Least squares model reduction

Lalonde, R.J.; Hartley, Tom T.; Abreu-Garcı́a, J.A. De

doi:10.1016/0016-0032(92)90030-k

Cited by 22 publications

(4 citation statements)

References 3 publications

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“…The topic of model reduction has been studied for many years now, and many methods have been suggested for obtaining suitable low-order approximations [1][2][3][4]. Most of the techniques in the literature take into account a criterion for the 'goodness' of the reduced model [1,4].…”

Section: Introductionmentioning

confidence: 99%

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Physical parameter sensitivity of system eigenvalues and physical model reduction

Orbak

Eşkinat

Türkay

2004

Journal of the Franklin Institute

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Section: Introductionmentioning

confidence: 99%

“…Most of the techniques in the literature take into account a criterion for the 'goodness' of the reduced model [1,4]. For example, the balancing approach of Moore [1] uses coordinate transformations to convert the system to a special balanced form from which a reduced model can be obtained.…”

Section: Introductionmentioning

confidence: 99%

Physical parameter sensitivity of system eigenvalues and physical model reduction

Orbak

Eşkinat

Türkay

2004

Journal of the Franklin Institute

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“…Bistritz (1982) gave a direct Routh stability method that avoids the bilinear transformation and inherits the favourable feature of stability preservation. Lalonde et al (1992) analysed the idea of least square parameter matching in discrete-time systems. Smith and Lucas (1998) solved the non-uniqueness property of the least-squares Padé method and also discussed it in relation to the reduced model’s stability.…”

Section: Introductionmentioning

confidence: 99%

Optimal least squares model approximation for large-scale linear discrete-time systems

Vasu¹,

Kumar²,

Ramalingaraju

2016

Transactions of the Institute of Measurement and Control

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A new computationally simple and precise model approximation method is described for large-scale linear discrete-time systems. By least squares matching of a suitable number of time moment proportionals and Markov parameters about [Formula: see text] of the original higher order system within the approximate model, stable denominator polynomial coefficients of the approximate model are determined. To improvise the accuracy of the approximate model, numerator polynomial coefficients are determined by minimizing the integral squared error (ISE) between the unit impulse responses of the original system and its approximate model. A matrix formula is formulated for evaluating numerator coefficients of the approximate model that leads to minimum ISE, and also for evaluating ISE. The efficacy of the proposed method is shown by illustrating three typical numerical examples employed from the literature, and the results are compared with many familiar reduction methods in terms of the ISE and relative ISE values pertaining to impulse input. Furthermore, time and frequency responses of the original system and the respective approximate model are plotted.

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“…Several time and frequency domain methods exist that generally provide good approximations. Some of the well-known time domain methods are the approximate moment matching method [2], which utilizes the elimination of some time moments with the employment of a singular-value decomposition approximation, and the least-squares model reduction method [3], which uses the power of curve-tting by calculating a low-order autoregressive moving average (ARMA) predictor equation. A number of the principal frequency domain methods are the following: the component cost analysis for model reduction [4], which uses a quadratic cost measure for eliminating the modes, Padé approximations [5] and continued fraction methods [6 ], which employ the continued fraction expansion and inversion processes with a generalized matrix Routh algorithm to expand a matrix transfer function into the matrix continued fraction of matrix Cauer forms.…”

Section: Introductionmentioning

confidence: 99%

Model reduction in the physical domain

Orbak

Türkay

Eşkinat

2003

Proceedings of the Institution of Mechanical Engineers, Part I:

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This paper is concerned with obtaining physical-based low-order approximations of linear physical systems. Low-order models possess some advantages, including the reduction of computational di culty and understanding of the physics of the original system in a simpler manner. Previously, a number of methods have been suggested to develop suitable low-order approximations. However, most of these approaches do not re ect the relation between the mathematical model and the physical subsystems. Speci cally, these techniques do not indicate which of the physical subsystems should be retained or eliminated in the reduced-order model. The proposed model reduction method is based on identifying subsystem types of a physical system using the bond graph method. These subsystems are then removed or retained based on the information from the physical system decomposition procedures and partial fraction expansion residues to obtain a reduced-order model. The physical model reduction procedure is veri ed on physical linear systems.

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Least squares model reduction

Cited by 22 publications

References 3 publications

Physical parameter sensitivity of system eigenvalues and physical model reduction

Physical parameter sensitivity of system eigenvalues and physical model reduction

Optimal least squares model approximation for large-scale linear discrete-time systems

Model reduction in the physical domain

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