data to be more faithful and informative to enhance the monitoring capability. Based on projection learning, the low-rank joint embedding can learn an explicit projection that transforms the data not involved in the training data into the low-dimensional space, avoiding the out-of-sample problem. Furthermore, a reconstruction-based contribution plots based on the low-rank joint embedding is developed to identify the potential faulty variables. Case studies on the Tennessee Eastman process and a real industrial application demonstrate the effectiveness of the proposed monitoring approach.