Change-point detection for density sequence extracted from SHM data, with application to distributional information break diagnosis encountered in structural condition assessment

Diagnosing the changes of structural behaviors using monitoring data is an important objective of structural health monitoring (SHM). The changes in structural behaviors are usually manifested as the feature changes in monitored structural responses; thus, developing effective methods for automatically detecting such changes is of considerable significance. Existing methods for change detection in SHM are mainly used for scalar or vector data, thus incapable of detecting the changes of the features represented by complex data, e.g., the probability density functions (PDFs). Detecting the abrupt changes occurred in the distributions (represented by PDFs) associated with the feature variables extracted from SHM data are usually of crucial interest for structural condition assessment; however, the SHM community still lacks effective diagnostic tools for detecting such changes. In this study, a change-point detection method is developed in the functional data-analytic framework for PDF-valued sequence, and it is leveraged to diagnose the distributional information break encountered in structural condition assessment. A major challenge in PDF-valued data modeling or analysis is that the PDFs are special functional data subjecting to nonlinear constraints. To tackle this issue, the PDFs are embedded into the Bayes space, and the associated change-point model is constructed by using the linear structure of the Bayes space; then, a hypothesis testing procedure is presented for distributional change-point detection based on the isomorphic mapping between the Bayes space and a functional linear space. Comprehensive simulation studies are conducted to validate the effectiveness of the proposed method as well as demonstrate its superiority over the competing method. Finally, an application to real SHM data illustrates its practical utility in structural condition assessment.