POD-based observer for estimation in Navier–Stokes flow

A proper orthogonal decomposition (POD)-based nonlinear estimator for fluid flow velocity fields is developed, which is capable of achieving finite-time convergence of the Galerkin coefficient estimates. Using Galerkin projection and POD-based model reduction, the incompressible Navier-Stokes equations are recast as a set of nonlinear ordinary differential equations in the Galerkin coefficients. A sliding-mode-based observer is designed to estimate the unknown time-varying Galerkin coefficients. Convergence of the estimates is proven to be achieved in finite time, and high-fidelity numerical simulation results are provided to complement the theoretical development.

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“…Since div () = 0, it can be shown that k (z) = 0 on the boundary of . Thus, the pressure term in (5) vanishes over a closed domain [5].…”

Section: A Pod-based Model Reductionmentioning

confidence: 96%

“…The state variables in the transformed set of equations are the time-varying coefficients of the POD modes. By building an observer to estimate the coefficients, an observer of the fluid flow velocity field can thus be obtained [4], [5].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear estimation of fluid flow velocity fields

MacKunis

Drakunov

Reyhanoglu

et al. 2011

IEEE Conference on Decision and Control and European Control Conference

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“…. ; w d have been calculated as explained in Section 4.2, the reduced ODE model can now be found as follows using (20). Substituting the approximation (18) into (14) yields…”

Section: Reduced Dynamical Modelmentioning

confidence: 99%

“…An overview on the model reduction method is given in Section 4.1. The two main steps, proper orthogonal decomposition (POD) [20,21] and Galerkin projection, are described in more detail in Sections 4.2 and 4.3, respectively.…”

Section: Model Reductionmentioning

confidence: 99%

Coupled DEM–CFD simulation of drying wood chips in a rotary drum – Baffle design and model reduction

Scherer

Mönnigmann

Berner

et al. 2016

Fuel

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“…Besides, the DPSs under consideration in [22][23][24][25] are linear and have no exogenous disturbances. Up to now, very little attention has been paid to the finite dimensional distributed consensus filtering design for nonlinear DPSs with exogenous disturbances using SNs.In practice, there are many industrially important DPSs, which are naturally described by dissipative PDEs [26][27][28][29][30][31][32][33][34][35]. This class of PDEs contains a large number of equations from mechanics, physics to chemistry, such as the reaction-diffusion equations [26][27][28][29][30], the Kuramoto-Sivashinsky equation (KSE) [31][32][33][34], the incompressible Navier-Stokes equations [35], to name a few.…”

mentioning

confidence: 99%

Design of finite dimensional robust H_∞ distributed consensus filters for dissipative PDE systems with sensor networks

Wang

2014

Intl J Robust & Nonlinear

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SUMMARYThis paper presents a design method of finite dimensional robust H 1 distributed consensus filters (DCFs) for a class of dissipative nonlinear partial differential equation (PDE) systems with a sensor network, for which the eigenvalue spectrum of the spatial differential operator can be partitioned into a finite dimensional slow one and an infinite dimensional stable fast complement. Initially, the modal decomposition technique is applied to the PDE system to derive a finite dimensional ordinary differential equation system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Then, based on the slow subsystem, a set of finite dimensional robust H 1 DCFs are developed to enforce the consensus of the slow mode estimates and state estimates of all local filters for all admissible nonlinear dynamics and observation spillover, while attenuating the effect of external disturbances. The Luenberger and consensus gains of the proposed DCFs can be obtained by solving a set of linear matrix inequalities (LMIs). Furthermore, by the existing LMI optimization technique, a suboptimal design of robust H 1 DCFs is proposed in the sense of minimizing the attenuation level. Finally, the effectiveness of the proposed DCFs is demonstrated on the state estimation of one dimensional Kuramoto-Sivashinsky equation system with a sensor network.

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POD-based observer for estimation in Navier–Stokes flow

Cited by 28 publications

References 14 publications

Nonlinear estimation of fluid flow velocity fields

Nonlinear estimation of fluid flow velocity fields

Coupled DEM–CFD simulation of drying wood chips in a rotary drum – Baffle design and model reduction

Design of finite dimensional robust H_∞ distributed consensus filters for dissipative PDE systems with sensor networks

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POD-based observer for estimation in Navier–Stokes flow

Cited by 28 publications

References 14 publications

Nonlinear estimation of fluid flow velocity fields

Nonlinear estimation of fluid flow velocity fields

Coupled DEM–CFD simulation of drying wood chips in a rotary drum – Baffle design and model reduction

Design of finite dimensional robust H ∞ distributed consensus filters for dissipative PDE systems with sensor networks

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Design of finite dimensional robust H_∞ distributed consensus filters for dissipative PDE systems with sensor networks