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Results for “Mathematical optimization”

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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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Space shuttle propulsion parameter estimation using optimal estimation techniques

The first twelve system state variables are presented with the necessary mathematical developments for incorporating them into the filter/smoother algorithm. Other state variables, i.e., aerodynamic coefficients can be easily incorporated into the estimation algorithm, representing uncertain parameters, but for initial checkout purposes are treated as known quantities. An approach for incorporating the NASA propulsion predictive model results into the optimal estimation algorithm was identified. This approach utilizes numerical derivatives and nominal predictions within the algorithm with global iterations of the algorithm. The iterative process is terminated when the quality of the estimates provided no longer significantly improves.

Source record↗
NASA NTRS1980

Handling qualities of large flexible control-configured aircraft

The effects on handling qualities of low frequency symmetric elastic mode interaction with the rigid body dynamics of a large flexible aircraft was analyzed by use of a mathematical pilot modeling computer simulation. An extension of the optimal control model for a human pilot was made so that the mode interaction effects on the pilot's control task could be assessed. Pilot ratings were determined for a longitudinal tracking task with parametric variations in the undamped natural frequencies of the two lowest frequency symmetric elastic modes made to induce varying amounts of mode interaction. Relating numerical performance index values associated with the frequency variations used in several dynamic cases, to a numerical Cooper-Harper pilot rating has proved successful in discriminating when the mathematical pilot can or cannot separate rigid from elastic response in the tracking task.

Swaim, R. L.↗
NASA NTRS1974

An assessment of separable fluid connector system parameters to perform a connector system design optimization study

The key to optimization of design where there are a large number of variables, all of which may not be known precisely, lies in the mathematical tool of dynamic programming developed by Bellman. This methodology can lead to optimized solutions to the design of critical systems in a minimum amount of time, even when there are a great number of acceptable configurations to be considered. To demonstrate the usefulness of dynamic programming, an analytical method is developed for evaluating the relationship among existing numerous connector designs to find the optimum configuration. The data utilized in the study were generated from 900 flanges designed for six subsystems of the S-1B stage of the Saturn 1B space carrier vehicle.

Prasthofer, W. P.↗
NASA NTRS1993

The analytical representation of viscoelastic material properties using optimization techniques

This report presents a technique to model viscoelastic material properties with a function of the form of the Prony series. Generally, the method employed to determine the function constants requires assuming values for the exponential constants of the function and then resolving the remaining constants through linear least-squares techniques. The technique presented here allows all the constants to be analytically determined through optimization techniques. This technique is employed in a computer program named PRONY and makes use of commercially available optimization tool developed by VMA Engineering, Inc. The PRONY program was utilized to compare the technique against previously determined models for solid rocket motor TP-H1148 propellant and V747-75 Viton fluoroelastomer. In both cases, the optimization technique generated functions that modeled the test data with at least an order of magnitude better correlation. This technique has demonstrated the capability to use small or large data sets and to use data sets that have uniformly or nonuniformly spaced data pairs. The reduction of experimental data to accurate mathematical models is a vital part of most scientific and engineering research. This technique of regression through optimization can be applied to other mathematical models that are difficult to fit to experimental data through traditional regression techniques.

Hill, S. A.↗
NASA NTRS1996

Optimality of Empirical Z-R Relations

This paper attempts to justify mathematically the two empirical approaches to the problem of deriving Z-R relations from (Z,R) measurements, namely the power-law regression and the probability matching method (PMM). The basic mathematical assumptions that apply in each case are explicitly identified.

rainfall estimation radar reflectivity Z-R relatio↗
NASA NTRS2007

General Mission Analysis Tool (GMAT) Mathematical Specifications

The General Mission Analysis Tool (GMAT) is a space trajectory optimization and mission analysis system developed by NASA and private industry in the spirit of the NASA Mission. GMAT contains new technology and is a testbed for future technology development.

Hughes, Steve↗
NASA NTRS1975

Optimization of duct acoustic liners of finite length

Lining design procedures generally ignore the effects of discontinuous impedance changes on reflection and modal redistribution of incident energy. The present study involves identification of the mechanisms of optimal suppression by segmented liners, including impedance discontinuity effects. The mathematical model involves rectangular ducts in the absence of mean flow. Segmented acoustic fields are represented by duct eigenfunction expansions, and mode matching is used to ensure continuity of the total field. Extensive parameter studies were used to identify attenuation mechanisms and to define preliminary liner configurations. These are used as starting values in conjugate-gradient optimization studies. Optimal segmented liners are presented and it is shown that, if the sound source is sufficiently well-defined, conventional infinite duct optimum attenuation rates can be improved upon by taking advantage of wall impedance discontinuities. Finally, follow-on work which will involve experimental verification and extension to the case with mean flow in the duct is described.

Beckemeyer, R. J.↗
NASA NTRS2012

Sensitivity Analysis for Atmospheric Infrared Sounder (AIRS) CO2 Retrieval

The Atmospheric Infrared Sounder (AIRS) is a thermal infrared sensor able to retrieve the daily atmospheric state globally for clear as well as partially cloudy field-of-views. The AIRS spectrometer has 2378 channels sensing from 15.4 micrometers to 3.7 micrometers, of which a small subset in the 15 micrometers region has been selected, to date, for CO2 retrieval. To improve upon the current retrieval method, we extended the retrieval calculations to include a prior estimate component and developed a channel ranking system to optimize the channels and number of channels used. The channel ranking system uses a mathematical formalism to rapidly process and assess the retrieval potential of large numbers of channels. Implementing this system, we identifed a larger optimized subset of AIRS channels that can decrease retrieval errors and minimize the overall sensitivity to other iridescent contributors, such as water vapor, ozone, and atmospheric temperature. This methodology selects channels globally by accounting for the latitudinal, longitudinal, and seasonal dependencies of the subset. The new methodology increases accuracy in AIRS CO2 as well as other retrievals and enables the extension of retrieved CO2 vertical profiles to altitudes ranging from the lower troposphere to upper stratosphere. The extended retrieval method for CO2 vertical profile estimation using a maximum-likelihood estimation method. We use model data to demonstrate the beneficial impact of the extended retrieval method using the new channel ranking system on CO2 retrieval.

sensitivity analysis↗
NASA NTRS2011

Optimal Control via Self-Generated Stochasticity

The problem of global maxima of functionals has been examined. Mathematical roots of local maxima are the same as those for a much simpler problem of finding global maximum of a multi-dimensional function. The second problem is instability even if an optimal trajectory is found, there is no guarantee that it is stable. As a result, a fundamentally new approach is introduced to optimal control based upon two new ideas. The first idea is to represent the functional to be maximized as a limit of a probability density governed by the appropriately selected Liouville equation. Then, the corresponding ordinary differential equations (ODEs) become stochastic, and that sample of the solution that has the largest value will have the highest probability to appear in ODE simulation. The main advantages of the stochastic approach are that it is not sensitive to local maxima, the function to be maximized must be only integrable but not necessarily differentiable, and global equality and inequality constraints do not cause any significant obstacles. The second idea is to remove possible instability of the optimal solution by equipping the control system with a self-stabilizing device. The applications of the proposed methodology will optimize the performance of NASA spacecraft, as well as robot performance.

Zak, Michail↗
NASA NTRS1975

Weight minimization of structures for fixed flutter speed via an optimality criterion

A rigorous optimality criterion is derived and a hybrid weight-reduction algorithm developed for the weight minimization of lifting surfaces with a constraint on flutter speed. The weight-reduction algorithm incorporates a simple recursion formula derived from the optimality criterion. Monotonic weight reduction is accomplished by dynamically adjusting a parameter in the recursion formula so as to achieve a predetermined weight decrease. The algorithm thus combines the simplicity of optimality-criterion methods with the convergence characteristics of mathematical-programming methods. The imposition of the flutter constraint is simplified by forcing to zero the imaginary part of the flutter eigenvalue, with the airspeed fixed. Four examples are discussed. The results suggest that significant improvements in efficiency are possible, in comparison with techniques based purely on mathematical programming.

Segenreich, S. A.↗
NASA NTRS1979

Spectral characteristics of convolutionally coded digital signals

The power spectral density of the output symbol sequence of a convolutional encoder is computed for two different input symbol stream source models, namely, an NRZ signaling format and a first order Markov source. In the former, the two signaling states of the binary waveform are not necessarily assumed to occur with equal probability. The effects of alternate symbol inversion on this spectrum are also considered. The mathematical results are illustrated with many examples corresponding to optimal performance codes.

Divsalar, D.↗
NASA NTRS1980

Spectral characteristics of convolutionally coded digital signals

The power spectral density of the output symbol sequence of a convolutional encoder is computed for two different input symbol stream source models, namely, an NRZ signaling format and a first-order Markov source. The effects of alternate symbol inversion on this spectrum are also considered. The mathematical results are illustrated with many examples corresponding to optimal performance codes. It is demonstrated that only for the case of a purely random input source (e.g., NRZ data with equiprobable symbols) and a particular class of codes is the output spectrum identical to the input spectrum except for a frequency scaling (expansion) by the reciprocal of the code rate.

Divsalar, D.↗
NASA NTRS1981

A model for the submarine depthkeeping team

The most difficult task the depthkeeping team must face occurs during periscope-depth operations during which they may be required to maintain a submarine several hundred feet long within a foot of ordered depth and within one-half degree of ordered pitch. The difficulty is compounded by the facts that wave generated forces are extremely high, depth and pitch signals are very noisy and submarine speed is such that overall dynamics are slow. A mathematical simulation of the depthkeeping team based on the optimal control models is described. A solution of the optimal team control problem with an output control restriction (limited display to each controller) is presented.

Ware, J. R.↗
NASA NTRS1981

A new approach to the minimum weight/loss design of switching power converters

A new technique using the mathematical nonlinear programming ALAG is proposed to facilitate design optimizations of switching power converters. This computer-aided approach provides a minimum weight (or loss) design down to the details of component level and concurrently satisfies all related power-circuit performance requirements. It also provides such design insights as tradeoffs between power loss and system weight as the switching frequency is increased.

Lee, F. C.↗
NASA NTRS1975

Computerized optimization of elastic booster autopilots. Volume 1: Technical manual

The philosophy and the mathematical basis of the nonlinear programming algorithm underlying the development of the COEBRA program were given. A User's Manual was given in a separate document. The purpose of this work was to convert the COEBRA program from the CDC 6400/6500 digital computer system to the UNIVAC 1108 at the George C. Marshall Space Flight Center and to provide an instruction manual on the use of the program.

Kelley, T.↗
NASA NTRS1987

Optimization of orbital assignment and specification of service areas in satellite communications

The mathematical nature of the orbital and frequency assignment problem for communications satellites is explored, and it is shown that choosing the correct permutations of the orbit locations and frequency assignments is an important step in arriving at values which satisfy the signal-quality requirements. Two methods are proposed to achieve better spectrum/orbit utilization. The first, called the delta S concept, leads to orbital assignment solutions via either mixed-integer or restricted basis entry linear programming techniques; the method guarantees good single-entry carrier-to-interference ratio results. In the second, a basis for specifying service areas is proposed for the Fixed Satellite Service. It is suggested that service areas should be specified according to the communications-demand density in conjunction with the delta S concept in order to enable the system planner to specify more satellites and provide more communications supply.

Wang, Cou-Way↗