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Interactive multiobjective optimization procedure

AIAA JOURNAL 1999年第7期37卷 881-889页

作者： Tappeta, RV Renaud, JE Univ Notre Dame Notre Dame IN 46556 USA

This research focuses on multiobjective system design and optimization. The primary goal is to develop and test a mathematically rigorous and efficient interactive multiobjective optimization algorithm that takes into account the designer's preferences during the design process. In this research, an interactive multiobjective optimization procedure (IMOOP) that uses an aspiration-level approach to generate Pareto points Is developed. This method provides the designer or the decision maker (DM) with a formal means for efficient design exploration around a given Pareto point. More specifically, the procedure provides the DM with the Pareto sensitivity information and the Pareto surface approximation at a given Pareto design for decision making and tradeoff analysis. The IMOOP has been successfully applied to two test problems. The first problem consists of a set of simple analytical expressions for its objective and constraints. The second problem is the design and sizing of a high-performance and low-cost Ill-bar structure that has multiple objectives. The results indicate that the Pareto designs predicted by the Pareto surface approximation are reasonable and the performance of the second-order approximation is superior compared to that of the first-order approximation. Using this procedure a set of new aspirations that reflect the DM's preferences are easily and efficiently generated, and the new Pareto design corresponding to these aspirations is close to the aspirations themselves. This is important in that it builds the confidence of the DM in this interactive procedure for obtaining a satisfactory final Pareto design in a minimal number of iterations.

关键词： sequential quadratic programming Sensitivity Analysis Pareto Optimality Elastic Structure Aerodynamics Trusses Aircraft Configurations Genetic Algorithm Structural Design Structural Weight

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Supervised vs Unsupervised Learning for Operator State Modeling in Unmanned Vehicle Settings

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JOURNAL OF AEROSPACE COMPUTING INFORMATION AND COMMUNICATION 2011年第3期8卷 71-85页

作者： Boussemart, Yves Cummings, Mary L. Fargeas, Jonathan Las Roy, Nicholas MIT Engn Syst Div Humans & Automat Lab Cambridge MA 02139 USA MIT Dept Aeronaut & Astronaut Humans & Automat Lab Cambridge MA 02139 USA MIT Comp Sci & Artificial Intelligence Lab Humans & Automat Lab Cambridge MA 02139 USA

In this paper, we model operator states using hidden Markov models applied to human supervisory control behaviors. More specifically, we model the behavior of an operator of multiple heterogeneous unmanned vehicle systems. The hidden Markov model framework allows the inference of higher operator states from observable operator interaction with a computer interface. For example, a sequence of operator actions can be used to compute a probability distribution of possible operator states. Such models are capable of detecting deviations from expected operator behavior as learned by the model. The difficulty with parametric inference models such as hidden Markov models is that a large number of parameters must either be specified by hand or learned from example data. We compare the behavioral models obtained with two different supervised learning techniques and an unsupervised hidden Markov model training technique. The results suggest that the best models of human supervisory control behavior are obtained through unsupervised learning. We conclude by presenting further extensions to this work.

关键词： Multiple Heterogeneous Unmanned Vehicles High Altitude Long Endurance Unmanned System Probability Density Functions sequential quadratic programming Dynamic programming Algorithm Air Traffic Control Machine Learning Command and Control Systems Discrete Event Simulation

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Nonlinear Optimal Control Analysis Using State-Dependent Matrix Exponential and Its Integrals

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2009年第1期32卷 309-313页

作者： Kim, Chang-Joo Park, Soo Hyung Sung, Sang Kyung Jung, Sung-Nam Konkuk Univ Seoul 14370 South Korea

A method was proposed for estimating the Karush-Kuhn-Tucker (KKT) system using the state-dependent matrix exponential and its weighted integrals. The state-dependent coefficient (SDC) factorization method was used in this method to obtain a linear system structure from the nonlinear motion equation. The KKT system was developed using the linear system theory to the SDC form of equations without resorting to any time integration and finite difference formula. It was revealed that the applications of this method to the rotorcraft trajectory tracking problem improved the convergence and the accuracy of the direct-multiple shooting (DMS) method. The proposed method also provided excellent numerical accuracy and faster convergence because its removed numerical errors of the time integrator and the finite difference formula.

关键词： Optimal Control Nonlinear Systems State Dependent Riccati Equation Nonlinear programming sequential quadratic programming Runge Kutta Methods Rotorcrafts Finite Difference Approximation Collective Pitch Control Linear System Theory

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A novel computing stochastic algorithm to solve the nonlinear singular periodic boundary value problems

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2022年第10期99卷 2091-2104页

作者： Sabir, Zulqurnain Baleanu, Dumitru Ali, Mohamed R. Sadat, R. Hazara Univ Dept Math & Stat Mansehra Pakistan Cankaya Univ Dept Math Ankara Romania Inst Space Sci Magurele Romania Future Univ Fac Engn & Technol Cairo Egypt Benha Univ Fac Engn Benha Dept Basic Sci Banha Egypt Zagazig Univ Zagazig Fac Engn Dept Math Zagazig Egypt

In this work, a class of singular periodic nonlinear differential systems (SP-NDS) in nuclear physics is numerically treated by using a novel computing approach based on the Gudermannian neural networks (GNNs) optimized by the mutual strength of global and local search abilities of genetic algorithms (GA) and sequential quadratic programming (SQP), i.e. GNNs-GA-SQP. The stimulation of offering this numerical computing work comes from the aim of introducing a consistent framework that has an effective structure of GNNs optimized with the backgrounds of soft computing to tackle such thought-provoking systems. Two different problems based on the SPNDS in nuclear physics will be examined to check the proficiency, robustness and constancy of the GNNs-GA-SQP. The outcomes obtained through GNNs-GA-SQP are compared with the true results to find the worth of designed procedures based on the multiple trials.

关键词： Periodic singular systems nuclear physics genetic algorithm sequential quadratic programming Gudermannian neural networks

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Pseudospectral methods for infinite-horizon optimal control problems

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2008年第4期31卷 927-936页

作者： Fahroo, Fariba Ross, I. Michael USN Postgrad Sch Dept Appl Math Monterey CA 93943 USA USN Postgrad Sch Dept Mech & Astronaut Engn Monterey CA 93943 USA

A central computational issue in solving infinite-horizon nonlinear optimal control problems is the treatment of the horizon. In this paper, we directly address this issue by a domain transformation technique that maps the infinite horizon to a finite horizon. The transformed finite horizon serves as the computational domain for an application of pseudospectral methods. Although any pseudospectral method may be used, we focus on the Legendre pseudospectral method. It is shown that the proper class of Legendre pseudospectral methods to solve infinite-horizon problems are the Radau-based methods with weighted interpolants. This is in sharp contrast to the unweighted pseudospectral techniques for optimal control. The Legendre-Gauss-Radau pseudospectral method is thus developed to solve nonlinear constrained optimal control problems. An application of the covector mapping principle for the Legendre-Gauss-Radau pseudospectral method generates a covector mapping theorem that provides an efficient approach for the verification and validation of the extremality of the computed solution. Several example problems are solved to illustrate the ideas.

关键词： Chebyshev Pseudospectral Method Algebraic Riccati Equation Nonlinear Control Model Predictive Control Gaussian Quadrature sequential quadratic programming Boundary Value Problems Feedback Control Quaternions International Space Station

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Extraction of substructural flexibility from global frequencies and mode shapes

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AIAA JOURNAL 1999年第11期37卷 1444-1451页

作者： Alvin, KF Park, KC Sandia Natl Labs Struct Dynam & Vibrat Control Dept Albuquerque NM 87185 USA Univ Colorado Dept Aerosp Engn Sci Boulder CO 80309 USA Univ Colorado Ctr Aerosp Struct Boulder CO 80309 USA

A computational procedure for extracting substructure-by-substructure flexibility properties from global modal parameters is presented. The present procedure consists of two key features: an element-based direct flexibility method, which uniquely determines the global flexibility without resorting to case-dependent redundancy selections, and the projection of kinematically inadmissible modes that are contained in the iterated substructural matrices. The direct flexibility. method is used as the basis of an inverse problem, whose goal is to determine substructural flexibilities given the global flexibility;geometrically determined substructural rigid-body modes, and the local to global assembly operators. The resulting procedure, given accurate global flexibility, extracts the exact element-by-element substructural flexibilities for determinate structures. For indeterminate structures, the accuracy depends on the iteration tolerance limits. The procedure is illustrated using both simple and complex numerical examples and appears to be effective for structural applications such as damage localization and finite element model reconciliation.

关键词： Finite Element Modeling Matrix Stiffness Method Inverse Problems Structural Modeling Lagrange Multipliers sequential quadratic programming Structural Vibration Computing Frequency Response Functions Structural Integrity

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OPTIMIZATION METHODS FOR PASSIVE DAMPER PLACEMENT AND TUNING

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1994年第4期17卷 848-856页

作者： MILMAN, MH CHU, CC California Institute of Technology Pasadena California 91109

The effectiveness of viscous elements in introducing damping in a structure is a function of several variables including their number, their location in the structure, and their physical properties. This paper addresses the questions of the placement of these elements and the selection of their physical parameters via optimization techniques. The paper investigates various metrics to define these optimization problems and compares the damping profiles that are obtained. Both discrete and continuous optimization problems are formulated and solved corresponding, respectively, to the problems of placement of damping elements and to the tuning of their parameters. Particular emphasis is placed on techniques to make feasible the large-scale problems resulting from the optimization formulations. Numerical results involving a lightly damped testbed structure are presented.

关键词： sequential quadratic programming Transient Response Computing Annealing Process Newton's Method Stiffness Matrices Resonant Frequencies Finite Difference Approximation Singular Value Decomposition Jet Propulsion Laboratory

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Nodal temperature estimation algorithms for nonlinear thermal network models

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AIAA JOURNAL 2002年第7期40卷 1451-1461页

作者： Papalexandris, MV Milman, MH Levine, MB CALTECH Jet Prop Lab Pasadena CA 91109 USA

Algorithms for estimating temperatures at arbitrary nodes of steady-state thermal network models, given noisy measured values of a subset of the nodes of the network, are described. Applications where temperature estimation is desired include correlation of test and analysis results, thermal-stress estimation, and others. An optimization problem is formulated to recover the temperatures at the unobservable nodes. This problem is an example of nonlinear, least-squares minimization with a single quadratic constraint (imposed by the measured data) and is solved with the method of Lagrange multipliers. New algorithms are developed that find local minima of the cost functional through a Newton-type iteration procedure. At each iteration a least-squares problem with a quadratic inequality is solved with a fast and memory-efficient method. The proposed algorithms are shown to be at least an order of magnitude faster than standard algorithms. Their accuracy and speed are examined through a series of tests on thermal models from ongoing NASA missions.

关键词： Thermal Modeling Lagrange Multipliers Thermal Stresses sequential quadratic programming Singular Value Decomposition Stiffness Matrices Telescopes Nonlinear programming Space Interferometry Mission Conduction

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Truss optimization on shape and sizing with frequency constraints

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AIAA JOURNAL 2004年第3期42卷 622-630页

作者： Wang, D Zhang, WH Jiang, JS Northwestern Polytech Univ Dept Aircraft Engn Xian 710072 Peoples R China Northwestern Polytech Univ Dept Aircraft Mfg & Engn Xian 710072 Peoples R China Northwestern Polytech Univ Inst Vibrat Engn Xian 710072 Peoples R China

An optimality criteria algorithm is presented for three-dimentional truss structure optimization with multiple constraints on its natural frequencies. Both nodal coordinates and element cross-sectional areas, which are quite different in their natures, are treated simultaneously in a unified design space for structural weight minimization. First the optimality criterion is developed for a single constraint based on differentiation of the Lagrangian function. It states that, at the optimum, all of the variables should have equal efficiencies. Then, the global sensitivity numbers are introduced to solve multiple constraints of frequencies, avoiding computation of the Lagrange multipliers. Finally, upon the sensitivity analysis, the most efficient variables are identified and modified in priority. The optimal solution is achieved gradually from the initial design with a minimum weight increment. Four typical trusses are used to demonstrate the feasibility and validity of the proposed method.

关键词： Planar Truss Structural Weight Sensitivity Analysis Lagrange Multipliers Young's Modulus Finite Element Method sequential quadratic programming Dynamic Analysis Shape Optimization Dynamic Response

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MULTIDISCIPLINARY OPTIMIZATION IN AIRCRAFT DESIGN USING ANALYTIC TECHNOLOGY MODELS

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JOURNAL OF AIRCRAFT 1995年第2期32卷 431-438页

作者： MALONE, B MASON, WH Virginia Polytechnic Institute and State University Blacksburg Virginia 24061

An approach to multidisciplinary optimization is presented that combines the global sensitivity equation method, parametric optimization, and analytic technology models. The result is a powerful yet simple procedure for identifying key design issues. It can be used both to investigate technology integration issues very early in the design cycle, and to establish the information flow framework between disciplines for use in multidisciplinary optimization projects using much more computationally intense representations of each technology. To illustrate the approach, an examination of the optimization of a short-takeoff, heavy transport aircraft is presented for numerous combinations of performance and technology constraints. The results show explicitly the takeoff weight penalty for transonic cruise Mach number and the wing sweep variation with cruise Mach number. Conceptual designs can be optimized rapidly with this approach.

关键词： Aircraft Design Drag Divergence Mach Number Transport Aircraft High Aspect Ratio Lift Coefficient Thrust to Weight Ratio Variable Sweep Wings Aircraft Sizing sequential quadratic programming Structural Weight

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