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Numerical derivative techniques for trajectory optimization

The adoption of robust numerical optimization techniques in trajectory simulation programs has resulted in powerful design and analysis tools. These trajectory simulation/optimization programs are widely used, and a representative list includes the GTS system, the POST program, and newer collocation methods such as OTIS and FONPAC. All of these programs rely on optimization algorithms which require objective function and constraint gradient data during the iteration process. However, most trajectory optimization problems lack simple analytical expressions for these derivatives. In the general case a function evaluation involves integrating aerodynamic, propulsive, and gravity forces over multiple trajectory phases with complex control models. With the newer collocation methods, the integration is replaced by defect constraints and cubic approximations for the state. While analytic gradient expressions can sometimes be derived for trajectory optimization problems, the derivation is cumbersome, time consuming, and prone to mistakes. Fortunately, an alternate method exists for the gradient evaluation, namely finite difference approximations. In this paper some finite difference gradient techniques developed for use with the GTS system are presented. These techniques include methods for computing first and second partial derivatives of single and multiple sets of functions. A key feature of these methods is an error control mechanism which automatically adjusts the perturbation size to obtain accurate derivative values.

Hallman, Wayne P.↗

Error Rates and Channel Capacities in Multipulse PPM

A method of computing channel capacities and error rates in multipulse pulse-position modulation (multipulse PPM) has been developed. The method makes it possible, when designing an optical PPM communication system, to determine whether and under what conditions a given multipulse PPM scheme would be more or less advantageous, relative to other candidate modulation schemes. In conventional M-ary PPM, each symbol is transmitted in a time frame that is divided into M time slots (where M is an integer >1), defining an M-symbol alphabet. A symbol is represented by transmitting a pulse (representing 1) during one of the time slots and no pulse (representing 0 ) during the other M 1 time slots. Multipulse PPM is a generalization of PPM in which pulses are transmitted during two or more of the M time slots.

Hamkins, Jon↗

Ways of achieving continuous service from computers

This paper outlines the methods used in the real-time computer complex to keep computers operating. Methods include selectover, high-speed restart, and low-speed restart. The hardware and software needed to implement these methods is discussed as well as the system recovery facility, alternate device support, and timeout. In general, methods developed while supporting the Gemini, Apollo, and Skylab space missions are presented.

Quinn, M. J., Jr.↗

Viscous transonic airfoil workshop results using ARC2D

Computations have been performed in response to the Viscous Transonic Airfoil Workshop associated with the AIAA 25th Aerospace Sciences Meeting (January 1987). The purpose of the workshop is to establish the capabilities of various methods for computing viscous flowfields for a range of conditions and geometries. The results of the test cases will demonstrate the capabilities of the methods in predicting both aerodynamic trends and flowfield details. ARC2D, a well-established Navier-Stokes code, was used to compute the flowfields for the designated airfoils, Mach numbers, angles of attack and other specifications of the Workshop committee.

Maksymiuk, Catherine M.↗

Mapping of electrical potential distributions with charged particle beams

Methods for measuring electrostatic potentials on and near dielectric surfaces charged to several kilovolts are studied. Secondary emission from those charged dielectrics is measured. Candidates for potential measurement include the induced charge, from which potential is calculated; the trajectory endpoints of either high or low energy particles traversing the region near the surface; trajectory impact on the surface; and creating ions at points of interest near the surface. Some of the methods require computer simulations and iterative calculation if potential maps are to be generated. Several approaches are described and compared. A method using a half-cylinder as a test chamber and low-energy probing beams is adapted for the measurement of seconary emission.

Robinson, J. W.↗

Performability analysis using semi-Markov reward processes

Beaudry (1978) proposed a simple method of computing the distribution of performability in a Markov reward process. Two extensions of Beaudry's approach are presented. The method is generalized to a semi-Markov reward process by removing the restriction requiring the association of zero reward to absorbing states only. The algorithm proceeds by replacing zero-reward nonabsorbing states by a probabilistic switch; it is therefore related to the elimination of vanishing states from the reachability graph of a generalized stochastic Petri net and to the elimination of fast transient states in a decomposition approach to stiff Markov chains. The use of the approach is illustrated with three applications.

Ciardo, Gianfranco↗

Determining noise temperatures in beam waveguide systems

A new 34-m research and development antenna was fabricated and tested as a precursor to introducing beam waveguide (BWG) antennas and Ka-band (32 GHz) frequencies into the NASA/JPL Deep Space Network. For deep space use, system noise temperature is a critical parameter. There are thought to be two major contributors to noise temperature in a BWG system: the spillover past the mirrors, and the conductivity loss in the walls. However, to date, there are no generally accepted methods for computing noise temperatures in a beam waveguide system. An extensive measurement program was undertaken to determine noise temperatures in such a system along with a correspondent effort in analytic prediction. Utilizing a very sensitive radiometer, noise temperature measurements were made at the Cassegrain focus, an intermediate focal point, and the focal point in the basement pedestal room. Several different horn diameters were used to simulate different amounts of spillover past the mirrors. Two analytic procedures were developed for computing noise temperature, one utilizing circular waveguide modes and the other a semiempirical approach. The results of both prediction methods are compared to the experimental data.

Imbriale, W.↗

The luminosity functions of embedded stellar clusters. 1: Method of solution and analytic results

We describe a method for computing the history of the luminosity function in a young cluster still forming within a molecular cloud complex. Our method, which utilizes detailed results from stellar evolution theory, assumes that clusters arise from the continuous collapse of dense cloud cores over a protracted period of time. It is also assumed that stars reaching the main sequence are distributed in mass according to a prescribed initial mass function (IMF). We keep track separately of the contributions to the luminosity function from the populations of protostars, pre-main-sequence stars, and main-sequence stars. We derive expressions for the fractional contribution of these populations to both the total number of stars produced and the total cluster luminosity. In our model, the number of protostars rises quickly at first, but then levels off to a nearly constant value, which it maintains until the dispersal of the cloud complex. The number fraction of protostars always decreases with time. Averaged over the life of the parent cloud, this fraction is typically a few percent. The protostar mass distribution can be expressed as an integral over the IMF.

Fletcher, Andre B.↗

Utilizing Flight Data to Update Aeroelastic Stability Estimates

Stability analysis of high performance aircraft must account for errors in the system model. A method for computing flutter margins that incorporates flight data has been developed using robust stability theory. This paper considers applying this method to update flutter margins during a post-flight or on-line analysis. Areas of modeling uncertainty that arise when using flight data with this method are investigated. The amount of conservatism in the resulting flutter margins depends on the flight data sets used to update the model. Post-flight updates of flutter margins for an F/A-18 are presented along with a simulation of on-line updates during a flight test.

Lind, Rick↗

NavP: Structured and Multithreaded Distributed Parallel Programming

This slide presentation reviews some of the issues around distributed parallel programming. It compares and contrast two methods of programming: Single Program Multiple Data (SPMD) with the Navigational Programming (NAVP). It then reviews the distributed sequential computing (DSC) method and the methodology of NavP. Case studies are presented. It also reviews the work that is being done to enable the NavP system.

parallel programming↗

Normalized Temperature Contrast Processing in Flash Infrared Thermography

The paper presents further development in normalized contrast processing of flash infrared thermography method by the author given in US 8,577,120 B1. The method of computing normalized image or pixel intensity contrast, and normalized temperature contrast are provided, including converting one from the other. Methods of assessing emissivity of the object, afterglow heat flux, reflection temperature change and temperature video imaging during flash thermography are provided. Temperature imaging and normalized temperature contrast imaging provide certain advantages over pixel intensity normalized contrast processing by reducing effect of reflected energy in images and measurements, providing better quantitative data. The subject matter for this paper mostly comes from US 9,066,028 B1 by the author. Examples of normalized image processing video images and normalized temperature processing video images are provided. Examples of surface temperature video images, surface temperature rise video images and simple contrast video images area also provided. Temperature video imaging in flash infrared thermography allows better comparison with flash thermography simulation using commercial software which provides temperature video as the output. Temperature imaging also allows easy comparison of surface temperature change to camera temperature sensitivity or noise equivalent temperature difference (NETD) to assess probability of detecting (POD) anomalies.

Koshti, Ajay M.↗

Measurement of Surface Deformation Related to the December 2018 Mt. Etna Eruption Using Time-Series Interferometry and Magma Modeling for Hazard Zone Mapping

Mount Etna has erupted several times since it was first formed. Recently, Mount Etna began erupting again over 24–27 December 2018. Because it erupts frequently, Mount Etna should be observed on a frequent basis. From June 2018 to October 2019, 34 and 56 interferometric synthetic aperture radar (InSAR) images were acquired from the ascending and descending tracks of the Sentinel-1 satellite, respectively. We employed the Stanford Method for Persistent Scatterers (StaMPS) and a refined small baseline subset (SBAS) InSAR method to produce a surface deformation time-series map. In the time-series analysis, the phase signal remained unaltered with time. The Okada model was then applied to the result to generate a modeled interferogram, and the Q-LavHA program was run to generate a lava flow prediction model. A direct comparison of the results showed that Persistent Scatterers Interferometry (PSI)-StaMPS and the refined SBAS technique were comparable in terms of the displacement pattern, with slightly different velocity values obtained for individual points. In particular, a velocity range of −25 to 21 cm/yr was obtained from PSI-StaMPS, whereas a range of −30 to 25 cm/yr was obtained from the refined SBAS method. Upon computation of the vertical and east-west displacement components based on ascending and descending track data using both methods, deformation velocities of 51.5 and 52.5 cm/yr in the westerly direction on the western flank of Mount Etna were obtained from PSI-StaMPS and the refined SBAS method, respectively, whereas on the eastern flank, deformation toward the east was estimated to occur at a velocity of 50.1 or 54.2 cm/yr, respectively. PSIStaMPS estimated a vertical deformation velocity of −5.3 to 18.3 cm/yr, whereas the refined SBAS method produced a velocity range of approximately −7 to 19 cm/yr. The interferogram obtained via Okada modeling showed two fault sources in the 2018 Mount Etna eruption and a total volume change of approximately 12.39 × 10 6 m 3 . From the modeling results, a lava flow prediction model was generated using the Q-LavHA program. The approaches described in this study can be used by government officials, authorities, and other decision-makers to monitor and assess the risk of volcanic activity in the region.

Suci Ramayanti↗

On-Orbit Performance of the NOAA-21 Advanced Technology Microwave Sounder (ATMS)

The Advanced Technology Microwave Sounder (ATMS) instrument provides sounding measurements of Earth’s atmosphere to collect temperature and water vapor data for NOAA’s Joint Polar Satellite System (JPSS) program. ATMS is a total-power passive microwave radiometer with 22 channels spanning a frequency range from 22 to 183 GHz. A general description of the ATMS instrument is detailed in [1]. Three ATMS units are currently on-orbit. The Suomi National Polar-orbiting Partnership (SNPP) unit was launched in 2011 and the NOAA-20 (previously JPSS-1) unit was launch in 2017. Both SNPP and NOAA-20 ATMS units are currently operational and the data is used for numerical weather prediction (NWP) models. The NOAA-21 (formerly JPSS-2) ATMS unit was launched on November 10, 2022 from Vandenberg Space Force Base in California [2]. The ATMS instrument began generating radiance data on November 21, 2022. At the time of this abstract NOAA-21 ATMS is currently completing on-orbit commissioning and checkout activities; it is expected that the commissioning activities will be complete by the IGARSS 2023 conference. This paper will focus on the on-orbit performance of the NOAA-21 ATMS instrument based on measurements and activities from the commissioning period. Comparisons will be made to specifications and to expected performance based on pre-launch test activities. Pre-launch JPSS-2 (NOAA-21) ATMS performance is detailed in [4]. Additionally, the NOAA-21 performance will be compared to the on-orbit performance of the SNPP and NOAA-21 ATMS units. The post-launch performance of SNPP ATMS is detailed in [1][5][6][7]. The post-launch performance of NOAA-20 ATMS is detailed in [5][7][8]. On-orbit performance is evaluated through data collects from nominal mission operations as well as specific post-launch tests and spacecraft maneuvers. Nominal mission operations can be used to evaluate parameters such as instrument thermal stability, Noise Equivalent Delta Temperature (NEDT)/radiometric sensitivity, geolocation, inter-channel noise correlation, striping, and radiometric bias and stability. Shortly after instrument activation, the instrument thermal stability as measured from onboard temperature sensors is evaluated to demonstrate stable and steady-state behavior. Methods for computing NEDT are described in [9][10][11]. Passive geolocation measurements are performed using the coastline inflection point (CIP) method, described in [8][12]. The striping index, used as a metric to quantify striping, is the ratio of along-track variance to cross-track variance of the observed brightness temperature [4][8][14]. Inter-channel noise correlation has been previously reported for SNPP and NOAA-20 [1][8]. Dedicated post-launch tests and spacecraft maneuvers are utilized during the commissioning phase for further evaluation of on-orbit instrument performance. These activities provide information on the optimal space view selection, noise power spectral density (PSD), gain stability, scan bias, interference from onboard transmitters, reflector emissivity, active geolocation, and radiometric bias and stability detection methods. The optimal space view selection is used to determine which of ATMS space view sectors is preferred for minimizing contamination of the space view [1]. Point and stare testing is used to generate noise PSD and gain stability information, as described in [1][8]. Spacecraft roll and pitch maneuvers allow the ATMS to view different zones, including deep space, and the data can be used to provide information on scan biases and antenna sidelobe contamination [1][8]. The pitch maneuver can also be used to assess interference from onboard Ka-band transmitters and reflector emissivity [8]. Active geolocation is evaluated as a method for geolocation, described in [15].

Edward Kim↗

Computationally Guided Development of Components for High Energy Density Solid-State Lithium-Sulfur Batteries

All electric vertical take-off and landing vehicles (eVTOL) for urban air mobility (UAM) concepts face numerous challenging technical barriers before their introduction into the consumer marketplace. The most challenging of these technical barriers to overcome is developing an energy storage system capable of meeting the rigorous aerospace safety and performance criteria1. The performance metrics for eVTOL craft, such as specific energy, specific power, and safety, exceed those of electric automobiles by a factor of two to four. Current state-of-the-art (SOA) lithium-ion batteries are incapable of meeting the key performance criteria of energy and safety for eVTOL. Therefore, next generation advanced chemistries and designs must be developed to meet required performance metrics for electric aviation2. Beyond lithium-ion chemistries, such as lithium-sulfur, show promise in their high energy, while limitations exist in their power and cyclability due to low electrical conductivity and high intermediate solubility in organic liquid electrolytes. Several strategies to overcome the low electrical conductivity involve the use of selenium as a dopant in the active sulfur material, along with the incorporation of 2-dimensional electron-conducting holey-graphene to improve the composite cathodes electronic conductivity. Furthermore, combining this chemistry with a solid-electrolyte avoids the components’ dissolution issues3. However, the development of composite solid-state cathodes is non-trivial as several components must be intimately mixed so that the active component has sufficient access to both electrons and lithium ions to undergo full electrochemical conversion. Mathematical modeling of battery components can assist experimental design through a robust and rigorous combination of computational modeling techniques covering multiple length scales. The objective is to leverage modern computational materials methods combined with battery multiphysics tools to develop radically advanced compatible cathode and electrolyte materials, build and test solid state lithium-sulfur cells and packs. A NASA-based cross-organizational team of high-powered experts combined integrated computational predictive modeling, fundamental chemistry analysis, advanced material science, and battery cell development to tackle this very challenging, multidisciplinary problem. This presentation will show a multiscale computational modeling approach that has produced a novel particle dynamics method called Solid Electrolyte Sphere Approximation Model (SESAM). SESAM modeling targets the 1-10 µm scale structures and provides electromechanical and grain interactions for predictive design guidelines for the manufacturing of solid-state components. Parameters such as particle size and volume fraction of the constituent materials were modeled and experimentally fabricated to optimize electrochemical performance through improved microstructure design. Experimental feedback was provided through ionic and electronic conductivity assessment and structural analysis of developed materials and cell components.

battery↗

Incompressible Navier-Stokes computations of rotating flows

Flow through pump components, such as an inducer and an impeller, is efficiently simulated by solving the incompressible Navier-Stokes equations. The solution method is based on the pseudocompressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. Current computations use one-equation Baldwin-Barth turbulence model which is derived from a simplified form of the standard k-epsilon model equations. The resulting computer code is applied to the flow analysis inside a generic rocket engine pump inducer, a fuel pump impeller, and SSME high-pressure fuel turbopump impeller. Numerical results of inducer flow are compared with experimental measurements. Flow analyses at 80-, 100-, and 120-percent of design conditions are presented.

Kiris, Cetin↗

Comparison of solution approaches for minimum-fuel, low-thrust, power-limited orbital transfers

An initial assessment of the feasibility of a function space gradient method for computing solutions to minimum-fuel power-limited transfers encompassing a wide range of thrust to weight ratios is conducted. Three transfers between coplanar ellipses are used as test cases. The gradient method performs best at the high end of the thrust to weight ratio range. At the lower end, there is reduced sensitivity of the fuel consumption to the control profiles. The minimum fuel consumption and the trajectory are computed quite accurately but the control profiles are in error. An approximate analytical solution, obtained by Edelbaum using the method of averaging, is discussed.

Mease, Kenneth D.↗

Computation of three-dimensional inviscid flow over hypersonic missile configurations using the GIM code

A three-dimensional computational technique was used to obtain flowfield solutions to the Euler equations over selected hypersonic missile configurations. The General Interpolants Method (GIM) computer code was used with interpolation functions in an algebraic approach to generate a discrete computational grid for each configuration. The spatial marching version of the GIM code, which treats the parabolized Navier-Stokes (PNS) equations or the Euler equations with a shock capturing, 'MacCormack-like' scheme, was used to advance the solution hyperbolically over each configuration. The inviscid flowfield solutions over the two three-dimensional missile configurations, calculated using the GIM hyperbolic scheme, are presented here. The flow field over a wing/body configuration at zero degree angle of attack is presented. Flow over the fuselage of a tactical missile, termed the TAME 10, at both zero degree and 7.5 degree angles of attack is presented. In addition, an inviscid, two-dimensional analysis of an inlet configuration designed to mount on the TAME 10 is included. Contour maps of velocity and pressure are included for each configuration. Comparison of calculation and data show good agreement.

Xiques, K. E.↗

The velocity dispersion of the caustic network due to random motion of individual stars in the lensing galaxy

We present a method of computing the velocity distribution of the caustic network due to the random motion of stars in the lensing galaxy. This method is illustrated on the example of the two-point mass lens and then applied to a large sample of stars. We conclude that the proper motion of the stars increases significantly the frequency of the high magnification events in comparison with a static lens configuration with constant stream or constant bulk velocity. The stream velocity is the velocity of the star field relative to the global bulk velocity of the galaxy. We show that the global bulk and the stream velocity of the star field have to be considered separately for any microlensing situation. The higher the surface mass density of the stars in the lensing galaxy, the higher the influence of proper motion of stars on the statistics of high magnification events. The influence of a Gaussian velocity distribution of the stars in the lensing galaxy compared with a constant stream velocity of the stars increases the number of high magnification events by a factor 1.30 +/- 0.06 for a normalized surface density of the stars cr = 0.1 and by a factor 1.7 +/- 0.1 for sigma = 0.5. This means that for some microlensing situations the proper motion of the stars in a lensing galaxy has to be considered for exact microlensing predictions.

Kundik, Tomislav↗