Search NASA⌕ Search

SEARCH · Search NASA

Results for “Mathematical Methods”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 649 records · Page 36
All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

A Safety Conundrum Illustrated: Logic, Mathematics, and Science Are Not Enough

In an ideal world, conversations about whether a particular system is safe, or whether a particular method or tool enhances safety, would be emotion-free discussions concentrating on the level of safety required, available evidence, and coherent logical, mathematical, or scientific arguments based on that evidence. In the real world, discussions about safety are often not emotion-free. Political and economic arguments may play a bigger role than logical, mathematical, and scientific arguments, and psychological factors may be as important, or even more important, than purely technical factors. This paper illustrates the conundrum that can result from this clash of the ideal and the real by means of an imagined conversation among a collection of fictional characters representing various types of people who may be participating in a safety discussion.

Holloway, C. M.↗
NASA NTRS1992

Tests characterizing bioprocessor hardware for analytical modeling

The tests outlined in this paper were used to characterize the hardware components of the Salad Machine, a small NASA-developed bioprocessor. The data from these tests are presented, and the methods by which this data can be integrated into system mathematical models are briefly discussed. The subsystems and physical processes discussed include the lighting system, the air loop (condensing heat exchanger and the blower), heat transfer to the surroundings, and leakage. Through this effort it was learned that in the development of a test protocol, care should be taken to order the tests such that environmental parameters, particularly humidity, require as few large adjustments as possible. Sensor calibration and installation take a substantial amount of time, which should be built into the test schedule. Two properties were particularly hard to quantify: the air flow rate and the energy from the lighting system entering into the growth volume. Flow rate can be measured using the appropriate device for the system configuration and airflow. Lighting system radiation level was measured using three methods. The results of these methods varied substantially, putting off conclusive quantification of this value.

Gustavino, S.↗
NASA NTRS1978

Summary of Voyager Design and Flight Loads

Estimates of flight loads for Voyager 1 and Voyager 2 are summarized and compared to the Voyager design loads obtained from the shock spectra/impedance method and to the loads obtained using space vehicle transient loads analysis. These estimates were obtained by using the measured flight accelerations at the launch vehicle/spacecraft interface as forcing functions for the Voyager mathematical model. Based on these data, an assessment of the shock spectra/impedance loads method used for Voyager is presented. The following conclusions were reached: (1) the shock spectra approach provided reasonable conservative design loads for Voyager, (2) care has to be executed to insure that all critical events are accounted for in constructing shock spectra envelopes, (3) the selection of critical events is not always obvious, especially for those flight events wherein the spacecraft dynamic characteristics are important, and (4) the success of the method is strongly dependent on the analysts' experience and judgement.

Chen, J. C.↗
NASA NTRS2011

Impacts of an Ammonia Leak on the Cabin Atmosphere of the International Space Station

Toxic chemical release into the cabin atmosphere is one of the three major emergency scenarios identified on the International Space Station (ISS). The release of anhydrous ammonia, the coolant used in the U.S. On-orbit Segment (USOS) External Active Thermal Control Subsystem (EATCS), into the ISS cabin atmosphere is one of the most serious toxic chemical release cases identified on board ISS. The USOS Thermal Control System (TCS) includes an Internal Thermal Control Subsystem (ITCS) water loop and an EATCS ammonia loop that transfer heat at the interface heat exchanger (IFHX). Failure modes exist that could cause a breach within the IFHX. This breach would result in high pressure ammonia from the EATCS flowing into the lower pressure ITCS water loop. As the pressure builds in the ITCS loop, it is likely that the gas trap, which has the lowest maximum design pressure within the ITCS, would burst and cause ammonia to enter the ISS atmosphere. It is crucial to first characterize the release of ammonia into the ISS atmosphere in order to develop methods to properly mitigate the environmental risk. This paper will document the methods used to characterize an ammonia leak into the ISS cabin atmosphere. A mathematical model of the leak was first developed in order to define the flow of ammonia into the ISS cabin atmosphere based on a series of IFHX rupture cases. Computational Fluid Dynamics (CFD) methods were then used to model the dispersion of the ammonia throughout the ISS cabin and determine localized effects and ventilation effects on the dispersion of ammonia. Lastly, the capabilities of the current on-orbit systems to remove ammonia were reviewed and scrubbing rates of the ISS systems were defined based on the ammonia release models. With this full characterization of the release of ammonia from the USOS TCS, an appropriate mitigation strategy that includes crew and system emergency response procedures, personal protection equipment use, and atmosphere monitoring and scrubbing hardware can be established.

Duchesne, Stephanie M.↗
NASA NTRS2012

Impacts of an Ammonia Leak on the Cabin Atmosphere of the International Space Station

Toxic chemical release into the cabin atmosphere is one of the three major emergency scenarios identified on the International Space Station (ISS). The release of anhydrous ammonia, the coolant used in the U.S. On-orbit Segment (USOS) External Active Thermal Control Subsystem (EATCS), into the ISS cabin atmosphere is one of the most serious toxic chemical release cases identified on board ISS. The USOS Thermal Control System (TCS) includes an Internal Thermal Control Subsystem (ITCS) water loop and an EATCS ammonia loop that transfer heat at the interface heat exchanger (IFHX). Failure modes exist that could cause a breach within the IFHX. This breach would result in high pressure ammonia from the EATCS flowing into the lower pressure ITCS water loop. As the pressure builds in the ITCS loop, it is likely that the gas trap, which has the lowest maximum design pressure within the ITCS, would burst and cause ammonia to enter the ISS atmosphere. It is crucial to first characterize the release of ammonia into the ISS atmosphere in order to develop methods to properly mitigate the environmental risk. This paper will document the methods used to characterize an ammonia leak into the ISS cabin atmosphere. A mathematical model of the leak was first developed in order to define the flow of ammonia into the ISS cabin atmosphere based on a series of IFHX rupture cases. Computational Fluid Dynamics (CFD) methods were then used to model the dispersion of the ammonia throughout the ISS cabin and determine localized effects and ventilation effects on the dispersion of ammonia. Lastly, the capabilities of the current on-orbit systems to remove ammonia were reviewed and scrubbing rates of the ISS systems were defined based on the ammonia release models. With this full characterization of the release of ammonia from the USOS TCS, an appropriate mitigation strategy that includes crew and system emergency response procedures, personal protection equipment use, and atmosphere monitoring and scrubbing hardware can be established.

Duchesne, Stephanie M.↗
NASA NTRS1995

Statistically generated weighted curve fit of residual functions for modal analysis of structures

A statistically generated weighting function for a second-order polynomial curve fit of residual functions has been developed. The residual flexibility test method, from which a residual function is generated, is a procedure for modal testing large structures in an external constraint-free environment to measure the effects of higher order modes and interface stiffness. This test method is applicable to structures with distinct degree-of-freedom interfaces to other system components. A theoretical residual function in the displacement/force domain has the characteristics of a relatively flat line in the lower frequencies and a slight upward curvature in the higher frequency range. In the test residual function, the above-mentioned characteristics can be seen in the data, but due to the present limitations in the modal parameter evaluation (natural frequencies and mode shapes) of test data, the residual function has regions of ragged data. A second order polynomial curve fit is required to obtain the residual flexibility term. A weighting function of the data is generated by examining the variances between neighboring data points. From a weighted second-order polynomial curve fit, an accurate residual flexibility value can be obtained. The residual flexibility value and free-free modes from testing are used to improve a mathematical model of the structure. The residual flexibility modal test method is applied to a straight beam with a trunnion appendage and a space shuttle payload pallet simulator.

Bookout, P. S.↗
NASA NTRS1993

Locating Damaged Truss Members From Responses To Vibrations

Method of on-orbit assessment for location of damage based on use of capabilities of vibration-control system to measure vibrations in structure. Experiment involved use of laboratory scale-model truss structure exhibiting expected characteristics of truss structures proposed for large spacecraft. Vibrations excited in truss, and measurements of responses of structure used in series of two identification algorithms to produce mathematical model of structure in current condition, possibly containing damage. Similar methods considered for examining buildings for damage by earthquakes.

Smith, S. W.↗
NASA NTRS2000

Gravitational Physics Research

Gravitational physics research at ISPAE is connected with NASA's Relativity Mission (Gravity Probe B (GP-B)) which will perform a test of Einstein's General Relativity Theory. GP-B will measure the geodetic and motional effect predicted by General Relativity Theory with extremely stable and sensitive gyroscopes in an earth orbiting satellite. Both effects cause a very small precession of the gyroscope spin axis. The goal of the GP-B experiment is the measurement of the gyroscope precession with very high precision. GP-B is being developed by a team at Stanford University and is scheduled for launch in the year 2001. The related UAH research is a collaboration with Stanford University and MSFC. This research is focussed primarily on the error analysis and data reduction methods of the experiment but includes other topics concerned with experiment systems and their performance affecting the science measurements. The hydrogen maser is the most accurate and stable clock available. It will be used in future gravitational physics missions to measure relativistic effects such as the second order Doppler effect. The HMC experiment, currently under development at the Smithsonian Astrophysical Observatory (SAO), will test the performance and capability of the hydrogen maser clock for gravitational physics measurements. UAH in collaboration with the SAO science team will study methods to evaluate the behavior and performance of the HMC. The GP-B data analysis developed by the Stanford group involves complicated mathematical operations. This situation led to the idea to investigate alternate and possibly simpler mathematical procedures to extract the GP-B measurements form the data stream. Comparison of different methods would increase the confidence in the selected scheme.

Wu, S. T.↗
NASA NTRS1991

Theoretical models for duct acoustic propagation and radiation

The development of computational methods in acoustics has led to the introduction of analysis and design procedures which model the turbofan inlet as a coupled system, simultaneously modeling propagation and radiation in the presence of realistic internal and external flows. Such models are generally large, require substantial computer speed and capacity, and can be expected to be used in the final design stages, with the simpler models being used in the early design iterations. Emphasis is given to practical modeling methods that have been applied to the acoustical design problem in turbofan engines. The mathematical model is established and the simplest case of propagation in a duct with hard walls is solved to introduce concepts and terminologies. An extensive overview is given of methods for the calculation of attenuation in uniform ducts with uniform flow and with shear flow. Subsequent sections deal with numerical techniques which provide an integrated representation of duct propagation and near- and far-field radiation for realistic geometries and flight conditions.

Eversman, Walter↗
NASA NTRS2005

Transonic-Small-Disturbance and Linear Analyses for the Active Aeroelastic Wing Program

Analysis serves many roles in the Active Aeroelastic Wing (AAW) program. It has been employed to ensure safe testing of both a flight vehicle and wind tunnel model, has formulated models for control law design, has provided comparison data for validation of experimental methods and has addressed several analytical research topics. Aeroelastic analyses using mathematical models of both the flight vehicle and the wind tunnel model configurations have been conducted. Static aeroelastic characterizations of the flight vehicle and wind tunnel model have been produced in the transonic regime and at low supersonic Mach numbers. The flight vehicle has been analyzed using linear aerodynamic theory and transonic small disturbance theory. Analyses of the wind-tunnel model were performed using only linear methods. Research efforts conducted through these analyses include defining regions of the test space where transonic effects play an important role and investigating transonic similarity. A comparison of these aeroelastic analyses for the AAW flight vehicle is presented in this paper. Results from a study of transonic similarity are also presented. Data sets from these analyses include pressure distributions, stability and control derivatives, control surface effectiveness, and vehicle deflections.

Wiesman, Carol D.↗
NASA NTRS1979

An improved analysis/synthesis capability based on dual methods - ACCESS 3

Approximation concepts and dual method algorithms are combined to create a new method for minimum weight design of structural systems. Approximation concepts convert the basic mathematical programming statement of the structural synthesis problem into a sequence of explicit primal problems of separable form. These problems are solved by constructing explicit dual functions, which are maximized subject to nonnegativity constraints. The dual method is successfully extended to deal with pure discrete and mixed continuous-discrete design variable problems. The power of the method presented is illustrated with numerical results for example problems, including a thin delta wing with fiber composite skins.

Schmit, L. A.↗
NASA NTRS1976

Design of structures for optimum geometry

A general method is proposed for geometric optimization of finite element structures on the assumption that a reasonable initial geometry is specified. The number of finite elements, number of joints, and the element-joint relationships are specified and are not changed during the optimization process. The structure may be statically indeterminate and may support multiple loading conditions. Design variables include geometric and member sizing parameters. Design objectives may be minimum weight or cost, and constraints include strength and stiffness limitations. The optimization procedure is a general mathematical programming approach. An iterative design algorithm is outlined, and the method is specialized for truss structures. Design examples are given.

Vanderplaats, G. N.↗
NASA NTRS1979

Modeling of polymer networks for application to solid propellant formulating

Methods for predicting the network structural characteristics formed by the curing of pourable elastomers were presented; as well as the logic which was applied in the development of mathematical models. A universal approach for modeling was developed and verified by comparison with other methods in application to a complex system. Several applications of network models to practical problems are described.

Marsh, H. E.↗
NASA NTRSDate not supplied

Intelligent Lemma Selection for Formal Methods Proofs

To help in formally verifying the correctness of various systems, NASA constructs mathematical proofs using the proof assistant PVS (Prototype Verification System). Throughout this effort, NASA has amassed a library of tens of thousands of proven lemmas. While these lemmas can often be applied to new problems, their abundance can make lemma selection a non-trivial task. This project focuses on creating a lemma selector for use in PVS based on existing systems MePo, MaSh, and MeSh, which were written for other proof assistants. An initial benchmark system makes selections based on symbol-level similarity while the final lemma selector is a hybrid system, combining the classical approach used in the benchmark with a machine learning approach which leverages the lemmas' past usage.

Connor T Baumler↗
NASA NTRS1977

Multi-attribute subjective evaluations of manual tracking tasks vs. objective performance of the human operator

A computational method to deal with the multidimensional nature of tracking and/or monitoring tasks is developed. Operator centered variables, including the operator's perception of the task, are considered. Matrix ratings are defined based on multidimensional scaling techniques and multivariate analysis. The method consists of two distinct steps: (1) to determine the mathematical space of subjective judgements of a certain individual (or group of evaluators) for a given set of tasks and experimental conditionings; and (2) to relate this space with respect to both the task variables and the objective performance criteria used. Results for a variety of second-order trackings with smoothed noise-driven inputs indicate that: (1) many of the internally perceived task variables form a nonorthogonal set; and (2) the structure of the subjective space varies among groups of individuals according to the degree of familiarity they have with such tasks.

Siapkaras, A.↗
NASA NTRS1980

Generation of boundary and boundary-layer fitting grids

The details of extended physical processes, such as the gas dynamic flow over an airfoil, the reactive flow through a combustor, or the electric field in a multi-contact transistor, are understood by solving the differential equations of a mathematical model of the process. The accuracy of finite difference methods for the numerical solution of the equations is increased if the underlying mesh fits the region boundaries and is closely spaced in regions where the solution is rapidly varying. Automatic methods for producing a satisfactorily adjusted mesh were developed for one dimensional problems. In one simple, effective scheme of this kind the unknown function and the distribution of mesh modes are found simultaneously, the nodes being placed so that they correspond to points uniformly spaced on the solution curve. In a two dimensional generalization, the nodes correspond to points equally spaced on the solution surface in two directions that are as nearly orthogonal as possible. Examples of such meshes are shown.

Ablow, C. M.↗