Bayesian modal identification of civil structures with known input

Abstract

Modal identification aims to identify the modal parameters of constructed structures based on the vibration data collected. The modal parameters of interest are mainly the natural frequencies, damping ratios and mode shapes. Forced vibration tests allow one to obtain data with a higher signal-to-noise ratio compared to free or ambient vibration tests. Modal identification techniques for forced vibration data exist but they do not provide a rigorous quantification of the remaining uncertainties of the modal parameters, which is becoming important in modern structural health monitoring and uncertainty propagation. In this regard, this thesis focuses on modal identification using forced vibration data following a Bayesian approach that properly accounts for uncertainty in accordance with probability logic. The first part of the thesis presents a fast Bayesian frequency-domain method for modal identification with a single shaker input and multiple output measured acceleration response. In the proposed method, only the data in a selected frequency band dominated by the contributing modes of interest is used. In this way, the modeling error caused by other frequency bands can be effectively eliminated. Assuming no prior information, the posterior probability density function (PDF) of the identified modal parameters given the data is proportional to the likelihood function, which can be derived based on the assumed model and the collected data. The most probable values (MPVs) are obtained by maximizing the posterior PDF, or by equivalently minimizing the negative log-likelihood function (NLLF). However, when directly performing the optimization, there are several serious computational difficulties which may hinder practical application. For the purpose of developing an efficient computational method, the NLLF is simplified by ignoring the influence of ambient vibration response. The partial analytical solution of other modal parameters can all be expressed by the natural frequency and damping ratio. A fast iterative procedure is developed to allow the proposed method to be applied in the field effectively and accurately. The posterior covariance matrix can also be derived analytically to quantify the uncertainty of the identified MPVs without resorting finite difference. In the second part, the proposed theory is verified using synthetic data where the ‘exact’ modal properties of the structure that generate the data are known. After the verification, the proposed method is applied to field data of a full-scale pedestrian bridge and a coupled floor slab system. Parametric studies regarding the effect of test configurations on the posterior uncertainties of modal parameters are performed, including the type of shaker excitation, duration of the excitation, effect of ambient vibration, effect of measurement noise, and comparison between sample coefficient of variation (c.o.v.) and posterior c.o.v.. Finally, the proposed method is compared with one existing method.

Date of Award	3 Oct 2012
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Siu Kui AU (Supervisor)