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

3. Measurement: Measurements from sensors in the damaged region Any Damage? Maintenance Decision Repair? Replacement? NDE? Yes Measurement: Damage Assessment and Characterization Damaged Region Damage Isolator Where? Damage Estimator Damaged Region Sensors in Critical Regions Damage detector 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. Reliability of Biologically Inspired (BI) Structures SHM-Based Adaptive Bayesian Assessment of Remaining Life Prediction for BI Structures Performance of BI Structures under Random Loading Effects of Structural Uncertainties on Performance of BI Structures Development of Minimum Life-Cycle Cost Design for BI Structures Simulation and Modeling of Stochastic Loading and System Uncertainties Optimal Maintenance Planning for Inspection/Repair/Replacement of BI Structures and Components Damaged Region Multi-level Structural Health Monitoring Using Advanced Sensing technology Performance of Data Interpretation Schemes under Uncertainties Probabilistic Structural Analysis Reliability Assessment and Life Prediction Structural Health Monitoring

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 Mexican Hat Meyer Meyer

10. Application Detection of Sudden Damage ASCE Benchmark Study for Health Monitoring

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

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

13. Application Monitoring Progressive Stiffness Degradation M1M1 K1K1 C1C1 M2M2 K2K2 C2C2 M3M3 K3K3 C3C3 Time (sec) Instantaneous Natural frequency (Hz) 1 st mode2 nd mode3 rd mode CWTModal analysis CWTModal analysis CWTModal analysis 51.29301.29323.61813.62345.23575.2360 151.26141.26193.59183.59565.05425.0586 251.22341.22303.55533.55894.87744.8824 3DOF Model with a damageable Spring Comparison with Analytical Results Wavelet ridges Instantaneous Frequencies 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. Application A Pseudo-Wavelet Based System Identification Technique Pseudo-wavelet for the 2 nd order system Pseudo-wavelet for the 1 st order system Scaling Shifting Scaling Pseudo-wavelet Transform

16. PWT-Based System Identification Technique Noised SignalFourier Spectrum First-order PWT Second-order PWT Time Constant  n (rad/sec)  Exact Value240.05 Truncated PWT (r cut= 80%) 2.023.990.053 Error1%0.25%6% Results

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

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

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

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

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

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

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