Analysis of the Scatter of a Deploying Airbag

This paper discusses some of the challenges faced by the automotive industry in dealing with the natural variation in input parameters and environmental factors that lead to scatter in results. We describe how a lack of consideration of this variation can lead to surprises during testing, with the associated risk of unplanned cost, and present a technique using Principal Components Analysis to improve the robustness of CAE crash models. In a purely virtual product development world, increasingly demanding functional requirements, and pressure on weight and cost, mean that analysis techniques must lead to designs that are robust with respect to external noise sources; large safety margins are no longer acceptable. Conventionally the CAE process has used nominal values for input parameters, and has been satisfied with single, deterministic solutions. However, virtual techniques have much to offer in understanding and managing scatter, and the consideration of variability in the CAE process is becoming more common-place. At the same time, the CAE method introduces its own issues associated with model stability, and these must also be addressed before design optimisation is attempted. Frequently, analysis approaches used to improve design robustness can also be applied to issues of model stability, and we describe an example where Principal Components Analysis within the Diffcrash software package has been used to identify a source of instability in an airbag model. The mathematical background to the PCA method is presented, explaining its application to the analysis of variation, and showing how it can help in locating a source of scatter in results. The airbag example illustrates how this can be applied to allow changes to the modelling technique (or to the design) to be made to reduce the scatter. In this example, the source of the different airbag behaviours shown in figure 1 was identified as being a contact issue at an earlier point in time (figure 2), and a modification to the contact definition led to a reduction in the dispersion in results. Lastly we offer insight into the requirements for deployment of such techniques, and describe how process integration is a fundamental necessity for a successful, sustained implementation.