A hybrid sensitivity function and Lanczos bidiagonalization-Tikhonov method for structural model updating: Application to a full-scale bridge structure

Structural model updating (SMU) by sensitivity analysis is a reliable and successful approach to adjusting finite element models of real structures by modal data. However, some challenging issues, including the incompleteness of measured modal parameters, the presence of noise, and the ill-posedness of the inverse problem of SMU may cause inaccurate and unreliable updating results. By deriving a hybrid sensitivity function based on a combination of modal strain and kinetic energies, this article proposes a sensitivity-based SMU method for simultaneously updating the elemental mass and stiffness matrices. The key idea of the proposed sensitivity function originates from the fundamental concepts of the equality-constrained optimization problem and Lagrange multiplier method. By combining the Lanczos bidiagonalization algorithm and Tikhonov regularization technique, a novel hybrid regularization method is presented to solve the ill-posed inverse problem of SMU in a robust manner. This scheme exploits new generalized cross-validation functions directly derived from the outputs of the Lanczos bidiagonalization algorithm to automatically specify the number of iterations and determine an optimal regularization parameter. The accuracy and effectiveness of the presented approaches are verified numerically and experimentally by a steel truss and the full-scale I-40 Bridge. All results show that the proposed methods are effective tools for SMU under incomplete noisy modal data.