Structural damage diagnosis with uncertainties quantified using interval analysis

Abstract

The in situ structural assessment by means of structural health monitoring (SHM) has received a great attention in all sorts of civil engineering applications. However, SHM implementations especially damage detections for real-world infrastructures are always overwhelmed with uncertainties of high dimensionality. A nonprobabilistic uncertainty-quantification-enhanced damage diagnosis method is proposed in this study with respect to interval analysis on SHM features. The diagonal elements of the vector auto-regressive model, constructed from the data measurements, are firstly extracted to form a vector, and this vector's Mahalanobis distance between pristine and unknown conditions is used as a damage-sensitive feature. Subsequently, the uncertainty sources, such as measurement inaccuracy and physical variability, are considered as influencing variables. A differential evolution algorithm is thereby introduced to convert the fluctuating interval of those variables into the uncertainty interval of Mahalanobis distance estimation. Finally, inspired by the idea of receiver operating characteristics when probability of detection is available, a modified mathematic metric is defined suited for interval analysis, and area under the modified receiver operating characteristics curve is employed to detect and localize damages. A contrived numerical mass-spring system and a laboratory-scale frame structure are used to validate the proposed framework; and in addition, the damage severity is able to be quantified via a proposed interval distance between pristine and inspection conditions.