Identification of Instantaneous Modal Parameter of Time‐Varying Systems via a Wavelet‐Based Approach and Its Application

Abstract

This work presents an efficient approach using time‐varying autoregressive with exogenous input (TVARX) model and a substructure technique to identify the instantaneous modal parameters of a linear time‐varying structure and its substructures. The identified instantaneous natural frequencies can be used to identify earthquake damage to a building, including the specific floors that are damaged. An appropriate TVARX model of the dynamic responses of a structure or substructure is established using a basis function expansion and regression approach combined with continuous wavelet transform. The effectiveness of the proposed approach is validated using numerically simulated earthquake responses of a five‐storey shear building with time‐varying stiffness and damping coefficients. In terms of accuracy in determining the instantaneous modal parameters of a structure from noisy responses, the proposed approach is superior to typical basis function expansion and regression approach. The proposed method is further applied to process the dynamic responses of an eight‐storey steel frame in shaking table tests to identify its instantaneous modal parameters and to locate the storeys whose columns yielded under a strong base excitation.

A Sparse Multiwavelet-Based Generalized Laguerre–Volterra Model for Identifying Time-Varying Neural Dynamics from Spiking Activities

“…Combine the output observation y and the full model candidates V 0,m j,k (t) , V r n ,m l,j,k (t) , the maximum likelihood estimatorα mle can be estimated by using a generalized linear model fitting method. The output spike probability g (θ (t)) can further be obtained using Equation (16). Assume G (t) =g (θ (t)) , t = 1, 2, · · · , T, to be a vector of the measured outputs with T time instants.…”

3D displacement measurement model for health monitoring of structures using a motion capture system

“…Accurate assessment of safety, however, is difficult, due to the analytical limitation and the fact that numerous assumptions must be made in the assessment process, considering the inherent uncertainties of large and complex civil structures. In this respect, in recent years many researchers have developed parametric system identification methods to estimate the structural parameters or non-parametric methods to estimate the structural response directly to be used in the analysis of the behavior of complex structures and determine their state of damage (Jiang and Adeli 2005;Adeli and Jiang 2006;Schoefs et al 2011;Marano et al 2011;Jafarkhani and Masri 2011;Sirca and Adeli 2012;Kang et al 2012;Hazra 2012;Yan and Ren 2012;Cho et al 2012;Fuggini et al 2013;Su et al, 2014). In addition, serviceability assessments using acceleration data require analysis of frequency and amplitude after measurements are completed making it difficult for the engineer to make a decision intuitively at the time of measurement.…”

A new music-empirical wavelet transform methodology for time–frequency analysis of noisy nonlinear and non-stationary signals

“…It does not decompose a time signal according to its contained information and consequently cannot estimate the instantaneous frequencies effectively. To introduce adaptability, the wavelet packet transform [24,34,41] was introduced, but, it is still based on the use of prescribed basis limiting its adaptability.…”