Data-Driven Modeling of Linear Dynamical Systems with Quadratic Output in the AAA Framework

Gosea, Ion Victor; Gugercin, Serkan

doi:10.1007/s10915-022-01771-5

Cited by 6 publications

(5 citation statements)

References 63 publications

(154 reference statements)

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“…In essence, if the damping matrix 𝐺 is defined via proportional damping with coefficients 𝛼 and 𝛽 as in Equation ( 7)), then Ref. [33] proposes choosing 𝑠 0 = √ 𝛼 𝛽 (14) as the interpolation point given an exact condenser distribution. In this case, as opposed to choosing multiple interpolation points and imposing the interpolation as in Equations (10,11) up to the first derivative, one chooses the single interpolation 𝑠 0 and matches 𝐻(𝑠) and its first 𝑟 − 1 derivatives at 𝑠 = 𝑠 0 .…”

Section: A Interpolation Point Selection Based On Exact Condenser Dis...mentioning

confidence: 99%

“…Some of the projection-based techniques mentioned above (and employed in this paper) have been extended to the structured models we consider here; see, e.g., Ref. [14][15][16][17][18][19] and the references therein for some of the data-driven approaches to structured dynamics. However, this is not our focus in this paper and these considerations are left to future work.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Application of Interpolatory Methods of Model Reduction to an Elevated Railway Pier

Bertero¹,

Gugercin²,

Sarlo³

2023

Proceedings of the 21th LACCEI International Multi-Conference for Engineering, Education and Technology (LACCEI 2023): “Leaders

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Be it due to time constraints or insufficient processing power -or a combination of both -the use of models with large numbers of degrees of freedom (DoF) may be unsuitable to provide a client with results in a timely manner. The use of physics-based reduced models -or proxy structures -are popular among practitioners to solve this issue, as they keep intact all the underlying properties of the second order problems at a fraction of the cost. In this paper, interpolatory methods of model reduction are explored as an alternative, and applied to a 3D Space Frame. The methods chosen allow for structure-preserving reduced models and differ mainly on the selection of interpolation points. A comparison between the response of these reduced models and a proxy structure against two different types of inputs show that interpolatory methods are a viable, more flexible option when it comes to reducing the internal DoF's of a structural model, though engineering judgement helps to ensure it adequately captures the most relevant aspects of the response for the specific application.

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Section: A Interpolation Point Selection Based On Exact Condenser Dis...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Application of Interpolatory Methods of Model Reduction to an Elevated Railway Pier

Bertero¹,

Gugercin²,

Sarlo³

2023

Proceedings of the 21th LACCEI International Multi-Conference for Engineering, Education and Technology (LACCEI 2023): “Leaders

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show abstract

“…Therefore, ERA is applicable to experiments and systems with full-state output. More recently, Gosea et al [52] extended this method for non-intrusive balancing transformation of continuous-time systems. Tu et al [53] showed that the linear operator obtained by ERA is related to the linear operator in dynamic mode decomposition (DMD) via a similarity transform.…”

Section: Introductionmentioning

confidence: 99%

Non-intrusive balancing transformation of highly stiff systems with lightly damped impulse response

Rezaian

Huang

Duraisamy

2022

Phil. Trans. R. Soc. A.

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Balanced truncation (BT) is a model reduction method that uses a coordinate transformation to retain eigen-directions that are highly observable and reachable. To address realizability and scalability of BT applied to highly stiff and lightly damped systems, a non-intrusive data-driven method is developed for balancing discrete-time linear systems via the eigensystem realization algorithm (ERA). The advantage of ERA for balancing transformation makes full-state outputs tractable. Further, ERA enables balancing despite stiffness, by eliminating computation of balancing modes and adjoint simulations. As a demonstrative example, we create balanced reduced-order models (ROMs) for a one-dimensional reactive flow with pressure forcing, where the stiffness introduced by the chemical source term is extreme (condition number 10 13 ), preventing analytical implementation of BT. We investigate the performance of ROMs in prediction of dynamics with unseen forcing inputs and demonstrate stability and accuracy of balanced ROMs in truly predictive scenarios, whereas without ERA, proper orthogonal decomposition-Galerkin and least-squares Petrov–Galerkin projections fail to represent the true dynamics. We show that after the initial transients under unit impulse forcing, the system undergoes lightly damped oscillations, which magnifies the influence of sampling properties on predictive performance of the balanced ROMs. We propose an output domain decomposition approach and couple it with tangential interpolation to resolve sharp gradients at reduced computational costs. This article is part of the theme issue ‘Data-driven prediction in dynamical systems’.

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“…The original formulation of the Loewner framework only considers the construction of unstructured systems (3), but it has been extended to find structured realizations in [44]. Recently, structured extensions of the barycentric form for second-order systems (4) have been proposed that allow the extension of further data-driven frequency domain methods to the structure-preserving setting [28,50].…”

Section: Introductionmentioning

confidence: 99%

Predicting near optimal interpolation points for parametric model order reduction using regression models

Aumann

Müller

2021

Proc Appl Math and Mech

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The design of vibro-acoustic systems, such as vehicle interiors, regarding optimal vibrational or sound radiation properties requires the solution of many numerical models under varying parameters, as often material or geometric uncertainties have to be considered. Vibro-acoustic systems are typically large and numerically expensive to solve, so it is desirable to use an efficient parametrized surrogate model for optimization tasks. High quality reduced models of non-parametric systems can be computed by projection, given a set of optimal expansion points. However, finding a set of optimal expansion points can be computationally expensive and each set is valid for a specific parameter realization only. The method presented in this contribution learns the map between a model's parameter realizations and the corresponding sets of expansion points using data-driven methods. Queried with an unknown set of parameters, the learned model returns a set of expansion points which are used to compute the corresponding reduced model efficiently. Numerical experiments on two vibro-acoustic models of different complexity are performed and three data driven regression methods are evaluated: multivariate polynomial regression, k-nearest neighbors, and support vector regression. Especially k-nearest neighbors regression yields accurate results for different types of physical models while being computationally inexpensive to fit.

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Data-Driven Modeling of Linear Dynamical Systems with Quadratic Output in the AAA Framework

Cited by 6 publications

References 63 publications

Application of Interpolatory Methods of Model Reduction to an Elevated Railway Pier

Application of Interpolatory Methods of Model Reduction to an Elevated Railway Pier

Non-intrusive balancing transformation of highly stiff systems with lightly damped impulse response

Predicting near optimal interpolation points for parametric model order reduction using regression models

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