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

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. Supplementary materials for this article are available online.

多元函数型数据在各类实际应用场景中愈发常见。不同过程变量间的互相关关系通常较为复杂：某一变量与多数其他变量之间可能仅存在弱相关，甚至无相关，且该互相关关系随时间变化，还可能受若干外生协变量调控。为解决上述两大挑战，本文提出一种协变量调控稀疏子空间学习（covariate-regulated sparse subspace learning, CSSL）模型。本文考虑如下场景：这些过程变量隶属于多个子空间，且仅来自同一子空间的过程变量之间存在互相关关系。为考量外生协变量对子空间结构的影响，本文将协变量的定义域划分为若干区域；在每个区域内，子空间结构视为恒定，且可独立进行学习。随后本文提出一种基于决策树的高效算法以求解该模型。所提方法可进一步应用于多元过程的过程监测与故障隔离任务。本文通过全面的仿真实验，以及针对某风力涡轮机监控与数据采集（supervisory control and data acquisition, SCADA）系统数据集的案例研究，验证了所提方法的有效性。本文的补充材料可在线获取。