Stochastic Crashworthiness Optimization Accounting for Simulation Noise

Finite element-based crashworthiness optimization is extensively used to improve the safety of motor vehicles. However, the responses of crash simulations are characterized by a high level of numerical noise, which can hamper the blind use of surrogate-based design optimization methods. It is therefore essential to account for the noise-induced uncertainty when performing optimization. For this purpose, a surrogate, referred to as Non-Deterministic Kriging (NDK), can be used. It models the noise as a non-stationary stochastic process, which is added to a traditional deterministic kriging surrogate. Based on the NDK surrogate, this study proposes an optimization algorithm tailored to account for both epistemic uncertainty, due to the lack of data, and irreducible aleatory uncertainty, due to the simulation noise. The variances are included within an extension of the well-known expected improvement infill criterion referred to as Modified Augmented Expected Improvement (MAEI). Because the proposed optimization scheme requires an estimate of the aleatory variance, it is approximated through a regression kriging, which is iteratively refined. The proposed algorithm is tested on a set of analytical functions and applied to the optimization of an Occupant Restraint System (ORS) during a crash.

Crashworthiness Optimization Based on the Probability of Traumatic Brain Injury Accounting for Simulation Noise and Impact Conditions

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.

Stochastic Kriging for Crashworthiness Optimization Accounting for Simulation Noise

Vehicle crash simulations are notoriously costly and noisy. When performing crashworthiness optimization, it is therefore important to include available information to quantify the noise in the optimization. For this purpose, a stochastic kriging can be used to account for the uncertainty due to the simulation noise. It is done through the addition of a non-stationary stochastic process to the deterministic kriging formulation. This stochastic kriging, which can also be used to include the effect of random non-controllable parameters, can then be used for surrogate-based optimization. In this work, a stochastic kriging-based optimization algorithm is proposed with an infill criterion referred to as the Augmented Expected Improvement, which, unlike its deterministic counterpart the Expect Improvement, accounts for the presence of irreducible aleatory variance due to noise. One of the key novelty of the proposed algorithm stems from the approximation of the aleatory variance and its update during the optimization. The proposed approach is applied to the optimization of two problems including an analytical function and a crashwor-thiness problem where the components of an occupant restraint system of a vehicle are optimized.

Sensitivity Analysis and Interval Multi-Objective Optimization for an Occupant Restraint System Considering Craniocerebral Injury

In vehicle collision accidents, an occupant restraint system (ORS) is crucial to protect the human body from injury, and it commonly involves a large number of design parameters. However, it is very difficult to quantify the importance of design parameters and determine them in the ORS design process. Therefore, an approach of the combination of the proposed approximate sensitivity analysis (SA) method and the interval multi-objective optimization design is presented to reduce craniocerebral injury and improve ORS protection performance. First, to simulate the vehicle collision process and obtain the craniocerebral injury responses, the integrated finite element model of vehicle-occupant (IFEM-VO) is established by integrating the vehicle, dummy, seatbelt, airbag, etc. Then, the proposed approximate SA method is used to quantify the importance ranking of design parameters and ignore the effects of some nonessential parameters. In the SA process, the Kriging metamodel characterizing the relationships between design parameters and injury responses is fitted to overcome the time-consuming disadvantage of IFEM-VO. Finally, according to the results of SA, considering the influence of uncertainty, an interval multi-objective optimization design is implemented by treating the brain injury criteria (BRIC, BrIC) as the objectives and regarding the head injury criterion (HIC) and the rotational injury criterion (RIC) as the constraints. Comparison of the results before and after optimization indicates that the maximum values of the translational and rotational accelerations are greatly reduced, and the ORS protection performance is significantly improved. This study provides an effective way to improve the protection performance of vehicle ORS under uncertainty.