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.