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NASA NTRS1993

Linear, multivariable robust control with a mu perspective

The structured singular value is a linear algebra tool developed to study a particular class of matrix perturbation problems arising in robust feedback control of multivariable systems. These perturbations are called linear fractional, and are a natural way to model many types of uncertainty in linear systems, including state-space parameter uncertainty, multiplicative and additive unmodeled dynamics uncertainty, and coprime factor and gap metric uncertainty. The structured singular value theory provides a natural extension of classical SISO robustness measures and concepts to MIMO systems. The structured singular value analysis, coupled with approximate synthesis methods, make it possible to study the tradeoff between performance and uncertainty that occurs in all feedback systems. In MIMO systems, the complexity of the spatial interactions in the loop gains make it difficult to heuristically quantify the tradeoffs that must occur. This paper examines the role played by the structured singular value (and its computable bounds) in answering these questions, as well as its role in the general robust, multivariable control analysis and design problem.

Packard, Andy↗

NASA NTRS1998

A Geometry Based Infra-Structure for Computational Analysis and Design

The computational steps traditionally taken for most engineering analysis suites (computational fluid dynamics (CFD), structural analysis, heat transfer and etc.) are: (1) Surface Generation -- usually by employing a Computer Assisted Design (CAD) system; (2) Grid Generation -- preparing the volume for the simulation; (3) Flow Solver -- producing the results at the specified operational point; (4) Post-processing Visualization -- interactively attempting to understand the results. For structural analysis, integrated systems can be obtained from a number of commercial vendors. These vendors couple directly to a number of CAD systems and are executed from within the CAD Graphical User Interface (GUI). It should be noted that the structural analysis problem is more tractable than CFD; there are fewer mesh topologies used and the grids are not as fine (this problem space does not have the length scaling issues of fluids). For CFD, these steps have worked well in the past for simple steady-state simulations at the expense of much user interaction. The data was transmitted between phases via files. In most cases, the output from a CAD system could go to Initial Graphics Exchange Specification (IGES) or Standard Exchange Program (STEP) files. The output from Grid Generators and Solvers do not really have standards though there are a couple of file formats that can be used for a subset of the gridding (i.e. PLOT3D data formats). The user would have to patch up the data or translate from one format to another to move to the next step. Sometimes this could take days. Specifically the problems with this procedure are:(1) File based -- Information flows from one step to the next via data files with formats specified for that procedure. File standards, when they exist, are wholly inadequate. For example, geometry from CAD systems (transmitted via IGES files) is defined as disjoint surfaces and curves (as well as masses of other information of no interest for the Grid Generator). This is particularly onerous for modern CAD systems based on solid modeling. The part was a proper solid and in the translation to IGES has lost this important characteristic. STEP is another standard for CAD data that exists and supports the concept of a solid. The problem with STEP is that a solid modeling geometry kernel is required to query and manipulate the data within this type of file. (2) 'Good' Geometry. A bottleneck in getting results from a solver is the construction of proper geometry to be fed to the grid generator. With 'good' geometry a grid can be constructed in tens of minutes (even with a complex configuration) using unstructured techniques. Adroit multi-block methods are not far behind. This means that a million node steady-state solution can be computed on the order of hours (using current high performance computers) starting from this 'good' geometry. Unfortunately, the geometry usually transmitted from the CAD system is not 'good' in the grid generator sense. The grid generator needs smooth closed solid geometry. It can take a week (or more) of interaction with the CAD output (sometimes by hand) before the process can begin. One way Communication. (3) One-way Communication -- All information travels on from one phase to the next. This makes procedures like node adaptation difficult when attempting to add or move nodes that sit on bounding surfaces (when the actual surface data has been lost after the grid generation phase). Until this process can be automated, more complex problems such as multi-disciplinary analysis or using the above procedure for design becomes prohibitive. There is also no way to easily deal with this system in a modular manner. One can only replace the grid generator, for example, if the software reads and writes the same files. Instead of the serial approach to analysis as described above, CAPRI takes a geometry centric approach. This makes the actual geometry (not a discretized version) accessible to all phases of the analysis. The connection to the geometry is made through an Application Programming Interface (API) and NOT a file system. This API isolates the top-level applications (grid generators, solvers and visualization components) from the geometry engine. Also this allows the replacement of one geometry kernel with another, without effecting these top-level applications. For example, if UniGraphics is used as the CAD package then Parasolid (UG's own geometry engine) can be used for all geometric queries so that no solid geometry information is lost in a translation. This is much better than STEP because when the data is queried, the same software is executed as used in the CAD system. Therefore, one analyzes the exact part that is in the CAD system. CAPRI uses the same idea as the commercial structural analysis codes but does not specify control. Software components of the CAD system are used, but the analysis suite, not the CAD operator, specifies the control of the software session. This also means that the license issues (may be) minimized and individuals need not have to know how to operate a CAD system in order to run the suite.

Haimes, Robert↗

NASA NTRS1993

Damage detection using experimentally measured mass and stiffness matrices

A method is presented for locating physical damage or change in a structure using experimentally measured mass and stiffness matrices. The approach uses a recently developed algorithm for transforming a state-space realization into a second order structural model with physical displacements as the generalized coordinates. This is accomplished by first rotating a state-space model of the identified structural dynamics into modal coordinates and approximating the mass normalized modal vectors for the output measurement set. Next, the physical mass, damping and stiffness matrices are synthesized directly from the measured modal parameters. This yields experimental mass and stiffness matrices for the structure without the use of a finite element model or a numerical search. The computed mass and stiffness are asymptotically equivalent to a static condensation of the global physical coordinate model. Techniques for solving the inverse connectivity problem are then developed whereby it is possible to assess the stiffness in a region of the structure bounded by several sensors. Applications to both simulated data and experimental data are used to discuss the effectiveness of the approach.

Peterson, L. D.↗

NASA NTRS2023

Testing theories of Gravitation with the Interstellar Probe Radio Experiment

General Relativity (GR) will soon celebrate its 110th birthday, holding up against all experimental enquiry. Nonetheless, unification theories attempting to quantize gravity, such as string theory, are gaining footing. These hypothesize additional scalar, vector, and tensor long-range fields that couple to matter (Will, 2014), introducing violations to GR. Although such violations have never been detected, it is likely that GR will not be the ultimate theory of gravity. What is certain is that gravity tests are alive and well, pushing the validity of GR to new scales and accuracies, or -potentially- suggesting alternative routes for new physics. Building upon the legacy of Voyager and Pioneer missions, which demonstrated the capability to survive in the outer reaches of the solar system, the Interstellar Probe mission concept (McNutt et al., 2022) aims to characterise our heliosphere through state-of-the-art instrumentation, opening new frontiers also for GR testing. In this work, we investigate the possibility of constraining the Nordtvedt parameter η and the mass of the graviton via the Compton wavelength λc, by simulating the processing of 10 years of radiometric data from the Interstellar Probe. Station calibration and clock synchronisation, as well as limiting spacecraft precession manoeuvres are highlighted as key strategies for obtaining high-quality estimates. In the most favourable scenario, η can be constrained to less than 1.5 · 10 -5 , reducing the uncertainty obtained via Lunar Laser Ranging (Hofmann and Müller, 2018), and a lower bound of 1.4 ‧ 10 14 km is set for λc, improving the estimates obtained from planetary ephemerides (Bernus et al., 2020) and gravitational wave detection (Abbott et al., Jun 2021). Extending ranging measurement acquisition to 20 years improves the results tenfold. This experiment interrogates fundamental physics from a unique dynamical setting, investigating possible violations of the Equivalence Principle (EP) underlying GR.

general relativity↗

NASA NTRS1999

Development of Formation Deployment and Intialization Concepts

NASA's Cross-Cutting Technology Development Program identified formation flying as a key enabler for the next generation Earth and Sciences campaign. It is hoped that this technology will allow a distributed network of autonomous satellites to act collaboratively as a single collective unit paving the way for extensive co-observing campaigns, coordinated multi-point observing programs, improved space-based interferometry, and entirely new approaches to conducting science. APL as a team member with GSFC, funded by the Earth Sciences and Technology Organization (ESTO), investigated formation deployment and initialization concepts which is central to the formation flying concept. This paper presents the analytical approach and preliminary results of the study. The study investigated a simple mission involving the deployment of six micro-satellites, one at a time, from a bus. At the initialization state, the satellites fly in an along-track trajectory separated by nominal spacing. The study entailed the development of a two-body (bus and satellite) relative motion propagator based on Clohessy-Wiltshire (C-W) equations with drag from which the relative motion of the micro-satellites is deduced. This code was used to investigate cluster development characteristics subject to "tip-off' (ejection) conditions. Results indicate that cluster development is very sensitive to the ballistic coefficients of the bus and satellites, and to relative ejection velocity. This information can be used to identify optimum deployment parameters, along with accuracy bounds for a particular mission, and to develop a cluster control strategy minimizing global fuel and cost. A suitable control strategy concept has been identified, however, it needs to be developed further.

Badesha, Surjit S.↗

NASA NTRS2015

Adaptive State Predictor Based Human Operator Modeling on Longitudinal and Lateral Control

Control-theoretic modeling of the human operator dynamic behavior in manual control tasks has a long and rich history. In the last two decades, there has been a renewed interest in modeling the human operator. There has also been significant work on techniques used to identify the pilot model of a given structure. The purpose of this research is to attempt to go beyond pilot identification based on collected experimental data and to develop a predictor of pilot behavior. An experiment was conducted to categorize these interactions of the pilot with an adaptive controller compensating during control surface failures. A general linear in-parameter model structure is used to represent a pilot. Three different estimation methods are explored. A gradient descent estimator (GDE), a least squares estimator with exponential forgetting (LSEEF), and a least squares estimator with bounded gain forgetting (LSEBGF) used the experiment data to predict pilot stick input. Previous results have found that the GDE and LSEEF methods are fairly accurate in predicting longitudinal stick input from commanded pitch. This paper discusses the accuracy of each of the three methods - GDE, LSEEF, and LSEBGF - to predict both pilot longitudinal and lateral stick input from the flight director's commanded pitch and bank attitudes.

Trujillo, Anna C.↗

NASA NTRS2004

Environment Partitioning and Reactivity of Polybrominated Diphenylethers

Polybrominated diphenyl ethers (PBDEs) are an important class of flame retardants. Annual global demand for these compounds was over 67,000 metric tons in 2001. PBDEs have recently been extensively investigated as environmental contaminants because they have been detected in air, sediment, and tissue samples from urban and remote areas. Important issues include quantifying PBDE partitioning in various environmental compartments, and elucidating transformation pathways. The partitioning of PBDE congeners to aerosols was estimated for 16 sites in the United States, Canada, and Mexico. The aerosol particles were PM2.5, the total suspended particle (TSP) concentration varied between 3.0 - 55.4 micro g/cubic meter, and the organic fraction ranged from 11 - 41%; these data are published values for each site. It is estimated that the largest fraction of each PBDE associated with the aerosol particles occurs in Mexico City, and the smallest fraction in Colorado Plateau. Although the organic fraction in Mexico City is about 60% of that observed in the Colorado Plateau, the TSP is larger by a factor of about 18.5, and it is the difference in TSP that strongly influences the fraction of particle-bound PBDE in this case. PBDE partitioning to PM2.5 particles also varies seasonally because of temperature variations. For the less brominated congeners the percentage that is particle-bound is relatively low, regardless of air temperature. In contrast, the heavier congeners exhibit a significant temperature dependence: as the temperature decreases (fall, winter) the percentage of PBDE that is particle-bound increases. The partitioning calculations complement experimental data indicating that decabromodiphenyl ether (DBDE) dissolved in hexane transforms very rapidly when irradiated with solar light. DBDE is the most highly brominated PBDE congener (10 bromine atoms) and occurs in the commercial formulation which is subject to the largest global demand.

Hua, Inez↗

NASA NTRS2011

Model Checking a Self-Stabilizing Distributed Clock Synchronization Protocol for Arbitrary Digraphs

This report presents the mechanical verification of a self-stabilizing distributed clock synchronization protocol for arbitrary digraphs in the absence of faults. This protocol does not rely on assumptions about the initial state of the system, other than the presence of at least one node, and no central clock or a centrally generated signal, pulse, or message is used. The system under study is an arbitrary, non-partitioned digraph ranging from fully connected to 1-connected networks of nodes while allowing for differences in the network elements. Nodes are anonymous, i.e., they do not have unique identities. There is no theoretical limit on the maximum number of participating nodes. The only constraint on the behavior of the node is that the interactions with other nodes are restricted to defined links and interfaces. This protocol deterministically converges within a time bound that is a linear function of the self-stabilization period.

Malekpour, Mahyar R.↗

NASA NTRS2012

Model Checking A Self-Stabilizing Synchronization Protocol for Arbitrary Digraphs

Malekpour, Mahyar R.↗

NASA NTRS2014

The Giant Planet Satellite Exospheres

Exospheres are relatively common in the outer solar system among the moons of the gas giant planets. They span the range from very tenuous, surface-bounded exospheres (e.g., Rhea, Dione) to quite robust exospheres with exobase above the surface (e.g., lo, Triton), and include many intermediate cases (e.g., Europa, Ganymede, Enceladus). The exospheres of these moons exhibit an interesting variety of sources, from surface sputtering, to frost sublimation, to active plumes, and also well illustrate another common characteristic of the outer planet satellite exospheres, namely, that the primary species often exists both as a gas in atmosphere, and a condensate (frost or ice) on the surface. As described by Yelle et al. (1995) for Triton, "The interchange of matter between gas and solid phases on these bodies has profound effects on the physical state of the surface and the structure of the atmosphere." A brief overview of the exospheres of the outer planet satellites will be presented, including an inter-comparison of these satellites exospheres with each other, and with the exospheres of the Moon and Mercury.

McGrath, Melissa A.↗

NASA NTRS2019

Steady-State Solution of a Solar Wind-Generated Electron Cloud in a Lunar Crater

We formulate an analytic description of a steady-state electron cloud and affiliated surface charge, formed in the plasma wake generated as the solar wind flows horizontally over a lunar crater. The solution is complementary to the well-known self-similar plasma expansion formulation, which breaksdown at the plasma wake front and thus fails to capture a substantial region of the crater interior. The present model establishes a theoretical basis for existing simulation results, which suggest that the cavity formed below the wake front is populated mainly by electrons, resulting in a substantial negative surface charge. The electrostatic potential throughout this subwake region is determined by solving Poisson'sequation for a Maxwellian electron cloud, bounded above by the self-similar plasma expansion front and below by the electrostatically charged surface.

Rhodes, Dov J.↗

NASA NTRS1977

Test particle propagation in magnetostatic turbulence. 3: The approach to equilibrium

The asymptotic behavior, for large time, of the quasi-linear diabatic solutions and their local approximations is considered. A time averaging procedure is introduced which yields the averages of these solutions over time intervals which contain only large time values. A discussion of the quasi-linear diabatic solutions which is limited to those solutions that are bounded from below as functions of time is given. It is shown that as the upper limit of the time averaging interval is allowed to approach infinity the time averaged quasi-linear diabatic solutions must approach isotropy (mu-independence). The first derivative with respect to mu of these solutions is also considered. This discussion is limited to first derivatives which are bounded functions of time. It is shown that as the upper limit of the time averaging interval is allowed to approach infinity, the time averaged first derivative must approach zero everywhere in mu except at mu = 0 where it must approach a large value which is calculated. The impact of this large derivative on the quasi-linear expansion scheme is discussed. An H-theorem for the first local approximation to the quasi-linear diabatic solutions is constructed. Without time averaging, the H-theorem is used to determine sufficient conditions for the first local approximate solutions to asymptote, with increasing time, to exactly the same final state which the time averaged quasi-linear diabatic solutions must approach as discussed above.

Klimas, A. J.↗

NASA NTRS2011

Supersonic/Hypersonic Correlations for In-Cavity Transition and Heating Augmentation

Laminar-entry cavity heating data with a non-laminar boundary layer exit flow have been retrieved from the database developed at Mach 6 and 10 in air on large flat plate models for the Space Shuttle Return-To-Flight Program. Building on previously published fully laminar and fully turbulent analysis methods, new descriptive correlations of the in-cavity floor-averaged heating and endwall maximum heating have been developed for transitional-to-turbulent exit flow. These new local-cavity correlations provide the expected flow and geometry conditions for transition onset; they provide the incremental heating augmentation induced by transitional flow; and, they provide the transitional-to-turbulent exit cavity length. Furthermore, they provide an upper application limit for the previously developed fully-laminar heating correlations. An example is provided that demonstrates simplicity of application. Heating augmentation factors of 12 and 3 above the fully laminar values are shown to exist on the cavity floor and endwall, respectively, if the flow exits in fully tripped-to-turbulent boundary layer state. Cavity floor heating data in geometries installed on the windward surface of 0.075-scale Shuttle wind tunnel models have also been retrieved from the boundary layer transition database developed for the Return-To-Flight Program. These data were independently acquired at Mach 6 and Mach 10 in air, and at Mach 6 in CF4. The correlation parameters for the floor-averaged heating have been developed and they offer an exceptionally positive comparison to previously developed laminar-cavity heating correlations. Non-laminar increments have been extracted from the Shuttle data and they fall on the newly developed transitional in-cavity correlations, and they are bounded by the 95% correlation prediction limits. Because the ratio of specific heats changes along the re-entry trajectory, turning angle into a cavity and boundary layer flow properties may be affected, raising concerns regarding the application validity of the heating augmentation predictions.

Everhart, Joel L.↗

NASA NTRS1991

Balancing antagonistic time and resource utilization constraints in over-subscribed scheduling problems

In this paper, we report work aimed at applying concepts of constraint-based problem structuring and multi-perspective scheduling to an over-subscribed scheduling problem. Previous research has demonstrated the utility of these concepts as a means for effectively balancing conflicting objectives in constraint-relaxable scheduling problems, and our goal here is to provide evidence of their similar potential in the context of HST observation scheduling. To this end, we define and experimentally assess the performance of two time-bounded heuristic scheduling strategies in balancing the tradeoff between resource setup time minimization and satisfaction of absolute time constraints. The first strategy considered is motivated by dispatch-based manufacturing scheduling research, and employs a problem decomposition that concentrates local search on minimizing resource idle time due to setup activities. The second is motivated by research in opportunistic scheduling and advocates a problem decomposition that focuses attention on the goal activities that have the tightest temporal constraints. Analysis of experimental results gives evidence of differential superiority on the part of each strategy in different problem solving circumstances. A composite strategy based on recognition of characteristics of the current problem solving state is then defined and tested to illustrate the potential benefits of constraint-based problem structuring and multi-perspective scheduling in over-subscribe scheduling problems.

Smith, Stephen F.↗

NASA NTRS2000

Coma Morphology Due to an Extended Active Region and Implications for the Spin State of Comet Hale-Bopp

We show that the circular character of continuum structures observed in the coma of comet Hale-Bopp around the perihelion passage is most likely due to a dust jet from a large extended active region on the surface. Coma morphology due to a wide jet is different from that due to a narrow jet. The latter shows foreshortening effects due to observing geometry, wider jet produces more circular features. This circularization effect provides a self-consistent explanation for the evolution of near-perihelion coma morphology. No changes in the direction of the rotational angular momentum vector are required during this period in contrast to the models of Schleicher et al. This circularization effect also enables us to produce near-circular coma features in the S-E quadrant during 1997 late February and therefore questions the basic premise on which Sekanina bases his morphological arguments for a gravitationally bound satellite nucleus.

Samarasinha, Nalin H.↗

NASA NTRS2004

Measuring the Mass Distribution in Z is Approximately 0.2 Cluster Lenses with XMM, HST and CFHT

Being the most massive gravitationally bound objects in the Universe, clusters of galaxies are prime targets for studies of structure formation and evolution. Specifically the comoving space density of virialized clusters of a given mass (or X-ray temperature), but also the frequency and degree of substructure, as well as the shape of the cluster mass profile are quantities whose current values and evolution as a function of lookback time can provide important constraints on the cosmological and physical parameters of structure formation theories. The project funded by NASA grant NAG 5-10041 intended to take such studies to a new level by combining observations of a well-selected cluster sample by three state-of-the-art telescopes: HST, to accurately measure the mass distribution in the cluster core (approx. 0.5 h(sup -1)(sub 50) Mpc) via strong gravitational lensing; CFHT, to measure the large scale mass distribution out to approx. 3 Mpc via weak lensing; and XMM, to measure the gas density and temperature distribution accurately on intermediate scales < 1.5 Mpc. XMM plays a pivotal role in this context as the calibration of X-ray mass measurements through accurate, spatially resolved X-ray temperature measurements (particularly in the cosmologically most sensitive range of kT> 5 keV) is central to the questions outlined above. This set of observations promised to yield the best cluster mass measurements obtained so far for a representative sample, thus allowing us to: 1) Measure the high-mass end of the local cluster mass function; 2) Test predictions of a universal cluster mass profile; 3) calibrate the mass-temperature and temperature-luminosity relations for clusters and the scatter around these relations, which is vital for studies of cluster evolution using the X-ray temperature and X-ray luminosity functions.

Source record↗

NASA NTRS2017

VIII. New Zr IV-VII, Xe IV-V, and Xe VII Oscillator Strengths and the Al, Zr, and Xe Abundances in the Hot White Dwarfs G191-B2B and RE0503-289

Context: For the spectral analysis of high-resolution and high-signal-to-noise spectra of hot stars, state-of-the-art non-local thermodynamic equilibrium (NLTE) model atmospheres are mandatory. These are strongly dependent on the reliability of the atomic data that is used for their calculation. Aims: To search for zirconium and xenon lines in the ultraviolet (UV) spectra of G191−B2B and RE 0503−289, new Zr iv-vii, Xe iv-v, and Xe vii oscillator strengths were calculated. This allows, for the first time, determination of the Zr abundance in white dwarf (WD) stars and improvement of the Xe abundance determinations.Methods: We calculated Zr iv-vii, Xe iv-v, and Xe vii oscillator strengths to consider radiative and collisional bound-bound transitions of Zr and Xe in our NLTE stellar-atmosphere models for the analysis of their lines exhibited in UV observations of the hot WDs G191−B2B and RE 0503−289. Results: We identified one new Zr iv, 14 new Zr v, and ten new Zr vi lines in the spectrum of RE 0503−289. Zr was detected for the first time in a WD. We measured a Zr abundance of −3.5 +/- 0.2 (logarithmic mass fraction, approx. 11 500 times solar). We identified five new Xe vi lines and determined a Xe abundance of −3.9 +/- 0.2 (approx. 7500 times solar). We determined a preliminary photospheric Al abundance of −4.3 +/- 0.2 (solar) in RE 0503−289. In the spectra of G191−B2B, no Zr line was identified. The strongest Zr iv line (1598.948 Å) in our model gave an upper limit of −5.6 +/- 0.3 (approx. 100 times solar). No Xe line was identified in the UV spectrum of G191−B2B and we confirmed the previously determined upper limit of −6.8 +/- 0.3 (ten times solar). Conclusions: Precise measurements and calculations of atomic data are a prerequisite for advanced NLTE stellar-atmosphere modeling. Observed Zr iv-vi and Xe vi-vii line profiles in the UV spectrum of RE 0503−289 were simultaneously well reproduced with our newly calculated oscillator strengths.

Rauch, T.↗

NASA NTRS1990

Masking failures of multidimensional sensors (extended abstract)

When a computer monitors a physical process, the computer uses sensors to determine the values of the physical variables that represent the state of the process. A sensor can sometimes fail, however, and in the worst case report a value completely unrelated to the true physical value. The work described is motivated by a methodology for transforming a process control program that can not tolerate sensor failure into one that can. In this methodology, a reliable abstract sensor is created by combining information from several real sensors that measure the same physical value. To be useful, an abstract sensor must deliver reasonably accurate information at reasonable computational cost. Sensors are considered that deliver multidimensional values (e.g., location or velocity in three dimensions, or both temperature and pressure). Geometric techniques are used to derive upper bounds on abstract sensor accuracy and to develop efficient algorithms for implementing abstract sensors.

Chew, Paul↗