Traffic measures to improve estimates of traffic flow conditions

Gennaro Ciccarelli1, Ernesto Cipriani2, Chiara Colombaroni1, Gaetano Fusco1,

Stefano Gori2, Livia Mannini2

Outline

• Research scope

• Problem Description

• Model Estimate

• Neural Network Estimate

• Kalman Filter Estimate

• Comparison

• Conclusions and Further Developments

Research scope

• Exploit traffic measures and models to improve estimation of traffic flow conditions

• Data available from different sources: probe vehicles; loop detectors; flows entering toll gates

• Different kinds of measures: travel times on road segments, speeds and traffic counts on fixed sections

• Different tools available: traffic model; direct travel time estimation; Kalman filter theory

Approaches to traffic prediction

• Traffic prediction can be categorized into model-based and data driven approaches.

• Model based methods predict traffic conditions based on traffic flow theory or real-time traffic simulation.

• Data-driven methods predict traffic conditions based on current and past real-world detector data, without explicitly considering the physical traffic processes.

A1 Italianmotorway

220 km

7 loop detectors

17 beacons

Rome ring freeway

68 km

5 loop detectors

1 000 000 GPS positions

Real case applications

MODEL ESTIMATE

Calibration framework

FORMULATION OF THE

OPTIMIZATION PROBLEM

OBJECTIVE FUNCTIONS

SCANNING AND CHOICE OF

PARAMETERS TO CALIBRATE

APPLICATION OF AN

EVOLUTIONARY ALGORITHMS

COMPARISON OF RESULTS

BASED ON FIXED AND MOBILE

SENSORS DATA

MODEL IMPLEMENTATION

FOR REAL CASE APPLICATIONS

State of the art on calibration of traffic flow models

• Ngoduy, D., Maher, M.J, 2012. Calibration of second order traffic models using continuous cross entropy method

• Luspay, T., Kulcsr, B., Varga, I., Bokor, J., 2010. Parameter-dependent modeling of freeway traffic flow

• Wang, Y., Papageorgiou, M., Messmer, A., 2006. RENAISSANCE: a unified macroscopic model-based approach to real-time freeway network traffic surveillance

• Wang, Y., Papageorgiou, M., 2005. Real-time freeway traffic state estimation based on extended Kalman filter: a general approach

• Papageorgiou, M., Blosseville, J.M., Hadi-Salem, H., 1989. Macroscopic modelling of traffic flow on the Boulevard Peripherique in Paris

13 km, 26 road segments, 10 on-off ramps

Case study 1: Rome Ring road (FCD)

Ricostruzione e previsione di traffico da

misure puntuali Pagina 9 30/10/2012

vf=120 km/h

ρcr=27 veh/km/lane

τ=36s

ν=35 km2/h

κ=13 veh/km

δ=0,9

Traffic variables updated every 10 s on segments of 500m

vi (k+1) =

vi (k)+

+T

Li

vi (k) vi-1(k)- vi (k)[ ] +

+T

tve(ri (k))- vi (k)é

ëùû+

-nT ri+1(k)- ri (k)[ ]

t Li ri (k)+k[ ]+

-dT

Lili

æ

èç

ö

ø÷ri (k)vi (k)

ri (k)+k

Convection term

Relaxation term

Anticipation term

On-ramp flows term

Current speed

30/10/2012 Pagina 10

Empirical calibration results

Influence of parameter Influence of parameter

30/10/2012 Pagina 11

n=1.5

d=7.2

Ricostruzione e previsione di traffico da

misure puntuali

Empirical calibration results

Case study 2: A1 motorway

L=38 km

• 2 lanessouthboundhighway • from km 221.9 to km 259.9 • 2 inductiveloop detectors • 3 tollgatescollectingtrafficcounts • probe vehiclesprovided with

tollpaymentdevices

Trafficvariablesupdatedevery 10 s on everysegments of 500m length

Main calibration issues

• Limited spatial coverage of the detectors: 1 loop on a 40 km length

• Accuracy of the detectors and/or missing traffic data

• Representativeness of the probe vehicle sample

• Estimation of flow entering/exiting the motorway (splitting rates): we only have flows at toll gates

Uncongested vs. congested scenarios for model calibration

0

500

1000

1500

2000

2500

3000

3500

4000

0:00 4:48 9:36 14:24 19:12 0:00

Flo

w (

veh

/h)

Time

Flow vs. time - Upstream inductive loop detector

January, 14th

January, 30th

0

20

40

60

80

100

120

0:00 4:48 9:36 14:24 19:12 0:00

Spee

d (

km/h

)

Time

Speed vs. time - Upstream inductive loop detector

January, 14 th

January, 30 th

0

500

1000

1500

2000

2500

3000

0:00 4:48 9:36 14:24 19:12 0:00

Flo

w (

veh

/h)

Time

Flow vs. time - Downstream inductive loop detector

January, 14th

January, 30th

0

20

40

60

80

100

120

0:00 4:48 9:36 14:24 19:12 0:00

Spee

d (

km/h

)

Time

Speed vs. time - Downstream inductive loop detector

January, 14 th

January, 30 th

Formulation of the optimization problem

3 objective function formulations (model estimates updated every 10 s on segments (77) of 500 m:

• Speed and flows from loop detectors

• Travel times on monitored sections from probe vehicles

• Speed and flows + travel times

ob_ fun1= min a

1

n_ loops×n_int(q(i, j )- qest (i, j )

j=1

n_int

åi=1

n_ loops

å )2

1

n_ loops×n_intq(i, j )

j=1

n_int

åi=1

n_ loops

å2

+

1

n_ loops×n_int(v(i, j )- vest (i, j )

j=1

n_int

åi=1

n_ loops

å )2

1

n_ loops×n_intv(i, j )

j=1

n_int

åi=1

n_ loops

å2

æ

è

ççççç

ö

ø

÷÷÷÷÷

ob_ fun2 = min

1

n_sec tion×n_int(t(i, j )- test (i, j )

j=1

n_int

åi=1

n_sec tion

å )2

1

n_sec tion×n_intt(i, j )

j=1

n_int

åi=1

n_sec tion

å2

æ

è

ççççç

ö

ø

÷÷÷÷÷

ob_ fun3= ob_ fun1+ob_ fun2

Particle swarm optimization Venter, G. and Sobieski, J., “Particle Swarm Optimization,” 2002

Calibration results – 30th January

RMSE_q=330 RMSEN_q=0.36

RMSE_v=12 RMSEN_v=0.12

Validation results – 28th-31th January

Cal

ibra

tio

n RMSEN_q=170

RMSEN_q=0.15

Cal

ibra

tio

n

RMSEN_v=6 RMSEN_v=0.06

ARTIFICIAL NEURAL NETWORK ESTIMATE

Travel time prediction by Neural Network

• Expected advantages:

– 1) NNs can produce accurate multiple step-ahead prediction.

– 2) NNs have been tested with significant success in modeling complex temporal and spatial relationships.

– 3) NNs is capable of modeling highly non-linear relationships in a multivariate setting (Zhang et al. 1998).

NNs applications to short-term traffic prediction

• Simple multilayer perceptron (MLP) (Fusco, Gori and Penna (1992); Smith and Demetsky, 1994; Park and Rilett, 1999; Zhang, 2000; Huisken and Van Berkum, 2003; Innamaa, 2005)

• MLP with a learning rule based on a Kalman filter (Vythoulkas, 1993)

• Modular neural networks (Park and Rilett, 1998)

• Radial basis neural networks (Park et al. 1998)

• Spectral basis neural networks (Park et al. 1999; Rilett and Park, 2001);

• Time-delayed neural networks (TDNN) (Yunet al. 1998; Abdulhaiet al. 1999; Dia, 2001; Lingraset al. 2002; Ishaket al. 2003);

• State-space neural networks (SSNN) (Van Lintet al. 2002; Van Lint et al. 2005; Van Lint, 2006; Liu, et al. 2006a, Singh, and Abu-Lebdeh, 2007).

Configuration of the neural network

• 4 input neurons (4 previous time intervals) • 10 hidden neurons • 1 output neuron (next time interval) • Linear transfer function • Swarm learning algorithm

• Application on a freeway stretch of 5 km

– RFID Beacons Telepass: detection of vehicles and corresponding time instants

– Loop detectors: detection of instant speed

• Data aggregate on time interval of 5 minutes • Learning data set: 5853 observations (1-28 Jan) • Validation data set: 847 observations (28-31 Jan)

Convergence of learning process to estimate

0 5 10 15 20 25 30 35 40 45 500

2

4

6

8

10

12

Number of iterations

Mea

n S

qu

are

Erro

r

0 5 10 15 20 25 30 35 40 45 500

0.2

0.4

0.6

0.8

1

1.2

1.4

Number of iterations

Mea

n s

qu

are

erro

r

Travel Mean Speed Travel Time

Comparison of observed data and corresponding output of ANN

(Validation Set 28-31 January 2011)

0 200 400 600 800 1000 12000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Detection Time Interval (5 min)

No

rmal

ized

Spe

ed

Observed speed

Simulated speed

RMSE=9.17 km/h RMSEN=0.10

0 100 200 300 400 500 600 700 800 9000.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Detection Time Interval (5min)

No

rmal

ized

Tra

vel T

ime

Observed Travel Time

Simulated Travel Time

RMSE=256.7s RMSEN=0.36

EXTENDED KALMAN FILTER

State of the art

• Wang Y., Papageorgiu M.[2005]. “Real-time freewa ytraffic state Estimation based on EKF: a general approach”.

• Wang Y., Papageorgiu M.[2008]. “Real-time freeway traffic state estimation based on EKF: Adaptive capabilities and real data testing”.

• Nanthanwichit C., Nakatsuji T., Suzuki H.[2007]. “Application of Probe-vehicle data for real time traffic state estimation and short term travel time prediction on a freeway”.

• Zuurbier F.S., L. H., Knoop V.L.[2006]. "State estimation using an EKF and the first order traffic flow model DSMART.“

• Yuan Y. et al. [2011]. “Freeway Traffic State Estimation using EKF on First-order Traffic Model in Lagrangian Coordinates”.

• Van Lint H., Hoogendoorn S.P.[2009].“A robust and efficient method for fusing heterogeneous data from traffic sensors on freeways”.

Data fusion State vector fusion:

Speed estimation

Error computed with respect to average segment speed

S by model Scorr. by loop S corr. by RFID S state vector fusion S corr. by loop, by RFID RMSE 18 14 10 11 7 RME 0,16 0,14 0,11 0,10 0,07 MAE 3,0 1,6 1,8 1,3 0,9

MANE 0,17 0,14 0,11 0,11 0,08

Travel Time estimation

Error computed with respec tto travel time detected

TT by model TT corr. by loop TT corr. by RFID TT state vector fusion TT corr. by loop,by RFID RMSE 77 58 44 66 51 RME 0,20 0,13 0,09 0,16 0,13 MAE 10,3 5,9 4,2 6,8 7,0

MANE 0,23 0,13 0,09 0,17 0,13

Speed estimation: Comparison EKF and NN

EKF NN RMSE 10 9

RMSEN 0,12 0,11 RME 0,09 0,07 MAE 8 6

Error computed with respect to speed detected by loop

EKF and NN applied on the basis of loop detector data

TT estimation – Comparison EKF and NN

Error computed with respect to TT detected by RFID

EKF and NN applied on the basis of RFID data

EKF NN RMSE 90 95

RMSEN 0,35 0,37 RME 0,19 0,20 MAE 48 50

Conclusions and further developments

• Traffic predictions obtained by using EKF and modeling approach have shown good results

• The two data driven approach EKF and NN provide similar results in terms of mean speed estimation and in terms of travel time estimation

• Improvements of estimates can be obtained with an accurate data treatment (high noise)

• Implementation of fusion technique based on EKF and NN are under way

• Further developments will focus on definition of a joint calibration framework for traffic state prediction and anomalous event detection