A harmonic piecewise linearisation-wavelet transforms method for identification of non-linear vibration “black box” systems: Application in wind-induced vibration of a high-rise building

In this work, a harmonic piecewise linearisation-wavelet transform method is proposed for identification of some kind of non-linear/linear vibration “black box” systems. The proposed method firstly looks at the non-linear vibration system as piecewise linear, and then identifies the time-varying damping ratio and frequency by the segmented amplitude log analysis and wavelet transform method, secondly it obtains the relationship between damping and frequency to time or amplitude by least squares method, and finally establishes its non-linear oscillation governing equation. The proposed harmonic piecewise linearisation-wavelet transform method is verified by two numerical examples and then is used to identify the wind-induced cross-wind non-linear/linear aerodynamic parameters of Shanghai's World Financial Centre by aeroelastic model vibration measurement wind tunnel test. The results show that the proposed harmonic piecewise linearisation-wavelet transform method is feasible for identification of some kind of non-linear/linear “black box” vibration systems, including in a flexible high-rise building subjected to strong wind: in this case, the non-linear/linear aeroelasticity effect cannot be ignored, which would generate additional weak non-linear damping and negative aerodynamic stiffness.