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NASA NTRS1998

Stable Inversion for Nonlinear Nonminimum-Phase Time Varying Systems

In this paper, we extend stable inversion to nonlinear time-varying systems and study computational issues; the technique is applicable to minimum-phase as well as nonminimum-phase systems. The inversion technique is new, even in the linear time-varying case, and relies on partitioning (the dichotomic split of) the linearized system dynamics into time-varying, stable, and unstable, submanifolds. This dichotomic split is used to build time-varying filters which are, in turn, the basis of a contraction used to find a bounded inverse input-state trajectory. Finding the inverse input-state trajectory allows the development or exact-output tracking controllers. The method is local to the time-varying trajectory and requires that the internal dynamics vary slowly; however, the method represents a significant advance relative to presently available tracking controllers. Present techniques are restricted to time-invariant nonlinear systems and, in the general case, track only asymptotically.

Devasia, S.↗

NASA NTRS1999

Efficient Multi-Stage Time Marching for Viscous Flows via Local Preconditioning

A new method has been developed to accelerate the convergence of explicit time-marching, laminar, Navier-Stokes codes through the combination of local preconditioning and multi-stage time marching optimization. Local preconditioning is a technique to modify the time-dependent equations so that all information moves or decays at nearly the same rate, thus relieving the stiffness for a system of equations. Multi-stage time marching can be optimized by modifying its coefficients to account for the presence of viscous terms, allowing larger time steps. We show it is possible to optimize the time marching scheme for a wide range of cell Reynolds numbers for the scalar advection-diffusion equation, and local preconditioning allows this optimization to be applied to the Navier-Stokes equations. Convergence acceleration of the new method is demonstrated through numerical experiments with circular advection and laminar boundary-layer flow over a flat plate.

Kleb, William L.↗

NASA NTRS1999

Global Monitoring of Precipitation on Monthly and Shorter Time Scales Utilizing Low-Orbit and Geosynchronous Satellite Observations

A satellite-based system to monitor global precipitation on monthly and shorter time scales is described. The monitoring system is based primarily on the Global Precipitation Climatology Project (GPCP) global, monthly, 2.5 degree by 2.5 degree latitude-longitude product which utilizes precipitation estimates from low-orbit microwave sensors (SSM/I) and geosynchronous IR sensors and raingauge information over land. The low-orbit microwave estimates are used to adjust or correct the geosynchronous IR estimates, thereby maximizing the utility of the more physically-based microwave estimates and the finer time sampling of the geosynchronous observations. Information from raingauges is blended into the analyses over land. This globally complete, monthly product is available from January 1986 to the present, with an extension back to January 1979 underway using non-SSM/I data. The monthly GPCP merged data product described in the previous paragraph is available a few (2-4) months after the end of the month. An analysis based solely on low-orbit microwave (SSM/1) data and the Goddard Profiling (GPROF) algorithm is used to bring the global monitoring up to real time. Anomalies from climatological means are produced from both the GPCP and GPROF fields to monitor the evolution of global precipitation, including the calculation of ENSO precipitation indices for real-time (five- day running means) climate monitoring and comparison with previous ENSO anomalies. The long-term climatology of the global precipitation field and the time and space variations thereof will be discussed, including the variations associated with the 1997- 1998 ENSO. The GPCP fields will also be compared to analyses based on the recently launched Tropical Rain Measuring Mission (TRMM). On an even shorter time scale, a new daily, 1 degree x 1 degree latitude-longitude global analysis has been developed starting in January 1997 utilizing low-orbit microwave and geosynchronous IR information using a similar method as is used to produce the monthly GPCP product. Retaining the overall small bias of the monthly product the daily product will allow greater utilization in the hydrology and other science communities.

Adler, Robert↗

NASA NTRS1999

Near-Surface Flow Fields Deduced Using Correlation Tracking and Time-Distance Analysis

Near-photospheric flow fields on the Sun are deduced using two independent methods applied to the same time series of velocity images observed by SOI-MDI on SOHO. Differences in travel times between f modes entering and leaving each pixel measured using time-distance helioseismology are used to determine sites of supergranular outflows. Alternatively, correlation tracking analysis of mesogranular scales of motion applied to the same time series is used to deduce the near-surface flow field. These two approaches provide the means to assess the patterns and evolution of horizontal flows on supergranular scales even near disk center, which is not feasible with direct line-of-sight Doppler measurements. We find that the locations of the supergranular outflows seen in flow fields generated from correlation tracking coincide well with the locations of the outflows determined from the time-distance analysis, with a mean correlation coefficient after smoothing of bar-r(sub s) = 0.840. Near-surface velocity field measurements can used to study the evolution of the supergranular network, as merging and splitting events are observed to occur in these images. The data consist of one 2048-minute time series of high-resolution (0.6" pixels) line-of-sight velocity images taken by MDI on 1997 January 16-18 at a cadence of one minute.

DeRosa, Marc↗

NASA NTRS2000

Advantages of Parallel Processing and the Effects of Communications Time

Many computing tasks involve heavy mathematical calculations, or analyzing large amounts of data. These operations can take a long time to complete using only one computer. Networks such as the Internet provide many computers with the ability to communicate with each other. Parallel or distributed computing takes advantage of these networked computers by arranging them to work together on a problem, thereby reducing the time needed to obtain the solution. The drawback to using a network of computers to solve a problem is the time wasted in communicating between the various hosts. The application of distributed computing techniques to a space environment or to use over a satellite network would therefore be limited by the amount of time needed to send data across the network, which would typically take much longer than on a terrestrial network. This experiment shows how much faster a large job can be performed by adding more computers to the task, what role communications time plays in the total execution time, and the impact a long-delay network has on a distributed computing system.

Eddy, Wesley M.↗

NASA NTRS2000

It's About Time!

Everything we do in VLBI is connected to time. In this contribution, we review 28 orders of magnitude of the spectrum of time ranging from a few hundred femtoseconds (i.e. one degree of phase at X-band - Pi x 10(exp -13) seconds) upwards to tens of millions of years (i.e. ten million years Pi x 10(exp 14) seconds). In this discussion, we will pay special attention to the relation between the underlying oscillator (the frequency standard that defines a clock's rate) and the time kept by the clock (which counts the oscillations of the frequency standard). We will consider two different types of time - time kept by counting an atomic frequency standard (Hydrogen Maser or Cesium), and time reckoned by the rotation of the Earth underneath the stars and sun.

Clark, Tom↗

NASA NTRS1999

A Post-Pathfinder Evaluation of Areocentric Solar Coordinates with Improved Timing Recipes for Mars Seasonal/Diurnal Climate Studies

The accurate determination of the Mars pole vector derived from Pathfinder and Viking Lander radio data, together with the VSOP87 representation of planetary orbits, have been applied to a new evaluation of the right ascension of the "fictitious mean sun" (FMS) at Mars. With DELTA t (sub J2000) the elapsed time in days from the J2000 epoch (J.D.2451545.0 (sup TT), alpha FMS = 270 degrees.3863 + 0.52403840(degrees/d) (raised dot) DELTA T (sub j2000) - 4 x 10 (exp -13) (degrees/d (sup 2)) (raised dot) DELTA t (sup 2) (sub J2000) represents a best least-squares quadratic fit of the FMS, including aberration, to each instance of the four equinox and solstice passages for each of 134 Mars orbits spanning the calendar years 1874-2127. The implied tropical orbit period for Mars, 686.9726 (sup d), closely agrees with the recent evaluations. Together with the Pathfinder radio determination of the Mars sidereal rotation, the derived FMS rate corresponds to a mean solar day (or "sol") of 1.027491251 (sup d). The new FMS determination would serve to define the Mean Solar Time at Mars to the nearest tenth-second, according to historical conventions originally established for terrestrial time keeping, once the Mars prime meridian defined by the crater Airy-O is navigated to the same accuracy. For convenient reference to current epochs, 2000 Jan 06 00:00 UTC (= MJD 51549.000 (sup UTC)) corresponds to a coincidence of (alpha (sub FMS)) and the rotation angle of the crater Airy-O measured with respect to the Mars equinox (i.e. "mean solar midnight" on the planet's prime meridian), to within the current uncertainty of several seconds in the locational definition of the planet's cartographic grid. As a further result of the analysis, the consistently derived Mars obliquity of date is epsilon = 25 degrees.192 + 3.45 x l0 (exp -7)(degrees/d)(raised dot) DELTA t (sub J2000). An improved analytic recipe for the calculation of the solar areocentric longitude (L (sub s)) of Mars to an accuracy of 0 degrees.01 is also provided, accounting for the primary perturbations of Earth, Jupiter, and Venus, which may in turn be applied to an efficient evaluation of Mars local true solar time (LTST) to within the uncertainty of the inertial position of the Mars prime meridian. For specific applications to the data archives for landed Mars spacecraft, simple conversion formulae are given for the determination of the Viking "Local Lander Time" and the Pathfinder "Local True Solar Time" in terms of the terrestrial calendar date and UTC.

Allison, Michael↗

NASA NTRS2001

Comparison of Fault Detection Algorithms for Real-time Diagnosis in Large-Scale System

In this paper, we present a review of different real-time capable algorithms to detect and isolate component failures in large-scale systems in the presence of inaccurate test results. A sequence of imperfect test results (as a row vector of I's and O's) are available to the algorithms. In this case, the problem is to recover the uncorrupted test result vector and match it to one of the rows in the test dictionary, which in turn will isolate the faults. In order to recover the uncorrupted test result vector, one needs the accuracy of each test. That is, its detection and false alarm probabilities are required. In this problem, their true values are not known and, therefore, have to be estimated online. Other major aspects in this problem are the large-scale nature and the real-time capability requirement. Test dictionaries of sizes up to 1000 x 1000 are to be handled. That is, results from 1000 tests measuring the state of 1000 components are available. However, at any time, only 10-20% of the test results are available. Then, the objective becomes the real-time fault diagnosis using incomplete and inaccurate test results with online estimation of test accuracies. It should also be noted that the test accuracies can vary with time --- one needs a mechanism to update them after processing each test result vector. Using Qualtech's TEAMS-RT (system simulation and real-time diagnosis tool), we test the performances of 1) TEAMSAT's built-in diagnosis algorithm, 2) Hamming distance based diagnosis, 3) Maximum Likelihood based diagnosis, and 4) HidderMarkov Model based diagnosis.

Kirubarajan, Thiagalingam↗

NASA NTRS2001

Timing the Geminga Pulsar with Gamma-Ray Observations

We present the COS-B/EGRET 1997 ephemeris for the rotation of the Geminga pulsar. This ephemeris is derived from high-energy gamma-ray observations that span 24 yr. The recently obtained accurate position and proper motion are assumed. A cubic ephemeris predicts the rotational phase of Geminga with errors smaller than 50 milliperiods for all existing high-energy gamma-ray observations that span a 24.2 yr timing baseline. The braking index obtained is 17 +/- 1. Further observation is required to ascertain whether this high value truly reflects the rotational energy loss mechanism, or whether it is a manifestation of timing noise. The ephemeris parameters are sufficiently constrained so that timing noise will be the limitation on forward extrapolation. If Geminga continues to rotate without a glitch, as it has for at least 23 yr, we expect this ephemeris to continue to describe the phase, with an error of less than 100 milliperiods, until 2008. Statistically significant timing residuals are detected in the EGRET data that depart from the cubic ephemeris at a level of 30 milliperiods. Although this could simply be an additional manifestation of timing noise, the EGRET timing residuals appear to have a sinusoidal modulation that is consistent with a planet of mass 1.7/sin i solar mass, orbiting Geminga at a radius of 3.3 AU.

Mattox, J. R.↗

NASA NTRS2001

Continued Investigations of the Accretion History of Extraterrestrial Matter over Geologic Time

This grant supported our ongoing project to characterize the accretion rate of interplanetary dust particles (IDPs) to Earth over geologic time using He-3 as a tracer. IDPs are derived from collisions in the asteroid belt and from disaggregation of active comets. Owing to their small size (few to few hundred micrometers diameter) these particles spiral into the sun under Poynting-Robertson drag typically in less than a few tens of kyrs. Thus IDPs must be continually resupplied to the zodiacal cloud, and because the processes of IDP production are likely to be sporadic, time variation in the IDP accretion rate to Earth is likely to be time-varying. For example, major asteroidal collisions and comet showers should greatly enhance the IDP accretion rate. Our ultimate objective (still ongoing) is to document this time variance so as to better understand the history of the solar system, the source of IDPs accreting to Earth, and the details of the mechanism by which particles are captured by Earth. To document variations in IDP accretion rate through time we use He-3 as a tracer. This isotope is in extremely low abundance in terrestrial matter, but IDPs have very high concentrations of He-3 from implantation of solar wind ions. By measuring He-3 in seafloor sediments, we can estimate the IDP accretion rate for at least the last few hundred Myrs. Under an earlier NASA grant we identified the existence of a large increase in He-3 flux in the Late Eocene (35 Myr ago), coincident with the two largest impact craters of the Cenozoic Era. The simplest interpretation of this observation is the occurrence of a shower of long period comets at that time, simultaneously increasing the impact cratering probability and accretion rate of IDPs to Earth (Farley et al., 1998). Comet showers produced by stellar perturbation of the Oort cloud should be fairly common in the geologic record, so this is not an unreasonable interpretation of our observations.

Farley, Kenneth↗

NASA NTRS2002

Resource Selection Using Execution and Queue Wait Time Predictions

Computational grids provide users with many possible places to execute their applications. We wish to help users select where to run their applications by providing predictions of the execution times of applications on space shared parallel computers and predictions of when scheduling systems for such parallel computers will start applications. Our predictions are based on instance based learning techniques and simulations of scheduling algorithms. We find that our execution time prediction techniques have an average error of 37 percent of the execution times for trace data recorded from SGI Origins at NASA Ames Research Center and that this error is 67 percent lower than the error of user estimates. We also find that the error when predicting how long applications will wait in scheduling queues is 95 percent of mean queue wait times when using our execution time predictions and this is 57 percent lower than if we use user execution time estimates.

Warren, Smith↗

NASA NTRS2002

Resource Selection Using Execution and Queue Wait Time Predictions

Smith, Warren↗

NASA NTRS2002

Prediction of Long-Term Strength of Thermoplastic Composites Using Time-Temperature Superposition

Accelerated tests for composite failure were investigated. Constant ramp transverse strength tests on thermoplastic composite specimens were conducted at four temperatures from 300 F to 450 F and five duration times from 0.5 sec to 24 hrs. Up to 400 F, the time-temperature-superposition method produces a master curve allowing strength at longer times to be estimated from strength tests conducted over shorter times but at higher temperatures. The shift factors derived from compliance tests applied well to the strength data. To explain why strength behaved similar to compliance, a viscoelastic fracture model was investigated based on the hypothesis that the work of fracture for crack initiation at some critical flaw remains constant with time and temperature. The model, which used compliance as input, was found to fit the strength data only if the critical fracture energy was allowed to vary with stress rate. Fracture tests using double cantilever beam specimens were conducted from 300 F to 450 F over time scales similar to the strength study. The toughness data showed a significant change with loading rate, less variation with temperature, did not form a master curve, and could not be correlated with the fracture model. Since the fracture model did not fit the fracture data, an alternative explanation based on the dilatational strain energy density was proposed. However the usefulness of this model is severely limited because it relies on a critical parameter which varies with loading rate.

Reeder, James R.↗

NASA NTRS2001

Diffusion Time-Scale of Porous Pressure-Sensitive Paint

Pressure-sensitive paint (PSP) is an optical pressure sensor that utilizes the oxygen quenching of luminescence. PSP measurements in unsteady aerodynamic flows require fast time response of the paint. There are two characteristic time-scales that are related to the time response of PSP. One is the luminescent lifetime representing an intrinsic physical limit for the achievable temporal resolution of PSP. Another is the time-scale of oxygen diffusion across the PSP layer. When the time-scale of oxygen diffusion is much larger than the luminescent lifetime, the time response of PSP is controlled by oxygen diffusion. In a thin homogenous polymer layer where diffusion is Fickian, the oxygen concentration 1021 can be described by the diffusion equation in one-dimension.

Liu, Tianshu↗

NASA NTRS2003

Characterization of the Crab Pulsar's Timing Noise

We present a power spectral analysis of the Crab pulsar's timing noise, mainly using radio measurements from Jodrell Bank taken over the period 1982-1989, an interval bounded by sparse data sampling and a large glitch. The power spectral analysis is complicated by nonuniform data sampling and the presence of a steep red power spectrum that can distort power spectra measurement by causing severe power 'leakage'. We develop a simple windowing method for computing red noise power spectra of uniformly sampled data sets and test it on Monte Carlo generated sample realizations of red power-law noise. We generalize time-domain methods of generating power-law red noise with even integer spectral indices to the case of noninteger spectral indices. The Jodrell Bank pulse phase residuals are dense and smooth enough that an interpolation onto a uniform time series is possible. A windowed power spectrum is computed revealing a periodic or nearly periodic component with a period of 568 +/- 10 days and a l/f(exp 3) power-law noise component in pulse phase with a noise strength S(sub infinity)=(1.24 +/- 0.067) x 10(exp 16) cycles(exp 2)/sec(exp 2) over the analysis frequency range f=0.003- 0.1 cycles/day. This result deviates from past analyses which characterized the pulse phase timing residuals as either l/f(sub 4) power-law noise or a quasiperiodic process. The analysis was checked using the Deeter polynomial method of power spectrum estimation that was developed for the case of nonuniform sampling, but has lower spectral resolution. The timing noise is consistent with a torque noise spectrum rising with analysis frequency as f implying blue torque noise, a result not predicted by current models of pulsar timing noise. If the periodic or nearly periodic component is due to a binary companion, we find a mass function f(M) = (6.8 +/- 2.4) x 10(exp -16) solar mass and a companion mass, M(sub c) is greater than or equal to 3.2 solar mass assuming a Crab pulsar mass of 1.4 solar mass.

Scott, D. M.↗

NASA NTRS2003

Flight Investigation of Prescribed Simultaneous Independent Surface Excitations for Real-Time Parameter Identification

Near real-time stability and control derivative extraction is required to support flight demonstration of Intelligent Flight Control System (IFCS) concepts being developed by NASA, academia, and industry. Traditionally, flight maneuvers would be designed and flown to obtain stability and control derivative estimates using a postflight analysis technique. The goal of the IFCS concept is to be able to modify the control laws in real time for an aircraft that has been damaged in flight. In some IFCS implementations, real-time parameter identification (PID) of the stability and control derivatives of the damaged aircraft is necessary for successfully reconfiguring the control system. This report investigates the usefulness of Prescribed Simultaneous Independent Surface Excitations (PreSISE) to provide data for rapidly obtaining estimates of the stability and control derivatives. Flight test data were analyzed using both equation-error and output-error PID techniques. The equation-error PID technique is known as Fourier Transform Regression (FTR) and is a frequency-domain real-time implementation. Selected results were compared with a time-domain output-error technique. The real-time equation-error technique combined with the PreSISE maneuvers provided excellent derivative estimation in the longitudinal axis. However, the PreSISE maneuvers as presently defined were not adequate for accurate estimation of the lateral-directional derivatives.

Moes, Timothy R.↗

NASA NTRS2004

Simulating Nonlinear Deformations of Solar Sail Membranes Using Explicit Time Integration

In this study, the explicit time integration method is employed to predict deformation of highly flexible solar sail structural components. The nonlinear static analysis of a highly flexible ribbon structure is presented to demonstrate the need for having the explicit time integration method in the analysis toolbox for solar sail. Static analyses of the ribbon structure produce ambiquous results whereas the explicit time integration method determines the correct results. Extensive benchmarking examples are also presented to build confidence in the use of the explicit method. Previously determined nonlinear wrinkling deformations of solar sail membranes are found by the explicit method. As the explicit method is known to often require more computational time than nonlinear static methods, a study on mass scaling was also conducted. The computational times are reported for the nonlinear static and explicit time integration solutions to calibrate the advantage of using mass scaling for these problems.

Wang, John T.↗

NASA NTRS2004

Using Fuzzy Clustering for Real-time Space Flight Safety

To ensure space flight safety, it is necessary to monitor myriad sensor readings on the ground and in flight. Since a space shuttle has many sensors, monitoring data and drawing conclusions from information contained within the data in real time is challenging. The nature of the information can be critical to the success of the mission and safety of the crew and therefore, must be processed with minimal data-processing time. Data analysis algorithms could be used to synthesize sensor readings and compare data associated with normal operation with the data obtained that contain fault patterns to draw conclusions. Detecting abnormal operation during early stages in the transition from safe to unsafe operation requires a large amount of historical data that can be categorized into different classes (non-risk, risk). Even though the 40 years of shuttle flight program has accumulated volumes of historical data, these data don t comprehensively represent all possible fault patterns since fault patterns are usually unknown before the fault occurs. This paper presents a method that uses a similarity measure between fuzzy clusters to detect possible faults in real time. A clustering technique based on a fuzzy equivalence relation is used to characterize temporal data. Data collected during an initial time period are separated into clusters. These clusters are characterized by their centroids. Clusters formed during subsequent time periods are either merged with an existing cluster or added to the cluster list. The resulting list of cluster centroids, called a cluster group, characterizes the behavior of a particular set of temporal data. The degree to which new clusters formed in a subsequent time period are similar to the cluster group is characterized by a similarity measure, q. This method is applied to downlink data from Columbia flights. The results show that this technique can detect an unexpected fault that has not been present in the training data set.

Lee, Charles↗