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EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Characteristics in Flight DataEstimation with Logistic Regression
and Support Vector Machines
ICRAT 2004Claus Gwiggner, LIX, Ecole Polytechnique Palaiseau
Gert Lanckriet, EECS, University of California, Berkeley
Characteristics in Flight Data
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Flow Management and Planning Differences
Time slots are distributed among aircraft to avoid congestion
•In reality, delays, re-reroutings, etc. lead to missed time slots
•Not the same number of aircraft than planned arrive in sectors:
•safety, lost capacity
Planning Differences
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Related Work
Factors/Causes [ATFM Study, PRR]Slot adherence, flight plan quality, in-flight change of
route, .... Simulations [Ky, Stortz]
Random noise on departure times Reactionary Delay [Toulouse Study]
microscopic model of departure times
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Unknown
Real situation at sector entries interplay of factorscompensations of delays ...
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Program
Problem Formulation Simple Characteristics Binary Classification Conclusion Future Work
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Planning Differences
Planning Differences = Regulated Demand – Real Demand
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
General Problem Formulation
Find 'regularities' of planning differences, useful to improve the current planning procedureWhy? Safety, suboptimal used capacityHow?
MACRO approach: relations between flows, not single deviations from flight plans
Daily basis, not extreme situations How? Data analysis
141 days of week-day data
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Today's Question
Are planning differences of different sectors the 'same'? if yes: any model can be greatly simplified if no: what are the differences?
Difficulty24 dimensions: one variable for each hour
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Comparison of Planning Differences
No visible regularities in both sectors ...
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Mean and Standard Deviation
...but similar mean and standard deviation over the time
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
H0: same underlying distribution ... reject on 1 % levelassumes that statistical properties do not vary over time
.... but what are the characteristics?e.g. 'if high peaks at noon => sector 1'? Find a rule that tells whether a sequence of values
belongs to sector 1Classification problem
Hypothesis Tests
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
(Binary) Classification
Probabilistic 'what is the probability
that a new item belongs to sector 1?'
Logistic Regression
Geometric 'on which side of the
boundary lies the new item?'
Support Vector Machines
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Comparison
Linear Logistic Regression vs SVMs linear vs non-linearsimple vs mathematically sophisticated traditional vs state-of-the-artprobabilistic vs geometric
Common points [Hastie et. al 2003], [Friedman 2003]SVM estimator of class probabilities logistic regression induces linear boundaries
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Experiments on ...
Data from 4 sectors in Upper Berlin airspaceRaw Data (random permutations)Data where number of instances in both classes are
balanced In total 8 experiments conducted
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Model Selection
Report Estimated Prediction Error (EPE) Model Selection:
Cross-Validation [Stone 1974]Wilcoxon-Mann-Whitney Test
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Parameters of SVMs
Kernel functionsLinear, Gauss, Poly, Linear CN, Gauss CN, Poly CN
Kernel parameters Cost Function
1 Norm, 2 Norm In total over 800 combinations possible
best one estimated by cross validation
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Results
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Summary
characteristics in high dimensional data
comparison of a very simple and a very complicated classification method
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Conclusions
There are systematic differences between different sectors
SVMs do not promise major improvementno more than 4% better than logistic regression
Linear Prediction is possibleExpected prediction errors around 15 %
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Future Work
(black box) prediction not satisfactory Better understanding of the underlying processes
reasons for the differencesmodel of the probability distribution of planned traffic and
realized traffic
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Questions ?
• Thanks for your attention!
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Results
Is Week End?
Sector Raw Bal+Perm Variable Sel RandomUR1 UR2 UR3 UR4
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Known: Causes for Planning Differences
Departure Slot adherenceInconsistent profile
CASA implementation
In flight change of route
Regulations too late Weekday, SeasonWeather
Source: Independent Study for the Improvement of ATFM, Final Report, 2000
Slot tolerance windowMissing flight plansIncorrect flight plan information
Priorities:Very HighHighMediumUnknown
time
# over-deliveries
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Little known: Dynamics of Planning Differences
X: timeY: Number of planning differences
Sector n...
'Error'Propagation
Sector 2Sector 1
Related Work: Simulation studies, reactionary delay studies
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Summary Motivation
Are planning differences unpredictable? Or are there hidden 'regularities'?
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Possible Research Questions
Propagation over the network Dependence on traffic density, sector complexity, ... ... Characteristics Comparison of different sectors
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Notation
A sector is represented as a vector of 24 variables, one for each hour
An instance is a value for this vector An instance belongs to class 1 or -1; dependent on the
sector from which it was drawn
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Binary Classification
● Given:
Instances from sectors 1 and -1● Question:
a rule to decide for a new instance to which sector it might belong
● Example: if 'high peaks at noon' then class 1Decision trees
EUROCONTROL EXPERIMENTAL CENTRE
INNOVATIVE RESEARCH
Geometric and Probabilistic Approaches
example: Instances are 2 dimensional
Geometric Instances are points in
Euclidean spaceRules are class boundaries
Problem: overlapping classes
ProbabilisticClasses have underlying
probability distributionRules are class-probabilities
Problem: which distribution?