Low-Rank Joint Embedding and Its Application for Robust Process Monitoring
Yuanjian Fu, Chaomin Luo, Zhuming Bi
Abstract
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.