Arti cial neural networks predicting pedestrian dynamics ...€¦ · Arti cial neural networks predicting pedestrian dynamics in complex buildings Antoine Tordeuxa, Mohcine Chraibi

Conference Stochastic Models, Statistics and their Application 2019

Session : Big data and the calibration of mobility simulations

Artificial neural networks predictingpedestrian dynamics in complex buildings

Antoine Tordeuxa, Mohcine Chraibib, Armin Seyfriedc, and Andreas Schadschneiderd

R aUniversity of Wuppertal (BUW) [email protected] vzu.uni-wuppertal.debForschungszentrum Jülich [email protected] fz-juelich.de/ias/ias-7c Forschungszentrum Jülich & BUW [email protected] asim.uni-wuppertal.ded University of Cologne [email protected] thp.uni-koeln.de/as

— SMSA2019, March 6th to 8th, 2019, TU Dresden, Germany —

http://vzu.uni-wuppertal.de/http://www.fz-juelich.de/ias/ias-7/EN/Home/home_node.html;jsessionid=17280AED1F561B537B07577C61774111https://www.asim.uni-wuppertal.de/http://www.thp.uni-koeln.de/~as/

Overview

Simulation of pedestrian dynamics

Artificial neural networks

Corridor and bottleneck experiments

Prediction for the speed

Summary

Slide 2 / 20


I Control of crowd and pedestrian flows in term of safety and performance

– Large infrastructures (train station, shopping malls) or large events (sport events, festivals)

I Pedestrian dynamics are not straightforward to predict

– Complex human behaviors including learning and anticipation / Complex multi-agent systems

I Management and control thanks to simulation tools

– Microscopic models inspired from physical, social, psychological or proxemics concepts / Examplesare force-based (social force), velocity-based or rule-based

– Models based on few interpretable parameters (desired speed, pedestrian size, ...)

I Fundamental diagram

– Phenomenological relationship between the speed (or the flow rate) and the density (or the meandistance spacing)

– Weidmann’s model (1992) W (s̄, v0,T , `) = v0

(1 − exp

(` − s̄v0T

))

Slide 3 / 20

Speed/Spacing relationship for the Weidmann’s model (1992)

Mean distance spacing

Sp

eed

`

0v 0

W(s) = v0(

1− exp(

`−sv0T

))v0 : Desired speed

T : Time gap

` : Pedestrian size

1/T

Slide 4 / 20

https://www.research-collection.ethz.ch/handle/20.500.11850/47999

Overview





Summary

Slide 5 / 20

Models for understanding versus Models for prediction1

INPUT

State of the system at t

Positions/velocities

of surrounding neigh-

bors and obstacles

OUTPUT

State of the system at t + 1

Velocity, acceleration

rate, jerk, etc. . .

Parametric models

Acc = f (xi , xj , ...) or Speed = g(xi , xj , ...)

with parameters v0, `, τ , ...

Non-linear function with few interpretable parameters


Non-linear function with many non-interpretable parameters

1See e.g. Saporta, COMPSTAT 2008, pp 315-322 (2008)

Slide 6 / 20

https://link.springer.com/chapter/10.1007/978-3-7908-2084-3_26


I Data-based machine learning approaches for the motion prediction

– For autonomous driving, motion of robots in crowded environments or pedestriandynamics in complex geometries2

– Artificial neural networks (convolutional, LSTM, deep learning, ...)

I Feed-forward neural networks for speed prediction according to the positions ofthe K nearest neighbors

1. Inputs are the relative positions to the K nearest neighbours (2K inputs)

NN1 = NN1(xi − x , yi − y , 1 ≤ i ≤ K

).

2. Speed prediction according to the relative positions and the mean distance spacing s̄Kto the K nearest neighbours (2K + 1 inputs)

NN2 = NN2(s̄K , (xi − x , yi − y , 1 ≤ i ≤ K)

).

2See e.g. Alahi et al., 2016; Chen et al., 2017; Das et al., 2015; Ma et al., 2016

Slide 7 / 20

http://openaccess.thecvf.com/content_cvpr_2016/html/Alahi_Social_LSTM_Human_CVPR_2016_paper.htmlhttps://ieeexplore.ieee.org/abstract/document/8202312https://link.springer.com/article/10.1007/s40534-015-0088-9https://ieeexplore.ieee.org/document/7464842

Overview





Summary

Slide 8 / 20


6m

2m

1.8m

Measurement area

Measurement area

1.8m ω

4m 8m

Waitingarea

Corridor

Bottleneck

1 Slide 9 / 20


Corridor Bottleneck

Slide 10 / 20

Speed/Spacing relationship

0.5 1.0 1.5 2.0 2.5 3.0

0.0

0.5

1.0

1.5

Mean spacing, m

Sp

eed

,m

/s

Experiment

Bottleneck

Corridor

Experiment Spacing (m) Speed (m/s) ` (m) T (s) V0 (m/s)

Corridor 1.03 ± 0.40 0.35 ± 0.33 0.64 0.85 1.50Bottleneck 1.14 ± 0.37 0.72 ± 0.34 0.61 0.49 1.64

Slide 11 / 20

Overview





Summary

Slide 12 / 20

Setting the network structures

I Fully connected neurons spread in hidden layers

I Setting the network structures: Optimal number of layers and neurons

→ Tested structures (1)3, (2), (3), (4,2), (5,2), (5,3), (6,3) and (10,4)4

I Cross-Validation: Split of the data in training and testing homogeneous datasets

I Training thanks to back-propagation algorithm, minimising the mean squarederror

MSE =1

N

N∑i=1

(vi − ṽi

)2.

I Training and testing in bootstrap loops (50 subsamples) to evaluate the precisionof estimation

3One hidden layer with 1 neuron4Two hidden layers with respectivelly 10 and 4 neurons

Slide 13 / 20

Network NN1 based on the relative positions

0.0

20

.04

0.0

60

.08

0.1

0

Hidden layers

MS

E

(1) (3) (5,2) (6,3)

(2) (4,2) (5,3) (10,4)

Testing

Training

± bootstrap SD

NN1

Slide 14 / 20

Network NN1 based on the relative positions

0.0

20

.04

0.0

60

.08

0.1

0

Hidden layers

MS

E

(1) (3) (5,2) (6,3)

(2) (4,2) (5,3) (10,4)

NN1

Slide 14 / 20

Network NN2 based on the relative positions and mean spacing

0.0

20

.04

0.0

60

.08

0.1

0

Hidden layers

MS

E

(1) (3) (5,2) (6,3)

(2) (4,2) (5,3) (10,4)

Testing

Training

± bootstrap SD

NN2

Slide 14 / 20

Network NN2 based on the relative positions and mean spacing

0.0

20

.04

0.0

60

.08

0.1

0

Hidden layers

MS

E

(1) (3) (5,2) (6,3)

(2) (4,2) (5,3) (10,4)

NN2

Slide 14 / 20


I Analyse of several combinations of training and testing sets to evaluate theprecision and robustness of the predictions

I Tested scenario Notation :Training set / Testing set

C: Corrridor experiment

B: Bottleneck experiment

– B/B and C/C.

Single dataset is used for both training and testing

– B/C and C/B.

Prediction ability in new situations

– C+B/B, C+B/C and C+B/C+B.

Prediction in heterogeneous situations

I Weidmann speed model used as benchmark

Slide 15 / 20

Mean squared errorNN1: based on relative positions — NN2: based furthermore on mean distance spacing

0.0

30

0.0

40

0.0

50

0.0

60

Scenario

Tes

tin

gM

SE

C/C C/B C+B/C C+B/C+B

B/B B/C C+B/B

Weidmann

NN1 with h = (5,3)

NN2 with h = (3)

Slide 16 / 20

Quality of the fit

I Weidmann’s model based on k0 = 3 parameters

I Artificial neural networks NN1 and NN2 based on k1 = 189 and k2 = 88

I Akaike Information Criterion for the quality of the fit (normal residuals)

AIC = 2k + n ln(MSE) + n(1 + ln(2π)

)

Weidmann

Residuals, m/s

Den

sity

-1.0 -0.5 0.0 0.5 1.0

0.0

1.0

2.0

NN1

Residuals, m/s

-1.0 -0.5 0.0 0.5 1.0

0.0

1.0

2.0

NN2

Residuals, m/s

-1.0 -0.5 0.0 0.5 1.0

0.0

1.0

2.0

Slide 17 / 20

AIC differenceNN1: based on relative positions — NN2: based furthermore on mean distance spacing

-20

00

20

06

00

Scenario

AIC

diff

eren

ce

C/C C/B C+B/C C+B/C+B

B/B B/C C+B/B

NN1 with h = (5,3)

NN2 with h = (3)

Slide 18 / 20

Overview





Summary

Slide 19 / 20

Summary

I Significant prediction improvement of pedestrian dynamics (MSE and AIC) with artificialneural networks in cases of heterogeneous scenarios

I First steps for the modelling of pedestrians behaviors in complex infrastructures/buildings

I Data-based approach for the prediction – No modelling of mechanisms governing thepedestrian motion

I Use of mean spacing as input, even if based on pedestrian relative positions alreadyprovided, allows improving the prediction and reducing the network complexity

I Training, testing and setting of the network complexity with large experimental datasets5

I Prediction of full trajectories in two dimensions and coupling to strategical routing modelsfor simulation in complex scenarios

I Comparison to other parametric models (force-based models) and multi-agent systems

5ped.fz-juelich.de/database

Slide 20 / 20

http://ped.fz-juelich.de/database/

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Many thanks for your attention!

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Simulation of pedestrian dynamicsArtificial neural networksCorridor and bottleneck experimentsPrediction for the speedSummary

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Arti cial neural networks predicting pedestrian dynamics ...€¦ · Arti cial neural networks predicting pedestrian dynamics in complex buildings Antoine Tordeuxa, Mohcine Chraibi

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