Matrix-free aerostructural optimization of aircraft wings

In structural optimization subject to failure constraints, computing the gradients of a large number of functions with respect to a large number of design variables may not be computationally practical. Often, the number of constraints in these optimization problems is reduced using constraint aggregation at the expense of a higher mass of the optimal structural design. This work presents results of structural and coupled aerodynamic and structural design optimization of aircraft wings using a novel matrix-free augmented Lagrangian optimizer. By using a matrix-free optimizer, the computation of the full constraint Jacobian at each iteration is replaced by the computation of a small number of Jacobian-vector products. The low cost of the Jacobian-vector products allows optimization problems with thousands of failure constraints to be solved directly, mitigating the effects of constraint aggregation. The results indicate that the matrix-free optimizer reduces the computational work of solving the optimization problem by an order of magnitude compared to a traditional sequential quadratic programming optimizer. Furthermore, the use of a matrix-free optimizer makes the solution of large multidisciplinary design problems, in which gradient information must be obtained through iterative methods, computationally tractable.     

经验粒子群算法在飞机着陆调度中的应用

为高效解决飞机着陆调度问题,对其离散解空间进行连续化编码,提出经验粒子群（experiential particle swarm optimization , EPSO）算法。提炼飞机着陆调度问题中的领域知识作为每个粒子的经验,优化粒子群算法的寻优过程,增加算法的稳定性。引入控制工程领域中的滚动时域控制（receding horizon control , RHC）策略,在尽量考虑问题完整性的前提下,最大限度降低求解的复杂度,形成最终的RHC‐EPSO算法。实验结果表明,该算法能够比现有算法更加高效和稳定地找到飞机着陆调度问题的最优解。     

Design of aircraft wings subjected to gust loads: A system reliability approach

A method for system reliability-based design of aircraft wing structures is presented. A wing of a light commuter aircraft designed for gust loads according to the FAA regulations is compared with one designed by system reliability optimization. It is shown that system reliability optimization has the potential of improving dramatically the safety and efficiency of new designs. The reasons for the differences between the deterministic and reliability-based designs are explained.     

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.     

舰载机起落架缓冲性能设计优化

为提高舰载机起落架的缓冲性能,采用多体系统仿真和多目标参数优化协同仿真分析相结合的方法,以iSIGHT为设计和仿真平台,在优化参数的同时调用多体系统仿真软件进行仿真分析.对前起落架缓冲系统进行受力分析,用MSC Adams/Aircraft建立某型舰载机起落架落震功能虚拟样机,实现可循环迭代求解落震质量的优化;考虑舰载...     

Reliability-based structural optimization under hazard loads

The present paper studies the reliability-based structural optimization of the civil engineering in the seismic zone. The objective is to minimize the sum of construction material cost and the expected failure loss under severe earthquake, which is obtained by the sum of the products of the failure probability and its failure losses for the important failure modes. The set of constraints includes the deterministic constraints, and the constraints based on structural reliability—the reliability index constraints of structural element failure for the serviceability state under minor earthquake and the failure probability of the structural system for the ultimate limit state under severe earthquake. By introducing the load roughness index, the structural system reliability computation under hazard load can be greatly simplified, which is approximately determined by its weakest failure mode. Finally, the numerical example of high rising shear RC frame is calculated.     

某飞机着陆的数值计算

为合理设计飞机着陆程序,采用数字仿真和高精度计算技术,通过分析飞行实际情况研究起落架、襟翼和地面效应对飞机空气动力特性的影响,建立某飞机着陆的精确数值模型,并用差分法离散该模型.编制数值计算程序实现飞机的地面滑跑和空中运动仿真,并利用该程序进行飞机着陆的数值分析.该研究有利于智能选择飞机最优着陆程序、保障飞行安全、提高...     

Aircraft landing problems with aircraft classes

This article focuses on the aircraft landing problem that is to assign landing times to aircraft approaching the airport under consideration. Each aircraft’s landing time must be in a time interval encompassing a target landing time. If the actual landing time deviates from the target landing time additional costs occur which depend on the amount of earliness and lateness, respectively. The objective is to minimize overall cost. We consider the set of aircraft being partitioned into aircraft classes such that two aircraft of the same class are equal with respect to wake turbulence. We develop algorithms to solve the corresponding problem. Analyzing the worst case run-time behavior, we show that our algorithms run in polynomial time for fairly general cases of the problem. Moreover, we present integer programming models. We show by means of a computational study how optimality properties can be used to increase efficiency of standard solvers.     

求解机场终端区飞机着陆调度问题的遗传算法

空中管制员需为到达的飞机安排跑道并计算着陆时间,以飞机空中延误最小为出发点研究了多跑道的飞机着陆调度问题,约束条件为每架飞机的着陆时间应落在规定的时间窗内及相邻两架飞机应满足最小时间间隔。针对该问题设计了一种遗传算法对问题进行求解,其中染色体由飞机排序链表和跑道链表组成,相应的交叉和变异算子也做了改进设计。仿真实验用数据库OR-Library中的实例验证了该算法的有效性。     

Structural optimization under uncertain loads and nodal locations

This paper presents algorithms for solving structural topology optimization problems with uncertainty in the magnitude and location of the applied loads and with small uncertainty in the location of the structural nodes. The second type of uncertainty would typically arise from fabrication errors where the tolerances for the node locations are small in relation to the length scale of the structural elements. We first review the discrete form of the uncertain loads problem, which has been previously solved using a weighted average of multiple load patterns. With minor modifications, we extend this solution to include loads described by continuous joint probability density functions. We then proceed to the main contribution of this paper: structural optimization under uncertainty in the nodal locations. This optimization problem is computationally difficult because it involves variations of the inverse of the structural stiffness matrix. It is shown, however, that for small uncertainties the problem can be recast into a simpler but equivalent structural optimization problem with equivalent uncertain loads. By expressing these equivalent loads in terms of continuous random variables, we are able to make use of the extended form of the uncertain loads problem presented in the first part of this paper. The optimization algorithms are developed in the context of minimum compliance (maximum stiffness) design. Simple examples are presented. The results demonstrate that load and nodal uncertainties can have dramatic impact on optimal design. For structures containing thin substructures under axial loads, it is shown that these uncertainties (a) are of first-order significance, influencing the linear elastic response quantities, and (b) can affect designs by avoiding unrealistically optimistic and potentially unstable structures. The additional computational cost associated with the uncertainties scales linearly with the number of uncertainties and is insignificant compared to the cost associated with solving the deterministic structural optimization problem.     

进近阶段飞机着陆调度优化

飞机着陆调度问题属于NP-hard问题,文中建立了进近阶段调度模型,在此模型基础上提出了一种改进的遗传算法来求解此问题.该算法基于双染色体编码方案,构建了满足MPS约束的初始种群,给出了启发式选择算子和自适应变异算子.针对多跑道飞机着陆调度问题,提出了随机分配和选择分配两种跑道分配策略.仿真结果表明,该方法能有效地减少飞机着陆调度中的总延迟,使待着陆飞机快速有序地进入机场着陆.     

Multicriteria optimization of cylindrical sandwich shells under combined loads

The paper is about multicriteria optimization of thin-walled cylindrical shells subjected to simple loads, such as axial compression and external pressure, and combined loads (axial compression and pressure). The optimization problem is given as a bicriterial one, with the weight of the shell as the first objective, and the flexibility of the shell as the second. The set of constraints includes the stability condition, strength conditions for each layer, technological and constructional requirements, and so on. Numerical calculations were obtained with the help of the program MOST. MOST is designed to solve multicriteria optimization problems for nonlinear engineering models with discrete and continuous decision variables. In MOST a concept of Pareto optimum is introduced for generating a set of optimal compromise solutions. The best optimal solution must be chosen from the Pareto optimal set with the help of the preference functions. Results of numerical calculations are presented in the form of tables and diagrams.     

Boundary control of flexible aircraft wings for vibration suppression

In this paper, we propose a boundary control strategy for vibration suppression of two flexible wings. As a basic approach, Hamilton's principle is used to ascertain the system dynamic model, which includes governing equations – four partial differential equations and boundary conditions – several ordinary differential equations. Considering the coupled bending and torsional deformations of flexible wings, boundary control force and torque act on the fuselage to regulate unexpected deformations of flexible wings. Then, we present the stability analysis of the closed-loop system through Lyapunov's direct method. Simulations are carried out by using finite difference method. The simulation experimental results illustrate the significant effect of the developed control strategies.     

Interval-based global optimization in engineering using model reformulation and constraint propagation

This paper deals with the preliminary design problem when the product is modeled as an analytic model. The analytic models based method aims to use mathematical equations to address both multi-physic and economic characteristics of a product. The proposed approach is to convert the preliminary design problem into a global constrained optimization problem. The objective is to develop powerful optimization methods enough to handle complex analytical models. We propose to adapt an approach to solve this problem based on interval analysis, constraint propagation and model reformulation. In order to understand the optimization algorithm used for engineering design problems, some basic definitions and properties of interval analysis are introduced. Then, the basic optimization algorithms for both unconstrained and constrained problems are introduced and illustrated. The next section introduces the reformulation technique as main accelerating device. An application of the reformulation device and its global optimization algorithm on the optimal design of electrical actuators is presented.     

Ultra-low risk assessment under the confirmed compliance of automatic aircraft landing characteristics with airworthiness requirements

Two techniques for approximating the tails of the probability distribution of automatic aircraft landing characteristics are considered: an approximation technique based on the Pareto distribution and a spline approximation technique. Computational algorithms designed based on these techniques allow assessing ultra-low risks (on the order of 10^–6–10^–8) under the confirmed compliance of aircraft landing characteristics with airworthiness requirements. The modeling shows good agreement between the results obtained by these techniques, which makes it possible to implement a simpler technique based on the Pareto distribution. This technique reduces the amount of statistical modeling by predicting accuracy characteristics in the unobservable range of their variation.     

An efficient hybrid meta-heuristic for aircraft landing problem

Aircraft landing problem is to assign an airport's runways to the arrival aircrafts as well as to schedule the landing time of these aircrafts. In this paper, first a mixed integer goal programming model is developed. Then, due to the complexity of the problem, which is NP-hard, we design a hybrid meta-heuristic applying simulated annealing framework. The computational results show that the proposed algorithm can obtain the optimal solution for instances up to 100 aircrafts, and also it is capable of finding very high quality and comparable solutions for the problems with up to 500 aircrafts and 5 runways in a short time.     

Fuzzy modelling control for aircraft automatic landing system

Aircraft landing control based on fuzzy modelling networks is presented. The proposed scheme uses a fuzzy controller combined with a linearized inverse aircraft model. A multi-layered fuzzy neural network is used as the controller, providing the control signals at each stage of the aircraft-landing phase. The algorithm used to train the network is the Backpropagation Through Time. The linearized inverse aircraft model provides the error signals that will be used to back-propagate through the controller at each stage. The objective of this study is to improve the performance of conventional automatic landing systems. The simulation results are described for the automatic landing system of a commercial aeroplane. Tracking performance and robustness are demonstrated through software simulations. Simulation results show that the fuzzy controller can successfully expand the safety envelope to include more hostile environments such as severe turbulence.     

Tracking control and robustness analysis for planar vertical takeoff and landing aircraft under bounded feedbacks

We study feedback tracking problems for the planar vertical takeoff and landing (PVTOL) aircraft dynamics, which is a benchmark model in aerospace engineering. We provide a survey of the literature on the model. Then we construct new feedback stabilizers for the PVTOL tracking dynamics. The novelty of our work is in the boundedness of our feedback controllers and their applicability to cases where the velocity measurements may not be available, coupled with the uniform global asymptotic stability and uniform local exponential stability of the closed‐loop tracking dynamics and the input‐to‐state stable performance of the closed‐loop tracking dynamics with respect to actuator errors. Our proofs are based on a new bounded backstepping result. We illustrate our work in a tracking problem along a circle. Copyright © 2011 John Wiley & Sons, Ltd.     

An efficient hybrid particle swarm optimization algorithm in a rolling horizon framework for the aircraft landing problem

This paper proposes a hybrid particle swarm optimization algorithm in a rolling horizon framework to solve the aircraft landing problem (ALP). ALP is an important optimization problem in air traffic control and is well known as NP-hard. The problem consists of allocating the arriving aircrafts to runways at an airport and assigning a landing time to each aircraft. Each aircraft has an optimum target landing time determined based on its most fuel-efficient airspeed and a deviation from it incurs a penalty which is proportional to the amount of deviation. The landing time of each aircraft is constrained within a specified time window and must satisfy minimum separation time requirement with its preceding aircrafts. The objective is to minimize the total penalty cost due to deviation of landing times of aircrafts from the respective target landing times. The performance of the proposed algorithm is evaluated on a set of benchmark instances involving upto 500 aircrafts and 5 runways. Computational results reveal that the proposed algorithm is effective in solving the problem in short computational time.