Abstract– This paper presents new sensitivity-based methods for detection of structural damage using incomplete noisy modal data. These methods are based on the first-order derivative of modal parameters. Changes of natural frequency do not usually provide spatial information on the structural damage. They are also not sensitive to the local damage. In this paper, a new sensitivity function is proposed using method of Lagrange multipliers in order to deal with these weaknesses when applying natural frequency in the sensitivity-based damage diagnosis. Mode shape is the other vibrational data which leads to better results in comparison with natural frequency. However, usually some mode shape’s sensitivities require all modes to obtain exact sensitivity functions. Thus, an improved sensitivity of mode shape is presented to constitute an applicable formulation based on using incomplete modes. To determine the damage quantity, a powerful iterative method named Least-Square Minimal Residual (LSMR) technique is proposed in the condition of incomplete modes. Subsequently, Regularized Least-Square Minimal Residual (RLSMR) method is presented to detect structural damage when the incomplete modal parameters are contaminated by noise. Applicability and effectiveness of the proposed methods are numerically verified using two practical examples consisting of a six-story shear building and a planner truss. Eventually, numerical results indicate that the LSMR and RLSMR are influential algorithms for precisely determining the damage severity. Furthermore, obtained results of damage diagnosis process in the free-noise data show that the proposed sensitivities of natural frequency and mode shape can provide reliable and accurate results for structural damage diagnosis.

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