Hilbert Huang Transform

This thesis (“The Hilbert-Huang Transform for Damage Detection in Plate Structures”) investigates the detection of structural damage in plate structures using the empirical mode decomposition method along with the Hilbert spectral analysis. In recent years there have been an extensive amount of research associated with the development of health monitoring methods for aerospace systems…

Contents

Chapter 1
Introduction
1.1 Motivation
1.2 Structural Health Monitoring Overview
1.2.1 Challenge and Goals of Structural Health Monitoring
1.2.2 Safety Issue
1.2.3 Cost Issue
1.2.4 Performance Issue
1.2.5 Summary
1.3 Signal Processing in SHM
1.3.1 Signal Processing
1.3.2 Spectral Analysis
1.3.3 Short-Time Fourier Transform (STFT)
1.3.4 Wavelet Transform
1.3.5 Hilbert-Huang Transform (HHT)
1.4 Present Study
1.5 Organization of the thesis Chapter 2
Time-Frequency Methods For Damage Detection
2.1 Short-Time Fourier Transform (STFT)
2.1.1 Description of The Method
2.1.2 Example
2.13 Conclusion
2.2 The Wavelet Transform
2.2.1 Description of the method
2.2.2 Example
2.2.3 Conclusion
2.3 The Wigner-Ville Distribution
2.3.1 Description of The Method
2.3.2 Example
2.3.3 Conclusion
2.4 Summary
Chapter 3
The Empirical Mode Decomposition (EMD) And The Associated Hilbert Spectral
Analysis
3.1 Fundamental Concepts
3.1.1 The Hilbert transform and analytical signal
Figure 3.2: Amplitude and phase of the Hilbert transform of a sine wave
3.1.2 The Instantaneous Frequency
3.1.3 The Hilbert-Huang transform
3.2 Program Implementation
3.2.1 Stop Criterion
3.2.2 Spline Fitting
3.2.3 End Effects
3.3 Program Validation and Comparison
3.3.1 Analyzed Signal
3.3.2 EMD Analysis
3.3.3 Comparison with the others time-frequency methods
3.3.4 Conclusion
3.5 Summary
Chapter 4
EMD Metrics For Damage Detection
4.1 The Hilbert instantaneous phase
4.1.1 Description
Figure 4.1: Hilbert phase example
4.1.2 1D finite element simulation
4.1.3 Simulation results
4.2 The energy metric
4.2.1 Wave and energy
4.2.2 The Hilbert spectrum and the reflected energy
4.2.3 The Hilbert-Huang spectrum as a damage detection parameter
4.3 The phase shift metric
4.3.1 Principle
4.3.2 Application
4.4 Summary
Chapter 5
Damage Detection In Isotropic Plates
5.1 Introduction
5.2 Basic wave mechanics
5.3 Lamb wave propagation in isotropic plates
5.3.1 Lamb wave for damage detection wave propagation
5.3.3 Modes selection for damage detection
5.4 Excitation and sensing of Lamb waves
5.4.1 Constitutive equations
5.4.2 PZT actuator
5.4.3 PVDF sensor array
5.5 Experimental setup and results
5.5.1 Equipment
5.5.2 Damage detection setup
5.5.3 Transient analysis
5.6 Hilbert-Huang Transform analysis
5.6.1 Empirical mode decomposition
5.6.2 Hilbert-Huang spectrum and the Energy metric
5.6.3 Energy-time spectrum and the Phase shift metric
5.7 Summary
Chapter 6
Damage detection in composite plates
6.1 Introduction
6.2 Wave propagation in composite laminates
6.2.1 Low-frequency wave propagation
6.2.2 High-frequency wave propagation
6.2.3 Wavenumber filtering
6.3 Composite plate manufacturing
6.4 Delaminations detection and characterization
6.4.1 Experimental setup
6.4.2 Transient analysis
6.4.3 Empirical mode decomposition
6.4.4 Directional filtering
6.4.5 Hilbert-Huang spectrum and the energy metric
6.4.6 The Hilbert phase
6.5 Stiffness changes
6.5.1 Experimental setup
6.5.2 Damage along the array axis
6.5.2 Non-axis damage detection
6.6 Low-velocity impact damage
6.6.1 Experimental Setup
6.6.2 Impact energy quantification
6.6.3 Transient signal analysis
6.6.4 Hilbert-Huang spectrum and Energy metric
6.6.5 Energy-time spectrum and the Phase shift metric
6.6.6 The Hilbert phase
6.7 Summary
Chapter 7
Conclusion
7.1 Contributions
7.2 Limitations of Current Methods
7.3 Recommendations for Future Work
Bibliography

Author: Zemmour, Arnaud Isaac

Source: University of Maryland

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