Discussion of user‐defined parameters for recursive subspace identification: Application to seismic response of building structures

Abstract

Structural damage assessment under external loading, such as earthquake excitation, is an important issue in structural safety evaluation. In this regard, an appropriate data analysis and system identification technique is required to interpret the measured data and to identify the state of the structure. Generally, the recursive system identification algorithm is used. In this study, the recursive subspace identification algorithm based on the matrix inversion lemma algorithm with oblique projection technique (RSI-Inversion-Oblique) is applied to investigate the time-varying dynamic characteristics. The user-defined parameters used in the RSI-Inversion-Oblique technique are carefully discussed, which include the size of the data Hankel matrix (i), model order to extract the physical modes, and forgetting factor (FF) to detect the time-varying system modal frequencies. Response data from the Northridge earthquake from the Sherman Oaks building (CSMIP) is used as an example to examine a systematic method to determine the suitable user-defined parameters in RSI. It is concluded that the number of rows in the data Hankel matrix significantly influences the identification of the time-varying fundamental modal frequency of the structure. An algorithmic model order selection method using the eigenvalue distribution of RSI-Inversion can detect the system modal frequencies at each appending data window without causing any abnormality.

Tracking Modal Parameters of Structures Online Using Recursive Stochastic Subspace Identification under Ambient Excitations

“…As a result, multiplying the sampling interval and the window length results in the first identification time, which can be observed in the following figures. According to past studies [35,37,38], i is assigned to cover the fundamental period of the simulated frame; it is 1 s in this example.…”

“…where L ij is different parts of the lower triangular matrix and Q ij is different parts of the orthogonal matrix from LQ decomposition. This approach is also known as "Multivariable Output-Error State sPace (MOESP)" and can be considered a time-efficient alternative for matrix projection [34,35]. Again, Γ i can be retrieved by repeating Equations ( 12)-( 14) and substituting O orth for O MOESP to identify the linear elastic system matrix, A.…”

“…Regardless of the approaches used, the continuous-time equations can ultimately be computed from discrete-time ones. Additionally, the modal parameters, including modal frequencies, damping ratios, and mode shapes, can be subsequently extracted [2,3,35,36]. The output parameters are essential for monitoring dynamic features in SHM.…”

Development of Recursive Subspace Identification for Real-Time Structural Health Monitoring under Seismic Loading

“…Tree main streams are available: one is sophisticatedly derived via matrix inversion lemma [26,27,36,37], the other is accomplished by the cross-multiplication of matrices from QR decomposition [30,31,38,39], and the last one rotates the newest vector in QR decomposition to update the projection [28,29,40,41]. Some comparative studies of these two methods can be found in the literature [32][33][34][35]42]. Despite the success brought by those methods, the same procedure with SI produces inevitable decomposition steps.…”

Modal Parameter Identification of a Structure Under Earthquake via a Wavelet-Based Subspace Approach

“…To enhance the efficiency of these original subspace approaches, an instrumental variable [34], a generalized Schur algorithm [35], empirical mode decomposition [36,37], a covariance-driven algorithm [38], and nuclear norm optimization [39] have been incorporated into subspace methods. To expand the application fields of subspace approaches from a time-invariant system to a time-variant system, the moving window technique [40,41] and recursive update algorithms [41][42][43][44][45] have been adopted.…”