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Statistical Evaluation and Improvement of Methods for Combining Random and Harmonic Loads

Structures in many environments experience both random and harmonic excitation. A variety of closed-form techniques has been used in the aerospace industry to combine the loads resulting from the two sources. The resulting combined loads are then used to design for both yield/ultimate strength and high- cycle fatigue capability. This Technical Publication examines the cumulative distribution percentiles obtained using each method by integrating the joint probability density function of the sine and random components. A new Microsoft Excel spreadsheet macro that links with the software program Mathematica to calculate the combined value corresponding to any desired percentile is then presented along with a curve tit to this value. Another Excel macro that calculates the combination using Monte Carlo simulation is shown. Unlike the traditional techniques. these methods quantify the calculated load value with a consistent percentile. Using either of the presented methods can be extremely valuable in probabilistic design, which requires a statistical characterization of the loading. Additionally, since the CDF at high probability levels is very flat, the design value is extremely sensitive to the predetermined percentile; therefore, applying the new techniques can substantially lower the design loading without losing any of the identified structural reliability.

Brown, A. M.

Statistical Comparison and Improvement of Methods for Combining Random and Harmonic Loads

Structures in many environments experience both random and harmonic excitation. A variety of closed-form techniques has been used in the aerospace industry to combine the loads resulting from the two sources. The resulting combined loads are then used to design for both yield ultimate strength and high cycle fatigue capability. This paper examines the cumulative distribution function (CDF) percentiles obtained using each method by integrating the joint probability density function of the sine and random components. A new Microsoft Excel spreadsheet macro that links with the software program Mathematics is then used to calculate the combined value corresponding to any desired percentile along with a curve fit to this value. Another Excel macro is used to calculate the combination using a Monte Carlo simulation. Unlike the traditional techniques, these methods quantify the calculated load value with a Consistent percentile. Using either of the presented methods can be extremely valuable in probabilistic design, which requires a statistical characterization of the loading. Also, since the CDF at high probability levels is very flat, the design value is extremely sensitive to the predetermined percentile; therefore, applying the new techniques can lower the design loading substantially without losing any of the identified structural reliability.

Brown, Andrew M.

Hologic QDR 2000 whole-body scans: a comparison of three combinations of scan modes and analysis software

This study reports on the short-term in vivo precision and absolute measurements of three combinations of whole-body scan modes and analysis software using a Hologic QDR 2000 dual-energy X-ray densitometer. A group of 21 normal, healthy volunteers (11 male and 10 female) were scanned six times, receiving one pencil-beam and one array whole-body scan on three occasions approximately 1 week apart. The following combinations of scan modes and analysis software were used: pencil-beam scans analyzed with Hologic's standard whole-body software (PB scans); the same pencil-beam analyzed with Hologic's newer "enhanced" software (EPB scans); and array scans analyzed with the enhanced software (EA scans). Precision values (% coefficient of variation, %CV) were calculated for whole-body and regional bone mineral content (BMC), bone mineral density (BMD), fat mass, lean mass, %fat and total mass. In general, there was no significant difference among the three scan types with respect to short-term precision of BMD and only slight differences in the precision of BMC. Precision of BMC and BMD for all three scan types was excellent: < 1% CV for whole-body values, with most regional values in the 1%-2% range. Pencil-beam scans demonstrated significantly better soft tissue precision than did array scans. Precision errors for whole-body lean mass were: 0.9% (PB), 1.1% (EPB) and 1.9% (EA). Precision errors for whole-body fat mass were: 1.7% (PB), 2.4% (EPB) and 5.6% (EA). EPB precision errors were slightly higher than PB precision errors for lean, fat and %fat measurements of all regions except the head, although these differences were significant only for the fat and % fat of the arms and legs. In addition EPB precision values exhibited greater individual variability than PB precision values. Finally, absolute values of bone and soft tissue were compared among the three combinations of scan and analysis modes. BMC, BMD, fat mass, %fat and lean mass were significantly different between PB scans and either of the EPB or EA scans. Differences were as large as 20%-25% for certain regional fat and BMD measurements. Additional work may be needed to examine the relative accuracy of the scan mode/software combinations and to identify reasons for the differences in soft tissue precision with the array whole-body scan mode.

NASA Discipline Musculoskeletal

Combinations of Earth Orientation Measurements: SPACE2003, COMB2003, and POLE2003

Independent Earth orientation measurements taken by the space-geodetic techniques of lunar and satellite laser ranging, very long baseline interferometry, and the global positioning system have been combined using a Kalman filter. The resulting combined Earth orientation series, SPACE2003, consists of values and uncertainties for Universal Time, polar motion, and their rates that span from September 28.0, 1976 to January 31.0, 2004 at daily intervals and is available in versions whose epochs are given at either midnight or noon. The space-geodetic measurements used to generate SPACE2003 have then been combined with optical astrometric measurements to form two additional combined Earth orientation series: (1) COMB2003, consisting of values and uncertainties for Universal Time, polar motion, and their rates that span from January 20.0, 1962 to January 31.0, 2004 at daily intervals and which is also available in versions whose epochs are given at either midnight or noon, and (2) POLE2003, consisting of values and uncertainties for polar motion and its rate that span from January 20, 1900 to January 21,2004 at 30.4375-day intervals.

Gross, Richard S.

Combinations of Earth Orientation Measurements: SPACE2004, COMB2004, and POLE2004

Independent Earth orientation measurements taken by the space-geodetic techniques of lunar and satellite laser ranging, very long baseline interferometry, and the global positioning system have been combined using a Kalman filter. The resulting combined Earth orientation series, SPACE2004, consists of values and uncertainties for Universal Time, polar motion, and their rates that span from September 28, 1976, to January 22, 2005, at daily intervals and is available in versions whose epochs are given at either midnight or noon. The space-geodetic measurements used to generate SPACE2004 have then been combined with optical astrometric measurements to form two additional combined Earth orientation series: (1) COMB2004, consisting of values and uncertainties for Universal Time, polar motion, and their rates that span from January 20, 1962, to January 22, 2005, at daily intervals and which is also available in versions whose epochs are given at either midnight or noon, and (2) POLE2004, consisting of values and uncertainties for polar motion and its rate that span from January 20, 1900, to January 20, 2005, at 30.4375-day intervals.

Gross, Richard R.

TOPEX/Poseidon Precision Orbit Determination Using Combined GPS, SLR, and DORIS

TOPEX/Poseidon (T/P) is a joint spaceborne oceanographic mission of U.W. NASA and France CNES design launched August 10, 1992. The satellite has a variety tracking systems for both operational and precision orbit determination. Three precise tracking systems: Satellite Laser Ranging (SLR), Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), and Global Positioning System (GPS) provide high quality measurements essential for reconstructing the T/P orbital height with centimeter precision. This paper presents results of simultaneously processing all three data types to exploit the inherent strength of each in a combined solution. SLR and DORIS are routinely combined to provide orbit solutions for the T/P science team. GPS orbit solutions are produced as part of the first demonstration flight of a high quality spaceborne GPS receiver. Coordinate frame and software system differences between the combined SLR/DORIS orbits and the GPS orbits induce orbital height differences of 2 to 3 centimeters. Combining the three data types within a single software system permits removal of software system differences while obtaining coordinate frame calibration information. These calibrations will aid future spaceborne GPS missions that are not complemented with SLR and/or DORIS.

TOPEX/Poseidon

Configuration and Sizing of a Test Fixture for Panels Under Combined Loads

Future air and space structures are expected to utilize composite panels that are subjected to combined mechanical loads, such as bi-axial compression/tension, shear and pressure. Therefore, the ability to accurately predict the buckling and strength failures of such panels is important. While computational analysis can provide tremendous insight into panel response, experimental results are necessary to verify predicted performances of these panels to judge the accuracy of computational methods. However, application of combined loads is an extremely difficult task due to the complex test fixtures and set-up required. Presented herein is a comparison of several test set-ups capable of testing panels under combined loads. Configurations compared include a D-box, a segmented cylinder and a single panel set-up. The study primarily focuses on the preliminary sizing of a single panel test configuration capable of testing flat panels under combined in-plane mechanical loads. This single panel set-up appears to be best suited to the testing of both strength critical and buckling critical panels. Required actuator loads and strokes are provided for various square, flat panels.

Lovejoy, Andrew E.

Combinations of Earth Orientation Measurements: SPACE2005, COMB2005, and POLE2005

Independent Earth orientation measurements taken by the space-geodetic techniques of lunar and satellite laser ranging, by very long baseline interferometry, and by the Global Positioning System have been combined using a Kalman filter. The resulting combined Earth orientation series, SPACE2005, consists of values and uncertainties for Universal Time, polar motion, and their rates that span from September 28, 1976, to January 7, 2006, at daily intervals and is available in versions whose epochs are given at either midnight or noon. The space-geodetic measurements used to generate SPACE2005 have then been combined with optical astrometric measurements to form two additional combined Earth orientation series: (1) COMB2005, consisting of values and uncertainties for Universal Time, polar motion, and their rates that span from January 20, 1962, to January 7, 2006, at daily intervals and which is also available in versions whose epochs are given at either midnight or noon; and (2) POLE2005, consisting of values and uncertainties for polar motion and its rate that span from January 20, 1900, to December 21, 2005, at 30.4375-day intervals.

laser ranging

Improved Design Formulae for Buckling of Orthotropic Plates under Combined Loading

Simple, accurate buckling interaction formulae are presented for long orthotropic plates with either simply supported or clamped longitudinal edges and under combined loading that are suitable for design studies. The loads include 1) combined uniaxial compression (or tension) and shear, 2) combined pure inplane bending and 3) shear and combined uniaxial compression (or tension) and pure inplane bending. The interaction formulae are the results of detailed regression analysis of buckling data obtained from a very accurate Rayleigh-Ritz method.

Weaver, Paul M.

Spatial Combining of Laser-Diode Beams for Pumping an NPRO

A free-space optical beam combiner now undergoing development makes it possible to use the outputs of multiple multimode laser diodes to pump a neodymium-doped yttrium aluminum garnet (Nd:YAG) non-planar ring oscillator (NPRO) laser while ensuring that the laser operates at only a single desired frequency. Heretofore, a Nd:YAG NPRO like the present one has been pumped by a single multimode laser-diode beam delivered via an optical fiber. It would be desirable to use multiple pump laser diodes to increase reliability beyond that obtainable from a single pump laser diode. However, as explained in this article, simplistically coupling multiple multimode laser-diode beams through a fiber-optic combiner would entail a significant reduction in coupling efficiency, and lasing would occur at one or more other frequencies in addition to the single desired frequency. To minimize coupling loss, one must ensure that the NA (approximately equal to 0.3) of the combined laser-diode beams is less than the NA of the fiber. The A(Omega) of the laser-diode beam in the slow-axis plane is 1/1.3 as large as that of the fiber. This A(Omega) is small enough to enable efficient coupling of light into the optical fiber, but too large for combining of beams in the slow-axis plane. Therefore, a pair of cylindrical lenses is used to cancel the slow-axis plane magnification introduced by the on-cylindrical lenses used to effect magnification in the fast-axis plane.

Gelsinger, Paul

Estimation of Sea Ice Thickness Distributions through the Combination of Snow Depth and Satellite Laser Altimetry Data

Combinations of sea ice freeboard and snow depth measurements from satellite data have the potential to provide a means to derive global sea ice thickness values. However, large differences in spatial coverage and resolution between the measurements lead to uncertainties when combining the data. High resolution airborne laser altimeter retrievals of snow-ice freeboard and passive microwave retrievals of snow depth taken in March 2006 provide insight into the spatial variability of these quantities as well as optimal methods for combining high resolution satellite altimeter measurements with low resolution snow depth data. The aircraft measurements show a relationship between freeboard and snow depth for thin ice allowing the development of a method for estimating sea ice thickness from satellite laser altimetry data at their full spatial resolution. This method is used to estimate snow and ice thicknesses for the Arctic basin through the combination of freeboard data from ICESat, snow depth data over first-year ice from AMSR-E, and snow depth over multiyear ice from climatological data. Due to the non-linear dependence of heat flux on ice thickness, the impact on heat flux calculations when maintaining the full resolution of the ICESat data for ice thickness estimates is explored for typical winter conditions. Calculations of the basin-wide mean heat flux and ice growth rate using snow and ice thickness values at the 70 m spatial resolution of ICESat are found to be approximately one-third higher than those calculated from 25 km mean ice thickness values.

Kurtz, Nathan T.

High Efficiency Ka-Band Solid State Power Amplifier Waveguide Power Combiner

A novel Ka-band high efficiency asymmetric waveguide four-port combiner for coherent combining of two Monolithic Microwave Integrated Circuit (MMIC) Solid State Power Amplifiers (SSPAs) having unequal outputs has been successfully designed, fabricated and characterized over the NASA deep space frequency band from 31.8 to 32.3 GHz. The measured combiner efficiency is greater than 90 percent, the return loss greater than 18 dB and input port isolation greater than 22 dB. The manufactured combiner was designed for an input power ratio of 2:1 but can be custom designed for any arbitrary power ratio. Applications considered are NASA s space communications systems needing 6 to 10 W of radio frequency (RF) power. This Technical Memorandum (TM) is an expanded version of the article recently published in Institute of Engineering and Technology (IET) Electronics Letters.

Wintucky, Edwin G.

Combined Load Diagram for a Wind Tunnel Strain-Gage Balance

Combined Load Diagrams for Direct-Read, Force, and Moment Balances are discussed in great detail in the paper. The diagrams, if compared with a corresponding combined load plot of a balance calibration data set, may be used to visualize and interpret basic relationships between the applied balance calibration loads and the load components at the forward and aft gage of a strain-age balance. Lines of constant total force and moment are identified in the diagrams. In addition, the lines of pure force and pure moment are highlighted. Finally, lines of constant moment arm are depicted. It is also demonstrated that each quadrant of a Combined Load Diagram has specific regions where the applied total calibration force is at, between, or outside of the balance gage locations. Data from the manual calibration of a Force Balance is used to illustrate the application of a Combined Load Diagram to a realistic data set.

Ulbrich, N.

VLBI-SLR Combination Solution Using GEODYN

We would like to generate a multi-technique solution combining all of the geodetic techniques (VLBI, SLR, GPS, and DORIS) using the same software and using the same a priori models. Here we use GEODYN software and consider only the VLBI-SLR combination. Here we report initial results of our work on the combination. We first performed solutions with GEODYN using only VLBI data and found that VLBI EOP solution results produced with GEODYN agree with results using CALC/SOLVE at the 1-sigma level. We then combined the VLBI normal equations in GEODYN with weekly SLR normal equations for the period 2007-2008. Agreement of estimated Earth orientation parameters with IERS C04 were not significantly different for the VLBI-only, SLR-only, and VLBI+SLR solutions

MacMillan, Dan

Combining Satellite and in Situ Data with Models to Support Climate Data Records in Ocean Biology

The satellite ocean color data record spans multiple decades and, like most long-term satellite observations of the Earth, comes from many sensors. Unfortunately, global and regional chlorophyll estimates from the overlapping missions show substantial biases, limiting their use in combination to construct consistent data records. SeaWiFS and MODIS-Aqua differed by 13% globally in overlapping time segments, 2003-2007. For perspective, the maximum change in annual means over the entire Sea WiFS mission era was about 3%, and this included an El NinoLa Nina transition. These discrepancies lead to different estimates of trends depending upon whether one uses SeaWiFS alone for the 1998-2007 (no significant change), or whether MODIS is substituted for the 2003-2007 period (18% decline, P less than 0.05). Understanding the effects of climate change on the global oceans is difficult if different satellite data sets cannot be brought into conformity. The differences arise from two causes: 1) different sensors see chlorophyll differently, and 2) different sensors see different chlorophyll. In the first case, differences in sensor band locations, bandwidths, sensitivity, and time of observation lead to different estimates of chlorophyll even from the same location and day. In the second, differences in orbit and sensitivities to aerosols lead to sampling differences. A new approach to ocean color using in situ data from the public archives forces different satellite data to agree to within interannual variability. The global difference between Sea WiFS and MODIS is 0.6% for 2003-2007 using this approach. It also produces a trend using the combination of SeaWiFS and MODIS that agrees with SeaWiFS alone for 1998-2007. This is a major step to reducing errors produced by the first cause, sensor-related discrepancies. For differences that arise from sampling, data assimilation is applied. The underlying geographically complete fields derived from a free-running model is unaffected by solar zenith angle requirements and obscuration from clouds and aerosols. Combined with in situ dataenhanced satellite data, the model is forced into consistency using data assimilation. This approach eliminates sampling discrepancies from satellites. Combining the reduced differences of satellite data sets using in situ data, and the removal of sampling biases using data assimilation, we generate consistent data records of ocean color. These data records can support investigations of long-term effects of climate change on ocean biology over multiple satellites, and can improve the consistency of future satellite data sets.

Gregg, Watson

Spacecraft Attitude Tracking and Maneuver Using Combined Magnetic Actuators

A paper describes attitude-control algorithms using the combination of magnetic actuators with reaction wheel assemblies (RWAs) or other types of actuators such as thrusters. The combination of magnetic actuators with one or two RWAs aligned with different body axis expands the two-dimensional control torque to three-dimensional. The algorithms can guarantee the spacecraft attitude and rates to track the commanded attitude precisely. A design example is presented for nadir-pointing, pitch, and yaw maneuvers. The results show that precise attitude tracking can be reached and the attitude- control accuracy is comparable with RWA-based attitude control. When there are only one or two workable RWAs due to RWA failures, the attitude-control system can switch to the control algorithms for the combined magnetic actuators with the RWAs without going to the safe mode, and the control accuracy can be maintained. The attitude-control algorithms of the combined actuators are derived, which can guarantee the spacecraft attitude and rates to track the commanded values precisely. Results show that precise attitude tracking can be reached, and the attitude-control accuracy is comparable with 3-axis wheel control.

Zhou, Zhiqiang

Estimating Sea Surface Salinity and Wind Using Combined Passive and Active L-Band Microwave Observations

Several L-band microwave radiometer and radar missions have been, or will be, operating in space for land and ocean observations. These include the NASA Aquarius mission and the Soil Moisture Active Passive (SMAP) mission, both of which use combined passive/ active L-band instruments. Aquarius s passive/active L-band microwave sensor has been designed to map the salinity field at the surface of the ocean from space. SMAP s primary objectives are for soil moisture and freeze/thaw detection, but it will operate continuously over the ocean, and hence will have significant potential for ocean surface research. In this innovation, an algorithm has been developed to retrieve simultaneously ocean surface salinity and wind from combined passive/active L-band microwave observations of sea surfaces. The algorithm takes advantage of the differing response of brightness temperatures and radar backscatter to salinity, wind speed, and direction, thus minimizing the least squares error (LSE) measure, which signifies the difference between measurements and model functions of brightness temperatures and radar backscatter. The algorithm uses the conjugate gradient method to search for the local minima of the LSE. Three LSE measures with different measurement combinations have been tested. The first LSE measure uses passive microwave data only with retrieval errors reaching 1 to 2 psu (practical salinity units) for salinity, and 1 to 2 m/s for wind speed. The second LSE measure uses both passive and active microwave data for vertical and horizontal polarizations. The addition of active microwave data significantly improves the retrieval accuracy by about a factor of five. To mitigate the impact of Faraday rotation on satellite observations, the third LSE measure uses measurement combinations invariant under the Faraday rotation. For Aquarius, the expected RMS SSS (sea surface salinity) error will be less than about 0.2 psu for low winds, and increases to 0.3 psu at 25 m/s wind speed for warm waters (25 C). To achieve the required 0.2 psu accuracy, the impact of sea surface roughness (e.g. wind-generated ripples) on the observed brightness temperature has to be corrected to better than one tenth of a degree Kelvin. With this algorithm, the accuracy of retrieved wind speed will be high, varying from a few tenths to 0.6 m/s. The expected direction accuracy is also excellent (less than 10 ) for mid to high winds, but degrades for lower speeds (less than 7 m/s).

Yueh, Simon H.

Combined Global Navigation Satellite Systems in the Space Service Volume

Besides providing position, velocity, and timing (PVT) for terrestrial users, the Global Positioning System (GPS) is also being used to provide PVT information for earth orbiting satellites. In 2006, F. H. Bauer, et. al., defined the Space Service Volume in the paper GPS in the Space Service Volume , presented at ION s 19th international Technical Meeting of the Satellite Division, and looked at GPS coverage for orbiting satellites. With GLONASS already operational, and the first satellites of the Galileo and Beidou/COMPASS constellations already in orbit, it is time to look at the use of the new Global Navigation Satellite Systems (GNSS) coming into service to provide PVT information for earth orbiting satellites. This presentation extends GPS in the Space Service Volume by examining the coverage capability of combinations of the new constellations with GPS GPS was first explored as a system for refining the position, velocity, and timing of other spacecraft equipped with GPS receivers in the early eighties. Because of this, a new GPS utility developed beyond the original purpose of providing position, velocity, and timing services for land, maritime, and aerial applications. GPS signals are now received and processed by spacecraft both above and below the GPS constellation, including signals that spill over the limb of the earth. Support of GPS space applications is now part of the system plan for GPS, and support of the Space Service Volume by other GNSS providers has been proposed to the UN International Committee on GNSS (ICG). GPS has been demonstrated to provide decimeter level position accuracy in real-time for satellites in low Earth orbit (centimeter level in non-real-time applications). GPS has been proven useful for satellites in geosynchronous orbit, and also for satellites in highly elliptical orbits. Depending on how many satellites are in view, one can keep time locked to the GNSS standard, and through that to Universal Time as long as at least one satellite is in view (the longest duration with no satellites in view is important in determining the maximum clock drift from GNSS time). Instantaneous position requires four satellites in view, but because orbital motion is predictable, it is possible to build up knowledge of the orbital position gradually through time without a need for constant four satellite coverage. However, it is desirable to have four satellite coverage when performing satellite maneuvers, since there can be significant changes in velocity, leading to large changes in orbit parameter, causing substantial divergence in position over time. The Space Service Volume has been defined as the volume between three thousand km altitude and geosynchronous altitude, and can be divided into medium orbit services between three thousand km altitude and eight thousand km altitude, and high orbit services above eight thousand km. The Terrestrial Service Volume includes the Earth s surface, the atmosphere, and space below the altitude of three thousand km. The Terrestrial Service Volume is the volume within which the GNSS systems will have very similar performance to the Earth surface, and satellites need only use the signals specified to provide terrestrial performance. Above three thousand km the use of signals passing by the Earth s limb becomes important, so it is desirable to have additional information on signal strength, phase delay, and group delay covering wider beam angles than are needed for terrestrial service (and which can be obtained by monitoring GNSS signals from the Earth s surface). This presentation will look at each of the new GNSS constellations in combination with GPS (GLONASS with GPS, Galileo with GPS, Beidou/COMPASS with GPS), and also at the combination of all four GNSS systems. The presentation will largely follow the format of GPS in the Space Service Volume , presenting data on the availability of one, two, three, or four of the various combinations of GNSS constellation satelles at approximately two thousand grid points evenly spaced and fixed in longitude and latitude, the duration of the longest single-fold outages (intervals when no satellites are available), and the duration of the longest four-fold outages (intervals when fewer than four satellites are available) at several altitudes. Following the original paper, we will use the altitudes of three hundred km (typical LEO satellite, and within the Terrestrial Service Volume), at three thousand km (border between Terrestrial Service Volume and Space Service Volume), at eight thousand km (the border between medium and high orbit service within the Space Service Volume), at fifteen thousand km (just below the GNSS constellations), at twenty five thousand km (just above the GNSS constellations), at thirty six thousand, five hundred km (limit of Space Service Volume definition, geosynchronous altitude), and at seventy thousand km (to show the potential usefulness of GNSS beyond geosynchronous altitude).

Force, Dale A.