ABC-NS: a new computational inference method applied to parameter estimation and model selection in structural dynamics

The inference of dynamical systems is a challenging issue, particularly when the dynamics include complex phenomena such as the existence of bifurcations and/or chaos. In this situation, the likelihood function formulated based on time-series data may be complex with several local minima and as a result not suitable for parameter inference. In the most challenging scenarios, the likelihood function may not be available in an analytical form, so a standard statistical inference is impossible to carry out. To overcome this problem, the inclusion of new features/invariants less sensitive to small variations from either the time or frequency domains seems to be potentially a very useful way to make Bayesian inference. The use of approximate Bayesian computation (ABC) or likelihood-free algorithms is an appropriate option as they offer the flexibility to use different metrics for parameter inference. However, most variants of the ABC algorithm are inefficient due to the low acceptance rate. In this contribution, a new ABC algorithm based on an ellipsoidal nested sampling technique is proposed to overcome this issue. It will be shown that the new algorithm performs perfectly well and maintains a relatively high acceptance rate through the iterative inference process. In addition to parameter estimation, the new algorithm allows one to deal with the model selection issue. To demonstrate its efficiency and robustness, a numerical example is presented.