Nonlinear model updating through a hierarchical Bayesian modeling framework

Multivariate joint probability distributions for seismic design parameters across multiple building codes

“…With the intention of exploring an appropriate domain of the parameters covering all observed values, the multivariate normal (MVN) distributions, and the coefficient of variation for each probability density function (i.e., the ratio between standard deviation, 𝜎, and the mean of a given probability density function, 𝜇), are selected so that the analysis is wider than 3 study cases. The joint probability density function (PDF) can be utilized in different probabilistic-based analysis and parameter-dependent analyses, such as bayesian modeling, rock mechanics, ground motion intensity measures, among others [5,7,9,21]. In this section, MVN distribution fits are generated over different sets of measurements to account for the variability in parameter values across data-sets, and the accuracy of the predictions made with each MVN case is assessed.…”

Hierarchical Bayesian learning framework for multi-level modeling using multi-level data

“…. Due to model and measurement errors and variabilities in the experimental testing and/or environmental/operational conditions, the parameter estimates are expected to vary from dataset to dataset [29,30]. In the Type B testing, the subsystem SS1 is considered as a member of a population of subsystems manufactured to be identical by an assembling process that involves the assemblance of components C1, C2 and C3, where C3 is a member of a population of identically manufactured components.…”

“…(2.2) Draw samples from the posterior distribution of unobserved QoI using (30), and use the samples to estimate the statistical properties, such as the mean, standard deviation and quantiles For observed QoI:…”

Probabilistic model updating of steel frame structures using strain and acceleration measurements: A multitask learning framework

“…As a more effective countermeasure for ill-posed and ill-conditioned inverse problems, the hierarchical Bayesian model (HBM) has received increasing interest in the context of model updating and structural health monitoring (SHM) [10][11][12][13][14][15][16][17]. Behmanesh et al [10] presented an HBM framework that flexibly quantified the inherent variability of structural parameters because of environmental variations (such as changing temperature) by setting hierarchical prior distributions over these parameters.…”

“…Behmanesh et al [10] presented an HBM framework that flexibly quantified the inherent variability of structural parameters because of environmental variations (such as changing temperature) by setting hierarchical prior distributions over these parameters. Similar formulations were made for quantifying the variability attributed to the excitation amplitude [11], time-domain model updating [12], and hysteretic model updating [13]. Sparse Bayesian learning (SBL) for model updating purposes was formulated based on the HBM [14][15][16][17], where the sparsity of damage locations in a structure was assumed in the absence of structural collapse.…”