Le 8 novembre 2017

Model selection and parameter estimation of dynamical systems using a novel variant of approximate Bayesian computation

Anis Ben Abdessalem (LARIS) *

Email: anis.ben-abdessalem @ univ-angers.fr (anis.ben-abdessalem @ univ-angers.fr)

Abstract:

Model selection is a challenging problem that is of importance in many branches of sciences and engineering particularly in structural dynamics. In definition, it is intended to select the most likely model among a set of competing models that matches well the dynamic behaviour of real structures and better predicts the measured data. The Bayesian approach based essentially on the evaluation of a likelihood function is arguably the most popular approach due to its efficiency. However, in some circumstances, the likelihood function is either intractable or not available in an analytical form (even in a closed form), so a standard statistical inference becomes challenging or impossible. To over-come this issue, likelihood-free or approximate Bayesian computation (ABC) algorithm has been introduced in the literature which relaxes the need of an explicit likelihood function to measure the level of agreement between model prediction and measurements. However, ABC algorithms suffer from the low acceptance rate which is actually a common problem with the traditional Bayesian methods. To overcome this shortcoming and alleviate the computational burden, a new variant of ABC algorithms based on an ellipsoidal Nested Sampling (NS) technique is introduced. It has been called ABC-NS. Through this talk, I will show how the new algorithm is a promising alternative to deal with parameter estimation and model selection issues. It promises drastic speedups and provides a good approximation of the posterior distributions. To demonstrate its practical applicability, two illustrative examples are given. Firstly, the efficiency of the algorithm is demonstrated to deal with parameter estimation (or model calibration) using simulated data from the g-and-k distribution. Secondly, a real structure which consists of a wire rope isolators mounted between a load mass and a base mass is used to further assess the performance of the algorithm in solving model selection issue. The aim of this part is to select a model which can be used to capture the dynamics of a wire rope isolators widely used for vibration isolation and make predictions under different excitation amplitudes.

REFERENCES

[1] A. Ben Abdessalem, N. Dervilis, D. Wagg, K. Worden, Model selection and parameter estimation in structural dynamics using approximate Bayesian computation, Mech. Syst. Signal Process. 99 (2018) 306–325.

[2] A. Ben Abdessalem, N. Dervilis, D. Wagg, K. Worden. Automatic Kernel Selection for Gaussian Processes Regression with Approximate Bayesian Computation and Sequential Monte Carlo. Front. Built Environ. (2017) 3:52. doi: 10.3389/fbuil.2017.00052

[3] A. Ben Abdessalem, N. Dervilis, D. Wagg, K. Worden, Identification of nonlinear dynamical systems using approximate Bayesian computation based on a sequential Monte Carlo sample, International Conference on Noise and Vibration Engineering, September 19-21, 2016, Leuven (Belgium).

[4] A. Ben Abdessalem, N. Dervilis, D. Wagg, K. Worden. ABC-NS: a new computational inference method applied to parameter estimation and model selection in structural dynamics, 23 Congrès Français de Mécanique, May 2017, Lille, France.

[5] A. Ben Abdessalem, K. Worden, N. Dervilis, D. Wagg, Recent advances in approximate Bayesian computation methodology: application in structural dynamics, ENL Workshop, January 2017, Bristol, United Kingdom