Proper orthogonal decomposition-based spectral higher-order stochastic estimation

A unique routine, capable of identifying both linear and higher-order coherence in multiple-input/output systems, is presented. The technique combines two well-established methods: Proper Orthogonal Decomposition (POD) and Higher-Order Spectra Analysis. The latter of these is based on known methods...

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Bibliographic Details
Published inPhysics of fluids (1994) Vol. 26; no. 5
Main Authors Baars, Woutijn J., Tinney, Charles E.
Format Journal Article
LanguageEnglish
Published Melville American Institute of Physics 01.05.2014
Subjects
Aeroacoustics
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
DEGREES OF FREEDOM
Dimensional analysis
Far fields
Fluid dynamics
INSTABILITY
JETS
KERNELS
MATERIAL BALANCE
NONLINEAR PROBLEMS
Nonlinear systems
Physics
Proper Orthogonal Decomposition
SIMULATION
SPECTRA
STOCHASTIC PROCESSES
VOIDS
WAVE FORMS
WAVE PACKETS
Waveforms
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Summary:A unique routine, capable of identifying both linear and higher-order coherence in multiple-input/output systems, is presented. The technique combines two well-established methods: Proper Orthogonal Decomposition (POD) and Higher-Order Spectra Analysis. The latter of these is based on known methods for characterizing nonlinear systems by way of Volterra series. In that, both linear and higher-order kernels are formed to quantify the spectral (nonlinear) transfer of energy between the system's input and output. This reduces essentially to spectral Linear Stochastic Estimation when only first-order terms are considered, and is therefore presented in the context of stochastic estimation as spectral Higher-Order Stochastic Estimation (HOSE). The trade-off to seeking higher-order transfer kernels is that the increased complexity restricts the analysis to single-input/output systems. Low-dimensional (POD-based) analysis techniques are inserted to alleviate this void as POD coefficients represent the dynamics of the spatial structures (modes) of a multi-degree-of-freedom system. The mathematical framework behind this POD-based HOSE method is first described. The method is then tested in the context of jet aeroacoustics by modeling acoustically efficient large-scale instabilities as combinations of wave packets. The growth, saturation, and decay of these spatially convecting wave packets are shown to couple both linearly and nonlinearly in the near-field to produce waveforms that propagate acoustically to the far-field for different frequency combinations.
ISSN:1070-6631
1089-7666
DOI:10.1063/1.4879255