A new discrete impulse response Gramian and its application to model reduction

Azou, Stéphane; Brehonnet, P.; Vilbe, P.; Calvez, L.C.

doi:10.1109/9.847738

Cited by 7 publications

(11 citation statements)

References 17 publications

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“…To illustrate the method two examples are presented. First, we have considered the seventh-order transfer function of a supersonic jet engine inlet [37][38] ( ) The value 24 . 0 = λ for the Laguerre parameter has been obtained using the suboptimal method described in [27,30].…”

Section: Examplesmentioning

confidence: 99%

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A simple algorithm for stable order reduction of z-domain Laguerre models

et al. 2013

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Section: Examplesmentioning

confidence: 99%

“…Response Gramian (GIRG5 see [38]) and Laguerre-SVD (LSVD5 see [40]). The latter was implemented using the same Laguerre parameter as LG5 ( 24 .…”

Section: Examplesmentioning

confidence: 99%

A simple algorithm for stable order reduction of z-domain Laguerre models

et al. 2013

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“…In model reduction of discrete-time systems, impulse response Gramians are very important, and they can be used to derive the reduced-order model. In [13] and [1], the concepts of weighted and generalized impulse response Gramians were respectively proposed, and it was shown that these Gramians can be obtained by solving the corresponding discrete Lyapunov matrix equations. In addition, the discrete Lyapunov matrix equation can also be used to analyze the stability of periodic discrete-time systems [12].…”

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confidence: 99%

Parametric Smith iterative algorithms for discrete Lyapunov matrix equations

Wu¹,

Zhang²,

Sun³

2020

Journal of Industrial &Amp; Management Optimization

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An iterative algorithm is established in this paper for solving the discrete Lyapunov matrix equations. The proposed algorithm contains a tunable parameter, and includes the Smith iteration as a special case, and thus is called the parametric Smith iterative algorithm. Some convergence conditions are developed for the proposed parametric Smith iterative algorithm. Moreover, the optimal parameter for the proposed algorithm to have the fastest convergence rate is also provided for a special case. Finally, numerical examples are employed to illustrate the effectiveness of the proposed algorithm.

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“…modeling turbomachinery, supersonic flows in jet engine inlets [4], [9], [37], [49], [115]- [117], efficient modeling of biological systems [50], [51], [120], rapid thermal processing [2], problems in chemical [61] or mechanical [59] engineering.…”

Section: Motivationmentioning

confidence: 99%

“…Due to this fast growing complexity, applicability of TBR methods for large-scale systems is limited. In order to overcome this difficulty methods based on approximate Grammian computation have been developed [4], [10], [64], [65], [71], [87], [99], [105], [121].…”

Section: Previous Work On Model Order Reductionmentioning

confidence: 99%

Nonlinear Dynamical Systems

Diks¹

1999

Nonlinear Time Series Analysis

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In this study we discuss the problem of Model Order Reduction (MOR) for a class of nonlinear dynamical systems. In particular, we consider reduction schemes based on projection of the original state-space to a lower-dimensional space e.g. by using Krylov methods. In the nonlinear case, however, applying a projection-based MOR scheme does not immediately yield computationally efficient macromodels. In order to overcome this fundamental problem, we propose to first approximate the original nonlinear system with a weighted combination of a small set of linearized models of this system, and then reduce each of the models with an appropriate projection method. The linearized models are generated about a state trajectory of the nonlinear system corresponding to a certain 'training' input.As demonstrated by results of numerical tests, the obtained trajectory quasi-piecewise-linear reduced order models are very cost-efficient, while providing superior accuracy as compared to existing MOR schemes, based on single-state Taylor's expansions. In this dissertation, the proposed MOR approach is tested for a number of examples of nonlinear dynamical systems, including micromachined devices, analog circuits (discrete transmission line models, operational amplifiers), and fluid flow problems. The tests validate the extracted models and indicate that the proposed approach can be effectively used to obtain system-level models for strongly nonlinear devices.This dissertation also shows an inexpensive method of generating trajectory piecewise-linear (TPWL) models based on constructing the reduced models 'on-the-fly', which accelerates simulation of the system response. Moreover, we propose a procedure for estimating simulation errors, which can be used to determine accuracy of the extracted trajectory piecewise-linear reduced order models. Finally, we present projection schemes which result in improved accuracy of the reduced order TPWL models, as well as discuss approaches leading to guaranteed stable and passive TPWL reduced-order models. AcknowledgmentsFirst, I would like to thank Professor Jacob White, my advisor for the last four years, for introducing me to the world of nonlinear simulation and modeling. Learning from him, especially learning how to ask the right questions, has proved an invaluable experience. His guidance and encouragement made this work possible.I am also very grateful to my thesis committee members, Professors Karen Willcox and Alexandre Megretski for the numerous, fruitful, and often very animated discussions on nonlinear dynamical systems and model order reduction, which substantially deepened my understanding of this problem and its challenges, and their important suggestions which contributed to improving and broadening this dissertation.I would like to thank Luca Daniel and Prof. John Wyatt for interesting discussions on passivity preservation for nonlinear reduced order models, as well as Prof. Jaime Peraire, Prof. Steven Senturia, and Dr. Joel Phillips from Cadence, for their valuable commen...

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A new discrete impulse response Gramian and its application to model reduction

Cited by 7 publications

References 17 publications

A simple algorithm for stable order reduction of z-domain Laguerre models

A simple algorithm for stable order reduction of z-domain Laguerre models

Parametric Smith iterative algorithms for discrete Lyapunov matrix equations

Nonlinear Dynamical Systems

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