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An EnKF-Based Flow State Estimator for Aerodynamic Problems


da Silva, Andre Fernando de Castro (2019) An EnKF-Based Flow State Estimator for Aerodynamic Problems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/W327-VF41.


Regardless of the plant model, robust flow estimation based on limited measurements remains a major challenge in successful flow control applications. Aiming to combine the robustness of a high-dimensional representation of the dynamics with the cost efficiency of a low-order approximation of the state covariance matrix, a flow state estimator based on the Ensemble Kalman Filter (EnKF) is applied to two-dimensional flow past a cylinder and an airfoil at high angle of attack and low Reynolds number. For development purposes, we use the numerical algorithm as both the estimator and as a surrogate for the measurements. In a perfect-model framework, a reduced number of either pressure sensors on the surface of the body or sparsely placed velocity probes in the wake are sufficient to accurately estimate the instantaneous flow state. Because the dynamics of these flows are restricted to a low-dimensional manifold of the state space, a small ensemble size is sufficient to yield the correct asymptotic behavior. The relative importance of each sensor location is evaluated by analyzing how they influence the estimated flow field, and optimal locations for pressure sensors are determined.

However, model inaccuracies are ubiquitous in practical applications. Covariance inflation is used to enhance the estimator performance in the presence of unmodeled freestream perturbations. A combination of parametric modeling and augmented state methodology is used to successfully estimate the forces on immersed bodies subjected to deterministic and random gusts. The robustness of high-dimensional representation of the dynamics to the choice of parameters such as the Reynolds number is inherited by the estimator, which was shown to successfully estimate the reference Reynolds number on the fly. Spatial and temporal discretization can constitute a second source of errors which can render numerical solutions a biased representation of reality. Left unaccounted for, biased forecast and observation models can lead to poor estimator performance. In this work, we propose a low-rank representation for the bias whose dynamics are represented by a colored-noise process. System state and bias parameters are simultaneously tracked online with the Ensemble Kalman Filter (EnKF) algorithm. The proposed methodology is demonstrated to achieve a 70% error reduction for the problem of estimating the state of the two-dimensional low-Re flow past a flat plate at high angle of attack using an ensemble of coarse-mesh simulations and pressure measurements at the surface of the body, compared to a bias-blind estimator. Strategies to determine the bias statistics and to deal with nonlinear observation functions in the context of ensemble methods are discussed.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Ensemble Kalman Filter, Flow Estimation, Bias Tracking, Data Assimilation, Low-Re Aerodynamics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Mechanical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Colonius, Tim
Thesis Committee:
  • Blanquart, Guillaume (chair)
  • McKeon, Beverley J.
  • Stuart, Andrew M.
  • Colonius, Tim
Defense Date:5 September 2018
Non-Caltech Author Email:andre.fernando.t10 (AT)
Funding AgencyGrant Number
Ministry of Education of Brazil (Capes Foundation)BEX 12966/13-4
Air Force Office of Scientific Research (AFOSR)FA9550-14-1-0328
Record Number:CaltechTHESIS:09072018-105527896
Persistent URL:
Related URLs:
URLURL TypeDescription for chapter 3 and 4. DOIConference paper for chapter 5.
da Silva, Andre Fernando de Castro0000-0002-8125-6010
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11176
Deposited By: Andre Fernando de Castro da Silva
Deposited On:29 Sep 2018 00:09
Last Modified:26 Oct 2023 19:36

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