Abstract
Finite element-based crashworthiness optimization is nowadays extensively used to improve the safety of vehicles. However, the responses of a crash simulation are notoriously noisy. In addition, the actual or simulated responses during a crash can be highly sensitive to uncertainties. These uncertainties appear in various forms such as uncontrollable random parameters (e.g., impact conditions).
To address these challenges, an optimization algorithm based on a Stochastic Kriging (SK) and an Augmented Expected Improvement (AEI) infill criterion is proposed. A SK enables the approximation of a response while accounting for the noise-induced aleatory variance. In addition, SK has the advantage of reducing the dimensionality of the problem by implicitly accounting for the influence of random parameters and their contribution to the overall aleatory variance. In the proposed algorithm, the aleatory variance is initially estimated through direct sampling and subsequently approximated by a regression kriging. This aleatory variance approximation, which is refined adaptively, is used for the computation of the infill criterion and probabilistic constraints.
The algorithm is implemented on a crashworthiness optimization problem that involves a sled and dummy models subjected to an acceleration pulse. The sled model includes components of a vehicle occupant restraint system such as an airbag, seatbelt, and steering column. In all problems considered, the objective function is the probability of traumatic brain injury, which is computed through the Brain Injury Criterion (BrIC) and a logistic injury risk model. In some cases, probabilistic constraints corresponding to other types of bodily injuries such as thoracic injury are added to the optimization problem. The design variables correspond to the properties of the occupant restraint system (e.g., loading curve that dictates the airbag vent area versus pressure). In addition to the inherent simulation noise, uncertainties in the loading conditions are introduced in the form of a random scaling factor of the acceleration pulse.
