|Jörg Hülsmann||Ralf Reuter|
|EASi Engineering GmbH||EASi Engineering GmbH|
|Siemensstr. 12||Siemensstr. 12|
|D-63755 Alzenau||D-63755 Alzenau|
|Hier können Sie den Vortrag als PDF-Dokument downloaden:|
As an example a MADYMO occupant simulation will be shown, where an advanced
driver airbag system is improved with respect to preset performance targets.
The focus will be on reducing the occupant injury criteria levels by finding
robust settings for the configuration of a new multiple airbag concept
that is intended to improve protection in cases of high steering wheel
But even if it were possible to find this solution, it would be of limited value, given the uncertainty or scatter of any system in the real world. While in the computer one can build (nearly) perfect models, real systems always have imperfections or deviations from the nominal state. So even if one finds the optimum for the computer model, one will not be able to build the actual product in exactly the same way and so one automatically gets sub-optimal solutions in practice. Optimization techniques ignore scatter of any kind in order to be able to build so called response surfaces. It is certainly possible to find an optimum on that surface, but once this solution is transferred back to the physical system its optimality vanishes because of the scatter which simply cannot be avoided. Then the performance may be far worse than expected.
In the light of these statements it seems to make much more sense to focus on robustness of improved solutions than on mathematical optimality. A solution that performs well even in the presence of scatter is clearly favorable to a fragile one that performs optimally under perfect conditions but performs poorly when scatter comes into play. Of course this does not necessarily happen, but the problem is that optimization tools neither proof the optimality of their solutions nor do they provide any information on the robustness of their solutions and therefore leave the engineer in a state of uncertainty.
The Monte-Carlo Simulation based stochastic improvement method described in this paper deliberately manages this uncertainty by introducing scatter into simulation models and enabling to quantify uncertainty in the results, i.e. in the performance of the simulated system.
Stochastic improvement differs from classic optimization tools in many respects:
Figure 1: Robust vs. Non-robust System
A simple way to assess the robustness of a system is to compare the coefficients of variation (CV) for both inputs and outputs obtained from a stochastic simulation. The coefficient of variation is basically the percentage of scatter (measured as the standard deviation) of a variable.
It therefore is independent from the magnitude of the variable and can
be used to compare variables of different magnitude.
The improvement procedure implemented in the ST-ORM software package , which was used for the simulations described in this paper, works as follows :
As stated above no assumptions have to be made in order to use this
method. Also the number of variables is nearly unlimited and does not influence
the number of solver calls that is required (, p. 113). So one can define
all variables that are stochastic in reality (=noise) as stochastic in
the model. The number of actual design variables is usually relatively
small for practical reasons, as not many things can be changed arbitrarily
in a complex system such as a car.
The following example will illustrate the application of the method using the MADYMO solver.
Figure 2: Asymmetric Driver Airbag
The starting point of the investigation is a driver airbag where diagonal straps are used to prevent the airbag from being pushed upwards by the occupant and the airbag itself is not concentric with the steering wheel but is mounted below the center of the wheel (Figure 3).
Figure 3: Asymmetric Airbag System
This system is obviously a perfect candidate for being non-robust. Though it works very well under nominal conditions, it is very likely to fail if the steering wheel is not in a perfect 0° position because of the asymmetry of the airbag.
The new Driver Double Airbag System (DDAS) concept, jointly developed by Eyrainer AutomotiveConcepts and EASi Engineering, is serving the same purpose of keeping the airbag in position. The DDAS includes an additional airbag located on top of the instrument panel. It fills the gap between the conventional steering wheel mounted driver airbag and the windscreen/roof of the vehicle. It has two important effects:
Figure 4: Driver Double Airbag System DDAS
Figure 5: The DDAS-bag - reference shape
Let us first compare the two deterministic models. Figure 6 depicts some of the injury criteria obtained from MADYMO analyses of the FMVSS 208 frontal crash test at 30 mph. The asymmetric airbag performs slightly better. The DDAS, however, is a design draft, which is not yet optimized in terms of airbag shape, inflator and time-to-fire.
Figure 6: Comparison of the deterministic models
It is, of course, much more interesting to compare the two systems under realistic conditions. Therefore scatter was added to many variables (including dummy position, airbag time-to-fire, airbag inflator, airbag vent size, steering wheel angle, steering wheel intrusion) in both models and a stochastic simulation with 100 shots was performed for each system. As it was of special interest a large amount of scatter (±180°) was defined for the steering wheel rotation. Even though this amount of scatter will not occur in the crash lab, it is a very realistic assumption if one considers real-world accidents.
Comparison of the coefficients of variation (%) of the two systems shows the advantage of the DDAS System in terms of robustness (Figure 7).
Figure 7: Comparison of the coefficients of variation (%)
Figure 8 and Figure 9 show a more detailed comparison of the results of the stochastic simulations. The bars show the mean value for each parameter. The horizontal line indicates the nominal result from the deterministic analysis. The vertical line shows the range of results obtained from the stochastic simulation. All values are normalized (nominal result = 100%) for better comparison.
Again the lack of robustness of the asymmetric system becomes very obvious. But these charts yield another important information: The deterministic model of the asymmetric system is too optimistic as for nearly all criteria. Their mean value is significantly higher than the nominal result.
Figure 8: Injury Criteria - Asymmetric Airbag
In case of the DDAS the nominal and mean are nearly the same for all criteria.
Figure 9: Injury Criteria - DDAS
One reason for the large scatter of the asymmetric system is the fact that in many cases (> 45%) the head impacts the windscreen resulting in high head accelerations and neck moments. Such contacts are completely avoided by the DDAS.
The next step is to further improve the DDAS’ performance. As mentioned above, the model used for this study was only a draft design. Changes of the airbag shape and the inflation process (time-to fire, inflator, venting) should further improve the performance. Due to the simple shape of the DDAS bag, its parameterized geometry could be used as a design variable during the improvement process. Using the BAGGEN  tool the airbag was re-meshed after each geometry modification. The geometry was changed by moving point P4 horizontally and moving P5 horizontally and vertically (Figure 10).
Figure 10: Geometry modification
The airbag was then scaled to obtain an initial geometry as the Initial-Metric-Method was used. The mass flow of the inflator was adapted to the modified size of the bag by calculating its new volume. The process is depicted in Figure 11.
Figure 11: Model generation process
The performance target was defined as follows:
|Chest a3ms||< 450 m/s2|
|Head a3ms||< 400 m/s2|
|VC||< 0.15 m/s|
|Neck ext||< 50 Nm|
|Neck flex.||< 190 Nm|
After 3 iterations with 15 analyses each, an improved state was reached, which was also acceptable in terms of robustness. The target was not reached in all respects by the selected solution. But some solutions that were even closer to the target (see "best solution" in Figure 13) were not accepted as they were identified as non-robust. This is the great advantage of the stochastic improvement method – classical optimization would not have yielded that information.
Figure 12: Modified Airbag Shape
The shape of the DDAS bag has changed significantly (Figure 12). In addition to that the time-to-fire of both airbags has been adjusted.
The improved system outperforms or matches the initial solution with respect to all selected injury criteria (Figure 13). Comparing the coefficients of variation one can see a slight increase in scatter. Compared to the asymmetric system the improved DDAS is still far more robust (Figure 14 and Figure 15). As the initial DDAS design, the improved design prevents head contacts with the windscreen.
Figure 13: Comparison of the deterministic models
Figure 14: Comparison of the coefficients of variation (%)
Figure 15: Injury Criteria – Improved DDAS
 Marczyk, J.: Meta-Computing and Computational Stochastic Mechanics. In: Marczyk, J. (Ed.): Computational Stochastic Mechanics in a Meta-Computing Perspective, CIMNE, Barcelona 1997, pp. 1-18.
 Reuter, R./Watermann, A.: Application of Uncertainty Management to MADYMO Occupant Simulations. In: Proceedings of the 2nd European MADYMO Users’ Conference, Stuttgart 1999.
 MADYMO v5.4 Utilities Manual – Part I: BAGGEN, TNO Road Vehicle Research Institute, Delft 1999.
 ST-ORM User’s Manual, EASi Engineering GmbH, 1999.
 Doltsinis, I./Rau, F./Werner M.: Analysis of random systems. In: Doltsinis, I. (Ed.): Stochastic Analysis of Multivariate Systems in Computational Mechanics and Engineering, CIMNE, Barcelona 1999.
|Last updated: 31. May 2000|
|© EASi Engineering GmbH 2000|