Operational modal identification using variational Bayes

Abstract

Operational modal analysis is the primary tool for modal parameter identification in civil engineering. Bayesian statistics offers an ideal framework for analyzing uncertainties associated with the identified modal parameters. However, the exact Bayesian formulation is usually intractable due to the high computational demand in obtaining the posterior distributions of modal parameters. In this paper, the variational Bayes method is employed to provide an approximate solution. Unlike the Laplace approximation and Monte Carlo sampling, the variational Bayes approach provides a gradient-free algorithm to analytically approximate the posterior distributions. Working with the state-space representation of a dynamical system, the variational Bayes approach for identification of modal parameters is derived by ignoring statistical correlation between latent variables and the model parameters. In this approach, the joint distribution of the state-transition and observation matrices as well as the joint distribution of the process noise and measurement error are firstly calculated analytically using conjugate priors. The distribution of modal parameters is extracted from these obtained joint distributions using a first-order Taylor series expansion. A robust implementation of the method is discussed by using square-root filtering and Cholesky decomposition. The proposed approach is illustrated by its application to an example mass-spring system and the One Rincon Hill Tower in San Francisco.

State-of-the-art review on Bayesian inference in structural system identification and damage assessment

“…Other recent popular techniques for Bayesian approximations are Approximate Bayesian Computation (ABC) methods (Chiachio et al, 2014; Marin et al, 2012; Vakilzadeh et al, 2017) and Variational Bayesian methods (Bishop, 2006; Fujimoto et al, 2011; Li and Der Kiureghian, 2017). ABC methods are applicable even when an analytical formula for the likelihood function ( p ( D | w , M ) in equation (1)) is elusive or it is computationally costly to evaluate it in Bayesian inference.…”

A Gibbs sampling algorithm for structural modal identification under seismic excitation

“…However, if the damping matrix C d is in classical form, i.e., satisfying K M −1 C d = C d M −1 K , the mode shape can be represented in real form without any approximation because all elements are either in phase or 180° out of phase. In this paper, we do not require classical damping so that the modal frequencies and damping ratios in Equation are only nominal values and mode shapes are generally complex, but we apply a postprocessing strategy to obtain approximated real mode shapes in displaying the identification results.…”

“…For the sake of comparability and reduction of computational burden, both sets of raw data are resampled down to 25 Hz. According to Li and Der Kiureghian, modes with frequencies below 5 Hz are of interest in this study. Applying the Gibbs sampling algorithm, the convergence process of the seismic responses is illustrated in Figure , from which 2400 stationary samples (= 4 chains × 600 samples/chain) are obtained based on the Gelman‐Rubin measure .…”

Real‐Time Evaluation of Compaction Quality by Using Artificial Neural Networks

“…Further analysis by Mazari et al [11] shows that roller type, machine operation setting variation, and instability of the machine in practicing operation commonly affect the accuracy of ICMVs. Furthermore, some researchers [12][13][14][15][16] use operational modal analysis (OMA) for the structural health monitoring of engineering. Different from the experimental modal analysis methods, OMA uses the output-only response to identify the structure properties; thus, the input excitation measures can be avoided.…”