Wavelet Transforms for System Identification in Civil Engineering

Abstract

The time-frequency character of wavelet transforms allows adaptation of both traditional time and frequency domain system identification approaches to examine nonlinear and non-stationary data. Although challenges did not surface in prior applications concerned with mechanical systems, which are characterized by higher frequency and broader-band signals, the transition to the time-frequency domain for the analysis of civil engineering structures highlighted the need to understand more fully various processing concerns, particularly for the popular Morlet wavelet. In particular, as these systems may possess longer period motions and thus require finer frequency resolutions, the particular impacts of end effects become increasingly apparent. This study discusses these considerations in the context of the wavelet's multiresolution character and includes guidelines for selection of wavelet central frequencies, highlights their role in complete modal separation, and quantifies their contributions to end-effect errors, which may be minimized through a simple padding scheme.

Wind-induced vibrations of buildings: role of transient events

“…Stationary analysis tools such as the Fourier power spectral density cannot provide an adequate representation of these transient responses, requiring an analysis that retains temporal information, such as the Morlet wavelet analysis framework introduced by Kijewski and Kareem (2003). Wavelet transforms have been shown by the co-author and her collaborators to offer interesting perspectives on non-linear systems and tall buildings with unique dynamic characteristics , thanks to their ability to detect subtle variations in frequency over time.…”

“…As the wavelet coefficients will take on their maximum values at the dominant frequency components at each instant in time, they provide clear ridges in the time-frequency plane that can be isolated and extracted to remove any redundant information in the scalogram (Kijewski and Kareem, 2003). This is effectively a tight bandpass filter around each mode.…”

“…This is effectively a tight bandpass filter around each mode. Through the use of analytic wavelets like the Morlet, the resulting wavelet coefficients along this ridge provide an important complex-valued representation: the analytic signal z(t ), which will later prove valuable for system identification (Kijewski and Kareem, 2003). Similarly, wavelet coefficients can be isolated at particular time instants by taking a slice of the scalogram, which produces an instantaneous power spectrum that will prove valuable for unlocking the contributing modes to various events within the responses.…”

Numerical simulation of wind effects: A probabilistic perspective

“…Such tracking of time-varying frequency content is typically accomplished by monitoring the instantaneous frequency of the signal and extracting ridges from wavelet scalograms to form the Wavelet Instantaneous Frequency Spectra discussed in Kareem and Kijewski (2002) and Kijewski and Kareem (2003). The complex coefficients associated with these ridges can be used directly in a traditional system identification approach based on analytic signal theory to identify the instantaneous frequency, and in the case of free vibration decay or random decrement signatures, damping.…”

Accurate structural identification for layered composite structures, through a wave and finite element scheme

“…Over the past decades, different system identification methods in the time domain [9,10,11], frequency domain [12,13] and time-frequency domain [14,15] have been proposed. System identification has been applied extensively in the field of structural dynamics and it has been proven to be useful in the analysis of the dynamic behavior of the structure.…”