Modal and Model Updating of Dynamical Systems

The problem of parametric identification for mathematical models using input-output or output-only dynamic measurements has received much attention over the years. One important special case is modal identification, in which the parameters for identification are the small-amplitude modal frequencies, damping ratios, mode shapes and modal participation factors of the lower modes of the dynamical system. In other words, the model class in modal identification is the class of linear modal models. Many time-domain and frequency-domain methodologies have been formulated for input excitation and output response measurements [24,48,75,81,187], 

Much attention has also been devoted to modal identification without measuring the input time history. In particular, a lot of effort has been dedicated to the case of free vibration (or impulse response) and to the case of ambient vibration. In the former case, often time-domain methods based on auto-regressive moving average (ARMA) models are employed, using least squares as the core ingredient in their formulations. However, it was found that the least-squares method yields biased estimates [76], A number of methods have been developed to eliminate this bias, including the instrumental matrix with delayed observations method [76], the correlation fit method [275], the double least-squares method [114,202] and the total least-squares method [92]. A detailed comparison of these methods can be found in Cooper [61], 

Another important practical category is the ambient vibration survey (AVS). It has attracted much interest because it offers a means of obtaining dynamic data in an economical and efficient manner, without requiring the setup of special dynamic experiments (e.g., actuators) which are usually costly, time consuming, and often obtrusive. In AVS, the naturally occurring vibration 

Bayesian Methods for Structural Dynamics and Civil Engineering Ka-Veng Yuen 2010 John Wiley Sons (Asia) Pte Ltd 

Bayesian Methods for Structural Dynamics and Civil Engineering 

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