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Evaluation of the Hilbert Huang Transformation of
Transient Signals for Bridge Condition Assessment
21st June 2017
This pr...
Outline
Research motivation and overview
Test data (Steel Truss Bridge)
Empirical Mode Decomposition
Application of Hilber...
Research Motivation
• Fourier Transforms (FTs) are commonly employed to assess the
structural condition of bridge structur...
Research Motivation
• Fourier Transforms (FTs) are commonly employed to assess the
structural condition of bridge structur...
Hilbert Huang Transform: Process Overview
Signal In
EMD HHT
IMFs Hilbert-Huang Spectrum
Hilbert Huang Transform: Process Overview
• EMD
Signal In
EMD HHT
IMFs Hilbert-Huang Spectrum
Marginal Hilbert SpectrumIns...
Steel Truss Bridge: Progressive Damage Test
• Steel truss bridge subjected to 4 damage
scenarios to central vertical membe...
Recorded Structural Response
Recorded Structural Response
Harmonic Free VibrationNoisy Forced Vibration
Empirical Mode Decomposition
10 20 30 40 50 60 70 80 90 100 110 120
-2
-1
0
1
2
IMF 1; iteration 0
Empirical Mode Decomposition
1. Identify all extrema in the signal 𝑥 𝑡
Empirical Mode Decomposition
1. Identify all extrema in the signal 𝑥 𝑡
2. Interpolate with cubic spline function
between m...
Empirical Mode Decomposition
1. Identify all extrema in the signal 𝑥 𝑡
2. Interpolate with cubic spline function
between m...
Empirical Mode Decomposition
1. Identify all extrema in the signal 𝑥 𝑡
2. Interpolate with cubic spline function
between m...
Empirical Mode Decomposition
1. Identify all extrema in the signal 𝑥 𝑡
2. Interpolate with cubic spline function
between m...
Empirical Mode Decomposition
Decomposed IMFs FFTs of IMFs
EMD: Advancements
Ensemble Empirical Mode Decomposition (EEMD)
 Gaussian white noise with the same variance as the noise
...
Ensemble Empirical Mode Decomposition
Decomposed IMFs FFTs of IMFs
Hilbert Transform
Hilbert transform can
be applied to the IMFs 𝑐𝑖(𝑡) to
obtain an analytic signal z(t)
that contains insta...
HHT Results: Marginal Hilbert Spectrum
All Sensors Undamaged All Sensors Damaged
HHT Results: Instantaneous Vibration Intensity
HHT Spectrum Results
Sensor 2 Undamaged Sensor 3 Undamaged Sensor 4 Undamaged
Sensor 2 Damage 3 Sensor 3 Damage 3 Sensor 4...
Conclusions
• EEMD is an adaptive method decomposing a non-
linear non-stationary signal with physical meaningful
results ...
THANK YOU FOR YOUR ATTENTION
This project has received funding from the European Union’s Horizon 2020 research and innovat...
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"Evaluation of the Hilbert Huang transformation of transient signals for bridge condition assessment" presented at ESREL2017 by JJ Moughty

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Abstract: The assessment of bridge condition from vibration measurements has generally been determined via the monitoring of modal parameters determined though adaptations of the standard Fast Fourier Transform (FFT) or other stationary time-series based transformations. However, the non-stationary nature of measured vibration signals from damaged structures can limit the quality of frequency content information estimated by such methods. The Hilbert–Huang Transform’s (HHT) ability to decompose non-stationary measured vibration data into a time-frequency-energy representation allows signal variations to be identified sooner than other stationary-based transformations, thus potentially allowing early detection of damage. The present study uses data obtained from a progressive damage test conducted on a real bridge subjected to excitation from a double axle passing vehicle as a test subject. Decomposed vibration signals from the HHT and associated marginal spectrums are assessed to determine structural condition for various damage states and different locations along the bridge.

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"Evaluation of the Hilbert Huang transformation of transient signals for bridge condition assessment" presented at ESREL2017 by JJ Moughty

  1. 1. Evaluation of the Hilbert Huang Transformation of Transient Signals for Bridge Condition Assessment 21st June 2017 This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 642453 John Moughty & Prof. Joan Ramon Casas Technical University of Catalonia (BarcelonaTech)
  2. 2. Outline Research motivation and overview Test data (Steel Truss Bridge) Empirical Mode Decomposition Application of Hilbert-Haung Transform (HHT) Conclusions
  3. 3. Research Motivation • Fourier Transforms (FTs) are commonly employed to assess the structural condition of bridge structures, however, FTs require the system response to be linear and strictly stationary. • Operational bridge vibrations are not generally linear or stationary. • Non-stationarity of response signals may increase with damage.
  4. 4. Research Motivation • Fourier Transforms (FTs) are commonly employed to assess the structural condition of bridge structures, however, FTs require the system response to be linear and strictly stationary. • Operational bridge vibrations are not generally linear or stationary. • Non-stationarity of response signals may increase with damage. Fourier Wavelet Hilbert-Haung Transform Frequency Calc. Global Convolution Global Convolution Local Differentiation Presentation Energy & Frequency Energy, Time & Frequency Energy, Time & Frequency Non-Linear No No Yes Non-Stationary No Yes Yes Table 1. Signal Transformations
  5. 5. Hilbert Huang Transform: Process Overview Signal In EMD HHT IMFs Hilbert-Huang Spectrum
  6. 6. Hilbert Huang Transform: Process Overview • EMD Signal In EMD HHT IMFs Hilbert-Huang Spectrum Marginal Hilbert SpectrumInstantaneous Energy MORE
  7. 7. Steel Truss Bridge: Progressive Damage Test • Steel truss bridge subjected to 4 damage scenarios to central vertical members • A 21kN double-axle vehicle with a velocity of 40km/hr was used for structural excitation • Vertical acceleration response of vehicle passage was recorded from 8 locations
  8. 8. Recorded Structural Response
  9. 9. Recorded Structural Response Harmonic Free VibrationNoisy Forced Vibration
  10. 10. Empirical Mode Decomposition 10 20 30 40 50 60 70 80 90 100 110 120 -2 -1 0 1 2 IMF 1; iteration 0
  11. 11. Empirical Mode Decomposition 1. Identify all extrema in the signal 𝑥 𝑡
  12. 12. Empirical Mode Decomposition 1. Identify all extrema in the signal 𝑥 𝑡 2. Interpolate with cubic spline function between minima points & maxima points to form an envelope 𝑒 𝑚𝑖𝑛 𝑡 & 𝑒 𝑚𝑎𝑥 𝑡
  13. 13. Empirical Mode Decomposition 1. Identify all extrema in the signal 𝑥 𝑡 2. Interpolate with cubic spline function between minima points & maxima points to form an envelope 𝑒 𝑚𝑖𝑛 𝑡 & 𝑒 𝑚𝑎𝑥 𝑡 3. Compute the mean of envelope 𝑚 𝑡 = 𝑒 𝑚𝑖𝑛 𝑡 +𝑒 𝑚𝑎𝑥 𝑡 2
  14. 14. Empirical Mode Decomposition 1. Identify all extrema in the signal 𝑥 𝑡 2. Interpolate with cubic spline function between minima points & maxima points to form an envelope 𝑒 𝑚𝑖𝑛 𝑡 & 𝑒 𝑚𝑎𝑥 𝑡 3. Compute the mean of envelope 𝑚 𝑡 = 𝑒 𝑚𝑖𝑛 𝑡 +𝑒 𝑚𝑎𝑥 𝑡 2 4. Extract the detail 𝑑 𝑡 = 𝑥 𝑡 − 𝑚(𝑡)
  15. 15. Empirical Mode Decomposition 1. Identify all extrema in the signal 𝑥 𝑡 2. Interpolate with cubic spline function between minima points & maxima points to form an envelope 𝑒 𝑚𝑖𝑛 𝑡 & 𝑒 𝑚𝑎𝑥 𝑡 3. Compute the mean of envelope 𝑚 𝑡 = 𝑒 𝑚𝑖𝑛 𝑡 +𝑒 𝑚𝑎𝑥 𝑡 2 4. Extract the detail 𝑑 𝑡 = 𝑥 𝑡 − 𝑚(𝑡) 5. Check if 𝑑 𝑡 ´𝑠 extrema & zero crossings differ by a maximum of 1, and if 𝑑 𝑡 satisfies the stopping criterion based on consecutive standard deviation values.
  16. 16. Empirical Mode Decomposition Decomposed IMFs FFTs of IMFs
  17. 17. EMD: Advancements Ensemble Empirical Mode Decomposition (EEMD)  Gaussian white noise with the same variance as the noise within the original signal is added for multiple realisations  Added noise alters the signal slightly while retaining its physical meaningful information  Mode mixing is reduced considerably
  18. 18. Ensemble Empirical Mode Decomposition Decomposed IMFs FFTs of IMFs
  19. 19. Hilbert Transform Hilbert transform can be applied to the IMFs 𝑐𝑖(𝑡) to obtain an analytic signal z(t) that contains instantaneous amplitude 𝑎𝑖(𝑡) and phase θ𝑖 𝑡 , which can be differentiated to obtain instantaneous frequency. 𝐻[𝑐𝑖 𝑡 ]
  20. 20. HHT Results: Marginal Hilbert Spectrum All Sensors Undamaged All Sensors Damaged
  21. 21. HHT Results: Instantaneous Vibration Intensity
  22. 22. HHT Spectrum Results Sensor 2 Undamaged Sensor 3 Undamaged Sensor 4 Undamaged Sensor 2 Damage 3 Sensor 3 Damage 3 Sensor 4 Damage 3
  23. 23. Conclusions • EEMD is an adaptive method decomposing a non- linear non-stationary signal with physical meaningful results (no mode-mixing). • Instantaneous Vibration Intensity may attain considerable damage sensitivity • HHT Spectrums demonstrated the ability to locate structural changes in a symmetrical structure • Additional work is required for multivariate EMD to enhance HHT Spectrum results
  24. 24. THANK YOU FOR YOUR ATTENTION This project has received funding from the European Union’s Horizon 2020 research and innovation pro This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 642453

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