Wavelet Analysis and Its Applications for Structural Health Monitoring and Reliability Analysis

1. Wavelet Analysis and Its Applications for Structural Health Monitoring and Reliability Analysis Zhikun Hou Worcester Polytechnic Institute and Mohammad Noori North Carolina State University September 4, 2003

2. Contents Introduction Background - Continuous Wavelet Transform - Discrete Wavelet Transform, - Wavelet Packet Analysis - Data Decomposition and Synthesis Applications - Detection of Sudden Damage - Monitoring Development of Stiffness Degradation - Pseudo-wavelet Based System Identification - Identification of Impact Loading on Composite Plates - Wavelet Packet- Based Sifting for Data Decomposition - Wavelet-based Monte Carlo Simulation Future Research Concluding Remarks

3. Yes Measurements from sensors in the damaged region Damaged Region Measurement: Any Damage? Where? Measurement: Damage detector Damage Isolator Damaged Region Measurement: Sensors in Critical Regions Damage Estimator Damage Assessment and Characterization Maintenance Decision Repair? Replacement? NDE? Decision Maker Structural Health Monitoring: - Damage detection - Damage isolation - Damage assessment - Maintenance Decision Uncertainties: - Randomness in loading - Uncertainties in material properties - Uncertainties in boundary conditions - Human errors Multilevel SHM: - Global monitoring - Local monitoring - NDE (local)

4. Probabilistic Structural Analysis Damaged Region Performance of BI Structures under Random Loading Simulation and Modeling of Stochastic Loading and System Uncertainties Effects of Structural Uncertainties on Performance of BI Structures Multi-level Structural Health Monitoring Using Advanced Sensing technology Reliability of Biologically Inspired (BI) Structures Development of Minimum Life-Cycle Cost Design for BI Structures Performance of Data Interpretation Schemes under Uncertainties SHM-Based Adaptive Bayesian Assessment of Remaining Life Prediction for BI Structures Optimal Maintenance Planning for Inspection/Repair/Replacement of BI Structures and Components Structural Health Monitoring Reliability Assessment and Life Prediction

5. Continuous Wavelet Transform (CWT) Admissibility Condition of (t):

6. Discrete Wavelet Transform (DWT)

7. Wavelet Details and Approximations Signal : The Detail at Level j : The Approximation at Level j :

8. Decomposition and Synthesis of a Signal

9. Typical Wavelets: • Mexican Hat • Meyer

10. ApplicationDetection of Sudden Damage ASCE Benchmark Study for Health Monitoring

11. Sudden damage detected on the first floor at t = 2.5s 50% stiffness loss of two braces on the first floor at t = 2.5s Robustness to measurement noise (2%RMS of response) Less that 5% change in the natural freqs. due to the local damage

12. Experimental Validation: Shaking Table Test of a Two-Story Full-Size Wooden Frame

13. K1 K2 K3 M1 M2 M3 C1 C2 C3 ApplicationMonitoring Progressive Stiffness Degradation Instantaneous Frequencies Wavelet ridges 3DOF Model with a damageable Spring Comparison with Analytical Results Instantaneous modeshapes

14. SODF oscillator with a damageable spring subjected to an harmonic input Damage development of a two-story wooden house during shaking table testing (Load level=300,350,400 gal)

15. ApplicationA Pseudo-Wavelet Based System Identification Technique Pseudo-wavelet for the 2nd order system Pseudo-wavelet for the 1st order system Scaling Scaling Pseudo-wavelet Transform Shifting

16. PWT-Based System Identification Technique First-order PWT Noised Signal Fourier Spectrum Second-order PWT Results

17. Yp(m) Xp(m) f(KHz) f(KHz) t a t ApplicationIdentification of Impact Loading on a Composite Plate Measurement of traveling wave Wavelet transform of measurement Identified impact location (x=0.5, y=0.7 unit) A composite plate impacted at a point with x=0.5 and y=0.7 unit)

18. Application Wavelet-Based Sifting Process and Its Application for Damage Detection Fourier Spectra Response data 3rd mode component 2nd mode component 1st mode component Decomposition of response data of a linear 3DOF system and its decomposition by a wavelet-based sifting process

19. Comparison with analytical results from modal analysis and results from the Empirical Modal Decomposition (EMD) method)

20. Total Response 3rd modal component Instantaneous Frequency Instantaneous frequency of the third mode for cases of progressive and sudden damage

21. ApplicationWavelet-based Monte Carlo Simulation for Random Vibration and Reliability Analysis Wavelet-based sample set using a 1940 El Centro ground motion Record as the mother sample Samples of a local harmonic with random disturbance

22. Intensity = 0 Intensity = 0.001 DIS VEL ACC Significance of small random disturbance on the second moment response of a linear SDOF oscillator to a input of a local harmonic

23. Concluding Remarks • Wavelet tools can be used to effectively detect sudden damage due to its sensitivity to singularity; • Wavelet tools can be used to monitor development of stiffness degradation and identify the system parameters; • Wavelet tools can be used to locate damaged region based on either spatial distribution spikes for sudden damage or change in mode shapes for progressive damage; • Wavelet tools have merits of less-model dependence, sensitivity to local damage, robustness to moderate noise, computational efficiency, and feasibility for on-line implementation; • Wavelet tools has great potentials to be used in multi-level structural health monitoring for BI aerospace structures to detect, locate, and assess structural damage as well as to make a maintenance decision in condition-based maintenance procedure ; • Wavelet tools has great potentials for structural reliability analysis of BI aerospace structures in Monte Carlo simulation, adaptive Bayesian reliability assessment, and life prediction.

24. On-going Research Activities: • Development of wavelet-based multi-level structural health monitoring Strategy for BI aerospace structures - Wavelet tools for monitoring sudden and progressive damage; - Wavelet-based performance indices for condition-based maintenance; - Guided Nondestructive Evaluation: when? where? Data interpretation? - Early warning system for aerospace structures; - Performance in noisy and random environment; - Integration with smart sensors and structural control - Experimental validation and Comparison with other approaches • Reliability Analysis and Life Prediction of BI Aerospace Structures - Wavelet-based sampling techniques for random vibration analysis; - Wavelet-based adaptive Bayesian system identification; - Adaptive reliability assessment of critical structural members and prediction of their remaining life; - Development of reliability-based maintenance procedure; - Application of developed techniques for aerospace structures.