A Covariate-Regulated Sparse Subspace Learning Model and Its Application to Process Monitoring and Fault Isolation

Abstract

Multivariate functional data are increasingly common in various applications. The cross-correlation of different process variables is typically complex in that a variable might be weakly correlated or not correlated with most of the other variables, and the cross-correlation is time-varying and might be regulated by some exogenous covariates. To address these two challenges, we propose a covariate-regulated sparse subspace learning (CSSL) model. We consider the scenario that these process variables lie in multiple subspaces, and only process variables from the same subspace are cross-correlated with each other. To take into account the effect of the exogenous covariates on the subspace structure, we partition the domain of the covariates into a number of regions. In each region, the subspace structure is treated as constant and can be learned independently. An efficient decision-tree-based algorithm is then proposed to obtain the solution. The proposed method can be further applied to process monitoring and fault isolation for multivariate processes. The efficacy of this method is demonstrated by comprehensive simulations and a case study on a dataset from the supervisory control and data acquisition (SCADA) system of the wind turbine.

Keywords:

• Decision tree
• Multivariate functional data
• SCADA data
• Variable selection
• Wind turbine

Supplementary Materials

The supplementary materials contain additional simulation results, figures, tables, derivative of proposition, the R code of CSSL, as well as the dataset of the real case study.

Acknowledgments

The authors are grateful to the editor, an associate editor, and three anonymous referees for their constructive comments and valuable suggestions, which have considerably helped improve an earlier version of this article.

Disclosure Statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article.

Additional information

Funding

Liu and Ye were partially supported by the National Science Foundation of China (72071138) and the Future Resilient Systems project supported by the National Research Foundation Singapore under its CREATE programme. Du was partially supported by National Natural Science Foundation of China (72001139).