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Incomplete sensed data in structures have made exact structural damage detection a serious challenge. In this paper, an effective method is presented for damage detection and estimation in structures based on incomplete modal data of a damaged structure via a pattern search algorithm. An objective function based on the condensed mass and stiffness matrices is formulated. The proposed method determines the damage to structural elements using optimization of the objective function by using pattern search algorithm. The performance of the presented method has been verified through two numerical examples, namely, a two-span continuous beam and a three-story plane frame with and without noise in the modal data containing several damages. Also, the effect of the discrepancy in mass and stiffness between the finite-element model and the actual tested dynamic system has been investigated. Furthermore, the experimental data from the vibration test of a mass–stiffness system are used for verification of the proposed approach. The results show that the presented method is sensitive to the location and severity of structural damage in spite of the incomplete modal data.

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