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

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Authors

  • M. Dätig
  • T. Schlurmann

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Original languageGerman
Pages (from-to)1783-1834
Number of pages52
JournalOcean engineering
Volume31
Issue number14-15
Publication statusPublished - 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.

Cite this

Performance and limitations of the Hilbert-Huang transformation (HHT) with an application to irregular water waves. / Dätig, M.; Schlurmann, T.
In: Ocean engineering, Vol. 31, No. 14-15, 2004, p. 1783-1834.

Research output: Contribution to journal › Article › Research › 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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title = "Performance and limitations of the Hilbert-Huang transformation (HHT) with an application to irregular water waves",
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.",
keywords = "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",
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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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Download

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T1 - Performance and limitations of the Hilbert-Huang transformation (HHT) with an application to irregular water waves

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 - Hilbert-Huang transformation

KW - Irregular second order Stokes wave theory

KW - Irregular water waves

KW - Perturbation expansion approach

KW - Time-frequency analysis techniques

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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