Structural damage identification using an optimization technique based on generalized flexibility matrix

A generalized flexibility matrix–based objective function utilized for structure damage identification is firstly constructed. After transforming the damage identification into a constrained nonlinear least squares optimization problem, the trust-region algorithm is applied to find the solution of the inverse problem in multiple damage cases. Thereinto, the sensitivity analysis of the objective function with respect to the design variables is derived using the Nelson's method. At last, two numerical examples with several damage cases are investigated, including a steel truss bridge model as well as a drilling rig derrick model. Based on the computational results, it is evident that the presented approach provides excellent validity and reliability for the large and complicated engineering structures.