Connecting Surrogate Safety Measures to Crash Probablity via Causal Probabilistic Time Series Prediction_2
2025-04-27
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Connecting Surrogate Safety Measures to Crash Probablity via
Causal Probabilistic Time Series Prediction
Jiajian Lua,∗, Offer Grembeka, Mark Hansenb
a
Safe Transportation Research and Education Center, University of California, Berkeley, 2614 Dwight Way #7374,
Berkeley, CA 94720, U.S.A.
b
114 McLaughlin Hall, Institute of Transportation Studies, University of California, Berkeley, Berkeley, CA 94720,
U.S.A.
Abstract
Surrogate safety measures can provide fast and pro-active safety analysis and give insights on
the pre-crash process and crash failure mechanism by studying near misses. However, validating
surrogate safety measures by connecting them to crashes is still an open question. This paper
proposed a method to connect surrogate safety measures to crash probability using probabilistic
time series prediction. The method used sequences of speed, acceleration and time-to-collision to
estimate the probability density functions of those variables with transformer masked autoregressive
flow (transformer-MAF). The autoregressive structure mimicked the causal relationship between
condition, action and crash outcome and the probability density functions are used to calculate the
conditional action probability, crash probability and conditional crash probability. The predicted
sequence is accurate and the estimated probability is reasonable under both traffic conflict context
and normal interaction context and the conditional crash probability shows the effectiveness of
evasive action to avoid crashes in a counterfactual experiment.
Keywords: Surrogate Safety Measure, Time to collision, Evasive Action, Crash Probability, Density
Estimation, Transformer, Deep Unsupervised Learning, Counterfactual Experiment
1. Introduction
Traditional crash-based safety analysis has many limitations since crash data has small sample
size which leads to unobserved heterogeneity (Lord and Mannering, 2010; Mannering and Bhat,
∗Corresponding author
Email addresses: jiajian_lu@berkeley.edu (Jiajian Lu), grembek@berkeley.edu (Offer Grembek),
mhansen@ce.berkeley.edu (Mark Hansen)
Preprint submitted to Journal of Accident Analysis & Prevention October 5, 2022
arXiv:2210.01363v1 [cs.LG] 4 Oct 2022
2014), lacks detailed information describing the crash process, and can improve traffic safety only
after crashes happen (Laureshyn et al., 2016; Johnsson et al., 2018). On the other hand, traffic
safety analysis using surrogate safety measures (SSM) have attracted more and more interest, since
it can provide fast, pro-active safety analysis, while also yielding insights on the pre-crash process
and crash failure mechanism by studying near misses (Tarko et al., 2009; Tarko, 2019).
The theoretical foundation of surrogate safety indicators assumes that all traffic events are
related to safety. These traffic events have different degree of severity (unsafety) and a relationship
exists between the severity and the frequency of events shown as Figure 1 (Hyd´en, 1987). The
severity of an event is often measured by the proximity in space or time two road users. Time to
collision (TTC) (Hayward, 1971) and post-encroachment time (PET) (Allen et al., 1978) are two
most often used indicators. TTC is the time remaining before the collision if the involved road users
continue with their respective speeds and trajectories and can be calculated as long when vehicles
are on a collision course. The minimum TTC during an interaction is compared to a pre-defined
threshold (1
.
5
s
(Sacchi et al., 2013)) to determine whether this event is a traffic conflict or a normal
interaction.
Figure 1: Safety Pyramid - the Interaction between Road Users as a Continuum of Events (Hyd´en, 1987)
If the relationships between the layers of the safety pyramid is known, it is theoretically possible
to calculate the frequency of the very severe but infrequent events (accidents) based on the known
frequency of the less severe but more frequently occurring events (Svensson and Hyd´en, 2006).
However, connecting traffic conflicts to crashes is still an open question and several methods have
been proposed (Zheng et al., 2021). Hauer and Garder proposed a regression model to relate conflicts
2
and crashes. Davis et al. used a structural equation to model causal relationships among initial
condition, action and crash outcome to estimate the crash probability. Songchitruksa and Tarko used
the extreme value theory (EVT) to model the distribution of TTC and calculated the probability
of TTC reaching the extreme level (
TTC
= 0) as the crash probability. A more detailed review of
these methods is in the next section.
With the development of deep unsupervised learning in computer science field, generative models
(Kingma et al., 2014) can learn the distribution of the data and generate new samples that are
similar to the original data. Some of the models have been applied in the transportation field. Chen
et al. used generative adversarial network (GAN) to generate traffic accident and Ding et al. used
probability graphic model to generate safety-critical scenarios. Lu et al. used transformer encoder
to learn the representation of time series of SSM data to identify traffic conflict. By incorporating
neural networks, such as Long short-term memory (LSTM) and transformer, that can deal with
time series data, probabilistic time series prediction models (Salinas et al., 2020) can predict the
distribution of the data every time step. Therefore, the distribution of time series of TTC can be
estimated and the crash probability can be calculated with probabilistic time series prediction.
In this paper, we propose a non-crash-based method to relate surrogate safety measures to
crashes based on the causal model. Our main contributions are:
1.
The method uses transformer-MAF to predict real time crash probability by estimating the
probability density function of surrogate safety measures for every time step.
2.
The method implements the dependency structure among condition, action and crash outcome
from the causal model into the probability density functions with an autoregressive network.
3.
The method overcomes the limitations of the causal model and uses all values of condition, action
and crash outcome by treating them as continuous variables .
4.
We estimates the model on real-world traffic data to compare the crash probability under traffic
conflict and normal interaction scenarios and calculate the effectiveness of evasive action.
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2. Literature Review
2.1. Connecting SSMs to Crashes
The regression-based method can directly model the relationship between traffic conflict and
crashes given the count of both data. Hauer used linear regression model with form as
λ
=
π·c
where
λ
is the number of crashes on an entity during a certain period of time,
c
is the number of
traffic conflicts on the same entity of the same time and
π
is the crash-to-conflict ratio. (El-Basyouny
and Sayed, 2013) estimated the counts of traffic conflict from traffic volume with Poisson-lognormal
model and incorporated it in a safety performance function with negative binomial model. The
regression-based model are easy to understand and apply but this approach still requires crash data
which suffers from the same issues of the traditional road safety analysis and the crash-to-conflict
ratios may vary for different road entities and time periods (Zheng et al., 2014).
The EVT method can extrapolate the distribution of the observed traffic conflicts to the
unobserved crashes to calculate the crash probability as shown in Figure 2a. Traffic conflicts are
measured by SSMs like TTC and if TTC reaches the extreme level (
TTC
= 0), traffic conflicts
would become crashes. The risk of crash can be calculated as Equation 1
R= Pr(Z≥0) = 1 −G(0) (1)
where
R
is the risk of crash,
Z
is the negated TTC, and
G
(
·
) is the generalized extreme value
distribution or the generalized Pareto distribution. There is growing interest in using EVT for traffic
conflict-based safety estimation through the application of advanced statistical methods. (Zheng
et al., 2018; Zheng and Sayed, 2019c) used bivariate generalized Pareto distribution to estimate
crashes with several different SSMs. With the combined use of different indicators, the model
provides a more holistic approach to measure the severity of an event. (Zheng and Sayed, 2019a,b)
developed Bayesian hierarchical extreme value models to combine traffic conflicts from different sites
for crash estimation in order to overcome the problem that severe traffic conflicts are rare for each
individual site. However, the traffic conflict indicators are mainly proximity metrics such as TTC
and PET while evasive action-based indicators are overlooked. Moreover, the statistical models have
their inherent model assumptions like the parameters of GEV distribution are linearly related to the
site properties (Fu and Sayed, 2021) that sometimes the data do not follow. Additionally, indicators
used in EVT are the extreme of a sequence of SSMs so the temporal correlations in the conflicts are
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not explored, and the EVT method can only be applied to a site-level safety analysis instead of an
individual real-time crash estimation.
The causal model is another non-crash-based method where the crash outcome
y
of an event
depends on its initial condition
u
and action
x
shown as Figure 2b. The probability distribution of
crash outcome is given by Equation 2:
p(y, x, u)=(y|x, u)p(x|u)p(u) (2)
where
p
(
u
) is the probability distribution of the initial condition and
p
(
x|u
) is the conditional
probability distribution of action under the initial condition. The crash probability is by summing
the probabilities of all the actions that could lead to a crash (Davis et al., 2011). The model can
also lead to a natural interpretation of the counterfactual element in the definition of conflict and
(Yamada and Kuroki, 2019) combined the causal model and the potential outcome model (Pearl,
2009) to create a traffic conflict measure that can quantify the effectiveness of a given evasive action
taken by a driver to avoid crashes. However, there are lots of assumptions for this causal model such
as defining a set of initial conditions
U
and a set of evasive actions
X
. It is complicated to estimate
the probability distribution for all possible evasive actions and initial condition and the studies that
employ this definition usually focus on a small subset of possible interactions and participants (Arun
et al., 2021).
(a) Distribution of TTC estimated from EVT model
(Songchitruksa, 2004)
(b) Dependency structure among initial condition u, action x
and crash outcome y(Davis et al., 2011)
Figure 2: Illustration of the EVT model and the causal model
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ConnectingSurrogateSafetyMeasurestoCrashProbablityviaCausalProbabilisticTimeSeriesPredictionJiajianLua,,O erGrembeka,MarkHansenbaSafeTransportationResearchandEducationCenter,UniversityofCalifornia,Berkeley,2614DwightWay#7374,Berkeley,CA94720,U.S.A.b114McLaughlinHall,InstituteofTransportationStudies...
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价格：10玖币
属性：34 页
大小：1.91MB
格式：PDF
时间：2025-04-27
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