Multi-scale structure damage detection using wavelet finite element method

Abstract

Damage detection of civil infrastructures will be essential in future decision making on structural maintenance and hazard mitigation. Damage-induced changes in dynamic characteristics and responses are commonly utilized to locate and quantify structural damages. Common vibration-based damage detection methods can be categorized into two groups, namely, frequency-and time-domain methods. This thesis focuses on developing multi-scale structural damage detection strategies in both frequency-and time-domain with the use of wavelet finite element models (WFEM). Such multi-scale strategies would optimize structural modeling in accordance with damage scenarios and external load conditions. These strategies are very efficient in terms of the number of degree-of-freedoms (DOFs) of structural models, number of sensors, and computation effort.Multi-scale dynamic formulations and corresponding lifting schemes were derived for beam and thin plate structures individually through the use of the cubic Hermite WFEM. In particular, the multi-scale formulation of beam structures under moving load excitation was derived. Such a formulation lays the theoretical foundation of multi-scale damage detection in a progressive manner.In frequency-domain, multi-scale damage detection methods to progressively detect sub-element damage in beam and plate structures were proposed based on modal strain energy and model updating technique in the context of WFEM. The structural modelling resolutions did not only spatially vary but also changed dynamically according to actual requirements. A coarse WFEM was utilized to identify the likely damaged regions first. Meanwhile, gradually lifted WFEMs with local refinement were utilized to estimate the exact damage location and severity. Numerical and experimental examples were conducted to demonstrate the high efficiency of the proposed methods in terms of the number of DOFs, number of sensors, and computation effort.In time-domain, the closed-form solution of the dynamic response of a simply supported damaged beam under a moving force was derived based on modal perturbation and modal superposition methods. With this solution, the damage effect on different components of the dynamic response was investigated. A simple and efficient damage localization approach that employs discrete wavelet transform (DWT) was then proposed. Numerical examples were utilized to validate the accuracy of the response computation algorithm and demonstrate the effectiveness of the damage localization approach. Subsequently, an adaptive-scale analysis strategy for beam structures subjected to moving loads was developed with WFEM. In this strategy, the wavelet element scales were dynamically changed to remain compatible with the moving load position. A two-phase damage detection method for beam structures under moving load was then proposed by combining the adaptive-scale analysis strategy, DWT-based damage localization, and progressive WFEM updating in time-domain. The scale of the wavelet elements were adaptively enhanced or reduced not only according to the moving loadbeam contact position but also to the progressively identified damage locations. Such a method can effectively minimize the number of modelling DOFs and updating parameters during optimization. A laboratory experiment was conducted to examine the feasibility and efficiency of the two-phase damage detection method.