Adaptive approximate Bayesian computation by subset simulation for structural model calibration

Abstract

This paper provides a new approximate Bayesian computation (ABC) algorithm with reduced hyper-parameter scaling and its application to nonlinear structural model calibration problems. The algorithm initially takes the ABC-SubSim algorithm structure and sequentially estimates the algorithm hyper-parameter by autonomous adaptation following a Markov chain approach, thus avoiding the error associated to modeler's choice for these hyper-parameters. The resulting algorithm, named A2BC-SubSim, simplifies the application of ABC-SubSim method for new users while ensuring better measure of accuracy in the posterior distribution and improved computational efficiency. A first numerical application example is provided for illustration purposes and to provide a comparative and sensitivity analysis of the algorithm with respect to initial ABC-SubSim algorithm. Moreover, the efficiency of the method is demonstrated in two nonlinear structural calibration case studies where the A2BC-SubSim is used as a tool to infer structural parameters with quantified uncertainty based on test data. The results confirm the suitability of the method to tackle with a real-life damage parameter inference and its superiority in relation to the original ABC-SubSim.