Date: Location: Den Haag - Nootdorp. Yufei Yuan Aurélien Duret Hans van Lint. Conference on Traffic and Granular Flow 15

Transcription

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: Location: Den Haag - Nootdorp Conference on Traffic and Granular Flow 15 1

2 Contents presentation & background for traffic management L-S LWR formulation Data assimilation methodology On-going research experiments, expected results 2

3 Introduction, control cycle current 3

4 Introduction, control cycle future 4

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 Sensor Model Variational LWR Fundamental Relation Data assimilation method Kalman Filter, Least square method 5

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. 6

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 7

8 Foreword traffic flow model x Eulerian / Lagrangian-time (x, n, t) plane n n Lagrangian-space (n, x) plane t x 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. 8

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 Variational theory in Lagrangian system Laval and Leclercq (2013) Variational theory in T system 9

10 Mesoscopic: Lagrangian-Space LWR formulation The passage time T of the vehicle n at the position x follows: 1/v Refer to: Laval and Leclercq (2013) kx 1/vm 1/w.kx h 10

11 Mesoscopic: L-S LWR numerical solution (graphical) Mesoscopic grid (n, x) plane Mesoscopic grid (x, t) plane n x n n-δn x+δx x x x+δx x t 11

12 Advantages of the L-S LWR formulation 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 12

13 How to incorporate Lagrangian data? Duret.et.al.(2016)* have proposed a data assimilation framework with loop data (x fixed) * 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 How about incorporating Lagrangian type data (n fixed)? And why? - More accurate - Additional info. 13

14 Data assimilation with probe data 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 14

15 Step 1: Estimation of local n indexes x - Space Node downstream xdown o x pi, w Floating car trajectory b n pi, Node upstream xup v m o t pi, t - Time 15

16 Step 1: Estimation of local n indexes x - Space Node downstream xdown a n p Floating car trajectory b n p,1 Node upstream xup b n p,2 t - Time 16

17 Step 2: Observation transformation (o-state) x - Space xdown o x p, end a n p Floating car trajectory o x p, start o τ p w xup n + ( x x ) k a o p p, start up x o o t p, start t p, end t - Time 17

18 Step 2: Observation transformation (o-state) x - Space xdown Floating car trajectory o τ1 o τ 2 o τ 3 xup S t - Time 18

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 19

20 Step 4: Model update CFL condition ΔT FCD FCD Δ T <ΔT S CFL S Δ T >ΔT S a h S CFL o-state b-state a-state u ΔT ~ P FCD u Source: Duret.et.al.(2016) 20

21 Step 4: Model update (1) Vehicle delaying (2) Contradiction (3) Vehicle delaying à similar to (1) (4) Vehicle advancing 21

22 Step 4: Model update (1) (1) Vehicle delaying Source: Duret.et.al.(2016) 22

23 Step 4: Model update (2) (2) Contradiction 23

24 Step 4: Model update (3) (3) Vehicle delaying Source: Duret.et.al.(2016) 24

25 Step 4: Model update (4) (4) Vehicle advancing Source: Duret.et.al.(2016) 25

26 Comparison DA with Loop and FCD Loop ΔT u Loop ΔT CFL ΔT Loop a h ΔT Loop o-state b-state a-state FCD Δ T <ΔT S CFL S ΔT FCD Δ T >ΔT S a h S CFL o-state b-state a-state u ΔT ~ P Loop u u ΔT ~ P FCD u 26

27 Future validation: experimental studies Introduction Formulation Methodology Follow-up 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 27

28 More to come. Thank you for listening! 28