Coupled adjoint aerostructural wing optimization using quasi-three-dimensional aerodynamic analysis

This paper presents a method for wing aerostructural analysis and optimization, which needs much lower computational costs, while computes the wing drag and structural deformation with a level of accuracy comparable to the higher fidelity CFD and FEM tools. A quasi-three-dimensional aerodynamic solver is developed and connected to a finite beam element model for wing aerostructural optimization. In a quasi-three-dimensional approach an inviscid incompressible vortex lattice method is coupled with a viscous compressible airfoil analysis code for drag prediction of a three dimensional wing. The accuracy of the proposed method for wing drag prediction is validated by comparing its results with the results of a higher fidelity CFD analysis. The wing structural deformation as well as the stress distribution in the wingbox structure is computed using a finite beam element model. The Newton method is used to solve the coupled system. The sensitivities of the outputs, for example the wing drag, with respect to the inputs, for example the wing geometry, is computed by a combined use of the coupled adjoint method, automatic differentiation and the chain rule of differentiation. A gradient based optimization is performed using the proposed tool for minimizing the fuel weight of an A320 class aircraft. The optimization resulted in more than 10 % reduction in the aircraft fuel weight by optimizing the wing planform and airfoils shape as well as the wing internal structure.     

Concurrent wing and high-lift system aerostructural optimization

A method is presented for concurrent aerostructural optimization of wing planform, airfoil and high lift devices. The optimization is defined to minimize the aircraft fuel consumption for cruise, while satisfying the field performance requirements. A coupled adjoint aerostructural tool, that couples a quasi-three-dimensional aerodynamic analysis method with a finite beam element structural analysis is used for this optimization. The Pressure Difference Rule is implemented in the quasi-three-dimensional analysis and is coupled to the aerostructural analysis tool in order to compute the maximum lift coefficient of an elastic wing. The proposed method is able to compute the maximum wing lift coefficient with reasonable accuracy compared to high-fidelity CFD tools that require much higher computational cost. The coupled aerostructural system is solved using the Newton method. The sensitivities of the outputs of the developed tool with respect to the input variables are computed through combined use of the chain rule of differentiation, automatic differentiation and coupled-adjoint method. The results of a sequential optimization, where the wing shape and high lift device shape are optimized sequentially, is compared to the results of simultaneous wing and high lift device optimization.     

A parallel aerostructural optimization framework for aircraft design studies

Preliminary aircraft design studies use structural weight models that are calibrated with data from existing aircraft. Computing weights with these models is a fast procedure that provides reliable weight estimates when the candidate designs lie within the domain of the data used for calibration. However, this limitation is too restrictive when we wish to assess the relative benefits of new structural technologies and new aircraft configurations early in the design process. To address this limitation, we present a computationally efficient aerostructural design framework for initial aircraft design studies that uses a full finite-element model of key structural components to better assess the potential benefits of new technologies. We use a three-dimensional panel method to predict the aerodynamic forces and couple the lifting surface deflections to compute the deformed aerodynamic flying shape. To be used early in the design cycle, the aerostructural computations must be fast, robust, and allow for significant design flexibility. To address these requirements, we develop a geometry parametrization technique that enables large geometric modifications, we implement a parallel Newton–Krylov approach that is robust and computationally efficient to solve the aeroelastic system, and we develop an adjoint-based derivative evaluation method to compute the derivatives of functions of interest for design optimization. To demonstrate the capabilities of the framework, we present a design optimization of a large transport aircraft wing that includes a detailed structural design parametrization. The results demonstrate that the proposed framework can be used to make detailed structural design decisions to meet overall aircraft mission requirements.     

改进的filter-SQP用于过程优化的研究(英文)

SQP法是求解非线性规划问题最有效的方法之一,在求解过程中,一般需要对惩罚函数进行线性搜索.惩罚因子的选择会带来一些问题,filter-SQP是Roger Fletcher和Sven Leyffer提出的一种不用惩罚函数的算法.本文红模块环境下应用改进的filter-SQP对化工过程优化进行了研究,提出了相应的算法.采用的优化策略是不可行路径法,filter中的约束目标是由断裂流方程、设计规定及不满足的不等式约束线性组合得到.使用filter检验是否接受QP步长作为下次迭代的出发点,避免了对惩罚函数进行线性搜索带来的弊端.当filter搜索失败时,提出了相应的处理策略,提高了算法的稳定性.用于判断优化是否收敛的判据不冉是K-T误差,而是目标函数和约束条件地同时收敛.提出了一个逐步规格化策略,提高了计算效率.计算实例表明,filter-SQP法优于传统的SQP法,本文提出的策略提高了算法的效率和稳定性.     

Metamodel-based collaborative optimization framework

This paper focuses on the metamodel-based collaborative optimization (CO). The objective is to improve the computational efficiency of CO in order to handle multidisciplinary design optimization problems utilising high fidelity models. To address these issues, two levels of metamodel building techniques are proposed: metamodels in the disciplinary optimization are based on multi-fidelity modelling (the interaction of low and high fidelity models) and for the system level optimization a combination of a global metamodel based on the moving least squares method and trust region strategy is introduced. The proposed method is demonstrated on a continuous fiber-reinforced composite beam test problem. Results show that methods introduced in this paper provide an effective way of improving computational efficiency of CO based on high fidelity simulation models.     

The implementation of a knowledge-based framework for the aerodynamic optimization of a morphing wing device

In the field of aerospace engineering currently a lot of research effort is directed towards the reduction of cruise drag of civil transport aircraft in order to reduce fuel burn, and hence environmental impact and costs. In order to reduce cruise drag, a promising method is under consideration by adjusting, or rather morphing the rear part of the aircraft’s wing during cruise flight. Given the premature state of knowledge of such a design implementation, a knowledge-based computational framework is developed. The purpose of this framework is to allow for an aerodynamic optimization of a section of the wing. The framework is set up in such a way that all relevant design knowledge generated in the process can be captured and used in a subsequent mechanical design process. In this fashion, the complex design process of a novel morphing wing device can be automated to a certain degree. This automation can be used to construct a large number of different feasible and optimized designs with varying boundary conditions of a complex experimental device.This article describes the initial 2-dimensional aerodynamic design step of the morphing device under consideration and how it is implemented in a knowledge-based optimization framework. It describes the initial stage of the development of this tool, as it will be expanded by a number of design steps that each adds more detail to the design in all relevant aspect fields (aerodynamic, structural, actuation, etc.). Ultimately, this tool will be used to obtain a thorough evaluation of a number of different proposed structural solutions and allow for a comparison between them.     

Some considerations regarding the use of multi-fidelity Kriging in the construction of surrogate models

Surrogate models or metamodels are commonly used to exploit expensive computational simulations within a design optimization framework. The application of multi-fidelity surrogate modeling approaches has recently been gaining ground due to the potential for further reductions in simulation effort over single fidelity approaches. However, given a black box problem when exactly should a designer select a multi-fidelity approach over a single fidelity approach and vice versa? Using a series of analytical test functions and engineering design examples from the literature, the following paper illustrates the potential pitfalls of choosing one technique over the other without a careful consideration of the optimization problem at hand. These examples are then used to define and validate a set of guidelines for the creation of a multi-fidelity Kriging model. The resulting guidelines state that the different fidelity functions should be well correlated, that the amount of low fidelity data in the model should be greater than the amount of high fidelity data and that more than 10 % and less than 80 % of the total simulation budget should be spent on low fidelity simulations in order for the resulting multi-fidelity model to perform better than the equivalent costing high fidelity model.     

Multi-fidelity design of stiffened composite panel with a crack

Crack propagation is an important concern in the design of aircraft composite fuselage and wing panels. However, numerical simulation of crack propagation is computationally expensive. This work proposes combining high-fidelity analysis model with low-fidelity model to calculate the crack propagation constraint in the design optimization process. Correction response surfaces are employed to relate the high-fidelity models to the low-fidelity models. Four different forms of correction response surface methods are explored and their prediction capabilities are compared. The multi-fidelity approach is found to be more accurate than single-fidelity response surface method at the same computational cost.     

Sequential optimization using multi-level cokriging and extended expected improvement criterion

To reduce the computational cost of metamodel based design optimization that directly relies on the computationally expensive simulation, the multi-fidelity cokriging method has gained increasing attention by fusing data from two or more models with different levels of fidelity. In this paper, an enhanced cokriging based sequential optimization method is proposed. Firstly, the impact of considering full correlation of data among all models on the hyper-parameter estimation during cokriging modeling is investigated by setting up a unified maximum likelihood function. Then, to reduce the computational cost, an extended expected improvement function is established to more reasonably identify the location and fidelity level of the next response evaluation based on the original expected improvement criterion. The results from comparative studies and one airfoil aerodynamic optimization application show that the proposed cokriging based sequential optimization method is more accurate in modeling and efficient in model evaluation than some existing popular approaches, demonstrating its effectiveness and relative merits.     

Optimization of airplane wing structures under gust loads

A methodology is presented for the optimum design of aircraft wing structures subjected to gust loads. The equations of motion, in the form of coupled integro-differential equations, are solved numerically and the stresses in the aircraft wing structure are found for a discrete gust encounter. The gust is assumed to be one minus cosine type and uniform along the span of the wing. In order to find the behavior of the wing structure under gust loads and also to obtain a physical insight into the nature of the optimum solution, the design of the typical section (symmetric double wedge airfoil) is studied by using a graphical procedure. Then a more realistic wing optimization problem is formulated as a constrained nonlinear programming problem based on finite element modeling and the optimum solution is found by using the interior penalty function method. A sensitivity analysis is conducted to find the effects of changes in design variables about the optimum point on the response quantities of the wing structure.     

Integrated cost/weight optimization of aircraft structures

A methodology for a combined cost/weight optimization of aircraft components is proposed. The objective function is formed by a simplified form of direct operating cost, i.e. by a weighted sum of the manufacturing cost and the component weight. Hence, the structural engineer can perform the evaluation of a design solution based on economical values rather than pure cost or weight targets. The parameter that governs the balance between manufacturing cost and weight is called weight penalty and incorporates the effect of fuel burn, environmental impact or contractual penalties due to overweight. Unlike previous work, the analytical cost model and structural models are replaced by commercially available software packages that allow a more realistic model of the manufacturing costs; further, arbitrary constraints for the structural analysis can be implemented. By means of parametric studies it is shown that the design solution strongly depends on the magnitude of the weight penalty.     

Parallelized structural topology optimization and CFD coupling for design of aircraft wing structures

A set of structural optimization tools are presented for topology optimization of aircraft wing structures coupled with Computational Fluid Dynamics (CFD) analyses. The topology optimization tool used for design is the material distribution technique. Because reducing the weight requires numerous calculations, the CFD and structural optimization codes are parallelized and coupled via a code/mesh coupling scheme. In this study, the algorithms used and the results obtained are presented for topology design of a wing cross-section under a given critical aerodynamic loading and two different spar positions to determine the optimum rib topology.     

Surrogate‐assisted EM‐driven miniaturization of wideband microwave couplers by means of co‐simulation low‐fidelity models

This article proposes a methodology for rapid design optimization of miniaturized wideband couplers. More specifically, a class of circuits is considered, in which conventional transmission lines are replaced by their abbreviated counterparts referred to as slow‐wave compact cells. Our focus is on explicit reduction of the structure size as well as on reducing the CPU cost of the design process. For the sake of computational feasibility, a surrogate‐based optimization paradigm involving a co‐simulation low‐fidelity model is used. The latter is a fundamental component of the proposed technique. The low‐fidelity model represents cascaded slow‐wave cells replacing the low‐impedance lines of the original coupler circuit. It is implemented in a circuit simulator (here, ADS) and consists of duplicated compact cell EM simulation data as well as circuit theory‐based feeding line models. Our primary optimization routine is a trust‐region‐embedded gradient search algorithm. To further reduce the design cost, the system response Jacobian is estimated at the level of the low‐fidelity model, which is sufficient due to good correlation between the low‐ and high‐fidelity models. The coupler is explicitly optimized for size reduction, whereas electrical performance parameters are controlled using a penalty function approach. The presented methodology is demonstrated through the design of a 1‐GHz wideband microstrip branch‐line coupler. Numerical results are supported by experimental validation of the fabricated coupler prototype.     

Optimization of airplane wing structures under landing loads

A methodology is presented for the optimum design of aircraft wing structures subjected to landing loads. The stresses developed in the wing during landing are computed by considering the interaction between the landing gear and the flexible airplane structure. The landing gear is assumed to have nonlinear characteristics typical of conventional gears, namely, velocity squared damping, polytropic air-compression springing and exponential tire force-deflection characteristics. The coupled nonlinear differential equations of motion that arise in the landing analysis are solved by using a step-by-step numerical integration technique. In order to find the behavior of the wing structure under landing loads and also to obtain a physical insight into the nature of the optimum solution, the design of the typical section (symmetric double-wedge airfoil) is studied by using a graphical procedure. Then a more realistic wing optimization problem is formulated as a constrained nonlinear programming problem based on finite element modeling. The optimum solutions are found by using the interior penalty function method. A sensitivity analysis is conducted to find the effect of changes in design variables about the optimum point on the various response parameters on the wing structure.     

飞机环控/发动机系统多目标优化分析

一种以系统熵产最小为目标函数的优化方法,应用到飞机环控/发动机系统的综合优化计算。由于在不同飞行阶段为使系统总的熵产减小对设计变量的要求不尽相同,甚至存在冲突,引入多目标优化的思想进行优化计算。将任务剖面内不同飞行阶段系统总的熵产最小视为不同的目标函数,通过分析系统之间交联关系、选取设计变量和分析约束条件建立多目标优化计算模型。采用自适应进化多目标粒子群优化算法对模型进行优化计算,得到非劣最优解集,为方案决策提供理论依据。仿真结果证实该方法的有效性,为飞机系统综合优化提供一种新思路。     

基于优化配平的机翼故障飞机飞行性能分析

分析飞机机翼故障对飞行性能的影响,对飞机故障后能够安全着陆或返航有着重要意义,飞机的机翼作为产生力和力矩的主要部件对飞行性能起着重要的作用。提出一种基于单纯形优化的机翼故障飞机飞行性能分析方法,建立机翼故障参数模型,根据飞机爬升转弯飞行条件进行优化配平计算,得到在不同状态下不同机翼故障的配平数据库,分析了故障后飞机的飞行性能。仿真结果表明所提算法的有效性。     

Optimal design of aircraft structures with damage tolerance requirements

Damage tolerance analysis (DTA) was considered in the global design optimization of an aircraft wing structure. Residual strength and fatigue life requirements, based on the damage tolerance philosophy, were investigated as new design constraints. The global/local finite element approach allowed local fatigue requirements to be considered in the global design optimization. AFGROW fatigue crack growth analysis provided a new strength criterion for satisfying damage tolerance requirements within a global optimization environment. Initial research with the ASTROS program used this damage tolerance constraint to optimize cracked skin panels on the lower wing of a fighter/attack aircraft. For an aerodynamic and structural model of this type of aircraft, ASTROS simulated symmetric and asymmetric maneuvers during the optimization. Symmetric maneuvers, without underwing stores, produced the highest stresses and drove the optimization of the inboard lower wing skin. Asymmetric maneuvers, with underwing stores, affected the optimum thickness of the outboard hard points. Subsequent design optimizations included DTA and von Mises stress constraints simultaneously. In the configuration with no stores, the optimization was driven by the DTA constraint and, therefore, DTA requirements can have an active role to play in preliminary aircraft design.     

Aerodynamic shape optimization of supersonic aircraft configurations via an adjoint formulation on distributed memory parallel computers

This work describes the application of a control theory-based aerodynamic shape optimization method to the problem of supersonic aircraft design. A high fidelity computational fluid dynamics (CFD) algorithm modelling the Euler equations is used to calculate the aerodynamic properties of complex three-dimensional aircraft configurations. The design process is greatly accelerated through the use of both control theory and parallel computing. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is then implemented in parallel using a domain decomposition approach, an optimized communication schedule, and the Message Passing Interface (MPI) Standard for portability and efficiency. In our earlier studies, the serial implementation of this design method, was shown to be effective for the optimization of airfoils, wings, wing–bodies, and complex aircraft configurations using both the potential equation and the Euler equations. In this work, our concern will be to extend the methodologies such that the combined capabilities of these new technologies can be used routinely and efficiently in an industrial design environment. The aerodynamic optimization of a supersonic transport configuration is presented as a demonstration test case of the capability. A particular difficulty of this test case is posed by the close coupling of the propulsion/airframe integration.     

CAD系统的二次开发在设计优化中的应用

多学科设计优化(MDO)已经由单一的优化方法工具向集成有优化器技术,不同学科代码,能实现不同学科分析代码间通信的接口以及MDO自动化进行的优化体系工具箱发展。目前MDO框架的开发中存在的一个主要问题是分析对象的几何描述过于简单,造成不同学科分析模块间计算信息很难转换。从建立一个三维运输机参数模型入手,通过CAD系统的二次开发,将模型集成到设计优化框架中,为各学科所有的分析和相关工程任务提供一个公共分析平台和基础。     

Blended wing body structures in multidisciplinary pre-design

The structural analysis of blended wing body (BWB) aircraft configurations is presented in the context of a preliminary, multidisciplinary aircraft design process by means of the aircraft design and optimization program (PrADO) of the Institut of Aircraft Design and Lightweight Structures of the TU Braunschweig. A multidisciplinary process is described that enables parametric creation of detailed finite element models and its loads. Iteratively different flight conditions are trimmed and corresponding pressure distributions calculated by the higher-order subsonic and supersonic panel code HISSS. Each defined loading condition is used for the iterative structural sizing of the primary structure. Based on finite element idealization, a mass estimation of all structural masses is performed. The primary and secondary masses are fed back into the closed overall aircraft optimization loop of PrADO until this iterative procedure shows convergence on calculated aircraft variables (e.g., aircraft masses and static engine thrust). This automated process enables further configuration improvements using manual parametric variations or optimization features of PrADO with an objective function being defined by fuel consumption, aircraft mass, or direct operating costs. Different structural solutions and their integration in the global model are presented for passenger versions of a 700 passenger BWB with special consideration of a pressurized cabin. As an example, structural masses and parametric studies on the influence of the center body rib spacing are presented and compared by weight breakdowns.