Fast Bayesian modal identification of structures using known single-input forced vibration data

Abstract

Modal identification aims to identify the modal parameters of constructed structures based on vibration data. Forced vibration tests allow one to obtain data with a higher signal-to-noise ratio compared with 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. This paper develops a Bayesian approach that properly accounts for uncertainty in accordance with probability logic for modal identification using forced vibration data. The posterior probability density function of the modal parameters to be identified given the data is derived based on the assumed model and the collected data. An efficient algorithm is developed that allows practical implementation in the case of a single shaker. It is applicable for both separated and closely-spaced modes even with a large number of measured degrees of freedom. The proposed method is verified and investigated using synthetic and field test data.

Structural health monitoring of a 250‐m super‐tall building and operational modal analysis using the fast Bayesian FFT method

“…Bayesian methods provide an important means to determine the most probable values of parameters and quantify the associated posterior uncertainty . They have been applied to many kinds of structures, for example, buildings, bridges, and towers, and extended to analyze free and forced vibration data.…”

Vibration properties monitoring and uncertainty quantification of precast and cast‐in‐situ shear wall buildings using a Bayesian framework

“…Based on this method, the operational modal analysis (OMA) of many different kinds of structures has been conducted . Based on the framework, Bayesian methods for forced and free modal identification have also been developed recently.…”

Modal identification of structures from input/output data using the expectation-maximization algorithm and uncertainty quantification by mean of the bootstrap

“…In any case, it is possible to include artificial (measured) inputs in addition to the operational and/or ambient loads: using impact hammers and drop weight systems, electrodynamic shakers,() and so forth. This new technique has been called operational modal analysis with exogenous inputs or OMAX and combined experimental‐operational modal analysis .…”

“…This fact requires the development of sophisticated system identification methods, such as the reference‐based combined deterministic‐stochastic subspace identification algorithm, what extends the well‐known subspace methods developed in the OMA framework. Another interesting approach is to use Bayesian modal identification, what allows the computation of the modal parameters uncertainty. In this paper, the use of maximum likelihood estimation of the state space model taking into account both inputs and outputs is investigated.…”

“…In this sense, Bayesian modal identification is a natural choice to estimate modal parameters and associated uncertainties. As mentioned before, Au and Ni present a (frequency domain) Bayesian approach to modal identification. However, in that work, only one known input was used, whereas the method presented in this work can be applied to more than one known input; besides, because it is a frequency domain method, modes with similar natural frequencies are difficult to deal with.…”