It is well known that the computational design for crashworthiness is tedious for several reasons. Besides the large computational times of crash simulations, they are also often highly sensitive to uncertainties.  These uncertainties can appear in various forms such as the random uncontrollable parameters (e.g., loading condition and material properties) and noise in the response which is inherent to crash simulations. These two types of uncertainties are referred to as aleatory uncertainties and are irreducible.

To perform the optimization, a Kriging metamodel is used to approximate the vehicle response. Kriging metamodels are often used as they provide the variance of the prediction at any point in the design space. In this work, instead of adding dimensions to represent aleatory uncertainty, they are directly included in the Kriging metamodel. This so-called stochastic Kriging is constructed by adding a second random process to the traditional Kriging. This added random process includes information on the aleatory variables (e.g., impact velocity and numerical noise).

In this study, a sequential kriging optimization algorithm for crashworthiness optimization is proposed. The main elements of the algorithm are as the following. An initial sampling is performed to approximate the aleatory uncertainties. The stochastic kriging formulation is used to approximate the response while accounting for random parameters and noise. An infill criterion is used to explore the design space and refine the kriging approximation. A regression kriging is trained based on the initial sampling to provide the aleatory variance required for the stochastic kriging and the infill criterion.

The crashworthiness optimization presented in this work is based on the probability of brain traumatic injury. For this purpose, a two-level finite element framework that reconstructs a frontal vehicle crash is used. The first level involves sled and dummy models that are subjected to an acceleration pulse. The sled model includes components of a vehicle Occupant Restraint System (ORS) such as airbag, seatbelt, and steering column. The second level of the finite element framework involves the simulation of the brain motion to assess the probability of traumatic brain injury using the Cumulative Strain Damage Measure (CSDM). For this purpose, the Simulated Injury Monitor (SIMon) brain finite element model is used in addition to an experiment-based logistic regression model.

While the probability of traumatic brain injury is used as the objective function, other injury metrics are used as constraints. The design variables correspond to the components of the ORS (e.g., loading curve that dictates the airbag vent area versus pressure). In addition to the simulation noise, the uncontrolled random parameters corresponding to the loading condition (e.g., acceleration pulse applied to the sled) and material properties of the SIMon model (e.g., short-term shear modulus of the Kelvin-Maxwell viscoelastic material model used to model the behavior of the brain tissues) are used.


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

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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