变可信度模型在气动优化中的应用

在气动外形优化中, 采用近似模型管理结构（AMF）方法,对变可信度模型进行组织和管理．这样能够充分利用低可信度模型,将主要计算量集中在低可信度模型的优化迭代过程中．同时,采用高可信度模型监控优化过程,使最终的优化解收敛到高可信度模型上．最后,设计了零阶变可信度气动特性优化管理结构与搜索算法,对某飞翼型无人机的翼型进行了气动优化．优化外形的气动性能与初始外形比有所提高．实际结果表明所提出的方法具有良好的可行性和适用性．     

Airfoil design optimization using the Navier-Stokes equations

A design optimization technique is presented which couples a computationally efficient Navier-Stokes code with a numerical optimization algorithm. The design method improves the aerodynamic performance of an airfoil subject to specified design objectives and constraints. Recent advances in computers and compputational fluid dynamics have permitted the use of the Navier-Stokes equations in the design procedure to include the nonlinear, rotational, viscous physics of transonic flows. Using numerical optimization guarantees that a better design will be produced even with strict design constraints. The method is demonstrated with several examples at transonic flow conditions.     

Optimization of aircraft structural components by using nature-inspired algorithms and multi-fidelity approximations

In this work, a flat pressure bulkhead reinforced by an array of beams is designed using a suite of heuristic optimization methods (Ant Colony Optimization, Genetic Algorithms, Particle Swarm Optimization and LifeCycle Optimization), and the Nelder-Mead simplex direct search method. The compromise between numerical performance and computational cost is addressed, calling for inexpensive, yet accurate analysis procedures. At this point, variable fidelity is proposed as a tradeoff solution. The difference between the low-fidelity and high-fidelity models at several points is used to fit a surrogate that corrects the low-fidelity model at other points. This allows faster linear analyses during the optimization; whilst a reduced set of expensive non-linear analyses are run “off-line,” enhancing the linear results according to the physics of the structure. Numerical results report the success of the proposed methodology when applied to aircraft structural components. The main conclusions of the work are (i) the variable fidelity approach enabled the use of intensive computing heuristic optimization techniques; and (ii) this framework succeeded in exploring the design space, providing good initial designs for classical optimization techniques. The final design is obtained when validating the candidate solutions issued from both heuristic and classical optimization. Then, the best design can be chosen by direct comparison of the high-fidelity responses.     

Parallel evolutionary algorithms for optimization problems in aerospace engineering

This paper presents the recent developments in hierarchical genetic algorithms (HGAs) to speed up the optimization of aerodynamic shapes. It first introduces HGAs, a particular instance of parallel GAs based on the notion of interconnected sub-populations evolving independently. Previous studies have shown the advantages of introducing a multi-layered hierarchical topology in parallel GAs. Such a topology allows the use of multiple models for optimization problems, and shows that it is possible to mix fast low-fidelity models for exploration and expensive high-fidelity models for exploitation. Finally, a new class of multi-objective optimizers mixing HGAs and Nash Game Theory is defined. These methods are tested for solving design optimization problems in aerodynamics. A parallel version of this approach running a cluster of PCs demonstrate the convergence speed up on an inverse nozzle problem and a high-lift problem for a multiple element airfoil.     

Natural laminar flow shape optimization in transonic regime with competitive Nash game strategy

The Natural Laminar Flow (NLF) airfoil/wing design optimization is an efficient method which can reduce significantly turbulence skin friction by delaying transition location at high Reynolds numbers. However, the reduction of the friction drag is competitively balanced with the increase of shock wave induced drag in transonic regime. In this paper, a distributed Nash Evolutionary Algorithms (EAs) is presented and extended to multi-level parallel computing, namely multi-level parallel Nash EAs. The proposed improved methodology is used to solve NLF airfoil shape design optimization problem. It turns out that the optimization method developed in this paper can easily capture a Nash Equilibrium (NE) between transition delaying and wave drag increasing. Results of numerical experiments demonstrate that both wave drag and friction drag performances of a NE are greatly improved. Moreover, performance of the NE is equivalent to that of cooperative Pareto-optimum solutions, but it is more efficient in terms of CPU time. The successful application validates efficiency of algorithms in solving complex aerodynamic optimization problem.     

Aerodynamic Optimization of Airfoils Using Adaptive Parameterization and Genetic Algorithm

A new method for airfoil shape parameterization is presented, and its influences on the optimum design and convergence of the evolutionary optimization process are investigated. An online adaptive method is used that alters the airfoil parametric function during the process of optimization. A geometric inverse design is carried out, and the capability of the method for producing general airfoil shapes is assessed. The performance of the method is then evaluated by aerodynamic shape optimization. The result indicates that the proposed method improves the optimum design airfoil significantly. In addition, it reduces the total number of flow solver calls, which consequently reduces the required computational time.     

Simultaneous kriging-based estimation and optimization of mean response

Robust optimization is typically based on repeated calls to a deterministic simulation program that aim at both propagating uncertainties and finding optimal design variables. Often in practice, the “simulator” is a computationally intensive software which makes the computational cost one of the principal obstacles to optimization in the presence of uncertainties. This article proposes a new efficient method for minimizing the mean of the objective function. The efficiency stems from the sampling criterion which simultaneously optimizes and propagates uncertainty in the model. Without loss of generality, simulation parameters are divided into two sets, the deterministic optimization variables and the random uncertain parameters. A kriging (Gaussian process regression) model of the simulator is built and a mean process is analytically derived from it. The proposed sampling criterion that yields both optimization and uncertain parameters is the one-step ahead minimum variance of the mean process at the maximizer of the expected improvement. The method is compared with Monte Carlo and kriging-based approaches on analytical test functions in two, four and six dimensions.     

On the Positive Definiteness of Cokriging Covariance Matrices

Variable-fidelity modeling (VFM), sometimes also termed multi-fidelity modeling, refers to the utilization of two or more data layers of different accuracy in order to construct an inexpensive emulator of a given numerical high-fidelity model. In practical applications, this situation arises when simulators of different accuracy for the same physical process are given and it is assumed that many low-fidelity sample points are affordable, but the high-fidelity model is extremely costly to assess. More precisely, the VFM objective is to construct a predictor function, which interpolates the primary sample data but is driven by the trend indicated by the secondary data. In view of the computational effort, the objective is to use as few high-fidelity sample points as possible to achieve a desired level of accuracy. A widely used VFM method is Cokriging. The technique yields the best linear unbiased estimator based on the given data, taking spatial correlation into account. One way to model spatial correlation is via positive definite correlation kernels that yield positive definite correlation matrices for distinct input sample points. In this contribution, we will address the positive definiteness of Cokriging correlation matrices which is necessary for the method but not granted, due to the modeling of the cross-correlations. We discuss both the cases of distinct and coincident low- and high-fidelity sample points. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Solution Remapping Technique to Accelerate Flow Convergence for Finite Volume Methods Applied to Shape Optimization Design

A solution remapping technique is applied to transonic airfoil optimization design to provide a fast flow steady state convergence of intermediate shapes for the finite volume schemes in solving the compressible Euler equations. Specifically, once the flow solution for the current shape is obtained, the flow state for the next shape is initialized by remapping the current solution with consideration of mesh deformation. Based on this strategy, the formula of deploying the initial value for the next shape is theoretically derived under the assumption of small mesh deformation. Numerical experiments show that the present technique of initial value deployment can attractively accelerate flow convergence of intermediate shapes and reduce computational time up to 70% in the optimization process.     

Hybrid evolutionary algorithm with Hermite radial basis function interpolants for computationally expensive adjoint solvers

In this paper, we present an evolutionary algorithm hybridized with a gradient-based optimization technique in the spirit of Lamarckian learning for efficient design optimization. In order to expedite gradient search, we employ local surrogate models that approximate the outputs of a computationally expensive Euler solver. Our focus is on the case when an adjoint Euler solver is available for efficiently computing the sensitivities of the outputs with respect to the design variables. We propose the idea of using Hermite interpolation to construct gradient-enhanced radial basis function networks that incorporate sensitivity data provided by the adjoint Euler solver. Further, we conduct local search using a trust-region framework that interleaves gradient-enhanced surrogate models with the computationally expensive adjoint Euler solver. This ensures that the present hybrid evolutionary algorithm inherits the convergence properties of the classical trust-region approach. We present numerical results for airfoil aerodynamic design optimization problems to show that the proposed algorithm converges to good designs on a limited computational budget.     

Global optimization of general constrained grey-box models: new method and its application to constrained PDEs for pressure swing adsorption

This paper introduces a novel methodology for the global optimization of general constrained grey-box problems. A grey-box problem may contain a combination of black-box constraints and constraints with a known functional form. The novel features of this work include (i) the selection of initial samples through a subset selection optimization problem from a large number of faster low-fidelity model samples (when a low-fidelity model is available), (ii) the exploration of a diverse set of interpolating and non-interpolating functional forms for representing the objective function and each of the constraints, (iii) the global optimization of the parameter estimation of surrogate functions and the global optimization of the constrained grey-box formulation, and (iv) the updating of variable bounds based on a clustering technique. The performance of the algorithm is presented for a set of case studies representing an expensive non-linear algebraic partial differential equation simulation of a pressure swing adsorption system for \(\hbox {CO}_{2}\). We address three significant sources of variability and their effects on the consistency and reliability of the algorithm: (i) the initial sampling variability, (ii) the type of surrogate function, and (iii) global versus local optimization of the surrogate function parameter estimation and overall surrogate constrained grey-box problem. It is shown that globally optimizing the parameters in the parameter estimation model, and globally optimizing the constrained grey-box formulation has a significant impact on the performance. The effect of sampling variability is mitigated by a two-stage sampling approach which exploits information from reduced-order models. Finally, the proposed global optimization approach is compared to existing constrained derivative-free optimization algorithms.     

An Improved Hybrid Adjoint Method in External Aerodynamics Using Variational Technique for the Boundary Integral Based Optimal Objective Function Gradient

An improved hybrid adjoint method to the viscous, compressible Reynold-Averaged Navier-Stokes Equation (RANS) is developed for the computation of objective function gradient and demonstrated for external aerodynamic design optimization. In this paper, the main idea is to extend the previous coupling of the discrete and continuous adjoint method by the grid-node coordinates variation technique for the computation of the variation in the gradients of flow variables. This approach in combination with the Jacobian matrices of flow fluxes refrained the objective function from field integrals and coordinate transformation matrix. Thus, it opens up the possibility of employing the hybrid adjoint method to evaluate the subsequent objective function gradient analogous to many shape parameters, comprises of only boundary integrals. This avoids the grid regeneration in the geometry for every surface perturbation in a structured and unstructured grid. Hence, this viable technique reduces the overall CPU cost. Moreover, the new hybrid adjoint method has been successfully applied to the computation of accurate sensitivity derivatives. Finally, for the investigation of the presented numerical method, simulations are carried out on NACA0012 airfoil in a transonic regime and its accuracy and effectiveness related to the new gradient equation have been verified with the Finite Difference Method (FDM). The analysis reveals that the presented methodology for the optimization provides the designer with an indispensable CPU-cost effective tool to reshape the complex geometry airfoil surfaces, useful relative to the state-of-the-art, in a less computing time.     

径向基函数参数化翼型的气动力降阶模型优化

基于小扰动和弱非线性假设,提出了一种基于气动力降阶模型和径向基函数参数化的翼型优化方法.其主要方法是用径向基函数参数化翼型扰动;通过CFD辨识参数扰动对翼型气动力影响的降阶模型核函数;基于叠加法建立了参数变化对翼型气动力影响的降阶模型;最后基于该气动力降阶模型计算并优化翼型升阻特性.NACA0012翼型优化的结果表明基于气动力降阶模型的优化方法是可行的,可以极大地提高翼型优化速度.     

A fast Kriging-based strategy for the optimization of electrical device

The primary goal of a shape optimization problem is to find the best design w.r.t. a given criterion. A however non less important goal is to achieve this task within a reasonable time. In realistic situations, a reliable but slow method might not always provide its best capacity if the computational resources are worked out before convergence. The expensive simulation-based optimization of a physical system is one of these situations. In order to tackle this issue, we consider a fast but low-fidelity model given by a Kriging method. We propose a simple adaptive scheme in order to enhance the reliability of the optimization procedure and thus avoid a premature convergence. Numerical experiments are conducted for the electrostatic design of a realistic device. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Quantile-based robust optimization of a supersonic nozzle for organic rankine cycle turbines

Organic Rankine Cycle (ORC) turbines usually operate in thermodynamic regions characterized by high-pressure ratios and strong non-ideal gas effects, complicating the aerodynamic design significantly. Systematic optimization methods accounting for multiple uncertainties due to variable operating conditions, referred to as Robust Optimization may benefit to ORC turbines aerodynamic design. This study presents an original and fast robust shape optimization approach to overcome the limitation of a deterministic optimization that neglects operating conditions variability, applied to a well-known supersonic turbine nozzle for ORC applications. The flow around the blade is assumed inviscid and adiabatic and it is reconstructed using the open-source SU2 code. The non-ideal gasdynamics is modeled through the Peng-Robinson-Stryjek-Vera equation of state. We propose here a mono-objective formulation which consists in minimizing the α-quantile of the targeted Quantity of Interest (QoI) under a probabilistic constraint, at a low computational cost. This problem is solved by using an efficient robust optimization approach, coupling a state-of-the-art quantile estimation and a classical Bayesian optimization method. First, the advantages of a quantile-based formulation are illustrated with respect to a conventional mean-based robust optimization. Secondly, we demonstrate the effectiveness of applying this robust optimization framework with a low-fidelity inviscid solver by comparing the resulting optimal design with the ones obtained with a deterministic optimization using a fully turbulent solver.     

基于卷积神经网络气动力降阶模型的翼型优化方法

针对非线性大扰动翼型气动力优化问题,提出了基于卷积神经网络气动力降阶模型的优化方法.该方法用不同形状参数下翼型的气动力数据作为训练信号,训练卷积神经网络翼型气动力降阶模型.采用该气动力降阶模型,以最大升阻比为目标,对翼型进行优化,结果表明该方法可用于大扰动下翼型气动力的预测和优化.该文同时还讨论了池化法和径向基法的训练...     

沉浮,俯仰及控制面振动引起的跨音速非定常气动载荷计算

本文将文献[9]提出改进的通量分裂方法,应用于随时间变化的贴体网格中,建立了可用于求解非定常Euler方程的通量分裂方法.该方法是以连续的特征值分离为基础,它具有方法简单,便于推广使用的特点.同时克服了Steger-Warming通量分裂方法存在的问题.对通量分裂后的Euler方程.利用MUSCL型迎风差分建立了具有二阶精度的有限体积方程.文中以NACA64A—10翼型为例,对其在跨音速流场中进行沉浮、俯仰及带有振动控制面引起的非定常气动载荷进行了计算.部分计算结果与相应的实验结果进行了比较,吻合良好     

Performance analysis of distributed solution approaches in simulation-based optimization

Applying computationally expensive simulations in design or process optimization results in long-running solution processes even when using a state-of-the-art distributed algorithm and hardware. Within these simulation-based optimization problems the optimizer has to treat the simulation systems as black-boxes. The distributed solution of this kind of optimization problem demands efficient utilization of resources (i.e. processors) and evaluation of the solution quality. Analyzing the parallel performance is therefore an important task in the development of adequate distributed approaches taking into account the numerical algorithm, its implementation, and the used hardware architecture. In this paper, simulation-based optimization problems are characterized and a distributed solution algorithm is presented. Different performance analysis techniques (e.g. scalability analysis, computational complexity) are discussed and a new approach integrating parallel performance and solution quality is developed. This approach combines a priori and a posteriori techniques and can be applied in early stages of the solution process. The feasibility of the approach is demonstrated by applying it to three different classes of simulation-based optimization problems from groundwater management.     

Advances in concrete arch dams shape optimization

This paper presents an efficient methodology to find the optimum shape of arch dams. In order to create the geometry of arch dams a new algorithm based on Hermit Splines is proposed. A finite element based shape sensitivity analysis for design-dependent loadings involving body force, hydrostatic pressure and earthquake loadings is implemented. The sensitivity analysis is performed using the concept of mesh design velocity. In order to consider the practical requirements in the optimization model such as construction stages, many geometrical and behavioral constrains are included in the model in comparison with previous researches. The optimization problem is solved via the sequential quadratic programming (SQP) method. The proposed methods are applied successfully to an Iranian arch dam, and good results are achieved. By using such methodology, efficient software for shape optimization of concrete arch dams for practical and reliable design now is available.