Nonlinear Aerodynamic and Aeroelastic Model Reduction Using a Discrete Empirical Interpolation Method

Yao, Weigang; Marques, Simão

doi:10.2514/1.j055143

Cited by 24 publications

(12 citation statements)

References 33 publications

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“…However, constructing the POD reduced mode of the corresponding parameter by constructing the response of each parameter in the complex system is not allowed from the point of calculation cost. In order to reduce the order of the complex system in parameter range and ensure the parameter robustness of POD reduced-order mode, scholars have proposed many improved POD methods: global POD method [142][143][144][145], local POD method [60,117,[146][147][148][149], adaptive POD method-POD modal interpolation method [141,[152][153][154][155][156], subspace angle interpolation method [157][158][159][160][161][162], Grassmann manifold tangent space interpolation method [163][164][165][166][167][168][169][170][171], and other adaptive POD methods.…”

Section: Parameter Adaptation Of Pod Methodmentioning

confidence: 99%

A Review of Model Order Reduction Methods for Large‐Scale Structure Systems

Zhang

et al. 2021

Shock and Vibration

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The large-scale structure systems in engineering are complex, high dimensional, and variety of physical mechanism couplings; it will be difficult to analyze the dynamic behaviors of complex systems quickly and optimize system parameters. Model order reduction (MOR) is an efficient way to address those problems and widely applied in the engineering areas. This paper focuses on the model order reduction of high-dimensional complex systems and reviews basic theories, well-posedness, and limitations of common methods of the model order reduction using the following methods: center manifold, Lyapunov–Schmidt (L-S), Galerkin, modal synthesis, and proper orthogonal decomposition (POD) methods. The POD is a powerful and effective model order reduction method, which aims at obtaining the most important components of a high-dimensional complex system by using a few proper orthogonal modes, and it is widely studied and applied by a large number of researchers in the past few decades. In this paper, the POD method is introduced in detail and the main characteristics and the existing problems of this method are also discussed. POD is classified into two categories in terms of the sampling and the parameter robustness, and the research progresses in the recent years are presented to the domestic researchers for the study and application. Finally, the outlooks of model order reduction of high-dimensional complex systems are provided for future work.

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Section: Parameter Adaptation Of Pod Methodmentioning

confidence: 99%

A Review of Model Order Reduction Methods for Large‐Scale Structure Systems

Zhang

et al. 2021

Shock and Vibration

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“…The methodology has been integrated into GeN-Foam. For different applications of DEIM in other fields of engineering, we refer the reader to [35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Application of multiphysics model order reduction to doppler/neutronic feedback

German

Ragusa

Fiorina

2019

EPJ Nuclear Sci. Technol.

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In this paper, a proper orthogonal decomposition based reduced-order model is presented for parametrized multiphysics computations. Our application physics is Doppler feedback in a simplified model of the molten salt fast reactor concept. The reduced model is created using the method of snapshots where the offline training set is obtained by exercising a full-order model created with the OpenFOAM based multiphysics solver, GeN-Foam. The steady state models solve the multi-group diffusion k-eigenvalue equations with moving precursors together with the energy equation. A fixed velocity field is assumed throughout the computations, hence the momentum and continuity equations are not solved. The discrete empirical interpolation method is used for the efficient coupling of the ROM solvers, while the input parameter space is surveyed using the improved distributed latin hypercube sampling algorithm.

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“…On the one hand, an extension of the POD method denoted as discrete empirical interpolation method (DEIM) for nonlinear applications has been applied to aerodynamic 14 and aeroelastic models. 15 The POD-DEIM method is a data-driven approach and as such requires the generation of a training dataset. Also, the predicted trajectories must remain close to the ones used in the training set.…”

Section: Introductionmentioning

confidence: 99%

An input-independent method for solving weakly nonlinear partial differential equations in the frequency domain: application to the Euler equations

Quero

2019

AIAA Aviation 2019 Forum

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In this work a novel approach in determining the first and second order frequencydomain Volterra kernels for weakly nonlinear partial differential equations (PDEs) in semidiscrete form based on the application of the harmonic probing (HP) method is presented. This represents a formal extension of the linearized-frequency domain (LFD) methods to a nonlinear framework, leading to a so-called LFD2 method. The method allows for the representation of weak nonlinearities by solving two input-independent linear algebraic systems of equations in the frequency domain and thus circumvents the solution of the nonlinear PDE by numerical integration for each different input, representing a nonlinear reduced-order model (ROM) for the physical phenomena. The general form of the equations is derived and an application to the well known viscous Burgers' equation to show its suitability in representing the nonlinear convective term is shown. Next, an application to the compressible quasi one-dimensional unsteady flow described by the Euler equations is presented. The proposed method overcomes two constraints present in other methods for the solution of nonlinear PDEs, namely, the consideration of exclusively periodic solutions as in the harmonic balance (HB) method and the dependency of the kernels with the input signal as in the Volterra kernel identification methods.

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Nonlinear Aerodynamic and Aeroelastic Model Reduction Using a Discrete Empirical Interpolation Method

Cited by 24 publications

References 33 publications

A Review of Model Order Reduction Methods for Large‐Scale Structure Systems

A Review of Model Order Reduction Methods for Large‐Scale Structure Systems

Application of multiphysics model order reduction to doppler/neutronic feedback

An input-independent method for solving weakly nonlinear partial differential equations in the frequency domain: application to the Euler equations

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