Probabilistic parameter estimation of a fluttering aeroelastic system in the transitional Reynolds number regime

Bayesian parameter estimation and model selection for strongly nonlinear dynamical systems

“…Bayesian inference gives the ability to combine knowledge from the observations to the model. Observations are characterized by the following measurement equation [9,16,29] …”

“…(30) in "Appendix 1," the likelihood p( D|φ, M i ) in Eq. (2) can be expressed as follows [9,10,12,13,16] …”

“…The accuracy and efficiency of the parameter estimation are crucial for model selection method. To this end, a general Bayesian framework of parameter estimation [9][10][11] and model selection [12,13] recently developed by the authors use the Metropolis-Hastings (M-H) Markov Chain Monte Carlo (MCMC) simulation and nonlinear filtering. The computation of the parameter likelihood function involves solving a state estimation problem.…”

“…The computation of the parameter likelihood function involves solving a state estimation problem. Due to the assimilation of dense observational data, the conditional probability density function (pdf) of the state is nearly Gaussian, explaining the effective performance of the extended Kalman filter (EKF) for certain applications [9,10,12,13]. The performance of EKF degrades for highly non-Gaussian states caused by strong nonlinearities in the model and measurement operators and(or) sparse observational data in time or in space.…”

“…In particular, we extend the Bayesian framework [9,10,12,13,15] to compute the likelihood function using an efficient particle filter (PF-EnKF) that exploits the estimates of the ensemble Kalman filter (EnKF) [16] to construct the proposal distribution [17][18][19][20]. The effectiveness of the proposed Bayesian algorithm is demonstrated for the model selection problem of a strongly nonlinear dynamical system having multiple fixed points.…”