Many real-world objects are designed by smooth curves, especially in the domain of aerospace and ship, where aerodynamic shapes (e.g., airfoils) and hydrodynamic shapes (e.g., hulls) are designed. To facilitate the design process of those objects, we propose a deep learning based generative model that can synthesize smooth curves. The model maps a low-dimensional latent representation to a sequence of discrete points sampled from a rational B 'ezier curve. We demonstrate the performance of our method in completing both synthetic and real-world generative tasks. Results show that our method can generate diverse and realistic curves, while preserving consistent shape variation in the latent space, which is favorable for latent space design optimization or design space exploration.
 Design and optimization benefit from understanding the dependence of a quantity of interest (e.g., a design objective or constraint function) on the design variables. A low-dimensional active subsp... The geometric representation and parameterization used in an aerodynamic wing design process determines the number of design variables and influences the smoothness of the wing representation. In an attempt to reduce the number of design variables while preserving good smoothness properties, the present research investigates the performance of an optimized nonuniform rational B-spline (NURBS) geometrical representation for the aerodynamic design of wings. As a first step, an approach is described whereby optimal spatial positions and weights of a fixed number of NURBS control points is determined using a quasi-Newton optimization algorithm to approximate a general airfoil section. The resulting optimized NURBS representation significantly reduces the number of design variables needed to define accurately a wing section while ensuring good smoothness properties. In a second step, the NURBS control point positions and weights are used as design variables in an aerodynamic optimization problem. This methodology results in a rapid and robust design process, as illustrated by examples of aerodynamic optimization for two- and three-dimensional cases The cost of dimensionality reduction in aerodynamic design applications involving high-dimensional design spaces and computational fluid dynamics is often prohibitive. In an attempt to overcome this challenge, a new method for dimensionality reduction is presented that scales as p log(p), where p is the number of design variables. It works by taking advantage of adjoint design methods to compute the covariance matrix of the gradient. This information is then used with principal component analysis to develop a linear transformation that allows an aerodynamic optimization problem to be reformulated in an equivalent coordinate system of lower dimensionality. To demonstrate its feasibility, the method is tested on a two-dimensional staggered airfoil problem, intentionally chosen as an abstraction of a more realistic overwing nacelle integration problem, and shown to exhibit similarities with the latter. Results show that the method rivals typical screening methods used in aerospace engineering in terms of eff... Abstract In aerodynamic optimization, global optimization methods such as genetic algorithms are preferred in many cases because of their advantage on reaching global optimum. However, for complex problems in which large number of design variables are needed, the computational cost becomes prohibitive, and thus original global optimization strategies are required. To address this need, data dimensionality reduction method is combined with global optimization methods, thus forming a new global optimization system, aiming to improve the efficiency of conventional global optimization. The new optimization system involves applying Proper Orthogonal Decomposition (POD) in dimensionality reduction of design space while maintaining the generality of original design space. Besides, an acceleration approach for samples calculation in surrogate modeling is applied to reduce the computational time while providing sufficient accuracy. The optimizations of a transonic airfoil RAE2822 and the transonic wing ONERA M6 are performed to demonstrate the effectiveness of the proposed new optimization system. In both cases, we manage to reduce the number of design variables from 20 to 10 and from 42 to 20 respectively. The new design optimization system converges faster and it takes 1 3 of the total time of traditional optimization to converge to a better design, thus significantly reducing the overall optimization time and improving the efficiency of conventional global design optimization method. This review paper presents an overview of simulation-based hydrodynamic design optimization of ship hull forms. A computational tool that is aimed to accomplishing early-stage simulation-based design in terms of hydrodynamic performance is discussed in detail. The main components of this computational tool consist of a hydrodynamic module, a hull surface modeling module, and an optimization module. The hydrodynamic module includes both design-oriented simple CFD tools and high-fidelity CFD tools. These integrated CFD tools are used for evaluating hydrodynamic performances at different design stages. The hull surface modeling module includes various techniques for ship hull surface representation and modification. This module is used to automatically produce hull forms or modify existing hull forms in terms of hydrodynamic performance and design constraints. The optimization module includes various optimization algorithms and surrogate models, which are used to determine optimal designs in terms of given hydrodynamic performance. As an illustration of the computational tool, a Series 60 hull is optimized for reduced drag using three different modification strategies to outline the specific procedure for conducting simulation-based hydrodynamic design of ship hull forms using the present tool. Numerical results show that the present tool is well suited for the hull form design optimization at early design stage because it can produce effective optimal designs within a short period of time. The numerical search for the optimum shape of an aerofoil is of great interest for aircraft and turbomachine designers. Unfortunately, this process is very computationally intense and can require a large number of individual flow field simulations resulting in very long CPU run times. One of the core issues that the designer must deal with is how to describe the shape of the airfoil. Clearly, we cannot treat the profile on a point by point basis as the problem would have an infinite number of degrees of freedom. Hence the typical practice is to resort to using a series of curves, such as polynomials and Bezier curves, to describe the profile. This typically reduces the number of degrees of freedom to a much smaller, manageable number. The influence of the selection of the parameterization on the optimization has received relatively little consideration to date. We can anticipate that some parameterizations will be less suitable for describing the profile shape and may result in slower convergence times. Our paper will discuss a new airfoil parameterization, Bezier-PARSEC, that was developed to extend and improve the typical Bezier parameterization found in use. This parameterization was found to fit the known shape of a wide range of existing airfoil profiles as well as resulting in accelerated convergence for aerodynamic optimization using Differential Evolution. Our presentation will present the development and details of the Bezier-PARSEC parameterization and provide evidence that the parameterization is suitable and accelerates convergence.