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NASA NTRS1999

Advanced Interactive Display Formats for Terminal Area Traffic Control

This research project deals with an on-line dynamic method for automated viewing parameter management in perspective displays. Perspective images are optimized such that a human observer will perceive relevant spatial geometrical features with minimal errors. In order to compute the errors at which observers reconstruct spatial features from perspective images, a visual spatial-perception model was formulated. The model was employed as the basis of an optimization scheme aimed at seeking the optimal projection parameter setting. These ideas are implemented in the context of an air traffic control (ATC) application. A concept, referred to as an active display system, was developed. This system uses heuristic rules to identify relevant geometrical features of the three-dimensional air traffic situation. Agile, on-line optimization was achieved by a specially developed and custom-tailored genetic algorithm (GA), which was to deal with the multi-modal characteristics of the objective function and exploit its time-evolving nature.

Grunwald, Arthur J.↗

NASA NTRS1999

Neural Network Training by Integration of Adjoint Systems of Equations Forward in Time

A method and apparatus for supervised neural learning of time dependent trajectories exploits the concepts of adjoint operators to enable computation of the gradient of an objective functional with respect to the various parameters of the network architecture in a highly efficient manner. Specifically. it combines the advantage of dramatic reductions in computational complexity inherent in adjoint methods with the ability to solve two adjoint systems of equations together forward in time. Not only is a large amount of computation and storage saved. but the handling of real-time applications becomes also possible. The invention has been applied it to two examples of representative complexity which have recently been analyzed in the open literature and demonstrated that a circular trajectory can be learned in approximately 200 iterations compared to the 12000 reported in the literature. A figure eight trajectory was achieved in under 500 iterations compared to 20000 previously required. Tbc trajectories computed using our new method are much closer to the target trajectories than was reported in previous studies.

Toomarian, Nikzad↗

NASA NTRS1999

Multidisciplinary Optimization Branch Experience Using iSIGHT Software

The Multidisciplinary Optimization (MDO) Branch at NASA Langley Research Center is investigating frameworks for supporting multidisciplinary analysis and optimization research. An optimization framework call improve the design process while reducing time and costs. A framework provides software and system services to integrate computational tasks and allows the researcher to concentrate more on the application and less on the programming details. A framework also provides a common working environment and a full range of optimization tools, and so increases the productivity of multidisciplinary research teams. Finally, a framework enables staff members to develop applications for use by disciplinary experts in other organizations. Since the release of version 4.0, the MDO Branch has gained experience with the iSIGHT framework developed by Engineous Software, Inc. This paper describes experiences with four aerospace applications: (1) reusable launch vehicle sizing, (2) aerospike nozzle design, (3) low-noise rotorcraft trajectories, and (4) acoustic liner design. All applications have been successfully tested using the iSIGHT framework, except for the aerospike nozzle problem, which is in progress. Brief overviews of each problem are provided. The problem descriptions include the number and type of disciplinary codes, as well as all estimate of the multidisciplinary analysis execution time. In addition, the optimization methods, objective functions, design variables, and design constraints are described for each problem. Discussions on the experience gained and lessons learned are provided for each problem. These discussions include the advantages and disadvantages of using the iSIGHT framework for each case as well as the ease of use of various advanced features. Potential areas of improvement are identified.

Padula, S. L.↗

NASA NTRS1999

Multidisciplinary Optimization Branch Experience Using iSIGHT Software

The Multidisciplinary Optimization (MDO) Branch at NASA Langley is investigating frameworks for supporting multidisciplinary analysis and optimization research. A framework provides software and system services to integrate computational tasks and allows the researcher to concentrate more on the application and less on the programming details. A framework also provides a common working environment and a full range of optimization tools, and so increases the productivity of multidisciplinary research teams. Finally, a framework enables staff members to develop applications for use by disciplinary experts in other organizations. This year, the MDO Branch has gained experience with the iSIGHT framework. This paper describes experiences with four aerospace applications, including: (1) reusable launch vehicle sizing, (2) aerospike nozzle design, (3) low-noise rotorcraft trajectories, and (4) acoustic liner design. Brief overviews of each problem are provided, including the number and type of disciplinary codes and computation time estimates. In addition, the optimization methods, objective functions, design variables, and constraints are described for each problem. For each case, discussions on the advantages and disadvantages of using the iSIGHT framework are provided as well as notes on the ease of use of various advanced features and suggestions for areas of improvement.

Padula, S. L.↗

NASA NTRS1999

Advanced Interactive Display Formats for Terminal Area Traffic Control

Grunwald, Arthur J.↗

NASA NTRS2000

Nontangent, Developed Contour Bulkheads for a Single-Stage Launch Vehicle

Dry weights for single-stage launch vehicles that incorporate nontangent, developed contour bulkheads are estimated and compared to a baseline vehicle with 1.414 aspect ratio ellipsoidal bulkheads. Weights, volumes, and heights of optimized bulkhead designs are computed using a preliminary design bulkhead analysis code. The dry weights of vehicles that incorporate the optimized bulkheads are predicted using a vehicle weights and sizing code. Two optimization approaches are employed. A structural-level method, where the vehicle's three major bulkhead regions are optimized separately and then incorporated into a model for computation of the vehicle dry weight, predicts a reduction of4365 lb (2.2 %) from the 200,679-lb baseline vehicle dry weight. In the second, vehicle-level, approach, the vehicle dry weight is the objective function for the optimization. For the vehicle-level analysis, modified bulkhead designs are analyzed and incorporated into the weights model for computation of a dry weight. The optimizer simultaneously manipulates design variables for all three bulkheads to reduce the dry weight. The vehicle-level analysis predicts a dry weight reduction of 5129 lb, a 2.6% reduction from the baseline weight. Based on these results, nontangent, developed contour bulkheads may provide substantial weight savings for single stage vehicles.

Wu, K. Chauncey↗

NASA NTRS1997

Preliminary Design of Low-Thrust Interplanetary Missions

For interplanetary missions, highly efficient electric propulsion systems can be used to increase the mass delivered to the destination and/or reduce the trip time over typical chemical propulsion systems. This technology is being demonstrated on the Deep Space 1 mission - part of NASA's New Millennium Program validating technologies which can lower the cost and risk and enhance the performance of future missions. With the successful demonstration on Deep Space 1, future missions can consider electric propulsion as a viable propulsion option. Electric propulsion systems, while highly efficient, produce only a small amount of thrust. As a result, the engines operate during a significant fraction of the trajectory. This characteristic makes it much more difficult to find optimal trajectories. The methods for optimizing low-thrust trajectories are typically categorized as either indirect, or direct. Indirect methods are based on calculus of variations, resulting in a two-point boundary value problem that is solved by satisfying terminal constraints and targeting conditions. These methods are subject to extreme sensitivity to the initial guess of the variables - some of which are not physically intuitive. Adding a gravity assist to the trajectory compounds the sensitivity. Direct methods parameterize the problem and use nonlinear programming techniques to optimize an objective function by adjusting a set of variables. A variety of methods of this type have been examined with varying results. These methods are subject to the limitations of the nonlinear programming techniques. In this paper we present a direct method intended to be used primarily for preliminary design of low-thrust interplanetary trajectories, including those with multiple gravity assists. Preliminary design implies a willingness to accept limited accuracy to achieve an efficient algorithm that executes quickly.

Sims, Jon A.↗

NASA NTRS1999

Co-evolution for Problem Simplification

This paper explores a co-evolutionary approach applicable to difficult problems with limited failure/success performance feedback. Like familiar "predator-prey" frameworks this algorithm evolves two populations of individuals - the solutions (predators) and the problems (prey). The approach extends previous work by rewarding only the problems that match their difficulty to the level of solut,ion competence. In complex problem domains with limited feedback, this "tractability constraint" helps provide an adaptive fitness gradient that, effectively differentiates the candidate solutions. The algorithm generates selective pressure toward the evolution of increasingly competent solutions by rewarding solution generality and uniqueness and problem tractability and difficulty. Relative (inverse-fitness) and absolute (static objective function) approaches to evaluating problem difficulty are explored and discussed. On a simple control task, this co-evolutionary algorithm was found to have significant advantages over a genetic algorithm with either a static fitness function or a fitness function that changes on a hand-tuned schedule.

Haith, Gary L.↗

NASA NTRS2000

Affordable Design: A Methodolgy to Implement Process-Based Manufacturing Cost into the Traditional Performance-Focused Multidisciplinary Design Optimization

The primary objective of this paper is to demonstrate the use of process-based manufacturing and assembly cost models in a traditional performance-focused multidisciplinary design and optimization process. The use of automated cost-performance analysis is an enabling technology that could bring realistic processbased manufacturing and assembly cost into multidisciplinary design and optimization. In this paper, we present a new methodology for incorporating process costing into a standard multidisciplinary design optimization process. Material, manufacturing processes, and assembly processes costs then could be used as the objective function for the optimization method. A case study involving forty-six different configurations of a simple wing is presented, indicating that a design based on performance criteria alone may not necessarily be the most affordable as far as manufacturing and assembly cost is concerned.

Bao, Han P.↗

NASA NTRS2000

Genetic Algorithm Approaches for Actuator Placement

This research investigated genetic algorithm approaches for smart actuator placement to provide aircraft maneuverability without requiring hinged flaps or other control surfaces. The effort supported goals of the Multidisciplinary Design Optimization focus efforts in NASA's Aircraft au program. This work helped to properly identify various aspects of the genetic algorithm operators and parameters that allow for placement of discrete control actuators/effectors. An improved problem definition, including better definition of the objective function and constraints, resulted from this research effort. The work conducted for this research used a geometrically simple wing model; however, an increasing number of potential actuator placement locations were incorporated to illustrate the ability of the GA to determine promising actuator placement arrangements. This effort's major result is a useful genetic algorithm-based approach to assist in the discrete actuator/effector placement problem.

Crossley, William A.↗

NASA NTRS2000

Self-Tuning of Design Variables for Generalized Predictive Control

Three techniques are introduced to determine the order and control weighting for the design of a generalized predictive controller. These techniques are based on the application of fuzzy logic, genetic algorithms, and simulated annealing to conduct an optimal search on specific performance indexes or objective functions. Fuzzy logic is found to be feasible for real-time and on-line implementation due to its smooth and quick convergence. On the other hand, genetic algorithms and simulated annealing are applicable for initial estimation of the model order and control weighting, and final fine-tuning within a small region of the solution space, Several numerical simulations for a multiple-input and multiple-output system are given to illustrate the techniques developed in this paper.

Lin, Chaung↗

NASA NTRS2001

Approach for Uncertainty Propagation and Robust Design in CFD Using Sensitivity Derivatives

This paper presents an implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for a quasi 1-D Euler CFD (computational fluid dynamics) code. Given uncertainties in statistically independent, random, normally distributed input variables, a first- and second-order statistical moment matching procedure is performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, the moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

Putko, Michele M.↗

NASA NTRS1994

Search Space Characterization for a Telescope Scheduling Application

This paper presents a technique for statistically characterizing a search space and demonstrates the use of this technique within a practical telescope scheduling application. The characterization provides the following: (i) an estimate of the search space size, (ii) a scaling technique for multi-attribute objective functions and search heuristics, (iii) a "quality density function" for schedules in a search space, (iv) a measure of a scheduler's performance, and (v) support for constructing and tuning search heuristics. This paper describes the random sampling algorithm used to construct this characterization and explains how it can be used to produce this information. As an example, we include a comparative analysis of an heuristic dispatch scheduler and a look-ahead scheduler that performs greedy search.

Bresina, John↗

NASA NTRS1997

When Gravity Fails: Local Search Topology

Local search algorithms for combinatorial search problems frequently encounter a sequence of states in which it is impossible to improve the value of the objective function; moves through these regions, called {\em plateau moves), dominate the time spent in local search. We analyze and characterize {\em plateaus) for three different classes of randomly generated Boolean Satisfiability problems. We identify several interesting features of plateaus that impact the performance of local search algorithms. We show that local minima tend to be small but occasionally may be very large. We also show that local minima can be escaped without unsatisfying a large number of clauses, but that systematically searching for an escape route may be computationally expensive if the local minimum is large. We show that plateaus with exits, called benches, tend to be much larger than minima, and that some benches have very few exit states which local search can use to escape. We show that the solutions (i.e. global minima) of randomly generated problem instances form clusters, which behave similarly to local minima. We revisit several enhancements of local search algorithms and explain their performance in light of our results. Finally we discuss strategies for creating the next generation of local search algorithms.

Frank, Jeremy↗

NASA NTRS1997

Optimizing Observation Scheduling Objectives

In this paper, we present an approach that enables the automatic generation of high quality schedules, with respect to a given objective function. The approach involves the combination of two techniques: GenH, which automatically generates a search heuristic specialized to the given problem instance, and HBSS, which employs the generated heuristic as a bias within a stochastic sampling method.

Bresina, John L.↗

NASA NTRS2002

A Convex Approach to Fault Tolerant Control

The design of control laws for dynamic systems with the potential for actuator failures is considered in this work. The use of Linear Matrix Inequalities allows more freedom in controller design criteria than typically available with robust control. This work proposes an extension of fault-scheduled control design techniques that can find a fixed controller with provable performance over a set of plants. Through convexity of the objective function, performance bounds on this set of plants implies performance bounds on a range of systems defined by a convex hull. This is used to incorporate performance bounds for a variety of soft and hard failures into the control design problem.

Maghami, Peiman G.↗

NASA NTRS2003

Terrain Model Registration for Single Cycle Instrument Placement

This paper presents an efficient and robust method for registration of terrain models created using stereo vision on a planetary rover. Our approach projects two surface models into a virtual depth map, rendering the models as they would be seen from a single range sensor. Correspondence is established based on which points project to the same location in the virtual range sensor. A robust norm of the deviations in observed depth is used as the objective function, and the algorithm searches for the rigid transformation which minimizes the norm. An initial coarse search is done using rover pose information from odometry and orientation sensing. A fine search is done using Levenberg-Marquardt. Our method enables a planetary rover to keep track of designated science targets as it moves, and to hand off targets from one set of stereo cameras to another. These capabilities are essential for the rover to autonomously approach a science target and place an instrument in contact in a single command cycle.

Deans, Matthew↗

NASA NTRS2004

Multiobjective Aerodynamic Shape Optimization Using Pareto Differential Evolution and Generalized Response Surface Metamodels

Differential Evolution (DE) is a simple, fast, and robust evolutionary algorithm that has proven effective in determining the global optimum for several difficult single-objective optimization problems. The DE algorithm has been recently extended to multiobjective optimization problem by using a Pareto-based approach. In this paper, a Pareto DE algorithm is applied to multiobjective aerodynamic shape optimization problems that are characterized by computationally expensive objective function evaluations. To improve computational expensive the algorithm is coupled with generalized response surface meta-models based on artificial neural networks. Results are presented for some test optimization problems from the literature to demonstrate the capabilities of the method.

Madavan, Nateri K.↗