TY - JOUR

T1 - Application of Cauchy wavelet transformation to identify time-variant modal parameters of structures

AU - Huang, Chiung-Shiann

AU - Liu, C. Y.

AU - Su, W. C.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - This work proposes a procedure for accurately identifying instantaneous modal parameters of a linear time-varying system using a time-varying autoregressive with exogenous input (TVARX) model with the continuous Cauchy wavelet transform (CCWT). An appropriate TVARX model is established using the velocity and displacement responses of the system under consideration. The time-varying coefficients of the TVARX are expanded as piecewise polynomial functions. CCWTs with various scale parameters are then applied to the TVARX model to evaluate the instantaneous modal parameters of different modes. The CCWTs of the velocity and displacement responses are analytically obtained from the CCWT of the measured acceleration responses. The effectiveness and accuracy of the proposed procedure are validated by numerical simulations of single and multiple degrees of freedom systems that have periodically varying and sharply varying stiffness and damping coefficients. The effects of noise, the Cauchy wavelet function and the order of the polynomial on the evaluation of the modal parameters are explored in processing the numerically simulated acceleration responses of systems with a single degree of freedom subjected to base excitation. Finally, the proposed procedure is adopted to determine the modal parameters of a five-story symmetric steel frame from its measured acceleration responses in a shaking table test. The measured strains reveal the yielding of columns in the first story. The variations of the identified instantaneous natural frequencies and modal damping ratios with time are consistent with the physical phenomena that are observed from the measured strains and base excitation acceleration.

AB - This work proposes a procedure for accurately identifying instantaneous modal parameters of a linear time-varying system using a time-varying autoregressive with exogenous input (TVARX) model with the continuous Cauchy wavelet transform (CCWT). An appropriate TVARX model is established using the velocity and displacement responses of the system under consideration. The time-varying coefficients of the TVARX are expanded as piecewise polynomial functions. CCWTs with various scale parameters are then applied to the TVARX model to evaluate the instantaneous modal parameters of different modes. The CCWTs of the velocity and displacement responses are analytically obtained from the CCWT of the measured acceleration responses. The effectiveness and accuracy of the proposed procedure are validated by numerical simulations of single and multiple degrees of freedom systems that have periodically varying and sharply varying stiffness and damping coefficients. The effects of noise, the Cauchy wavelet function and the order of the polynomial on the evaluation of the modal parameters are explored in processing the numerically simulated acceleration responses of systems with a single degree of freedom subjected to base excitation. Finally, the proposed procedure is adopted to determine the modal parameters of a five-story symmetric steel frame from its measured acceleration responses in a shaking table test. The measured strains reveal the yielding of columns in the first story. The variations of the identified instantaneous natural frequencies and modal damping ratios with time are consistent with the physical phenomena that are observed from the measured strains and base excitation acceleration.

KW - Cauchy wavelet transform

KW - Instantaneous modal parameters

KW - Piecewise polynomial basis functions

KW - System identification

KW - TVARX

UR - http://www.scopus.com/inward/record.url?scp=84971350805&partnerID=8YFLogxK

U2 - 10.1016/j.ymssp.2016.05.007

DO - 10.1016/j.ymssp.2016.05.007

M3 - Article

AN - SCOPUS:84971350805

SN - 0888-3270

VL - 80

SP - 302

EP - 323

JO - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

ER -