Bayesian Updating: Reducing Epistemic Uncertainty in Hysteretic Degradation Behavior of Steel Tubular Structures

This paper proposes a probabilistic framework for updating the governing parameters in the hysteretic constitutive model for tubular steel with strength degradation. The hysteretic constitutive model is formulated to track the strength degradation due to the local buckling of square hollow steel beam-columns imposed by cyclic loadings with large elastoplastic deformation. Despite various hysteretic laws that have been proposed to model the steel tubular strength degradation, limitations for determining parameter values remain in numerical analysis. The parameters are generally obfuscated by the inevitable epistemic uncertainties from material and geometric properties. The updating process of the material parameters is performed within the Bayesian framework employing the Markov chain Monte Carlo algorithm. The epistemic uncertainty involved in the computational procedure is initially represented as predefined intervals of the uncertain parameters. The proposed Markov chain Monte Carlo (MCMC) algorithm can generate samples from the posterior distributions of the parameters according to the experimental results. The epistemic uncertainty is hence significantly reduced by the Bayesian updating process such that the updated model is feasible to predict the degradation behavior of square hollow steel beam-columns subjected to cyclic loadings. The benchmark example indicates that the proposed framework can find the optimal path for updating key parameter values to accurately assess the condition of steel tubular structures in terms of the degradation behavior.