Accounting for Modeling Errors and Inherent Structural Variability through a Hierarchical Bayesian Model Updating Approach: An Overview

Abstract

Mechanics-based dynamic models are commonly used in the design and performance assessment of structural systems, and their accuracy can be improved by integrating models with measured data. This paper provides an overview of hierarchical Bayesian model updating which has been recently developed for probabilistic integration of models with measured data, while accounting for different sources of uncertainties and modeling errors. The proposed hierarchical Bayesian framework allows one to explicitly account for pertinent sources of variability such as ambient temperatures and/or excitation amplitudes, as well as modeling errors, and therefore yields more realistic predictions. The paper reports observations from applications of hierarchical approach to three full-scale civil structural systems, namely (1) a footbridge, (2) a 10-story reinforced concrete (RC) building, and (3) a damaged 2-story RC building. The first application highlights the capability of accounting for temperature effects within the hierarchical framework, while the second application underlines the effects of considering bias for prediction error. Finally, the third application considers the effects of excitation amplitude on structural response. The findings underline the importance and capabilities of the hierarchical Bayesian framework for structural identification. Discussions of its advantages and performance over classical deterministic and Bayesian model updating methods are provided.

Hierarchical Bayesian modeling of contrast sensitivity functions in a within-subject design

“…It explicitly quantifies the covariance of the hyperparameters and parameters ( Daniels & Kass, 1999 ; Klotzke & Fox, 2019 ; Thall, Wathen, Bekele, Champlin, Baker, & Benjamin, 2003 ; Wang, Lin, & Nelson, 2020 ; Yang, Zhu, Choi, & Cox, 2016 ). By sharing information within and across levels via conditional dependencies, it reduces the variance of the test-level estimates through (1) decomposition of variabilities from different sources (test, subject, and population) with parameters and hyperparameters ( Song, Behmanesh, Moaveni, & Papadimitriou, 2020 ), and (2) shrinkage of the estimated parameters at the lower levels toward the mean of the higher levels when there is not sufficient data at the lower level ( Kruschke, 2015 ; Rouder & Lu, 2005 ; Rouder, Sun, Speckman, Lu, & Zhou, 2003 ).…”

Methodology Maps for Model-Based Sensor-Data Interpretation to Support Civil-Infrastructure Management

“…Assuming these parameters to be the same at all locations may not be accurate. Due to these challenges, solutions obtained with BMU, while possibly suitable for damage assessment applications, are not suitable to support extrapolation predictions in civilengineering contexts (Song et al, 2020).…”

“…These include parameterization of the model error terms (Kennedy and O'Hagan 2001) as explained in Bayesian Model Updating With Parameterized Model-Error. Users have to be careful while employing these advanced methods as they may provide more precise solutions than EDMF Pasquier and Smith 2015), while also being prone to unidentifiability challenges (Prajapat and Ray-Chaudhuri 2016;Song et al, 2020) due to requirements of estimating many parameters relative to information available from measurements.…”

Nonlinear model updating through a hierarchical Bayesian modeling framework

“…However, the conventional Bayesian inference framework cannot properly account for an underlying variability in model parameters and uncertainties arising from multiple data sets under different excitations, operational, environmental and experimental conditions. The variability in the model parameters can originate from the presence of model and experimental error [40]. The uncertainty of the model parameters due to these variabilities is irreducible, in contrast to the identification uncertainty which is usually inversely proportional to the amount of data considered in a data set.…”