Detecting and testing multiple change points in distributions of damage-sensitive feature data for data-driven structural condition assessment: A distributional time series change-point analytic approach

Structural change detection is a core component of structural health monitoring (SHM). One appealing aspect of SHM is that structural changes can be detected by detecting the changes in extracted damage-sensitive features (DSFs). The feature changes of the data are usually attributed to the changes of the underlying distributions; thus, developing reliable change-point detectors for automatically detecting and testing various potential changes in the distributions of DSF data are particularly beneficial for automatic structural health diagnosis. However, methodological researches devoted to detecting change points for probability distributions are rare either in statistics or engineering literature, and state-of-the-art approaches mainly focus on single change-point detection and have restrictive assumptions on the distributions or the types of change points. This motivates us to develop a more flexible multiple change-point detection method for the distributions of DSF data employed for data-driven structural condition assessment. To accommodate a large dataset, the DSF data are summarized by a distributional time series that consists of probability density functions (PDFs) estimated from blocks of DSF data. Then, detecting the distributional changes for the massive DSF data can be phrased as detecting the changes in the resulting distributional time series with much less data objects. To overcome the obstacle that the PDF-valued data are special functional data residing in nonlinear abstract spaces, this study employs two transformations to convert the PDFs into more tractable vector spaces. Then, by using the linear structures possessed by the vector spaces, a nonparametric multiple change-point detection method is presented for the distributional time series based on the techniques of functional principal component analysis and E-Divisive data segmentation. The proposed method possesses various nice features, such as being capable for multiple change-point detection, having fewer restrictive assumptions and scalability to large datasets. Moreover, it also shows superiority in revealing the modes of distributional variations. An application to distributional change detection involved in cable condition assessment for a long-span cable-stayed bridge demonstrates the applicability and versatility of our proposal, and some interesting results are also discovered.