&lt;title&gt;Applications of sampling theorems in wavelet spaces to multiresolution visualization and data segmentation&lt;/title&gt;

Wavelet analysisfor ltering and system identi cation is used to improve the estimation of aeroservoelastic (ASE) stability margins.Computationof robust stability margins for stability boundaryprediction depends on uncertainty descriptions derived from the test data for model validation. Nonideal test conditions, data acquisition errors, and signal processing algorithms cause uncertainty descriptions to be intrinsically conservative. The conservatism of the robust stability margins is reduced with parametric and nonparametric time-frequency analysis of ight data in the model validation process. Nonparametric wavelet processing of data is used to reduce the effects of external disturbances and unmodeled dynamics. Parametric estimates of modal stability are also extracted using the wavelet transform. F-18 High Alpha Research Vehicle ASE ight test data are used to demonstrate improved robust stability prediction by extension of the stability boundary from within the ight envelope to conditions suf cently beyond the actual ight regime. Stability within the ight envelope is con rmed by ight test. Practical aspects and guidelines for ef ciency of these procedures are presented for on-line implementation. Nomenclature a, a i = wavelet scale, indexed scale values (dimensionless) F.P; 1/ = feedback interconnection structure g = wavelet basis function K = feedback control system P.s/; O P.s/ = Laplace transform of system plant, estimate W add ; W in ; W ns = weightings on 1 add , 1 in , noise W g = continuous wavelet transform with basis g X .¿; !/; O X.¿; !/ = wavelet-transformed signal, ltered signal X .!/; O X .!/ = frequency-domain signal, estimate x.t /; O x.t / = time-domain signal, ltered signal 0 = robust stability margin 1; O 1 = uncertainty operator, estimate ± N q = uncertainty in ight condition = damping ratio ¹ = structured singular value ¿ = wavelet translation time Á.t /; Á 0 = signal phase, constant phase lag ! d ; ! n = modal damped and natural frequency ! 0 = wavelet peak frequency

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“…10 frequency bands. 19 Nonorthonormal Morlet wavelets are approximated with (harmonic-like) discretizations on multiple-wavelet scales.…”

Section: A Nonparametric Estimation: Wavelet Filteringmentioning

confidence: 98%

Wavelet-Processed Flight Data for Robust Aeroservoelastic Stability Margins

Brenner

Lind

1998

Journal of Guidance, Control, and Dynamics

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“…These wavelets form a non-orthogonal redundant basis for the signal space [16]. Adjustment to satisfy the competing requirements of time and frequency resolution is accomplished with a combination of compact orthogonal and harmonic wavelet properties [17,18].…”

Section: Time-frequency Wavelet Decompositionmentioning

confidence: 99%

Non-Stationary Dynamics Data Analysis With Wavelet-SVD Filtering

Brenner¹

2003

Mechanical Systems and Signal Processing

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“…Real parameters 1H contributing to roll rate are the other perturbations important in the instability mechanism, as seen from the row and scatter of points plotted at the bottom. There are no critical real perturbations in the yaw rate (indices [14][15][16][17][18][19][20][21][22][23][24][25] or lateral acceleration (indices 26-37) loops.…”

Section: Aeroservoelastic Flight Data Analysismentioning

confidence: 99%

“…24 Competing requirements of time and frequency resolution, subject to the uncertainty principle, 23 is accomplished with a combination of dyadic multiscale decomposition, compact orthogonality,and harmonic wavelet properties. 25 Parameter estimates are derived from time-frequency representations using Morlet wavelet ltering (see Refs. 15 and 16).…”

Section: Wavelet Filtering and Modal Identi Cationmentioning

confidence: 99%

Aeroservoelastic Model Uncertainty Bound Estimation from Flight Data

Brenner

2002

Journal of Guidance, Control, and Dynamics

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Uncertainty modeling is a critical element in the estimation of robust stability margins for stability boundary prediction and robust ight control system development. There has been a serious de ciency to date in aeroservoelastic data analysis with attention to uncertainty modeling. Uncertainty can be estimated from ight data using both parametric and nonparametric identi cation techniques. The model validation problem addressed here is to identify aeroservoelastic models with associated uncertainty structures from a limited amount of controlled excitation inputs over an extensive ight envelope. The challenge is to update analytical models from ight data estimates while also deriving nonconservative uncertainty descriptions consistent with the ight data. Transfer function estimates are incorporated in a robust minimax estimation scheme to update models and get error bounds consistent with the data and model structure. Uncertainty estimates derived from the data in this manner provide an appropriate and relevant representation for model development and robust stability analysis. The method incorporates parametric and nonparamteric uncertainty into various uncertainty structures for quantitative measures of robust stability relating to parameter variations and unmodeled dynamics. This model-plus-uncertainty identi cation procedure is applied to aeroservoelastic ight data from the NASA Dryden Flight ResearchCenter F-18 Systems Research Aircraft. Nomenclature f A; B; C; Dg = plant state-space matrices f O A; O B; O C ; O Dg = estimated plant state-space matrices K = controller P = aeroservoelasticplant O P = updated aeroservoelasticplant T = complementary sensitivity function W = uncertainty weightings y = output frequency response vector 1C = uncertainty in C matrix 1H = uncertainty in model-multiplier parameter vector 1 a = complex additive uncertainty 1 i = complex input-multiplicativeuncertainty 1 o = complex output-multiplicativeuncertainty 1 r = real output-multiplicativeuncertainty 1 r o = mixed output-multiplicativeuncertainty ² = minimum upper bound of " " = frequency-dependentadditive uncertainty H = model-multiplier parameter vector O H = estimated model-multiplier parameter vector ¹ = structured singular value U = matrix of modal frequency responses Á = model frequency response vector

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<title>Applications of sampling theorems in wavelet spaces to multiresolution visualization and data segmentation</title>

Cited by 5 publications

References 0 publications

Wavelet-Processed Flight Data for Robust Aeroservoelastic Stability Margins

Wavelet-Processed Flight Data for Robust Aeroservoelastic Stability Margins

Non-Stationary Dynamics Data Analysis With Wavelet-SVD Filtering

Aeroservoelastic Model Uncertainty Bound Estimation from Flight Data

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