1. No category

Novelty Detection in
Projected Spaces for
Structural Health Monitoring
Janne Toivola, Miguel A. Prada, and Jaakko Hollmén
- Department of Information and Computer Science,
Aalto University School of Science and Technology,
Finland
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maanantaina 10. toukokuuta 2010
Outline
Introduction to SHM
-Transmissibility features
Dimensionality reduction
-Random projections,
Principal Component Analysis,
Curvilinear Component Analysis
Novelty Detection
-k-NN, Gaussian, Mixture of Gaussians, Parzen
Experiments and Results
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Novelty Detection in Projected Spaces for Structural Health Monitoring
maanantaina 10. toukokuuta 2010
Introduction to Structural Health
Monitoring
Motivation and Scope
Challenges
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maanantaina 10. toukokuuta 2010
The scope of our project
Structural Health Monitoring
-monitor the condition of structures, like buildings,
bridges, cranes, etc.
-detect damages before they become apparent faults
Multidisciplinary research project: ISMO
-Intelligent Structural Health Monitoring System
Two major problems:
-no practical sensors to indicate damage
-large structures require wireless sensors
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Novelty Detection in Projected Spaces for Structural Health Monitoring
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Vibration-based SHM
Structures vibrate due to input excitation
from the environment
-for example, traffic and wind cause bridges to shake
-properties of the structure affect the response
Accelerometers for measuring the vibration
output from the structure
Major problem: input signal from the
environment remains unknown!
-environmental variability vs. state of the structure?
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Novelty Detection in Projected Spaces for Structural Health Monitoring
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Modeling disciplines
Physics-based models
-complex and detailed numerical models of structures
-require lots of prior information: ”blueprints”
-enable more elaborate damage assessment etc.
Data-based models
-simple and generic models
-rely more on machine learning and acquired data
-useful mainly for detecting damages
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Novelty Detection in Projected Spaces for Structural Health Monitoring
maanantaina 10. toukokuuta 2010
Transmissibility features
Ratio of vibration amplitudes
-one sensor location s1 compared to another s2
-specific to a given frequency f
!
!
! Xs1 (f ) !
!
T (s1 , s2 , f ) = !!
Xs2 (f ) !
Attempts to measure how well energy
propagates between two points
-eliminates environmental variability (overall amplitude)
-combinations of sensor pairs and monitoring
frequencies lead to a large feature space
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Novelty Detection in Projected Spaces for Structural Health Monitoring
maanantaina 10. toukokuuta 2010
Dimensionality Reduction
Random Projections
Principal Component Analysis
Curvilinear Component Analysis
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maanantaina 10. toukokuuta 2010
Background
Previous results reported in [IDA2009]
-randomly selected feature sets of different sizes
-supervised damage classification
-result: damage detection possible with few
transmissibility features (32 out of 6300)
However: supervised learning not realistic
-data from damaged structures not available IRL
-novelty detection instead of pattern classification
-feature selection not possible in advance, but how
about projections to lower dimensions?
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Novelty Detection in Projected Spaces for Structural Health Monitoring
maanantaina 10. toukokuuta 2010
Random Projections
projection
matrix
Select a random
Rk×d

√
according to  P (rij = − 3) = 1/6
P (rij = √
0) = 2/3

P (rij = 3) = 1/6
Project data from d to k dimensions by
y = Rx
Motivated by Johnson-Lindenstrauss lemma
Computationally inexpensive
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Novelty Detection in Projected Spaces for Structural Health Monitoring
maanantaina 10. toukokuuta 2010
Principal Component Analysis
Classical signal decomposition method
used in pattern recognition
Selects a new orthogonal basis for the data
points according to eigenvectors
By selecting k leading eigenvalues and
corresponding eigenvectors, most of the
variance represented in the new basis
Linear projection...
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Novelty Detection in Projected Spaces for Structural Health Monitoring
maanantaina 10. toukokuuta 2010
Curvilinear Component An.
Nonlinear projection method
Based on a neural network
-an intermediate layer of model vectors
Cost function to minimize
-considers inter-point distances in both input and output
space ! "
2
(Dij − Yij ) Fλ (Yij )
if Yij > Dij
E=
2
2
(Dij
− Yij2 )2 Fλ (Yij )/4Dij
if Yij <= Dij
ij
Interpolation and extrapolation provided for
projecting new data
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Novelty Detection in Projected Spaces for Structural Health Monitoring
maanantaina 10. toukokuuta 2010
Novelty Detection Methods
k-Nearest Neighbor
Gaussian
Mixture of Gaussians
Parzen density estimation
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maanantaina 10. toukokuuta 2010
Nearest Neighbor method
Memorize all projected training data points
Compute distance between the new point x
and its (kth) nearest neighbor NN(x)
As a reference, compute the distance
between the nearest neighbor NN(x) and its
nearest neighbor NN(NN(x))
Ratio of these distances is a novelty score
-assumes the distances are suitable for the projected
feature space
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Novelty Detection in Projected Spaces for Structural Health Monitoring
maanantaina 10. toukokuuta 2010
Gaussian Densities
Fit a single multivariate normal distribution
to the training data
Assign the area of low density, below some
threshold, to outliers
-unimodal, symmetric ellipsoid as decision boundary
”Rescales” the projected feature space
according to the covariance matrix
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Novelty Detection in Projected Spaces for Structural Health Monitoring
maanantaina 10. toukokuuta 2010
Mixtures of Gaussians
Fit a sum of several multivariate normal
distributions to the training data
-achieved via Expectation Maximization algorithm
-diagonal covariance matrices used
Assign the area of low density, below some
threshold, to outliers
-several symmetric and axis-aligned ellipsoids as the
decision boundary
Allows few (separate) clusters of data
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Novelty Detection in Projected Spaces for Structural Health Monitoring
maanantaina 10. toukokuuta 2010
Parzen Density Estimation
Sum of multivariate normal distributions at
each training data point
-spherical covariance used and the width parameter
determined by Maximum Likelihood solution
Assign the area of low density, below some
threshold, to outliers
-superposition of many spheres as decision boundary
Combines aspects of k-NN and MoG
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Novelty Detection in Projected Spaces for Structural Health Monitoring
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Experiments and Results
The Bridge
AUROC values for combinations of methods
Examples of ROC curves
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maanantaina 10. toukokuuta 2010
The Bridge
Wooden model
bridge used
Shaker
Wired sensors
1
4
10
7
2
5
11
8
13
9
shaker
19
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Novelty Detection in Projected Spaces for Structural Health Monitoring
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3
15
6
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Data and Preprocessing
15 wired accelerometers produced
-2509 time series of 32 seconds each
-sampling frequency of 256 Hz
attached various small weights as damages
-masses range from 23.5 g to 193 g
transmissibility features extracted
-for 19 pairs of adjacent sensors (not for all 105 pairs)
-with 512-point FFT, averaging each 8 blocks (16 s)
-resulting data stream: 4541 feature values / 16 s
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Novelty Detection in Projected Spaces for Structural Health Monitoring
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AUROC for k-NN
AUROC values with k−NN
0.75
0.7
AUROC
0.65
0.6
0.55
0.5
None
Random
PCA
CCA
0.45
0
10
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1
10
2
10
dimensionality of classifier input space
Novelty Detection in Projected Spaces for Structural Health Monitoring
maanantaina 10. toukokuuta 2010
3
10
4
10
AUROC for Gaussian
AUROC values with Gaussian
0.75
0.7
AUROC
0.65
0.6
0.55
0.5
None
Random
PCA
CCA
0.45
0
10
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1
10
2
10
dimensionality of classifier input space
Novelty Detection in Projected Spaces for Structural Health Monitoring
maanantaina 10. toukokuuta 2010
3
10
4
10
AUROC for MoG
AUROC values with MoG
None
Random
PCA
CCA
0.75
0.7
AUROC
0.65
0.6
0.55
0.5
0.45
0
10
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1
10
2
10
dimensionality of classifier input space
Novelty Detection in Projected Spaces for Structural Health Monitoring
maanantaina 10. toukokuuta 2010
3
10
4
10
AUROC for Parzen Method
AUROC values with Parzen
None
Random
PCA
CCA
0.75
0.7
AUROC
0.65
0.6
0.55
0.5
0.45
0
10
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1
10
2
10
dimensionality of classifier input space
Novelty Detection in Projected Spaces for Structural Health Monitoring
maanantaina 10. toukokuuta 2010
3
10
4
10
Examples of ROC with k-NN
ROC curves of k−NN with 500−D projection by CCA
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0.9
0.9
0.8
0.8
0.7
0.7
true positive rate
true positive rate
ROC curves of k−NN with 16−D projection by PCA
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0.6
0.5
0.4
0.6
0.5
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0
false positive rate
0.1
0.2
0.3
0.4
0.5
0.6
false positive rate
16-dim. PCA versus 500-dim. CCA
-median AUROC of 0.7112 and 0.7448
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Novelty Detection in Projected Spaces for Structural Health Monitoring
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0.7
0.8
0.9
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Summary I
Application domain considered
-Need for dimensionality reduction
-Need for novelty detection
General level solution as combination of
projections and novelty detection methods
-The problem of distributing the computation still not
considered at this stage
-Application requirements were open: Will a certain
combination of methods work in SHM, or not?
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Novelty Detection in Projected Spaces for Structural Health Monitoring
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Summary II
Several combinations of methods
benchmarked with a real-world data set
-Experience gained about the performance of several
methods
-Nonlinear projections reach better performance
-k-NN and Parzen density estimates outperform simpler
density-based novelty detection methods
More research still required
-Applicability domain of transmissibility features?
-More and better data sets and density models?
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Novelty Detection in Projected Spaces for Structural Health Monitoring
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Thanks for listening!
...any questions or comments?
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Novelty Detection in Projected Spaces for Structural Health Monitoring
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