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NASA NTRS1989

Robustness analysis for real parametric uncertainty

Some key results in the literature in the area of robustness analysis for linear feedback systems with structured model uncertainty are reviewed. Some new results are given. Model uncertainty is described as a combination of real uncertain parameters and norm bounded unmodeled dynamics. Here the focus is on the case of parametric uncertainty. An elementary and unified derivation of the celebrated theorem of Kharitonov and the Edge Theorem is presented. Next, an algorithmic approach for robustness analysis in the cases of multilinear and polynomic parametric uncertainty (i.e., the closed loop characteristic polynomial depends multilinearly and polynomially respectively on the parameters) is given. The latter cases are most important from practical considerations. Some novel modifications in this algorithm which result in a procedure of polynomial time behavior in the number of uncertain parameters is outlined. Finally, it is shown how the more general problem of robustness analysis for combined parametric and dynamic (i.e., unmodeled dynamics) uncertainty can be reduced to the case of polynomic parametric uncertainty, and thus be solved by means of the algorithm.

Sideris, Athanasios↗

NASA NTRS1991

Methods for evaluating the predictive accuracy of structural dynamic models

Modeling uncertainty is defined in terms of the difference between predicted and measured eigenvalues and eigenvectors. Data compiled from 22 sets of analysis/test results was used to create statistical databases for large truss-type space structures and both pretest and posttest models of conventional satellite-type space structures. Modeling uncertainty is propagated through the model to produce intervals of uncertainty on frequency response functions, both amplitude and phase. This methodology was used successfully to evaluate the predictive accuracy of several structures, including the NASA CSI Evolutionary Structure tested at Langley Research Center. Test measurements for this structure were within + one-sigma intervals of predicted accuracy for the most part, demonstrating the validity of the methodology and computer code.

Hasselman, Timothy K.↗

NASA NTRSDate not supplied

Backshell Radiative Heating and Shock Layer Kinetic Measurement in NASA’s Electric Arc Shock Tube Facility

A methodology for creating incident shocks with similarity to the backshell radiative heating environment on planetary probes is presented. Two test series were carried out in the Electric Arc Shock Tube (EAST) at NASA Ames to quantify the backshell environment for planned and executed missions entering the atmospheres of Mars and Titan. The comparison of measured radiance in the shock tube to predicted post shock radiation levels is used to quantify the uncertainty in the model. This model uncertainty may then be related back to the flight condition to assess the error in the flight heating prediction. Tests for Mars entry show the shock tube measurements to be bracketed between two kinetic models by 2-7%. This suggests an 8% error in predicting the measured heating cannot be attributed to radiation. Comparisons to planned Titan entry suggest a substantial overprediction of the backshell radiation, which suggests opportunity for future refinement of radiative heating models.

radiation↗

NASA NTRS1989

Regional quasigeoid determination in Northern Germany and comparison with GPS

For the northern part of the Federal Republic of Germany, new quasigeoid solutions were computed by least squares collocation and fast Fourier transformation (FFT) techniques using point and mean gravity data, a digital terrain model, and a global geopotential model. As severe accuracy limitations for precise regional quasigeoid determination come from global model uncertainties, different geopotential models were investigated by combining them with gravimetric data and comparing the quasigeoid heights with GPS and leveling. Optimum results were obtained by a global model tailored to gravity data in Europe. Collocation and FFT results based on this model agree well. The comparison with GPS and leveling yields rms discrepancies of + or - 2 cm over approximately 400 km range.

Denker, Heiner↗

NASA NTRS2006

The Advanced Modeling, Simulation and Analysis Capability Roadmap Vision for Engineering

This paper summarizes a subset of the Advanced Modeling Simulation and Analysis (AMSA) Capability Roadmap that was developed for NASA in 2005. The AMSA Capability Roadmap Team was chartered to "To identify what is needed to enhance NASA's capabilities to produce leading-edge exploration and science missions by improving engineering system development, operations, and science understanding through broad application of advanced modeling, simulation and analysis techniques." The AMSA roadmap stressed the need for integration, not just within the science, engineering and operations domains themselves, but also across these domains. Here we discuss the roadmap element pertaining to integration within the engineering domain, with a particular focus on implications for future observatory missions. The AMSA products supporting the system engineering function are mission information, bounds on information quality, and system validation guidance. The Engineering roadmap element contains 5 sub-elements: (1) Large-Scale Systems Models, (2) Anomalous Behavior Models, (3) advanced Uncertainty Models, (4) Virtual Testing Models, and (5) space-based Robotics Manufacture and Servicing Models.

Zang, Thomas↗

NASA NTRS2007

Evaluating Model Performance of an Ensemble-based Chemical Data Assimilation System During INTEX-B Field Mission

We present a global chemical data assimilation system using a global atmosphere model, the Community Atmosphere Model (CAM3) with simplified chemistry and the Data Assimilation Research Testbed (DART) assimilation package. DART is a community software facility for assimilation studies using the ensemble Kalman filter approach. Here, we apply the assimilation system to constrain global tropospheric carbon monoxide (CO) by assimilating meteorological observations of temperature and horizontal wind velocity and satellite CO retrievals from the Measurement of Pollution in the Troposphere (MOPITT) satellite instrument. We verify the system performance using independent CO observations taken on board the NSFINCAR C-130 and NASA DC-8 aircrafts during the April 2006 part of the Intercontinental Chemical Transport Experiment (INTEX-B). Our evaluations show that MOPITT data assimilation provides significant improvements in terms of capturing the observed CO variability relative to no MOPITT assimilation (i.e. the correlation improves from 0.62 to 0.71, significant at 99% confidence). The assimilation provides evidence of median CO loading of about 150 ppbv at 700 hPa over the NE Pacific during April 2006. This is marginally higher than the modeled CO with no MOPITT assimilation (-140 ppbv). Our ensemble-based estimates of model uncertainty also show model overprediction over the source region (i.e. China) and underprediction over the NE Pacific, suggesting model errors that cannot be readily explained by emissions alone. These results have important implications for improving regional chemical forecasts and for inverse modeling of CO sources and further demonstrate the utility of the assimilation system in comparing non-coincident measurements, e.g. comparing satellite retrievals of CO with in-situ aircraft measurements. The work described above also brought to light several short-comings of the data assimilation approach for CO profiles. Because of the limited vertical resolution of the measurement, the retrievals at different altitudes are correlated which can lead to problems with numerical error and overall efficiency. This has resulted in a manuscript that is about to be submitted to JGR:

Arellano, A. F., Jr.↗

NASA NTRS2019

PACE Technical Report Series, Volume 6: Data Product Requirements and Error Budgets Consensus Document

This chapter summarizes ocean color science data product requirements for the Plankton, Aerosol, Cloud,ocean Ecosystem (PACE) mission's Ocean Color Instrument (OCI) and observatory. NASA HQ delivered Level-1 science data product requirements to the PACE Project, which encompass data products to be produced and their associated uncertainties. These products and uncertainties ultimately determine the spectral nature of OCI and the performance requirements assigned to OCI and the observatory. This chapter ultimately serves to provide context for the remainder of this volume, which describes tools developed that allocate these uncertainties into their components, including allowable OCI systematic and random uncertainties, observatory geo location uncertainties, and geophysical model uncertainties.

Cetinic, Ivona↗

NASA NTRS2024

Spectral Correlation in MODIS Water-Leaving Reflectance Retrieval Uncertainty

Spectral remote sensing reflectance, Rrs(λ) (sr−1), is the fundamental quantity used to derive a host of bio-optical and biogeochemical properties of the water column from satellite ocean color measurements. Estimation of uncertainty in those derived geophysical products is therefore dependent on knowledge of the uncertainty in satellite-retrieved R rs . Furthermore, since the associated algorithms require R rs at multiple spectral bands, the spectral (i.e., band-to-band)error covariance in R rs is needed to accurately estimate the uncertainty in those derived properties. This study establishes a derivative-based approach for propagating instrument random noise, instrument systematic uncertainty, and forward model uncertainty into R rs as retrieved using NASA’s multiple-scattering epsilon (MSEPS) atmospheric correction algorithm, to generate pixel-level error covariance in R rs . The approach is applied to measurements from Moderate Resolution Imaging Spectroradiometer (MODIS) on the Aqua satellite and verified using Monte Carlo (MC) analysis. We also make use of this full spectral error covariance in R rs to calculate uncertainty in phytoplankton pigment chlorophyll-a concentration (chl a , mg/m 3 ) and diffuse attenuation coefficient of downwelling irradiance at 490 nm (K d (490), m -1 ). Accounting for the error covariance in R rs generally reduces the estimated relative uncertainty in chl a by ∼1-2% (absolute value) in waters with chl a < 0.25 mg/m 3 where the color index (CI) algorithm is used. The reduction is ∼5-10% in waters with chl a > 0.35 mg/m 3 where the blue-green ratio (OCX) algorithm is used. Such reduction can be higher than 30% in some regions. For K d (490), the reduction by error covariance is generally ∼2%, but can be higher than 20% in some regions. The error covariance in R rs is further verified through forward-calculating chl a from MODIS-retrieved and in situ R rs and comparing estimated uncertainty with observed differences. An 8-day global composite of propagated uncertainty shows that the goal of 35% uncertainty in chl a can be achieved over deep ocean waters (chl a ≤ 0.1 mg/m3). While the derivative-based approach generates reasonable error covariance in R rs some assumptions should be updated as our knowledge improves. These include the inter-band error correlation in top-of-atmosphere reflectance, and uncertainties in the calibration of MODIS 869 nm band, in ancillary data, and in the in situ data used for system vicarious calibration.

Ocean color↗

NASA NTRS2013

Lessons Learned from the AIRS Pre-Flight Radiometric Calibration

The Atmospheric Infrared Sounder (AIRS) instrument flies on the NASA Aqua satellite and measures the upwelling hyperspectral earth radiance in the spectral range of 3.7-15.4 micron with a nominal ground resolution at nadir of 13.5 km. The AIRS spectra are achieved using a temperature controlled grating spectrometer and HgCdTe infrared linear arrays providing 2378 channels with a nominal spectral resolution of approximately 1200. The AIRS pre-flight tests that impact the radiometric calibration include a full system radiometric response (linearity), polarization response, and response vs scan angle (RVS). We re-derive the AIRS instrument radiometric calibration coefficients from the pre-flight polarization measurements, the response vs scan (RVS) angle tests as well as the linearity tests, and a recent lunar roll test that allowed the AIRS to view the moon. The data and method for deriving the coefficients is discussed in detail and the resulting values compared amongst the different tests. Finally, we examine the residual errors in the reconstruction of the external calibrator blackbody radiances and the efficacy of a new radiometric uncertainty model. Results show the radiometric calibration of AIRS to be excellent and the radiometric uncertainty model does a reasonable job of characterizing the errors.

Sounder↗

NASA NTRS1993

Quantification of model error via an interval model with nonparametric error bound

The quantification of model uncertainty is becoming increasingly important as robust control is an important tool for control system design and analysis. This paper presents an algorithm that effectively characterizes the model uncertainty in terms of parametric and nonparametric uncertainties. The algorithm utilizes the frequency domain model error which is estimated from the spectra of output error and input data. The parametric uncertainty is represented as an interval transfer function while the nonparametric uncertainty is bounded by a designed error bound transfer function. Both discrete and continuous systems are discussed in this paper. The algorithm is applied to the Mini-Mast example, and the detail analysis is given.

Lew, Jiann-Shiun↗

NASA NTRS2020

Modeling the Uncertainties of Solar System Ephemerides for Robust Gravitational-wave Searches with Pular-timing Arrays

The regularity of pulsar emissions becomes apparent once we reference the pulses’ times of arrivals to the inertial rest frame of the solar system. It follows that errors in the determination of Earthʼs position with respect to the solar system barycenter can appear as a time-correlated bias in pulsar-timing residual time series, affecting the searches for low-frequency gravitational waves performed with pulsar-timing arrays. Indeed, recent array data sets yield different gravitational-wave background upper limits and detection statistics when analyzed with different solar system ephemerides. Crucially, the ephemerides do not generally provide usable error representations. In this article, we describe the motivation, construction, and application of a physical model of solar system ephemeris uncertainties, which focuses on the degrees of freedom (Jupiterʼs orbital elements) most relevant to gravitational-wave searches with pulsar-timing arrays. This model, BAYESEPHEM, was used to derive ephemeris-robust results in NANOGravʼs 11 yr stochastic-background search, and it provides a foundation for future searches by NANOGrav and other consortia. The analysis and simulations reported here suggest that ephemeris modeling reduces the gravitational-wave sensitivity of the 11 yr data set and that this degeneracy will vanish with improved ephemerides and with pulsar-timing data sets that extend well beyond a single Jovian orbital period.

M Vallisneri↗

NASA NTRS2004

Integrated Modeling Activities for the James Webb Space Telescope (JWST): Structural-Thermal-Optical Analysis

This is a continuation of a series of papers on modeling activities for JWST. The structural-thermal- optical, often referred to as "STOP", analysis process is used to predict the effect of thermal distortion on optical performance. The benchmark STOP analysis for JWST assesses the effect of an observatory slew on wavefront error. The paper begins an overview of multi-disciplinary engineering analysis, or integrated modeling, which is a critical element of the JWST mission. The STOP analysis process is then described. This process consists of the following steps: thermal analysis, structural analysis, and optical analysis. Temperatures predicted using geometric and thermal math models are mapped to the structural finite element model in order to predict thermally-induced deformations. Motions and deformations at optical surfaces are input to optical models and optical performance is predicted using either an optical ray trace or WFE estimation techniques based on prior ray traces or first order optics. Following the discussion of the analysis process, results based on models representing the design at the time of the System Requirements Review. In addition to baseline performance predictions, sensitivity studies are performed to assess modeling uncertainties. Of particular interest is the sensitivity of optical performance to uncertainties in temperature predictions and variations in metal properties. The paper concludes with a discussion of modeling uncertainty as it pertains to STOP analysis.

Johnston, John D.↗

NASA NTRS1993

Robust time-optimal control of uncertain structural dynamic systems

A time-optimal open-loop control problem of flexible spacecraft in the presence of modeling uncertainty has been investigated. The results indicate that the proposed approach significantly reduces the residual structural vibrations caused by modeling uncertainty. The results also indicate the importance of proper jet placement for practical tradeoffs among the maneuvering time, fuel consumption, and performance robustness.

Wie, Bong↗

NASA NTRS2018

Comparisons of Two Spatial Implementations of a Crop Model Using Remotely Sensed Observations over Southeastern United States

Global food security is one of the most pressing issues of the current century, particularly for developing nations. Agricultural simulation models can be a key component in testing new technologies, seeds and cultivars etc. However, inaccurate input information, model related errors and the mode of implementation can also add to model uncertainties. In this study, the crop model is implemented in two separate fashions: a)gridded (GriDSSAT model) and b) using random spatial ensembles (RHEAS model). This is done in the Southeastern US to evaluate and understand the modelperformance over a region data availabilities. Once the model performance is assessed, multiple satellite based earth observation parameters such as soil moisture, vegetation index etc. can be assimilated into crop models to reduce input and model related uncertainties particularly in data limited regions. In this study, the National Agricultural Statistical Services (NASS) reported yield data at county levels are used for comparison andvalidation purposes. The GriDSSAT model estimation of corn yields in comparison with the reported NASS yields showed an overall RMSD of nearly 3720 (kg/ha) whereas RMSD for the RHEAS model implementation was 3550 (kg/ha). Overall the GriDSSAT model had negative bias of nearly 2400 kg/ha (except for 2013) while RHEAS had a slight positive bias of 400 kg/ha (approx.).

SERVIR↗

NASA NTRS2011

Trajectory-Based Loads for the Ares I-X Test Flight Vehicle

In trajectory-based loads, the structural engineer treats each point on the trajectory as a load case. Distributed aero, inertial, and propulsion forces are developed for the structural model which are equivalent to the integrated values of the trajectory model. Free-body diagrams are then used to solve for the internal forces, or loads, that keep the applied aero, inertial, and propulsion forces in dynamic equilibrium. There are several advantages to using trajectory-based loads. First, consistency is maintained between the integrated equilibrium equations of the trajectory analysis and the distributed equilibrium equations of the structural analysis. Second, the structural loads equations are tied to the uncertainty model for the trajectory systems analysis model. Atmosphere, aero, propulsion, mass property, and controls uncertainty models all feed into the dispersions that are generated for the trajectory systems analysis model. Changes in any of these input models will affect structural loads response. The trajectory systems model manages these inputs as well as the output from the structural model over thousands of dispersed cases. Large structural models with hundreds of thousands of degrees of freedom would execute too slowly to be an efficient part of several thousand system analyses. Trajectory-based loads provide a means for the structures discipline to be included in the integrated systems analysis. Successful applications of trajectory-based loads methods for the Ares I-X vehicle are covered in this paper. Preliminary design loads were based on 2000 trajectories using Monte Carlo dispersions. Range safety loads were tied to 8423 malfunction turn trajectories. In addition, active control system loads were based on 2000 preflight trajectories using Monte Carlo dispersions.

Vause, Roland F.↗

NASA NTRSDate not supplied

Simulation of Vacuum Chamber Pressure Distribution with Surrogate Modeling and Uncertainty Quantification

A major challenge in understanding differences in electric propulsion performance in ground tests and in space operations concerns the pressure distribution within the test vacuum chamber. The chamber backpressure is much higher than experienced in space, modifying thruster performance and plume dynamics. Numerical simulation is a key element to determining the background conditions in non-ideal vacuum chamber environments. An important parameter for the accurate simulation of chamber backpressure is the probability that an atom will stick to a cryogenic panel used to pump away the plume gases. This quantity can be used to model vacuum pumps in particle-based kinetic numerical methods. In this work, a three-dimensional direct simulation Monte Carlo code is used to model neutral xenon atoms flowing from the anode of the H9 Hall Effect Thruster within the University of Michigan’s Large Vacuum Test Facility. Simulated pressures are compared with ion gauge pressure measurements to infer the effective sticking coefficient of the chamber’s vacuum pumps. A pressure predicting surrogate model is developed for inference of pump sticking coefficients and for uncertainty quantification. This information enables accurate and useful kinetic simulations of electric propulsion thruster plasma plumes in vacuum chambers.

DSMC↗

NASA NTRSDate not supplied

Aerodynamics of a Uranus Aerocapture System Using a Mars-Heritage Entry Vehicle

Aerodynamic characteristics of an aerocapture system intended to deliver a flagship-class orbiter and probe planetary science mission to Uranus are presented. The aeroshell of the Mars Science Laboratory and Mars 2020 entry vehicles is proposed as a baseline for this system to reduce the amount of necessary technology development. Direct Simulation Monte Carlo and Navier-Stokes computational fluid dynamics solutions are used to characterize the aerodynamic performance of the Mars-heritage vehicle for aerocapture flight at Uranus. These results are incorporated into an aerodatabase for use in six degree-of-freedom trajectory studies and mission design. Updates are made to the Mars-heritage aerodynamic uncertainty model based on observations in the Uranus-specific computational data to ensure the model is conservatively bounding for the proposed flight space. Necessary modifications to the aeroshell for system packaging are found to have minimal effect on aerodynamic performance. The resulting aerodatabase and uncertainty model are used to show the existing Mars-heritage entry vehicles have sufficient aerodynamic performance to achieve required control margin for Uranus aerocapture.

Eli R Shellabarger↗

NASA NTRSDate not supplied

Aerodynamics of a Uranus Aerocapture System Using a Mars-Heritage Entry Vehicle

Eli Shellabarger↗