Influence of Hankel matrix dimension on system identification of structures using stochastic subspace algorithms

Abstract

In stochastic subspace methods, the modal analysis results are highly dependent on the dimensions of the Hankel matrix. Increasing the dimensions of the Hankel matrix (especially the number of rows) improves the estimation of the modal features by decreasing the impact of noise effects. Due to processing time and memory use, it is impossible to adjust the size of the Hankel matrix to the maximum compatible value. Therefore, this study uses a sensitivity analysis of the dimensions of the Hankel matrix to pick models with the slightest estimate error in the data-driven (DD-SSI) method. First, using the condition number criteria, the desirable models in which the effects of system errors are not predominating are determined. Second, the modal properties of desired models are validated by clustering the damping ratios and modal frequencies using the Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm and assessing the complexity of shape modes with the Modal Complexity Factor (MCF). Finally, the optimum models are identified by analyzing the estimated error of modal properties (particularly damping ratio) and the coefficient of variation (CV) of damping of validated clusters. The proposed method was investigated for a two-dimensional simulated concrete building frame, a three-dimensional experimental model, and the Namin city Overpass Bridge ambient vibration tests. Sensitivity analysis was performed for canonical correlation analysis (SSI-CCA) and canonical variate analysis (SSI-CVA) methods. Analyses of computational and laboratory models revealed that the likelihood of non-physical modes arising outside the system's maximum order is relatively high. Also, the MCF is valuable for identifying computational and noise modes. These criteria accurately detected the flexural mode of the foundation set, which was clustered as the stable mode of the slab deck in the practical bridge. Furthermore, the CV analysis revealed that the desired dimension obtained from the condition number could be a reasonable estimate of the optimal system dimension.