System Identification through Nonstationary Response: Wavelet and Transformed Singular Value Decomposition—Based Approach

Abstract

The full-scale data measured from tall buildings and long-span bridges are usually nonstationary due to transient earthquake ground motion, sudden changes in wind speed and/or direction, or time-varying motion of vehicles. The dynamic properties (i.e., frequency, damping, etc.) of these structures during nonstationary events closely relate to their operational safety, so their accurate identification is critical. Traditional system identification methods may fail to provide reliable results (especially for damping estimation) in these situations due to a lack of long segments of stationary data. In addition, these methods are not able to track the time-varying system properties caused by large amplitude response due to strong earthquakes or winds. This highlights the necessity of developing system identification methods suitable for nonstationary/transient data. In response to this need, this paper proposes a new nonstationary system identification scheme which first utilizes the wavelet transform (WT) to uncover the time-varying features of nonstationary data. Then the transformed singular value decomposition (TSVD) is introduced in tandem to automate the identification of analysis regions in the time-frequency domain. Subsequently, Laplace wavelet filtering is adopted to extract impulse-type signals from the WT coefficients in the identified analysis regions, thus enabling a reliable damping estimation from transient nonstationary data. Finally, the frequency and damping ratio are reliably identified from the extracted impulse-type signals by the wavelet modulus decay (WMD) or from the parameters of the Laplace wavelet, whereas mode shapes can be easily identified using SVD. Thanks to the automatic identification of the analysis regions by the TSVD, the proposed scheme can be readily used to conduct online nonstationary system identification from a set of streaming signals, which can be extremely advantageous for a quick structural condition assessment under extreme events. The efficacy of the proposed scheme is first evaluated using simulated nonstationary data with and without noise and compared with the existing approaches in the literature. Then, its ability in handling closely spaced modes is compared with the second order blind identification (SOBI) method. Finally, the performance of the proposed scheme for full-scale nonstationary data is investigated and compared with other methods in the literature.