General treatment of essential boundary conditions in reduced order models for non-linear problems

The high dimensions and governing non-linear dynamics in wind farm systems make the design of numerical optimal controllers computationally expensive. A possible pathway to circumvent this challenge lies in finding reduced order models which can accurately embed the existing non-linearities. The work presented here applies the ideas motivated by non-linear dynamical systems theory—the Koopman Operator—to an innovative algorithm in the context of wind farm systems—Input Output Dynamic Mode Decomposition (IODMD)—to improve on the ability to model the aerodynamic interaction between wind turbines in a wind farm and uncover insights into the existing dynamics. It is shown that a reduced order linear state space model can reproduce the downstream turbine generator power dynamics and reconstruct the upstream turbine wake. It is further shown that the fit can be improved by judiciously choosing the Koopman observables used in the IODMD algorithm without jeopardizing the models ability to rebuild the turbine wake. The extensions to the IODMD algorithm provide an important step towards the design of linear reduced order models which can accurately reproduce the dynamics in a wind farm.

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Numerical comparison of reduced order models for non-linear vibrations of damped plates

European Journal of Computational Mechanics ◽

10.13052/17797179.2012.719317 ◽

2012 ◽

Author(s):

F. Boumediene ◽

L. Duigou ◽

A. Miloudi ◽

J.M. Cadou

Keyword(s):

Harmonic Balance ◽

Harmonic Balance Method ◽

Computational Time ◽

Numerical Comparison ◽

Processing Unit ◽

Reduced Order Models ◽

Reduced Order ◽

Central Processing ◽

Non Linear ◽

Linear Vibrations

This work deals with the computation of the non-linear solutions of the vibration of damped plates by coupling a harmonic balance method and the asymptotic numerical method. These computations can lead to lengthy central processing unit (CPU) times if the solution sought contains an important number of harmonics. In this study, we propose two reduced order models which can be applied to solve this type of problem. Both reduced methods are based on a first computation carried out with a small number of harmonics (here two). Numerical examples of plate vibration show that these algorithms help save a great deal of computational time and can be applied to problems involving numerous harmonics.

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Numerical comparison of reduced order models for non-linear vibrations of damped plates

European Journal of Computational Mechanics ◽

10.1080/17797179.2012.719317 ◽

2012 ◽

Vol 21 (3-6) ◽

pp. 174-183 ◽

Cited By ~ 1

Author(s):

F. Boumediene ◽

L. Duigou ◽

A. Miloudi ◽

J.M. Cadou

Keyword(s):

Numerical Comparison ◽

Reduced Order Models ◽

Reduced Order ◽

Non Linear ◽

Linear Vibrations

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An Adaptive Aeroelastic Control Approach using Non Linear Reduced Order Models

14th AIAA Aviation Technology, Integration, and Operations Conference ◽

10.2514/6.2014-2590 ◽

2014 ◽

Cited By ~ 3

Author(s):

Nikolaos D. Tantaroudas ◽

Andrea Da Ronch ◽

Guanqun Gai ◽

Kenneth J. Badcock

Keyword(s):

Reduced Order Models ◽

Reduced Order ◽

Control Approach ◽

Non Linear

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Stable and Efficient Galerkin Reduced Order Models for Non-Linear Fluid Flow

6th AIAA Theoretical Fluid Mechanics Conference ◽

10.2514/6.2011-3110 ◽

2011 ◽

Cited By ~ 10

Author(s):

Irina Kalashnikova ◽

Matthew Barone

Keyword(s):

Fluid Flow ◽

Reduced Order Models ◽

Reduced Order ◽

Non Linear

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Closure modeling in reduced-order model of Burgers’ equation for control applications

Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering ◽

10.1177/0954410016641443 ◽

2016 ◽

Vol 231 (4) ◽

pp. 642-656 ◽

Cited By ~ 5

Author(s):

Haroon Imtiaz ◽

Imran Akhtar

Keyword(s):

Boundary Conditions ◽

Turbulent Flows ◽

Reduced Order Model ◽

Reduced Order Models ◽

Closure Model ◽

Order Model ◽

Control Applications ◽

Reduced Order ◽

Nonhomogeneous Boundary ◽

Nonhomogeneous Boundary Conditions

A proper orthogonal decomposition (POD) technique has been successfully employed to develop reduced-order models for flow control purposes. For complex flows, higher POD modes also play a significant role in the stability and accuracy of the reduced-order model, thus require a closure, as in turbulent flows. In the presence of nonhomogeneous boundary conditions, developing a closure model becomes a challenging task. This paper discusses nonlinear closure modeling approaches for homogeneous and nonhomogeneous boundary conditions. Burgers’ equations, both one-dimensional and two-dimensional, are considered as the governing equations to develop reduced-order models with different boundary conditions. Homogeneous and nonhomogeneous boundary conditions are considered to demonstrate the effectiveness of the proposed closure modeling technique in boundary control applications. Numerical results show that the proposed closure model improves the accuracy of the reduced-order model.

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