In this work, a strategy is developed to deal with the error affecting the objective functions in uncertainty-based optimization. We refer to the problems where the objective functions are the statistics of a quantity of interest computed by an uncertainty quantification technique that propagates some uncertainties of the input variables through the system under consideration. In real problems, the statistics are computed by a numerical method and therefore they are affected by a certain level of error, depending on the chosen accuracy. The errors on the objective function can be interpreted with the abstraction of a bounding box around the nominal estimation in the objective functions space. In addition, in some cases the uncertainty quantification methods providing the objective functions also supply the possibility of adaptive refinement to reduce the error bounding box. The novel method relies on the exchange of information between the outer loop based on the optimization algorithm and the inner uncertainty quantification loop. In particular, in the inner uncertainty quantification loop, a control is performed to decide whether a refinement of the bounding box for the current design is appropriate or not. In single-objective problems, the current bounding box is compared to the current optimal design. In multi-objective problems, the decision is based on the comparison of the error bounding box of the current design and the current Pareto front. With this strategy, fewer computations are made for clearly dominated solutions and an accurate estimate of the objective function is provided for the interesting, non-dominated solutions. The results presented in this work prove that the proposed method improves the efficiency of the global loop, while preserving the accuracy of the final Pareto front

The paper presents a multifidelity robust optimization technique with application to the design of rotor blade airfoils in hover. A genetic algorithm is coupled with a non-intrusive uncertainty propagation technique based on polynomial chaos expansion to determine the robust optimal airfoils that maximize the mean value of the lift-to-drag ratio while minimizing the variance, under uncertain operating conditions. Uncertainties on the blade pitch angle and induced velocity are considered. To deal with the variable operating conditions induced by the considered uncertainties and to alleviate the computational cost of the optimization procedure, a multifidelity strategy is developed that exploits two aerodynamic models of different fidelity. The two models correspond to different physical descriptions of the flowfield around the airfoil; thus, the multifidelity method employs the low-fidelity model in regions of the stochastic space where the physics of the problem is well captured by the model, and it switches to high-fidelity estimates only where needed. The proposed robust optimization technique is compared with the robust optimization based on the high-fidelity aerodynamic model and the deterministic optimization, to assess the capability of finding a consistent Pareto set and to evaluate the numerical efficiency. The results obtained show how the robust multifidelity approach is effective in reducing the sensitivity of the designed airfoils with respect to variation in the operating conditions

This paper is devoted to the formulation of a novel optimization under uncertainty framework for the definition of optimal shapes for morphing airfoils, applied here to advancing/retreating 2D airfoils. In particular, the morphing strategy is conceived with the intent of changing the shape at a given frequency to enhance aerodynamic performance. The optimization of morphing airfoils presented here only takes into account the aerodynamic performance. The paper is then focused on an aerodynamic optimization to set the optimal shape with respect to performance, where technological aspects are inserted through geometrical constraints. In fact, this paper presents an exploratory work on morphing geometries which aims at understanding the relationship between shape degree of freedom and actual aerodynamic gain. Thus, exploring and demonstrating the gain of the aerodynamic shape may drive the development of new mechanism for the realization of morphing structures, which could be applied to helicopter rotor blades

The paper deals with the shape optimization of an isolated airfoil to minimize the drag when operating in a transonic inviscid flow with some prescribed constraints. A nondominated Sorting Genetic Algorithm is used to solve the optimization problem. Other numerical ingredients of the optimization loop are given by the Class/Shape function Transformation used for the parameterization of the airfoil shape and a finite-volume Computational Fluid Dynamics solver of the Euler equations.

A computational study of non-classical aileron buzz is presented, which focuses on computational grid details for accurate simulations of this type of nonlinear transonic phenomenon. The analysis points out that mesh refinement is crucial to obtain reliable results and that the choice between a smoothed and non-smoothed geometry has an influence on the system response, both quantitatively and qualitatively. As a matter of fact, grid details affect the simulation of shock dynamics, which is the driving mechanism for non-classical aileron buzz