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Abstract: Modal strain energy has been widely utilized as a damage-sensitive feature to detect structural damage. Based on the closed-form of element modal strain energy sensitivity, a statistic structural damage detection algorithm is proposed in this paper. The method is oriented to the ambient vibration measurements where only the operational mode shapes are available. The established element damage equations are incorporated with the modal scaling factors so that the damage and modal scaling factor can be solved simultaneously. The statistic analysis is implemented to take into account the uncertainties existing in the structural model and measured structural modal parameters. The sensitivity formulas of system matrix and residual vector with respect to noise are derived. The proposed statistics based element damage equations have a compact algebraic form, which does not require a large computation time and a high storage capacity. The method is verified by a numerical simply supported beam with different assumed damage. The effects of noise and damage levels on damage detection are investigated. It is demonstrated that the proposed method can identify most likely damaged elements. [Copyright &y& Elsevier]