Output-Error Methods in Structural Modal Identification

Document Type : Research Article


1 Department of Civil Engineering, Sarab Branch, Islamic Azad University, Sarab, Iran

2 Department of Civil Engineering, Malekan Branch, Islamic Azad University, Malekan, Iran


Stochastic subspace identification (SSI) is a process that linearizes the identification problem by utilizing singular value decomposition (SVD) and QR factorization. This technique enables the extraction of system matrices through linear least squares. However, the estimated systems in these methods are affected by the user-defined dimensions of the data space (Hankel matrix). Also, SSI does not explicitly minimize a cost function for estimating system matrices, making statistical analysis difficult. To enhance the accuracy of modal specifications obtained from SSI, especially the damping ratios, this research suggests using output-error methods (OEM). During OEM, the process involves iteratively adjusting the model parameters to match the outputs of the simulated model with those of the observed system. The following steps are taken to enhance the OEM for extracting structural properties: Firstly, the initial term is derived using the SSI to reduce the number of optimization iterations. Secondly, by using the Gauss-Newton approach, the nonlinearity of the objective function is reduced by treating the second-order derivatives as a linear system. Finally, Gradient project minimization is utilized in SSI to ensure the injectivity of estimated systems. The OEM was validated by analyzing the response of a 3-DOF excited by white noise with an SNR of 1 db. Then, the model was then applied to seismic observations of Pacoima Dam during the 2001 San Fernando and 2008 Chino Hills earthquakes. The two main modes of the structure were extracted, and they had the least error compared to the developed finite element models.


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