Structural Health Monitoring using Parametric Models in System Identification

1
Structural Health Monitoring using Parametric
Models in System Identification

• Tricia Maruki
• University of California-Irvine
• REUJAT 2004
• 23 July 2004

Dr. Masanobu Shinozuka, UC Irvine Dr. Akira Mita,
Keio University
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Outline

• Background
• General procedure
• Models
• Experiment setup and results
• Conclusion and acknowledgements

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Structural Health Monitoring

• Gathering signals
• Cleansing of signals
• System identification
• Diagnosis and prognosis

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System Identification

• Previous damage detection methods
• Time consuming
• Require knowledge of location of damage
• System Identification
• Predict systems behavior based on measured data
• Locate damage or deterioration of a structure
  based on changes in structural properties

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System IdentificationProcess

• Gather Data - Input (Base), Output (Roof)
• Non-parametric Identification - find appropriate
  resampling
• Select Data - Pick out high amplitude section
• Parametric Models - ARX and ARMAX
• Validate Models - compare fit between models to
  actual known Output data
• Choose Model - Which model is best for this
  structure?

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Non-Parametric Identification

• Empirical Transfer Function Estimate (ETFE)
• Frequency Response Function
• Fourier Transform, input-output relationship
• Noise included, less accurate
• Spectrum Analysis
• Output signal not correlated with noise?more
  accurate
• Coherence Function
• Indicates correlation coefficient between input
  and output sequences
• Used to find new resampling period and frequency

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Parametric Models

• Auto-Regression Models A(q)
• Where q is the shift operator
• ARX (eXtra Input)
• A(q)y(t) B(q)u(t) e(t)
• ARMAX (Moving Average eXtra Input)
• A(q)y(t) B(q)u(t) C(q)e(t)
• Where C(q)e(t) is moving average of white noise

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Model Validation

• Maximize the percentage fit between model
  prediction and measured output acceleration
• Minimize error between model and actual data
• Akaikes Final Prediction Error (FPE)

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Poles and Modal Properties

• Poles
• Z-transform for discrete time systems (similar to
  Laplace transform)
• Amplitude of pole? Damping ratio
• Phase of pole ?Frequency

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Experiment Setup
Sensors
Mita Laboratory Keio University
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Experiment Data collection
y output (Roof floor) u input (Base floor)

• Sampling Frequency 500 Hz
• Time 10 seconds

Acceleration (cm/s/s) vs. time (s)
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Experiment Non-Parametric Identification
Coherence Function

• Empirical Transfer Function Estimate (ETFE)

Power Spectrum
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ExperimentPolishing and processing data
Original Data
Resampled Data
Sampling Frequency 500 Hz 50 Hz Sampling
Period 0.002 sec 0.02 sec Time 0 to 10
sec 2 to 10 sec (high amplitude section)
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Experiment Parametric Models

• ARX A(q)y(t) B(q)u(t) e(t)
• A(q) 1 - 1.555 q-1 2.144 q-2 - 2.789 q-3
  2.904 q-4 - 2.712 q-5 2.068 q-6 - 1.49 q-7
  0.8884 q-8
  
• B(q) -0.2265 q-2 0.1299 q-3 0.4918 q-4
  0.1551 q-5 - 0.2355 q-6 - 0.01897 q-7 - 0.04258
  q-8
• ARMAX A(q)y(t) B(q)u(t) C(q)e(t)
• A(q) 1 - 1.662 q-1 2.204 q-2 - 2.919 q-3
  3.058 q-4 - 2.862 q-5 2.168 q-6 - 1.623 q-7
  0.9367 q-8
  
  
• B(q) -0.3074 q-2 0.1161 q-3 0.474 q-4
  0.1036 q-5 - 0.2755 q-6 - 0.04954 q-7 - 0.01773
  q-8
  
  
• C(q) 1 - 0.5326 q-1 - 0.4614 q-2 0.4486 q-3 -
  0.5441 q-4 0.2542 q-5 0.1483 q-6 - 0.08879
  q-7

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Experiment Results

• ARX Model ARMAX Model

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ExperimentPoles
Blue ETFE Green ARX Red ARMAX
Plot of Poles
Amplitude and Phase correspond with damping and
frequency
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ExperimentModal Properties

• Modal parameters (frequencies, mode shapes, and
  modal damping) are functions of the physical
  properties of the structure (mass, damping, and
  stiffness).
• Changes in the physical properties, (i.e.
  reductions in stiffness) will cause detectable
  changes in these modal properties.

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Conclusion and Future Work

• For this system, ARMAX was a more suitable model
  (97.04 fit)
• Modal properties can help identify damage and
  location
• Future Work
• Apply system identification methods to real data
  and structures
• Learn and implement more parametric models

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Acknowledgements

• Dr. Masanobu Shinozuka, UC Irvine
• Dr. Akira Mita, Keio University
• Dr. Shirley Dyke, Washington Univ. St. Louis
• Dr. Makola Abdullah, Florida AM Univ.
• Dr. Yozo Fujino, University of Tokyo
• National Science Foundation (NSF)
• REUJAT Program

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Thank You!