Bayesian model selection for nonlinear aeroelastic systems using wind-tunnel data

Sandhu, Rimple; Khalil, Mohammad; Sarkar, Abhijit; Poirel, Dominique

doi:10.1016/j.cma.2014.06.013

Cited by 22 publications

(22 citation statements)

References 38 publications

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“…For instance, it was found that AIC tends to select more complex models (see Table 3 in [12]). The posterior parameter distribution of nonlinear dynamical systems having multiple fixed points may be non-Gaussian.…”

Section: Introductionmentioning

confidence: 97%

“…More traditional statistical methods such as Akaike information criteria (AIC) and Bayesian information criteria (BIC) [14] were previously investigated by the authors [12,13]. For instance, it was found that AIC tends to select more complex models (see Table 3 in [12]).…”

Section: Introductionmentioning

confidence: 98%

“…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.…”

Section: Introductionmentioning

confidence: 98%

“…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.…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian parameter estimation and model selection for strongly nonlinear dynamical systems

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The Bayesian model selection and parameter estimation framework developed by Khalil et al. (J Sound Vib 332(15):3670-3691, 2013, Bayesian inference for complex and large-scale engineering systems. Ph.D. thesis, Carleton University, 2013) and Sandhu et al. (J Comput Methods Appl Mech Eng 282:161-183, 2014, Bayesian model selection and parameter estimation for a nonlinear fluid-structure interaction problem. Master's thesis, Carleton University, 2012, 54th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, 2013) is extended to handle strongly nonlinear systems. The evidence required to estimate the posterior probability of each proposed model is computed using the ChibJeliazkov method. The posterior parameter samples generated using Metropolis-Hastings (M-H) Markov Chain Monte Carlo (MCMC) simulations are required by this method. The M-H MCMC-based parameter estimation procedure is complemented by an efficient particle filter and an ensemble Kalman filter for the strongly non-Gaussian state estimation problem. A strongly nonlinear system having multiple fixed (equilibrium) points is analyzed to demonstrate the efficacy of the algorithm.

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Section: Introductionmentioning

confidence: 97%