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MULTIOBJECTIVE TRAJECTORY OPTIMIZATION BY GOAL programming WITH FUZZY DECISIONS

JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1994年第2期17卷 297-303页

作者： SUZUKI, S YOSHIZAWA, T University of Tokyo Bunkyo-ku Tokyo 113 Japan

A sequential goal programming approach is considered for not only well-defined flight trajectory problems but also ill-defined problems that have no feasible solutions satisfying all design requirements due to strict boundary conditions or tight path constraints. By using a time integration algorithm, trajectory optimization problems am transformed into numerical optimization problems that seek optimal control variables at discrete time points to minimize an objective function and satisfy various design constraints. By defining the target goal values of both the constraints and the objective functions and by prioritizing each goal according to its significance, the GP formulation modifies ill-defined problems as multiobjective design problems. Additionally, a fuzzy decision making method is applied for those goals that are prioritized, not precisely, but in a fuzzy manner. Numerical applications for simple ascent trajectory problems show that this method can efficiently find the trajectories when various kinds of design requirements are imposed for the ill-defined problem.

关键词： Trajectory Optimization Flight Trajectory Numerical Optimization Integration Algorithm sequential quadratic programming Control Optimization sequential Linear programming Propellant Finite Difference Method Interplanetary Mission

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Efficient shape optimization under uncertainty using polynomial chaos expansions and local sensitivities

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AIAA JOURNAL 2006年第5期44卷 1112-1116页

作者： Kim, NH Wang, HY Queipo, NV Univ Florida Dept Mech & Aerosp Engn Gainesville FL 32606 USA Univ Zulia Fac Engn Appl Comp Inst Maracaibo 4011 Venezuela

An efficient reliability-based design optimization (RBDO) technique addressing the issues based on stochastic response surface (SRS) constructed using outputs at heuristically selected collocation points is presented. The proposed SRS is a polynomial chaos expansion and provides a convergent and robust uncertainty propagation scheme. The accuracy, efficiency, and convergence of the method for RBDO are depicted using a benchmark problem related to the RBRO of a structural part. The efficiency of the proposed SRS is improved using local sensitivity information. It was found that as the nonlinearity of the problem increases, the errors using the traditional moment-based methods are expected to increase, but the accuracy of the method can still be maintained.

关键词： Shape Optimization Cumulative Distribution Function Sensitivity Analysis Finite Element Analysis Monte Carlo Simulation sequential quadratic programming Numerical Modeling Material Derivatives Tolerance Analysis Poisson's Ratio

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Performance of an Autonomous Multi-Maneuver Algorithm for Lunar Trans-Earth Injection

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JOURNAL OF SPACECRAFT AND ROCKETS 2012年第1期49卷 165-174页

作者： Whitley, Ryan J. Ocampo, Cesar A. Williams, Jacob NASA Johnson Space Ctr Houston TX 77068 USA Univ Texas Austin Dept Aerosp Engn & Engn Mech Austin TX 78712 USA ERC Inc ESCG Houston TX 77058 USA

Using a fully analytic initial estimate, a self-starting algorithm that constructs a flyable multiburn maneuver sequence to transfer a spacecraft from a closed low-lunar parking orbit to a desired Earth-entry state is developed and implemented. The algorithm is built to support the need for a human spacecraft to abort anytime during the mission and return automatically from a variety of lunar mission scenarios. This study presents a large set of representative test cases for algorithm evaluation, including highly constrained Earth-entry interface states that return the spacecraft to a specific landing site. For all cases, an optimal finite-burn solution is obtained successfully in computation time suitable for real-time on-board operation.

关键词： Trans Earth Injection Earth Propellant Elliptical Orbit Flight Path Angle sequential quadratic programming Lift to Drag Ratio Thrust to Weight Ratio Algorithm Performance Search Algorithm

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Surrogate-Assisted Differential Evolution Using Knowledge-Transfer-Based Sampling for Expensive Optimization Problems

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AIAA JOURNAL 2022年第5期60卷 3251-3266页

作者： Long, Teng Ye, Nianhui Shi, Renhe Wu, Yufei Tang, Yifan Beijing Inst Technol Sch Aerosp Engn Beijing Peoples R China Beijing Inst Technol Key Lab Dynam & Control Flight Vehicle Minist Educ Beijing 100081 Peoples R China Simon Fraser Univ Sch Mech Syst Engn Surrey BC V3T 0A3 Canada

To sufficiently reuse the knowledge from previous optimization efforts, a surrogate-assisted differential evolution using knowledge-transfer-based sampling (denoted as SADE-KTS) method is proposed for solving expensive black-box optimization problems. In SADE-KTS, a novel knowledge-transfer-based sampling method is integrated with the differential evolution framework to generate promising initial sample points. In this way, a least-squares support vector machine classifier is constructed based on the prior optimization knowledge database to calibrate the initial sample points adaptively, which improves the exploration performance via transferring the existed optimization efforts to the current optimization task. Moreover, the radial basis function and kriging surrogates are employed to replace the expensive simulation models for evolutionary operations, where the tailored differential evolution operators are cooperated with the sequential quadratic programming optimizer to lead the search to the global optimum efficiently. A number of numerical benchmarks are tested to illustrate the optimization capacity of SADE-KTS compared with several competitive optimization algorithms. Finally, SADE-KTS is applied to an airfoil aerodynamic knowledge-based optimization problem considering the existed optimization knowledge, which demonstrates the practicality and effectiveness of the proposed SADE-KTS in engineering practices.

关键词： Airfoil sequential quadratic programming Support Vector Machine Black Box Numerical Simulation Multi Objective Evolutionary Algorithms Lagrange Multipliers Lift Coefficient Finite Element Analysis Multidisciplinary Design Optimization

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Design "feasilization" using knowledge-based engineering and optimization techniques

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JOURNAL OF AIRCRAFT 2007年第6期44卷 1776-1786页

作者： Schut, E. J. van Tooren, M. J. L. Delft Univ Technol Fac Aerosp Engn NL-2629 HS Delft Netherlands

The multidisciplinary design optimization process can be supported by partial automation of analysis and optimization steps. Design-and-engineering engines are a useful concept to structure this automation. Within the design-and-engineering engines, a product is parametrically defined using knowledge-based engineering. This parametric product model needs to be initiated before global multidisciplinary optimization can be performed. The "feasilization" is done by the initiator component in the design-and-engineering engines that simulates the heuristic methods normally used by designers to estimate the first values for the parameters and variables describing their designs. The initiation of values for structural parameters and variables is elaborated for a sample composite-stiffened panel structure. It is shown that the initiator function of the design-and-engineering-engine concept can be implemented on the basis of optimization techniques using sirnplification of the design requirements, simplified representations of the design options, and the class of so-called schematic models to mimic the designer's job in the preliminary sizing phase of the design. An implementation of the initiator is used in a sample design-and-engineering engine for aircraft vertical tail design.

关键词： Finite Element Modeling Buckling Analysis Aircraft Configurations Nastran Maximum Shear Stresses sequential quadratic programming Multidisciplinary Design Optimization Structural Response Wing Configurations Airbus

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Stochastic transfer function model and neural networks to estimate soil moisture

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JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION 2008年第4期44卷 847-865页

作者： Ramirez-Beltran, Nazarto D. Castro, Joan Manuel Harmsen, Eric Vasquez, Ramon Univ Puerto Rico Dept Ind Engn Mayaguez PR 00680 USA Univ Puerto Rico Dept Elect & Comp Engn Mayaguez PR 00680 USA UPRM Dept Agr & Biosyst Engn Mayaguez PR 00680 USA

A practical methodology is proposed to estimate the three-dimensional variability of soil moisture based on a stochastic transfer function model, which is an approximation of the Richard's equation. Satellite, radar and in situ observations are the major sources of information to develop a model that represents the dynamic water content in the soil. The soil-moisture observations were collected from 17 stations located in Puerto Rico (PR), and a sequential quadratic programming algorithm was used to estimate the parameters of the transfer function (TF) at each station. Soil texture information, terrain elevation, vegetation index, surface temperature, and accumulated rainfall for every grid cell were input into a self-organized artificial neural network to identify similarities on terrain spatial variability and to determine the TF that best resembles the properties of a particular grid point. Soil moisture observed at 20 cm depth, soil texture, and cumulative rainfall were also used to train a feedforward artificial neural network to estimate soil moisture at 5, 10, 50, and 100 em depth. A validation procedure was implemented to measure the horizontal and vertical estimation accuracy of soil moisture. Validation results from spatial and temporal variation of volumetric water content (vwc) showed that the proposed algorithm estimated soil moisture with a root mean squared error (RMSE) of 2.31% vwc, and the vertical profile shows a RMSE of 2.50% vwc. The algorithm estimates soil moisture in an hourly basis at I km spatial resolution, and up to I in depth, and was successfully applied under PR climate conditions.

关键词： soil moisture transfer function neural networks sequential quadratic programming vertical profile

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Targeting Ballistic Lunar Capture Trajectories Using Periodic Orbits

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2011年第3期34卷 893-902页

作者： Griesemer, Paul Ricord Ocampo, Cesar Cooley, D. S. Univ Texas Austin Dept Aerosp Engn & Engn Mech Austin TX 78712 USA NASA Goddard Space Flight Ctr Nav & Miss Design Branch Greenbelt MD 20771 USA

A particular periodic orbit in the Earth sun circular restricted three-body problem is shown to have the characteristics needed for a ballistic lunar capture transfer. An injection from a circular parking orbit into the periodic orbit serves as an initial guess for a nonlinear targeting algorithm. By targeting appropriate parameters incrementally in increasingly complicated force models and using precise derivatives calculated from the state transition matrix, a reliable algorithm is produced. Ballistic lunar capture trajectories in restricted four-body systems are produced in a systematic way.

关键词： Moon Earth Elliptical Orbit Libration Points Ecliptic Targeting Algorithms Low Energy Transfer Perigee sequential quadratic programming Orbital Elements

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Flight path optimization passing through waypoints for autonomous flight control systems

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ENGINEERING OPTIMIZATION 2005年第7期37卷 755-774页

作者： Moon, G Kim, Y Seoul Natl Univ Sch Mech & Aerosp Engn Seoul 151742 South Korea

Trajectory optimization is performed to generate a flight path passing specified waypoints. To deal with the unspecified time of passing through a waypoint, an auxiliary variable is introduced. Normalization of the time variable by the auxiliary variable transforms the waypoint optimization problem into the conventional optimization problem. The condition for passing through the waypoints can be relaxed, so that the vehicle passes specified waypoints within a certain acceptable range. sequential quadratic programming is used to solve the optimization problem. As a numerical example, six degree-of-freedom vehicle dynamics is considered. Two-dimensional and three-dimensional trajectory optimization problems with several waypoints are solved to verify the effectiveness of the proposed algorithm.

关键词： trajectory optimization flight path design waypoint guidance sequential quadratic programming autonomous flight

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Variational Equations for a Generalized Spacecraft Trajectory Model

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2010年第5期33卷 1615-1622页

作者： Ocampo, Cesar Munoz, Jean-Philippe Univ Texas Austin Dept Aerosp Engn & Engn Mech Austin TX 78712 USA

Linear perturbation theory is used to develop the variational equations needed to determine the sensitivities of the state at some final time with respect to all of the independent variables associated with a spacecraft trajectory model that is general enough for most applications of interest. The state vector is an augmented vector that includes the position, velocity, mass, and all other control-related variables, such as thrust magnitude and direction. The force model is general and the trajectory can have any number of impulsive and/or finite burn maneuvers. The gradient expressions depend, in part, on the system state transition matrix associated with the given state and its corresponding equations of motion. As an example, the procedure developed is applied to the numerical optimization of a multi-impulse escape trajectory from the moon.

关键词： Interplanetary Trajectories sequential quadratic programming Periapsis Numerical Optimization Parking Orbit Earth Finite Difference Approximation Perturbation Theory Exhaust Velocity Optimal Control

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Slotted Waveguide Stress Concentration Factor

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AIAA JOURNAL 2022年第6期60卷 3844-3851页

作者： Brooks, Joseph Canfield, Robert A. Virginia Polytech Inst & State Univ Kevin T Crofton Dept Aerosp & Ocean Engn Randolph Room 215460 Old Turner St Blacksburg VA 24061 USA Virginia Polytech Inst & State Univ Kevin T Crofton Dept Aerosp & Ocean Engn 460 Old Turner StMS 0203 Blacksburg VA 24061 USA

Sharp turns or corners within a structure lead to local failures well before the rest of the structure due to the creation of stress concentrations. For a load-bearing waveguide, these occur at the corners of the slots. After modeling a test waveguide, a bivariate curve fit was created to model these stress concentrations, based on four configurations for a single slot length, then refined into a trivariate form based on an expanded eight cases across two slot lengths. Once properly formatted, the integration of the bivariate function into an optimization allowed stress concentration to be estimated at the slot corners within a coarse low-fidelity model, rather than the high-fidelity model otherwise required, following the expected behavior and acting as a verification case. Implementation of the full trivariate form into a design optimization enabled use of the concentration factor to estimate the critical stress. The study showed that the inset copper waveguide could not be loaded from the outset, and that an offset of the copper waveguide could avoid overloading it.

关键词： Stress Concentration Finite Element Modeling Compressive Stress Factor of Safety MATLAB sequential quadratic programming Numerical Modeling Aircraft Wings Shear Modulus Comsol Multiphysics

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