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Abstract: A new structural damage identification method using limited test static displacement based on grey system theory is proposed in this paper. The grey relation coefficient of displacement curvature is defined and used to locate damage in the structure, and an iterative estimation scheme for solving nonlinear optimization programming problems based on the quadratic programming technique is used to identify the damage magnitude. A numerical example of a cantilever beam with single or multiple damages is used to examine the capability of the proposed grey-theory-based method to localize and identify damages. The factors of measurement noise and incomplete test data are also discussed. The numerical results showed that the damage in the structure can be localized correctly through using the grey-related coefficient of displacement curvature, and the damage magnitude can be identified with a high degree of accuracy, regardless of the number of measured displacement nodes. This proposed method only requires limited static test data, which is easily available in practice, and has wide applications in structural damage detection.

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