AIAA Journal · 1998 · 130 citations · 8 references
Numerical AnalysisMethod Of Fundamental SolutionReduced Order ModelingFrequency-domain Karhunen-loeve MethodLinear SystemsEngineeringNumerical ComputationMechanical SystemsSpectral AnalysisReduced Order AerodynamicsSystems EngineeringDynamic AnalysisThekarhunen ‐LoeveKl EigenmodesSystem IdentificationVibration ControlBoundary Element MethodNumerical Method For Partial Differential Equation
The paper discusses selecting system responses to enable efficient KL mode calculation and to build reduced‑order models using KL eigenmodes. The authors derive a frequency‑domain KL method by formulating a variational problem on the discrete Fourier transform of a probe‑energy time average, yielding an eigenvalue problem that is applied to both mechanical and fluid dynamic models. The frequency‑domain KL procedure successfully computes eigenmodes of linear systems and can extract eigenmodes from experimental data. Nomenclature: c = wing chord length, F = snapshot matrix, (13) F = Fourier operator, GIk = impulse response for the kth input, GSk = step response for the kth input.
Forthee rsttime,theKarhunen ‐Loeve(KL)procedureisderivedinthefrequencydomainasatoolforcalculating eigenmodes of linear systems. The new derivation is based on the discrete Fourier transform representation of a time average of proe le energy including a proper system response and a proe le function. Taking the variational problem posed as such with respect to the proe le function leads to an eigenformulation in the frequency domain. Choice of a system response for efe cient KL mode calculation and construction of reduced-order systems using the KL eigenmodes are also discussed. To demonstrate themethod, both mechanical and e uid dynamic models are considered. The method is equally useful in extracting eigenmodes of an experimentally generated database. Nomenclature c = wing chord length F = snapshot matrix as dee ned in Eq. (13) F = Fourier operator GIk = impulse response for the kth input GSk = step response for the kth input i
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