Analysis and comparison of several numerical optimization methods.
Numerical method solution of nonlinear two- point boundary value problem associated with optimum transfer of spacecraft
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A new approach to mixed H2/H infinity controller synthesis using gradient-based parameter optimization methods
In the past few years, the mixed H(sub 2)/H-infinity control problem has been the object of much research interest since it allows the incorporation of robust stability into the LQG framework. The general mixed H(sub 2)/H-infinity design problem has yet to be solved analytically. Numerous schemes have considered upper bounds for the H(sub 2)-performance criterion and/or imposed restrictive constraints on the class of systems under investigation. Furthermore, many modern control applications rely on dynamic models obtained from finite-element analysis and thus involve high-order plant models. Hence the capability to design low-order (fixed-order) controllers is of great importance. In this research a new design method was developed that optimizes the exact H(sub 2)-norm of a certain subsystem subject to robust stability in terms of H-infinity constraints and a minimal number of system assumptions. The derived algorithm is based on a differentiable scalar time-domain penalty function to represent the H-infinity constraints in the overall optimization. The scheme is capable of handling multiple plant conditions and hence multiple performance criteria and H-infinity constraints and incorporates additional constraints such as fixed-order and/or fixed structure controllers. The defined penalty function is applicable to any constraint that is expressible in form of a real symmetric matrix-inequity.
Ly, Uy-Loi↗
Trajectory Optimization Methods and Applications at NASA Goddard
The process of spacecraft trajectory design frequently incorporates an optimization step in which one or more objectives, such as propellant consumption or time of flight, is minimized. Optimization is especially crucial for low-thrust mission design, due to the need to specify a thrust vector at every instant in time along a trajectory. At NASA's Goddard Space Flight Center (GSFC) a number of open-source tools have been developed for spacecraft trajectory optimization that utilize direct shooting and collocation methods. These tools have been effectively applied to cislunar, libration point, and interplanetary mission design for the Lunar IceCube, SWFO, and DAVINCI missions, among others. This presentation outlines the theory underlying these optimization tools along with the details of their application to several trajectory design problems, with a focus on the Lunar IceCube (LIC) mission. The LIC mission required a low-thrust trajectory from a high-energy deployment state to a lunar orbit, and its limited control authority necessitated the use of optimization tools and low-energy trajectory design techniques. The tools discussed demonstrate how the use of optimization methods expands mission capabilities and enables transformational science.
Robert Pritchett↗
A decomposition-based design optimization method with applications
A two-level design optimization metholology is described. A progress report of its application to Printed Wiring Board (PWB) assembly examples is given. The design of PWB assemblies is a complex task which is generally conducted as a sequential process. Individual PWBs are usually designed first, followed by the composition of the PWBs into an assembly. As a result, optimizing design considerations such as assembly reliability cannot be accomplished. This study showed that a two-level decomposition method can be employed to optimize for reliability at both the PWB- and the assembly-level in a coupled manner. The two-level decomposition method also resolved the mixed-integer nonlinear programming nature of the problem rather easily.
Azarm, Shapour↗
Multidisciplinary Optimization Methods for Aircraft Preliminary Design
This paper describes a research program aimed at improved methods for multidisciplinary design and optimization of large-scale aeronautical systems. The research involves new approaches to system decomposition, interdisciplinary communication, and methods of exploiting coarse-grained parallelism for analysis and optimization. A new architecture, that involves a tight coupling between optimization and analysis, is intended to improve efficiency while simplifying the structure of multidisciplinary, computation-intensive design problems involving many analysis disciplines and perhaps hundreds of design variables. Work in two areas is described here: system decomposition using compatibility constraints to simplify the analysis structure and take advantage of coarse-grained parallelism; and collaborative optimization, a decomposition of the optimization process to permit parallel design and to simplify interdisciplinary communication requirements.
Kroo, Ilan↗
Application of multidisciplinary optimization methods to the design of a supersonic transport
A new optimization based design method is discussed. This method is based on integrating existing disciplinary analysis and sensitivity analysis techniques by means of generalized sensitivity equations. A generic design system implementing this method is described. The system is being used to design the configuration and internal structure of a supersonic transport wing for optimum performance. This problem combines the disciplines of linear aerodynamics, structures, and performance. Initial results which include the disciplines of aerodynamics and structures in a conventional minimum weight design under static aeroelastic constraints are presented.
Barthelemy, J.-F. M.↗
Optimization methods and silicon solar cell numerical models
An optimization algorithm for use with numerical silicon solar cell models was developed. By coupling an optimization algorithm with a solar cell model, it is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junction depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm was developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAP1D). SCAP1D uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the performance of a solar cell. A major obstacle is that the numerical methods used in SCAP1D require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the values associated with the maximum efficiency. This problem was alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution.
Girardini, K.↗
Improved Optimization Method for Array Feed Calculations
Reflector antenna optimization schemes using array feeds have been used to recover antenna losses resulting from antenna distortions and aberrations and to generate contour coverage patterns.
focal plane array feed antennas gain optimization ↗
A Knowledge-Based Optimization Method for Aerodynamic Design
A new aerodynamic design method, CODISC, has been developed that combines a legacy knowledge-based design method, CDISC, with a simple optimization module known as SOUP. The primary goal of this new design system is to improve the performance gains obtained using CDISC without adding significant computational time. An additional objective of this approach is to reduce the need for a priori knowledge of good initial input variable values, as well as for subsequent manual revisions of those values as the design progresses. Several test cases illustrate the development of the process to date and some of the options available at transonic and supersonic speeds for turbulent flow designs. The test cases generally start from good baseline configurations and, in all cases, were able to improve the performance. Several new guidelines for good initial values for the design variables, as well as new design rules within CDISC itself, were developed from these cases.
SOUP↗
Development of a Knowledge-Based Optimization Method for Aerodynamic Design
A new aerodynamic design method, CODISC, has been developed that combines an existing knowledgebased design method, CDISC, with a simple optimization module known as SOUP. The primary goal of this new design system is to improve the performance gains obtained using CDISC without adding significant computational time. An additional benefit of this approach is a reduction in the need for a priori knowledge of good initial input variable values as well as for subsequent manual revisions of those values as the design progresses. A series of 2D and 3D test cases are used to illustrate the development of the process and some of the options available at transonic and supersonic speeds for both laminar and turbulent flow. The test cases start from good baseline configurations and, in all cases, were able to improve the performance. Several new guidelines for good initial values for the design variables, as well new design rules within CDISC itself, were developed from these cases.
Campbell, Richard L.↗
Multidisciplinary Optimization Methods for Preliminary Design
An overview of multidisciplinary optimization (MDO) methodology and two applications of this methodology to the preliminary design phase are presented. These applications are being undertaken to improve, develop, validate and demonstrate MDO methods. Each is presented to illustrate different aspects of this methodology. The first application is an MDO preliminary design problem for defining the geometry and structure of an aerospike nozzle of a linear aerospike rocket engine. The second application demonstrates the use of the Framework for Interdisciplinary Design Optimization (FIDO), which is a computational environment system, by solving a preliminary design problem for a High-Speed Civil Transport (HSCT). The two sample problems illustrate the advantages to performing preliminary design with an MDO process.
Korte, J. J.↗
A Requirements-Driven Optimization Method for Acoustic Liners Using Analytic Derivatives
More than ever, there is flexibility and freedom in acoustic liner design. Subject to practical considerations, liner design variables may be manipulated to achieve a target attenuation spectrum. But characteristics of the ideal attenuation spectrum can be difficult to know. Many multidisciplinary system effects govern how engine noise sources contribute to community noise. Given a hardwall fan noise source to be suppressed, and using an analytical certification noise model to compute a community noise measure of merit, the optimal attenuation spectrum can be derived using multidisciplinary systems analysis methods. In a previous paper on this subject, a method deriving the ideal target attenuation spectrum that minimizes noise perceived by observers on the ground was described. A simple code-wrapping approach was used to evaluate a community noise objective function for an external optimizer. Gradients were evaluated using a finite difference formula. The subject of this paper is an application of analytic derivatives that supply precise gradients to an optimization process. Analytic derivatives improve the efficiency and accuracy of gradient-based optimization methods and allow consideration of more design variables. In addition, the benefit of variable impedance liners is explored using a multi-objective optimization.
Aircraft Noise↗
Application of an impulsive trajectory optimization method to the comet rendezvous problem
Multiple impulsive spacecraft trajectory optimization technique application to comet rendezvous problem, using computer program
Waters, J. I.↗
Flow analysis and design optimization methods for nozzle afterbody of a hypersonic vehicle
This report summarizes the methods developed for the aerodynamic analysis and the shape optimization of the nozzle-afterbody section of a hypersonic vehicle. Initially, exhaust gases were assumed to be air. Internal-external flows around a single scramjet module were analyzed by solving the three dimensional Navier-Stokes equations. Then, exhaust gases were simulated by a cold mixture of Freon and Argon. Two different models were used to compute these multispecies flows as they mixed with the hypersonic airflow. Surface and off-surface properties were successfully compared with the experimental data. In the second phase of this project, the Aerodynamic Design Optimization with Sensitivity analysis (ADOS) was developed. Pre and post optimization sensitivity coefficients were derived and used in this quasi-analytical method. These coefficients were also used to predict inexpensively the flow field around a changed shape when the flow field of an unchanged shape was given. Starting with totally arbitrary initial afterbody shapes, independent computations were converged to the same optimum shape, which rendered the maximum axial thrust.
Baysal, Oktay↗
Flow analysis and design optimization methods for nozzle-afterbody of a hypersonic vehicle
This report summarizes the methods developed for the aerodynamic analysis and the shape optimization of the nozzle-afterbody section of a hypersonic vehicle. Initially, exhaust gases were assumed to be air. Internal-external flows around a single scramjet module were analyzed by solving the 3D Navier-Stokes equations. Then, exhaust gases were simulated by a cold mixture of Freon and Ar. Two different models were used to compute these multispecies flows as they mixed with the hypersonic airflow. Surface and off-surface properties were successfully compared with the experimental data. The Aerodynamic Design Optimization with Sensitivity analysis was then developed. Pre- and postoptimization sensitivity coefficients were derived and used in this quasi-analytical method. These coefficients were also used to predict inexpensively the flow field around a changed shape when the flow field of an unchanged shape was given. Starting with totally arbitrary initial afterbody shapes, independent computations were converged to the same optimum shape, which rendered the maximum axial thrust.
Baysal, O.↗
On the application of deterministic optimization methods to stochastic control problems
A technique is presented by which deterministic optimization techniques, for example, the maximum principle of Pontriagin, can be applied to stochastic optimal control problems formulated around linear systems with Gaussian noises and general cost criteria. Using this technique, the stochastic nature of the problem is suppressed but for two expectation operations, the optimization being deterministic. The use of the technique in treating problems with quadratic and nonquadratic costs is illustrated.
Kramer, L. C.↗
A Comparison of Trajectory Optimization Methods for the Impulsive Minimum Fuel Rendezvous Problem
In this paper we present a comparison of optimization approaches to the minimum fuel rendezvous problem. Both indirect and direct methods are compared for a variety of test cases. The indirect approach is based on primer vector theory. The direct approaches are implemented numerically and include Sequential Quadratic Programming (SQP), Quasi-Newton, Simplex, Genetic Algorithms, and Simulated Annealing. Each method is applied to a variety of test cases including, circular to circular coplanar orbits, LEO to GEO, and orbit phasing in highly elliptic orbits. We also compare different constrained optimization routines on complex orbit rendezvous problems with complicated, highly nonlinear constraints.
Hughes, Steven P.↗
Optimization methods and silicon solar cell numerical models
The goal of this project is the development of an optimization algorithm for use with a solar cell model. It is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junctions depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm has been developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAPID). SCAPID uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the operation of a solar cell. A major obstacle is that the numerical methods used in SCAPID require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the value associated with the maximum efficiency. This problem has been alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution. Adapting SCAPID so that it could be called iteratively by the optimization code provided another means of reducing the cpu time required to complete an optimization. Instead of calculating the entire I-V curve, as is usually done in SCAPID, only the efficiency is calculated (maximum power voltage and current) and the solution from previous calculations is used to initiate the next solution.
Girardini, K.↗