Author(s)

Qianhui Gao, Zhu Li, Yongping Yu, Shaopeng Zheng^*

College of Construction Engineering, Jilin University, Changchun, China.

A generalized flexibility–based objective function utilized for structure damage identification is constructed for solving the constrained nonlinear least squares optimized problem. To begin with, the generalized flexibility matrix (GFM) proposed to solve the damage identification problem is recalled and a modal expansion method is introduced. Next, the objective function for iterative optimization process based on the GFM is formulated, and the Trust-Region algorithm is utilized to obtain the solution of the optimization problem for multiple damage cases. And then for computing the objective function gradient, the sensitivity analysis regarding design variables is derived. In addition, due to the spatial incompleteness, the influence of stiffness reduction and incomplete modal measurement data is discussed by means of two numerical examples with several damage cases. Finally, based on the computational results, it is evident that the presented approach provides good validity and reliability for the large and complicated engineering structures.

Generalized Flexibility Matrix, Damage Identification, Constrained Nonlinear Least Squares, Trust-Region Algorithm, Sensitivity Analysis, Incomplete Modal Data

Gao, Q. , Li, Z. , Yu, Y. and Zheng, S. (2023) Damage Identification under Incomplete Mode Shape Data Using Optimization Technique Based on Generalized Flexibility Matrix. Journal of Applied Mathematics and Physics, 11, 3887-3901. doi: 10.4236/jamp.2023.1112246.