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Road Risk Modeling and Cloud-Aided Safety-Based Route Planning

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  • Nikola Motor Company

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This paper presents a safety-based route planner that exploits vehicle-to-cloud-to-vehicle (V2C2V) connectivity. Time and road risk index (RRI) are considered as metrics to be balanced based on user preference. To evaluate road segment risk, a road and accident database from the highway safety information system is mined with a hybrid neural network model to predict RRI. Real-time factors such as time of day, day of the week, and weather are included as correction factors to the static RRI prediction. With real-time RRI and expected travel time, route planning is formulated as a multiobjective network flow problem and further reduced to a mixed-integer programming problem. A V2C2V implementation of our safety-based route planning approach is proposed to facilitate access to real-time information and computing resources. A real-world case study, route planning through the city of Columbus, Ohio, is presented. Several scenarios illustrate how the "best" route can be adjusted to favor time versus safety metrics.
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IEEE TRANSACTIONS ON CYBERNETICS 1
Road Risk Modeling and Cloud-Aided
Safety-Based Route Planning
Zhaojian Li, Student Member, IEEE, Ilya Kolmanovsky, Fellow, IEEE, Ella Atkins, Senior Member, IEEE,
Jianbo Lu, Senior Member, IEEE, Dimitar P. Filev, Fellow, IEEE, and John Michelini
Abstract—This paper presents a safety-based route planner
that exploits vehicle-to-cloud-to-vehicle (V2C2V) connectivity.
Time and road risk index (RRI) are considered as metrics to
be balanced based on user preference. To evaluate road seg-
ment risk, a road and accident database from the highway
safety information system is mined with a hybrid neural net-
work model to predict RRI. Real-time factors such as time
of day, day of the week, and weather are included as correc-
tion factors to the static RRI prediction. With real-time RRI
and expected travel time, route planning is formulated as a
multiobjective network flow problem and further reduced to a
mixed-integer programming problem. A V2C2V implementation
of our safety-based route planning approach is proposed to facil-
itate access to real-time information and computing resources.
A real-world case study, route planning through the city of
Columbus, Ohio, is presented. Several scenarios illustrate how
the “best” route can be adjusted to favor time versus safety
metrics.
Index Terms—Data mining, mixed-integer program-
ming (MIP), neural network modeling, road risk index (RRI),
route planning.
I. INTRODUCTION
ACCORDING to a recent report [1] from the United States
(U.S.) National Highway Traffic Safety Administration
(NHTSA), 33 561 people lost their lives on U.S. roadways
during 2012. The estimated property damage caused by auto
accidents exceeded U.S. $200 billion. To increase vehicle
safety, various improvements in vehicle design and control
are being pursued. For example, adaptive cruise control sys-
tems [2], [3] are being implemented to automatically adjust
the vehicle speed to maintain a safe following distance. Lane
keeping assist systems [4], [5] can alert the driver when the
system detects that the vehicle is about to deviate from a traf-
fic lane. In addition, the AAA Foundation for traffic safety has
implemented the U.S. road assessment program to rank road
risk into five levels, helping drivers plan their travel routes and
Manuscript received February 2, 2015; revised May 14, 2015; accepted
September 1, 2015. This work was supported by the Ford Motor
Company—University of Michigan Alliance. This paper was recommended
by Associate Editor D. D. Wu.
Z. Li, I. Kolmanovsky, and E. Atkins are with the Department of Aerospace
Engineering, University of Michigan, Ann Arbor, MI 48105 USA (e-mail:
zhaojli@umich.edu;ilya@umich.edu;ematkins@umich.edu).
J. Lu, D. P. Filev, and J. Michelini are with the Research and
Innovation Center, Ford Motor Company, Dearborn, MI 48121 USA (e-mail:
jlu10@ford.com;dfilev@ford.com;jmichel1@ford.com).
Color versions of one or more of the figures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TCYB.2015.2478698
assisting road agencies to improve the roads [6]. In this paper,
we propose road risk management through risk-aware route
planning, with the goal of determining routes with low risk of
accident as well as fast travel time. While modern vehicle nav-
igation systems are able to generate optimal routes in terms
of travel time, distance, or fuel economy, in this paper, we
augment such cost terms with a safety-based risk metric. The
developments in this paper fall within the broader context of
risk management which is important not only in engineering
but also in business applications [7]–[9].
Due to road geometries, distractors, traffic density, and other
factors, some roads are more prone to accidents than others.
To assess relative risk level and in turn implement safety-
based route planning, a quantitative risk metric is required.
Road risk index (RRI), which is modeled as a function
of risk exposure, crash rate, and severity, is accepted as
a quantitative metric to reflect the relative crash risk as a
function of road segment [10]–[12]. If available, RRI can
also be used in safety-based route planning. However, crash
rate records classified by route segment are not commonly
available. As a result, some objective crash rate prediction
models have been developed to predict crash rate based on
road geometry. Shaw-Pin and Harry [10] studied the relation
between highway crash rates and road geometries with ordi-
nary least squares (OLSs) and Poisson regression (PR) models.
A quantile regression (QR) model was developed in [12] and
demonstrated to have a better prediction performance com-
pared with the OLS and PR models proposed in [10]. In
this paper, a hybrid artificial neural network (ANN) is devel-
oped and demonstrated to have a better performance than the
previously proposed models.
To develop the crash prediction model, an informative
database with 30 682 road segments and 144 821 crashes from
the highway safety information system (HSIS) is processed.
While many advanced modeling techniques such as poly-
nomial regression, support vector regression, and ANN are
available, the ANN has been demonstrated to effectively model
complex relationships and has been successfully applied in a
variety of applications such as handwriting recognition [13],
vehicle fuel economy modeling [14], and traffic prediction
modeling [15]. From a practical implementation standpoint,
ANNs have an important advantage in that they are familiar
to automotive engineers and represent proven technology that
has been used in production vehicles [16]. Automotive engi-
neers thus already understand ways to make the ANN-based
solutions robust to real-world variability and noise factors.
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2IEEE TRANSACTIONS ON CYBERNETICS
Fig. 1. Architecture of cloud-aided safety-based route planning.
In this paper, a hybrid ANN model is developed for road
crash rate prediction. The ANN modeling process itself is not
new but our crash rate prediction ANN is a new ANN applica-
tion. The inputs of this ANN include road geometries (segment
length, curvature, grade, etc.) and traffic density (annual aver-
age daily traffic). The outputs are the predicted crash rates
categorized in three severity levels (fatality, injury, and prop-
erty damage only). Furthermore, the raw data are partitioned
into three clusters with a fuzzy C-means clustering algorithm
and three separate neural networks from data in each cluster
are trained. This hybrid ANN model accurately predicts RRI
as a function of road geometries and traffic information.
While this static hybrid neural network model can accu-
rately predict RRI given road geometries and historical traffic
information, real-time factors such as weather, time of day, or
day of the week, which can affect the risk level, need to be
also considered. We, therefore, augment the prediction model
with a dynamic layer to include such influences by employing
multiplicative correction factors; these factors have not been
considered in previous crash prediction models [10]–[12].
Safety-based route planning considers both travel time and
risk in selecting the best route. The aim is to find a route with
a minimum composite cost, which, in this paper, is based on
the travel time and RRI. Cost function weights reflect driver
preferences. This problem can be specified as a multiobjective
optimization problem that reduces to a mixed-integer program-
ming (MIP) problem. A real-world route planning from Scioto
Downs Inc, Ohio to Delaware, Ohio, is used to demonstrate
this route planning functionality. Several examples are pre-
sented to illustrate how the “safe” route can be different from
the fastest route and how real-time factors can influence the
resulting routes.
The proposed safety-based route planning functionality is
envisioned within the framework of a vehicle-to-cloud-to-
vehicle (V2C2V)-equipped vehicle fleet. Interest in cloud
computing has been growing as the cloud provides capac-
ity to rapidly perform complex computations, provide stor-
age capacity, and just-in-time service with pay-as-you-go
pricing [17]–[19]. In our proposed V2C2V route planning
architecture, safety is factored into planner decisions as illus-
trated in Fig. 1. As in other V2C2V applications, vehicles
communicate with the cloud through a wireless channel.
Fig. 2. Safety-based route planning overview.
The user initiates planning by providing the origin (current
position by default), the destination, preferences that inform
RRI weights, and vehicle identification number. If the driver
fails to follow the planned route, the vehicle keeps sending
its global positioning system coordinates to the cloud so that
the planner can replan and update the routes accordingly. The
cloud hosts our RRI model (see Section II) and the planning
algorithm. Real-time traffic and weather information can be
obtained from a variety of sources. For example, INRIX XD
Traffic delivers detailed traffic speeds every 800 ft (250 m)
across four million miles of roads in 37 countries [20]. While
INRIX and other traffic data sources can ultimately be inte-
grated within our route planner, incorporation of this data
is beyond the scope of this paper. We therefore generate
representative data for our simulation studies.
The overview of this paper is given in Fig. 2. A road and
accident database from the HSIS is first processed to extract
road characteristics. With a hybrid neural network, the data are
then translated to a road risk database which is subsequently
combined with real-time factors to provide a safety-based route
planning. The real-time factors include time of day, day of
the week, real-time weather, and traffic. Then a safety-based
route planning is realized using an MIP algorithm with the
real-time RRI, traffic, and a used-specified weighting factor.
The contributions of this paper include the following. First,
by processing an informative road and accident database from
HSIS, a hybrid ANN model is developed to efficiently pre-
dict crash rate. The hybrid ANN is demonstrated to have a
better performance than existing models presented in previous
publications [10]–[12]. In addition, real-time factors such as
weather, time of day, and day of the week which have not been
considered in previous models are incorporated as correction
factors to a static RRI. An original framework for safety-
based route planning is presented to provide optimal routes
balancing safety and the traditional metrics such as travel time.
Last but not least, real-world case studies are presented to
demonstrate the applicability of the proposed route planning
framework. While comprehensive time-based route planners
and a number of road risk models have been studied previ-
ously, this paper integrates risk and time together in a holistic
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LI et al.: ROAD RISK MODELING AND CLOUD-AIDED SAFETY-BASED ROUTE PLANNING 3
route planning framework. As compared to conference version
of [21], this paper is significantly extended with additional
details, interpretations, and case studies.
The remainder of this paper is organized as follows.
Section II develops a neural-network-based risk prediction
model and compares it with QR and OLSs to quantify perfor-
mance improvement. Model sensitivity to changes in inputs
are analyzed and RRI dependence on various factors is estab-
lished in Section III. Real-time factors affecting road risk and
their modeling are discussed in Section IV. The safety-based
route planning problem is formulated using an MIP problem in
Section V. Real-world case studies are presented to illustrate
the safety-based route planning in Section VI, and Section VII
concludes this paper.
II. ROAD RISK MODELING
A. Road Risk Index
A natural way to model the risk level of a road segment is
to associate it with a crash rate (e.g., number of accidents per
year). However, this method has two deficiencies: 1) it cannot
be used for roads with no historical crash data and 2) it is
not able to predict the dependence on dynamic factors such as
traffic density and road geometries.
In the past two decades, a different approach based on an
RRI has emerged. De Leur and Sayed [11] studied a driver-
based subjective assessment of existing road risks. Objective
statistical crash prediction models have also been devel-
oped. Shaw-Pin and Harry [10] proposed a PR model and
Wu and Zhang [12] presented a QR method. These statisti-
cal risk models relate crash counts to influencing factors such
as road geometries and traffic information and can be used
to predict crash rate, generate road risk indices, and suggest
improved road designs.
In [11] and [12], RRI is modeled as a function of exposure,
crash rate, and severity. Exposure represents the amount of
activity in which a crash may occur; vehicle miles traveled
is the most common measure of exposure. Crash rate is the
number of crashes per unit of exposure. It is proportional to the
probability of a crash. Crash severity reflects the consequence
of crashes in terms of injuries and property damage. Crash
severity is officially classified in three categories: 1) fatality;
2) injury; and 3) property damage only [1]. Since we develop
RRI for individual drivers, we only consider crash rate and
severity in defining RRI so that
RRI(i)=F
j=1,2,3
nijSj/AADTi
(1)
where iis road segment number, RRI(i)is the risk index of
road segment i,j=1,2,3, represents the severity level of
fatality, injury, and property damage only, respectively, nij is
the predicted number of accidents of level jto occur over
road segment iin a certain period of time, e.g., during one
year, Sjis the cost of an accident of type j, and F(·)is a
function that scales the cost of most homogenous segments
to an index between 0 and 100. According to a report from
the Bureau of transportation statistics [12], the average costs
of fatality, injury, and property damage accidents are S1=
$4 113 956, S2=$144 291, and S3=$6783, respectively.
The AADTiin (1) represents the annual average daily traffic
on road segment i. In this paper, a linear function F(x)=x/10
is used and (1) becomes
RRI(i)=1
10
j=1,2,3
nijSj/AADTi.(2)
We develop a data-driven model to predict the number of
accidents nij as a function of road segment geometry, traffic
conditions, and weather conditions.
B. HSIS Database
Road and crash data from the HSIS [22] are utilized
to develop a crash rate prediction model. The HSIS has
a multistate database that contains crash, roadway inven-
tory, and traffic volume data for a select group of states
(Washington, California, Minnesota, Illinois, Ohio, Maine, and
North Carolina). Crash data and road information for Ohio
from 2006 are used in this paper to develop a risk prediction
model. The Ohio data provided by HSIS include the following.
1) Accident (accident, vehicle, and occupant).
2) Roadway inventory file, denoted Roadlog.
3) State supplemental inventory, containing curve and
grade.
Accidents are recorded case-by-case. Separate files contain-
ing vehicle and occupant information can be linked to accident
data for specific cases using the accident case number. The
accident data can also be linked to a Roadlog file using three
common variables: 1) county; 2) route number; and 3) mile-
post. Unlike an accident file, each record in the Roadlog file
contains information on a homogeneous section of the road-
way (i.e., a stretch of road that is consistent in terms of certain
characteristics), with each new section being defined by a new
beginning reference point. Each record in the Roadlog file
contains current characteristics of the road system including
surface type and width, shoulder and median information, and
lane information.
Data on 30 682 homogeneous road segments and 144 822
accidents for the year 2006 in Ohio were processed and eight
features were extracted as inputs to the model. These features
include the following.
1) Pavement roughness, defined as the international rough-
ness index (IRI). Generally, a road segment is smooth if
its IRI is under 100 and rough if its IRI is above 180.
RRI varies from 30 to 562.
2) Speed limit, the officially marked speed limit of the road
segment in mile per hour (mph). Speed limit varies from
20 to 65 mph.
3) Segment length, the length of a homogenous road
segment in miles. It varies from 0.01 to 16.97 miles.
4) Number of lanes, representing the total number of lanes
over both travel directions. The range is from 1 to 11.
5) Annual average daily traffic per lane, reflecting aver-
age traffic density. AADT per lane varies from
27.5 to 56 980.
6) Width per lane, varying from 7 to 36 ft.
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4IEEE TRANSACTIONS ON CYBERNETICS
TAB LE I
EXPLANATORY AND RESPONSE VARIABLE STATISTICS
7) Curvature, the maximum degree of curvature in that
road segment. An n-degree curve turns in the forward
direction by ndegrees over 100 ft. Curvature ranges
from 0 to 270 degrees.
8) Grade, representing the largest slope over the road seg-
ment in percent, which is the tangent of the angle of
inclination times 100. Grade ranges from 0% to 20%.
To build an objective model relating database features to acci-
dent rate, the above eight features are used as the explanatory
variables and accidents of each type in Ohio in 2006 are the
response variables. The statistics of these variables are listed
in Table I. We next explore models to capture relationships
between explanatory and response variables.
C. Crash Rate Prediction
In this section, we develop and compare OLSs, QR, and
neural network models to predict the crash rates based on
explanatory variables in Table I.Let{xi,yij}represent the
observations for road segment i,i=1,2,...,30 682. xiis
the vector of explanatory variables as in Table I, and yij is
the number of level jaccidents occurring on road segment i,
where j=1,2,3 represents fatality, injury, and property dam-
age only, respectively. We note that the difference between
yij and nij in (1) is that yij represents database statistics while
nij is the prediction with a certain model.
1) Ordinary Least Squares: OLS is a linear regression
model linking the explanatory variable xiand response
variable yij
yij =xT
iβj+ij (3)
where βjis the 8 ×1 vector of identified parameters and ij
represents fitting errors. Note that since there are three separate
response variables denoting each one of severity levels, we
have three sets of linear models for j=1,2,3. For each linear
model, βjminimizes the sum of fitting error squared and is
given by
ˆ
βj=XTX1XTYj(4)
where Yjis a 30 682 ×1 vector, and Xis an 30682 ×8matrix
of regressors. With ˆ
βjidentified, the number of accidents of
level jcan be predicted by
nij =xT
iˆ
βj.(5)
2) Quantile Regression: Wu and Zhang [12] developed a
crash rate prediction model with QR. QR provides a more
comprehensive representation of effects of the explanatory
variables on the response variable. QR models the relation
between a set of explanatory variables and specific percentiles
(or quantiles) of the response variable. It specifies changes
in the quantiles of the response. A QR model generates an
ensemble of models for each accident type j,j=1,2,3, cor-
responding to specified quantiles. For each severity level jand
a quantile τ, the linear model with parameter vector βjτcan
be obtained by solving
min
βjτR8
30 682
i=1
ρτyij xT
iβjτ(6)
where ρτ(·)is the tilted absolute value function as in Fig. 5.
The resulting minimization problem can be solved by linear
programming methods [23].
With the models of corresponding quantiles, predictions can
be made by dividing quantiles into intervals and associating
each interval with a quantile in the middle of the interval. Let
xibe the vector of explanatory variables of road segment i
in Table Iand τkbe the middle quantile of the kth interval,
k=1,2,...,N. With ˆ
βjτidentified, the number of accidents
of level jcan be predicted by
nij =
N
k=1
pk·xT
iˆ
βjτk(7)
where Nis the number of divided intervals, and pkis the
probability of the occurrence of crash rate falling into the kth
quantile interval.
3) Neural Network Model: A neural network model map-
ping explanatory variables in Table Ito the number of
accidents of each type is illustrated in Fig. 3. The network
uses a single layer with 20 neurons in the hidden layer. The
MATLAB neural network toolbox was used network training
and testing.
4) Comparison: We next compare the performances of the
aforementioned models. A dataset with 30 862 road segments
was randomly partitioned such that 70% of the samples were
used to train the models and 30% were reserved for cross-
validation. All models used the same training and testing data.
Root mean square error (RMSE) is selected as the performance
criterion, where
RMSE =
j=1,2,3
30 682
i=1nij yij2.(8)
In (8), nij is the predicted number of level jaccidents for a
road segment i, and yij is the observation from data. The per-
formance comparison is illustrated in Table II, where acc/yr is
number of accidents per year which is the unit of RMSE. The
comparison shows that the proposed neural network model has
the best RMSE. To further improve the model performance, a
hybrid neural network architecture is considered next.
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LI et al.: ROAD RISK MODELING AND CLOUD-AIDED SAFETY-BASED ROUTE PLANNING 5
Fig. 3. Neural network for crash rate prediction.
Fig. 4. Hybrid neural network model.
5) Hybrid Neural Network Model: A hybrid neural network
scheme is shown in Fig. 4. Input data were first partitioned
into three groups with a fuzzy C-means clustering algo-
rithm [24]. Then for each cluster, a separate neural network
was developed. The RMSE of the three networks are 3.12,
3.24, and 2.96, respectively, which is an improvement over the
conventional neural network. Each of these three networks has
three outputs corresponding to the three crash ratings. To com-
pute the output of the hybrid neural network, we first compute
the Euclidean norms (distance) between the input and cluster
centers. Then we apply the neural network corresponding to
the minimum-distance cluster. As a result, accident rates of
each type can be predicted and the risk index can be gener-
ated using (1). Since the best RMSE results are obtained with
the hybrid neural network, it is chosen as the model for the
analysis and optimization to follow.
III. MODEL SENSITIVITY ANALYSIS
In this section, we use the hybrid neural network model
to analyze the sensitivity of RRIs to changes in the inputs
around nominal values. Sensitivity analysis can reveal interest-
ing trends and, provided the trends are reasonable, help build
confidence in the model. The nominal road segment corre-
sponds to 150 IRI, 55 mph speed limit, 1 mile length, 2 lanes,
2700 AADT per lane, an 18 ft lane width, 13.5 degrees of cur-
vature, 3% grade, and no-adverse weather. By varying each
variable one at a time, we obtain the results in Figs. 613,
where circles represent the nominal values.
TAB LE I I
MODEL PERFORMANCE COMPARISON
Fig. 5. Function ρτ(x)in 6.
Fig. 6shows that RRI varies negligibly when IRI is under
200 and it increases abruptly with an approximate slope of
3/100 RRI per IRI when IRI is above 200. Fig. 7shows
that segments with a speed limit between 35 and 55 mph
have the lowest risk index. Fig. 8shows that the risk index
increases almost linearly as road segment length increases with
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6IEEE TRANSACTIONS ON CYBERNETICS
Fig. 6. RRI dependence on road roughness.
Fig. 7. RRI dependence on speed limit.
Fig. 8. RRI dependence on road segment length.
Fig. 9. RRI dependence on number of lanes.
an approximate slope of 4.5 RRI per mile. Fig. 9indicates that
segments with more lanes tend to carry higher risk. This result
assumes that the AADT per lane is fixed at a nominal value.
More lanes thus correspond to more traffic and higher risk.
Fig. 10 shows that as AADT per lane increases, the risk tends
to first decrease and then increase between 8000 and 15 000.
This is not surprising given that RRI in (10) is proportional to
the probability of having an accident. As a result, more traffic
may lead to more total accidents but lower probability of an
accident for any particular vehicle. Fig. 11 indicates that the
wider the lane, the safer the road segment. Fig. 12 shows risk
first decreases and then increases with curvature and Fig. 13
shows that higher slope leads to higher risk.
Fig. 10. RRI dependence on AADT per lane.
Fig. 11. RRI dependence on width per lane.
Fig. 12. RRI dependence on curvature.
Fig. 13. RRI dependence on grade.
Note that the model has been developed for homogeneous
road segments, in which the number of lanes, lane width, speed
limit, etc., do not change. The homogeneous road segments
are atomic, i.e., any route is composed of these segments.
However, for the purpose of route planning, it is more conve-
nient and yields a more tractable search space to represent road
segments as edges between intersections, where each edge may
consist of multiple homogeneous segments. The RRI of an
edge between intersections can be obtained by summing RRIs
over homogeneous segments. Note that for those edges that
include only a part of a homogeneous segment, according to
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LI et al.: ROAD RISK MODELING AND CLOUD-AIDED SAFETY-BASED ROUTE PLANNING 7
Fig. 14. Edge RRI composition of multiple homogeneous road segments.
Fig. 8, we can add the RRI according to the proportion of
the homogeneous segment included. An illustrative example
is shown in Fig. 14.Theith edge with vertices Viand Vi+1
consists of homogenous road segments sm+2,sm+3, and sm+4
and part of road segments sm+1and sm+5, then the RRI of the
edge iis computed as
RRI(i)=1/2·RRI(sm+1)+RRI(sm+2)+RRI(sm+3)
+RRI(sm+4)+2/3·RRI(sm+2). (9)
Remark 1: RRIs of homogenous road segments are
summed to obtain the overall RRI of a road edge between
intersections as in (9). It is noted that the summation is valid
if we assume that the events of having an accident over the
road segments are mutually independent. Since RRI is a linear
function of probabilities of accidents as in (1), it is easy to
check that the summation of RRIs directly follows from the
definition.
IV. REAL-TIME FACTORS INFLUENCING ROAD RISK
Besides road geometries and historical traffic density, real-
time factors can have a significant impact on road risk. For
example, a snowy road segment is more risky than a normal
road segment and driving at midnight on the weekend can be
more dangerous because of greater likelihood of impaired and
fatigued drivers. Unfortunately, these factors were not avail-
able in the HSIS database and could not be treated as ANN
inputs in the same way as in the previous section. In this sec-
tion, we describe how such factors are incorporated into the
model.
A. Weather
Weather can have a significant impact on traffic safety.
Adverse weather conditions such as snow, fog, and rain can
worsen the driving environment. In the HSIS crash database,
accidents are recorded with the weather conditions present
when the accident happened. To see how those adverse weather
conditions affect crash risk, we investigate the average number
of accidents happening in each recorded weather condition.
By processing raw accident data, we determine the average
number of daily accidents in Ohio in 2006 versus weather con-
ditions, as shown in Table III. The average number of daily
accidents over all weather conditions was 396.77. We apply a
TABLE III
AVERAGE DAILY ACCIDENTS UNDER DIFFERENT WEATHER CONDITIONS
Fig. 15. Accident distribution over day of the week.
Fig. 16. Accident distribution over time of day.
correction factor as the ratio of number of accidents at spe-
cific weather conditions to total number of daily accidents. For
instance, if we obtain an RRI of 4.5 for a segment from the
neural network model and it is currently snowy or predicted
to be snowy, then the RRI is corrected to
4.5×452.68
396.77 =5.13.
B. Time of Day and Day of Week
According to a report from the NHTSA [25], the later hours
of the weekend and late afternoon to evening on the weekdays
tend to be the riskiest periods for driving. The HSIS accident
database includes hour of the day and day of the week of
each accident. The distribution of number of accidents ver-
sus day of the week is illustrated in Fig. 15.Asshownin
Fig. 15, the number of accidents occurring during a week is
evenly distributed except that Fridays and Sundays are a lit-
tle above and below average, respectively. Fig. 16 illustrates
the distribution of weighted number of accidents over time
of day for weekdays and weekends. The weighted number of
accidents is defined as the number of accidents divided by
the AADT distribution over a given one hour time interval, as
shown in Fig. 17. Each bin in Fig. 17 histogram corresponds
to a 1-h period. For example, the bin centered at 0.5 describes
the period from 0:00 to 0:59 A.M. The figures reveal similar
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8IEEE TRANSACTIONS ON CYBERNETICS
Fig. 17. AADT distribution over time of day (1996–2006) [26].
conclusions to these presented in [25]. For instance, accidents
are most likely in late nights during the weekend. This fact
can be explained by a considerable number of drivers in the
late night of the weekend being fatigued or impaired. Based
on Fig. 16, a correction factor can be defined as the ratio of
the weighted number of accidents to the average. For instance,
travel at 1:30 A.M. on Saturday will have a correction factor
of 580/304 =1.91,where 580 is the weighted number of
accidents in the 1–2 A.M. period in the weekend and 304 is
the average weighted number of hourly accidents over a week.
C. Driving Style and Vehicle Conditions
Driver characteristics and vehicle conditions are also impor-
tant factors influencing safety. Aggressive drivers are more
prone to accidents than nonaggressive drivers. Older or
improperly maintained vehicles may also result in more acci-
dents. Onboard driving style identification [27], [28] and
vehicle condition monitoring [29], [30] are becoming avail-
able. In this paper, we assume compounding correction factors
of 1.2 and 1.1 for an aggressive driver and a poorly maintained
vehicle, respectively.
V. SAFETY-BASED ROUTE PLANNING
Route planning is a network flow problem [31]. A road
network can be modeled as a directed graph as shown in
Fig. 19(a). Intersections and road segments are abstracted
as nodes and edges, respectively, in this directed graph.
A route planner generates an optimal route in the transporta-
tion network based on specified cost functions. Traditional
planners mainly consider time, distance, or fuel economy.
Route planners have been applied to a variety of applications.
For example, evacuation planning has been studied for victim
evacuation [32]–[34]. This paper focuses on traditional route
planning but with time and our new RRI cost metrics.
A variety of searching/optimization algorithms can be
exploited to solve the road-based route planning prob-
lem, e.g., Dijkstra’s algorithm [35], Aalgorithm [36],
and the genetic algorithm [37]. In this paper, we apply
an MIP approach as a prototype. This choice is moti-
vated by the existence of commercial MIP solvers such as
CPLEX [38] or Gurobi [39] that have been deployed in
cloud-based applications. The MIP-based approaches have also
been previously used for route planning applications as in [40].
A. Problem Formulation
Safety-based route planning is a multiobjective graph traver-
sal problem. The goal is to find an optimal route that
minimizes a weighted sum of cumulative travel time and RRIs.
The problem can be defined as follows.
Problem 1: For a directed graph G={V,E}, where Vis the
set of vertices and Eis the set of edges, we assign each edge
ei,ja pair (ti,j,ri,j), where i,jVare two adjacent vertices,
ei,jErepresents an edge from ito j, and the pair (ti,j,ri,j)
represents expected real-time travel time red from the cloudp
and RRI of ei,j, respectively. Let sand dbe the start and
destination vertices, respectively. We denote by Pthe set of
all paths from sto d, where a path Pis a sequence of vertices
from sto d, i.e., {s,v1,v2,...,vn,d}. The problem is to find
an optimal route that minimizes the following cost function:
min
PPts,v1+tv1,v2+···+tvn,d+α
×(rs,v1+rv1,v2+···+rvn,d)(10)
where αis the weight on cumulative RRI reflecting the relative
driver weighting of route safety to travel time.
B. Optimal Route Planning by Mixed-Integer Programming
In this paper, we employ MIP [41], [42] to solve the prob-
lem (10). For each edge ei,j, we assign a binary decision
variable xi,j∈{0,1}which determines if the edge is traveled,
and we redefine the problem as follows:
J=1
2
ei,jE
xi,jti,j+αxi,jri,jmin
xi,j(11)
subject to
es,vE
xs,v=1 (12)
ev,dE
xv,d=1 (13)
ei,jE
xi,j=
ej,kE
xj,k,jV,j= s&j= d.(14)
Constraints (12) and (13) imply that there is only one edge in
the path from the start node and only one to the destination.
Constraint (14) dictates that each vertex in-between has the
same number of incoming and outgoing edges.
We use CPLEX [38] to solve the above problem. Note that
since route optimization can be performed on the cloud, pow-
erful solvers such as CPLEX can be made readily available
and can reasonably be expected to quickly generate optimal
long-distance routes.
VI. ROUTE PLANNING CASE STUDY
In this section, we consider a real-world route planning case
study. As illustrated in the Google Maps snapshot in Fig. 18(a),
our goal is to plan a route from Scioto Downs Inc, Ohio to
Delaware, Ohio. To plan the route, we first abstract the road
network into the graph as shown in Fig. 19(a). Nodes rep-
resent intersections of main roads included in the database.
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LI et al.: ROAD RISK MODELING AND CLOUD-AIDED SAFETY-BASED ROUTE PLANNING 9
Fig. 18. Optimal routes with different αs.(a)α=0. (b) α=0.2.
Fig. 19. Abstracted road maps. (a) Abstracted road network map. (b) Roads
with local snow to the east.
For example, node 2 represents the intersection of route 23
and interstate 270. The goal is to find a path from node 1 to
node 29 with a minimum cost specified in (10). For each edge,
we define a pair of metrics (ti,j,ri,j), which are the traveling
time and dynamic RRI, respectively. The expected travel time
is measured using Google Maps at 04:30 P.M., 10/16/2014
(Thursday) EST. The RRIs are generated using the model we
developed in Section II and dynamic factors in Section IV.
To accomplish this, we link map road segments to the cor-
responding homogenous road segments in the HSIS database
according to the county, road number, and milepost. We will
next illustrate the optimal route under the following scenarios
to identify the specific road segment characteristics (but not
RRIs which are computed from the model). We assume that
Fig. 20. Route changes with real-time RRI adjustments. (a) Optimal route
for travel at 1 A.M. on Saturday. (b) Optimal routes with local snow.
the driver’s driving style and the vehicle conditions are both
nominal.
A. Time Optimal Route
When α=0,the user does not care about road risk and
desires a time-optimal route. As expected, the CPLEX results
match the Google Maps results as shown in Fig. 18(a).
The optimal time route in terms of Fig. 19(a) nodes is
1-2-3-9-14-18-24-27-29. The expected traveling time is 42
min and the total risk index is 161.89. The final cost is
J=42 +161.89 ×0=42.
B. α=0.2
When α=0.2,the optimal route is 1-2-3-9-14-15-20-26-
28-29, as shown in Fig. 18(b). The expected traveling time
is 44 min and the total risk index is 103.57. The final cost
J=44 +0.2×103.57 =64.71.This second route has 36%
less risk than the first route but requires 2 additional minutes
of travel time.
The above example pair shows that a route can indeed
change if safety is taken into account. We now show that real-
time factors such as weather and time of day can also lead to
different optimal routes.
C. Route Changes With Time of Day and Day of Week
Suppose the time is now 1:00 A.M. on Saturday, as dis-
cussed in Section IV-B, all the RRI will be updated by
applying a correction factor of 585/304 =1.92. Again
assume weighting factor α=0.2. As a result of the day and
time, RRI is greatly increased for each road segment. These
changes result in a safety-optimal route as 1-2-3-9-14-15-20-
26-25-27-29 which is visualized in Fig. 20(a). The expected
traveling time is 45 min and the total risk index is 204.42.
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10 IEEE TRANSACTIONS ON CYBERNETICS
The final cost J=45 +0.2×204.42 =85.88.We note
that this route is also the “safest” route when independent
of time (α=∞).
D. Route Changes With Weather Conditions
We now change our travel time back to 04:30 P.M.on
Thursday and suppose it is snowing in east Columbus as seen
in the pink area of Fig. 19(b). As discussed in Section II,
the RRIs in the affected roads are adjusted using a correction
factor β=452.68/396.77,where 452.68 and 396.77 are the
average number of daily accidents in snowy days and overall
average number of accidents, respectively. A snow cover can
significantly impact travel time as well as risk. While attributes
of a road such as grade and curvature would certainly factor
into travel speed reduction, in this paper, we adopt a repre-
sentative 20% travel time increase based on a report showing
data indicating a 5%–19% speed reduction range in snow [43].
With the updated time, RRIs [in red in Fig. 19(b)] and weight
α=0.2, the optimal route generated with CPLEX changes
to 1-2-3-9-14-18-24-25-27-29. The expected traveling time is
42 min and the total risk index is 161.89. The final cost is
J=42 +161.89 ×0.2=74.38.
VII. CONCLUSION
In this paper, a safety-based route planner has been pro-
posed. This planner optimizes over both travel time and road
risk metrics. Primary contributions of this paper are in process-
ing of accident data to an RRI metric in route optimization that
balances time and safety metrics. Advantages of its V2C2V
implementation include access to extensive computational and
regularly updated database resources not available onboard.
We have demonstrated that a hybrid neural network model
can be developed to model RRI based on the available acci-
dent data. We have shown that this model outperforms several
model alternatives in terms of RMSE. A sensitivity analy-
sis of this model has been performed showing reasonable
trends.
The route planning problem was reduced to an MIP problem
and solved with CPLEX. Real-world case studies have been
considered that demonstrate changes in the route when safety
is included in the optimization. We have also illustrated how
real-time information such as weather, time of day, and day of
the week can be factored in route planning. Future work will
include RRI database management, tradeoff analysis of how
long the route buffer is downloaded, and a demonstration with
a V2C2V-equipped vehicle.
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Zhaojian Li (S’15) received the B.S. degree in civil
aviation from the Nanjing University of Aeronautics
and Astronautics, Nanjing, China, in 2010, and the
M.S. degree from the Department of Aerospace
Engineering, University of Michigan, Ann Arbor,
MI, USA, in 2014, where he is currently pursuing
the Ph.D. degree in flight dynamics and control in
aerospace engineering.
From 2010 to 2012, he was an Air Traffic
Controller with the Shanghai Area Control Center,
Shanghai, China. From 2014 and 2015, he was an
Intern with Ford Motor Company, Dearborn, MI, USA. Since 2013, he
has been a Graduate Research Assistant with the Department of Aerospace
Engineering, University of Michigan. His current research interests include
optimal control, system modeling, estimation, and intelligent transportation
systems.
Mr. Li was a recipient of the National Scholarship from China.
Ilya Kolmanovsky (F’08) received the M.S. and
Ph.D. degrees in aerospace engineering and the
M.A. degree in mathematics from the University of
Michigan, Ann Arbor, MI, USA, in 1993, 1995, and
1995, respectively.
He is currently a Full Professor with the
Department of Aerospace Engineering, University
of Michigan. His current research interests include
control theory for systems with state and control
constraints, and control applications to aerospace
and automotive systems.
Dr. Kolmanovsky was a recipient of the Donald P. Eckman Award of
American Automatic Control Council. He has previously been with Ford
Research and Advanced Engineering in Dearborn, Michigan, for close to 15
years. He is named as an Inventor on 92 United States patents.
Ella Atkins (SM’14) received the advanced
degrees in aeronautics and astronautics from the
Massachusetts Institute of Technology, Cambridge,
MA, USA, and in computer science and engineer-
ing from the University of Michigan, Ann Arbor,
MI, USA.
She is an Associate Professor with the Department
of Aerospace Engineering, University of Michigan,
where she is also the Director of the Autonomous
Aerospace Systems Laboratory. She has authored
over 150 refereed journal and conference publi-
cations. Her current research interests include task and motion planning,
guidance, and control strategies to support increasingly autonomous cyber-
physical aerospace systems.
Dr. Atkins serves as an Associate Editor of the AIAA Journal of Aerospace
Information Systems. She serves on the National Academy’s Aeronautics and
Space Engineering Board. She is the Graduate Program Chair for the new
University of Michigan Robotics Program. She was a member of the Institute
for Defense Analyses Defense Science Studies Group from 2012 to 2013.
Jianbo Lu (SM’09) received the Ph.D. degree in
aeronautics and astronautics from Purdue University,
West Lafayette, IN, USA, in 1997.
He is currently a Technical Expert in advanced
vehicle controls with Controls Research and
Advanced Engineering, Research and Innovation
Center, Ford Motor Company, Dearborn, MI, USA.
He has published over 70 referred research articles.
He is an Inventor or Co-Inventor of over 100 U.S.
patents. His invented technologies have been widely
implemented in the tens and millions of vehicles
with brand names such as Ford, Lincoln, Volvo, and Land Rover. His current
research interests include automotive controls, intelligent and adaptive vehi-
cle systems, integrated sensing systems, driving assistance and active safety
systems, and future mobility.
Dr. Lu was a two-time recipient of the Henry Ford Technology Award at
Ford Motor Company. He currently serves as an Associate Editor for the
IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY.Heisonthe
editorial board of the International Journal of Vehicle Autonomous Systems
and the International Journal of Vehicle Performance. He also serves as the
Chair of Intelligent Vehicular Systems and Control Technical Committee under
the IEEE Society of Systems, Man and Cybernetics. From 2008 to 2014, he
served as an Associate Editor for the IFAC Journal of Control Engineering
Practice. He served as the Vice Chair for Industry and Applications at the
2015’s American Control Conference.
Dimitar P. Filev (F’08) received the Ph.D. degree
in electrical engineering from Czech Technical
University in Prague, Prague, Czech Republic, in
1979.
He is an Executive Technical Leader in intelli-
gent controls with the Ford Research and Innovation
Center, Dearborn, MI, USA. He is conducting
research in modeling and control of complex sys-
tems, intelligent control, fuzzy and neural systems,
and their applications to automotive engineering. He
has published four books and over 200 articles in
refereed journals and conference proceedings, and held numerous U.S. and
foreign patents.
Dr. Filev was a recipient of the 2015 IEEE Computational Intelligence
Society Pioneer’s Award, the 2008 Norbert Wiener Award of the IEEE
SYSTEM,MAN,AND CYBERNETICS (SMC) Society, and the 2007
International Fuzzy Systems Association (IFSA) Outstanding Industrial
Applications Award. He is the President-Elect of the IEEE SMC Society.
He is a fellow of the IFSA.
John Michelini received the B.S. degree from the
University of Detroit, Detroit, MI, USA, and the
M.S. degree from the University of Michigan, Ann
Arbor, MI, USA, both in mechanical engineering,
and the degree in engineering management from
Wayne State University, Detroit.
He has been with Powertrain Control Research
and Advanced Engineering for over 10 years and
with Ford Motor Company, Dearborn, MI, USA,
for over 26 years. He has co-authored four con-
ference papers and held over 70 U.S. patents. He
has researched on powertrain controls for various engine fuel economy
technologies, Ti-VCT, and camless (EVA).
... Therefore, we have shown the bound in (10). Note that the above results hold true for generic constraints on the predicted statesx τ and controls u τ imposed in the cloud MPC optimization problem (6). We now consider specific state constraints in the form of (3). ...
... This proves the result. On the basis of the above two results, we now show that the modified switching policy (34) leads to the following constraint satisfaction result: Proposition 3. Suppose (i) at the initial time t = 0, the stateconstrained cloud MPC problem (i.e., (6) with the generic constraint (6c) elaborated as (17)) is feasible, and (ii) at each time instant t = 0, . . . , T − 1, the control that is applied to the actual system (1) is determined by the switching policy (34). ...
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... Devours et al. [27] determine the best route by rapidly investigating random trees. Li et al. [28] used a hybrid neural network model to calculate road-related data and calculate the danger index of a road. Meanwhile, Liu et al. [29] proposed cargo fleet route optimization for transportation missions. ...
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... With increasingly enhanced sensing capabilities on modern vehicles, there is a growing interest in employing road information such as road roughness in intelligent vehicle systems to improve road safety [1], ride comfort [2], and fuel economy [3], [4]. Real-time and crowd-sourced road information can increase situation awareness, enhance control performance, and provide additional functionalities. ...
Preprint
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... [17] uses rapidly-exploring random trees to discern the optimal route while [18] applies a hybrid neural network model to calculate road-related data and identify a road's risk index. Meanwhile, [19] offers route optimization for cargo fleets on transportation missions. ...
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