A Data Compression Approach for PGD Reduced-Order Modeling

2012 ◽  
Author(s):  
David Néron ◽  
Pierre Ladevèze
Keyword(s):  
A Priori ◽  
Global Strategy ◽  
Reduction Technique ◽  
Reduced Order Models ◽  
Proper Generalized Decomposition ◽  
Space Domain ◽  
Reduced Order ◽  
Time Space ◽  
Algebraic Framework ◽  
Model Reduction Technique

This work concerns the Proper Generalized Decomposition (PGD) which is used to solve problems defined over the time-space domain and which are possibly nonlinear. The PGD is an a priori model reduction technique which allows to decrease CPU costs drastically by seeking the solution of a problem in a reduced-order basis generated automatically by a dedicated algorithm. The algorithm which is used herein is the LATIN method, a non incremental iterative strategy which enables to generate the approximations of the solution over the entire time-space domain by successive enrichments. The problematics which is addressed in this paper is the construction of the resulting reduced-order models along the iterations, which can represent a large part of the remaining global CPU cost. To make easier the construction of these models, we propose an algebraic framework adapted to PGD which allows to define a “compressed” version of the data. The space of the compressed fields exhibits some very interesting properties that lead to an important increase of the performances of the global strategy.

scholarly journals Thermomechanical Model Reduction for Efficient Simulations of Rotor-Stator Contact Interaction

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Nicolas Guérin ◽  
Anders Thorin ◽  
Fabrice Thouverez ◽  
Mathias Legrand ◽  
Patricio Almeida
Keyword(s):  
Krylov Subspace ◽  
Frictional Contact ◽  
Recent Literature ◽  
Unilateral Contact ◽  
Reduction Technique ◽  
Thermomechanical Coupling ◽  
Reduced Order Models ◽  
Thermomechanical Model ◽  
Reduced Order ◽  
Prediction Tools

Turbomachinery rotor–stator unilateral contact induced interactions play a growing role in lifecycle analysis and thus motivate the use of accurate numerical prediction tools. Recent literature confirmed by ongoing in-house experiments have shown the importance of thermomechanical coupling effects in such interactions. However, most available (possibly reduced-order) models are restricted to the sole mechanical aspects. This work describes a reduction technique of thermomechanical models involving unilateral contact and frictional contact occurrences between rotor and stator components. The proposed methodology is grounded on Guyan and Craig–Bampton methods for the reduction of the structural dynamics in conjunction with Krylov subspace techniques, and specifically the Craig–Hale approach, for the reduction of the thermal equations. The method has the capability to drastically reduce the size of the model while preserving accuracy. It stands as a reliable strategy to perform simulations of thermomechanical models with localized mechanical and thermal loads.

scholarly journals New Results On Partial Fraction Based Frequency Weighted Balanced Truncation Technique For Discrete–Time System

2012 ◽  
Author(s):  
Shafishuhaza Sahlan ◽  
Victor Sreeram
Keyword(s):  
Discrete Time ◽  
A Priori ◽  
Partial Fraction ◽  
Discrete Time System ◽  
Time System ◽  
Model Order ◽  
Reduced Order ◽  
Partial Fraction Expansion ◽  
Weighted Model ◽  
Model Reduction Technique

Artikel in membentangkan keputusan baru bagi kaedah pengurangan model frekuensi tertimbang berdasarkan kaedah pengembangan fraksi separa didalam masa diskrit. Rangka pengurangan model bagi kaedah baru yang dicadangkan diperolehi melalui pemotongan langsung, menghasilkan kesalahan yang lebih rendah berbanding kaedah–kaedah lain yang sudah ada. Kaedah baru ini dijamin akan stabil bahkan untuk tertimbang bersisi ganda. Sebuah batas kesalahan a priori yang mudah dan senang dihitung juga diperoleh. Contoh berangka dengan perbandingan dengan teknik yang ada menunjukkan keberkesanan kaedah yang dicadangkan Kata kunci: Rangka pengurangan model; batas kesalahan; kaedah pengembangan fraksi spara In this paper, we present some new results on frequency weighted model reduction technique based on partial fraction expansion idea in discrete–time system. The reduced order models of the newly proposed method obtained by direct truncation, produces lower errors when compared to existing techniques. The new method is guaranteed to be stable even for double sided weightings. A simple and easily computable a priori error bound is also derived. Numerical examples with comparisons to the existing techniques show the effectiveness of the proposed method. Key words: Model order reductions; error bounds; partial fraction expansion

scholarly journals Thermomechanical Model Reduction for Efficient Simulations of Rotor-Stator Contact Interaction

2018 ◽  
Author(s):  
Nicolas Guérin ◽  
Anders Thorin ◽  
Fabrice Thouverez ◽  
Mathias Legrand ◽  
Patricio Almeida
Keyword(s):  
Krylov Subspace ◽  
Frictional Contact ◽  
Recent Literature ◽  
Unilateral Contact ◽  
Reduction Technique ◽  
Thermomechanical Coupling ◽  
Reduced Order Models ◽  
Thermomechanical Model ◽  
Reduced Order ◽  
Prediction Tools

Turbomachinery rotor-stator unilateral contact induced interactions play a growing role in lifecycle analysis and thus motivate the use of accurate numerical prediction tools. Recent literature confirmed by ongoing in-house experiments have shown the importance of thermomechanical coupling effects in such interactions. However, most available (possibly reduced-order) models are restricted to the sole mechanical aspects. This work describes a reduction technique of thermomechanical models involving unilateral contact and frictional contact occurrences between rotor and stator components. The proposed methodology is grounded on Guyan and Craig–Bampton methods for the reduction of the structural dynamics in conjunction with Krylov subspace techniques, and specifically the Craig–Hale approach, for the reduction of the thermal equations. The method has the capability to drastically reduce the size of the model while preserving accuracy. It stands as a reliable strategy to perform simulations of thermomechanical models with localized mechanical and thermal loads.

A Comparison of Two Finite Element Reduction Techniques for Mistuned Bladed Disks

2002 ◽  
Vol 124 (4) ◽  
pp. 942-952 ◽  
Author(s):  
F. Moyroud ◽  
T. Fransson ◽  
G. Jacquet-Richardet
Keyword(s):  
Finite Element ◽  
Reduction Technique ◽  
Mode Shapes ◽  
Reduced Order Models ◽  
Bladed Disks ◽  
Mode Localization ◽  
Reduced Order ◽  
Bladed Disk ◽  
Reduction Techniques ◽  
Modal Reduction

The high performance bladed disks used in today’s turbomachines must meet strict standards in terms of aeroelastic stability and resonant response level. One structural characteristic that can significantly impact on both these areas is that of bladed disk mistuning. To predict the effects of mistuning, computational efficient methods are much needed to make free-vibration and forced-response analyses of full assembly finite element (FE) models feasible in both research and industrial environments. Due to the size and complexity of typical industrial bladed disk models, one must resort to robust and systematic reduction techniques to produce reduced-order models of sufficient accuracy. The objective of this paper is to compare two prevalent reduction methods on representative test rotors, including a modern design industrial shrouded bladed disk, in terms of accuracy (for frequencies and mode shapes), reduction order, computational efficiency, sensitivity to intersector elastic coupling, and ability to capture the phenomenon of mode localization. The first reduction technique employs a modal reduction approach with a modal basis consisting of mode shapes of the tuned bladed disk which can be obtained from a classical cyclic symmetric modal analysis. The second reduction technique uses Craig and Bampton substructure modes. The results show a perfect agreement between the two reduced-order models and the nonreduced finite element model. It is found that the phenomena of mode localization is equally well predicted by the two reduction models. In terms of computational cost, reductions from one to two orders of magnitude are obtained for the industrial bladed disk, with the modal reduction method being the most computationally efficient approach.

Reduced-order models of structures with viscoelastic components

AIAA Journal ◽  
1999 ◽  
Vol 37 ◽  
pp. 1318-1325 ◽  
Author(s):  
Michael I. Friswell ◽  
Daniel J. Inman
Keyword(s):  
Reduced Order Models ◽  
Reduced Order
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