Parametric Study of Stochastic Subspace Algorithms in Modal Analysis of Moment‐Resistant Frames

Abstract

The Finite Element Model (FEM) derived from the design drawings may not precisely depict the behavior of the actual structure. This is due to various factors, such as construction variations, uncertainties in boundary conditions, discrepancies in material properties, inaccuracies in FEM discretization, uncertainties in external excitations, and more. Hence, this paper proposes a process that employs stochastic subspace identification (SSI) to estimate the modal parameters of the structural system with minimal user-defined parameters from ambient vibration data, which is then used to update the FEM. Firstly, the optimal dimensions of the matrix with minimal noise errors are determined by analyzing the condition number of the Hankel matrix. Next, the models are filtered to remove modes caused by numerical instabilities resulting from over-determination in the system. Finally, selecting structural modes involves utilizing Density-Based Spatial Clustering of Applications with Noise (DBSCAN) clustering and confirming the complexity of the shape modes. The algorithm was tested on a numerical model of a 2D concrete frame and used to analyze ambient vibration data from a 6-story building. The first five modes of the residential building with irregular plans were extracted well. So, the first two modes of the structure have a difference of less than 15%, and the other three modes have a 95% agreement with the results of the updated finite element model. It is important to note that the initial FEM did not accurately show seismic behavior due to the used concrete strength.

Keywords

• hankel matrix
• stochastic subspace
• inverse problem
• sensitivity analysis
• system identification