Vehicle occupant restraint system design under uncertainty by using multi-objective robust design optimization
CHALLENGE - Performance of a vehicle occupant restraint system is affected by interaction among occupant restraint equipment, such as an airbag and a seat belt. Furthermore, situations of crashes, such as speed at the crash and posture of occupants, are various. Therefore, performance of the system requires robustness under the interactions and the uncertainties of the design, the condition and the situation. In this research, the Multi-Objective Robust Design Optimization (MORDO) is employed for the vehicle occupant restraint system design. The optimization aims to improve the safety performance of the system and its robustness simultaneously.
SOLUTION - The safety of the system is evaluated by some indexes based on some safety regulations, which are calculated by response surface model of an occupant at a crash. Input variables for controlling the behaviour of the model, consists of six design variables regarding the restraint equipment, which strongly affect safety indexes, an airbag, a seatbelt and a knee bolster. Output variables are three safety indexes based on the Japan NCAP, head injury criterion, thoracic resultant acceleration in 3 msec. and femur load. The head injury criterion, HIC is an index of head injury risk. The thoracic resultant acceleration in 3 msec., T3MS is measured by an accelerometer mounted on centre of mass of a crash dummy’s chest. The femur load, FL is measured by load cells mounted on the dummy’s left and right femurs. FL_L is the left femur’s value, and FL_R is the right femur’s value. The four response surface models of HIC, T3MS, FL_L and FL_R are employed for optimization of the vehicle occupant restraint system.
The optimization problem is defined as four-objective minimization problem. The objective functions are the mean value and the standard deviation of the HIC and the T3MS. The FL_L and the FL_R are set as constraints. An evolutionary multi-objective optimization algorithm, the Adaptive Range Multi-Objective Genetic Algorithm (ARMOGA), provided by modeFRONTIER software, is employed as an optimizer. In order to taking account of perturbation of detecting time of a crash, AB_TTF and Belt_Preten_TTF are selected as robust parameter. The AB_TTF and the Belt_Preten_TTF are the parameters that define the operation timing of the airbag and the seatbelt pretensioner. Normal distribution is selected as the probabilistic distribution for Monte Carlo simulation.
All design candidates, which were explored and evaluated by the MORDO, are shown in Fig. 5. Pareto optimal solutions, which were extracted from the above all design candidates, are shown in Fig. 6. The horizontal axis represents the mean of the HIC. The vertical axis represents the mean of the T3MS. The diameter of each circle represents the standard deviation of the HIC. The small circle means stable and large circle means unstable. The colour of each circle indicates the standard deviation of the T3MS. Cool colour means stable and warm colour means unstable.
BENEFITS - The effectiveness of MORDO was shown by visualizing and analysing with some results, such as scatter plot, frequency distribution of Monte Carlo sampling designs and shape of response surface of an objective function.