TY - JOUR

T1 - Nonparametric Bayesian stochastic model updating with hybrid uncertainties

AU - Kitahara, Masaru

AU - Bi, Sifeng

AU - Broggi, Matteo

AU - Beer, Michael

PY - 2022/1/15

Y1 - 2022/1/15

N2 - This work proposes a novel methodology to fulfil the challenging expectation in stochastic model updating to calibrate the probabilistic distributions of parameters without any assumption about the distribution formats. To achieve this task, an approximate Bayesian computation model updating framework is developed by employing staircase random variables and the Bhattacharyya distance. In this framework, parameters with aleatory and epistemic uncertainties are described by staircase random variables. The discrepancy between model predictions and observations is then quantified by the Bhattacharyya distance-based approximate likelihood. In addition, a Bayesian updating using the Euclidian distance is performed as preconditioner to avoid non-unique solutions. The performance of the proposed procedure is demonstrated with two exemplary applications, a simulated shear building model example and a challenging benchmark problem for uncertainty treatment. These examples demonstrate feasibility of the combined application of staircase random variables and the Bhattacharyya distance in stochastic model updating and uncertainty characterization.

AB - This work proposes a novel methodology to fulfil the challenging expectation in stochastic model updating to calibrate the probabilistic distributions of parameters without any assumption about the distribution formats. To achieve this task, an approximate Bayesian computation model updating framework is developed by employing staircase random variables and the Bhattacharyya distance. In this framework, parameters with aleatory and epistemic uncertainties are described by staircase random variables. The discrepancy between model predictions and observations is then quantified by the Bhattacharyya distance-based approximate likelihood. In addition, a Bayesian updating using the Euclidian distance is performed as preconditioner to avoid non-unique solutions. The performance of the proposed procedure is demonstrated with two exemplary applications, a simulated shear building model example and a challenging benchmark problem for uncertainty treatment. These examples demonstrate feasibility of the combined application of staircase random variables and the Bhattacharyya distance in stochastic model updating and uncertainty characterization.

KW - Approximate Bayesian computation

KW - Bhattacharyya distance

KW - Nonparametric probability-box

KW - Staircase random variable

KW - Stochastic model updating

UR - http://www.scopus.com/inward/record.url?scp=85109901390&partnerID=8YFLogxK

U2 - 10.1016/j.ymssp.2021.108195

DO - 10.1016/j.ymssp.2021.108195

M3 - Article

AN - SCOPUS:85109901390

VL - 163

JO - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

SN - 0888-3270

M1 - 108195

ER -