Structural Damage Detection Algorithms Based On The Sparsity Recovery Theory

Damage localization and quantification is a parametric problem in structural dynamics. However, it is an ill-conditioned inversion problem since available modal information is always incomplete, and its performance is negatively influenced by the massive redundant information. Faced with this problem,we utilize reasonable prior knowledge that damages are sparsely distributed along structural domain, to compensate the incompleteness of modal information. Then new algorithms with strong robustness for damage detection are developed using the theory of sparsity recovery. The specific works are in following:Firstly, a parametric model for damage identification is establish based on modal parameter’s sensitivity to damage indexes. Then a new algorithm for damage detection is developed based on Orthogonal Matching Pursuit. Numetical simulation of a planar truss is used to illustrate the performance of proposed algorithm. Results show that the proposed method is more robust solve in solving for the damage indexes using incomplete and polluted modal information. However, as the increase of potential damages, the robustness of the proposed method tends to be worse since the assumption of sparsity in damage distribution starting to be broken.Furthermore, taking the uncertainty in damage detection into consideration, a probabilistic algorithm of damage detection based on Sparse Bayesian Learning is proposed. The uncertainty is mainly accounted for by both incompleteness and randomness of modal information. Numerical simulation of a cantilever beam and a planar truss are respectively used to demonstrate how the proposed algorithm performs when modal frequencies are available and how it works when modal flexibility is avaibable. Results show that, compared with non-sparsity Bayesian damage detection algorithm, the proposed algorithm not only more solve damage indexes accurately, but also quantify their uncertainty and correlation more reasonably.Finally, a model of 16-bay spatial truss is used for experimental investigation in order to demonstrate the effectiveness of the proposed algorithms. Compared with the numerical simulation above, the experimental examples are exposed to less modal information, and are troubled by the deviation between finite element(FE) model and actual structure. Experimental results show that, even when FE model obviously diverging from the actual structure, the results of the proposed methods are still more reliable than those of non-sparsity method. Besides, FE model update has also been carried out and however, it has not improved the performance of damage detection algorithms. This is due to the deviation between predefined damage indexes’ s physical meanings and those of actual damages.