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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

A method to stabilize linear systems using eigenvalue gradient information

Formal optimization methods and eigenvalue gradient information are used to develop a stabilizing control law for a closed loop linear system that is initially unstable. The method was originally formulated by using direct, constrained optimization methods with the constraints being the real parts of the eigenvalues. However, because of problems in trying to achieve stabilizing control laws, the problem was reformulated to be solved differently. The method described uses the Davidon-Fletcher-Powell minimization technique to solve an indirect, constrained minimization problem in which the performance index is the Kreisselmeier-Steinhauser function of the real parts of all the eigenvalues. The method is applied successfully to solve two different problems: the determination of a fourth-order control law stabilizes a single-input single-output active flutter suppression system and the determination of a second-order control law for a multi-input multi-output lateral-directional flight control system. Various sets of design variables and initial starting points were chosen to show the robustness of the method.

Wieseman, C. D.↗
NASA NTRS1987

Assimilation of scalar versus horizontal gradient information from the VAS into a mesoscale model

Comparisons are made between analyses and forecasts which incorporate VAS geopotential data as either scalar or horizontal gradient information for a case study on the AVE/VAS day of Mar. 6, 1982. On this day, incorporating the VAS information in analysis as a variational constraint on horizontal geopotential gradients significantly mitigated the effects of large data biases which made VAS assimilation by standard scalar methods very difficult. A subsequent forecast made from the gradient assimilation was superior to one made from the standard analysis and of comparable quality in geopotentials to a control forecast from synoptic data. Most impact was noted in the forecasts of vertical motion and precipitation in the gradient vs this control simulation.

Diak, George↗
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 NTRS1973

CONMIN: A FORTRAN program for constrained function minimization: User's manual

CONMIN is a FORTRAN program, in subroutine form, for the solution of linear or nonlinear constrained optimization problems. The basic optimization algorithm is the Method of Feasible Directions. The user must provide a main calling program and an external routine to evaluate the objective and constraint functions and to provide gradient information. If analytic gradients of the objective or constraint functions are not available, this information is calculated by finite difference. While the program is intended primarily for efficient solution of constrained problems, unconstrained function minimization problems may also be solved, and the conjugate direction method of Fletcher and Reeves is used for this purpose. This manual describes the use of CONMIN and defines all necessary parameters. Sufficient information is provided so that the program can be used without special knowledge of optimization techniques. Sample problems are included to help the user become familiar with CONMIN and to make the program operational.

Vanderplaats, G. N.↗
NASA NTRS2015

The Swarm Initial Field Model for the 2014 Geomagnetic Field

Data from the first year of ESA's Swarm constellation mission are used to derive the Swarm Initial Field Model (SIFM), a new model of the Earth's magnetic field and its time variation. In addition to the conventional magnetic field observations provided by each of the three Swarm satellites, explicit advantage is taken of the constellation aspect by including east-west magnetic intensity gradient information from the lower satellite pair. Along-track differences in magnetic intensity provide further information concerning the north-south gradient. The SIFM static field shows excellent agreement (up to at least degree 60) with recent field models derived from CHAMP data, providing an initial validation of the quality of the Swarm magnetic measurements. Use of gradient data improves the determination of both the static field and its secular variation, with the mean misfit for east-west intensity differences between the lower satellite pair being only 0.12 nT.

Olsen, Nils↗
NASA NTRSDate not supplied

Gradient-Enhanced Reliability Analysis of Transonic Aeroelastic Flutter

Reliability computation for transonic aeroelastic systems is a challenging task, given the complex physical mechanisms involved, and broader challenges associated with computing small probabilities of failure/flutter. This paper demonstrates the use of four different reliability estimation tools, with a particular focus on tools that can utilize gradient information: the derivative of flutter boundaries with respect to random parametric inputs. Results are shown for two test cases: the AGARD 445.6 case and the Common Research Model, and the strength and weaknesses of each UQ tool are compared in terms of cost and accuracy. Two of the UQ tools used here require gradients as part of a search process, but the other two are sample-based, and are able to leverage the existence of gradients for improved performance.

Bret K Stanford↗
NASA NTRSDate not supplied

Analysis of CDC Bioreactor Internal Thermal Measurements and Sample Coupon Temperatures

The Center for Disease Control and Prevention (CDC) bioreactor is an integral laboratory tool for the Environmental Control and Life Support Systems (ECLSS) biofilm formation and growth research program. Critical to this research is the need to adjust and maintain various surface temperatures of the coupons housed within the CDC Bioreactor. The purpose of this study was to provide quantitative temperature gradient information when the CDC Bioreactor was operating according to several process scenarios. Two primary process parameters were evaluated. For the first set of test parameters, the liquid level was maintained at 350 mL, with an inlet flowrate of 0.1 mL/min, 1 mL/min, 10 mL/min. The liquid was allowed to gravity drain out of the outlet spout. For the second set of test parameters, the liquid level within the reactor was maintained at 550 mL, with an inlet flow of 0.1 mL/min, 1 mL/min, 10 mL/min and draining intermittently controlled to 0.8 mL/min to maintain the 550 mL level. Due to the placement of the thermocouple in the reactor, a difference in temperature occurred between the coupon surfaces and target Bioreactor temperature when operated according to the first set of test parameters. When the reactor was operated according to the second set of parameters, which resulted in the thermocouple being submerged, the temperature gradient was eliminated. The results demonstrated minimal temperature gradient between the top and bottom coupon surfaces for coupons placed in a single rod within the CDC Bioreactor for both sets of test parameters evaluated. The collection of this information helped to explain previous ECLSS biofilm formation test runs, along with providing guidance on best operating practices for future ECLSS experiments. The placement of the thermocouple also helps to explain the challenge of achieving and maintaining bulk liquid temperatures when biofilm is grown according to the standardized test methods.

CDC Bioreactor↗
NASA NTRSDate not supplied

Analysis of CDC Bioreactor Internal Thermal Measurements and Sample Coupon Temperatures

The CDC Biofilm Reactor is an integral laboratory tool for the Environmental Control and Life Support Systems (ECLSS) biofilm formation and growth research program. Critical to this research is the need to adjust and maintain various surface temperatures of the coupons housed within the CDC Biofilm Reactor. The purpose of this study was to provide quantitative temperature gradient information when the CDC Biofilm Reactor was operating according to several process scenarios. Two primary process parameters were evaluated. For the first set of test parameters, the liquid level was maintained at 350 mL, with an inlet flowrate of 0.1 mL/min, 1 mL/min, 10 mL/min. The liquid was allowed to gravity drain out of the outlet spout. For the second set of test parameters, the liquid level within the reactor was maintained at 550 mL, with an inlet flow of 0.1 mL/min, 1 mL/min, 10 mL/min and draining intermittently controlled to 0.8 mL/min to maintain the 550 mL level. Due to the placement of the thermocouple in the reactor, a difference in temperature occurred between the coupon surfaces and target biofilm reactor temperature when operated according to the first set of test parameters. When the reactor was operated according to the second set of parameters, which resulted in the thermocouple being submerged, the temperature gradient was eliminated. The results demonstrated minimal temperature gradient between the top and bottom coupon surfaces for coupons placed in a single rod within the CDC Biofilm Reactor for both sets of test parameters evaluated. The collection of this information helped to explain previous ECLSS biofilm formation test runs, along with providing guidance on best operating practices for future ECLSS experiments. The placement of the thermocouple also helps to explain the challenge of achieving and maintaining bulk liquid temperatures when biofilm is grown according to the standardized test methods.

CDC Bioreactor↗
NASA NTRS1994

Multidisciplinary design optimization using genetic algorithms

Multidisciplinary design optimization (MDO) is an important step in the conceptual design and evaluation of launch vehicles since it can have a significant impact on performance and life cycle cost. The objective is to search the system design space to determine values of design variables that optimize the performance characteristic subject to system constraints. Gradient-based optimization routines have been used extensively for aerospace design optimization. However, one limitation of gradient based optimizers is their need for gradient information. Therefore, design problems which include discrete variables can not be studied. Such problems are common in launch vehicle design. For example, the number of engines and material choices must be integer values or assume only a few discrete values. In this study, genetic algorithms are investigated as an approach to MDO problems involving discrete variables and discontinuous domains. Optimization by genetic algorithms (GA) uses a search procedure which is fundamentally different from those gradient based methods. Genetic algorithms seek to find good solutions in an efficient and timely manner rather than finding the best solution. GA are designed to mimic evolutionary selection. A population of candidate designs is evaluated at each iteration, and each individual's probability of reproduction (existence in the next generation) depends on its fitness value (related to the value of the objective function). Progress toward the optimum is achieved by the crossover and mutation operations. GA is attractive since it uses only objective function values in the search process, so gradient calculations are avoided. Hence, GA are able to deal with discrete variables. Studies report success in the use of GA for aircraft design optimization studies, trajectory analysis, space structure design and control systems design. In these studies reliable convergence was achieved, but the number of function evaluations was large compared with efficient gradient methods. Applicaiton of GA is underway for a cost optimization study for a launch-vehicle fuel-tank and structural design of a wing. The strengths and limitations of GA for launch vehicle design optimization is studied.

Unal, Resit↗
NASA NTRS2019

Real-Time Background Oriented Schlieren: Catching Up With Knife Edge Schlieren

Background Oriented Schlieren (BOS) is a widely used technique that provides density gradient information in flow fields of interest, without imposing stringent optical quality requirements on the facility/experiment windows and/or optics used in the BOS setup. Typically, the BOS reference image is acquired before the test begins (flow off) and then the "live" image data are acquired during the actual testing/experiment (flow on). The raw BOS image data, while displayed in real-time as they are acquired from the camera, unfortunately provide little if any visual indication of the density gradients in the flow. Generally, the "live" images must be processed off-line after the testing is completed, providing no indication of the success of the BOS setup and no feedback on the operational success of the test. Advances in computer processing hardware enables the implementation of real-time processing and display of the BOS image data. Two different approaches to implementing the real-time BOS (RT-BOS) processing capability are described herein. First, a traditional multi-core Central Processing Unit (CPU) based approach using scheduled parallel threads is used to build a RT-BOS processing engine. In the second approach, a Graphical Processing Unit (GPU) approach is used to costruct a RT-BOS processing engine. Generally, high core count CPU processors can provide a useful processing rate for RT-BOS. However, the GPU based approach exceeds the processing capability of the CPU approach, at a fraction of the cost. The GPU approach places no restrictions on the Host PC processing capability, except that it be capable of acquiring the BOS image data from the camera in real-time.

Wernet, Mark P.↗
NASA NTRS1985

Variational assimilation of VAS data into a mesoscale model Assimilation method and sensitivity experiments

The assimilation of temperature and moisture gradient information from the Visible IR Spin-Scan Radiometer's Atmospheric Sounder (VAS) into a mesoscale model is presently undertaken by means of a variational method and followed by tests of the sensitivity of both diabatic and adiabatic versions of the model to VAS data assimilations for the case of July 20-21, 1981. The synoptic scale effects of the assimilation of VAS data are noted to be negligible; the greatest impact was instead on mesoscale forecasts of convective instability patterns. The additional assimilation of relative humidity gradients did not significantly change the patterns of the forecast instabilities. The greatest improvements from assimilation resulted from the resolution of the strong mesoscale temperature gradients by the asynoptic VAS data.

Cram, J. M.↗
NASA NTRS1988

Estimating noise levels of remotely sensed measurements from satellites using spatial structure analysis

A technique is presented whereby the noise level of satellite measurements of the atmosphere and earth can be estimated. The technique analyzes a spatial array of data measured by a satellite instrument. A minimum of about 200 satellite measurements is required, preferably in a regular pattern. Statistical structure analysis is used to describe a combination of the mean gradient and noise in the data. The noise level is then estimated by separating out the gradient information and leaving only the noise. Results are presented for four satellite sounding instruments, and effective blackbody or brightness temperature noise levels were compared to prelaunch specifications or inflight calibrations for each instrument. Comparisons showed that in the absence of cloud-contaminated measurements (in the case of infrared data) and away from the highly variable ground surface, the noise level of various satellite instruments can be obtained without the need for calibration data. The noise levels imply how much spatial averaging is possible, without smearing the detected geophysical gradient, and how much is necessary, to meet the absolute signal accuracy requirements for the intended use of the satellite measurements.

Hillger, Donald W.↗
NASA NTRS1973

A nonlinear programming approach for optimizing two-stage lifting vehicle ascent to orbit

An optimal atmospheric flight branched trajectory-shaping capability is presented based on the Davidon-Fletcher-Powell variable metric parameter optimization technique. Gradient information is generated using finite difference methods. A typical atmospheric flight branched optimization problem is analyzed which requires the determination of 31 parameters. This parameter set includes the three-dimensional description of vehicle attitude control angles for three branches of flight: first-stage ascent, second-stage ascent, and first-stage flyback. The important inflight inequality contraints required to maintain the integrity of the vehicles are considered. Some of the numerical methods employed are discussed, along with several new auxiliary techniques developed to improve the compatibility of the numerical gradient and iterator.

Kamm, J. L.↗
NASA NTRS2004

A Study of Penalty Function Methods for Constraint Handling with Genetic Algorithm

COMETBOARDS (Comparative Evaluation Testbed of Optimization and Analysis Routines for Design of Structures) is a design optimization test bed that can evaluate the performance of several different optimization algorithms. A few of these optimization algorithms are the sequence of unconstrained minimization techniques (SUMT), sequential linear programming (SLP) and the sequential quadratic programming techniques (SQP). A genetic algorithm (GA) is a search technique that is based on the principles of natural selection or "survival of the fittest". Instead of using gradient information, the GA uses the objective function directly in the search. The GA searches the solution space by maintaining a population of potential solutions. Then, using evolving operations such as recombination, mutation and selection, the GA creates successive generations of solutions that will evolve and take on the positive characteristics of their parents and thus gradually approach optimal or near-optimal solutions. By using the objective function directly in the search, genetic algorithms can be effectively applied in non-convex, highly nonlinear, complex problems. The genetic algorithm is not guaranteed to find the global optimum, but it is less likely to get trapped at a local optimum than traditional gradient-based search methods when the objective function is not smooth and generally well behaved. The purpose of this research is to assist in the integration of genetic algorithm (GA) into COMETBOARDS. COMETBOARDS cast the design of structures as a constrained nonlinear optimization problem. One method used to solve constrained optimization problem with a GA to convert the constrained optimization problem into an unconstrained optimization problem by developing a penalty function that penalizes infeasible solutions. There have been several suggested penalty function in the literature each with there own strengths and weaknesses. A statistical analysis of some suggested penalty functions is performed in this study. Also, a response surface approach to robust design is used to develop a new penalty function approach. This new penalty function approach is then compared with the other existing penalty functions.

Ortiz, Francisco↗
NASA NTRS1973

Structural optimization by methods of feasible directions.

A general design algorithm based on methods of feasible directions is presented. Zoutendijk's method of feasible directions is first presented as applied to structural design. This method is modified to improve numerical stability of the design process and is then further modified to deal efficiently with infeasible designs. The algorithm requires the analytic gradient of the objective function and the constraint functions which are active at a given stage in the design process. Gradient information is not required for nonactive constraints. Complex constraint functions may be ignored in the initial design stages because violation of these constraints is efficiently overcome later in the design process. The algorithm is demonstrated with elastic design of redundant trusses.

Vanderplaats, G. N.↗
NASA NTRS1973

Utilizing remote sensing data for land use decisions for Indian lands in South Dakota.

Evaluation of photographic and thermal infrared imagery acquired at an altitude of 11,500 ft above ground level (in southwestern South Dakota) on Oct. 15, 1970, June 30, 1971, and Aug. 2, 1971, for use in mapping range sites and soils. A density slicing system was used to enhance film optical density differences associated with range sites and soils. The range site boundaries in native rangeland areas were found to be delineated best by a density slicing analysis of color infrared film obtained in August 1971. The range site maps produced by density slicing were superior to existing range inventory maps. The density slicing analysis of color infrared film from the August 1971 flight was best for locating soil boundaries in rangeland areas. To adequately map soils in rangeland areas, data based on density slicing used in conjunction with slope gradient information derived from stereoscopic analyses provided more detailed and accurate information than is presently available from range site and soil maps of the area.

Frazee, C. J.↗
NASA NTRS1974

Study of genetic direct search algorithms for function optimization

The results are presented of a study to determine the performance of genetic direct search algorithms in solving function optimization problems arising in the optimal and adaptive control areas. The findings indicate that: (1) genetic algorithms can outperform standard algorithms in multimodal and/or noisy optimization situations, but suffer from lack of gradient exploitation facilities when gradient information can be utilized to guide the search. (2) For large populations, or low dimensional function spaces, mutation is a sufficient operator. However for small populations or high dimensional functions, crossover applied in about equal frequency with mutation is an optimum combination. (3) Complexity, in terms of storage space and running time, is significantly increased when population size is increased or the inversion operator, or the second level adaptation routine is added to the basic structure.

Zeigler, B. P.↗
NASA NTRS1984

Efficient calculation of optimum design sensitivity

Two methods for obtaining the sensitivity of an optimized design to changes in problem parameters are presented. The first-order method uses gradient information to estimate the required sensitivity. The second-order method uses second derivatives of the design objective and constraint functions to provide a quadratic approximation to the new design which results from changing the specified parameter. It is shown that the sensitivity of the optimized design may be discontinuous with respect to the new parameter. This discontinuity is accounted for in the present methods. These methods are compared to a previous approach based on the Kuhn-Tucker necessary conditions for optimality. It is shown that the present methods provide the appropriate sensitivity information in an efficient manner. The methods are demonstrated by a structural synthesis example.

Vanderplaats, G. N.↗