Fault Detection Algorithm based on Null-Space Analysis for On-Line Structural Health Monitoring

Early diagnosis of structural damages or machinery malfunctions allows to reduce the maintenance cost of systems and to increase their reliability and safety. This paper addresses the damage detection problem by statistical analysis on output-only measurements of structures. The developed method is based on subspace analysis of the Hankel matrices constructed by vibration measurement data. The column active subspace of the Hankel matrix defined by the first principal components is orthonormal to the column null-subspace defined by the remaining principal components. The residue in the orthonormality relation obtained from different data sets may be used to detect structural damages. It is illustrated that this null-space-based method constitutes an enhancement of the classical damage detection method based on principal component analysis (PCA). Several damage indicators are proposed to characterize the resulting residue matrices. The method is first illustrated on a a numerical example and then, it is applied to vibration fatigue testing of a street-lighting device. Because of its simplicity and efficiency, the proposed algorithm is expected to be suitable for continuous on-line health monitoring of structures in practical situations.