The study of damage identification based on compressive sampling

Abstract

This paper proposes a novel and effective method to identify the damage in the 2-D beam via Lamb wave. Two problems in the structural damage identification: damage location and damage severity are solved based on the theory of compressive sampling (CS) which indicates that sparse or compressible signals can be reconstructed using just a few measurements. Because of the sparsity nature of the damage, a database of damage features is established via a sparse representation for damage identification and assessing. Specifically, this proposed method consists of two steps: damage database establishing and feature matching. In the first step, the features database of both the healthy structure and the damaged structure are represented by the Lamb wave which propagates in the 2-D beam. Then in the matching step, expressing the test modal feature as a linear combination of the bases of the over-complete reference feature database which is constructed by concatenating all modal features of all candidate damage locations builds a highly underdetermined linear system of equations with an underlying sparse representation, which can be correctly recovered by l1-minimization based on CS theory; the non-zero entry in the recovered sparse representation directly identifies the damage location and severity. In addition, numerical simulation is conducted to verify the method. This method of identifying damage location and assessing damage severity, using limited Lamb wave features, obtains good result.