Bayesian Updating by Utilization of Bayesian Optimization for Estimation of VIV Load Parameters

The purpose of the present paper is to summarize the findings from Bayesian updating methods applied to VIV cross-flow response. The Bayesian updating approach is formulated in terms of a prior statistical model for the quantities of interest (i.e. two parameters entering the VIV load model in the time domain for the present case), and subsequently this statistical model is modified based on a set of available observations. The statistical properties of the observation for a given set of values of the quantities of interest are represented by the so-called likelihood function. By combining the prior model with the likelihood function, the resulting posterior statistical model is obtained. An experiment with a rigid pendulum subjected to pure cross-flow VIV is analysed. The cross-flow (lift) coefficient and the nondimensional center frequency of the lock-in region are represented as random variables. The following parameter studies are performed: (i) Application of different types of likelihood functions corresponding to different inherent “measurement noise levels” (ii) Introducing the exponent of the Posterior pdf as an objective function rather than the pdf itself (iii) Application of Bayesian optimization (by utilization of Gaussian Process Regression/Kriging) for identification of the extremal point of the objective function. A main objective is to clarify the relationship between the applied Prior model/likelihood function and the so-called Bayesian optimization scheme in order to identify the most likely values of the input parameters for a given set of measured data..