Adaptive Sampling for Monitoring Multi-Profile Data with Within-and-between Profile Correlation

Multi-profile data can provide within-and-between profile information for efficiently modeling and monitoring system status. In practice, however, acquisition of such data requires large number of sensors, which raises various concerns and difficulties, for example, cost, energy, and data transmission bandwidth, in accessing the full data from each sensor. In this article, we propose an adaptive sampling strategy for multi-profile monitoring by using limited portion of data. The proposed sampling and monitoring scheme incorporates the within-and-between profile correlation and features the balance between random search and greedy search in identifying the most informative profiles. More specifically, the multivariate functional principal component analysis (MFPCA) is used to capture the within-and-between profile correlation, and the MFPC scores are augmented for unobservable profiles to feed into a multivariate CUSUM chart. Two properties of the proposed method for allocating sampling resources among sensors are investigated. Numerical and case studies are conducted under various scenarios to demonstrate the effectiveness of the method.