Combined selection of the dynamic model and modeling error in nonlinear aeroelastic systems using Bayesian Inference

Bisaillon, Philippe; Sandhu, Rimple; Pettit, Chris; Khalil, Mohammad; Poirel, Dominique; Manohar, C. S.; Sarkar, Abhijit

doi:10.1016/j.jsv.2021.116418

Combined selection of the dynamic model and modeling error in nonlinear aeroelastic systems using Bayesian Inference

Journal Article · Tue Sep 21 00:00:00 EDT 2021 · Journal of Sound and Vibration

DOI:https://doi.org/10.1016/j.jsv.2021.116418· OSTI ID:1834094

Bisaillon, Philippe ^[1]; ^[2]; Pettit, Chris ^[3]; Khalil, Mohammad ^[4]; Poirel, Dominique ^[5]; Manohar, C. S. ^[6]; Sarkar, Abhijit ^[1]

Carleton Univ., Ottawa, ON (Canada)
Carleton Univ., Ottawa, ON (Canada); National Renewable Energy Lab. (NREL), Golden, CO (United States)
US Naval Academy, Annapolis, MD (United States)
Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Royal Military College of Canada, Kingston, ON (Canada)
India Institute of Science, Bangalore (India)

Here, we report a Bayesian framework for concurrent selection of physics-based models and (modeling) error models. We investigate the use of colored noise to capture the mismatch between the predictions of calibrated models and observational data that cannot be explained by measurement error alone within the context of Bayesian estimation for stochastic ordinary differential equations. Proposed models are characterized by the average data-fit, a measure of how well a model fits the measurements, and the model complexity measured using the Kullback–Leibler divergence. The use of a more complex error models increases the average data-fit but also increases the complexity of the combined model, possibly over-fitting the data. Bayesian model selection is used to find the optimal physical model as well as the optimal error model. The optimal model is defined using the evidence, where the average data-fit is balanced by the complexity of the model. The effect of colored noise process is illustrated using a nonlinear aeroelastic oscillator representing a rigid NACA0012 airfoil undergoing limit cycle oscillations due to complex fluid–structure interactions. Several quasi-steady and unsteady aerodynamic models are proposed with colored noise or white noise for the model error. The use of colored noise improves the predictive capabilities of simpler models.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-CA), Livermore, CA (United States)

Sponsoring Organization:: USDOE; Department of National Defense

Grant/Contract Number:: NA0003525

OSTI ID:: 1834094

Report Number(s):: SAND--2019-13241J; 680940

Journal Information:: Journal of Sound and Vibration, Journal Name: Journal of Sound and Vibration Vol. 522; ISSN 0022-460X

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (37)

Using a bias aware EnKF to account for unresolved structure in an unsaturated zone model: BIAS AWARE ENKF FOR UNRESOLVED STRUCTURE Erdal, D.; Neuweiler, I.; Wollschläger, U. Water Resources Research, Vol. 50, Issue 1 https://doi.org/10.1002/2012WR013443	journal	January 2014
Bayesian system identification based on probability logic Beck, James L. Structural Control and Health Monitoring, Vol. 17, Issue 7 https://doi.org/10.1002/stc.424	journal	October 2010
Robust estimation of background noise and signal detection in climatic time series Mann, Michael E.; Lees, Jonathan M. Climatic Change, Vol. 33, Issue 3 https://doi.org/10.1007/BF00142586	journal	July 1996
Adaptive proposal distribution for random walk Metropolis algorithm Haario, Heikki; Saksman, Eero; Tamminen, Johanna Computational Statistics, Vol. 14, Issue 3 https://doi.org/10.1007/s001800050022	journal	September 1999
Accounting for model errors in iterative ensemble smoothers Evensen, Geir Computational Geosciences, Vol. 23, Issue 4 https://doi.org/10.1007/s10596-019-9819-z	journal	April 2019
Bayesian parameter estimation and model selection for strongly nonlinear dynamical systems Bisaillon, Philippe; Sandhu, Rimple; Khalil, Mohammad Nonlinear Dynamics, Vol. 82, Issue 3 https://doi.org/10.1007/s11071-015-2217-8	journal	July 2015
DRAM: Efficient adaptive MCMC Haario, Heikki; Laine, Marko; Mira, Antonietta Statistics and Computing, Vol. 16, Issue 4 https://doi.org/10.1007/s11222-006-9438-0	journal	December 2006
Bayesian analysis of uncertainty for structural engineering applications Igusa, T.; Buonopane, S. G.; Ellingwood, B. R. Structural Safety, Vol. 24, Issue 2-4 https://doi.org/10.1016/S0167-4730(02)00023-1	journal	April 2002
Response probability structure of a structurally nonlinear fluttering airfoil in turbulent flow Poirel, D.; Price, S. J. Probabilistic Engineering Mechanics, Vol. 18, Issue 2 https://doi.org/10.1016/S0266-8920(03)00013-4	journal	April 2003
Bayesian model selection for nonlinear aeroelastic systems using wind-tunnel data Sandhu, Rimple; Khalil, Mohammad; Sarkar, Abhijit Computer Methods in Applied Mechanics and Engineering, Vol. 282 https://doi.org/10.1016/j.cma.2014.06.013	journal	December 2014
Bayesian model selection using automatic relevance determination for nonlinear dynamical systems Sandhu, Rimple; Pettit, Chris; Khalil, Mohammad Computer Methods in Applied Mechanics and Engineering, Vol. 320 https://doi.org/10.1016/j.cma.2017.01.042	journal	June 2017
Bayesian inference of nonlinear unsteady aerodynamics from aeroelastic limit cycle oscillations Sandhu, Rimple; Poirel, Dominique; Pettit, Chris Journal of Computational Physics, Vol. 316 https://doi.org/10.1016/j.jcp.2016.03.006	journal	July 2016
Self-sustained aeroelastic oscillations of a NACA0012 airfoil at low-to-moderate Reynolds numbers Poirel, D.; Harris, Y.; Benaissa, A. Journal of Fluids and Structures, Vol. 24, Issue 5 https://doi.org/10.1016/j.jfluidstructs.2007.11.005	journal	July 2008
Aerodynamics of laminar separation flutter at a transitional Reynolds number Poirel, D.; Yuan, W. Journal of Fluids and Structures, Vol. 26, Issue 7-8 https://doi.org/10.1016/j.jfluidstructs.2010.06.005	journal	October 2010
Computational aeroelastic simulations of self-sustained pitch oscillations of a NACA0012 at transitional Reynolds numbers Poirel, D.; Métivier, V.; Dumas, G. Journal of Fluids and Structures, Vol. 27, Issue 8 https://doi.org/10.1016/j.jfluidstructs.2011.05.009	journal	November 2011
Noise modeling concepts in nonlinear state estimation Kolås, S.; Foss, B. A.; Schei, T. S. Journal of Process Control, Vol. 19, Issue 7 https://doi.org/10.1016/j.jprocont.2009.03.002	journal	July 2009
Probabilistic parameter estimation of a fluttering aeroelastic system in the transitional Reynolds number regime Khalil, Mohammad; Poirel, Dominique; Sarkar, Abhijit Journal of Sound and Vibration, Vol. 332, Issue 15 https://doi.org/10.1016/j.jsv.2013.02.012	journal	July 2013
The estimation of time-invariant parameters of noisy nonlinear oscillatory systems Khalil, Mohammad; Sarkar, Abhijit; Adhikari, Sondipon Journal of Sound and Vibration, Vol. 344 https://doi.org/10.1016/j.jsv.2014.10.002	journal	May 2015
Quantifying inflow and RANS turbulence model form uncertainties for wind engineering flows Gorlé, Catherine; Garcia-Sanchez, Clara; Iaccarino, Gianluca Journal of Wind Engineering and Industrial Aerodynamics, Vol. 144 https://doi.org/10.1016/j.jweia.2015.03.025	journal	September 2015
Annealed importance sampling Neal, Radford M. Statistics and Computing, Vol. 11, Issue 2, p. 125-139 https://doi.org/10.1023/A:1008923215028	journal	April 2001
Analyzing input and structural uncertainty of nonlinear dynamic models with stochastic, time-dependent parameters: ANALYZING INPUT AND STRUCTURAL UNCERTAINTY Reichert, Peter; Mieleitner, Johanna Water Resources Research, Vol. 45, Issue 10 https://doi.org/10.1029/2009WR007814	journal	October 2009
Investigating the origins and significance of low-frequency modes of climate variability Allen, Myles R.; Smith, Leonard A. Geophysical Research Letters, Vol. 21, Issue 10 https://doi.org/10.1029/94GL00978	journal	May 1994
Bayesian Learning Using Automatic Relevance Determination Prior with an Application to Earthquake Early Warning Oh, Chang Kook; Beck, James L.; Yamada, Masumi Journal of Engineering Mechanics, Vol. 134, Issue 12 https://doi.org/10.1061/(ASCE)0733-9399(2008)134:12(1013)	journal	December 2008
Computationally Efficient Bayesian Model Selection for Locally Nonlinear Structural Dynamic Systems De, Subhayan; Johnson, Erik A.; Wojtkiewicz, Steven F. Journal of Engineering Mechanics, Vol. 144, Issue 5 https://doi.org/10.1061/(ASCE)EM.1943-7889.0001397	journal	May 2018
Accurate Approximations for Posterior Moments and Marginal Densities Tierney, Luke; Kadane, Joseph B. Journal of the American Statistical Association, Vol. 81, Issue 393 https://doi.org/10.1080/01621459.1986.10478240	journal	March 1986
CAPABILITY MEASURES FOR m -DEPENDENT STATIONARY PROCESSES Chen, Sy-Mien; Hsu, Yu-Sheng; Pearn, W. L. Statistics: A Journal of Theoretical and Applied Statistics, Vol. 37, Issue 1 https://doi.org/10.1080/02331880309257	journal	January 2003
Generalised information criteria in model selection Konishi, S. Biometrika, Vol. 83, Issue 4 https://doi.org/10.1093/biomet/83.4.875	journal	December 1996
On the Theory of the Brownian Motion Uhlenbeck, G. E.; Ornstein, L. S. Physical Review, Vol. 36, Issue 5 https://doi.org/10.1103/PhysRev.36.823	journal	September 1930
Exact numerical simulation of the Ornstein-Uhlenbeck process and its integral Gillespie, Daniel T. Physical Review E, Vol. 54, Issue 2 https://doi.org/10.1103/PhysRevE.54.2084	journal	August 1996
Generation of non-Gaussian stationary stochastic processes Cai, G. Q.; Lin, Y. K. Physical Review E, Vol. 54, Issue 1 https://doi.org/10.1103/PhysRevE.54.299	journal	July 1996
Bayesian calibration of computer models Kennedy, Marc C.; O'Hagan, Anthony Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 63, Issue 3 https://doi.org/10.1111/1467-9868.00294	journal	August 2001
Calculation of Posterior Probabilities for Bayesian Model Class Assessment and Averaging from Posterior Samples Based on Dynamic System Data: Calculation of posterior probabilities Cheung, Sai Hung; Beck, James L. Computer-Aided Civil and Infrastructure Engineering, Vol. 25, Issue 5 https://doi.org/10.1111/j.1467-8667.2009.00642.x	journal	February 2010
Estimating the evidence - a review Friel, Nial; Wyse, Jason Statistica Neerlandica, Vol. 66, Issue 3 https://doi.org/10.1111/j.1467-9574.2011.00515.x	journal	January 2012
Marginal likelihood estimation via power posteriors Friel, N.; Pettitt, A. N. Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 70, Issue 3 https://doi.org/10.1111/j.1467-9868.2007.00650.x	journal	July 2008
Marginal Likelihood From the Metropolis–Hastings Output Chib, Siddhartha; Jeliazkov, Ivan Journal of the American Statistical Association, Vol. 96, Issue 453 https://doi.org/10.1198/016214501750332848	journal	March 2001
Nested sampling for general Bayesian computation Skilling, John Bayesian Analysis, Vol. 1, Issue 4 https://doi.org/10.1214/06-BA127	journal	December 2006
The Color of Environmental Noise Vasseur, David A.; Yodzis, Peter Ecology, Vol. 85, Issue 4 https://doi.org/10.1890/02-3122	journal	April 2004

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