Order and parameter estimation of time‐varying system by subspace method

Earthq Engng Struct Dyn

et al. 2020

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.

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“…First, consider the method from [7] for model order estimation with two different i (20 and 45). Based on the normalized difference of a maximum value of lsvps (i.e.…”

Section: Comparison Of Rsi Results Using Different Model Order Estimatmentioning

confidence: 99%

“…This method was originally proposed by [7] to determine the model order. Since the singular value (si) shown in Eq.…”

Section: Determining the Model Order For Rsimentioning

confidence: 99%

Section: _ Max Ps Lsvmentioning

confidence: 99%

Section: _ Max Ps Lsvmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Huang

Earthq Engng Struct Dyn

et al. 2020

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Two‐stage damage detection algorithms of structure using modal parameters identified from recursive subspace identification

Earthq Engng Struct Dyn

2017

Summary Structural damage assessment under external loading, such as earthquake excitation, is an important issue in structural safety evaluation. In this regard, appropriate data analysis and feature extraction techniques are required to interpret the measured data and to identify the state of the structure and, if possible, to detect the damage. In this study, the recursive subspace identification with Bona‐fide LQ renewing algorithm (RSI‐BonaFide‐Oblique) incorporated with moving window technique is utilized to identify modal parameters such as natural frequencies, damping ratios, and mode shapes at each instant of time during the strong earthquake excitation. From which the least square stiffness method (LSSM) combined with the model updating technique, called efficient model correction method (EMCM), is used to estimate the first‐stage system stiffness matrix using the simplified model from the previously identified modal parameters (nominal model). In the second stage, 2 different damage assessment algorithms related to the nominal system stiffness matrix were derived. First, the model updating technique, called EMCM, is applied to correct the nominal model by the newly identified modal parameters during the strong motion. Second, the element damage index can be calculated using element damage index method (EDIM) to quantify the damage extent in each element. Verification of the proposed methods through the shaking table test data of 2 different types of structures and a building earthquake response data is demonstrated to specify its corresponding damage location, the time of occurrence during the excitation, and the percentage of stiffness reduction.

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Discussion of Several “RSID” Algorithms to Linear Time-Varying System and System with Abrupt Change of Joint Failure

Lecture Notes in Civil Engineering

2017