Optimization Under Uncertainty and Total Predictive Uncertainty for a Tractor-Trailer Base-Drag Reduction Device

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Virginia Tech


One key outcome of this research is the design for a 3-D tractor-trailer base-drag reduction device that predicts a 41% reduction in wind-averaged drag coefficient at 57 mph (92 km/h) and that is relatively insensitive to uncertain wind speed and direction and uncertain deflection angles due to mounting accuracy and static aeroelastic loading; the best commercial device of non-optimized design achieves a 12% reduction at 65 mph. Another important outcome is the process by which the optimized design is obtained. That process includes verification and validation of the flow solver, a less complex but much broader 2-D pathfinder study, and the culminating 3-D aerodynamic shape optimization under uncertainty (OUU) study.

To gain confidence in the accuracy and precision of a computational fluid dynamics (CFD) flow solver and its Reynolds-averaged Navier-Stokes (RANS) turbulence models, it is necessary to conduct code verification, solution verification, and model validation. These activities are accomplished using two commercial CFD solvers, Cobalt and RavenCFD, with four turbulence models: Spalart-Allmaras (S-A), S-A with rotation and curvature, Menter shear-stress transport (SST), and Wilcox 1998 k-ω. Model performance is evaluated for three low subsonic 2-D applications: turbulent flat plate, planar jet, and NACA 0012 airfoil at α = 0°.

The S-A turbulence model is selected for the 2-D OUU study. In the 2-D study, a tractor-trailer base flap model is developed that includes six design variables with generous constraints; 400 design candidates are evaluated. The design optimization loop includes the effect of uncertain wind speed and direction, and post processing addresses several other uncertain effects on drag prediction. The study compares the efficiency and accuracy of two optimization algorithms, evolutionary algorithm (EA) and dividing rectangles (DIRECT), twelve surrogate models, six sampling methods, and surrogate-based global optimization (SBGO) methods. The DAKOTA optimization and uncertainty quantification framework is used to interface the RANS flow solver, grid generator, and optimization algorithm. The EA is determined to be more efficient in obtaining a design with significantly reduced drag (as opposed to more efficient in finding the true drag minimum), and total predictive uncertainty is estimated as ±11%. While the SBGO methods are more efficient than a traditional optimization algorithm, they are computationally inefficient due to their serial nature, as implemented in DAKOTA.

Because the S-A model does well in 2-D but not in 3-D under these conditions, the SST turbulence model is selected for the 3-D OUU study that includes five design variables and evaluates a total of 130 design candidates. Again using the EA, the study propagates aleatory (wind speed and direction) and epistemic (perturbations in flap deflection angle) uncertainty within the optimization loop and post processes several other uncertain effects. For the best 3-D design, total predictive uncertainty is +15/-42%, due largely to using a relatively coarse (six million cell) grid. That is, the best design drag coefficient estimate is within 15 and 42% of the true value; however, its improvement relative to the no-flaps baseline is accurate within 3-9% uncertainty.



aerodynamic shape optimization, optimization under uncertainty, predictive uncertainty, verification and validation, drag reduction, evolutionary algorithm, uncertainty quantification