Vehicle Restraint Systems (VRS) are specially designed to restrain an errant vehicle by dissipating or absorbing the impact energy and redirecting the vehicles to reduce crash accident severity and protect the roadside equipment. Before being installed on the roadside, a VRS must be tested by crashing with vehicles to evaluate its performances for severity reduction in traffic accident. Europe Norm, EN1317, normalized the crash test conditions, and defined the qualitative and quantitative performance criteria of the device. Dynamic simulation of the crash test has been used for development of new VRS.

Uncertainties exist in the VRS: a crash test of the VRS can't be repeated even under the same impact condition; as for the numerical simulations, in fact a model cannot be validated to ‘have simulated the crash test accurately'; what's more, uncertainty is inevitable and it may significantly influence the reliability or robustness of a design.

The crash test of a steel VRS has been carried out by LIER-TRANSPOLIS according to the norm EN1317. Considering the existence of uncertain factors, the device is optimized with Multi-Objective Non-deterministic Optimization (MONO) approach. The challenges for MONO of complex engineering systems such as the VRS include: high calculation cost of model simulation; numerous uncertain factors. In the previous studies:

• The crash test of VRS was simulated by LS-DYNA with a simplified VRS & Vehicle model.
• The numerical model has been used for Sensitivity Analysis (SA) of the VRS: uncertainties in mechanical properties of material, in tolerances of fabrication, in installation conditions of the device were considered and eleven uncertain factors were chosen. SA helps to identity the factors whose uncertainties have great influence on the robustness of the VRS. The two influential uncertain factors were identified and their influences were quantified after the SA.

The MONO of the VRS will be discussed in the article:

• The ‘objectives' of the optimization are to increase the capability of the VRS in reducing crash accident severity, and in the same time to minimize the deformation of the VRS during the crash process;
• Dimensions of the VRS components are chosen as the ‘design variables'
• Robustness of the VRS is mainly influenced by the two influential uncertain factors identified after the SA. Considering influences of the two uncertain factors, along with the mass of device (i.e. cost of production), the robustness of the device are defined as the constraints of the design;
• Kriging interpolation is used to create the surrogate model of the crash test. Genetic Algorithm is used for the multi-objective optimization;
• Generalization of impact conditions: the device is optimized under the impact condition specified by EN1317. Performances of the optimized design are evaluated under different impact conditions.

Simulations considering the variations of the uncertain factors help to evaluate the robustness of a design and give a cloud of results in which the result of an experimental test could be contained; SA helps to identity the influential uncertain factors; with robustness of the device defined as the constraints of design, the non-deterministic approach optimized the performances of the VRS with their variations controlled under the defined thresholds; the norm EN1317 provides a guideline for the design of VRS, robust analysis and generalization analysis provide useful information about the performance of a design and the norm EN1317 could be enriched.