Arti cial neural networks predicting pedestrian dynamics ...€¦ · Arti cial neural networks...
Transcript of Arti cial neural networks predicting pedestrian dynamics ...€¦ · Arti cial neural networks...
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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/
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Overview
Simulation of pedestrian dynamics
Artificial neural networks
Corridor and bottleneck experiments
Prediction for the speed
Summary
Slide 2 / 20
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Overview
Simulation of pedestrian dynamics
Artificial neural networks
Corridor and bottleneck experiments
Prediction for the speed
Summary
Slide 2 / 20
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Simulation of pedestrian dynamics
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
))
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Simulation of pedestrian dynamics
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
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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
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https://www.research-collection.ethz.ch/handle/20.500.11850/47999
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Overview
Simulation of pedestrian dynamics
Artificial neural networks
Corridor and bottleneck experiments
Prediction for the speed
Summary
Slide 5 / 20
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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
Artificial neural networks
Non-linear function with many non-interpretable parameters
1See e.g. Saporta, COMPSTAT 2008, pp 315-322 (2008)
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https://link.springer.com/chapter/10.1007/978-3-7908-2084-3_26
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Artificial neural networks
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
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Artificial neural networks
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
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Overview
Simulation of pedestrian dynamics
Artificial neural networks
Corridor and bottleneck experiments
Prediction for the speed
Summary
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Corridor and bottleneck experiments
6m
2m
1.8m
Measurement area
Measurement area
1.8m ω
4m 8m
Waitingarea
Corridor
Bottleneck
1 Slide 9 / 20
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Corridor and bottleneck experiments
Corridor Bottleneck
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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
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Overview
Simulation of pedestrian dynamics
Artificial neural networks
Corridor and bottleneck experiments
Prediction for the speed
Summary
Slide 12 / 20
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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
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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
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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
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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
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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
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Prediction for the speed
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
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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)
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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
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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)
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Overview
Simulation of pedestrian dynamics
Artificial neural networks
Corridor and bottleneck experiments
Prediction for the speed
Summary
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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
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http://ped.fz-juelich.de/database/
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Simulation of pedestrian dynamicsArtificial neural networksCorridor and bottleneck experimentsPrediction for the speedSummary
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