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.     

Interval-based optimization of aircraft wings under landing loads

An interval-based automated optimization of aircraft wing structures subjected to landing loads is discussed in this paper. The interaction between landing gear and flexible airplane structure is considered as a coupled system. The uncertain system parameters are described as interval numbers. The computational aspects of the optimization procedure are illustrated with two examples – symmetric double-wedge airfoil, and supersonic airplane wing. Since, in most cases only the ranges of uncertain parameters are known with their probability distribution functions unknown, the present methodology is expected to be more realistic for the optimum design of aircraft structures under landing loads.     

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.     

Automated optimum design of wing structures: A probabilistic approach

The optimization of aircraft wing structures is presented by considering the dynamic stresses developed during landing impact and gust load conditions. The random nature of the sinking speed and the forward velocity at the instant of contact is considered in the calculation of landing stresses. The vertical velocity due to gust is treated as a stochastic process for the computation of gust-induced stresses. The optimum designs of a symmetric double wedge airfoil, based on beam type of analysis, and a supersonic airplane wing, based on finite element analysis, are considered to illustrate the procedure. A graphical procedure is used in the case of the double wedge airfoil, and nonlinear programming techniques are used in the case of the supersonic wing, for finding the optimum solutions.     

Conceptual design of aeroelastic structures by topology optimization

A topology optimization methodology is presented for the conceptual design of aeroelastic structures accounting for the fluid–structure interaction. The geometrical layout of the internal structure, such as the layout of stiffeners in a wing, is optimized by material topology optimization. The topology of the wet surface, that is, the fluid–structure interface, is not varied. The key components of the proposed methodology are a Sequential Augmented Lagrangian method for solving the resulting large-scale parameter optimization problem, a staggered procedure for computing the steady-state solution of the underlying nonlinear aeroelastic analysis problem, and an analytical adjoint method for evaluating the coupled aeroelastic sensitivities. The fluid–structure interaction problem is modeled by a three-field formulation that couples the structural displacements, the flow field, and the motion of the fluid mesh. The structural response is simulated by a three-dimensional finite element method, and the aerodynamic loads are predicted by a three-dimensional finite volume discretization of a nonlinear Euler flow. The proposed methodology is illustrated by the conceptual design of wing structures. The optimization results show the significant influence of the design dependency of the loads on the optimal layout of flexible structures when compared with results that assume a constant aerodynamic load.     

Reliability-based design optimization of aeroelastic structures

Aeroelastic phenomena are most often either ignored or roughly approximated when uncertainties are considered in the design optimization process of structures subject to aerodynamic loading, affecting the quality of the optimization results. Therefore, a design methodology is proposed that combines reliability-based design optimization and high-fidelity aeroelastic simulations for the analysis and design of aeroelastic structures. To account for uncertainties in design and operating conditions, a first-order reliability method (FORM) is employed to approximate the system reliability. To limit model uncertainties while accounting for the effects of given uncertainties, a high-fidelity nonlinear aeroelastic simulation method is used. The structure is modelled by a finite element method, and the aerodynamic loads are predicted by a finite volume discretization of a nonlinear Euler flow. The usefulness of the employed reliability analysis in both describing the effects of uncertainties on a particular design and as a design tool in the optimization process is illustrated. Though computationally more expensive than a deterministic optimum, due to the necessity of solving additional optimization problems for reliability analysis within each step of the broader design optimization procedure, a reliability-based optimum is shown to be an improved design. Conventional deterministic aeroelastic tailoring, which exploits the aeroelastic nature of the structure to enhance performance, is shown to often produce designs that are sensitive to variations in system or operational parameters.     

基于干扰估计的非对称运动下飞机刹车系统模型预测控制

针对飞机在非对称运动下的双侧机轮协调控制问题, 提出一种基于滑模干扰估计的模型预测控制方法. 首先, 通过对飞机制动过程横纵方向力矩机理分析并分别考虑左右机轮对刹车性能的影响, 建立全面刻画系统动态的地面滑跑动力学模型. 在此基础上, 设计滑模观测器对侧风干扰进行实时估计, 利用补偿机制实现对侧风扰动的有效抑制. 此外, 提出基于前轮荷载状态门限特征和结合系数阈值范围特征的分析方法, 解决切换跑道环境辨识问题. 设计非线性模型预测算法, 实现飞机纵向防滑刹车和横向跑道纠偏的协调控制. 最后, 在侧风干扰、跑道切换以及不对称着陆等情况下进行仿真实验, 验证了所提出的控制策略能够有效提升刹车系统的防滑效率及纠偏性能.     

Optimal earthquake-resistant design: A reliability-based,global cost approach

This paper presents a methodology for incorporating into the decision-making process of design the explicit consideration of possible future performance of the designed structure in the presence of uncertainty in both loading and structural parameters assumed in the design process. Design is viewed as an optimization problem, taking into account as a merit function terms related to building cost as well as possible future damage. Randomness of loads, load-effects, structural resistances and structural parameters affecting response are considered. In this framework a method suited both to linear as well as nonlinear structural behavior is presented. Approximate expressions of the probabilities of the above random variables as functions of the central moment of their distributions are introduced. Together with a firstorder expansion of the input-output response function characterizing the structural model, this procedure gives computational feasibility for actual design applications. An example is included to clarify the methodology proposed and to illustrate typical features of problem formulation and solution.     

精确求解进港飞机调度双目标优化问题的epsilon约束算法

随着机场客流的持续增长,航班延误日益严重。同时,对于机场最重要的跑道资源而言,积雪结冰等会造成 飞机 打滑,从而出现事故。对于机场管理者,周期性地维护跑道至关重要,以防雨雪天气出现飞机打滑事故。该研究主要针对跑道上的 航班调度问题,考虑恶劣天气环境下跑道的周期性维护(如周期性喷洒除雪盐等)。为了在保证航班的服务质量的同时提高机场跑道的使用效率,文中以最小化航班总延误和跑道使用时间为优化的双目标。首先,提出该双目标优化问题混合整数规划模型;其次,为了精确求解出Pareto前沿,开发出epsilon约束算法;最后,给出算例来说明模型和算法的可行性。通过数学规划理论建模并开发精确求解算法,为机场资源优化研究提供参考。     

多Agent的航空器滑行策略优化

快速发展的民航事业导致很多机场容量不足。为缓解大型机场交通拥堵的现状,研究了航空器滑行策略优化问题。滑行路径优化是指在特定的时间段内,根据机场资源信息和地面运行管理系统对进离场航空器在跑道和停机位之间的距离进行优化管理。通过深入剖析机场地面的网络结构,综合考虑滑行冲突、地面运行规则等因素,提出了多Agent滑行策略优化方法,该方法提升了机场资源利用率;基于地面网络链路结构的概念,建立了航空器滑行策略优化模型;结合多Agent的基本理论,设计了跑道出口选择概率函数和多Agent系统滑行路径优化结构,以寻求航空器的最优滑行路径。以国内某大型机场的实际情况为研究背景进行了航空器滑行策略实验,结果表明,与以往的算法相比,多Agent滑行策略优化方法的效果更为显著。设置跑道口的速度和同一交叉口航空器的最小间隔距离,通过对跑道出口的选择和Agent间的交互协商,航空器能够对原滑行路径进行有效调整,并缩短其在机场场面上的滑行时间。与最短路径算法相比,多Agent滑行策略方法在航空器的总滑行距离、航空器在滑行道上的密度以及平均等待时间方面的优化效果更好,且其对滑行道资源的分配更合理。其中,航空器在节点处的平均等待时间减少了8.26%。所提策略可有效缓解机场交通拥堵的现状,提高场面运行效率,对减少航空器延误和保障机场的运营安全具有重要意义。     

Optimal design of adaptive structures: Part I. Remodeling for impact reception

The paper (written in two parts) is devoted to the presentation of numerical tools, based on the so-called virtual distortion method (VDM) for fast structural reanalysis and to the application of this tools for optimal design of adaptive structures exposed to impact loads. The first paper deals with fast modifications of the material distribution (coupled stiffness and mass redistribution) in dynamically loaded structures, which allows their optimal remodeling, e.g., to minimize average deflections. The VDM-based approach allows analytical sensitivity determination, which is very helpful in efficient implementation of the optimization procedure, utilized to solve the defined remodeling problem. The presented methodology is illustrated with a numerical example of truss–beam structure exposed to random impact loads.     

A design methodology for structural and control systems of a prosthetic leg

A design methodology is proposed to optimize a prosthetic leg considering the structural and control aspects. Previous studies mainly focused on each of a structural design problem or a control problem. The structural design variables of a prosthetic leg are determined in a structural design problem while the trajectory tracking based on the human gait cycle is found to be a control problem. The two problems have been separately solved. However, they should be simultaneously considered to obtain a better design. Then the problem would be nonlinear dynamic response optimization of structural and control systems. An optimization method was recently developed for a linear system of structural and control design problems using the equivalent static loads (ESLs). In this study, a design methodology for the prosthetic leg is presented by expanding the equivalent static loads method (ESLM) to nonlinear dynamic systems. A simple example is solved to validate the proposed methodology, and then a prosthetic leg is optimized to reduce the weight and energy consumption.     

Finite element procedures for nonlinear structures in moving coordinates. Part 1: Infinite bar under moving axial loads

This paper deals with analyzing nonlinear structures under high-speed moving loads by use of the finite element method. The stationary response of an infinite bar posed on a Winkler foundation under constant moving loads is investigated. Instead of the transient analysis, the stationary solution of this problem is obtained by solving a static system in a reference frame which moves with the load for reducing the computation cost. To overcome the difficulty due to numerical instabilities when considering very fast loads (supersonic loads), a new procedure to govern the finite element formulation in moving coordinates is proposed. Comparing numerical solutions with analytical ones shows that the proposed method is valid for all values of load speed. Last, an example of nonlinear elastic foundation is considered to outline the nonlinear effects.     

无人机基于视觉自主着陆的跑道识别跟踪

跑道检测识别与跟踪是基于视觉的无人机自主着陆的前提和难点,本文根据固定翼无人机基于视觉自主着陆的特点设计了包括跑道检测、跑道特征提取、跑道识别和跑道跟踪的方案,并在ARM Cortex-A9处理器中基于Linux系统使用OpenCV实现了该方案.最后按照逐步递进的方式分别对检测、检测识别、检测识别与跟踪结果进行了实验验证,并对实时性进行了分析.实验结果表明,通过该方案可以准确地识别图像中的跑道并具有较快的跟踪速度.     

Optimum geometry design of nonlinear braced domes using genetic algorithm

Domes are lightweight and cost effective structures that are used to cover large areas. They are mainly comprised of a complex network of triangles made out of slender members. The behaviour of flexible dome is nonlinear under the external loads which makes it necessary to consider the geometrical non-linearity in their analysis to obtain realistic response of these structures. Furthermore, instability check during the nonlinear analysis is of prime importance. In this paper, an algorithm is presented for the optimum geometry design of nonlinear braced domes. The height of crown is taken as design variable in addition to the cross-sectional properties of members. A procedure is developed that calculates the joint coordinates automatically for a given height of the crown. The optimum design algorithm takes into account the nonlinear response of the dome due to the effect of axial forces on the flexural stiffnesses of members. It considers serviceability requirements as well as combined strength limitations set by BS 5950. The solution of the design problem is obtained by genetic algorithm. The elastic instability analysis is then carried out for each individual in the initial population until the ultimate load factor is reached. During this analysis, checks on the overall stability of the dome is conducted. If the loss of stability takes place, this individual is taken out of the population and replaced by a new randomly generated individual. This replacement policy is repeated until an individual is found which does not have instability problem. Once the initial population is established where all the individuals are free of instability problem, the regular genetic operations are applied to generate a new population. Number of design examples are included to demonstrate the application of the algorithm.     

Gain-scheduled directional guidance controller design using a genetic algorithm for automatic precision landing

This paper discusses the guidance controller design problem of an aircraft in automatic landing and touchdown flight, subject to dangerous and unpredictable gusts known as wind-shear and to directional crosswind. The associated airplane in the landing flight was statically unstable in this paper. The wind-shear, based on the Dryden gust model, was included in the nonlinear airplane model. A directional guidance control system with gain-scheduling fuzzy logic was proposed in this paper. In fuzzy logic, an even number of exponential membership functions in the output are considered and their shape, decay rate, and scaling factors are optimized using a genetic algorithm. In this control system, the glide slope capture logic and the flare logic were also included for longitudinal and lateral control, respectively. The nonlinear aircraft model simulation illustrated that the proposed guidance control system shows satisfactory performances in accurate touchdowns and is adequately robust to the strong crosswind and wind-shear turbulences.     

Optimum design of plano-milling machine structure using finite element analysis

The problem of optimum design of plano-milling machine structure is formulated as a nonlinear mathematical programming problem with the objective of minimizing the structural weight. The plano-milling machine structure is idealized with triangular plate elements and three dimensional frame elements based on finite element displacement method. Constraints are placed on static deflections and principal stresses in the problem formulation. The optimization problem is solved by using an interior penalty function method in which the Davidon-Fletcher-Powell variable metric unconstrained minimization technique and cubic interpolation method of one dimensional search are employed. A numerical example is presented for demonstrating the effectiveness of the procedure outlined. The results of sensitivity analysis conducted with respect to design variables and fixed parameters about the optimum point are also reported.     

Improved optimum structural design by passive control

The problem of optimum structural design by passive control is stated in a nonlinear programming form. A solution procedure, based on a successive selection of design and control variables, is presented. Neglecting the implicit analysis equations, the solution becomes independent of the control variables and a lower bound (LB) on the optimum can easily be obtained. The control variables are then selected to satisfy all constraints. If this cannot be achieved, the LB constraints are modified and the control variables are chosen for the revised optimal design. These two steps are repeated until the final optimum is reached.Employing the proposed procedure on various structural systems subjected to static loads showed that the final optimum has been achieved after a very small number of iteration cycles. The numerical examples illustrate a solution with two types of control devices: a linear spring device and a limited displacement device. It has been found that the final optimum is often identical or close to the initial LB solution. Savings of 14 to 63 percent in weight, compared with conventional optima without control, have been demonstrated for some common structures.     

Evaluating and optimizing resilience of airport pavement networks

This paper addresses the problem of assessing and maximizing the resilience of an airport's runway and taxiway network under multiple potential damage-meteorological scenarios. The problem is formulated as a stochastic integer program with recourse and an exact solution methodology based on the integer L-shaped decomposition is proposed for its solution. The formulation seeks an optimal allocation of limited resources to response capabilities and preparedness actions that facilitate them. The overall aim is to quickly restore post-event takeoff and landing capacities to pre-event operational levels taking into account operational, budgetary, time, space, and physical resource limitations. Details, such as aircraft size impacts, reductions in capacity due to joint takeoff and landing maneuvers on common runways or bidirectional flows on taxiways, potential for outsourcing repair work, and multi-team response, are incorporated. The mathematical model and solution methodology are embedded within a decision support tool, the capabilities and applicability of which are demonstrated on an illustrative case study. Potential benefits to airport operators are described, including, for example: the tool's utility in suggesting equipment to have at the ready, identifying the critical pavement system components, and vulnerabilities for prioritizing future facility developments.