Basic Civil Engineering first year Notes- Chapter 4 Building.pptx
PhD research (Yuan)
1. What does it mean to be a PhD?
—Experience & Current Research
12-11-2010 Yufei Yuan, PhD Candidate
Delft University of Technology MasterClass T&P / TIL
Leading to Doctoral Research…
Master — T & P
Internship:
Urban & Inter-Urban traffic control scenario management
Master Thesis:
Coordination of ramp metering control in motorway networks
PhD
Traffic state estimation of prediction for road network traffic control
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2. What does it mean to be a PhD?
Research
e.g. (in my case)
Traffic state estimation and prediction for road network control
Publishing results Papers Conferences/Journals
Give or follow courses/workshops (TUD or TRAIL)
Contract projects with other parties (B.V. or Gov.)
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0.
Research scope and current research
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3. Research Scope
real traffic system
real traffic system
traffic
traffic (a) state estimation
traffic
traffic
actuators
actuators
• Monitoring / (b) state prediction
sensors
sensors
state estimation
(c)
optimization State State
State
initial
prediction estimation /
estimation /
• State estimation / state data fusion
data fusion
goals
state prediction
optimize
• State prediction / DTM input: OD matrices,
capacity constraints,
measures
optimization network specs, etc
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Current research & results
— Lagrangian Traffic State Estimation for Freeways
Brief overview
Eulerian/Lagrangian formulation of LWR (first-order traffic flow model)
Lagrangian state estimator and application
Empirical and simulation study
Comparing with Eulerian case
Conclusions and Further research
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4. 1.
Brief overview
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Eulerian formulation of LWR
Eulerian Coordinates
Coordinates
Variables
Kinematic wave model No. of Vehices
Fundametal diagrams
(Daganzo, Smulders)
Numerical solution
(Mode switching)
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5. Eulerian Coordinates
Lagrangian Coordinates
How about Lagrangian coordinates?
Rencent Studies…
Leonhard Euler Joseph Louis Lagrange
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Lagrangian formulation of LWR
Lagrangian Coordinates
Coordinates
Variables
Kinematic wave model Position of Vehices
Fundametal relations
Numerical solution An upwind scheme…(Next)
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6. Lagrangian formulation
Lagrangian Coordinates
Numerical solution An upwind scheme [less non-linear]
Traffic characteristics only move in the
same (downstream) direction
(increasing vehicle number instead of space)
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2.
New state estimator and application
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7. Traffic state estimation based on EKF
Eulerian Coordinates
Discretized LWR model Process model
ρ ti+1 − ρ ti qti − qti −1
+ =0
Δt Δx
Fundametal relations Observation (measurement) model
However,
the process model is highly
non-linear, hard to solve;
mode-switching,
large error (wrong sign)…
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A new model-based EKF state estimator
Lagrangian Coordinates
(Explicit) Discretized Lagrangian model Process model
s ti+1 − s ti vti − vti −1
+ =0
Δt Δn
Fundametal relations Observation (measurement) model
Both Eulerian and Lagrangian sensing data are considered
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8. Application to Freeway Traffic
State Estimation [Essence]
The essence : to reproduce the freeway traffic conditions
based on limited measurement data
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Traffic state estimator based on EKF
Advantage in Lagrangian Coordinates
Exactness: ‘less non-linear’, more accurate, less
numerical diffusion
Implementation: more straightforward
Linearization: more accurate , ‘same’ sign (Differentiability)
A natural observation equation for floating car data
Challenge in Lagrangian Coordinates
Formulating proper observation models for spatially fixed
observations (Loop data) Solved!
Modelling network discontinuity (complex)
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9. Challenge:
Network Discontinuity
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3.
Empirical and simulation study
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10. Empirical Study
comparing with Eulerian Case
Upstream in-flow known
M42 motorway in UK
Full individual data
Same (speed)
observations
1. Lagrangian: FCD
2. Eulerian: Loops
3. Ground truth data Study area: downstream of onramp
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Empirical Study
Figure: RMSE comparison between two methods for 8
simulation runs of scenario 200m-loop. Blue(E) Red(L)
The most important observation:
in all scenarios the Lagrangian state estimator out-performs its
Eulerian counterpart by up to 24% for density and 75% for speed.
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11. Empirical Study
Figure: Snapshots of a small region from the whole x-t speed map
for the Eulerian estimation (Left) and the Lagrangian estimation (right)
Rectangles: discritized (calculation) cells
Curved lines: trajectories of vehicle groups
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Simulation Study
with Network Discontinuity
Off-Ramp On-Ramp
Origin
Driving direction Destination
Inflow
Von-Neumann out-flow condition
Upstream in-flow known
On-ramp & off-ramp flow known
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12. Simulation Study
with Network Discontinuity
Node models in Lagrangian state estimator
To do:
Further compared with Eulerian approach
FOSIM synthetic data realistic
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4.
Preliminary conclusion and
further research
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13. Preliminary conclusion
• Lagrangian state estimation out-performs Eulerian state
estimation more accurate estimates.
• Both Eulerian & Lagrangian sensing data are well incorporated
• Promotes the application of EKF
(Solution to the mode-switching problem[upwind or downwind])
• Validates the (elementary) node models
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Further research directions
Developing more advanced Node Models and application
Comparing the performance of Lagrangian model with its
Eulerian counterpart at network levels (on/off ramp)
Using different combinations of data sources
Realistic data at network levels
Implementing the method in a real traffic network (A10)
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