Optimization Design and Injury Analysis of Driver’s Restraint System in Sedan Small Offset Collision

Abstract

A combination of airbag, seatbelt, and other restraint systems greatly reduces injury to drivers in small offset collisions. However, the airbag causes accidental injury to the driver in the deployment process. To maximize the protection effect of the restraint system on the driver, this study proposes a pre-tensioned force-limiting seatbelt. A small offset collision accident with video information was simulated by using a Neon sedan and the THUMS (v.4.0.2) finite element model. The effectiveness of the accident model and the matching use of a pre-tensioned force-limiting seatbelt and airbag for driver protection were verified. To obtain the best parameter matching of protection effect, first, the seatbelt force-limiting A, pre-tensioned force B, pre-tensioned time C, airbag ignition time D, and mass flow coefficient E were selected as influencing factors, and orthogonal tests with different factor levels were designed. Then, the direct analysis method was applied to analyze the influence laws of each factor on driver dynamic response and injury. In addition, the radial basis function surrogate model was constructed by synthesizing each kind of critical injury value to the human body. Combined with NSGA-II multi-objective genetic algorithm, the structural performance parameters of the restraint system were optimized and matched. Results showed that the optimal protection matching parameters of the restraint system were 4933.5 N−2499.9 N−16 ms−15.3 ms−0.5 (A−B−C−D−E). Finally, the best matching parameters were input into the accident model for verification. After optimization, the WIC and $N_{ij}$ of drivers were reduced by 37.9% and 45.3%, respectively. The results show that the optimized restraint system can protect the driver the most.

1. Introduction

In the process of automobile collision, frontal collision is the main type of automobile collision accident. Small offset collisions account for approximately 1/5 of frontal collision fatalities [1].

In 2012, the Insurance Institute for Highway Safety of the United States released the test specification [2] and evaluation standard [3] for small offset frontal collision of vehicles. In a small offset frontal collision, the impact force is applied to the outside of the longitudinal frame track of the vehicle [4]. Moreover, the front suspension, left front wheel, and bottom of the A-pillar play a major role in absorbing energy during the collision. Therefore, occupant compartment invasion is the main factor that causes driver injury.

Mueller [5] proposed to strengthen the passenger compartment, increase the structure to promote lateral translation of the vehicle, and design the wing plate with better energy absorption effect. This method reduced the extent of intrusion into the occupant compartment and improved the motion posture of the dummy. Chen et al. [6] proposed to optimize crashworthiness in the A-pillar and side panels by filling structural foam, adding roof beams, and strengthening the rear wall of the cab. Urbina et al. [7] and Elliott et al. [8] proposed different energy-absorbing structures to improve crashworthiness.

Compared with 100% frontal overlap collision, small offset collision not only increases the amount of invasion deformation of the occupant cabin but also changes the trajectory of the occupant’s head [9]. With the increased amount of invasion in the occupant cabin, the injury value of lower limb and chest fracture of the occupant also increases significantly [10]. The obvious lateral acceleration generated by the offset collision causes the occupant’s head track to deviate from the center position of the airbag and contact with the side components of the car (such as the door), thereby making the side components become the source of head injury [11]. Traffic accident statistics show that using the airbag alone can reduce collision mortality by 32%, while using the airbag and seatbelt at the same time can reduce the mortality by 67% [12]. Therefore, the reasonable matching use of the airbag and seatbelt plays an important role in improving vehicle safety performance. At present, research on restraint systems mainly focuses on the seatbelt, airbag and seat, as well as coordination and matching design for them to achieve optimal restraint performance and reduce the risk of occupant injury [13,14,15]. To reduce the injury risk caused by airbag deployment, Tian et al. [16] used computer simulation methods to study the single-stage and double-stage airbag, and the results showed that the double-stage generator airbag had a better protection effect on the occupant. To improve the protective performance of seatbelts on the occupants, Liu et al. [17] corrected the numerical model of seatbelts through real vehicle crash experiments and optimized the dynamic characteristic parameters of seatbelts by using IP-GA genetic algorithm. Zhang et al. [18] applied approximate model parameter optimization technology and the robustness optimization method to optimize the vehicle member restraint system. The results show that the performance of the occupant restraint system is improved and robustness is considered.

The combination of airbag and seatbelt can significantly improve the protective effect of the restraint system [19,20]. However, in a small offset collision, the movement track of the driver’s head deviates from the center position of the airbag and the restraint of the seatbelt is not reasonable, so the airbag and seatbelt do not protect the driver well. Therefore, matching the appropriate restraint system can effectively restrain the driver’s motion attitude and reduce the injury. To improve the protection effect of the restraint system, Hirosuke et al. [21] and Zhang et al. [22], combined with the engineering optimization theories such as multi-objective optimization design, robustness optimization design, and reliability optimization design, established an optimization platform and conducted matching optimization analysis on the key parameters of the restraint system. NSGA-II is an improved version of the non-dominated sorting genetic algorithm (NSGA), which exhibits excellent exploration performance [23,24]. Ge et al. [25] used the NSGA-II genetic algorithm for multi-objective optimization of the occupant restraint system, and the results showed that the optimized restraint system could effectively reduce the weighted injury criterion of dummy frontal collision and offset collision.

The purpose of this study is to obtain the matching parameters of the seatbelt and airbag that achieve the best effect on driver protection in a small offset collision. HyperMesh software was used to reconstruct a case small offset collision accident of the sedan, which has a detailed injury report and video record. The effectiveness of the simulation model and pre-tensioned force-limiting seatbelt were verified, and the effects of different structural performance parameters of the restraint system on the occupant’s head, neck, chest, and leg are analyzed. Moreover, based on the radial basis function (RBF) replacement model, the key parameters of seat belt and airbag restraint system were optimized by using NSGA-II genetic algorithm. The results show that the optimized restraint system can protect the driver well, which provides a reference for the engineering design of this type of restraint system.

2. Methods

2.1. Accident Data

Our study is based on the in-depth accident investigation conducted by a research team at the Surgical Institute of Army Military University in Chongqing, China, which collected more than 2700 road traffic accidents with detailed injury information from 2013 to 2018 and established a database [26]. For each accident case, relevant data are collected from the traffic police department to determine how the accident occurred. A small offset collision accident involving a sedan was selected from the database, which has detailed accident scene photos, a police traffic accident scene map, an injury report, vehicle trace deformation information, and clear monitoring video. The whole motion process of the sedan collision with obstacles can be clearly observed from the video. The details of the accident are that the left front of a Toyota sedan collided with the right rear of a red truck parked in front. The collision velocity of the sedan was 64 km/h. The driver was wearing a seat belt and the airbag deployed at the time of the collision. The injury information of drivers in accidents was coded according to the abbreviated injury scale (AIS), which was revised in 2005. According to this standard, AIS values of 1, 2, 3, 4, 5 and 6 represent minor, moderate, serious, severe, critical, and untreated injuries, respectively.

Table 1. Information of driver, vehicle, and collision.

Collision Information
Weather	Sunny
Ground	Dry asphalt pavement
Collision type	25% offset collision
Impact velocity	64 km/h [27]
Driver information
Age	48
Gender	Male
Height	168 cm
Seat belt	Use
Airbag	Deploy
Vehicle information
Vehicle type	Toyota sedan
Curb weight (kg)	1295
Wheelbase (mm)	2700
Length × Width × Height (mm)	4630 × 1775 × 1480
Driver injury
Injury part	Injury information	AIS
Head	Left ear fracture, bleeding on wound surface, left occipital scalp hematoma	3
Neck	Fracture of thyroid cartilage of neck	2+
Thorax	Fractures of the left 3rd, 5th, 6th and 8th ribs, traumatic wet lung	4
Upper limb	Contusion and laceration of left shoulder and open fracture of left scapula	3
Lower limb	A large open laceration was seen in the anterior middle of the left calf	3
Extent of vehicle damage
The front of the sedan was seriously deformed, the front windshield was broken, the door of the left driver’s side was seriously deformed, the left front window glass fell off, and the airbag of the driver was ignited.

summarizes collision information, vehicle information and damage, and driver information and injuries.

2.2. Accident Reconstruction

The workflow chart of the accident reappearance is shown in Figure 1. Step 1 in Figure 1 shows that the driver’s seat of the Neon sedan model is depressed in this paper. Steps 2–5 demonstrate that, based on the Neon sedan finite element model, a small offset collision model was established by assembling the occupant restraint system model (including dummy, seatbelt, and airbag) and the barrier. First, step 2: Import the human body model into the vehicle model, and position it correctly. Then, steps 3–4 display that the three-point seatbelt and airbag were installed. Finally, a small offset collision model is established based on the simplified rigid barrier model of arc structure. Finally, the simulation results are compared with the dynamic response of the vehicle and the driver in the accident, as well as the injury of each part of the driver.

Occupant Restraint System Model

(1)

Vehicle, dummy, and barrier model

According to the accident information, it can be determined that the traffic accident case vehicle in this study is a Toyota sedan, but we do not have the interior matching the finite element model of Toyota sedan. Therefore, in order to better reproduce the accident case, we chose a Neon model similar to Toyota model with the same level to replace it. The Neon model was jointly developed by the National Center for Collision Analysis (NCAC) and the National Highway Traffic Safety Administration (NHTSA). Figure 1 (step 1) shows that the Neon sedan model has passed the credibility verification of the real vehicle test and finite element simulation [28]. The model includes the body, windshield, steering system, seat system, pedal, instrument panel, and others. The model consists of 1,487,639 elements, and the materials and properties meet the basic requirements of collision regulations. The essence of the automobile collision process is to absorb the kinetic energy of the vehicle in the form of deformation and friction, and the mass of the accident vehicle is one of the main factors affecting the kinetic energy. Therefore, in order to improve the accuracy of the accident reconstruction study of the Neon model, we weighted the whole vehicle model, or some parts are weighted by the Assign ms function module in the preprocessing software Oasys Primer. Make the mass and centroid position of the model consistent with the accident vehicle. To better simulate the relative position between the dummy and the seat, we need to under press the seat model in advance [29]. This study adopts the THUMS human body finite element model (v.4.0.2), which was jointly studied by the Central Research Institute of Japan and Toyota Corporation. The attitude of the human model has an important influence on the motion state of dummy after the collision of accident vehicles. As shown in Figure 1 (step 2), the dummy posture was adjusted by applying initial force or initial velocity [30]. According to the regulations of C-IASI, and to improve the efficiency of calculation, the rigid barrier with simplified arc structure was used to simulate the barrier in the actual test. As shown in Figure 1 (step 5), the height of the barrier is 1524 mm; the radius of the arc circle is 150 mm; the radian is 115°.

The boundary conditions include the relative position of the collision between the sedan, the barrier, and the ground. The barrier is located on the left side of the sedan body, and the overlap rate with the sedan body is 25% of the vehicle width. The barrier is set as full constraint. The vehicle is set as the slave surface, the barrier is the main surface, the static friction coefficient is 0.2, and the dynamic friction coefficient is 0.1. The ground in the accident is dry asphalt pavement, which can be defined as a rigid body [31]. The friction coefficient is set to 0.7, and the vehicle velocity is 64 km/h.

(2)

Seatbelt model

• Ordinary seatbelt
  In case of vehicle collision, the seatbelt is the most important protective device in the occupant restraint system. At present, three-point seatbelts are commonly used. As shown in Figure 1 (step 3), a finite element model of the ordinary three-point seatbelt was established according to the seatbelt performance of the vehicle in a collision accident. The model mainly includes safety belt webbing, retractor, D-ring, and fixing device.
• Pre-tensioned force-limiting seatbelt
  Hong et al. [32] verified that the combination of pre-tensioned force and limiting force has a significant effect on the injuries of various parts of the driver, and they explored the optimal combination form to provide the best protection for the driver. The pre-tensioned force-limiting seatbelt is modeled by adding a force limiter and pretensioner device based on the seatbelt model of the accident sedan. The force limiter device is defined by the card * ELEMENT_SEATBELT_RETRACTOR in PRIMER to achieve the function of the force limiter. The pretensioner device is simulated by the card * ELEMENT_SEATBLET_PRETENSIONER. As shown in Figure 2a, the Seatbelt_1D unit and Seatbelt_2D unit constitute the seatbelt webbing. Figure 2b shows the material characteristic curve of the Seatbelt_1D unit. Figure 2c,d show the force limiting characteristic curve and pre-tensioned characteristic curve of the seatbelt, respectively.

(3)

Airbag model

An airbag is a device that prevents the head and chest of occupants from directly contacting the steering wheel and plays a cushioning role for them. Therefore, studying the sensitivity analysis of the effect of the airbag on driver protection is an important task. The finite element model is established by taking the airbag in the collision accident as the prototype. The airbag model is mainly composed of the air sac, gas generator, and steering wheel. At present, three main methods are applied to establish the airbag model: computational fluid dynamics, pressure equalization, and the particle method [33]. Among them, the pressure equalization method has the advantages of data stability, lack of ease in reporting errors in simulation, and high calculation efficiency. As shown in Figure 3a, this study uses HyperMesh and Primer software and pressure equalization method to model the airbag. The modeling process involves static tiling size, folding mode, weaving material, gas generator, and other related parameters. The diameter of the airbag in the tiled state is 680 mm, which is divided into upper and lower layers of fabric that is divided by a triangular grid with a size of 10 mm. Finally, the divided model was imported into Primer software for airbag folding. The keyword * AIRBAG_WANG_NNEFSKE_ID is used to define the airbag, and the inflating characteristics are defined by the mass flow curve. Figure 3b,c show the airbag structure diagram and mass flow curve, respectively. In the simulation, the airbag ignition time is controlled by the type in Sen, and the airbag ignition time is set to 18 ms, according to the airbag performance parameters of the original accident vehicle.

2.3. Restraint System Design Based on Pre-Tensioned Force-Limiting Seatbelt

In a small offset collision, the driver’s head movement trajectory deviates from the center position of the airbag. At this time, if the seatbelt and airbag are not properly matched, the driver may suffer serious secondary injuries. Therefore, this study designs a restraint system based on a pre-tensioned force-limiting seatbelt. By reasonably matching the key parameters of the pre-tensioned force-limiting seatbelt and the airbag, the driver’s motion state is restrained, and the violent secondary collision energy is buffered, which further improves the driver’s protection performance of the restraint system. These parameters include seatbelt force-limiting A, pre-tensioned force B, pre-tensioned time C, airbag ignition time D, and mass flow coefficient E.

2.4. Injury Criteria

The head is the most important part of the body and has the highest percentage of injuries statistically available. At present, the most commonly used evaluation criteria for a head injury in automobile collisions is head injury criteria (HIC) [34]. The calculation formula of HIC value is

$$HIC=\underset{T_0\le t_1\le t_2\le T_E}{max}\left\{\left(t_2-t_1\right){\left[\frac{1}{t_2-t_1}{{\displaystyle \int }}_{t_1}^{t_2}a\left(t\right)dt\right]}^{2.5}\right\}$$

(1)

where $a\left(t\right)$ is the synthetic acceleration of the human head during vehicle collision, and $T_0$ and $T_E$, respectively, represent the start and end times of the simulation. Furthermore, $t_1$ and $t_2$ are the start and end times when the HIC value reaches the maximum value during the collision. We use $t_2-t_1=15 \mathrm{ms}$ according to regulations.

In the process of vehicle collision, neck injury of humans mainly includes compression injury, rotation injury, and so on. In this study, the biomechanical neck injury predictor $N_{ij}$ was used to evaluate the neck injury of the vehicle occupants, and the calculation formula is

$$N_{ij}=\left|\frac{F_z}{F_{zc}}\right|+\left|\frac{M_{ocy}}{M_{yc}}\right|$$

(2)

where $F_z$ is the axial force of neck, and $F_{zc}$ is the tolerance limit value of axial force of neck. $M_{ocy}$ is the neck-bending moment, and $M_{yc}$ is the neck-bending moment tolerance limit. FMVSS208 standard stipulates that the tolerance of the biomechanical neck injury prediction index in a collision accident is 1 [35].

Chest injury is usually caused by the compression of the thoracic cavity of occupants caused by the restraint of the seatbelt and airbag, which can lead to rib fracture, lung contusion, heart contusion, and hemopneumothorax. The key indexes to evaluate the degree of chest injury in frontal impact are the continuous 3 ms injury standard and maximum compression degree of chest. FMVSS208 standard stipulates that the maximum synthetic acceleration of the chest shall not exceed 60 g within a continuous period of 3 ms. That is, $C_{3\mathrm{ms}}\le$ 60 g [35].

Human lower limb fracture is one of the common injuries in traffic accidents, especially in a small offset collision. In this study, the tibial index (TI) was used to evaluate the leg injury, and its calculation formula is

$$TI=\frac{M\left(t\right)}{Mc}+\frac{F\left(t\right)}{Fc}$$

(3)

$$M\left(t\right)=\sqrt{{\left(Mx\right)}^2+{\left(My\right)}^2}$$

(4)

where $M\left(t\right)$ is the instantaneous composite bending moment of the tibia, $Mx$ is the bending moment in X direction, and $My$ is the bending moment in Y direction. $F\left(t\right)$ is the instantaneous axial compressive force of the tibia, $Mc$ is the critical composite bending moment (valued at 225 Nm), and $Fc$ is the axial critical compressive f force (valued at 35.9 kN). TI has a tolerance limit of 1.3 [36].

There is a different degree of injury to each part of the driver’s body in the small offset collision. In this study, weighted injury criterion (WIC) was used to comprehensively evaluate the injury degree of the driver’s head, chest, and leg [37]. The calculation formula of WIC is

$$WIC=0.6\left(\frac{HI{C}_{15}}{700}\right)+\frac{0.35\left(\frac{C_{3\mathrm{ms}}}{60}+\frac{C_{comp}}{63}\right)}{2}+0.05\left(\frac{F_L+F_R}{20}\right)$$

(5)

where $C_{comp}$ is the compression of the chest, left and right legs have maximum axial forces of $F_L$ and $F_R$, respectively, in units of KN.

2.5. Terms and Definitions

To better understand the accident reconstruction process of this study and the comparison between numerical simulation and real vehicle recorded collision, the terms in this paper are clearly and formally defined. The terms and definitions used in this paper are shown in

Table 2. Terms and definitions.

Terms	Defined
IIHS	Insurance Institute for Highway Safety
NSGA	Non-dominated Sorting Genetic Algorithms
IP-GA	Intergeneration Projection Genetic Algorithms
RBF	Radial Basis Function
AIS	Abbreviated Injury Scale
NHTSA	National Highway Traffic Safety Administration
NCAC	National Crash Analysis Center
THUMS	Total Human Model for Safety
C-IASI	China Insurance Automotive Safety Index
HIC	Head Injury Criteria
WIC	Weighted Injury Criterion
RE	Relative Error
ME	Maximum Error
RMSE	Root Mean Square Error
$R^2$	Determination Coefficient

.

3. Results and Discussion

3.1. Accident Model Verification

Figure 4a shows the small offset collision scene of the sedan under the simulation and real-world accident (white sedan rear-end collision with a stationary red van), and the deformation of the sedan at different times is observed. The small offset kinematics of the sedan, reconstructed in the simulation, is compared with the video recording. The reconstructed small offset kinematics of the sedan is basically consistent with the video recording. Figure 4b shows the simulation results in which the front left side of the sedan is severely deformed, the left front wheel tire is burst, the hub is broken, the left front door is severely deformed, the window glass falls off, and the left A-pillar is bent and deformed. Compared with the sedan deformation in a real-world accident, the vehicle deformation is basically the same. The contact position between the vehicle model and barrier is close to the collision position of the accident vehicle (with an overlap rate of 25%), and the airbag is all deployed during the collision. As can be seen from Figure 4c, kinetic energy is converted into internal energy in the collision process, the curve is smooth and the fluctuation is small, and the total energy is basically stable, which meets the requirements of energy conservation law. At the same time, the hourglass can be kept within an acceptable 5% of the total energy. Therefore, the results of the simulation model are reliable.

To obtain the difference of the driver protection effect between the pre-tensioned force-limiting seatbelt and ordinary seatbelt, we compared the dynamic response of the dummy and injuries of various parts of the body when two types of seatbelts were used. Figure 5 shows that the dummy has a dynamic response of the left front motion during the collision process, which is caused by the action of X and Y acceleration forces on the dummy. Figure 5a shows that, during the collision, the legs of the dummy first contact the interior of the vehicle body. Then, due to the inertia effect, the dummy continues to move forward to the front left. There was contact between the airbag and the dummy’s chest, head, and neck. Finally, under the action of the tension of the ordinary seatbelt, the dummy stops moving forward and instead moves backward. Figure 5b shows that the contact time between the dummy’s head, chest, and the airbag is shortened under the action of the pre-tensioned force-limiting seatbelt, thereby protecting the head.

In the simulation collision, according to the dynamic response, one can conclude that the pre-tensioned force-limiting seatbelt can effectively protect the head and neck of the dummy. To effectively verify the protection effect, the injuries of the dummy’s head, neck, chest, and leg, when using ordinary seatbelt and pre-tensioned force-limiting seatbelt, were compared.

Table 3. Injury values of various parts of the dummy in a simulation test.

	Injury Indexes	Injury Threshold	Ordinary Seat Belts	Pre-Tensioned Force-Limiting Seat Belts	Reduction
Head [34,38,39]	Skull von mises stress (MPa)	10	9.6	5.4	43.8%
	Intracranial pressure (kPa)	235	232	185	20.3%
	Intracranial von mises stress (kPa)	15–20	19.1	12.3	35.6%
	HIC	700	798	497	37.7%
Neck [35]	$N_{ij}$	1	1.04	0.76	26.9%
Thorax [35,37]	$C_{3\mathrm{ms}}$ (g)	60	98	102	−0.04%
	$C_{comp}$ (mm)	50	37	44	−0.19%
	Rib strain	3%	12%	16%	−0.33%
	Lung strain	30%	29.4%	31.3%	−0.06%
	Cardiac strain	30%	12%	11%	0.08%
	Liver strain	30%	19.4%	17.3%	0.11%
Leg [36]	TI (left)	1.3	1.49	1.35	0.09%
	TI (right)	1.3	0.93	0.78	0.16%

shows the injury values for each dummy.

As shown in Table 2, the skull von Mises stress, intracranial pressure, and intracranial von Mises stress of the ordinary seatbelt dummy are all close to the threshold, which may lead to a severe head injury. This is basically consistent with the driver’s head injury recorded as AIS3 in Table 1. This injury may be caused by the contact of the driver’s head and face with the airbag, steering wheel, and instrument panel [40]. The neck $N_{ij}$, chest $C_{3\mathrm{ms}}$, and rib indexes all exceed the threshold, and the lung indexes are close to the threshold. These index values indicate the possible serious injury to the driver’s neck and chest. This is basically consistent with the driver’s neck injury AIS2+ and chest injury AIS4 recorded in Table 1. This is caused by the driver’s chest being squeezed by the seatbelt webbing and a direct violent collision with the airbag. TI of the dummy’s left and right legs were 1.49 and 0.93, respectively, and TI (left) exceeded the threshold of 1.3, indicating that the driver’s left lower limb was seriously injured. This is basically consistent with AIS3 recorded by the driver’s leg injury in Table 1. The reason is that the collision area is on the front-left side of the vehicle, the area has a large amount of invasion, and the left lower limb contacts with the foot pedal, A-pillar lower hinge, and sill [41]. Video-based deep accident reconstruction can verify the kinematics of the sedan small offset collision and ensure the reliability of the accident simulation model. By comparing the vehicle deformation and driver’s injury in the simulation results to the real-world accident, the effectiveness of the simulation model is further verified.

As shown in Table 2, compared with the ordinary seatbelt, the use of the pre-tensioned force-limiting seatbelt has improved the injuries on the dummy’s head, neck, and legs, and the injury values of the head and neck are lower than the threshold. The chest injury was slightly greater than that of the dummy under the ordinary seatbelt, but the difference was not significant. In a small offset collision, the head injury of the driver is affected by the mass flow impact of the airbag [42], which affects the hardness of the airbag when the dummy head contacts the airbag [43]. The strongest impact on the injury value of the driver’s chest is the mass flow coefficient of the airbag, followed by the force-limiting level of the seatbelt. Therefore, the injury values of the driver’s head, neck, chest, and legs can be reduced by adjusting the design parameters of the restraint system [44].

3.2. Effects of Different Parameters of Restraint System on Driver Injury

To minimize the injuries caused to the driver by the mass flow coefficient of the airbag and force-limiting level of the seatbelt, we selected seatbelt force-limiting A, pre-tensioned force B, pre-tensioned time C, airbag ignition time D, and mass flow coefficient E as optimization parameters. Five-factor and five-level orthogonal experimental design was used with a total of 25 sample points. These sample points were input in the model for simulation calculation using LS-DYNA software. The orthogonal experimental design is shown in

Table 4. Orthogonal experimental design.

Design Variables	Initial Value	Level 1	Level 2	Level 3	Level 4	Level 5
Force-limiting, A (N)	4500	4500	4750	5000	5250	5500
Pre-tensioned force, B (N)	2500	1500	1750	2000	2250	2500
Pre-tensioned time, C (ms)	18	16	18	20	22	24
Ignition time, D (ms)	9	0	5	10	15	20
Mass flow coefficient, E	1.02	0.5	0.7	0.9	1.1	1.3

.

The range analysis method is used to analyze the driver injury under different restraint system matching parameters, and the influence of each design variable on the driver’s body injury is studied.

Table 5. Results of the injury simulation for each part of the dummy.

Index	HIC					${\mathit{N}}_{\mathit{i}\mathit{j}}$					${\mathit{C}}_{3\mathbf{ms}}$					TI
	A	B	C	D	E	A	B	C	D	E	A	B	C	D	E	A	B	C	D	E
K1	1420	2483	2063	2328	2109	4.06	4.74	2.93	3.58	4.33	560	411	474	458	514	4.68	6.62	5.66	5.59	5.91
K2	1978	2206	1978	2790	2691	3.66	4.62	3.19	4.23	4.16	541	467	500	550	485	5.57	6.44	5.93	5.81	4.9
K3	2232	2385	2225	2094	2504	4.11	4.14	4.79	4.11	4.1	454	607	506	493	473	5.15	5.57	4.94	5.75	5.64
K4	2976	2219	2252	1987	1824	3.72	3.51	4.26	3.87	3.62	448	510	464	442	486	5.84	4.9	5.81	5.61	6.01
K5	2529	1842	2617	1936	2007	4.16	2.7	4.54	3.92	3.5	421	429	480	480	466	6.72	4.43	5.62	5.2	5.5
k1	284	497	413	466	422	0.81	0.95	0.59	0.72	0.87	112	82	95	92	103	0.94	1.32	1.13	1.12	1.18
k2	396	441	396	558	538	0.73	0.92	0.64	0.85	0.83	108	93	100	110	97	1.11	1.29	1.19	1.16	0.98
k3	446	477	445	419	501	0.82	0.83	0.96	0.82	0.82	91	121	101	99	95	1.03	1.11	0.99	1.15	1.13
k4	595	444	450	397	365	0.74	0.7	0.85	0.77	0.72	90	102	93	88	97	1.17	0.98	1.16	1.12	1.2
k5	506	368	523	387	401	0.83	0.54	0.91	0.78	0.7	84	86	96	96	93	1.34	0.89	1.12	1.04	1.1
R	311	129	127	171	173	0.1	0.41	0.37	0.13	0.17	28	39	16	22	10	0.4	0.43	0.2	0.12	0.22

displays the results of the analysis, where Ki (i = 1, 2, 3, 4, 5) is the sum of the test results of each factor and level. The average of the test results for each factor and level is the ki (i = 1, 2, 3, 4, 5). Under the same factor and at different levels, the R represents the range of test results.

By comparing range R, the change of the pre-tensioned force B has the most remarkable effect on the driver’s neck, chest, and legs, while the change of force-limiting A has a strong impact on the head. At the same time, the driver’s head and chest have the lowest sensitivity to the changes of pre-tensioned time C and mass flow coefficient E, respectively, while the neck and leg have the least impact on the changes of force-limiting A and ignition time D, respectively.

The aim of the range analysis results of orthogonal experimental design was to gain an intuitive understanding of the effects of different levels of each factor on the dummy’s injury. We obtained the influence degree of each factor on the dummy’s head, neck, chest, and leg injury.

As shown in Figure 6, with the continuous increase in force-limiting A, the driver’s chest injury decreases, while the neck injury fluctuates continuously. As the force-limiting A was greater than 4750 N, causing the head injury value to increase first, then decrease, and the leg injury value to decrease first, then increase. With the continual increase in pre-tensioned force B, the injury value of the driver’s neck and leg decreases without interruption, while the degree of chest injury increases first and then decreases with the change of pre-tensioned force B. The head injury first increases and then decreases when the pre-tensioned force B is greater than 1750 N. With the change of pre-tightening time C, the neck and chest injuries of the driver first increased, then decreased, and then increased, with the maximum value at 20 ms. The head injury value of the driver increases with the increase in pre-tightening time C. In addition, leg injury fluctuates continuously. With the further increase in ignition time D, the head and leg injuries of the driver were improved. With the change of ignition time D, the neck and chest injury values of the driver first increased, then decreased, and then increased, with the maximum value at 5 ms. With the continual increase in the mass flow coefficient E, the neck and chest injury values of the driver decreased. The head injury value of the driver increased first, then decreased, and then increased, while the change trend of the leg injuries were the opposite.

According to the relationship between each injury value and the design variables of the constraint system, when one target reaches the optimal state, another injury target may reach the worst state. This condition leads to the driver’s overall failure to achieve the optimal low injury value. Therefore, using Isight optimization software, this study achieved the optimum compromise of design variables, of the constraint system matching, by optimizing multiple objectives of the driver injury at the same time.

4. Multi-Objective Optimization of Constraint System Matching Design Variables

After comprehensive consideration, the weighted injury values WIC of the driver’s head, chest, and leg were selected, and the neck injury predictor $N_{ij}$ was taken as the design objective. Additionally, force-limiting A, pre-tensioned force B, pre-tightening time C, ignition time D, and mass flow coefficient E were used as design variables. The orthogonal experimental design approach is then utilized to pick sample points for the model’s construction.

4.1. Approximate Model of Radial Basis Function and Error Analysis

The radial basis function model (RBF) was created using Isight optimization software in conjunction with the aforementioned design experiments. Then, the relationship between WIC and neck injury criterion ($N_{ij}$) and the force-limiting A, pre-tensioned force B, pre-tightening time C, ignition time D, and mass flow coefficient E were studied [45]. The approximate expression of the design variable’s response function in the design space can be expressed as

$$Y\left(X\right)=\tilde{y}\left(x\right)+\epsilon =\left({\displaystyle \sum }_{i=1}^N{a}_i{g}_i\left(\Vert x-x_i\Vert {}^{c_i}+a_{N+1}\right)\right)+\epsilon$$

(6)

where $\tilde{y}\left(x\right)$ indicates the approximate function of the objective. The relative error (RE) between the actual and approximation values, the number of terms of the basis function $g_i$, the indeterminate coefficient, and the Euclidean distance of the basis function are indicated by $N$, $a_i$, and $x-x_i$, respectively. The shape parameter is represented by $c_i$. The accuracy rate of the RBF approximate model varies with the shape parameters. Using Isight optimization software, the shape parameters were optimized internally when the RBF approximate model was established. By constantly changing the shape parameter c, the established approximate model minimized errors. In general, the value of c was between 0.2 and 0.3.

To evaluate whether the fitting response surface was reasonable, The RBF response surface was evaluated using relative error ($RE$), maximum error ($ME$), root mean square error ($RMSE$), and determination coefficient ($R^2$). The specific formula is as follows:

$$RE=100\%\times \frac{\left|\widetilde{y_i}-y_i\right|}{y_i}$$

(7)

$$ME=100\%\times \left(\widetilde{y_i}-y_i\right)$$

(8)

$$RMSE=\sqrt{\frac{{{\displaystyle \sum }}_{i=1}^M{\left(\widetilde{y_i}-y_i\right)}^2}{M}}$$

(9)

$$R^2=1-\frac{SSE}{\mathrm{SST}}=1-\frac{{{\displaystyle \sum }}_{i=1}^m{\left(\widetilde{y_i}-y_i\right)}^2}{{{\displaystyle \sum }}_{i=1}^m{\left(y_i-\overline{y}\right)}^2}$$

(10)

where M stands for the number of samples used to test the accuracy of the model, $y_i$ represents the simulation analysis value of the ith response, and $\widetilde{y_i}$ represents the predicted value of the model. $\overline{y}$ indicates the average of the samples in the simulation analysis. The determination coefficient R*2 has a range of values from [0, 1]. The accuracy of the model increases as the value approaches 1. The maximum allowable error for RE, MR, and RMSE in this model is 0.2, 0.3, and 0.2, respectively. It is better if the value is smaller. Analyzed were the errors of 25 sample points. In

Table 6. Error estimation for the RBF model.

Response	$\mathit{R}\mathit{E}$	$\mathit{M}\mathit{E}$	$\mathit{R}\mathit{M}\mathit{S}\mathit{E}$	${\mathit{R}}^2$
$WIC$	1.64564 × 10−15	2.91092 × 10−15	1.80383 × 10−15	0.9985
$N_{ij}$	2.26274 × 10−15	3.96508 × 10−15	2.40359 × 10−15	0.9973

, we demonstrate that the RBF response surface model is highly accurate and can be applied to analyze multi-objective optimization problems further.

4.2. Multi-Objective Optimization Model

The multi-objective optimization mathematical model can be expressed, as follows, using the multi-objective genetic algorithm NSGA-II:

$$\left\{\begin{array}{c}minWIC=WIC\left(\mathrm{A},\mathrm{B},\mathrm{C},\mathrm{D},\mathrm{E}\right)\\ min{N}_{ij}=N_{ij}\left(\mathrm{A},\mathrm{B},\mathrm{C},\mathrm{D},\mathrm{E}\right)\\ s.t. 4500 N\le \mathrm{A}\le 5500 N\\ 1500 N\le \mathrm{B}\le 2500 N\\ 16 \mathrm{ms}\le \mathrm{C}\le 24 \mathrm{ms}\\ 0 \mathrm{ms}\le \mathrm{D}\le 20 \mathrm{ms}\\ 0.5\le \mathrm{E}\le 1.3\end{array}\right.$$

(11)

Figure 7 shows the multi-objective Pareto frontier of the protection matching parameters, of the optimal driver restraint system, derived from the genetic algorithm NSGA-II [46]. Based on the response surface model, the figure shows the optimal solutions of WIC and $N_{ij}$, and WIC and $N_{ij}$ always show an inverse ratio. $N_{ij}$, a neck injury predictor, decreased as WIC increased. Furthermore, reducing WIC can continuously increase the predictor $N_{ij}$ of neck injury. Additionally, the two endpoints of the Pareto frontier correspond to optimal single-objective values for different response surface models. The minimum neck injury response value of the driver is $N_{ij}$ = 0.330 (A = 4853 N, B = 2500 N, C = 16 ms, D = 5.3 ms, and E = 0.89) at optimal point F. Based on the response model, the minimum weighted injury value for the driver obtained is WIC = 0.498 (A = 4879.9 N, B = 2500 N, C = 17.9 ms, D = 16.7 ms, and E = 0.5) at the optimal point E.

In addition to the optimal-single objective value at both ends of Pareto frontier in the collision, the optimal values of WIC and $N_{ij}$ of the driver should also be considered comprehensively so that each part of the driver ’s body with a slight injury is the focus of our research. In this study, the balance point between WIC and $N_{ij}$ in optimization was found using the distance minimization method. In accordance with the principle of distance minimization, if it meets the condition that the sum of distances between two response values of the Pareto optimal point are the smallest, we will obtain the comprehensive optimal point [47]. The equation is

$$\mathit{minZ}=\left(\sum _{i=1}^n{(f_i^k-\mathit{min}\left(f_i\right))}^2\right)$$

(12)

The number of optimization objectives is indicated by n, and n = 2 indicates that WIC and $N_{ij}$ are the two optimization objectives. The response value of the ith optimization goal, at the ith Pareto response point, is denoted by $f_i^k$. Point G in Figure 7 represents the equilibrium solution of the conflict between two response values, according to the multi-objective optimal solution set computed by formula (8). The WIC and N_ij values, derived by the response model at the equilibrium point G, are 0.545 and 0.403 (A = 4933.5 N, B = 2499.9 N, C = 16 ms, D = 15.3 ms, and E = 0.5), respectively.

4.3. Results

The optimal parameter value 4933.5−2499.9−16−15.3−0.5 was input into LS-DYNA for calculation. The results show that the WIC value is 0.558 with an error of 2.3%, and the $N_{ij}$ value is 0.416 with an error of 3.1%. Based on the preceding results, all errors are within a reasonable range, which further verifies the accuracy of the surrogate model, as shown in

Table 7. Comparison of simulation injury of dummy results before and after optimization.

	Force-Limiting, A	Pre-Tensioned Force, B	Pre-Tensioned time, C	Ignition Time, D	Mass Flow Coefficient, E	WIC	${\mathit{N}}_{\mathit{i}\mathit{j}}$
Before	4500	2500	18	9	1.02	0.899	0.760
After	4933.5	2499.9	16	15.3	0.5	0.558	0.416
Reduction	-	-	-	-	-	37.9%	45.3%

. The results show that after optimization, the WIC and $N_{ij}$ of drivers are reduced by 37.9% and 45.3%, respectively. The above results show that the optimized restraint system has great application potential in driver protection.

5. Limitations and Future Work

Some limitations in the present study still exist. First, the finite element model of the vehicle corresponding to the accident is lacking, so a small offset crash accident reproduction study is carried out using the adjusted Neon vehicle model. Although the verification results are ideal, there are still some errors. The next step is to expand the model base of vehicles and make specific analyses for specific models. Second, this study only focuses on the protection of sedan drivers. In future research, it is necessary to study the safety performance of restraint system for drivers of other models. Third, this paper only qualitatively analyzes the driver’s injury caused by the pre-tensioned force-limiting seat belt, and the future work will focus on the optimization of the restraint system parameters of the inflatable seat belt and the airbag.

6. Conclusions

In this work, based on the detailed accident case information, a sedan small offset collision simulation model is established to verify its accuracy. The protection effect of pre-tensioned force-limiting seatbelt on the driver is studied. The orthogonal experimental design method of five factors and five levels is designed. The influence law of each factor to the driver’s injury is determined by using the direct analysis method. Finally, combined with the RBF model and the NSGA-II multi-objective genetic algorithm, the structural performance parameters of pre-tensioned force-limiting seatbelt and airbag are optimized. The results show that the optimized restraint system can protect the driver well, which provides a reference for the engineering design of this type of restraint system.

The specific conclusions are as follows:

(1)

The injury values of each part of the driver were evaluated by reconstructing the sedan small offset collision accident. The simulation results showed that the accident model could accurately analyze the driver’s dynamic response and effectively evaluate the injury degree. The feasibility of the accident model was verified. The effectiveness of the matching use of the pre-tensioned force-limiting seatbelt and the airbag for driver protection was also verified.

(2)

The change of pre-tensioned force B had a remarkable effect on the neck, chest, and legs of the vehicle occupants, and the change of force-limiting A had the most serious influence on the head. In addition, the neck and legs were the least sensitive to the changes of force-limiting A and airbag ignition time D, respectively, while the changes of pre-tightening time C and airbag mass flow coefficient E had the least impact on the injury of the occupant’s head and chest, respectively.

(3)

When the variable of the restraint system is 4933.5−2499.9−16−15.3−0.5, the driver’s WIC was reduced by 37.9%, and the $N_{ij}$ value was reduced by 45.3%. This condition indicates that the optimized restraint system has great potential in improving driver protection.