Proper orthogonal decomposition-based spectral higher-order stochastic estimation

Baars, W and Tinney, C 2014, 'Proper orthogonal decomposition-based spectral higher-order stochastic estimation', Physics of Fluids, vol. 26, no. 5, pp. 1-21.

Document type: Journal Article
Collection: Journal Articles

Title Proper orthogonal decomposition-based spectral higher-order stochastic estimation
Author(s) Baars, W
Tinney, C
Year 2014
Journal name Physics of Fluids
Volume number 26
Issue number 5
Start page 1
End page 21
Total pages 21
Publisher A I P Publishing LLC
Abstract A unique routine, capable of identifying both linear and higher-order coherence in multiple-input/output systems, is presented. The technique combines two wellestablished 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 PODcoefficients 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.
Subject Aerodynamics (excl. Hypersonic Aerodynamics)
DOI - identifier 10.1063/1.4879255
Copyright notice © 2014 AIP Publishing LLC.
ISSN 1070-6631
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