System Identification for Time-Varying Systems under Non-White Excitations

Abstract

Accurate identification of structural properties such as natural frequency and damping under extreme wind conditions is critical for assessing the structural performances. Full-scale monitoring has witnessed that dynamic properties of structures may change over time under extreme winds. System identification (SI) is non-trivial in this case. While wavelet and short time Fourier transforms have been used in tracking time-varying frequencies, they have seldom been used to identify the time-varying damping ratio. This is because the short window (required to capture the temporal information) will amplify the bandwidth significantly and lead to considerably overestimated damping ratios. To address this challenge, this paper proposes a novel non-stationary SI approach to identify time-varying systems under general non-white excitations by extending an earlier approach proposed by the authors. To solve this problem, this study innovatively adapted theoretical frequency response functions (FRF) of systems for marginal spectra of the wavelet transform by adding short window effects explicitly. In this way, both the natural frequency and damping ratio at each time instant can be identified accurately. However, the initially proposed method assumed the excitation to be white in the vicinity of the structural natural frequencies. This assumption might not be strictly valid in some cases. For example, for wind-excited structures, the spectrum of wind force is a function of frequency derived from the turbulent wind spec-trum and aerodynamic admittance function. To better handle these non-white excitations, the method proposed in this paper directly models the non-white spectrum of excitation in the frequency domain. Then both the parameters of the force spectrum and the system properties are identified using the out-put data. The uncertainties of the SI results are evaluated. The performance of the proposed method is demonstrated by numerical examples considering structures under extreme wind conditions.