Modal Reduction Based on Accurate Input-Output Relation Preservation

Vakilzadeh, Majid Khorsand; Rahrovani, Sadegh; Abrahamsson, Thomas

doi:10.1007/978-1-4614-6585-0_31

Cited by 6 publications

(6 citation statements)

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“…Vakilzadeh et al [8] also proposed to utilize the QR factorization to functionally improve the performance of the dominancy analysis method in case of equal or closely spaced eigenvalues. Toward this end, let the modally projected input matrix corresponding to the subsystem associated to a given eigenvalue j of multiplicity n m , b B j 2 R n m n u , where n m n u , be factorized into a unitary matrix Q 2 R n m n m whose columns are orthonormal and an upper triangular matrix R 2 R n m n u as follows…”

Section: Modal Truncationmentioning

confidence: 98%

“…Fortunately, these integrals can be expressed in explicit form [8]. Consequently, the truncation error resulted from elimination of the ith modal coordinates in the H 2 sense is defined as…”

Section: Modal Truncationmentioning

confidence: 99%

“…It is, hence, of central importance to develop an appropriate measure to include a combination of the most dominant eigenmodes in the projection basis. In this paper, the modal dominancy criterion developed by Vakilzadeh et al [8] is considered as an appropriate input-output measure.…”

Section: Modal Truncationmentioning

confidence: 99%

“…This section presents a complete summary of the modal based model reduction technique proposed in [8] to govern an approximant which contains the dominant eigensolutions of the original system, (1) Given the state-space matrix A, compute its eigensolution (˚, ). …”

Section: Improved Modal Truncation Algorithmmentioning

confidence: 99%

“…Our main goal is to show that the calibrated beam model cannot capture all the couplings found in the baseline model which in turn results in low prediction accuracy. To this end, a second simplified model is developed by applying a recent model reduction algorithm [8]. Within this algorithm, the baseline model is projected to a smaller subspace using a projection matrix that includes the most dominant eigensolutions.…”

Section: Introductionmentioning

confidence: 99%

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Development of Simplified Models for Wind Turbine Blades with Application to NREL 5 MW Offshore Research Wind Turbine

Vakilzadeh

Johansson

Lindholm³

et al. 2014

Dynamics of Coupled Structures, Volume 1

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Integration of complex models of wind turbine blades in aeroelastic simulations places an untenable demand on computational resources and, hence, means of speed-up become necessary. This paper considers the process of producing simplified rotor blade models which accurately approximate the dynamics of interest. The novelty, besides applying an efficient model updating procedure to the wind turbine blade, is to challenge the conventional beam element formulation utilized in the majority of aeroelastic codes. First, a 61.5 m blade, previously reported by the National Renewable Energy Laboratory, is selected as a case study and a verified industry-standard three dimensional shell model is developed based on its actual geometry. Next, given the reported spanwise cross sectional properties of the blade, a calibrated beam model is developed, using an efficient model updating process, that shows an excellent agreement to the low frequency dynamics of the baseline model in terms of mode shapes, resonance frequency and frequency response function. The simulation study provides evidence that a beam model cannot capture all the important features found in a large-scale 3D blade. This motivates a departure from conventional beam element formulation and suggests addressing the problem of producing simplified models in the framework of model reduction techniques. A modified modal truncation algorithm is applied to the baseline model to produce a simpler model which accurately approximates its input-output behavior in a given frequency range. It is concluded that besides the computational efficiency of the reduction algorithm, the resulting approximation error is guaranteed to be bounded and the yielded low-order model can, in turn, be served in wind turbine design codes. Keywords Model calibration • Model reduction • Wind turbine blade • Frequency response calibration • Beam modeling IntroductionWind energy as one of the most promising sources of renewable energy is going to provide 7-8 % of the demanded world's electricity power by 2020. However, for wind energy to meet such an impressive rate of growth, future wind turbines must be designed for maximum energy conversion efficiency. In response to this demand, the size of wind turbine blades has dramatically increased within the last few years and it is predicted that the wind turbines installed within the next 10-15 years will have rotor diameter of 180-200 m [1]. To design for future wind turbine blades, development of models will become more and more crucial to performing entire wind turbine simulations by using aeroelastic modeling tools and with the purpose of aerodynamic load estimation, reliability analysis and so forth. While coupling high fidelity large scale three dimensional Finite Element (FE) blade models in such aeroelastic settings results in more accurate prediction of performance, it also poses overwhelming demands on computational resources making the development of simplified engineering models become more and more necessary. For this reason, the pr...

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Section: Modal Truncationmentioning

confidence: 98%

Section: Modal Truncationmentioning

confidence: 99%

Section: Modal Truncationmentioning

confidence: 99%

Section: Improved Modal Truncation Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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