Purpose – A probabilistic non-dominated sorting genetic algorithm (P-NSGA) for multi-objective optimization under uncertainty is presented. The purpose of this algorithm is to create a tight coupling between the optimization and uncertainty procedures, use all of the possible probabilistic information to drive the optimizer, and leverage high-performance parallel computing. Design/methodology/approach – This algorithm is a generalization of a classical genetic algorithm for multi-objective optimization (NSGA-II) by Deb et al. The proposed algorithm relies on the use of all possible information in the probabilistic domain summarized by the cumulative distribution functions (CDFs) of the objective functions. Several analytic test functions are used to benchmark this algorithm, but only the results of the Fonseca-Fleming test function are shown. An industrial application is presented to show that P-NSGA can be used for multi-objective shape optimization of a Formula 1 tire brake duct, taking into account the geometrical uncertainties associated with the rotating rubber tire and uncertain inflow conditions. Findings – This algorithm is shown to have deterministic consistency (i.e. it turns back to the original NSGA-II) when the objective functions are deterministic. When the quality of the CDF is increased (either using more points or higher fidelity resolution), the convergence behavior improves. Since all the information regarding uncertainty quantification is preserved, all the different types of Pareto fronts that exist in the probabilistic framework (e.g. mean value Pareto, mean value penalty Pareto, etc.) are shown to be generated a posteriori. An adaptive sampling approach and parallel computing (in both the uncertainty and optimization algorithms) are shown to have several fold speed-up in selecting optimal solutions under uncertainty. Originality/value – There are no existing algorithms that use the full probabilistic distribution to guide the optimizer. The method presented herein bases its sorting on real function evaluations, not merely measures (i.e. mean of the probabilistic distribution) that potentially do not exist.

The flowfield around a 60% scale rotating Formula 1 tire in contact with the ground in a closed wind tunnel at a Reynolds number of 500,000 was examined computationally and experimentally. The goal of this study was to assess the accuracy of unsteady Reynolds-averaged Navier–Stokes (URANS) equations and confirm the existence of large scale vortical and flow recirculating features. A replica deformable F1 tire model that includes four tire treads and all brake components was used to determine the sensitivity of the wake to cross flow within the tire hub as well as the flow blockage caused by the brake assembly. Several turbulence closures were employed and the one that matched closest to the experimental PIV data was the Reynolds stress model. The variability between the six turbulence closures is shown by comparing velocity profiles, pressure distributions, and vortex eccentricity. The sensitivity of the wake to four different hub geometries, contact patch boundary conditions, multiple reference frame (MRF) rotor and spoke treatment, and time step size are also discussed.

The flowfield around a 60% scale stationary Formula 1 tire in contact with the ground in a closed wind tunnel at a Reynolds number of 500,000 was computationally examined in order to assess the accuracy of different turbulence modeling techniques and confirm the existence of large scale flow features. A simplified and replica tire model that includes all brake components was tested to determine the sensitivity of the wake to cross flow within the tire hub along with the flow blockage caused by the brake assembly. The results of steady and unsteady Reynolds averaged Navier-Stokes (URANS) equations and a large eddy simulation (LES) were compared with the experimental data. The LES closure and the RANS closure that accounted for unsteadiness with low eddy viscosity (unsteady kω-SST) matched closest to the experimental data both in point wise velocity comparisons along with location and intensity of the strong counter-rotating vortex pair dominating the far wake of the tire.

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