Modal analysis of earthquake records for dams using stochastic subspace based on error analysis

Abstract

System identification based on seismic data is crucial for updating numerical analyses and implementing health monitoring strategies for critical structures such as dams. However, most system identification methods have been developed with the assumption of white noise and stationarity of excitations, which is inconsistent with the nature of seismic data. As a result, the systems estimated from such methods are often associated with high uncertainties, making obtaining accurate and reliable results challenging. In this study, a new figure of merit (FOM) is proposed for tracking the ill‐conditioning of systems by analyzing the errors in stochastic subspace identification (SSI) through the inversion process. Unlike the condition number, which measures the ratio between the largest and smallest singular values, this FOM uses all singular values to assess the system's ill‐conditioning comprehensively. A semi‐automatic identification method based on SSI has been developed using the proposed FOM. The optimal dimensions of the Hankel matrix are obtained so that none of the system error components dominate. Frequency/damping clustering is used to overcome the identified system's over‐determination and remove outliers. Finally, the complexity of the modal shapes resulting from clustering is examined to validate the structural modal characteristics. The procedure was validated using seismic data from the Finite Element Model of Koyna Dam. It identified the first four modal frequencies of the structure with less than 2% error rate. The average error in estimating damping ratios was below 20%. The algorithm was then used to analyze the seismic monitoring data of Pacoima Dam for the Chino Hill 2008 and Granada Hills 2020 earthquakes. Despite the closely spaced Pacoima Dam modes, the study demonstrated excellent accuracy and robust methodology performance. By distinguishing the structural modes related to the dam body from other modes of the “dam‐foundation‐reservoir” system, the proposed method helps to determine the existing model's nonlinearity.