Michael Do¨hler, Falk Hille, Xuan-Binh Lam, Laurent Mevel and Werner Ru¨cker figures, especially when evaluating changes in a system (e.g. due to damage) where identified modal parameters are compared. The problem consists in quantifying the uncertainty related to the identified modal parameters of a structure subject to ambient unmeasured vibrations. In [9], an algorithm was derived to automatically compute confidence intervals in covariance driven SSI, based on [8]. In [4] and [5], some propositions were made that improve this algorithm in efficiency and generality. Using covariance driven SSI and data driven SSI with the Unweighted Principal Component Algorithm (UPC), the resulting algorithm is applied in this paper on the S101 Bridge in Austria to compute confidence intervals, together with an automated monitoring procedure, during the progressive damage test of the bridge. 2 Stochastic Subspace Identification 2.1 State Space Model The mechanical system is supposed to be a stationary linear dynamical system M ¨Z(t)+C ˙Z(t)+KZ(t) =ν(t) Y(t) =LZ(t) , with • Z: displacements of the degrees of freedom, • M, C, K: mass, damping, stiffness matrices, • t: continuous time, • ν: excitation (Gaussien, zero-mean, white), • L: observation matrix giving the observationY. The modal characteristics • μ vibration modes or eigenfrequencies • ψμ modal shapes or eigenvectors are solutions of the following equation: (Mμ2 +Cμ+K)Ψμ =0 , ψμ =LΨμ. We switch to the state space model in discrete time by sampling at the rate 1/δ with Xk = Z(kδ) ˙Z(kδ) , Yk =Y(kδ) andget Xk+1 =FXk +Vk Yk =HXk . (1) 238
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