Damage Detection in a Multi-Level Structure Using Hilbert-Huang Transform

1. Damage Detection in a Multi-Level Structure Using Hilbert-Huang Transform Shaoqing Xu Master of Science Candidate Department of Mechanical and Aeronautical Engineering Clarkson University, Potsdam, NY Examining Committee Dr. Ratneshwar Jha (Advisor, Dept. of MAE) Dr. Goodarz Ahmadi (Co-advisor, Dept. of MAE) Dr. Pier Marzocca(Dept. of MAE)

2. Outline • Background • Objectives • EMD and Hilbert Transform (HHT) • Detect Damage Time Instants using HHT • Detect Damage Location using Marginal HHT • Detect Damage Location using HHT of the Vibrational Deflection Shape • Future Work

3. Background • SHM is crucial for safety and maintenance of aerospace, civil, and mechanical systems. • Damage state: Existence, Location, Type, Severity, Prognosis. • Current methods based on visual or localized experimental techniques (acoustic or ultrasonic, magnetic field, radiography, and eddy-current). • All of these localized techniques require that the vicinity of the damage is known a priori and that the portion of the structure is readily accessible. • A quantitative global damage detection method that can be used to locate damage is required urgently.

4. Vibration-Based SHM • Structural properties (natural frequency, mode shape, modal damping) are functions of physical parameters (geometry, connectivity, boundary condition, mass, stiffness, damping). • Recent technological advancements have helped vibration-based SHM (computation power, sensors, FE, system identification). • Limited practice of vibration-based SHM by engineering community so far. • Difficult to identify damage by examining response-time histories directly, compounded by excitation sources and/or environmental conditions.

5. Objectives • Identify the time instants and the locations of the damage to the three-level structure by applying the EMD on the acceleration data recorded during the damage event. The structural damage is simulated by gently placing the modification mass (a small cylindrical object) on different level or energizing the PZT actuator. • Evaluate the performance of the HHT when various levels of noises are added into the experiment system.

6. Structural Health Monitoring Methodology • Detect the existence of the damage in a system. • Determine the location of damage in a system. • Quantify the detail of the damage such as the type, size and severity of the damage in a system. • Determine the impact of the damage for the entire system. • Predict the remaining lifetime of a system.

7. The Hilbert-Huang Transform (HHT) • HHT suitable for analyzing nonlinear and non-stationary data (Huang et al, 1998) • Empirical Mode Decomposition (EMD): Decomposes data into a finite, and often small, number of ‘intrinsic mode functions’ (IMF) which represent the nature of the vibration. • Hilbert Transform: Provides instantaneous frequencies and magnitudes as functions of time that give sharp identifications of imbedded structures. • Giving instantaneous frequency and magnitude rather than the global frequency and magnitude defined by traditional Fourier transform, the HHT makes physical sense at every point.

8. Hilbert Transform Let Analytic Signal: Where: and

9. The EMD Method (Sifting) IMF Sifting Result: Two Conditions for Intrinsic Mode Function (IMF): • The number of extremes and that of zero crossings must either equal or differ at most by one. • At any point, the mean value of the envelopes is zero. Example of a Typical IMF

10. IMFs of The Three level Structure Response

11. Hilbert Spectrum • By performing the Hilbert Transform to the IMFs, we have the Hilbert spectrum • The residue can be treated as an IMF or simply left out. Figure 2.4 A time plot of a band limited white noise signal Magnitude-Frequency-Time Distribution of a band limited white noise

12. Summary • The simulations show that the method is very sensitive to sudden change in structural stiffness. • The ratios between the frequency dispersal of each level’s response can be used as the indicator of damage location • The EMD and Hilbert transform based SHM method is suitable for identification of damage instants under constant harmonic excitation. • The closer the excitation frequency to the natural frequency of the structure, the larger is the size of the frequency dispersal, thus it is easier to identify the occurrence and location of the damage.

13. Detection Procedure 1. Record the vibration deflection shape (VDS) of the structure, vibrating at steady state. 2. Estimate the curvature distribution from the vibrational deflection shape. 3. Apply EMD to curvature. Keep only the IMF which represents the dominant vibration mode. Get rid of useless or redundant information. 4. Apply Hilbert transform to the IMF. Transfer curvature concentration into frequency domain. 5. Examine the Hilbert spectrum. An abnormal frequency discontinuity can be found at the damage location.

14. Hilbert-Huang Marginal Spectrum Figure 2.6 The marginal Hilbert spectrum plot of the band-limited white noise

15. Test Equipment Setup Figure 3.1 Test equipment setup

16. Test Equipment Setup Figure 3.2 Block diagram of test equipment setup

17. Shaker and Power Amplifier Figure 3.5 Bruel & Kjar power amplifier, Type 2706 Bruel & Kjar Vibration Exciter, Type 4809

18. Fix-Fix Beam, undamaged

19. ICP Accelerometers and 8-Channel Signal Conditioner PCB 8-channel signal conditioner Figure 3.6 ICP Accelerometers attached to the sidewall of the structure

20. Fix-Fix Beam, undamaged Figure 3.9 ACX QuickPack Piezoelectric actuator Figure 3.10 Actuator Peak-to-peak strain versus excitation voltage (above) and actuator peak-to-peak stain versus peak-to-peak force (bottom)

21. PZT Actuator and Power Amplifier Figure 3.12 ACX QuickPack power amplifier connected with a QuickPack piezoelectric actuator Figure 3.11 piezoelectric actuator attached to the surface of the sidewall

22. MultiQ-3 A/D – D/A Control Board Figure 3.13 Analog and digital ports on the MultiQ-3 A/D – D/A control board Figure 3.14 Terminal box

23. Software Configeration

24. Fix-Fix Beam, undamaged

25. Fix-Fix Beam, undamaged Figure 3.18 WinCon solver parameter setup dialog window Figure 3.17 WinCon output to power amplifier block dialog window

26. Fix-Fix Beam, undamaged Figure 3.20 WinCon Server window Figure 3.21 Real time plot of a band limited white noise input signal

27. Mass Modification Damage

28. Fix-Fix Beam, undamaged Figure 4.25 Place the modification mass on level 1 (left figure), and level 2 (right figure)

29. Fix-Fix Beam, undamaged Figure 4.25 Place the modification mass on level 1 (left figure), and level 2 (right figure)

30. Piezoelectric (PZT) Actuation Damage

31. External Excitation Noise

32. Fix-Fix Beam, undamaged

33. Fix-Fix Beam, undamaged

34. Fix-Fix Beam, undamaged (a) Original Level1 response and IMF 1-3 (b) IMF 4-7 (c) IMF 8 and Residue

35. Fix-Fix Beam, undamaged (a) Original Level2 response and IMF 1-3 (b) IMF 4-7 (c) IMF 8 and Residue

36. Fix-Fix Beam, undamaged (a) Original Level2 response and IMF 1-3 (b) IMF 4-7 (c) IMF 8 and Residue

37. Damage, Mass Modification

38. Structure Response to PZT Actuation

39. Successive Damage Detection

40. External Excitation Noise

41. Sensor Noise

42. Conclusion • This method is effective, and has high sensitivity to damage. • Sensitivity to damage is highest in the middle and attenuates towards tips. • Higher frequency brings better sensitivity, but requires higher sensitivity and accuracy of equipments. • HHT is good for dynamic response. It has many good properties that can be used in various SHM methods.

43. Future Work • Experiments on real structures to examine the performance of these methods. • Study the effects of structural parameters and environmental factors to these methods. • Refine the algorithm of the EMD method to increase speed of calculation.

44. THE END THANK YOU