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NASA NTRS1983

Separation of time scales in aircraft trajectory optimization

Two methods for analyzing the time-scale properties of aircraft trajectory optimization problems are presented. Time-scale properties must be identified before solutions can be obtained by using singular perturbation methods. Both methods only require a knowledge of the state equations, the aircraft characteristics, and the bounds on the state and control variables. Although these methods give only rough estimates of time-scale separation, they do not require that an 'exact' optimal trajectory be known, as do the more rigorous methods, and they are an improvement on the ad hoc methods currently in use. The two methods are applied to an example problem for a high performance aircraft.

Ardema, M. D.↗

NASA NTRS2003

Aerodynamic Shape Optimization Using Hybridized Differential Evolution

An aerodynamic shape optimization method that uses an evolutionary algorithm known at Differential Evolution (DE) in conjunction with various hybridization strategies is described. DE is a simple and robust evolutionary strategy that has been proven effective in determining the global optimum for several difficult optimization problems. Various hybridization strategies for DE are explored, including the use of neural networks as well as traditional local search methods. A Navier-Stokes solver is used to evaluate the various intermediate designs and provide inputs to the hybrid DE optimizer. The method is implemented on distributed parallel computers so that new designs can be obtained within reasonable turnaround times. Results are presented for the inverse design of a turbine airfoil from a modern jet engine. (The final paper will include at least one other aerodynamic design application). The capability of the method to search large design spaces and obtain the optimal airfoils in an automatic fashion is demonstrated.

Madavan, Nateri K.↗

NASA NTRS1989

Numerical experience with a class of algorithms for nonlinear optimization using inexact function and gradient information

For optimization problems associated with engineering design, parameter estimation, image reconstruction, and other optimization/simulation applications, low accuracy function and gradient values are frequently much less expensive to obtain than high accuracy values. Here, researchers investigate the computational performance of trust region methods for nonlinear optimization when high accuracy evaluations are unavailable or prohibitively expensive, and confirm earlier theoretical predictions when the algorithm is convergent even with relative gradient errors of 0.5 or more. The proper choice of the amount of accuracy to use in function and gradient evaluations can result in orders-of-magnitude savings in computational cost.

Carter, Richard G.↗

NASA NTRS1997

Enhanced Multiobjective Optimization Technique for Comprehensive Aerospace Design

A multidisciplinary design optimization procedure which couples formal multiobjectives based techniques and complex analysis procedures (such as computational fluid dynamics (CFD) codes) developed. The procedure has been demonstrated on a specific high speed flow application involving aerodynamics and acoustics (sonic boom minimization). In order to account for multiple design objectives arising from complex performance requirements, multiobjective formulation techniques are used to formulate the optimization problem. Techniques to enhance the existing Kreisselmeier-Steinhauser (K-S) function multiobjective formulation approach have been developed. The K-S function procedure used in the proposed work transforms a constrained multiple objective functions problem into an unconstrained problem which then is solved using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. Weight factors are introduced during the transformation process to each objective function. This enhanced procedure will provide the designer the capability to emphasize specific design objectives during the optimization process. The demonstration of the procedure utilizes a computational Fluid dynamics (CFD) code which solves the three-dimensional parabolized Navier-Stokes (PNS) equations for the flow field along with an appropriate sonic boom evaluation procedure thus introducing both aerodynamic performance as well as sonic boom as the design objectives to be optimized simultaneously. Sensitivity analysis is performed using a discrete differentiation approach. An approximation technique has been used within the optimizer to improve the overall computational efficiency of the procedure in order to make it suitable for design applications in an industrial setting.

Chattopadhyay, Aditi↗

NASA NTRS2004

Software for Analyzing Laminar-to-Turbulent Flow Transitions

Software assurance is the planned and systematic set of activities that ensures that software processes and products conform to requirements, standards, and procedures. Examples of such activities are the following: code inspections, unit tests, design reviews, performance analyses, construction of traceability matrices, etc. In practice, software development projects have only limited resources (e.g., schedule, budget, and availability of personnel) to cover the entire development effort, of which assurance is but a part. Projects must therefore select judiciously from among the possible assurance activities. At its heart, this can be viewed as an optimization problem; namely, to determine the allocation of limited resources (time, money, and personnel) to minimize risk or, alternatively, to minimize the resources needed to reduce risk to an acceptable level. The end result of the work reported here is a means to optimize quality-assurance processes used in developing software. This is achieved by combining two prior programs in an innovative manner

Chang, Chau-Lyan↗

NASA NTRS2004

Software for Optimizing Quality Assurance of Other Software

Feather, Martin↗

NASA NTRS2014

Spatio-Temporal Video Segmentation with Shape Growth or Shrinkage Constraint

We propose a new method for joint segmentation of monotonously growing or shrinking shapes in a time sequence of noisy images. The task of segmenting the image time series is expressed as an optimization problem using the spatio-temporal graph of pixels, in which we are able to impose the constraint of shape growth or of shrinkage by introducing monodirectional infinite links connecting pixels at the same spatial locations in successive image frames. The globally optimal solution is computed with a graph cut. The performance of the proposed method is validated on three applications: segmentation of melting sea ice floes and of growing burned areas from time series of 2D satellite images, and segmentation of a growing brain tumor from sequences of 3D medical scans. In the latter application, we impose an additional intersequences inclusion constraint by adding directed infinite links between pixels of dependent image structures.

Segmentation↗

NASA NTRS1993

Neurocomputing strategies in decomposition based structural design

The present paper explores the applicability of neurocomputing strategies in decomposition based structural optimization problems. It is shown that the modeling capability of a backpropagation neural network can be used to detect weak couplings in a system, and to effectively decompose it into smaller, more tractable, subsystems. When such partitioning of a design space is possible, parallel optimization can be performed in each subsystem, with a penalty term added to its objective function to account for constraint violations in all other subsystems. Dependencies among subsystems are represented in terms of global design variables, and a neural network is used to map the relations between these variables and all subsystem constraints. A vector quantization technique, referred to as a z-Network, can effectively be used for this purpose. The approach is illustrated with applications to minimum weight sizing of truss structures with multiple design constraints.

Szewczyk, Z.↗

NASA NTRS2002

Multidisciplinary Optimization of a Transport Aircraft Wing using Particle Swarm Optimization

The purpose of this paper is to demonstrate the application of particle swarm optimization to a realistic multidisciplinary optimization test problem. The paper's new contributions to multidisciplinary optimization is the application of a new algorithm for dealing with the unique challenges associated with multidisciplinary optimization problems, and recommendations as to the utility of the algorithm in future multidisciplinary optimization applications. The selected example is a bi-level optimization problem that demonstrates severe numerical noise and has a combination of continuous and truly discrete design variables. The use of traditional gradient-based optimization algorithms is thus not practical. The numerical results presented indicate that the particle swarm optimization algorithm is able to reliably find the optimum design for the problem presented here. The algorithm is capable of dealing with the unique challenges posed by multidisciplinary optimization as well as the numerical noise and truly discrete variables present in the current example problem.

Sobieszczanski-Sobieski, Jaroslaw↗

NASA NTRS1989

Euler procedure for three-dimensional transonic wall interference

Based on an optimization formulation, a procedure has been developed to evaluate Mach number and angle-of-attack corrections. The Euler equations are assumed to be the flow governing equations. To obtain efficient solutions for the optimization problem, the iterative solutions for the flow variables and the design parameters are simultaneously updated. In addition to the model lift and geometry, the procedure requires pressure measurements near the tunnel walls. The tunnel boundary conditions are based on the introduction of Reimann invariants for a one-dimensional flow normal to the boundary. Computations are performed to verify that the errors introduced by this approximate boundary-condition formulation are acceptably small. The correction scheme is applied to an aircraft configuration in an open jet. The results indicate that the optimization scheme is highly efficient with the rate of convergence of the flow solution nearly equal to the corresponding rate of a regular analysis problem.

Rizk, Magdi H.↗

NASA NTRS1992

Model validation - A connection between robust control and identification

The gap between the models used in control synthesis and those obtained from identification experiments is considered by investigating the connection between uncertain models and data. The model validation problem addressed is: given experimental data and a model with both additive noise and norm-bounded perturbations, is it possible that the model could produce the observed input-output data? This problem is studied for the standard H-infinity/mu framework models. A necessary condition for such a model to describe an experimental datum is obtained. For a large class of models in the robust control framework, this condition is computable as the solution of a quadratic optimization problem.

Smith, Roy S.↗

NASA NTRS1988

Fuel-optimal trajectories for aeroassisted coplanar orbital transfer problem

The optimal-control problem arising in coplanar orbital transfer using aeroassist technology is addressed. The maneuver involves the transfer from high earth orbit to low earth orbit with minimum fuel consumption. Simulations are carried out to obtain a corridor of entry conditions which are suitable for flying the spacecraft through the atmosphere. A highlight of the present work is the application of an efficient multiple shooting method for handling the difficult nonlinear two-point boundary value problem resulting from the optimization procedure.

Naidu, D. S.↗

NASA NTRS1993

Component modes damping assignment methodology for articulated, multiflexible body structures

To simulate the dynamical motion of articulated, multiflexible body structures, one can use multibody simulation packages such as DISCOS. To this end, one must supply appropriate reduced-order models for all of the flexible components involved. The component modes projection and assembly model reduction (COMPARE) methodology is one way to construct these reduced-order component models, which when reassembled capture important system input-to-output mapping of the full-order model at multiple system configurations of interest. In conjunction, we must also supply component damping matrices which when reassembled generate a system damping matrix that has certain desirable properties. The problem of determining the damping factors of components' modes to achieve a given system damping matrix is addressed here. To this end, we must establish from first principles a matrix-algebraic relation between the system's modal damping matrix and the components' modal damping matrices. An unconstrained/constrained optimization problem can then be formulated to determine the component modes' damping factors that best satisfy that matrix-algebraic relation. The effectiveness of the developed methodology, called ModeDamp, has been successfully demonstrated on a high-order, finite element model of the Galileo spacecraft.

Lee, Allan Y.↗

NASA NTRS2005

Integrated System-Level Optimization for Concurrent Engineering With Parametric Subsystem Modeling

The introduction of concurrent design practices to the aerospace industry has greatly increased the productivity of engineers and teams during design sessions as demonstrated by JPL's Team X. Simultaneously, advances in computing power have given rise to a host of potent numerical optimization methods capable of solving complex multidisciplinary optimization problems containing hundreds of variables, constraints, and governing equations. Unfortunately, such methods are tedious to set up and require significant amounts of time and processor power to execute, thus making them unsuitable for rapid concurrent engineering use. This paper proposes a framework for Integration of System-Level Optimization with Concurrent Engineering (ISLOCE). It uses parametric neural-network approximations of the subsystem models. These approximations are then linked to a system-level optimizer that is capable of reaching a solution quickly due to the reduced complexity of the approximations. The integration structure is described in detail and applied to the multiobjective design of a simplified Space Shuttle external fuel tank model. Further, a comparison is made between the new framework and traditional concurrent engineering (without system optimization) through an experimental trial with two groups of engineers. Each method is evaluated in terms of optimizer accuracy, time to solution, and ease of use. The results suggest that system-level optimization, running as a background process during integrated concurrent engineering sessions, is potentially advantageous as long as it is judiciously implemented.

Schuman, Todd↗

NASA NTRS1990

Structural optimization with constraints from dynamics in Lagrange

Structural optimization problems are mostly solved under constraints from statics, such as stresses, strains, or displacements under static loads. But in the design process, dynamic quantities like eigenfrequencies or accelerations under dynamic loads become more and more important. Therefore, it is obvious that constraints from dynamics must be considered in structural optimization packages. This paper addresses the dynamics branch in MBB-LAGRANGE. It will concentrate on two topics, namely on the different formulations for eigenfrequency constraints and on frequency response constraints. For the latter the necessity of a system reduction is emphasized. The methods implemented in LAGRANGE are presented and examples are given.

Pfeiffer, F.↗

NASA NTRS2007

Analytical Approach for Estimating Preliminary Mass of ARES I Crew Launch Vehicle Upper Stage Structural Components

In January 2004, President Bush gave the National Aeronautics and Space Administration (NASA) a vision for Space Exploration by setting our sight on a bold new path to go back to the Moon, then to Mars and beyond. In response to this vision, NASA started the Constellation Program, which is a new exploration launch vehicle program. The primary mission for the Constellation Program is to carry out a series of human expeditions ranging from Low Earth Orbit to the surface of Mars and beyond for the purposes of conducting human exploration of space, as specified by the Vision for Space Exploration (VSE). The intent is that the information and technology developed by this program will provide the foundation for broader exploration activities as our operational experience grows. The ARES I Crew Launch Vehicle (CLV) has been designated as the launch vehicle that will be developed as a "first step" to facilitate the aforementioned human expeditions. The CLV Project is broken into four major elements: First Stage, Upper Stage Engine, Upper Stage (US), and the Crew Exploration Vehicle (CEV). NASA's Marshall Space Flight Center (MSFC) is responsible for the design of the CLV and has the prime responsibility to design the upper stage of the vehicle. The US is the second propulsive stage of the CLV and provides CEV insertion into low Earth orbit (LEO) after separation from the First Stage of the Crew Launch Vehicle. The fully integrated Upper Stage is a mix of modified existing heritage hardware (J-2X Engine) and new development (primary structure, subsystems, and avionics). The Upper Stage assembly is a structurally stabilized cylindrical structure, which is powered by a single J-2X engine which is developed as a separate Element of the CLV. The primary structure includes the load bearing liquid hydrogen (LH2) and liquid oxygen (LOX) propellant tanks, a Forward Skirt, the Intertank structure, the Aft Skirt and the Thrust Structure. A Systems Tunnel, which carries fluid and electrical power functions to other Elements of the CLV, is included as secondary structure. The MSFC has an overall responsibility for the integrated US element as well as structural design an thermal control of the fuel tanks, intertank, interstage, avionics, main propulsion system, Reaction Control System (RCS) for both the Upper Stage and the First Stage. MSFC's Spacecraft and Vehicle Department, Structural and Analysis Design Division is developing a set of predicted mass of these elements. This paper details the methodology, criterion and tools used for the preliminary mass predictions of the upper stage structural assembly components. In general, weight of the cylindrical barrel sections are estimated using the commercial code Hypersizer, whereas, weight of the domes are developed using classical solutions. HyperSizer is software that performs automated structural analysis and sizing optimization based on aerospace methods for strength, stability, and stiffness. Analysis methods range from closed form, traditional hand calculations repeated every day in industry to more advanced panel buckling algorithms. Margin-of-safety reporting for every potential failure provides the engineer with a powerful insight into the structural problem. Optimization capabilities include finding minimum weight panel or beam concepts, material selections, cross sectional dimensions, thicknesses, and lay-ups from a library of 40 different stiffened and sandwich designs and a database of composite, metallic, honeycomb, and foam materials. Multiple different concepts (orthogrid, isogrid, and skin stiffener) were run for multiple loading combinations of ascent design load with and with out tank pressure as well as proof pressure condition. Subsequently, selected optimized concept obtained from Hypersizer runs was translated into a computer aid design (CAD) model to account for the wall thickness tolerance, weld land etc for developing the most probable weight of the components. The flow diram summarizes the analysis steps used in developing these predicted mass.

Aggarwal, Pravin↗

NASA NTRS1971

Application of the steepest ascent optimization method to a reentry trajectory problem

The direct optimization method is presented in detail. Nominal values of the control variables are input parameters. Perturbations are introduced into the control variables and the resulting first order predictions of changes in the payoff, and constraint functions are then determined. Through a sequence of prescribed cycles, a trajectory is eventually obtained which is reasonably close to the optimum. The method is successfully applied to an Apollo three-dimensional reentry problem. The study of this Apollo application problem has resulted in the development of a highly flexible computer program that can be modified to consider other trajectory optimization problems.

Junkin, B. G.↗

NASA NTRS1986

Combined optimization of image-gathering optics and image-processing algorithm for edge detection

This paper investigates the relationships between the image-gathering and image-processing systems for minimum mean-squared error estimation of scene characteristics. A stochastic optimization problem is formulated in which the objective is to determine a spatial characteristic of the scene rather than a feature of the already blurred, sampled, and noisy image data. The Wiener filter for the sampled image case is obtained as a special case, where the desired characteristics is scene restoration. Optimal edge detection is investigated. It is shown that the optimal edge detector compensates for the blurring introduced by the image-gathering optics, and, notably, that it is not circularly symmetric. The lack of circular symmetry is largely due to the geometric effects of the sampling lattice used in image acquisition.

Halyo, N.↗