Hypervolume scalarization for shape optimization to improve reliability and cost of ceramic components

In engineering applications one often has to trade-off among several objectives as, for example, the mechanical stability of a component, its efficiency, its weight and its cost. We consider a biobjective shape optimization problem maximizing the mechanical stability of a ceramic component under tensile load while minimizing its volume. Stability is thereby modeled using a Weibull-type formulation of the probability of failure under external loads. The PDE formulation of the mechanical state equation is discretized by a finite element method on a regular grid. To solve the discretized biobjective shape optimization problem we suggest a hypervolume scalarization, with which also unsupported efficient solutions can be determined without adding constraints to the problem formulation. FurthIn this section, general properties of the hypervolumeermore, maximizing the dominated hypervolume supports the decision maker in identifying compromise solutions. We investigate the relation of the hypervolume scalarization to the weighted sum scalarization and to direct multiobjective descent methods. Since gradient information can be efficiently obtained by solving the adjoint equation, the scalarized problem can be solved by a gradient ascent algorithm. We evaluate our approach on a 2 D test case representing a straight joint under tensile load.

Shape optimization of a blended-wing-body underwater glider using surrogate-based global optimization method IESGO-HSR

As a novel flying-wing configuration underwater glider, the blended-wing-body underwater glider (BWBUG) has the satisfactory hydrodynamic performance in comparison to the conventional cylindrical autonomous underwater gliders (AUGs). The complicated shape optimization of BWBUG is significant for improving its hydrodynamic efficiency while it has to require huge computation time and efforts. A novel surrogate-based shape optimization (SBSO) framework is proposed to deal with the BWBUG shape optimization problem for improving the optimization efficiency and quality. During the optimization search, the parametric geometric model of the BWBUG is constructed depending on seven specific sectional airfoils, with the planar surface being unaltered. Moreover, an improved ensemble of surrogates based global optimization method using a hierarchical design space reduction strategy (IESGO-HSR) is used for optimizing the chosen sectional airfoils. The optimum shape of BWBUG can be obtained using all sectional airfoils which are successfully optimized. The maximum lift to drag ratio (LDR) of the optimal BWBUG is improved by 24.32% with acceptable computational resources. The optimization results show that the proposed SBSO framework is more superior and efficient in handling the BWBUG shape optimization problem.