Abstract
The present paper describes a solution to a problem of identifying damage in a building based on experimentally measured vibrational eigenvalue and eigenmode pairs. The healthy rate, which is defined as the stiffness rate with respect to a perfect material, is chosen as the design target to be identified. The range of the healthy rate is restricted to within the range of 0–1. In order to overcome this restriction, we define a function with no restriction on the range defined in the domain of a linear elastic body for a building as a design variable and assume that the healthy rate is given by a sigmoid function of the function of the design variable. The linear coupling of the mean squared errors of vibrational eigenvalues and eigenmodes with respect to the measured values are used as a cost function. The derivative of the cost function with respect to the design variable is evaluated by the adjoint variable method. In order to resolve the identification problem of the damaged area, we use an iterative algorithm based on the \(H^{1}\) gradient method using the finite-element method to obtain numerical solutions. A numerical example using experimental data demonstrates that a damaged area can be identified by the proposed approach.
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Tago, K., Aoki, T. & Azegami, H. Identification of building damage using vibrational eigenvalue and eigenmode pairs. Japan J. Indust. Appl. Math. 32, 297–313 (2015). https://doi.org/10.1007/s13160-015-0180-x
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DOI: https://doi.org/10.1007/s13160-015-0180-x