Identifying the Modal Parameters of a Structure from Ambient Vibration Data via the Stationary Wavelet Packet

Abstract

Ambient vibration tests are conducted widely to estimate the modal parameters of a structure. The work proposes an efficient wavelet‐based approach to determine the modal parameters of a structure from its ambient vibration responses. The proposed approach integrates the time series autoregressive (AR) model with the stationary wavelet packet transform. In addition to providing a richer decomposition and allowing for an improved time–frequency localization of signals over that of the discrete wavelet transform, the stationary wavelet packet transform also has significantly higher computational efficiency than the wavelet packet transform in terms of decomposing time‐shifted signals because the former has a time‐invariance property. The correlation matrices needed in determining the coefficient matrices in an AR model are established in subspaces expanded by stationary wavelet packets. The formulation for estimating the correlation matrices is shown for the first time. Because different subspaces contain signals with different frequency subbands, the fine filtering property enhances the ability of the proposed approach to identify not only the modes with strong modal interference, but also many modes from the responses of very few measured degrees of freedom. The proposed approach is validated by processing the numerically simulated responses of a seven‐floor shear building, which has closely spaced modes, with considering the effects of noise and incomplete measurements. Furthermore, the present approach is employed to process the velocity responses of an eight‐storey steel frame subjected to white noise input in a shaking table test and ambient vibration responses of a cable‐stayed bridge.

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“…It is observed that these methodologies present similar results to the estimated by FEA model, which indicates that they can be considered as accurate; however, it is important to mention that the methodology proposed by Su et al [53] requires calibration for each structure analyzed, limiting an automatic estimation of the parameters. On the other hand, it is also seen a slightly difference between the estimated DR values using the methodologies proposed by Su et al [53], Perez-Ramirez et al [11], and the values obtained with the proposal. It should be noticed that for this case, there are no reference values for the DR; thus, the comparison is performed in a qualitative way, that is, how similar are the values obtained with the different methodologies.…”

“…From these works, it is evident that the ones that use multi-paradigm approaches lead to better estimations of the modal parameters. Further, it is worth noting that Su et al [53] mentioned that for obtaining an accurate value, it should be present a maximum error of 2% and 20% for natural frequency and damping ratio, respectively. In this regard, the proposed methodology contributes to demonstrate the abovementioned statement, as the obtained results can be considered as accurate.…”

“…The base of the building was subjected to white noise excitation in the long-span direction. This structure is located in the National Center for Research on Earthquake Engineering, Taiwan, and is also used by Su et al [53]. The responses were measured using eight velocity sensors distributed on the eight stories and located at the center of each floor.…”

“…Table 3 presents the values of estimated natural frequencies and damping ratios values using the proposal and FEA. Further, the estimated modal parameters of eight-story steel frame using the methodologies proposed by Su et al [53] and Perez-Ramirez et al [11] are also presented. It is observed that these methodologies present similar results to the estimated by FEA model, which indicates that they can be considered as accurate; however, it is important to mention that the methodology proposed by Su et al [53] requires calibration for each structure analyzed, limiting an automatic estimation of the parameters.…”

“…Further, the estimated modal parameters of eight-story steel frame using the methodologies proposed by Su et al [53] and Perez-Ramirez et al [11] are also presented. It is observed that these methodologies present similar results to the estimated by FEA model, which indicates that they can be considered as accurate; however, it is important to mention that the methodology proposed by Su et al [53] requires calibration for each structure analyzed, limiting an automatic estimation of the parameters. On the other hand, it is also seen a slightly difference between the estimated DR values using the methodologies proposed by Su et al [53], Perez-Ramirez et al [11], and the values obtained with the proposal.…”