On model-based damage detection by an enhanced sensitivity function of modal flexibility and LSMR-Tikhonov method under incomplete noisy modal data

Sensitivity-based methods by the model updating strategy are still influential and reliable for structural damage detection. The major issue is to utilize a well-established sensitivity function that should be directly relevant to damage. Under noisy modal data, it is well known that the sensitivity-based model updating strategy is an ill-posed problem. The main aim of this article is to locate and quantify damage using incomplete noisy modal parameters by improving a sensitivity function of modal flexibility and proposing a new iterative regularization method for solving an ill-posed problem. The main contribution of the enhanced sensitivity formulation is to develop the derivative of eigenvalue and establish a more relevant sensitivity function to damage. The new regularization method is a combination of an iterative approach called least squares minimal residual and the well-known Tikhonov regularization technique. The key novel element of the proposed solution method is to choose an optimal regularization parameter during the iterative process rather than being required a prior. Numerical simulations are used to validate the accuracy and efficiency of the improved and proposed methods. Results demonstrate that the enhanced sensitivity function of the modal flexibility is more sensitive to damage in comparison with the basic formulation. Moreover, one can observe the robustness of the proposed solution method to solve the ill-posed problem for damage localization and quantification under noise-free and noisy modal data.