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Research Papers

Application of Hilbert–Huang Transform With Improved Ensemble Empirical Mode Decomposition in Nonlinear Flight Dynamic Mode Characteristics Estimation

[+] Author and Article Information
S. Abolfazl. Mokhtari

Aerospace Engineering Department,
Amirkabir University,
Hafez Avenue,
Tehran 15875-4413, Iran

Mehdi. Sabzehparvar

Aerospace Engineering Department,
Amirkabir University,
424 Hafez Avenue,
Tehran 15875-4413, Iran
e-mail: sabzeh@aut.ac.ir

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received January 28, 2018; final manuscript received November 8, 2018; published online November 28, 2018. Assoc. Editor: Bogdan I. Epureanu.

J. Comput. Nonlinear Dynam 14(1), 011006 (Nov 28, 2018) (10 pages) Paper No: CND-18-1041; doi: 10.1115/1.4042016 History: Received January 28, 2018; Revised November 08, 2018

Identification of aircraft flight dynamic modes has been implemented by adopting highly nonlinear flight test data. This paper presents a new algorithm for identification of the flight dynamic modes based on Hilbert–Huang transform (HHT) due to its superior potential capabilities in nonlinear and nonstationary signal analysis. Empirical mode decomposition and ensemble empirical mode decomposition (EEMD) are the two common methods that apply the HHT transform for decomposition of the complex signals into instantaneous mode frequencies; however, experimentally, the EMD faces the problem of “mode mixing,” and EEMD faces with the signal precise reconstruction, which leads to imprecise results in the estimation of flight dynamic modes. In order to overcome (handle) this deficiency, an improved EEMD (IEEMD) algorithm for processing of the complex signals that originate from flight data record was introduced. This algorithm disturbing the original signal using white Gaussian noise, IEEMD, is capable of making a precise reconstruction of the original signal. The second improvement is that IEEMD performs signal decomposition with fewer number of iterations and less complexity order rather than EEMD. This algorithm has been applied to aircraft spin maneuvers flight test data. The results show that implication of IEEMD algorithm on the test data obtained more precise signal extractions with fewer iterations in comparison to EEMD method. The signal is reconstructed by summing the flight modes with more accuracy respect to the EEMD. The IEEMD requires a smaller ensemble size, which results in saving of a significant computational cost.

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Figures

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Fig. 1

The IEEMD versus EMD as decomposers and Hilbert spectral analysis versus FME as spectrum analyzers of the Hilbert–Huang transform model

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Fig. 2

Decomposition of a 512-sample long delta function [22] by: (a) EEMD (IMF¯) and (b) IEEMD (IMF̃). Noise standard deviation;ε=0.02. Ensemble size I=500.

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Fig. 3

Spectra of modes from 3 to 7 obtained by: (a) EEMD (IMF¯) and (b) IEEMD (IMF̃)

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Fig. 4

The proposed process for the flight dynamic mode characteristics estimation [16]

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Fig. 5

Spin maneuver flight output [18]: (a) inputs, (b) angle of attack and side slip angle, (c) forces, (d) moments, (e), angular velocity, and (f) body velocity

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Fig. 6

Angle of attack signal and IMFs

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Fig. 7

Longitudinal velocity IMFs

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Fig. 8

Side slip angle signal and IMFs

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Fig. 9

Roll angular velocity signal and IMFs

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Fig. 10

Flight dynamic modes' instantons frequencies (a) angle of attack and longitudinal velocity and (b) side slip angle and roll angular velocity

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Fig. 11

Flight dynamic modes' instantons damping ratio (a) angle of attack and longitudinal velocity and (b) side slip angle and roll angular velocity

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Fig. 12

The root loci for the mean value of the obtained modes

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