presentation-final

Inflight Engine Shutdown Abnormality Detection
Using One Class Support Vector Machines
Team Members: Lin Han
Shuowei Li
Xiyu Peng
Client: NASA
Advisor: Dr. David Matteson
Date: 05/01/2015

Inflight Engine Shutdown (IFESD)

Data Description
• 35*6000 Flights
• 200 Variables (14 selected)[1][2]
• Length Varies (2,000-‐50,000)
• One Single Flight
• Data Source: https://c3.nasa.gov/dashlink/projects/85/
…… ……
[1]. Mack, D.L.C., et al. (2011). Using Augmented Naive Bayesian classifers to Improve Engine Fault Models.
[2]. Mack, D.L.C., et al. (2011). Deriving Bayesian Classifiers from Flight Data to Enhance Air-‐ craft Diagnosis Models.

Data Type
• Abnormal Flight (n=5)• Ground Test• Normal Flight

Var_x
Abnormal
happens A reaction
window wRandomly
choose the end
Flight start
Flight end
Var_x
Normal Abnormal
Length = 𝑙 Length = 𝑙
Data Transformation

Normal Abnormal
FF_1 FF_2 FF_3 N_1
……
FF_1 FF_2 FF_3 N_1
……
14 subsets, from the
same location of 14
variables in one dataset
14 subsets, from the
same location of 14
variables in one dataset
Data Transformation

Normal Abnormal
…… ……
𝑋
Data Transformation (Vectorization)

min
&,(

1
2
ω
-
+ 𝐶 0 𝜉2
3
245
𝑆𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜:
𝑦2 𝝎 𝑻
𝒙2 + 𝑏 ≥ 1 − 𝜉2 𝑎𝑛𝑑 𝜉2 ≥ 0
for all i = 1, … , n
Tricks
• Tuning Parameter Cost C
• Kernel Map Function
Support Vector Machines (SVM)
Margin
Support Vector
y = 1
y = -‐1

Two Class SVM
……Train
Data
Matrix
Response: (0, 0, …, 0, 1, 1, 1, 1)
Train Data:
600 Normal + 4 Abnormal
Test Data:
100 Normal + 1 Abnormal
C = 2P-
~25R
Kernel: laplacedot

• Worse performance with more data.
• Two-‐Class is not ideal for our data, and we propose another
way.
Two-‐Class Result

All normals are alike;
each abnormal is
different in its own way.
Normal
Flights
Abnormal
Flights
One-‐class SVM
Happy families are all alike; every unhappy
family is unhappy in its own way.
-‐-‐-‐-‐ Leo Tolstoy

min
&,(,S

1
2
ω
-
+
1
𝑣𝑛
0 𝜉2 − 𝜌
3
245
𝑆𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜: 𝜔 ∗ 𝜙 𝑥2 ≥ 𝜌 − 𝜉2 𝑎𝑛𝑑 𝜉2 ≥ 0 for all i = 1, … , n
• Tuning Parameter 𝜈
• upper bound on the training error
• lower bound on the fraction of data points to become Support Vectors
One Class SVM for Novelty Detection

Package:
Kernel:
Num train datasets:
𝜈:
𝑙:
𝑤:
Test datasets: 100 normal flights, 5 abnormal flights
Model selection
Tasks
√ kernlab
laplacedot√
𝑙𝑜𝑔5](𝜈)
√ 800
√ 10P5.-
√ 500

• Tuning Parameters
§ Number of training datasets = 800
§ Length = 500
§ 𝜈 = 10P5.-
• Other Model Parameters
§ Kernel Hyperparameter 𝜎 = 5.959 ∗ 10Pd
§ Number of support vectors = 53
§ Objective Function Value : 1104.189
§ Performance
§ Training Error rate = 6.34%
§ 10-‐fold cross validation error rate: 7.18%
§ Normal flight test error rate = 3.6%
§ Abnormal flight test error rate = 0%
Best Model
Package:
Kernel:
Num train datasets:
𝜈:
𝑙:
𝑤:
Tasks
√ kernlab
laplacedot√
√ 800
√ 10P5.-
√ 500

• The reaction window 𝑤: ending point of truncated data to abnormality
Abnormal Prediction
Prediction = Abnormal
𝑙
Package:
Kernel:
Num train datasets:
𝜈:
𝑙:
𝑤:
Tasks
√ kernlab
laplacedot√
√ 800
√ 10P5.-
√ 500

Abnormal Prediction
Further look into historical flight data

• One-‐class SVM fits our situation better.
• The cause of abnormality might be accumulated from previous flights.
• This research can be furthered by comparing different algorithms.
• Recommend client to take longer historical data into consideration.
Summary

Ackownledgements
We would like to thank:
• Cornell University, Department of Statistical Science for providing this
research opportunity
• The National Aeronautics and Space Administration
• Our mentor, Dr. David Matteson, for his support during the
completion of this project

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