Performance and limitations of the Hilbert-Huang transformation (HHT) with an application to irregular water waves

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • M. Dätig
  • T. Schlurmann

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Details

OriginalspracheDeutsch
Seiten (von - bis)1783-1834
Seitenumfang52
FachzeitschriftOcean engineering
Jahrgang31
Ausgabenummer14-15
PublikationsstatusVeröffentlicht - 2004

Abstract

This paper relates to the newly developed Hilbert-Huang transformation (HHT). An overview of this time-frequency analysis technique and its applications are given. Key elements of the numerical procedure and principles of the Hilbert transformation (HT) are established. A simple parameter study with trigonometric functions to get an idea about the numerical performance of the empirical mode decomposition (EMD) is performed. The main results of estimating relative standardized errors made between analytically exact defined sine waves and disintegrated intrinsic functions as well as their specific influence on each other are determined. Practical applications are carried out next to evaluate computed nonlinear irregular water waves based on Stokes perturbation expansion approach and measurements on fully nonlinear irregular water waves recorded in a laboratory wave flume. Correspondence between simulated and recorded wave trains is given for narrow-banded fundamental components. Deviations are unveiled when carrier and riding waves get broad banded. Time-dependent spectral representation shows signs of an interesting phenomenon as instantaneous frequencies and amplitudes exhibit strong correlations with water surface elevations of both numerical and measured data series. © 2004 Elsevier Ltd. All rights reserved.

Schlagwörter

    Empirical mode decomposition, Hilbert-Huang transformation, Irregular second order Stokes wave theory, Irregular water waves, Perturbation expansion approach, Time-frequency analysis techniques, Computer simulation, Correlation methods, Frequencies, Mathematical transformations, Water waves, Empirical mode decomposition (EMD), Hilbert transformation (HT), Ocean engineering, fluid mechanics, frequency analysis, mathematical analysis, perturbation, water wave

Zitieren

Performance and limitations of the Hilbert-Huang transformation (HHT) with an application to irregular water waves. / Dätig, M.; Schlurmann, T.
in: Ocean engineering, Jahrgang 31, Nr. 14-15, 2004, S. 1783-1834.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Dätig M, Schlurmann T. Performance and limitations of the Hilbert-Huang transformation (HHT) with an application to irregular water waves. Ocean engineering. 2004;31(14-15):1783-1834. doi: 10.1016/j.oceaneng.2004.03.007
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abstract = "This paper relates to the newly developed Hilbert-Huang transformation (HHT). An overview of this time-frequency analysis technique and its applications are given. Key elements of the numerical procedure and principles of the Hilbert transformation (HT) are established. A simple parameter study with trigonometric functions to get an idea about the numerical performance of the empirical mode decomposition (EMD) is performed. The main results of estimating relative standardized errors made between analytically exact defined sine waves and disintegrated intrinsic functions as well as their specific influence on each other are determined. Practical applications are carried out next to evaluate computed nonlinear irregular water waves based on Stokes perturbation expansion approach and measurements on fully nonlinear irregular water waves recorded in a laboratory wave flume. Correspondence between simulated and recorded wave trains is given for narrow-banded fundamental components. Deviations are unveiled when carrier and riding waves get broad banded. Time-dependent spectral representation shows signs of an interesting phenomenon as instantaneous frequencies and amplitudes exhibit strong correlations with water surface elevations of both numerical and measured data series. {\textcopyright} 2004 Elsevier Ltd. All rights reserved.",
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note = "Cited By :230 Export Date: 1 February 2021 Funding details: Deutsche Forschungsgemeinschaft, DFG Funding text 1: This study was performed within the framework of an extensive research project “On the generating mechanism of transient water from the application of the Hilbert transformation technique” (SCHL503/5-1) funded by the Deutsche Forschungsgemeinschaft (DFG). In this context, the present article summarizes the essential part of the first half of the research project. The financial support is gratefully acknowledged by the authors.",
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AU - Dätig, M.

AU - Schlurmann, T.

N1 - Cited By :230 Export Date: 1 February 2021 Funding details: Deutsche Forschungsgemeinschaft, DFG Funding text 1: This study was performed within the framework of an extensive research project “On the generating mechanism of transient water from the application of the Hilbert transformation technique” (SCHL503/5-1) funded by the Deutsche Forschungsgemeinschaft (DFG). In this context, the present article summarizes the essential part of the first half of the research project. The financial support is gratefully acknowledged by the authors.

PY - 2004

Y1 - 2004

N2 - This paper relates to the newly developed Hilbert-Huang transformation (HHT). An overview of this time-frequency analysis technique and its applications are given. Key elements of the numerical procedure and principles of the Hilbert transformation (HT) are established. A simple parameter study with trigonometric functions to get an idea about the numerical performance of the empirical mode decomposition (EMD) is performed. The main results of estimating relative standardized errors made between analytically exact defined sine waves and disintegrated intrinsic functions as well as their specific influence on each other are determined. Practical applications are carried out next to evaluate computed nonlinear irregular water waves based on Stokes perturbation expansion approach and measurements on fully nonlinear irregular water waves recorded in a laboratory wave flume. Correspondence between simulated and recorded wave trains is given for narrow-banded fundamental components. Deviations are unveiled when carrier and riding waves get broad banded. Time-dependent spectral representation shows signs of an interesting phenomenon as instantaneous frequencies and amplitudes exhibit strong correlations with water surface elevations of both numerical and measured data series. © 2004 Elsevier Ltd. All rights reserved.

AB - This paper relates to the newly developed Hilbert-Huang transformation (HHT). An overview of this time-frequency analysis technique and its applications are given. Key elements of the numerical procedure and principles of the Hilbert transformation (HT) are established. A simple parameter study with trigonometric functions to get an idea about the numerical performance of the empirical mode decomposition (EMD) is performed. The main results of estimating relative standardized errors made between analytically exact defined sine waves and disintegrated intrinsic functions as well as their specific influence on each other are determined. Practical applications are carried out next to evaluate computed nonlinear irregular water waves based on Stokes perturbation expansion approach and measurements on fully nonlinear irregular water waves recorded in a laboratory wave flume. Correspondence between simulated and recorded wave trains is given for narrow-banded fundamental components. Deviations are unveiled when carrier and riding waves get broad banded. Time-dependent spectral representation shows signs of an interesting phenomenon as instantaneous frequencies and amplitudes exhibit strong correlations with water surface elevations of both numerical and measured data series. © 2004 Elsevier Ltd. All rights reserved.

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KW - Computer simulation

KW - Correlation methods

KW - Frequencies

KW - Mathematical transformations

KW - Water waves

KW - Empirical mode decomposition (EMD)

KW - Hilbert transformation (HT)

KW - Ocean engineering

KW - fluid mechanics

KW - frequency analysis

KW - mathematical analysis

KW - perturbation

KW - water wave

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