Investigations of different likelihood functions for the use in Bayesian model updating in structural applications

Abstract

Model updating is a popular tool for damage localisation and quantification for structural applications like buildings, infrastructure and wind turbines. Taking into account the prevailing uncertainty inter alia due to measurements is very important for a more reliable result. A frequently used method to conduct model updating and simultaneously taking into account measurement uncertainty is the Transitional Markov Chain Monte Carlo (TMCMC) method. Model updating in general relies on a shift of damage sensitive features, mostly natural frequencies. This work shows, that the state-of-the-art method of TMCMC is leading to inaccurate results in structural application because of formulations in the likelihood function. In the state-of-the-art method, natural frequencies which are measured more certainly are more heavily weighted. Even though this approach is meaningful in general, for the application in structural application, this is leading to inaccurate results. This work will present the issues with the state-of-the-art method and presents an option to solve this by a new formulation, which is weighting every natural frequency equally. The two methods will be applied and compared on a laboratory steel beam with reversible damage mechanisms. This allows comparing the results on a variety of different damage scenarios. The first four natural frequencies related to pure vertical bending mode shapes are identified using the Bayesian operational model analysis (BAYOMA). BAYOMA is able to quantify the uncertainty in the natural frequencies.