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All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Interpolant Improvements and Lessons Learned

This presentation is for the OpenMDAO workshop 2022 and updates users on recent improvements to interpolant methods. Specifically, we discuss computational improvements, visualization capabilities, and suggested best practices for using interpolants. The term interpolants is used synonymously with metamodels and surrogate models. The goal of the presentation is to increase adoption of efficient interpolant methods and increase users’ awareness to built-in features within OpenMDAO.

Multidisciplinary Design Optimization↗
NASA NTRS1984

A climatically-derived global soil moisture data set for use in the GLAS atmospheric circulation model seasonal cycle experiment

Algorithms for point interpolation and contouring on the surface of the sphere and in Cartesian two-space are developed from Shepard's (1968) well-known, local search method. These mapping procedures then are used to investigate the errors which appear on small-scale climate maps as a result of the all-too-common practice of of interpolating, from irregularly spaced data points to the nodes of a regular lattice, and contouring Cartesian two-space. Using mean annual air temperatures field over the western half of the northern hemisphere is estimated both on the sphere, assumed to be correct, and in Cartesian two-space. When the spherically- and Cartesian-approximted air temperature fields are mapped and compared, the magnitudes (as large as 5 C to 10 C) and distribution of the errors associated with the latter approach become apparent.

Willmott, C. J.↗
NASA NTRS1985

Numerical analysis of flow non-uniformity in the hot gas manifold of the Space Shuttle main engine

Three-dimensional viscous flow in a conceptual hot gas manifold (HGM) for the Space Shuttle Main Engine High Pressure Fuel Turbopump (SSME HPFTP) was numerically analyzed. A finite difference scheme was used to solve the Navier-Stokes equations. The exact geometry of the SSME HGM was modeled using boundary fitted curvilinear coordinates and the General Interpolants Method (GIM) code. Slight compressibility of the subsonic flow was modeled using a linearized equation of state with artificial compressibility. A time relaxation method was used to obtain a steady state solution. The feasibility and potential usefulness of computational methods in assisting the design of SSME components which involves the flow of fluids within complex geometrical shapes is demonstrated.

Thoenes, J.↗
NASA NTRS1980

Instrumented aircraft verification of clear-air radar detection of low-level wind shear

A technique is described in which the longitudinal wind component at airports, measured by Doppler radar, is put through a Fourier transformation to produce an energy density spectrum. The result is multiplied by the aircraft response characteristics to produce quantitative data on aircraft performance in a wind shear situation. The Doppler radar measurements are made along the intended flight path. Two case studies, along a 3 deg approach path, are described from measurements in two modes: Lagrangian, where predictions were computed one range gate ahead of the plane, and Eulerian, where samples were measured instantaneously along the flight path. Wind data obtained every second were interpolated to fit a numerical model by using a cubic spline. Eulerian data were superior to Lagrangian data in terms of ranging, and nearly equal for wind speeds. Improvements in current 75% accuracy are noted to be possible with shrouded antennas to reduce sidelobes and use of Doppler radar with higher resolution to eliminate effects of small scale disturbances within the pulse volume.

Mccarthy, J.↗
NASA NTRS1983

Relative Elevation Determination from LANDSAT Imagery

In LANDSAT imagery, spectral and spatial information can be used to detect the drainage network as well as the relative elevation model in mountainous terrain. To do this, the mixed information of material reflectance and topographic modulation in the original LANDSAT imagery must be first separated. From the material reflectance information, big visible rivers can be detected. From the topographic modulation information, ridges and valleys can be detected and assigned relative elevations. Finally, a relative elevation model can be generated by interpolating values for nonridge and nonvalley pixels.

Haralick, R. M.↗
NASA NTRS1986

Physical and numerical sources of computational inefficiency in integration of chemical kinetic rate equations: Etiology, treatment and prognosis

The design of a very fast, automatic black-box code for homogeneous, gas-phase chemical kinetics problems requires an understanding of the physical and numerical sources of computational inefficiency. Some major sources reviewed in this report are stiffness of the governing ordinary differential equations (ODE's) and its detection, choice of appropriate method (i.e., integration algorithm plus step-size control strategy), nonphysical initial conditions, and too frequent evaluation of thermochemical and kinetic properties. Specific techniques are recommended (and some advised against) for improving or overcoming the identified problem areas. It is argued that, because reactive species increase exponentially with time during induction, and all species exhibit asymptotic, exponential decay with time during equilibration, exponential-fitted integration algorithms are inherently more accurate for kinetics modeling than classical, polynomial-interpolant methods for the same computational work. But current codes using the exponential-fitted method lack the sophisticated stepsize-control logic of existing black-box ODE solver codes, such as EPISODE and LSODE. The ultimate chemical kinetics code does not exist yet, but the general characteristics of such a code are becoming apparent.

Pratt, D. T.↗
NASA NTRS1985

Analysis/forecast experiments with a multivariate statistical analysis scheme using FGGE data

A three-dimensional, multivariate, statistical analysis method, optimal interpolation (OI) is described for modeling meteorological data from widely dispersed sites. The model was developed to analyze FGGE data at the NASA-Goddard Laboratory of Atmospherics. The model features a multivariate surface analysis over the oceans, including maintenance of the Ekman balance and a geographically dependent correlation function. Preliminary comparisons are made between the OI model and similar schemes employed at the European Center for Medium Range Weather Forecasts and the National Meteorological Center. The OI scheme is used to provide input to a GCM, and model error correlations are calculated for forecasts of 500 mb vertical water mixing ratios and the wind profiles. Comparisons are made between the predictions and measured data. The model is shown to be as accurate as a successive corrections model out to 4.5 days.

Baker, W. E.↗
NASA NTRS1992

Coupled 2D-3D finite element method for analysis of a skin panel with a discontinuous stiffener

This paper describes a computationally efficient analysis method which was used to predict detailed stress states in a typical composite compression panel with a discontinuous hat stiffener. A global-local approach was used. The global model incorporated both 2D shell and 3D brick elements connected by newly developed transition elements. Most of the panel was modeled with 2D elements, while 3D elements were employed to model the stiffener flange and the adjacent skin. Both linear and geometrically nonlinear analyses were performed on the global model. The effect of geometric nonlinearity induced by the eccentric load path due to the discontinuous hat stiffener was significant. The local model used a fine mesh of 3D brick elements to model the region at the end of the stiffener. Boundary conditions of the local 3D model were obtained by spline interpolation of the nodal displacements from the global analysis. Detailed in-plane and through-the-thickness stresses were calculated in the flange-skin interface near the end of the stiffener.

Wang, J. T.↗
NASA NTRS2015

Maintaining Atmospheric Mass and Water Balance Within Reanalysis

This report describes the modifications implemented into the Goddard Earth Observing System Version-5 (GEOS-5) Atmospheric Data Assimilation System (ADAS) to maintain global conservation of dry atmospheric mass as well as to preserve the model balance of globally integrated precipitation and surface evaporation during reanalysis. Section 1 begins with a review of these global quantities from four current reanalysis efforts. Section 2 introduces the modifications necessary to preserve these constraints within the atmospheric general circulation model (AGCM), the Gridpoint Statistical Interpolation (GSI) analysis procedure, and the Incremental Analysis Update (IAU) algorithm. Section 3 presents experiments quantifying the impact of the new procedure. Section 4 shows preliminary results from its use within the GMAO MERRA-2 Reanalysis project. Section 5 concludes with a summary.

IAU↗
NASA NTRS2022

Assimilation of GPM-retrieved Ocean Surface Meteorology Data for Two Snowstorm Events during ICE-POP 2018

As a component of the National Aeronautics and Space Administration (NASA) Weather Focus Area and Global Precipitation Measurement (GPM) Ground Validation participation in the International Collaborative Experiments for PyeongChang 2018 Olympic and Paralympic Winter Games (ICE-POP 2018) field research and forecast demonstration programs, hourly ocean surface meteorology properties were retrieved from the GPM microwave observations for January – March 2018. In this study, the retrieved ocean surface meteorological products – 2-m temperature, 2-m specific humidity, and 10-m wind speed were assimilated into a regional numerical weather prediction (NWP) framework to explore the application of these observations for two heavy snowfall events during the ICE-POP 2018: 27-28 February, and 7-8 March 2018. The Weather Research and Forecasting (WRF) model and the community Gridpoint Statistical Interpolation (GSI) were used to conduct high resolution simulations and data assimilation experiments. The results indicate that the data assimilation has a large influence on surface thermodynamic and wind fields in the model initial condition for both events. With cycled data assimilation, significantly positive influence of the retrieved surface observation was found for the March case with improved quantitative precipitation forecast and reduced error in temperature forecast. A slightly smaller yet positive impact was also found in the forecast of the February case.

assimilation↗
NASA NTRSDate not supplied

Impact of Thermoplastic Composites: Testing and Modeling

Thermoplastic Composites (TPCs) are being increasingly considered for aerospace applications given their faster manufacturing cycles and lower cost. The NASA High-Rate Composite Aircraft Manufacturing (HiCAM) project aims to evaluate and mature thermoplastic manufacturing technologies to achieve a 4X – 6X increase in the production rate of Next Generation Single Aisle (NGSA) commercial aircraft. Within the purview of the NASA HiCAM project, this work investigates the response of thermoplastic composites under High Energy Dynamic Impact (HEDI) conditions. HEDI tests were conducted on panels fabricated with a carbon fiber reinforced low melt semi-crystalline resin TC1225 LMPAEK T700G (T700/LMPAEK) material system. A blunt metal projectile was chosen as the impactor which impacted the T700/LMPAEK panels over a range of impact velocities imparted by a gas gun test setup. As expected, lower velocity impacts caused the projectile to rebound, whereas higher velocity impacts resulted in the projectile penetrating the test panels. For the test cases in which the projectile rebounded, the predominant damage modes recorded with Ultrasonic (UT) scans included interlaminar delaminations which exhibited a “rotating fan” like structure when viewed in the through-thickness direction. Additionally, the dynamic deflection of the center point of the back face of the test panels and the velocity of the projectile was also measured during the test. Finite element models were developed to model a test case in which the projectile rebounded. These models were developed using LS-DYNA® wherein the primary objective was to evaluate the ability of the material model MAT299 to capture the dynamic response and damage modes in the T700/LMPAEK test panels. MAT299 is a Deformation Gradient Decomposition (DGD) based Continuum Damage Mechanics (CDM) material model. The interlaminar delaminations were modeled using the cohesive contact formulation available within LS-DYNA, wherein the mixed-mode fracture is captured via the Benzegaggh-Kenane (B-K) mode-dependent fracture energy interpolation law. The above-mentioned modeling methods have mostly been applied to thermoset composites and adapting them to TPCs involves addressing challenges associated with appropriately representing material behavior. Therefore, the proposed paper would discuss the systematic approach taken to adapt thermoset composites modeling practices for applications to TPCs, while appropriately addressing material behavior. The proposed paper would show that the predicted back face center point deflection correlated reasonably well with experimental data and the peak deflection was predicted to be within 5% of the experimental measurements. The projectile rebound velocity, while predicted to be higher than the experimental measurement, was within reasonable bounds. Additionally, it will be shown that the predicted delamination shapes were in reasonable agreement with experimental data.

Composite Materials↗
NASA NTRS1999

A Priori Subgrid Analysis of Temporal Mixing Layers with Evaporating Droplets

Subgrid analysis of a transitional temporal mixing layer with evaporating droplets has been performed using three sets of results from a Direct Numerical Simulation (DNS) database, with Reynolds numbers (based on initial vorticity thickness) as large as 600 and with droplet mass loadings as large as 0.5. In the DNS, the gas phase is computed using a Eulerian formulation, with Lagrangian droplet tracking. The Large Eddy Simulation (LES) equations corresponding to the DNS are first derived, and key assumptions in deriving them are first confirmed by computing the terms using the DNS database. Since LES of this flow requires the computation of unfiltered gas-phase variables at droplet locations from filtered gas-phase variables at the grid points, it is proposed to model these by assuming the gas-phase variables to be the sum of the filtered variables and a correction based on the filtered standard deviation; this correction is then computed from the Subgrid Scale (SGS) standard deviation. This model predicts the unfiltered variables at droplet locations considerably better than simply interpolating the filtered variables. Three methods are investigated for modeling the SGS standard deviation: the Smagorinsky approach, the Gradient model and the Scale-Similarity formulation. When the proportionality constant inherent in the SGS models is properly calculated, the Gradient and Scale-Similarity methods give results in excellent agreement with the DNS.

Okongo, Nora↗
NASA NTRS1992

A catchment scale water balance model for FIFE

A catchment scale water balance model is presented and used to predict evaporation from the King's Creek catchment at the First ISLSCP Field Experiment site on the Konza Prairie, Kansas. The model incorporates spatial variability in topography, soils, and precipitation to compute the land surface hydrologic fluxes. A network of 20 rain gages was employed to measure rainfall across the catchment in the summer of 1987. These data were spatially interpolated and used to drive the model during storm periods. During interstorm periods the model was driven by the estimated potential evaporation, which was calculated using net radiation data collected at site 2. Model-computed evaporation is compared to that observed, both at site 2 (grid location 1916-BRS) and the catchment scale, for the simulation period from June 1 to October 9, 1987.

Famiglietti, J. S.↗
NASA NTRS2007

Semianalytical Propagation of Satellite Orbits about an Arbitrary Central Body

Precision mean element (PME) satellite theories play a key role in orbit dynamics analyses. These theories employ: nonsingular orbital elements comprehensive force models Generalized Method of Averaging Numerical interpolation concepts The Draper Semianalytical Satellite Theory (DSST) (Refs. 1 - 6), whose development was led by the author, and the independently-developed Universal Semianalytical Method (USM) (Ref. 7) are examples of such theories. These theories provide the capability to tailor the force modeling to meet the desired computational speed vs. accuracy trade-off. The flexibility of such theories is demonstrated by their ability to include complicated atmosphere density models and spacecraft models in the perturbation theory context. The value of high speed satellite theories, in this era of computational plenty, is that they allow new ways of looking at astrodynamical problems such as orbit design (Refs. 8, 9) and atmosphere density updating (Refs. 10, 11). In the mid to late-1980 s, the geodynamics community led the development of very precise geopotential models such as GEM T2 and GEM T3 (Ref. 12), and with the subsequent analysis of the TOPEX flight data, JGM-2 and JGM-3 (Ref. 13). These were high degree and order geopotentials, at least 50 x 50. In 1993, the DSST implementation in the GTDS program was extended to include the 50 x 50 geopotential models (Ref. 14). The 50 x 50 geopotential, J2000 integration coordinate system, and solid Earth tide capabilities were integrated in GTDS by Scott Carter (Ref. 15). This capability demonstrated 1 m accuracy versus the TOPEX Precise Orbit Ephemerides. Subsequently the DSST Standalone program was also extended to include high degree and order geopotential models (Ref. 5). More recently GTDS has been hosted in the Linux PC environment. However, all of these efforts have been limited to modeling the motion of an artificial Earth satellite. They did not consider the additional complexities associated with lunar, planetary, or other natural satellite orbiters. Such complexities include: additional coordinate systems (associated with the direction of the north pole of rotation and the prime meridian of the new central bodies) (Ref. 16) normalized gravity model coefficients (desirable for high degree and order fields) (Ref. 17) indirect oblateness

Cefola, Paul J.↗
NASA NTRS2010

Kepler Mission's Focal Plane Characterization Models Implementation

The Kepler Mission photometer is an unusually complex array of CCDs. A large number of time-varying instrumental and systemic effects must be modeled and removed from the Kepler pixel data to produce light curves of sufficiently high quality for the mission to be successful in its planet-finding objective. After the launch of the spacecraft, many of these effects are difficult to remeasure frequently, and various interpolations over a small number of sample measurements must be used to determine the correct value of a given effect at different points in time. A library of software modules, called Focal Plane Characterization (FC) Models, is the element of the Kepler Science Data Pipeline (hereafter "pipeline") that handles this. FC, or products generated by FC, are used by nearly every element of the SOC processing chain. FC includes Java components: database persistence classes, operations classes, model classes, and data importers; and MATLAB code: model classes, interpolation methods, and wrapper functions. These classes, their interactions, and the database tables they represent, are discussed. This paper describes how these data and the FC software work together to provide the pipeline with the correct values to remove non-photometric effects caused by the photometer and its electronics from the Kepler light curves. The interpolation mathematics is reviewed, as well as the special case of the sky-to-pixel,pixel-to-sky coordinate transformation code, which incorporates a compound model that is unique in the SOC software.

mission↗
NASA NTRS2003

Response Surface Methods For Spatially-Resolved Optical Measurement Techniques

Response surface methods (or methodology), RSM, have been applied to improve data quality for two vastly different spatially-resolved optical measurement techniques. In the first application, modern design of experiments (MDOE) methods, including RSM, are employed to map the temperature field in a direct-connect supersonic combustion test facility at NASA Langley Research Center. The laser-based measurement technique known as coherent anti-Stokes Raman spectroscopy (CARS) is used to measure temperature at various locations in the combustor. RSM is then used to develop temperature maps of the flow. Even though the temperature fluctuations at a single point in the flowfield have a standard deviation on the order of 300 K, RSM provides analytic fits to the data having 95% confidence interval half width uncertainties in the fit as low as +/- 30 K. Methods of optimizing future CARS experiments are explored. The second application of RSM is to quantify the shape of a 5-meter diameter, ultra-lightweight, inflatable space antenna at NASA Langley Research Center. Photogrammetry is used to simultaneously measure the shape of the antenna at approximately 500 discrete spatial locations. RSM allows an analytic model to be developed that describes the shape of the majority of the antenna with an uncertainty of 0.4 mm, with 95% confidence. This model would allow a quantitative comparison between the actual shape of the antenna and the original design shape. Accurately determining this shape also allows confident interpolation between the measured points. Such a model could, for example, be used for ray tracing of radio-frequency waves up to 95 GHz. to predict the performance of the antenna.

Danehy, P. M.↗
NASA NTRS2023

First VLTI/GRAVITY Observations of HIP 65426 b: Evidence for a Low or Moderate Orbital Eccentricity

Giant exoplanets have been directly imaged over orders of magnitude of orbital separations, prompting theoretical and observational investigations of their formation pathways. In this paper, we present new VLTI/GRAVITY astrometric data of HIP 65426 b, a cold, giant exoplanet which is a particular challenge for most formation theories at a projected separation of 92 au from its primary. Leveraging GRAVITY's astrometric precision, we present an updated eccentricity posterior that disfavors large eccentricities. The eccentricity posterior is still prior dependent, and we extensively interpret and discuss the limits of the posterior constraints presented here. We also perform updated spectral comparisons with self-consistent forward-modeled spectra, finding a best-fit ExoREM model with solar metallicity and C/O = 0.6. An important caveat is that it is difficult to estimate robust errors on these values, which are subject to interpolation errors as well as potentially missing model physics. Taken together, the orbital and atmospheric constraints paint a preliminary picture of formation inconsistent with scattering after disk dispersal. Further work is needed to validate this interpretation. Analysis code used to perform this work is available on GitHub: https://github.com/sblunt/hip65426.

Sarah Blunt↗
NASA NTRS2001

Investigating Uncertainty in Predicting Carbon Dynamics in North American Biomes: Putting Support-Effect Bias in Perspective

A fundamental strategy in NASA's Earth Observing System's (EOS) monitoring of vegetation and its contribution to the global carbon cycle is to rely on deterministic, process-based ecosystem models to make predictions of carbon flux over large regions. These models are parameterized (that is, the input variables are derived) using remotely sensed images such as those from the Moderate Resolution Imaging Spectroradiometer (MODIS), ground measurements and interpolated maps. Since early applications of these models, investigators have noted that results depend partly on the spatial support of the input variables. In general, the larger the support of the input data, the greater the chance that the effects of important components of the ecosystem will be averaged out. A review of previous work shows that using large supports can cause either positive or negative bias in carbon flux predictions. To put the magnitude and direction of these biases in perspective, we must quantify the range of uncertainty on our best measurements of carbon-related variables made on equivalent areas. In other words, support-effect bias should be placed in the context of prediction uncertainty from other sources. If the range of uncertainty at the smallest support is less than the support-effect bias, more research emphasis should probably be placed on support sizes that are intermediate between those of field measurements and MODIS. If the uncertainty range at the smallest support is larger than the support-effect bias, the accuracy of MODIS-based predictions will be difficult to quantify and more emphasis should be placed on field-scale characterization and sampling. This talk will describe methods to address these issues using a field measurement campaign in North America and "upscaling" using geostatistical estimation and simulation.

Dungan, Jennifer L.↗