Data-driven parameterized modeling of LTI systems with guaranteed stability

We propose a theoretical framework and an automated algorithm for the construction of a parameterized reduced-order model of a general LTI system from its sampled input-output responses. The model is cast as a parameterized rational function in Generalized Sanathanan-Koerner form, which allows for implicit parameterization of the model poles. Our main result is the guaranteed enforcement of uniform stability of the model in the parameter space through a sufficient condition, which requires the (strict) positive realness of the denominator subsystem. This condition is enforced through adaptive constraints during the model construction loop. Several applications to the field of Electronic Design Automation are presented.

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A data-driven reduced-order model of nonlinear processes based on diffusion maps and artificial neural networks

Chemical Engineering Journal ◽

10.1016/j.cej.2020.125475 ◽

2020 ◽

Vol 397 ◽

pp. 125475

Author(s):

E.D. Koronaki ◽

A.M. Nikas ◽

A.G. Boudouvis

Keyword(s):

Neural Networks ◽

Artificial Neural Networks ◽

Reduced Order Model ◽

Data Driven ◽

Diffusion Maps ◽

Nonlinear Processes ◽

Order Model ◽

Reduced Order ◽

Artificial Neural

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Two-stage data-driven homogenization for nonlinear solids using a reduced order model

European Journal of Mechanics - A/Solids ◽

10.1016/j.euromechsol.2017.11.007 ◽

2018 ◽

Vol 69 ◽

pp. 201-220 ◽

Cited By ~ 22

Author(s):

Felix Fritzen ◽

Oliver Kunc

Keyword(s):

Reduced Order Model ◽

Data Driven ◽

Order Model ◽

Two Stage ◽

Reduced Order ◽

Nonlinear Solids

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Data-driven Reduced Order Model for prediction of wind turbine wakes

Journal of Physics Conference Series ◽

10.1088/1742-6596/625/1/012009 ◽

2015 ◽

Vol 625 ◽

pp. 012009 ◽

Cited By ~ 17

Author(s):

G V Iungo ◽

C Santoni-Ortiz ◽

M Abkar ◽

F Porté-Agel ◽

M A Rotea ◽

...

Keyword(s):

Wind Turbine ◽

Reduced Order Model ◽

Data Driven ◽

Order Model ◽

Reduced Order

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Reduced Order Model for Unsteady Fluid Flows via Recurrent Neural Networks

Volume 2: CFD and FSI ◽

10.1115/omae2019-96543 ◽

2019 ◽

Author(s):

Sandeep B. Reddy ◽

Allan Ross Magee ◽

Rajeev K. Jaiman ◽

J. Liu ◽

W. Xu ◽

...

Keyword(s):

Neural Networks ◽

Reynolds Number ◽

Flow Field ◽

Unsteady Flow ◽

Recurrent Neural Networks ◽

Reduced Order Model ◽

Data Driven ◽

Order Model ◽

Reduced Order ◽

Low Dimensional

Abstract In this paper, we present a data-driven approach to construct a reduced-order model (ROM) for the unsteady flow field and fluid-structure interaction. This proposed approach relies on (i) a projection of the high-dimensional data from the Navier-Stokes equations to a low-dimensional subspace using the proper orthogonal decomposition (POD) and (ii) integration of the low-dimensional model with the recurrent neural networks. For the hybrid ROM formulation, we consider long short term memory networks with encoder-decoder architecture, which is a special variant of recurrent neural networks. The mathematical structure of recurrent neural networks embodies a non-linear state space form of the underlying dynamical behavior. This particular attribute of an RNN makes it suitable for non-linear unsteady flow problems. In the proposed hybrid RNN method, the spatial and temporal features of the unsteady flow system are captured separately. Time-invariant modes obtained by low-order projection embodies the spatial features of the flow field, while the temporal behavior of the corresponding modal coefficients is learned via recurrent neural networks. The effectiveness of the proposed method is first demonstrated on a canonical problem of flow past a cylinder at low Reynolds number. With regard to a practical marine/offshore engineering demonstration, we have applied and examined the reliability of the proposed data-driven framework for the predictions of vortex-induced vibrations of a flexible offshore riser at high Reynolds number.

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Data-driven construction of a reduced-order model for supersonic boundary layer transition

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.470 ◽

2019 ◽

Vol 874 ◽

pp. 1096-1114 ◽

Cited By ~ 5

Author(s):

Ming Yu ◽

Wei-Xi Huang ◽

Chun-Xiao Xu

Keyword(s):

Compressible Flows ◽

Incompressible Flows ◽

Temporal Evolution ◽

Reduced Order Model ◽

Boundary Layer Transition ◽

Galerkin Projection ◽

Data Driven ◽

Dynamic Mode ◽

Order Model ◽

Reduced Order

In this study, a data-driven method for the construction of a reduced-order model (ROM) for complex flows is proposed. The method uses the proper orthogonal decomposition (POD) modes as the orthogonal basis and the dynamic mode decomposition method to obtain linear equations for the temporal evolution coefficients of the modes. This method eliminates the need for the governing equations of the flows involved, and therefore saves the effort of deriving the projected equations and proving their consistency, convergence and stability, as required by the conventional Galerkin projection method, which has been successfully applied to incompressible flows but is hard to extend to compressible flows. Using a sparsity-promoting algorithm, the dimensionality of the ROM is further reduced to a minimum. The ROMs of the natural and bypass transitions of supersonic boundary layers at $Ma=2.25$ are constructed by the proposed data-driven method. The temporal evolution of the POD modes shows good agreement with that obtained by direct numerical simulations in both cases.

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