An MPPCA-based approach for anomaly detection of structures under multiple operational conditions and missing data

Structural anomaly detection based on the structural health monitoring (SHM) data has attracted significant attention owing to its important role in the early warning of structural damage to existing civil structures. Data-driven approaches, where damage-sensitive features are extracted directly from the SHM data using statistical pattern recognition (SPR) techniques without physical models of structures, have been widely studied. Principal component analysis (PCA) and probabilistic PCA (PPCA) are powerful and efficient SPR methods for linear or weakly nonlinear cases. However, some special structures may be subjected to multiple operational conditions, wherein structural configurations such as geometry and mass distribution may change due to the movement of parts or the whole structure, as in retractable roof structures. These changes may give erroneous results in the SPR of the SHM data and eventually in the anomaly detection by a single PCA or PPCA model. This paper presents an improved approach using a mixture of probabilistic principal component analysis (MPPCA) for the anomaly detection of structures under multiple operational conditions with missing measurement data. First, the baseline MPPCA model was constructed for stress data collected under healthy conditions, where the estimation of the MPPCA parameters was reformulated for the missing data cases. Second, three anomaly statistics were presented for newly monitored incomplete data to detect and localize structural anomalies. The probability distributions of the anomaly statistics were estimated to obtain thresholds for outlier detection. Finally, the effectiveness of the MPPCA-based method was investigated by applying the method to the anomaly detection of a retractable roof structure with numerically simulated and real monitored stress data.