network-wide mesoscopic traffic state estimation based on ... · • introduction & background...
TRANSCRIPT
![Page 1: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/1.jpg)
1
Network-wide mesoscopic traffic state estimation based on a variational formulation of the LWR model and
using both Lagrangian and Eulerian observations
• Yufei Yuan • Aurélien Duret • Hans van Lint
Date: 28-10-2015 Location: Den Haag - Nootdorp
Conference on Traffic and Granular Flow ‘15
![Page 2: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/2.jpg)
2
• Introduction & background for traffic management
• L-S LWR formulation • Data assimilation methodology
• On-going research – experiments, expected results
Contents presentation
• Introduction • Formulation • Methodology • Follow-up…
![Page 3: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/3.jpg)
3
Introduction, control cycle current
• Introduction • Formulation • Methodology • Follow-up…
![Page 4: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/4.jpg)
4
Introduction, control cycle future
• Introduction • Formulation • Methodology • Follow-up…
![Page 5: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/5.jpg)
5
Data assimilation framework Estimation of state: combine real-time measurements and simulation model in order to represent current traffic situation. Also known as data assimilation.
Process Model
Variational LWR
Sensor Model
Fundamental Relation
Data assimilation method
Kalman Filter, Least square method…
• Introduction • Formulation • Methodology • Follow-up…
![Page 6: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/6.jpg)
6
Data assimilation framework, data
Fixed location (infrastructure) … e.g., Loop data have considerable noise and bias
Along with the traffic (vehicles) … e.g., Probe vehicle data provide x, t, v.
• Introduction • Formulation • Methodology • Follow-up…
![Page 7: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/7.jpg)
7
Data assimilation framework, model
As main traffic flow model type, traffic flow models at macroscopic or mesoscopic levels are chosen: • Describes traffic at a more aggregated level • Views traffic as a fluid • Fast computation
• Discretization: divide network into cells
• Introduction • Formulation • Methodology • Follow-up…
![Page 8: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/8.jpg)
8
Foreword – traffic flow model
n
x
Lagrangian-space (n, x) plane
x
t
Eulerian / Lagrangian-time (x, n, t) plane
n
q Eulerian formulation: distance and time (x, t) - prevailing
q Lagrangian-time coordinates: vehicle no - time (n, t)
q Lagrangian-space coordinates: vehicle no - distance (n, x) – T coord.
• Introduction • Formulation • Methodology • Follow-up…
![Page 9: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/9.jpg)
9
Mesoscopic: Lagrangian-Space LWR formulation
Conservation law (LWR) in Lagrangian-space coordinates
Variational principle (considering travel time flux) Daganzo 2005 – Variational theory in Eulerian system Leclercq et al. 2007 – Variational theory in Lagrangian system Laval and Leclercq (2013) – Variational theory in T system
• Introduction • Formulation • Methodology • Follow-up…
![Page 10: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/10.jpg)
10
Mesoscopic: Lagrangian-Space LWR formulation The passage time T of the vehicle n at the position x follows:
• Introduction • Formulation • Methodology • Follow-up…
Refer to: Laval and Leclercq (2013) 1/v
h
1/vm
kx
1/w.kx
![Page 11: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/11.jpg)
11
Mesoscopic: L-S LWR numerical solution (graphical)
n
x
x
t
Mesoscopic grid (n, x) plane
Mesoscopic grid (x, t) plane
x+Δx
x
x+Δx x
n-Δn n
• Introduction • Formulation • Methodology • Follow-up…
![Page 12: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/12.jpg)
12
Advantages of the L-S LWR formulation
• Introduction • Formulation • Methodology • Follow-up…
• Variational formulation – simple to implement, numerical accurate
• Mesoscopic scale – individual vehicle tracking with macroscopic behavioural rules
• Easy to address spatial discontinuities (merges, diverges,
lane-drops) & computational efficiency (#node, #veh.)
• Convenient for state estimation
![Page 13: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/13.jpg)
13
• Duret.et.al.(2016)* have proposed a data assimilation framework with loop data (x fixed)
• How about incorporating Lagrangian type data (n fixed)?
• And why?
How to incorporate Lagrangian data?
• Introduction • Formulation • Methodology • Follow-up…
* Duret.et.al.(2016). Data assimilation based on a mesoscopic-LWR modeling framework and loop detector data : methodology and application on a large-scale network
- More accurate - Additional info.
![Page 14: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/14.jpg)
14
Four steps in each sequence: • Estimation of local vehicle indexes of probe data
• Observation transformation (observation state)
• Global analysis & Data assimilation
(background state + observation state => analysis state)
• Model update
Data assimilation with probe data
• Introduction • Formulation • Methodology • Follow-up…
![Page 15: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/15.jpg)
15
Step 1: Estimation of local n indexes
• Introduction • Formulation • Methodology • Follow-up…
t - Time
Nodedownstream
xdown
Nodeupstreamxup
x - Space
,op ix
,op it
,bp in
Floating car trajectory
w
mv
![Page 16: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/16.jpg)
16
Step 1: Estimation of local n indexes
t - Time
Nodedownstream
xdown
Nodeupstreamxup
x - Space
Floating car trajectory
apn
• Introduction • Formulation • Methodology • Follow-up…
,1bpn
,2bpn
![Page 17: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/17.jpg)
17
Step 2: Observation transformation (o-state)
t - Time
xdown
xup
x - Space
Floating car trajectory
apn
opτ,
op startx
,op endx
,op startt ,
op endt
,( )a op p start up xn x x k+ − ⋅
w
• Introduction • Formulation • Methodology • Follow-up…
![Page 18: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/18.jpg)
18
Step 2: Observation transformation (o-state)
• Introduction • Formulation • Methodology • Follow-up…
t - Time
xdown
xup
x - Space
Floating car trajectory
S
1oτ
2oτ
3oτ
![Page 19: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/19.jpg)
19
Step 3: Global analysis (b+o => a state)
Determine analysis state (based on o-state and b-state) By data assimilation - e.g., Kalman filter, least square method…
• Introduction • Formulation • Methodology • Follow-up…
![Page 20: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/20.jpg)
20
Step 4: Model update – CFL condition
FCD o-stateFCDTΔ
b-state
a-stateCFL
ST TΔ < Δ
~u uFCDT PΔ
aSh
S
CFLST TΔ > Δ
• Introduction • Formulation • Methodology • Follow-up…
Source: Duret.et.al.(2016)
![Page 21: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/21.jpg)
21
Step 4: Model update
(1) Vehicle delaying
(2) Contradiction
(3) Vehicle delaying à similar to (1)
(4) Vehicle advancing
• Introduction • Formulation • Methodology • Follow-up…
![Page 22: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/22.jpg)
22
Step 4: Model update (1)
(1) Vehicle delaying
• Introduction • Formulation • Methodology • Follow-up…
Source: Duret.et.al.(2016)
![Page 23: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/23.jpg)
23
Step 4: Model update (2)
(2) Contradiction
• Introduction • Formulation • Methodology • Follow-up…
![Page 24: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/24.jpg)
24
Step 4: Model update (3)
(3) Vehicle delaying
• Introduction • Formulation • Methodology • Follow-up…
Source: Duret.et.al.(2016)
![Page 25: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/25.jpg)
25
Step 4: Model update (4)
(4) Vehicle advancing
• Introduction • Formulation • Methodology • Follow-up…
Source: Duret.et.al.(2016)
![Page 26: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/26.jpg)
26
Comparison DA with Loop and FCD
Loop o-stateLoopTΔ
b-state
a-stateLoop
aThΔ
u CFLLoopT TΔ ≤ Δ
~u uLoopT PΔ
FCD o-stateFCDTΔ
b-state
a-stateCFL
ST TΔ < Δ
~u uFCDT PΔ
aSh
S
CFLST TΔ > Δ
• Introduction • Formulation • Methodology • Follow-up…
![Page 27: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/27.jpg)
27
• Mesoscopic simulation platform: validation done with loop • Addition with FCD data for validation
• 5 node case in a synthetic network, with both loop and FCD
Future validation: experimental studies
• Introduction • Formulation • Methodology • Follow-up…
![Page 28: Network-wide mesoscopic traffic state estimation based on ... · • Introduction & background for traffic management • L-S LWR formulation • Data assimilation methodology •](https://reader035.vdocument.in/reader035/viewer/2022070711/5ec9d0a1ea65d0120411f624/html5/thumbnails/28.jpg)
28
More to come….
Thank you for listening!
• Introduction • Formulation • Methodology • Follow-up…