Parametric design velocity computation for CAD-based design optimization using adjoint methods

Abstract

This paper presents an efficient optimization process, where the parameters defining the features in a feature-based CAD model are used as design variables. The process exploits adjoint methods for the computation of gradients, and as such the computational cost is essentially independent of the number of design variables, making it ideal for optimization in large design spaces. The novelty of this paper lies in linking the adjoint surface sensitivity information with geometric sensitivity values, referred to as design velocities, computed for CAD models created in commercial CAD systems (e.g. CATIA V5 or Siemens NX). This process computes gradients based on the CAD feature parameters, which are used by the optimization algorithm, which in turn updates the values of the same parameters in the CAD model. In this paper, the design velocity and resulting gradient calculations are validated against analytical and finite-difference results. The proposed approach is demonstrated to be compatible with different commercial CAD packages and computational fluid dynamics solvers.

Enhancing CAD-based shape optimisation by automatically updating the CAD model’s parameterisation

“…The calculation of design velocity can be complex for industrial models, where due to the nature of the boundary representation produced by the CAD system, the shape changes caused by a parameter perturbation can be highly constrained, or the model can suffer from robustness issues. The approach used in this work for calculating design velocity is detailed in [22], where the design velocities were calculated for CAD models of industrial complexity, and where the parameters defining the CAD model were used as design variables. The approach is based on the facetted approximations of CAD model geometry generated using open-source mesh generator GMSH [40].…”

“…al. [22] have shown an approach based on adjoint sensitivities which enables this. However, the ability to optimize the model is limited by the choice of CAD features in the model, and sometimes the parameters used to define these features may not be the best choice for optimization (in many instances they are not selected with optimization in mind).…”

Optimization of the LS89 Axial Turbine Profile Using a CAD and Adjoint Based Approach †

“…One of the limitations of using the CAD in a gradient-based optimization framework is the computation of the grid sensitivities i.e., the partial derivative of the grid points with respect to the design parameters. These sensitivities can be approximated by finite differences using the design velocity approach [7], which is robust against the possible changes in boundary topology of the model. However, this approach is based on computing shape differences between two surface meshes and can introduce issues of surface to surface projection when computing the distances between the two surface meshes.…”

Aerodynamic Shape Optimization Using Feature based CAD Systems and Adjoint Methods

“…The details regarding the calculation of geometric sensitivities, convergence of primal and adjoint CFD solutions can be found in reference, 14 where an unconstrained optimization of ONERA M6 wing was performed. The gradient of lift constraint with respect to CAD parameters is calculated by performing one additional adjoint analysis in SU 2 with Lift as objective.…”

“…A number of approaches have been identified by other researchers for computing design velocity fields for shape sensitivity optimization. [11][12][13] The approach used in this paper is described in reference 14 and is based on faceted approximations of CAD geometry generated by using an open-source surface mesh generator GMSH. The displacement of the model due to a parametric perturbation is calculated by projecting a point at the centroid of each facet (C 0 ) in the unperturbed model onto the facets in the perturbed model in the normal direction to get the projection point P p .…”