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Results for “RESEARCH TECHNIQUE, MATHEMATICS”

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 19 records

On the representation of the stability region in oscillation problems with the aid of the Hurwitz determinants

This report concerns the use of the Hurwitz determinants in defining boundaries of regions where oscillatory phenomena are to be stable or unstable. A simplification is suggested as an aid in reducing the computations usually required, although it is emphasized that point checks in the various regions defined are required using the complete set of Hurwitz determinants or some other complete stability determination.

MATHEMATICS - MATRICES - HURWITZ↗

From linear mechanics to nonlinear mechanics

Consideration is given to the techniques used in telecommunication where a nonlinear system (the modulator) results in a linear transposition of a signal. It is then shown that a similar method permits linearization of electromechanical devices or nonlinear mechanical devices. A sweep function plays the same role as the carrier wave in radio-electricity. The linearizations of certain nonlinear functionals are presented.

RESEARCH TECHNIQUE, MATHEMATICS↗

The structure of Airy's stress function in multiply connected regions

In solving two-dimensional problems using Airy's stress function for multiply connected regions, the form of the function depends on the dislocations and boundary forces present. The structure of Airy's function is shown to consist of a part expressible in terms of boundary forces and a part expressible in the manner of Poincare. Meanings of the constants occurring in Poincare's expression are discussed.

FRAMES, GRIDWORKS AND TRUSSES↗

Mathematical and statistical analysis

The goal of the mathematical and statistical analysis component of RICIS is to research, develop, and evaluate mathematical and statistical techniques for aerospace technology applications. Specific research areas of interest include modeling, simulation, experiment design, reliability assessment, and numerical analysis.

Houston, A. Glen↗

Estimation of Unsteady Aerodynamic Models from Dynamic Wind Tunnel Data

Demanding aerodynamic modelling requirements for military and civilian aircraft have motivated researchers to improve computational and experimental techniques and to pursue closer collaboration in these areas. Model identification and validation techniques are key components for this research. This paper presents mathematical model structures and identification techniques that have been used successfully to model more general aerodynamic behaviours in single-degree-of-freedom dynamic testing. Model parameters, characterizing aerodynamic properties, are estimated using linear and nonlinear regression methods in both time and frequency domains. Steps in identification including model structure determination, parameter estimation, and model validation, are addressed in this paper with examples using data from one-degree-of-freedom dynamic wind tunnel and water tunnel experiments. These techniques offer a methodology for expanding the utility of computational methods in application to flight dynamics, stability, and control problems. Since flight test is not always an option for early model validation, time history comparisons are commonly made between computational and experimental results and model adequacy is inferred by corroborating results. An extension is offered to this conventional approach where more general model parameter estimates and their standard errors are compared.

Murphy, Patrick↗

The materials processing research base of the Materials Processing Center. Report for FY 1982

The work described, while involving research in the broad field of materials processing, has two common features: the problems are closed related to space precessing of materials and have both practical and fundamental significance. An interesting and important feature of many of the projects is that the interdisciplinary nature of the problem mandates complementary analytical modeling/experimental approaches. An other important aspect of many of the projects is the increasing use of mathematical modeling techniques as one of the research tools. The predictive capability of these models, when tested against measurements, plays a very important role in both the planning of experimental programs and in the rational interpretation of the results. Many of the projects described have a space experiment as their ultimate objective. Mathematical models are proving to be extremely valuable in projecting the findings of ground - based experiments to microgravity conditions.

Flemings, M. C.↗

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.↗

The Strengths and Weaknesses of Logic Formalisms to Support Mishap Analysis

The increasing complexity of many safety critical systems poses new problems for mishap analysis. Techniques developed in the sixties and seventies cannot easily scale-up to analyze incidents involving tightly integrated software and hardware components. Similarly, the realization that many failures have systemic causes has widened the scope of many mishap investigations. Organizations, including NASA and the NTSB, have responded by starting research and training initiatives to ensure that their personnel are well equipped to meet these challenges. One strand of research has identified a range of mathematically based techniques that can be used to reason about the causes of complex, adverse events. The proponents of these techniques have argued that they can be used to formally prove that certain events created the necessary and sufficient causes for a mishap to occur. Mathematical proofs can reduce the bias that is often perceived to effect the interpretation of adverse events. Others have opposed the introduction of these techniques by identifying social and political aspects to incident investigation that cannot easily be reconciled with a logic-based approach. Traditional theorem proving mechanisms cannot accurately capture the wealth of inductive, deductive and statistical forms of inference that investigators routinely use in their analysis of adverse events. This paper summarizes some of the benefits that logics provide, describes their weaknesses, and proposes a number of directions for future research.

Johnson, C. W.↗

Development of a flutter suppression control law by use of linear quadratic Gaussian and constrained optimization design techniques

A control law to suppress symmetric flutter for a mathematical model of an aeroelastic research vehicle is developed. An implementable control law is attained by including modified linear quadratic Gaussian design techniques, controller order reduction, and gain scheduling. A complementary design approach for a flight condition wherein nongradient-based constrained optimization techniques are applied to maximize controller robustness is illustrated.

Adams, W. M.↗

Development of a flutter suppression control law by use of Linear Quadratic Gaussian and constrained optimization design techniques

A control law is developed to suppress symmetric flutter for a mathematical model of an aeroelastic research vehicle. An implementable control law is attained by including modified LQG (Linear Quadratic Gaussian) design techniques, controller order reduction, and gain scheduling. An alternate (complementary) design approach is illustrated for one flight condition wherein nongradient-based constrained optimization techniques are applied to maximize controller robustness.

Adams, W. M., Jr.↗

Concerning the extrapolation of solar nonlinear force-free magnetic fields

This paper contains a review and discussion of the mathematical basis of the extrapolation techniques involved in using photospheric vector magnetograms to obtain the coronal field above the surface. The two basic techniques employing the Cauchy initial value problem and the variational techniques are reviewed in terms of the mathematical and practical applications. A short review is presented of the current research on numerical modeling techniques in the area of extrapolating vector magnetograms; specifically, algorithms to extrapolate nonlinear force-free magnetic fields from the photosphere are considered.

Gary, G. Allen↗

Effects of Humidity Swings on Adsorption Columns for Air Revitalization: Modeling and Experiments

Air purification systems are necessary to provide clean air in the closed environments aboard spacecraft. Trace contaminants are removed using adsorption. One major factor concerning the removal of trace contaminants is relative humidity. Water can reduce adsorption capacity and, due to constant fluctuations, its presence is difficult to incorporate into adsorption column designs. The purpose of the research was to allow for better design techniques in trace contaminant adsorption systems, especially for feeds with water present. Experiments and mathematical modeling research on effects of humidity swings on adsorption columns for air revitalization were carried out.

LeVan, M. Douglas↗

Analysis of head-down tilt as an analog of weightlessness using a methematical simulation model

Antiorthostasis or head down tilt of a moderate degree was used as a ground based analog of weightless space flight to study headward fluid shifts, decreased plasma volume, orthostatic intolerance and muscular skeletal degradation. A mathematical model was used to help interpret these observations. The model proved most valuable for these studies was originally developed as a description of the major circulatory, fluid and electrolyte control systems. Two different experimental studies are employed to validate the model. The first is a 24 hour head down tilt study and the second is a 7 day head down bed rest study. The major issues addressed include the reduction in plasma volume, the dynamic changes of venous pressure and cardiac output, the extent of central hypervolemia during long term zero g exposure, the existence of an early diuresis, the mechanisms which alter the renal regulating hormones during the short term and long term periods, the significance of potassium loss on other zero g responses, and the role of transcapillary filtration in adjusting fluid shifts. The use of mathematical models as an interpretive and analysis technique for experimental research for space life science is illustrated.

Leonard, J. I.↗

Basic research planning in mathematical pattern recognition and image analysis

Fundamental problems encountered while attempting to develop automated techniques for applications of remote sensing are discussed under the following categories: (1) geometric and radiometric preprocessing; (2) spatial, spectral, temporal, syntactic, and ancillary digital image representation; (3) image partitioning, proportion estimation, and error models in object scene interference; (4) parallel processing and image data structures; and (5) continuing studies in polarization; computer architectures and parallel processing; and the applicability of "expert systems" to interactive analysis.

Bryant, J.↗

Information and Statistics in Nuclear Experiment and Theory (ISNET)

As with all empirical sciences, nuclear physics operates in the virtuous cycle of the scientific method: observations inspire theoretical models; models lead to new predictions; predictions are tested in experiments; experiments lead to new observations; and so on. Evaluating what we are inferring, and how certain we are of it, is key to this process. These requirements, and a general interest in applying novel statistical, mathematical, and computational techniques, led to the formation of a dedicated research community entitled “Information and Statistics in Nuclear Experiment and Theory (ISNET)” (https://isnet-series.github.io/), which now includes more than 300 members. While the community’s interests lean toward nuclear theory, the unifying theme for this group is the inference of knowledge from data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A Hierarchical Gibbs Sampler for Spatially Varying Multi-Regularization Image Reconstructions

This is a presentation for SIAM's (Society for Industrial and Applied Mathematics) conference on computational science and engineering. This presentation describes research on novel techniques to deblur images under a Bayesian framework. The title of the conference is SIAM Conference on Computational Science and Engineering (CSE21). This is a VIRTUAL conference; it was originally scheduled in Fort Worth, TX. The conference dates are March 1-5, 2021. The link to the conference's website is https://www.siam.org/conferences/cm/conference/cse21

97 MATHEMATICS AND COMPUTING↗

Signal processing of spectroscopic data for engine diagnostic applications

A description is given of research based on a series of spectra taken from the Diagnostic Test Facility (DTF) plume at NASA-Stennis Space Center. The DTF was designed to obtain spectra scaling approximately to that of the SSME, yet allow full control of dopant and thruster conditions. DTF spectra were used in this research to develop a technique for quantitative identification of an alloy. A mathematically based identification technique was tried, with reasonable sucess for one-element alloys, and only fair success for a two-element alloy. This approach was found to have the simplicity required for DSP implementation, thus allowing real-time diagnosis as a possibility. Spreadsheets were organized to handle the proliferation of development equations required, which number about 50,000. The identification work reinforced the presence of nonlinearity to dopant level.

Nail, Bert↗