Structural damage assessment from modal data using a system
identification algorithm with a regularization technique
Joo Sung Kang
This paper presents an improved damage assessment algorithm using modal data based on the system identification algorithm with a regularization technique. In this algorithm, the regularization technique is introduced to overcome ill-posedness of the inverse problem. Both the Frobenius norm and the Tikhonov function are used as the regularization function. The Variable Regularized Factor Scheme(VRFS) is employed for the Frobenius norm and the Geometric Mean Scheme(GMS) is employed for the Tikhonov function to determine a regularization factor.
In the optimization process, sensitivities of modal responses are required. First order sensitivity of mode shape normalized with mass matrix can be calculated by modal method. However, in the real situation, measurement data of entire DOFs cannot be obtained. Therefore, the sensitivity of the normalized mode shape by an arbitrary matrix is proposed. The Gauss-Newton Hessian is used for second order sensitivity.
Statistical approach is used to estimate more reliable system parameter to overcome sparseness and noise of measurement data.
The validity of the proposed algorithm is demonstrated by numerical examples of frame and grid model and results are compared with those of others method.
damage assessment, mode shape, ill-posedness, regularization technique, Frobenius norm, Tikhonov function, VRFS, GMS, sensitivity, statistical approach