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Wavelet Analysis and Its Applications for Structural Wavelet Analysis and Its Applications for Structural Health Monitoring and Reliability AnalysisHealth Monitoring and Reliability Analysis
Zhikun HouZhikun HouWorcester Polytechnic InstituteWorcester Polytechnic Institute
andand
Mohammad NooriMohammad NooriNorth Carolina State UniversityNorth Carolina State University
September 4, 2003September 4, 2003
ContentsContents• IntroductionIntroduction• BackgroundBackground
- - Continuous Wavelet TransformContinuous Wavelet Transform - Discrete Wavelet Transform,- Discrete Wavelet Transform, - Wavelet Packet Analysis- Wavelet Packet Analysis - Data Decomposition and Synthesis- Data Decomposition and Synthesis• ApplicationsApplications - 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 ResearchFuture Research• Concluding RemarksConcluding Remarks
Measurement:
Measurements from sensors in the damaged
region
Any Damage
?
Maintenance DecisionRepair?
Replacement?NDE?
YesMeasurement:
Measurement:
Damage Assessment
and Characterizatio
n
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)
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
Continuous Wavelet Transform (CWT)Continuous Wavelet Transform (CWT)
Admissibility Condition of (t):
Discrete Wavelet Transform (DWT)Discrete Wavelet Transform (DWT)
Wavelet Details and ApproximationsWavelet Details and Approximations
Signal :Signal :
The Detail at Level j :The Detail at Level j :
The Approximation at Level j :The Approximation at Level j :
Zj Zk
kj tkjCtS )(),()( ,
Zj
kjj tkjCtD )(),()( ,
Jj
jJ tDtA )()(
Decomposition and Synthesis of a SignalDecomposition and Synthesis of a Signal
Typical Wavelets:Typical Wavelets:
Mexican HatMexican Hat
MeyerMeyer
ApplicationApplication
Detection of Sudden DamageDetection of Sudden Damage
ASCE Benchmark Study for Health Monitoring
Natural frequencies
0
2040
60
80
100120
140
160
1 2 3 4 5 6 7 8
vibration mode
freq
uenc
y (r
ad/s
) Health structureDamaged structure
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)
Experimental Validation: Experimental Validation: Shaking Table Test of a Two-Story Full-Size Wooden FrameShaking Table Test of a Two-Story Full-Size Wooden Frame
ApplicationApplicationMonitoring Progressive Stiffness DegradationMonitoring Progressive Stiffness Degradation
M
1
K1
C1M
2
K2
C2M
3
K3
C3
Time(sec)
Instantaneous Natural frequency (Hz)
1st mode 2nd mode 3rd mode
CWT Modal analysis
CWT Modal analysis
CWT Modal analysis
5 1.2930
1.2932 3.6181
3.6234 5.2357
5.2360
15 1.2614
1.2619 3.5918
3.5956 5.0542
5.0586
25 1.2234 1.2230 3.5553 3.5589 4.8774 4.8824
3DOF Model with a damageable Spring
Comparison with Analytical Results
Wavelet ridges Instantaneous Frequencies
Instantaneous modeshapes
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)
ApplicationApplicationA Pseudo-Wavelet Based System Identification TechniqueA Pseudo-Wavelet Based System Identification Technique
Pseudo-wavelet for the 2nd order system
Pseudo-wavelet for the 1st order system
Scaling
Shifting
Scaling
dTWFTC
dWFC
F
F
; )(
,; ),(
1
0
*0
*02
0
*0
*0
Pseudo-wavelet Transform
PWT-Based System Identification Technique
Noised Signal Fourier Spectrum
First-order PWT
Second-order PWT
Time Constant
n
(rad/sec)
Exact Value 2 4 0.05
Truncated PWT (rcut=80%)
2.02 3.99 0.053
Error 1% 0.25% 6%
Results
ApplicationApplicationIdentification of Impact Loading on a Composite PlateIdentification of Impact Loading on a Composite Plate
tt
a
Xp(m)
f(KHz)
Yp(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
Application Application Wavelet-Based Sifting Process and Its Application for Wavelet-Based Sifting Process and Its Application for
Damage DetectionDamage Detection
Decomposition of response data of a linear 3DOF system and its decomposition by a wavelet-based sifting process
Response data
3rd mode component
1st mode component
2nd mode component
Fourier Spectra
Comparison with analytical results from modal analysis and results from the Empirical Modal Decomposition (EMD) method)
Instantaneous frequency of the third mode for cases of progressive and sudden damage
Total Response
3rd modal component
Instantaneous Frequency
ApplicationApplicationWavelet-based Monte Carlo Simulation for Random Wavelet-based Monte Carlo Simulation for Random
Vibration and Reliability AnalysisVibration and Reliability Analysis
Samples of a local harmonic with random disturbance
Wavelet-based sample set usinga 1940 El Centro ground motion
Record as the mother sample
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 = 0 Intensity = 0.001
Concluding RemarksConcluding Remarks
Wavelet tools can be used to effectively detect sudden damage Wavelet tools can be used to effectively detect sudden damage due to its sensitivity to singularity;due to its sensitivity to singularity;
Wavelet tools can be used to monitor development of stiffness Wavelet tools can be used to monitor development of stiffness degradation and identify the system parameters;degradation and identify the system parameters;
Wavelet tools can be used to locate damaged region based on Wavelet tools can be used to locate damaged region based on either spatial distribution spikes for sudden damage or change in either spatial distribution spikes for sudden damage or change in mode shapes for progressive damage;mode shapes for progressive damage;
Wavelet tools have merits of less-model dependence, sensitivity to Wavelet tools have merits of less-model dependence, sensitivity to local damage, robustness to moderate noise, computational local damage, robustness to moderate noise, computational efficiency, and feasibility for on-line implementation;efficiency, and feasibility for on-line implementation;
Wavelet tools has great potentials to be used in multi-level Wavelet tools has great potentials to be used in multi-level structural health monitoring for BI aerospace structures to detect, structural health monitoring for BI aerospace structures to detect, locate, and assess structural damage as well as to make a locate, and assess structural damage as well as to make a maintenance decision in condition-based maintenance procedure ; maintenance decision in condition-based maintenance procedure ;
Wavelet tools has great potentials for structural reliability analysis Wavelet tools has great potentials for structural reliability analysis of BI aerospace structures in Monte Carlo simulation, adaptive of BI aerospace structures in Monte Carlo simulation, adaptive Bayesian reliability assessment, and life prediction. Bayesian reliability assessment, and life prediction.
On-going Research Activities:On-going Research Activities: Development of wavelet-based multi-level structural health Development of wavelet-based multi-level structural health
monitoring Strategy for BI aerospace structuresmonitoring 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 StructuresReliability 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.