Struct Multidisc Optim (2013) 47:465–477 DOI 10.1007/s00158-012-0811-7
INDUSTRIAL APPLICATION
Multiobjective optimization design for vehicle occupant restraint system under frontal impact Xianguang Gu · Guangyong Sun · Guangyao Li · Xiaodong Huang · Yongchi Li · Qing Li
Received: 16 January 2012 / Revised: 7 April 2012 / Accepted: 10 May 2012 / Published online: 30 May 2012 c Springer-Verlag 2012
Abstract Occupant Restraint System (ORS) can effectively protect passengers from severe injury in vehicle collision, thus its design signifies a key issue in automobile engineering. To ensure a high safety rating, e.g. five or at least four stars in the European New Car Assessment Program (Euro-NCAP) rating system, which has been widely used to rate the different vehicles from different manufacturers, design optimization becomes essential. Nevertheless, the effectiveness of conventional mathematical programming methods directly integrated with numerical simulation and sensitivity analysis for optimization is of limited practical value, due to high complexity of structures, nonlinearity of materials and deformation involved. To address the issue, this paper combines a Kriging (KRG) model with Non-dominated Sorting Genetic Algorithm II (NSGA-II) for vehicle ORS design. The ORS design of a 40% Offset Deformable Barrier (ODB) frontal impact test with the collision speed of 64 km/h is exemplified for the presented X. Gu · Y. Li Department of Modern Mechanics, The University of Science and Technology of China, Hefei, 230027, China X. Gu Chery Automobile Corporation, Wuhu, 241000, China G. Sun (B) · G. Li State Key Laboratory of Advanced Design and Manufacture for Vehicle Body, Hunan University, Changsha, 410082, China e-mail:
[email protected] X. Huang School of Civil, Environment and Chemical Engineering, RMIT University, Melbourne, 3001, Australia Q. Li School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW 2006, Australia
method. The results show that the KRG model can well predict the ORS responses for the design. Finally, the optimum result is verified by using sled physical tests. It is found that the ORS performance can be substantially improved for meeting product development requirements through the proposed approach. Keywords Occupant Restraint Systems · Kriging · Simulation analysis · Multiobjective optimization
1 Introduction Occupant Restraint Systems (ORS) have been of primary interest in automotive industry to ensure compliance with the government regulations and more importantly the occupants’ safety in a crash event. Over the past two decades, some mandatory standards, such as Federal Motor Vehicle Safety Standard No. 208 (FMVSS208 2010) in the United States and Economic Commission for Europe Regulation No. 94 (ECER94 2007) in Europe, have been established and appreciated for the protection of vehicle occupants in frontal crashes. Except for the governmental regulations, consumer information programs, such as the European New Car Assessment Program (Euro-NCAP) and the National Highway Traffic Safety Administration (NHTSA) for star rating, impose further requirements to vehicle safety design. These governmental regulations and consumer information programs enhance the quality of development of ORS to a considerable extent. On the other hand, these also increase the complexity of ORS and make its design and optimization a challenging task. To assess the effectiveness of ORS and other safety systems, the dummy responses are recorded in the three representative crash configurations: frontal impact (Yang et al. 2005a, b; Mizuno et al. 2008;
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Kim and Jeong 2010), side impact (Gu et al. 2001; Youn et al. 2004) and rear impact (Luo and Zhou 2010). Since the applications of ORS have proven to reduce occupants’ injury effectively, it has been widely adopted as a key safety system in modern development of vehicles (Kan et al. 2001; Huang et al. 2009). However, conventional design of new ORS has largely relied on empirical data and often requires a tedious trial-and-error process involving numerous prototyping tests, which leads to a rather long design cycle and remarkably high cost. Fortunately, with the rapid development of computational modeling, represented by nonlinear finite analysis and multi-rigid-body dynamics, the design philosophy has been changing significantly over the past years. Computer Aided Engineering (CAE) allows us to precisely model the performance of ORS at the design stage, which reduces prototyping cost to a considerable extent. In this respect, the analysis of ORS has been well reported in literature. For example, Bose et al. (2010) predicted the risk of occupants’ injury in frontal collisions, using commercial multi-body program MADYMO to couple multi-body models of the vehicle interior structure with the standard restraint system; Jang et al. (1999) simulated the occupant responses in sled impact and barrier crash tests by commercial code of Dynamic Analysis and Design System (DADS); Elmarakbi (2006) tried to analyze the dynamic responses and injury values of occupants by numerical simulations. However, to determine proper design parameters and achieve a satisfactory product quality, many trials of numerical analysis may be needed by manually adjusting the design models or parameters, whereas this cannot guarantee a global optimum (Sun et al. 2011a, b). In this sense, how to transform CAE from a passive verification means to a more active design tool is of significant theoretical interest and practical value (Sun et al. 2010; Avalle et al. 2002). Thus CAE-based optimization has been considered as a promising alternative to conventional ORS design. As an effective approach, surrogate modeling, such as Polynomial Response Surface (PRS), Kriging (KRG) and Radial Basis Function (RBF), has been exhaustively adopted in engineering applications to alleviate the computational burden and explore design space for an optimum (Acar et al. 2011; Bi et al. 2010; Zarei and Kroger 2006; Forsberg and Nilsson 2006; Redhe and Nilsson 2006; Craig et al. 2005; Lanzi et al. 2004; Kurtaran et al. 2002; Yang et al. 2000, 2005a; Yang and Gu 2004). For example, Huang et al. (2011) proposed a design optimization method based on the KRG surrogate models, and applied it to the shape optimization of an aerospace engine turbine disc. In the optimization process, the KRG model was built to provide efficient approximations to time-consuming computations. Yang et al. (2005b) adopted the stepwise regression, moving least square, Kriging, multiquadric, and adaptive and
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interactive modeling system to approximate the real-life design problems involving frontal impact. Su et al. (2011) optimized the design of bus structure with strength and rollover safety constraints on the basis of surrogate models, in which the stiffness and stress of the bus body were modeled using response surface method, while the stress of the intrusions in rollover crash with hybrid radial basis function. Liao et al. (2008a) developed a two-stage approach to the ORS design, in which the vehicle structure was optimized first without considering the ORS details, then the ORS were further optimized based on the optimal structure. In their study, KRG was adopted for the surrogate model of vehicle crashworthiness under frontal impact. Zhang et al. (2011) used successive response surface (RS) model to identify the material parameters for high strength steel under crash loading. Sun et al. (2010) used the RBF model to approximate the energy absorption characteristics of honeycomb-type cellular material under crashing status and obtained satisfactory optimal results. Although there has been substantial published work on the effectiveness of different surrogate models for structural crashworthiness design, limited reports have been available to validate the surrogate models via physical tests. This paper aims to demonstrate a KRG based computational design procedure for ORS to improve vehicle safety. Furthermore, the ORS design of full-scale vehicles involves optimizing a number of objectives. Some of these objectives often conflict each other, e.g., any further improvement in one objective could worsen one or more others at the certain optimization stage. Thus, the best way is to search for a solution in a Pareto sense (Liao et al. 2008b). A common approach to multiobjective optimization is to select a primary or predominant goal from a list of design requirements as the objective function, while the rest as design constraints. For example, conventional single objective optimization algorithms can be applied for an optimal solution. However, for general real-world engineering problems, the selection of objective function can be very difficult. For this reason, some genuine multiobjective algorithms have been developed. For example, Sun et al. (2011a) used Multiobjective Particle Swarm Optimization (MOPSO) to improve the crashworthiness of vehicle structure; Yu et al. (2001) proposed a multilevel optimization approach to the ORS design, whose results indicated significant improvement in safety; Jiang and Gu (2010) applied Non-dominated Sorting Genetic Algorithm II (NSGA-II) for obtaining the Pareto optimum in the crashworthiness design of the fender structure; Sinha (2007) developed a reliability-based multiobjective optimization design for vehicle structural crashworthiness and occupant safety under side impact, in which NSGA-II was also applied; Del Prete et al. (2010) optimized the design for high performance aeronautic seat structure as per the SAE-AS Standards in occupant protection;
Multiobjective optimization design for vehicle occupant restraint system under frontal impact
Liao et al. (2008a, b) and Zhan et al. (2011) more recently formulated the NSGA-II multiobjective optimization for the ORS designs. From the researches mentioned above, the NSGA-II multiobjective optimization algorithm can effectively generate Pareto frontier and will be in this study to optimize the ORS design. The paper presents an application of Design of Experiment (DOE), surrogate model and multiobjective optimization algorithm to reduce the Head Injury Criteria (HIC) and chest displacement together with enhancing the EuroNCAP scores. Considering that the KRG can well fit to the nonlinear response of dynamic impacting problems, it is used to model the true responses of ORS for the optimization. Importantly, the effectiveness and accuracy of simulation modeling and optimum results are both verified by the real physical experiments. The rest of the paper is organized as follows: Section 2 describes the optimization method; Section 3 provides the assessment of occupant safety in frontal impact according to the Euro-NCAP code; Section 4 depicts the simulation and experimental validation; Section 5 presents the ORS optimization, and finally Section 6 draws major conclusions from the study.
2 Surrogate and multiobjective optimization algorithm 2.1 Kriging approximation model The KRG method was originated from the geostatistics community and used for modeling computer experiments. In the recent years, the KRG model has been widely applied in crashworthiness design of vehicle structure and sheet
Fig. 1 The flowchart of elitist non-dominated sorting genetic algorithm (NSGA-II)
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metal forming. A general KRG model can be written as (Zhao and Xue 2011): y(x) = f (x) + Z (x)
(1)
where x is the vector of design variables, y(x) is the response function of interest, f (x) is a known polynomial function that approximates the response globally, and Z (x) is a stochastic component which generates deviations such that the KRG model interpolates the sample response data. The stochastic component has a mean value of zero and variance of σ 2 . More details regarding the KRG model can be consulted from literature (Timothy et al. 2001). 2.2 Non-dominated Sorting Genetic Algorithm II (NSGA-II) The NSGA-II was proposed by Deb et al. (2000) in Kanpur Genetic Algorithms Laboratory (KanGAL). The main steps of the NSGA-II are given as follows and the flowchart in Fig. 1, respectively. (1) Randomly initialize the parent population, and evaluate the population by computing the constraints and objectives of each individual. (2) Rank the population using non-domination criteria. Also compute the crowding distance to identify the relative closeness of a solution to others in the functional space and differentiate among the solutions of the same rank. (3) Apply genetic operators to create a child population and validate the child population. (4) Combine the parent and child populations, rank them, and re-compute the crowding distance. Apply elitism
Initialization of parent population (size N) Initialize an empty archive
Rank population
Evaluate parent population
Selection
Crossover
Mutation
No Evaluate child population Yes
Stopping criteria
Output the optimization results
Copy all rank 1 individuals to the archive
Combine parent and child population and rank population
Remove duplicates and dominated individuals from the archive
Pick the best N individuals from the combined population
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to select the best N individuals from the combined population. These individuals constitute the parent population for the next generation. (5) Add all rank = 1 solutions to the archive and update the archive by removing all dominated and duplicated solutions. (6) If the termination criterion is not met, return to Step (3). Otherwise, record the candidate Pareto optimal set in the archive and output the results. Fig. 2 Test under 40% offset frontal impact onto deformable barrier
3 Performance assessment of restraint system for baseline model The new EuroNCAP ratings for adult, child and pedestrian protection have been used since 2012, and have become internationally recognized as a reliable indicator of independent consumer information about car safety. To ensure four stars in the Euro-NCAP system (2011), the development goal of new vehicle should meet the requirements shown in Table 1. From Table 1, it is observed that the frontal impact is of foremost concern and may dominate the overall design requirements. Note that ORS optimization for the frontal impact should not significantly affect to other crash conditions such as side impact, rear impact and child protection etc. Therefore, this paper focuses on the ORS design for improving in safety performance under the front crash scenario. For the dummy response data under frontal impact, the Euro-NCAP assessment applies a sliding scale system of
scoring for calculating points in each measured criterion. The smaller injury parameter value indicates the larger score and vice versa, and there are two limits for each parameter, i.e., a more demanding limit (higher performance): below which a maximum score is obtained; and a less demanding limit (lower performance): beyond which no points are scored. If the test value recorded falls between the lower and upper limits, the points score is calculated using linear interpolation. The contribution of the frontal impact tests to the adult occupant protection score is calculated by summing the scores of the relevant body regions. Then, the lower one of the driver and passenger scores is used for the EuroNCAP rating. Note that the score generated from driver dummy may be modified where the protection for differently sized occupants, occupants in different seating positions, or accidents of slightly different severity, is expected to be worse than that indicated by the dummy readings or deformation data
Table 1 Decomposition of the score for development of EuroNCAP four stars Description
1. Adult protection
2. Children protection
3. Pedestrian protection
4. Safety assist
NCAP full
Four stars
Development
Target total
score
requirement
target score
score
Front impact
16.00
25.20
11.00
27.00
Side impact
8.00
8.00
Side pole impact
8.00
6.00
Whiplash
4.00
2.00
Dynamic test
24.00
CRS based assessment
12.00
Vehicle whole value
13.00
Head protection
24.00
29.40
18.00
36.00
12.00 6.00 18.00
13.00
Legform protection
6.00
6.00
Upper legform protection
6.00
0.00
SBR
3.00
ESC
3.00
3.00
SLD
1.00
0.00
3.00
2.00
19.00
5.00
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Table 2 The assessment of driver and passenger injury according to the Euro-NCAP
Head and neck
Chest Femur and knee
Lower leg
Protection criteria
Higher
Lower
Diver
Passenger
HIC36 Value
650
1000
719
473
A3 ms head
72
88
58.45
65.39
Neck shear force
1.9
3.1
1.2
0.75
Neck tension force
2.7
3.3
1.09
0.89
Neck extension-my
42
57
20.14
13.61
Chest displacement
22
50
32.28
19
VC-value chest
0.5
1
0.26
0.16
Left femur force
3.8
9.07
0.23
0.74
Right femur force
3.8
9.07
0.81
0.92
Left knee dis.
6
15
0.15
1.6
Right knee dis.
6
15
0.47
2.3
Left axial force
2
8
1.81
1.53 0.27
Left upper TI
2
8
0.39
Left lower TI
0.4
1.3
0.36
0.32
2
8
2.31
0.69
Right upper TI
0.4
1.3
0.59
0.35
Right lower TI
0.4
1.3
0.38
0.21
Right axial force
Points
Modified
Total
3.21
−1.00a
9.90
2.53
−1.00b
4.00
3.16
0
−1.00c
a Unstable
contact on the airbag of the passenger compartment c Footwell rupture b Integrity
alone. In any single body region, the score may be reduced by a maximum of two points. The more details behind the modifiers are explained in the Euro-NCAP system (2011). To assess the safety performance under frontal impact, a test of 40% offset frontal impact onto deformable barrier with a collision speed of 64 km/h was performed, as shown in Fig. 2. The dummy response data indicated a reasonably good protection of all driver and passenger body regions except the head, chest and lower leg of the driver, which were not adequate. The test results and dummy scores of the baseline design are listed in Table 2 according to Euro-NCAP. Considering the frontal impact modifiers, 3 points were deducted which led to the total score of occupants’ injury performance to 9.9 as shown in Table 2. Then the score is expected to improve from 9.9 to 11 on the driver’s side to meet the development requirements, as shown in Table 1. As the improvement of vehicle structure will lead to higher cost, whilst an optimal ORS match can decrease dummy injury data easily with lower cost. If we only relied on the design experience and adopted a trialand-error approach to determining a set of suitable ORS parameters, the design cycle could be rather long and the cost would be considerably high. Therefore, it is necessary to seek an effective optimization procedure to improve the ORS performances for achieving a higher score evaluated with Euro-NCAP.
4 Numerical modeling and experimental validation To optimize the ORS design, the numerical model must be created and validated by physical tests to ensure the practical effectiveness. 4.1 Numerical model of vehicle restraint system A typical ORS model consists of occupant restraint components, vehicle interior environment and the occupant. Currently three major software packages, namely LS-DYNA, PAMCRASH and MADYMO, have proven effective in the automotive ORS analysis,. The LS-DYNA and PAMCRASH solvers are based on Finite Element (FE) methods, which also include limited rigid/ flexible multi-body functions. However, single run of the ORS based on LSDYNA and PAMCRASH can be relatively long. On the other hand, MADYMO represents a rigid/flexible multibody dynamics solver and its major advantage is to combine the rigid/flexible multi-body model for the occupant and the FE model for the key occupant restraint components such as airbag and seat belts, which gives sufficient details of the system responses within a shorter computing time. Therefore, MADYMO with the combination of both multi-body and FE model was selected as the simulation engine in this study.
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Fig. 3 Restraint system model a components b load conditions
(a)
(b)
Since the restraint system of passenger side has primarily met the design requirement, we focus more on the safety of the restraint system on the driver side. A restraint system and a driver-side dummy provided by our industrial partner were used to create a baseline model for numerical simulation. The baseline model, as shown in Fig. 3a and b, consists of the following groups of components:
undeformed area of vehicle occupant compartment in Fig. 4b. 4.2 Experimental validation of the baseline model Although CAE has promoted the development of vehicle restraint system to a considerable extent, the numerical models that have not been verified might lead to unreliable design. Therefore, it is critical to validate the simulation results by using the full-scale physical tests prior to an effective parametric study and design optimization. In this study, the validation of computer model was conducted by comparing the simulation results with the corresponding experimental results from a full vehicle test, with these criteria of chest, pelvis, and head accelerations and chest displacement. The four simulation curves agree well with the corresponding test results, as shown in Fig. 5. The maximum difference between simulation and test is less than 5% and the trends of curves are rather similar. Figure 6 exhibits the airbag deformations and dummy movements of the simulation and corresponding physical
(1) A front impact Hybrid III 50th dummy, represented by a 50th percentile anthropomorphic multi-body dummy model built-in the MADYMO package, (2) The restraint system with airbag and seat belt using the finite element model. (3) The vehicle interior environment includes steering wheel, seat, floor pan, toe pan, dash, roof, etc., using the multi-body models. (4) As shown in Fig. 4a, the histories of the integrated values of X Acceleration and Y Acceleration were taken from the frontal impact test onto deformable barrier (Fig. 2). The triaxial accelerometer is mounted to the rocker panels at the base of the B-pillar in an
Acc X Acc Y
40
Acceleration (g)
Fig. 4 The acceleration curves for MADYMO modeling. a Deceleration pulse b the location of accelerometer
30 20 10 0 0
20
40
60
80
100 120 140 160
Time (ms)
(a)
(b)
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50 Test CAE
30 20 10
30 20 10
0 0
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0
30
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Time (ms)
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(b)
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36 Test CAE
60 50 40 30 20 10
Chest Displacement (mm)
70
Head AccX (g)
Test CAE
40
Chest AccX (g)
40
Pelvic AccX (g)
Fig. 5 Comparison between CAE (simulation) and physical test. a Chest acceleration X b Pelvis acceleration X c Head acceleration X d Chest displacement
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0 0
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Time (ms)
0
30
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(d)
5 Design optimization of vehicle restraint system The multi-objective optimization design procedure is described in detail in Fig. 7. The proposed methodology is applied to the following ORS design under the frontal impact.
Fig. 6 Comparison of simulation and full vehicle test in three different time steps. a t = 60 ms b t = 90 ms c t = 120 ms
(a)
150
Time (ms)
(c)
tests under the frontal crash at (a) t = 60 ms, (b) t = 90 ms and (c) t = 120 ms, respectively. Obviously, the simulation results also agree well with the corresponding snapshots of the physical test video. Therefore, the MADYMO simulation model is considered accurate and effective for the subsequent ORS optimization.
Test CAE
30
(b)
(c)
472 Fig. 7 Flowchart of the design optimization process
X. Gu et al. Optimization problem definition Objective functions Design variables and ranges Constraints
DOE: generate initial sample points
Construct approximate models
Non-dominated Sorting Genetic Algorithm II Obtain current optimal design
Numerical analysis (Model validation)
Kriging
Output results Validate the optimum design satisfied ?
Error evaluation of the surrogate model
Satisfied with the accuracy of metamodels
No Verify ? Yes Obtain optimal pareto sets
No Verify ? Yes
5.1 Design objectives and variables This study aims to optimize the ORS for reducing the dummy injury values, thereby making the best possible combination of these components under typical impact conditions. From Table 2, it can be easily found that all injury values of the passenger body regions did not exceed the limits, and thus will not be considered in the ORS optimization. However, the total score of the driver side does not exceed 11 points, as some scores are lost on the driver’s chest, head and right lower leg, which directly cause the baseline design failed to meet the safety requirements (i.e. four stars in the Euro-NCAP). In addition, the improvement of the lower leg injury performance is often limited by the design space of diver compartment and seat structure etc.; therefore it appears very difficult to improve the score by reducing the injury value of lower leg. In order to meet the design requirements, improvements of the chest displacement and HIC36 appear an effective alternative. From engineering experience and literature data (Rao et al. 2006; Hou et al. 1995), size of airbag vent (double), limiter load, webbing stiffness of seat belts, length of airbag strap, trigger time of airbag, mass flow rate of airbag inflator and stiffness of seat cushion have significant influences on the head and chest injury values. Thus, these parameters are taken as design variables. We first attempted to use the NCAP score as the only objective function for optimization and the chest displacement and HIC36 value as constraints, which led to a better
End
solution than the baseline design. Nevertheless, it is found that due to the limitations of the vehicle body structure, the HIC36 and chest displacement injury value cannot simultaneously generate the higher levels of performance. In order to obtain a good tradeoff, the constraint values need to be constantly tweaked. A good alternative to this problem can be to define the HIC36 and chest displacement injury value as two objective functions and formulate them as a multiobjective optimization problem to seek a Pareto solution, from which one can select an effective design point. If the HIC36 and chest displacement injury value are reduced whilst all other performances have not been changed appreciably, the overall score will be improved. Since the cumulative 3 ms acceleration of head, chest VC value, neck shear force, neck tension force and neck tension force are sensitive to the seven design variables according to engineering experience, they are chosen as the constraints. Considering the perturbations of design variables and noises of system parameters in real life, 80∼90% of higher performance value was adopted as the constraint level. Since the injury values of femur and lower leg are not affected by the design variables parameters significantly, they will not be considered as constraint values. Table 3 summarizes the responses of baseline design and the allowance of each constraint. Table 4 provides a list of design variables and the values for the baseline design and the corresponding lower and upper bounds. The design ranges of all the parameters are determined based on practical experience.
Multiobjective optimization design for vehicle occupant restraint system under frontal impact Table 3 The baseline design and the design space Response
Baseline
Target
Chest displacement f 1 (x)
32.28 mm
Minimize
HIC36 f 2 (x)
719
Minimize
Acc. 3 ms head (cum.) G 1 (x)
58.45 g
≤65 g
Chest VC-value G 2 (x)
0.26
≤0.45
Neck shear force G 3 (x)
1.2 KN
≤1.7 KN
Neck tension force G 4 (x)
1.09 KN
≤2.5 KN
Neck extension-My G 5 (x)
20.14 Nm
≤38 Nm
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the fitness of the KRG model. To evaluate the extrapolation ability of the KRG model, additional 30 MADYMO simulation results are generated to compare with the KRG 2 and max (RE) measures results. In this study, the R 2 , Radj are adopted to evaluate the accuracy of the KRG models of objective and constraint functions (Hou et al. 2008). The error results are listed in Table 5. And it can be noted that 2 , as well as the smaller value the larger values of R 2 and Radj RE, indicate a higher goodness of fit of the KRG models. Obviously the accuracy of the KRG models is fairly high and they can be used to perform design optimization. 5.3 Analysis of optimization results
5.2 Optimization process The ORS multiobjective optimization problem can be formulated as a standard form in terms of design objectives, constraints, and variables and their bounds as follows: ⎧ Min ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ s.t. ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩
F (x) = f 1 (x) , f 2 (x) ⎧ G 1 (x) ≤ 65 ⎪ ⎪ ⎪ ⎪ G ⎪ 2 (x) ≤ 0.45 ⎪ ⎨ G 3 (x) ≤ 1.7 G 4 (x) ≤ 2.5 ⎪ ⎪ ⎪ ⎪ ⎪ G (x) ≤ 38 ⎪ ⎩ L5 x ≤ x ≤ xU
(2)
For these seven continuous variables x = (x1 , x2 , · · · , x7 ), the Optimal Latin Hypercube sampling (OLHS) method (Yang et al. 2005a, b; Gu and Yang 2006) is adopted for the Design of Experiments (DOE). A total of 40 sampling points is generated in the design space. The objective and constraint values of each sampling point are obtained by using MADYMO 6.3 (2005) in a personal computer. A single simulation of 160 ms takes about half an hour. Following this, the KRG models are constructed based on the response results of these sampling points. It is critical to validate
Through the sensitivity analysis (Hou et al. 1995), we can plot the sensitivity of each design variable in relation to the objective functions, as shown in Fig. 8. The length of the bar is called effective size, which indicates the strength of the relationship between the output results and the input variables. The effective size greater than zero indicates a direct relationship to the input variable; whereas a value of less than zero indicates an inverse relationship. Thus from Fig. 8, the following sensitivity information can be derived: (1) The chest displacement is very sensitive to the belt limiter load, trigger time, seat cushion stiffness and webbing stiffness. The effect from changing vent diameter, inflator mass flow and strap length is negligible. (2) The HIC36 is sensitive to inflator mass flow and strap length. The vent diameter and webbing stiffness are modestly sensitive whilst the effect of the others can be neglected. From above, it is easily found that sensitivities of all the design variables are mutually converse, i.e. positively sensitive to HIC36 , whilst negatively sensitive to the chest displacement. In other words, HIC36 and chest displacement
Table 4 The initial values and the ranges of design variables Initial values
Varying ranges
Table 5 Accuracy evaluation
Lower
Upper
Description
R2
2 Radj
max(RE) %
a = Vent diameter (x1 )
30 mm
25 mm
35 mm
Chest displacement
0.958
0.911
4.7%
b = Belt limiter load (x2 )
3.5 KN
2.5 KN
5.0 KN
HIC36
0.925
0.895
5.6%
c = Strap length (x3 )
270 mm
240 mm
320 mm
Acc. 3 ms head (cum.)
0.923
0.899
5.3%
d = Trigger time (x4 )
28 ms
25 ms
35 ms
Chest VC-value
0.912
0.908
6.8%
e = Inflator mass flow (x5 )
1.0
0.8
1.3
Neck shear force
0.956
0.946
4.6%
Design variables
f = Seat cushion stiffness (x6 )
1.0
0.8
1.3
Neck tension force
0.943
0.938
3.9%
g = Webbing stiffness (x7 )
1.0
0.8
1.3
Neck extension-My
0.927
0.916
4.2%
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c
c
e
e
Design variable
Design variable
Fig. 8 Effects of design parameter changes on objectives a HIC36 b chest displacement
b d a
b d a
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-10
-8
-6
-4
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(a)
(b)
strongly competes with each other and any improvement in one objective must sacrifice another. Although the sensitivity analysis provides a guideline to the effects on injury levels by changing the design variables, it may not directly lead to a best possible system configuration for maximizing injury reduction. To solve this problem, multiobjective optimization can be adopted. In this study, we adopt the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to optimize the ORS. The NSGA-II parameters chosen are summarized in Table 6. The optimal Pareto frontier with 100 generations is obtained in Fig. 9. It is noted that the Pareto frontier provides the designers with many applicable solutions. In fact, any point in the Pareto frontier can be a solution. For example, if the designer wishes to emphasize more on the HIC36 value, the chest displacement must be compromised and become higher, and vice versa. Although the Pareto set can provide designer with a large number of design solutions for their decision-making, some more ideal solution, which has the highest overall satisfaction, is still expected (e.g. to be termed as the “knee point” from Pareto set as illustrated in Fig. 9). Traditionally, the most satisfactory solution is often decided by weighting method that aggregates many objectives into a single cost function in terms of weighted average to enable comparison of their relative importance. However, to assign proper
weight to each objective can be difficult, even for an experienced engineer. Therefore, in this study, we adopted the minimum distance selection method (TMDSM) (Sun et al. 2011a) to define the most satisfactory solution from the Pareto-set as shown in Fig. 9. The optimum results at the knee point are summarized in Table 7, in which the relative errors of the optimal solution are also presented. It is noted that the optimal results obtained from the KRG models have sufficient accuracy compared with the simulation values. Clearly the optimal design has significantly improved the safety. The injury values of HIC36 and Chest compression are reduced by 36.0% and 23.8% relative to the baseline design, respectively. Figure 10a and b compare the time histories of the acceleration value of head and the chest displacement, before and after optimization, respectively. The Servo-Sled system was used to verify the optimization result from the simulation. Figure 11 shows the simulation of the optimum and the corresponding experimental test at different times. According to the response values of simulation and physical tests, the scores of ORS are computed, as shown in Table 8. The score of simulation resulted from the presented method herein achieved 11.95, while the score of test physical sledding test was 11.89, both of which exceed 11. Therefore, the optimum satisfies the
Table 6 Details of NSGA-II parameters used in this study NSGA-II parameter name
Value
Population size
100
Number of generations
100
Crossover probability
0.9
Mutation probability
0.9
Distribution index for crossover
20
Distribution index for mutation
20
4
Fig. 9 Optimal Pareto front of all design
Multiobjective optimization design for vehicle occupant restraint system under frontal impact Optimization result Description Objectives Constraints
Variables
Knee point
Simulation
Error (%)
f 1 (x)
719
443
460
3.8
36.0
f 2 (x)
32.28 mm
23.9 mm
24.6 mm
2.9
23.8
G 1 (x)
58.45 g
52.4 g
50.6 g
3.3
13.4
G 2 (x)
0.26
0.29
0.31
6.8
−19.2
G 3 (x)
1.20 KN
1.28 KN
1.31 KN
2.3
−9.2
G 4 (x)
1.09 KN
1.23 KN
1.21 KN
1.6
−11.0
G 5 (x)
20.14 Nm
19.3 Nm
18.6 Nm
3.6
7.6
x1
30 mm
34 mm
–
x2
3.5KN
3.2KN
–
x3
270 mm
263 mm
–
x4
28 ms
26.5 mm
–
x5
1.0
1.12
–
x6
1.0
0.81
–
x7
1.0
0.83
–
35
Basline Optimization
60
Head acceleration(g)
Fig. 10 Comparison between the baseline and the optimized results. a head acceleration b chest displacement
Reduction (%)
Baseline
Chest Displacement (mm)
Table 7 Comparison between initial (baseline) and knee point of optimal design
475
50 40 30 20 10
Basline Optimization
30 25 20 15 10 5 0
0 0
20
40
60
80
100 120 140 160
0
20
40
60
80
100 120 140 160
Time (ms)
Time (ms)
(a)
(b)
Fig. 11 Snapshot comparison for the optimized design. a t = 60 ms b t = 90 ms c t = 120 msc
(a)
(b)
(c)
476 Table 8 The score of simulation analysis and sledding test
X. Gu et al. Description
Head
Chest
Femur
Lower leg
Modified
Total score
Full vehicle test
3.21
2.53
4
3.16
−3
9.90
Simulation analysis result
4
3.62
4
3.33
−3
11.95
Sledding test
4
3.71
4
3.18
−3
11.89
design requirements. In summary, the presented method is effective for the ORS design. Note that this paper exemplifies the frontal impact loading case for its dominant role in safety assessment and design. The multiobjective optimization methodology presented herein allows accommodating multiple loading cases, e.g. side, rear and pole impacts. Such a multiloading and multiobjective optimization might result in different optimal solutions.
6 Conclusion In this paper, we developed an effective optimization approach to design optimization of the Occupant Restraint Systems (ORS), which integrated the design of experiments (DOE), computer aided engineering (CAE), Kriging (KRG) and Non-dominated Sorting Genetic Algorithm II (NSGAII). The safety of occupant restraint system was improved by applying the presented design procedure, in which the design of ORS is formulated as an optimization problem in terms of two objectives and 5 functional constraints with seven design variables. Through the sensitive analysis, the influences of the seven variables in HIC36 and chest displacement are explored, and it is found that these two objective functions strongly compete with each other in the design domain. The KRG models are constructed to establish the surrogate relationships between the design variables and response functions. After evaluating the KRG models, the multiobjective genetic algorithm, i.e. NSGA-II, is applied to seek the Pareto solutions. From the Pareto frontier, the minimum distance selection method (TMDSM) can be applied to determine the knee point. The safety performance has been significantly improved and the required design criterion has been achieved under frontal impact. In summary, the presented method can be used to promote the ORS development. Acknowledgments The support from National 973 Project of China (2010CB328005), The Open Fund of State Key Laboratory of Vehicle NVH and Safety Technology (NVHSKL-201002), The Open Fund of State Key Laboratory of Automotive Simulation and Control (20111113), and The Open Fund of Key Laboratory for Automotive Transportation Safety Enhancement Technology of the Ministry of Communication, PRC (CHD2011SY008) are acknowledged.
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