Adaptive approximate Bayesian computation by subset simulation for structural model calibration

This work was supported by the SINDE (Research and Development System of the Catholic University of Santiago de Guayaquil, Ecuador) under project Cod. Pres #491/Cod. Int. #170. The first author would also like to thank the University of Granada (Spain) for hosting him during the course of this work. Finally, the authors thank the work of Berry et al. (2004) and Pratap and Pujol (2021) for their valuable set of data.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.SINDE (Research and Development System of the Catholic University of Santiago de Guayaquil, Ecuador) 491/Cod- 17