Calculation of Posterior Probabilities for Bayesian Model Class Assessment and Averaging from Posterior Samples Based on Dynamic System Data

Abstract

In recent years, Bayesian model updating techniques based on dynamic data have been applied in system identification and structural health monitoring. Because of modeling uncertainty, a set of competing candidate model classes may be available to represent a system and it is then desirable to assess the plausibility of each model class based on system data. Bayesian model class assessment may then be used, which is based on the posterior probability of the different candidates for representing the system. If more than one model class has significant posterior probability, then Bayesian model class averaging provides a coherent mechanism to incorporate all of these model classes in making probabilistic predictions for the system response. This Bayesian model assessment and averaging requires calculation of the evidence for each model class based on the system data, which requires the evaluation of a multi-dimensional integral involving the product of the likelihood and prior defined by the model class. In this article, a general method for calculating the evidence is proposed based on using posterior samples from any Markov Chain Monte Carlo algorithm. The effectiveness of the proposed method is illustrated by Bayesian model updating and assessment using simulated earthquake data from a ten-story nonclassically damped building responding linearly and a four-story building responding inelastically.

Probabilistic Earthquake–Tsunami Multi-Hazard Analysis: Application to the Tohoku Region, Japan

“…The work can be extended using a Bayesian robust methodology (Cheung and Beck, 2010) to make more reliable estimations of earthquake-tsunami hazards. The proposed method can be further integrated into an operational tool for real-time earthquake-tsunami forecast (Tsushima et al, 2011) using data from offshore buoy and ocean-bottom pressure gauges.…”

Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances

“…The Bayesian method then allows a posterior probability distribution to be constructed from the optimal prior probability distribution and the experimental data. Many works have been published in the literature (see for instance textbooks on the Bayesian method such as [59,60,61,62] and papers devoted to the use of the Bayesian method in the context of uncertain mechanical and dynamical systems such as [12,128,129,130,131,132,133]. We will use such a Bayesian approach in Sections 4.6 and 6.…”

Structural identification with systematic errors and unknown uncertainty dependencies

“…In [11,12,15,19,20,24,29,32,39,[42][43][44]. In most applications to civil structures, authors have assumed that modelling uncertainties can be represented by independent Gaussian noise centered on zero.…”