Structural damage identification via a combination of blind feature extraction and sparse representation classification

• Develops a novel classification framework for both locating damage and assessing damage severity.
• Alleviates the training process required by traditional pattern recognition based methods.
• Straightforward formulations by sparse representation and compressed sensing.
• Efficient implementations verified by numerical and experimental examples.

This paper addresses two problems in structural damage identification: locating damage and assessing damage severity, which are incorporated into the classification framework based on the theory of sparse representation (SR) and compressed sensing (CS). The sparsity nature implied in the classification problem itself is exploited, establishing a sparse representation framework for damage identification. Specifically, the proposed method consists of two steps: feature extraction and classification. In the feature extraction step, the modal features of both the test structure and the reference structure model are first blindly extracted by the unsupervised complexity pursuit (CP) algorithm. Then in the classification step, expressing the test modal feature as a linear combination of the bases of the over-complete reference feature dictionary—constructed by concatenating all modal features of all candidate damage classes—builds a highly underdetermined linear system of equations with an underlying sparse representation, which can be correctly recovered by ℓ1ℓ1-minimization; the non-zero entry in the recovered sparse representation directly assigns the damage class which the test structure (feature) belongs to. The two-step CP–SR damage identification method alleviates the training process required by traditional pattern recognition based methods. In addition, the reference feature dictionary can be of small size by formulating the issues of locating damage and assessing damage extent as a two-stage procedure and by taking advantage of the robustness of the SR framework. Numerical simulations and experimental study are conducted to verify the developed CP–SR method. The problems of identifying multiple damage, using limited sensors and partial features, and the performance under heavy noise and random excitation are investigated, and promising results are obtained.