Presentation from NORTHMOST - a new biannual series of meetings on the topic of mathematical modelling in transport. Hosted at its.leeds.ac.uk, NORTHMOST 01 focussed on academic research, to encourage networking and collaboration between academics interested in the methodological development of mathematical modelling applied to transport. The focus of the meetings will alternate; NORTHMOST 02 - planned for Spring 2017 - will be led by practitioners who are modelling experts. Practitioners will give presentations, with academic researchers in the audience. In addition to giving a forum for expert practitioners to meet and share best practice, a key aim of the series is to close the gap between research and practice, establishing a feedback loop to communicate the needs of practitioners to those working in university research.

1. BAYESIAN RISK ASSESSMENT OF
AUTONOMOUS VEHICLES
Christos Katrakazas
Mohammed Quddus
Wen-Hua Chen*
Transport Studies Group
School of Civil and Building Engineering
*Department of Aeronautics and Automobile Engineering
Loughborough University
NORTHMOST 01: ITS-Leeds Monday 12th Dec.

2. Overview
 Introduction to the problem
 Bayesian & Dynamic Bayesian Networks (DBN)
 DBN models and risk assessment of autonomous vehicles
- Variables, estimation of probabilities and inference
 Preliminary findings
 Potential contribution

3. 3
Introduction
Human error is responsible for causing 75 – 90% traffic accidents
Examples:
• Blind-spots & line of sight
• Risk perception
• Reaction time
• Impaired driving
• Fails to look properly
• Excessive/inappropriate speed
Removing the human element from
the task of driving
Potential Solution?
Autonomous vehicles

4. Road to Autonomy
Potential obstacles?
- Reliability
- High quality data
- Perception horizon
How could Transport
Professional help?
4
© European Commission
Roadmap for automated driving

5. 5
Robotics
 Expensive sensors
 Real-time effectiveness
 Lack of context
Collision Prediction (vehicle-level)
In-vehicle sensors
Dangerous road user

6. 6
Transport Engineering
 Aggregated data
 Location-based variables
 Spatio-temporal risk
Could network-level collision predication in transport engineering be
integrated to vehicle-level risk assessment of autonomous vehicles?
- Bayesian Inference?
Collision Prediction (network-level)
Dangerous road segment
Classification
Real-time traffic data

7. Bayesian Networks
 Directed Acyclic Probabilistic
Graphs
 Every node represents a random
variable
 Edges represent probabilistic
dependencies or influences
 Joint Probability Distribution
shows how a situation is
modelled (e.g. the probabilistic
relationship between the
variables of the whole system)
7

8. Bayesian Networks
• Suitable for learning causal
relationships
• Ideal representation for combining
prior knowledge and data
• Help in modelling noisy systems
• Can handle situations where data is
incomplete
BUT
Are applied for events in a particular
point in time!
8

9. Dynamic Bayesian Networks (DBN)
 Bayesian Networks used to model a
system that dynamically changes or
evolves over time
 Probabilistic reasoning over time
 How do the variables affect each
other over time?
 Requirements for DBNs:
1. A prior probability P(x1)
2. A state-transition function P(xt|xt-1)
3. An observation function P(Yt|xt)
Time slice
9

10. Dynamic Bayesian Networks (DBN)
1. A prior (initial) probability
distribution P(x1) in the beginning of
the process;
2. A state-transition function P(xt|xt-1)
specifies time dependencies between
states/variables;
3. An observation function P(Yt|xt)
Specifies dependencies of
observation nodes regarding to
other nodes at time slice t.
10
Time slice

11. Dynamic Bayesian Network (DBN): Example
Raint-1 P(Raint-1)
True (T) 0.7
False (F) 0.3
Raint P(Umbrellat|Raint)
T 0.9
F 0.1
Rain : Hidden Variable
Umbrella : Observed Variable
11

12. Research Question
How could fundamental principles of robotics and transport
engineering be integrated in addressing research challenges
associated with real-time crash prediction of autonomous vehicles?
 Act proactively for the ego-vehicle
 Improve real-time prediction by using network-level hint
 Take traffic environment into account
 May reduce the need for expensive (“super”- accurate) sensor measurements
Potential improvements?

13. Modelling crash prediction in real-time
Required variables:
 Network-level Risk (CRN): “Is the road segment on which the vehicle
travels dangerous or not?”
 Vehicle-level Risk (CRV): “Are the vehicles in the vicinity of the ego-
vehicle dangerous or not?”
 Vehicle Kinematics (K): “How likely is that the vehicles will follow the
same course according to a physical model of motion?”
 Sensor Measurements (Z): “How likely is that the measurements from
the sensors are giving the correct values?”

14. How are the variables connected?
Observations
(Z)
Kinematics
(K)
Crash Risk
Vehicle-Level
(CRV)
Crash Risk
Network-Level
(CRN)
What happens on the road segment
influences the behaviour of the vehicles
If a situation between
vehicles is dangerous,
their motion will be
affected
The motion of the vehicles is depicted in the
sensors’ observations

15. Variable relationship depicted as a DBN
t t + 1 t+2
Figure: Dynamic Bayesian
Network
Markov State Space model
Multi-vehicle dependencies
Single vehicle dependencies

16.  Use traffic flow parameters to estimate the risk of an accident
happening in real-time
 Compare & Contrast traffic conditions just before an accident with
normal conditions
Data: Highways England & DfT
• 15-min Traffic flow data (HATRIS JTDB)
• Historical Accident data (STATS 19)
• Traffic microsimulation (PTV VISSIM) -> 30second traffic data
Method : Machine learning classifiers (i.e. SVMs, RVMs, Random
Forests, k-Nearest Neighbours)
Network – Level Risk

17.  Represents the probability of a crash happening between two
vehicles
 Needs a well-calibrated metric or risk indicator
Data
 Sensor measurements, Maps, Vehicle trajectories
 Methods
 Unscented Kalman Filter for sensor data fusion, Time-to-
collision metrics
 Problems: Efficient data fusion, crashes in real-world
environments
Vehicle – Level Risk

18. Safe and dangerous vehicle contexts
Which of the vehicle trajectories end
up in a collision?
Vehicle – Level Risk
𝑓𝐾 = 𝑓(TTCn
t−1
)
= ቊ
1: dangerous 𝑖𝑓 TTCn
t
< 𝐶𝑟𝑖𝑡𝑖𝑐𝑎𝑙 𝑇𝑇𝐶
0: 𝑠𝑎𝑓𝑒; 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

19. Kinematics/ Vehicle motion
Kinematics
• Kinematics variable describes the probability that the vehicle will
follow a certain course according to the context.
• Uses information on position, heading and speed to distinguish
between contexts

20. Kinematics/ Vehicle motion
Kinematics
Bicycle model
Compromise between bicycle model estimations
and context thresholds
Accuracy of the sensors’ system

21. Sensor measurements
• Each measurement from the sensors contains only partial
information about the environment
• This variable (Z) describes the probability that the sensor
readings correspond correctly to the real values of the
attributes that are measured
Sensor Measurements

22. Correct measurements probability
Sensor Measurements
𝑃 Τ𝑍 𝑛
𝑡
𝐾 𝑛
𝑡
~ 𝑆𝑡𝑢𝑑𝑒𝑛𝑡 𝐶 𝑇
𝐾 𝑛
𝑡
, 𝜎2
𝛪, 𝜈
where C is a rectangular matrix that selects entries from
the kinematic (physical state), ν are the degrees of
freedom, Ι is the identity matrix and σ is related to the
accuracy of the sensor system.

23. Inference
t t + 1 t+2
𝑷 𝑪𝑹𝑽 𝒏
𝒕
= 𝒅 𝑪𝑹𝑽 𝑵
𝒕−𝟏
𝑲 𝑵
𝒕−𝟏
𝑪𝑹𝑵 𝒏
𝒕
> λ

24. Preliminary Findings:
Vehicle-level risk estimation
𝑷 𝑪𝑹𝑽 𝒏
𝒕
= 𝒅 𝑪𝑹𝑽 𝑵
𝒕−𝟏
𝑲 𝑵
𝒕−𝟏
𝑪𝑹𝑵 𝒏
𝒕
and assuming 6 vehicles are sensed
by the ego-vehicle
With network-level hint
σ 𝒏=𝟏
𝑵
(𝒇 𝑲 𝒏
= 𝟏) + σ 𝒏=𝟏
𝑵
(𝒇 𝑪𝑹𝑽 𝒏
= 𝟏) + σ 𝒏=𝟏
𝑵
(𝒇 𝑪𝑹𝑵 𝒏
= 𝟏)
𝑵
=
𝟏+𝟏+𝟏
𝟔
= 𝟎. 𝟓
Without network-level hint
σ 𝒏=𝟏
𝑵
(𝒇 𝑲 𝒏
= 𝟏) + σ 𝒏=𝟏
𝑵
(𝒇 𝑪𝑹𝑽 𝒏
= 𝟏)
𝑵
=
𝟏 + 𝟏
𝟔
= 𝟎. 𝟑𝟑
By simply adding a function checking the network-level collision
risk, hazardous vehicle identification is potentially improved!

25. 25
Potential contribution
 Improve real-time effectiveness of
vehicle-level collision prediction by
making use of network-level risk
- Knowing the road segment
where an accident is likely to
happen
- Find faster which car is going
to trigger the accident in this
road segment
 Make AVs drive in a human-like cautious
way in road segments which are flagged
dangerous (e.g reduce speed)
 Assist obstructed or low-cost AV sensor’
systems.

26. Inspiring Winners Since 1909
Thank you!
Christos Katrakazas
c.katrakazas@lboro.ac.uk