How to quantitatively evaluate safety of driver behavior upon accident? A biomechanical methodology
How to quantitatively evaluate safety of driver behavior upon accident? A biomechanical methodology
Wen Zhang 0 1 2
Jieer Cao 2
Jun Xu 1 2
0 Shenyuan Honors College, Beihang University , Beijing , China , 4 Department of Applied Mechanics, Chalmers University of Technology , Gothenburg , Sweden
1 Department of Automotive Engineering, School of Transportation Science and Engineering, Beihang University , Beijing , China , 2 Advanced Vehicle Research Center, Beihang University , Beijing , China
2 Editor: Xiaosong Hu, Chongqing University , CHINA
How to evaluate driver spontaneous reactions in various collision patterns in a quantitative way is one of the most important topics in vehicle safety. Firstly, this paper constructs representative numerical crash scenarios described by impact velocity, impact angle and contact position based on finite element (FE) computation platform. Secondly, a driver cabin model is extracted and described in the well validated multi-rigid body (MB) model to compute the value of weighted injury criterion to quantitatively assess drivers' overall injury under certain circumstances. Furthermore, based on the coupling of FE and MB, parametric studies on various crash scenarios are conducted. It is revealed that the WIC (Weighted Injury Criteria) value variation law under high impact velocities is quite distinct comparing with the one in low impact velocities. In addition, the coupling effect can be elucidated by the fact that the difference of WIC value among three impact velocities under smaller impact angles tends to be distinctly higher than that under larger impact angles. Meanwhile, high impact velocity also increases the sensitivity of WIC under different collision positions and impact angles. Results may provide a new methodology to quantitatively evaluate driving behaviors and serve as a significant guiding step towards collision avoidance for autonomous driving vehicles.
Data Availability Statement: All relevant data are
within the paper.
Funding: This work is financially supported by
Fundamental Research Funds for the Central
Universities, Beihang University and start-up funds
of ``The Recruitment Program of Global Expertsº
awardee (YWF-16-RSC-011), Beihang University.
The funders had no role in study design, data
collection and analysis, decision to publish, or
preparation of the manuscript.
Competing interests: The authors have declared
that no competing interests exist.
Critical vehicle crash conflict (CVCC) situation refers to a scenario within the final seconds
and milliseconds before actual collision. Drivers' reactions upon critical crash conflict right
before the accident may determine the severity of accident consequences in a large extent [1±
3]. Previous researches have revealed that both extrinsic factors, e.g. drugs [
], alcohol [4, 6±
8], weather [
], light conditions [
], scenario's kinematics [
], as well as intrinsic factors,
e.g. personality [
], age [
], experience [
4, 7, 15
], visual performance [
type [17±20] may jointly contribute to the final driver response manners. Therefore, a series of
experiment designs, carryout, analyses and simulations focus on the effect of those factors on
driving behaviors subjected to critical situations by creating simplified scenarios using driving
simulators [21±23]. To gain a more realistic driving behavior upon CVCC situation, realistic
vehicles were adopted with the installation of data collector, providing further data analysis
]. Also, driver models based on experiments have been developed to analyze
pre-accident scenarios . However, little work uses direct biomechanical indicators, rather than
oversimplified indices, e.g. impact velocity, angle, to quantitatively evaluate the effectiveness of
On the other hand, different CVCC situations may result in various driving behaviors with
different response mechanisms, although drivers, especially for inexperienced ones, usually
behave based on their intuitions or random choice of swerve to the road sides [
example, in a frontal impact accident, the typical responses of drivers are straightening their arms
and bracing backward to seats [
]; in a rear-end collision, drivers tend to brake more quickly
with an increasing situational urgency [
]. No systematic study about driving behavior upon
various CVCC situations is available since it is rather difficult to control crash angle, speed and
timing simultaneously using driving simulators, not to mention in real-world vehicles.
To quantitatively establish the relationship between driving behavior and accident
consequence upon CVCC situation is still lacking with limited studying samples and
time-consuming procedures. Additionally, collision avoidance (CA) technology is a crucial subset of active
safety, which is generally applied to avoid a potential collision in autonomous driving system
]. Various algorithms for evaluating collision scenarios of autonomous driving were
investigated in previous literatures using data from both real traffic situations and simulated
scenarios, including threat-assessment algorithm and multilevel collision mitigation method [30±
32], while recent fast development of autonomous driving requires algorithms equipped with
more rational driving behavior reactions upon possible evitable accidents. On the other hand,
numerical simulation may provide a possible solution with much improved efficiency and
sufficient data to cover all possible scenarios. To bridge this gap, in this study, a novel
methodology of drivers' spontaneous reaction evaluation based on numerical simulation with validate
models is proposed. In Section 2, the methodology would be described in detail and all model
related information including accident scenario setting and the biomechanical indicator is
depicted. In Section 3, a typical result would be presented and analyzed, underlying the
mechanisms between driving behavior and passenger injury outcome. In addition, assessment of
drivers' spontaneous reaction is provided. A further detailed discussion with coupling effects
of various impact scenarios is considered.
To improve the computation efficiency, FE couple with MB computation strategy is suggested
in Fig 1 without the loss of accuracy. Vehicles are depicted by full FE way to obtain a complete
and accurate crash pulse while the detailed passenger cabin is described by MB with fully
validated passenger dummy model [
2.1 Traffic accident scenarios
To evaluate drivers' spontaneous reactions in traffic accidents, a series of traffic accident
scenarios in view of impact velocities, angles and positions at the cross road are set. It is worth
noting that only side impact cases are taken into account to demonstrate the methodology in
The impact velocity is far more complicated due to the various pre-crash maneuvers and
crash situations. To cover the wide impact speed range, three different impact velocities, i.e. 25
mph, 35 mph, and 45 mph were selected as input conditions to create crash scenarios. To
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Fig 1. Schematic flow-chart of the proposed methodology by using coupled FE and MB models.
further quantify the collision points on vehicles, we divide the impact positions into four parts
(position 1, position 2, position 3 and position 4) evenly along the longitudinal direction of
vehicle demonstrated in Fig 2A. In the meantime, five impact angles ranging from 30o to 150o
(30o, 60o, 90o, 120o, 150o) are selected, defined in Fig 2B to 2G.
The parametric matrix of various traffic accident scenarios is listed in Table 1. In this case,
we have 60 crash scenarios and in essence, representing various outcomes of driver's
spontaneous reaction upon CVCC situations. Consequently, there are altogether 60 simulation cases
and it takes about 80 hours with eight cores in LS-DYNA and about 2.5 hours with two cores
in MADYMO for each case.
Fig 2. Impact scenario parameters with (a) four impact positions, (b) schematic diagram of impact angle in CVCC situation,
impact angles of numerical simulations are (c) 30o, (d) 60o, (e) 90o, (f) 120o, (g) 150o, respectively.
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2.2 FE vehicle model
The FE vehicle model used in this study is 2010 edition of Toyota Yaris sedan model developed
and validated by National Crash Analysis Center (NCAC) under a contract with National
Highway Traffic Safety Administration (NHTSA) of the US DOT. Fig 3A illustrates the profile
and corresponding dimensions of vehicle model. More information about this model is
available on NCAC website [
]. To simplify and eliminate possible crash incompatibility
problems, a same FE vehicle model is used. The vehicle-to-vehicle friction coefficient is set to 0.2
according to previous literature which analyzed the frontal vehicle-to-vehicle crash scenarios
]. The vehicle-to-ground friction coefficient is set to 0.8 to mimic real-world general impact
process with braking.
2.3 Human model with restraint system
As shown in Fig 3B, the fully validated and widely accepted by automotive industry as human
injury evaluation index, Hybrid III 50th percentile Dummy model is chosen for this study for
its valuable application in injury analysis [36±38]. This model is given as an include file
ªd_hyb350el_inc.xmlº, consisting of rigid elliptical structures. More detailed information
about this human model is presented in Ref.[
To mimic the real-world setup for drivers, occupant restraint system model for impact
scenarios should be built. Major parts of the restraint system in available FE model constructed
and validated by NCAC for frontal impact scenarios are converted to MADYMO platform,
also shown in Fig 3B. In the meantime, ª7±30º rule suggested by NCAC [
] is applied to set
airbag and retractor triggering time. It is worth noting that the retractor triggering time is set
to be 15 ms ahead of the airbag triggering time for successful synergic efforts between airbag
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Fig 3. (a) The rough profile and the corresponding dimensions of 2010 edition aof Toyota Yaris sedan finite
element model; (b) The Hybrid III 50th percentile dummy model used in the present study and occupant
restraint system model provided by NCAC.
Appropriate contact types are crucial to gain satisfactory results. In accordance with the
model settings by NCAC, user-slave contact is chosen as the type of vehicle interiors-human
arms contact, vehicle interiors-human body contact, seats-human body contact and
doorhuman body contact in the present study. In addition, a friction coefficient of 0.3 is used for
seats-human body contact and 0.1 is used for other three contacts. The vehicle
interiorshuman's lower limbs contact is set as the user-master type and the friction coefficient is 0.5.
The input data of this model is the crash pulse obtained from initiative vehicle (vehicle 1) in
various simulated vehicle-to-vehicle crash scenarios mentioned before.
2.4 Injury evaluation index
Injury indices serve as quantitative measurements to the consequences of drivers' spontaneous
behaviors, i.e. various impact scenarios. Occupant injury during vehicle accidents may involve
head, neck, chest, femur or other body parts [41±43]. As such, for a fair comparison, Weighted
Injury Criterion (WIC), a multi-criteria analysis combined with head, thorax and femur
injury, widely used for quantitatively evaluating driver's general injury is adopted. WIC can be
expressed as [
WIC 0:6 HIC
C3ms D =2 0:05
where the head injury criteria (HIC) measured over 36 ms is used to evaluate the head injury
of the dummy model [
], C3ms and D are 3-ms chest acceleration and chest deflection,
respectively, which can assess the thorax injury of the dummy model during traffic accidents. Left
and right femur loads (FFL and FFR) are also considered in WIC to take femur injury into
account. Values of all variables defined above could be numerically calculated based on
numerical computation results.
Crash pulse is obtained via FE simulation of two identical vehicles modeled above. As shown
in Fig 4, resultant acceleration curve under velocity of 35 mph, impact angle of 90o in impact
position 2 is chosen to illustrate the typical curve.
Fig 4. The typical resultant acceleration curve with an impact angle of 90o, impact velocity of 35 mph and
collision position of position 2, combined with the deformation animation of vehicles and the
corresponding response of occupant restraint system model.
Intuitively, one may observe a distinct peak of about 33 g during the crash. In the initial
stage, the interaction between two vehicles with initial velocities plays a leading role in the
upclimbing phase of resultant acceleration-time curve where the kinetic energy decreases sharply.
In accordance with the deformation patterns of two vehicles, energy absorption structures,
such as, bumper, crash box, etc. may be essential to protect passenger cabin during this stage.
Shortly afterwards, the resultant acceleration reaches the maximum value when the kinetic
energy is changing most drastically when the interaction among high stiffness vehicle parts
After the strong collision, two vehicles run apart, reducing the resultant acceleration and
the rate of deformation of vehicle parts is also reduced. It is obvious that the front part of
initiative vehicle (vehicle 1) and the side part of passive vehicle (vehicle 2) experience quite extensive
damage. In the meantime, the corresponding response of occupant restraint system model at
different stages is also exhibited in Fig 4, where the airbag fully deploys at the distinct peak of
resultant acceleration curve.
During the declining stage of resultant acceleration curve, the interaction between airbag
and the head of dummy model plays a critical role in protecting driver in crash situation since
it avoids direct impact between vehicle interiors and the head of dummy model when
combined with the function of seatbelt. Dummy model tends to brace backwards to the seat and
straighten its arms due to inertia effect at the end of collision process.
In view of the consequences of drivers' spontaneous behaviors, Fig 5 illustrates the detailed
kinematic response process of drivers for the cases of three different impact velocities, divided
into four stages. Stage 1 is the initial stage of vehicle-to-vehicle crash, where no distinct
response of occupant restraint system is observed. In Stage 2, the airbag deploys and seatbelt is
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Fig 5. The detailed kinematic response process of drivers for the case of three different impact velocities with an impact
angle of 90o and collision position of position 2: (a) 25 mph, (b) 35 mph, (c) 45 mph.
tightened along with the interaction of head and airbag, chest and seatbelt, knee and bolster,
resulting in different types of injuries. Afterwards, the driver seems to move backwards to seat
and separate from airbag during Stage 3. Finally, in Stage 4, the interaction of head and
headrest becomes the dominant source of injury. Notably, according to the deformation of the
airbag and other parts of vehicles, the driver tends to suffer severer injuries under higher impact
velocities because of the effect of inertia and the sharply decreasing interior space with
intrusion of the door and other parts. In addition, the interaction between driver head and airbag
(Stage 2) occurs visibly earlier under higher impact velocity compared to low impact velocity.
Similar analysis could be performed on various impact angles and collision positions. On
one hand, it is found that the motion processes under different impact angles are quite
different. In those cases with an impact angle lower than 90o, driver tends to move towards door,
making interactions between driver's head and window while interaction between driver's
torso and door becomes dominant. Nevertheless, drivers appear to move in the direction to
passenger seat with smaller stiffness compared with doors and other interiors of vehicle in the
cases with an impact angle higher than 90o, thus driver injury could be relatively lower. On the
other hand, although the motion processes under four collision positions seem to be similar,
the initial time and duration of interaction as well as the deformation could be quite distinct.
Indeed, when impact positions are close to the front of vehicles, structural differences
compared to other collision positions may result in severer injuries.
Actually, most drivers tend to brake spontaneously under emergency although the reaction
time could be quite different. This critical behavior combined with the initial states of two
vehicles will finally determine the impact velocity of CVCC situation. On the other hand, the
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steering response of driver has a decisive role in collision positions as well as impact angles.
Nevertheless, steering response is much more complicated than brake reaction.
In previous literature, the impact velocity has been generally studied as a dominant factor
of occupant protection considering various collision patterns [
]. Nevertheless, the impact
velocity as a single variable may not illustrate the drivers' spontaneous behavior, complicated
collision process as well as all kinds of collision patterns in detail, which is exactly the major
advantage of our established methodology. Consequently, the coupling effect of impact angle,
collision position and the impact velocity is comprehensively investigated.
4.1 Coupling effect of impact velocity and collision position
A series of vehicle-to-vehicle models varying in impact angles and collision positions are
established and simulated with an impact velocity of 25 mph, 35 mph and 45 mph, crash pulse from
which then served as input data to corresponding occupant restraint system model to obtain
drivers' injury data under different CVCC situations.
WIC of drivers under different impact velocities and collision positions are illustrated in
Fig 6, which helps to thoroughly analyze coupling effect of impact velocity and collision
position on overall injury rather than partial injury of drivers. The variation range of WIC with
increasing impact velocity is 0.07 to 0.15 at 25 mph, 0.06 to 0.24 at 35 mph and 0.12 to 0.32 at
45 mph, respectively. In general, the WIC value has a positive correlation with impact velocity
under different collision positions and the difference of WIC value among three impact
velocities under front collision position is distinctly higher than that under rear collision position.
Fig 6. Comparison of WIC under different impact velocities and collision positions with an impact angle of
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Furthermore, the ratio of WIC value among three impact velocities in Fig 6 reveals that WIC
tends to increase by 38% with an increasing impact velocity of 10 mph in average and this
general rule may only be applied to position 1, position 2 and position 3. Nonetheless, the
seemingly unusual situation in position 4 is quite normal since interaction time between two
vehicles could be longer under an impact velocity of 25 mph even if the comparing case might
equip with relatively higher impact velocity, while impact velocity will switch to a dominant
role as impact velocity increases continuously.
Actually, comprehensive coupling analysis of driver's general injury under different CVCC
situations may provide several valuable guidelines for collision avoidance of autonomous
driving vehicles since current algorithms have difficulty in predicting kinematics of complex
collision situations. Hence, it is worth taking coupling effect of impact velocity and collision
position into account, especially the distinct rule under high impact velocity.
4.2 Coupling effect of vehicle-to-vehicle impact angle and impact velocity
To systematically study driving behavior upon various CVCC situations, the coupling effect of
vehicle-to-vehicle impact angle and impact velocity is considered in the present study using
five different impact angles and three impact velocities. These two critical factors may not only
affect the field of view of drivers before crashing but the collision forms under the CVCC
Fig 7 shows WIC under different impact angles and impact velocities in position 2, where
the variation range of WIC value arising from various impact angles and impact velocities is
Fig 7. Comparison of WIC under different impact angles and impact velocities in position 2.
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0.13 to 0.32 at 30o, 0.19 to 0.37 at 60o, 0.15 to 0.26 at 90o, 0.11 to 0.22 at 120o and 0.06 to 0.07 at
150o, indicating that WIC with an impact angle of 150o tends to be distinctly lower than other
impact angles since vehicles separate with each other soon after collisions happen. Namely,
shorter duration of interaction time during a scratch collision may lead to less dangerous
situations. The maximum value of WIC appears on 60o and 45 mph, exposing drivers to a more
dangerous situation compared with other cases. Similarly, crash scenarios with higher impact
velocities appear to be more sensitive to impact angle.
In accordance with the ratio of WIC value among five different impact angles under three
impact velocities, the variation law of WIC value attributed to each impact angle shows similar
trend across varying values of impact velocities, which can be divided into three sections. The
impact angle ranging from 30o to 60o can be defined as the first section, where WIC value rises
at an approximately 30% rate in average with an increasing impact angle of 30o. However,
WIC value declines steadily in the second section with an impact angle ranging from 60o to
120o and decreases by 23% per 30o. A sharp fall (about 58%) of WIC value follows from 120o
to 150o in the third section. Overall, impact velocity is demonstrated with dominant effect
on consequences, especially in higher impact velocity situation. Indeed, improved braking
maneuvers of collision avoidance for autonomous driving vehicles coupling with influencing
mechanism of impact angles and impact velocities can be obtained to assist brake actuators in
optimum operation by adjusting acceleration change rate within a limited range.
4.3 Coupling effect of collision position and impact angle
From the structural aspect, the structural interaction plays a vital role in energy absorption,
which may well explain the injury severity level of drivers upon CVCC situation. The
structural interaction is closely related to collision position and impact angle, thus it is essential to
investigate the coupling effect of these two factors during CVCC situation.
WICs under different collision positions and impact angles with an impact velocity of 35
mph is shown in Fig 8, which makes it clear that the general injuries of drivers tend to be severer
when collision positions locate near the front of vehicles under all impact angles since actual
interaction time of vehicles is longer under these circumstances. Likewise, the variation range of
WIC value in accordance with an extensive parametric study is 0.08 to 0.30 at position 1, 0.07 to
0.27 at position 2, 0.06 to 0.15 at position 3, 0.05 to 0.08 at position 4, respectively, implying that
injuries under position 1 appear to be several times higher than injuries under position 4.
The coupling effect can be elucidated by the fact that the difference of WIC value among
four impact positions under smaller impact angles tends to be distinctly higher than that
under larger impact angles. At lower impact angles (30o-90o), there is a tendency that WIC
value of the rear position is 37% lower than that of the front one averagely, whereas the similar
decreasing rate is only 19% at higher impact angles (120o-150o). In general, the collision
position is a governing factor contributing to WIC value when compared with impact angle.
Similarly, the influencing mechanism of impact angle and collision position can help to
modify controlled steering maneuvers of collision avoidance technology for autonomous
driving vehicles. Under certain collision situations judged by various sensors and radar, the most
reasonable steering angle and the corresponding steering angle rate combined with coordinate
system can be figured out to avoid or mitigate a collision.
4.4 Coupling effect of impact velocity, collision position and impact angle
WICs resulting from various impact velocities, collision positions and impact angles are
shown in Fig 9, indicating that relatively high impact velocity may enhance the sensitivity of
WIC with the variation of collision positions and impact angles. For instance, WIC ranges
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Fig 8. Comparison of WIC under different collision positions and impact angles with an impact velocity of
from 0.04 to 0.20 with an impact velocity of 25 mph, 0.05 to 0.30 with an impact velocity of 35
mph and 0.06 to 0.46 with an impact velocity of 45 mph, respectively. In these cases, it is
apparent that the impact velocity plays a crucial role in the value of WIC, whereas collision position
serves as a secondary factor and the influence of impact angle is relatively unremarkable when
compared with other two factors in general. However, for cases with impact velocity of 45
mph, the governing factor could be disparate. WIC in both 60o and 120o impact angle are
relatively high when compared with other impact angle cases resulting from the actual impact
position between driver's body and interiors of the vehicle, demonstrating that even
approximate scratch collision may lead to quite deteriorated damage under high impact velocities.
Moreover, WIC value in position 3 and 150o illustrates similar rule that rear collision position
combined with large impact angle can also result in great risk under high impact velocities.
Actually, the distinction among the effects of three different factors on WIC is derived from
diverse influencing mechanisms. In accordance with the detailed kinematic response processes
of drivers in all kinds of cases, the impact velocity appears to affect the intensity of impact
between dummy's body and interiors of vehicle, resulting in increasing deformation of
collision parts with the increase of impact velocity. Additionally, the impact angle has a decisive
effect on the deflecting direction of driver's body, leading to the ultimate impact position
between driver's body and interiors of the vehicle, which is also influenced by the collision
position. Besides, the collision position significantly affects the direction of rotation of the
vehicle. Consequently, all these factors contribute to the complicated variation of WIC in
various cases, namely, the severity of driver's general injury could be quite distinct under different
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Fig 9. Coupling effect of the impact velocity, collision position and impact angle on WIC.
5. Concluding remarks
Rational driver spontaneous reaction stays an essential factor to protect drivers from harm. In
this study, we focus on the evaluation of drivers' spontaneous reactions during a variety of
CVCC situations based on coupled FE and MD numerical simulation. A quantitative
indicator, i.e. WIC is used to describe the overall injury for the driver during an accident. Based on
the numerical analysis, it could be reasonably concluded that the impact velocity has a
dominant effect on the value of WIC, whereas collision position serves as a secondary factor and the
influence of impact angle is relatively unremarkable by comparison. The general injury
influencing mechanisms are discovered through kinematic response processes of drivers under
different cases, indicating that the intensity of impact, rotating direction of vehicles as well as
ultimate impact position are closely related to these factors, which will finally bring about
distinct severity of injury. Nevertheless, the results under high impact velocities is quite different
that large impact angles or rear positions could also result in dangerous situations.
This study provides thoroughly simulation results for crash safety of various traffic accident
scenarios and serves as a preliminary step toward quantitative assessment of driver
spontaneous reactions in CVCC situations, paving a new road for future safe driving training and useful
insights on vehicle safety designs, as well as collision avoidance/mitigation algorithm
development for autonomous driving vehicles.
This work is financially supported by Fundamental Research Funds for the Central
Universities, Beihang University and start-up funds of ``The Recruitment Program of Global Expertsº
awardee (YWF-16-RSC-011), Beihang University. The authors appreciate Dr. Ciaran Simms
at Trinity College Dublin for the valuable discussions and suggestions for this paper.
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Conceptualization: Jun Xu.
Data curation: Jieer Cao.
Formal analysis: Wen Zhang, Jieer Cao.
Funding acquisition: Jun Xu.
Investigation: Wen Zhang.
Project administration: Jun Xu.
Resources: Jun Xu.
Supervision: Jun Xu.
Validation: Wen Zhang.
Writing ± original draft: Wen Zhang.
Writing ± review & editing: Jun Xu.
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2016; 95:209±26. https://doi.org/10.1016/j.aap.2016.07.007 PubMed PMID: WOS:000383527600025.
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