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NASA NTRS2014

Combined Uncertainty and A-Posteriori Error Bound Estimates for General CFD Calculations: Theory and Software Implementation

This workshop presentation discusses the design and implementation of numerical methods for the quantification of statistical uncertainty, including a-posteriori error bounds, for output quantities computed using CFD methods. Hydrodynamic realizations often contain numerical error arising from finite-dimensional approximation (e.g. numerical methods using grids, basis functions, particles) and statistical uncertainty arising from incomplete information and/or statistical characterization of model parameters and random fields. The first task at hand is to derive formal error bounds for statistics given realizations containing finite-dimensional numerical error [1]. The error in computed output statistics contains contributions from both realization error and the error resulting from the calculation of statistics integrals using a numerical method. A second task is to devise computable a-posteriori error bounds by numerically approximating all terms arising in the error bound estimates. For the same reason that CFD calculations including error bounds but omitting uncertainty modeling are only of limited value, CFD calculations including uncertainty modeling but omitting error bounds are only of limited value. To gain maximum value from CFD calculations, a general software package for uncertainty quantification with quantified error bounds has been developed at NASA. The package provides implementations for a suite of numerical methods used in uncertainty quantification: Dense tensorization basis methods [3] and a subscale recovery variant [1] for non-smooth data, Sparse tensorization methods[2] utilizing node-nested hierarchies, Sampling methods[4] for high-dimensional random variable spaces.

CFD↗

NASA NTRS2014

Combined Uncertainty and A-Posteriori Error Bound Estimates for CFD Calculations: Theory and Implementation

Simulation codes often utilize finite-dimensional approximation resulting in numerical error. Some examples include, numerical methods utilizing grids and finite-dimensional basis functions, particle methods using a finite number of particles. These same simulation codes also often contain sources of uncertainty, for example, uncertain parameters and fields associated with the imposition of initial and boundary data,uncertain physical model parameters such as chemical reaction rates, mixture model parameters, material property parameters, etc.

CFD↗

DOE OSTI2021

Meta-uncertainty for particle image velocimetry

Uncertainty quantification for Particle Image Velocimetry (PIV) is critical for comparing experimentally measured flow fields with Computational Fluid Dynamics (CFD) results, and model design and validation. However, PIV features a complex measurement chain with coupled, non-linear error sources, and quantifying the uncertainty is challenging. Multiple assessments show that none of the current methods can reliably measure the actual uncertainty across a wide range of experiments, and estimates can vary. Because the current methods differ in assumptions regarding the measurement process and calculation procedures, it is not clear which method is best to use for an experiment where the error distribution is unknown. To address this issue, we propose a method to estimate an uncertainty method's sensitivity and reliability, termed the Meta-Uncertainty. The novel approach is automated, local, and instantaneous, and based on perturbation of the recorded particle images. We developed an image perturbation scheme based on adding random unmatched particles to the interrogation window pair considering the signal-to-noise (SNR) of the correlation plane. Each uncertainty scheme's response to several trials of random particle addition is used to estimate a reliability metric, defined as the rate of change of the inter-quartile range (IQR) of the uncertainties with increasing levels of particle addition. We also propose applying the meta-uncertainty as a weighting metric to combine uncertainty estimates from individual schemes, based on ideas from the consensus forecasting literature. We use planar and stereo PIV measurements across a range of canonical flows to assess the performance of the uncertainty schemes. Further, a novel method is introduced to assess an uncertainty scheme's performance based on a quantile comparison of the error and uncertainty distributions, generalizing the current method of comparing the RMS of the two distributions. Here, the results show that the combined uncertainty method outperforms the individual methods, and this work establishes the meta-uncertainty as a useful reliability assessment tool for PIV uncertainty quantification.

47 OTHER INSTRUMENTATION↗

DOE OSTI2023

(U) Correlated Sampling Using Batch Statistics to Reduce the Uncertainty of Combinations of KSEN Outputs with MCNP6

The relative sensitivity of k eff to the densities of nuclides in a material are combined to compute relative sensitivities to other inputs. When computed in a single Monte Carlo run, the nuclide density sensitivities are correlated, and the statistical uncertainties propagated to other inputs will be incorrect unless those correlations are accounted for. Equations are presented to apply correlated sampling using batch statistics for the sum of an arbitrary number of random tallies and the difference of two random tallies when each is multiplied by a different constant. When correlated sampling is used on a recent benchmark evaluation, the correct statistical uncertainties for certain combinations of sensitivities are dramatically smaller than the incorrect uncertainties. A user-controlled, regular output of MCNP6’s KSEN sensitivities that allows batch statistics to be applied to combinations would be extremely valuable.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS2023

Reducing Aerosol Forcing Uncertainty by Combining Models With Satellite and Within-The-Atmosphere Observations: A Three-Way Street

Aerosol forcing uncertainty represents the largest climate forcing uncertainty overall. Its magnitude has remained virtually undiminished over the past 20 years despite considerable advances in understanding most of the key contributing elements. Recent work has produced modest increases only in the confidence of the uncertainty estimate itself. This review summarizes the contributions toward reducing the uncertainty in the aerosol forcing of climate made by satellite observations, measurements taken within the atmosphere, as well as modeling and data assimilation. We adopt a more measurement-oriented perspective than most reviews of the subject in assessing the strengths and limitations of each; gaps and possible ways to fill them are considered. Currently planned programs supporting advanced, global-scale satellite and surface-based aerosol, cloud, and precursor gas observations, climate modeling, and intensive field campaigns aimed at characterizing the underlying physical and chemical processes involved, are all essential. But in addition, new efforts are needed: (a) to obtain systematic aircraft in situ measurements capturing the multi-variate probability distribution functions of particle optical, microphysical, and chemical properties (and associated uncertainty estimates), as well as co-variability with meteorology, for the major aerosol airmass types; (b) to conceive, develop, and implement a suborbital (aircraft plus surface-based) program aimed at systematically quantifying the cloud-scale microphysics, cloud optical properties, and cloud-related vertical velocities associated with aerosol-cloud interactions; and (c) to focus much more research on integrating the unique contributions of satellite observations, suborbital measurements, and modeling, to reduce the persistent uncertainty in aerosol climate forcing.

aerosol climate forcing↗

DOE OSTI2021

Uncertainty quantification for Multiphase-CFD simulations of bubbly flows: a machine learning-based Bayesian approach supported by high-resolution experiments

In this paper, we developed a machine learning-based Bayesian approach to inversely quantify and reduce the uncertainties of multiphase computational fluid dynamics (MCFD) simulations for bubbly flows. The proposed approach is supported by high-resolution two-phase flow measurements, including those by double-sensor conductivity probes, high-speed imaging, and particle image velocimetry. Local distributions of key physical quantities of interest (QoIs), including the void fraction and phasic velocities, are obtained to support the Bayesian inference. In the process, the epistemic uncertainties of the closure relations are inversely quantified while the aleatory uncertainties from stochastic fluctuations of the system are evaluated based on experimental uncertainty analysis. The combined uncertainties are then propagated through the MCFD solver to obtain uncertainties of the QoIs, based on which probability-boxes are constructed for validation. The proposed approach relies on three machine learning methods: feedforward neural networks and principal component analysis for surrogate modeling, and Gaussian processes for model form uncertainty modeling. The whole process is implemented within the framework of an open-source deep learning library PyTorch with graphics processing unit (GPU) acceleration, thus ensuring the efficiency of the computation. The results demonstrate that with the support of high-resolution data, the uncertainties of MCFD simulations can be significantly reduced. The proposed approach has the potential for other applications that involve numerical models with empirical parameters.

42 ENGINEERING↗

NASA NTRS2013

Assessing the Temperature Dependence of Narrow-Band Raman Water Vapor Lidar Measurements: A Practical Approach

Narrow-band detection of the Raman water vapor spectrum using the lidar technique introduces a concern over the temperature dependence of the Raman spectrum. Various groups have addressed this issue either by trying to minimize the temperature dependence to the point where it can be ignored or by correcting for whatever degree of temperature dependence exists. The traditional technique for performing either of these entails accurately measuring both the laser output wavelength and the water vapor spectral passband with combined uncertainty of approximately 0.01 nm. However, uncertainty in interference filter center wavelengths and laser output wavelengths can be this large or larger. These combined uncertainties translate into uncertainties in the magnitude of the temperature dependence of the Raman lidar water vapor measurement of 3% or more. We present here an alternate approach for accurately determining the temperature dependence of the Raman lidar water vapor measurement. This alternate approach entails acquiring sequential atmospheric profiles using the lidar while scanning the channel passband across portions of the Raman water vapor Q-branch. This scanning is accomplished either by tilt-tuning an interference filter or by scanning the output of a spectrometer. Through this process a peak in the transmitted intensity can be discerned in a manner that defines the spectral location of the channel passband with respect to the laser output wavelength to much higher accuracy than that achieved with standard laboratory techniques. Given the peak of the water vapor signal intensity curve, determined using the techniques described here, and an approximate knowledge of atmospheric temperature, the temperature dependence of a given Raman lidar profile can be determined with accuracy of 0.5% or better. A Mathematica notebook that demonstrates the calculations used here is available from the lead author.

Raman lidar↗

DOE OSTI2023

Sister Rod Destructive Examinations (FY23) Appendix F3: Uncertainty and Conservative Bias in the Cyclic Integrated Reversible-Bending Fatigue Test

The development and application of the Cyclic Integrated Reversible-Bending Fatigue Tester (CIRFT) has been documented over the past 10 years. The CIRFT system was developed in collaboration with the U.S. Nuclear Regulatory Commission (NRC) to address the concern that high-burnup fuel rod fatigue performance was degraded compared to cladding-only behavior. Fatigue data measured by CIRFT on high-burnup fuel rods were then used by the NRC to develop a fatigue response curve for pressurized water reactor fuel rods with Zircaloy-4 cladding in NUREG-2224. Subsequently, CIRFT has been used in the sister rod project to test whether reoriented hydrides associated with vacuum drying influenced the fatigue lifetime, to extend the fatigue testing database to include fuel rods with ZIRLO cladding, and to add to the experience on both Zircaloy-4 and M5 cladding. These data will be used as a reference for subsequent characterization of fuel rods removed from the high-burnup demonstration cask to better understand the effects of long-term dry storage, which can be thought of as a multiyear elevated temperature anneal. The objective of fatigue testing is to provide data that can be used to develop a best-estimate fatigue curve and a conservative fatigue design curve that accounts for uncertainty and can be compared with actual transportation conditions. The process for defining a design fatigue curve for commercial used fuel rods was developed by Oak Ridge National Laboratory (ORNL) in FY22. One issue noted in the fatigue evaluation was that the calculated combined uncertainty in the strain amplitude values determined from the measured data was large. It was proposed then to directly measure the uncertainty in the strain amplitude to either validate the calculated combined uncertainty or update the uncertainty based on the measurement data. Thus, the purpose of this appendix is to document the measured uncertainty in the strain amplitude data. In the process, it was determined that there has been a conservative bias in the calculated strain amplitude that is small enough to be within the measurement uncertainty. This observation is discussed herein, and a case is made to continue to include the conservative bias in the data.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

Quantifying modeling uncertainties when combining multiple gravitational-wave detections from binary neutron star sources

Here, with the increasing sensitivity of gravitational-wave detectors, we expect to observe multiple binary neutron-star systems through gravitational waves in the near future. The combined analysis of these gravitational-wave signals offers the possibility to constrain the neutron-star radius and the equation of state of dense nuclear matter with unprecedented accuracy. However, it is crucial to ensure that uncertainties inherent in the gravitational-wave models will not lead to systematic biases when information from multiple detections is combined. To quantify waveform systematics, we perform an extensive simulation campaign of binary neutron-star sources and analyze them with a set of four different waveform models. For our analysis with 38 simulations, we find that statistical uncertainties in the neutron-star radius decrease to ± 250 m (2% at 90% credible interval) but that systematic differences between currently employed waveform models can be twice as large. Hence, it will be essential to ensure that systematic biases will not become dominant in inferences of the neutron-star equation of state when capitalizing on future developments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS2019

Exploring Oxidation in the Remote Free Troposphere: Insights From Atmospheric Tomography (ATom)

Earth's atmosphere oxidizes the greenhouse gas methane and other gases, thus determining their lifetimes and oxidation products. Much of this oxidation occurs in the remote, relatively clean free troposphere above the planetary boundary layer, where the oxidation chemistry is thought to be much simpler and better understood than it is in urban regions or forests. The NASA airborne Atmospheric Tomography study (ATom) was designed to produce cross sections of the detailed atmospheric composition in the remote atmosphere over the Pacific and Atlantic Oceans during four seasons. As part of the extensive ATom data set, measurements of the atmosphere's primary oxidant, hydroxyl (OH), and hydroperoxyl (HO2) are compared to a photochemical box model to test the oxidation chemistry. Generally, observed and modeled median OH and HO2 agree to within combined uncertainties at the 2σ confidence level, which is ~±40%. For some seasons, this agreement is within ~±20% below 6-km altitude. While this test finds no significant differences, OH observations increasingly exceeded modeled values at altitudes above 8 km, becoming ~35% greater, which is near the combined uncertainties. Measurement uncertainty and possible unknown measurement errors complicate tests for unknown chemistry or incorrect reaction rate coefficients that would substantially affect the OH and HO2 abundances. Future analysis of detailed comparisons may yield additional discrepancies that are masked in the median values.

atmosphere's primary oxidant, hydroxyl (OH), and h↗

NASA NTRS2011

Assessment of Radiative Heating Uncertainty for Hyperbolic Earth Entry

This paper investigates the shock-layer radiative heating uncertainty for hyperbolic Earth entry, with the main focus being a Mars return. In Part I of this work, a baseline simulation approach involving the LAURA Navier-Stokes code with coupled ablation and radiation is presented, with the HARA radiation code being used for the radiation predictions. Flight cases representative of peak-heating Mars or asteroid return are de ned and the strong influence of coupled ablation and radiation on their aerothermodynamic environments are shown. Structural uncertainties inherent in the baseline simulations are identified, with turbulence modeling, precursor absorption, grid convergence, and radiation transport uncertainties combining for a +34% and ..24% structural uncertainty on the radiative heating. A parametric uncertainty analysis, which assumes interval uncertainties, is presented. This analysis accounts for uncertainties in the radiation models as well as heat of formation uncertainties in the flow field model. Discussions and references are provided to support the uncertainty range chosen for each parameter. A parametric uncertainty of +47.3% and -28.3% is computed for the stagnation-point radiative heating for the 15 km/s Mars-return case. A breakdown of the largest individual uncertainty contributors is presented, which includes C3 Swings cross-section, photoionization edge shift, and Opacity Project atomic lines. Combining the structural and parametric uncertainty components results in a total uncertainty of +81.3% and ..52.3% for the Mars-return case. In Part II, the computational technique and uncertainty analysis presented in Part I are applied to 1960s era shock-tube and constricted-arc experimental cases. It is shown that experiments contain shock layer temperatures and radiative ux values relevant to the Mars-return cases of present interest. Comparisons between the predictions and measurements, accounting for the uncertainty in both, are made for a range of experiments. A measure of comparison quality is de ned, which consists of the percent overlap of the predicted uncertainty bar with the corresponding measurement uncertainty bar. For nearly all cases, this percent overlap is greater than zero, and for most of the higher temperature cases (T >13,000 K) it is greater than 50%. These favorable comparisons provide evidence that the baseline computational technique and uncertainty analysis presented in Part I are adequate for Mars-return simulations. In Part III, the computational technique and uncertainty analysis presented in Part I are applied to EAST shock-tube cases. These experimental cases contain wavelength dependent intensity measurements in a wavelength range that covers 60% of the radiative intensity for the 11 km/s, 5 m radius flight case studied in Part I. Comparisons between the predictions and EAST measurements are made for a range of experiments. The uncertainty analysis presented in Part I is applied to each prediction, and comparisons are made using the metrics defined in Part II. The agreement between predictions and measurements is excellent for velocities greater than 10.5 km/s. Both the wavelength dependent and wavelength integrated intensities agree within 30% for nearly all cases considered. This agreement provides confidence in the computational technique and uncertainty analysis presented in Part I, and provides further evidence that this approach is adequate for Mars-return simulations. Part IV of this paper reviews existing experimental data that include the influence of massive ablation on radiative heating. It is concluded that this existing data is not sufficient for the present uncertainty analysis. Experiments to capture the influence of massive ablation on radiation are suggested as future work, along with further studies of the radiative precursor and improvements in the radiation properties of ablation products.

Johnston, Christopher O.↗

DOE OSTI2026

Creating high-precision reference gas standards of 85Kr for groundwater age-dating

Absolute gas counting (AGC) was applied to two gas blends of 85Kr in argon-methane (P10) counting gas to establish a high-precision specific activity (Bq/cm3) reference value for characterizing 85Kr detection efficiency for groundwater age dating measurements. The AGC or length-compensated technique has been utilized by the metrology community for decades and is an accepted method for developing radioactive gas standards. The AGC capability at Pacific Northwest National Laboratory (PNNL) uses a set of nine unequal-length proportional counters with precisely-measured internal volumes, and a gas loading system with high-precision pressure and temperature sensors. A series of AGC measurements were collected at multiple pressures to determine the inverse pressure relationship (1/P) for 85Kr and define a wall-effect correction that accounts for events decaying into the detector wall and not depositing sufficient energy in the gas to be detected. In addition to the wall-effect, two additional corrections were evaluated and are discussed in detail. Specifically, the threshold effect which accounts for events deposited below the analysis threshold and a detection efficiency as a function of detector volume effect that was observed during analysis. A robust uncertainty model was developed using the Guide to the expression of Uncertainty in Measurements (GUM) approach. The combination of carefully scrutinized correction factors, precise measurements of pressure, temperature and detector volume, and robust counting statistics resulted in the determination of high-precision specific activity values with 0.50% or less total combined uncertainty for two Kr-in-P10 reference gas standards (KP10) that will enable new groundwater age-dating measurements at PNNL.

Kr-85↗

NASA NTRS1982

A tutorial assessment of atmospheric height uncertainties for high-precision satellite altimeter missions to monitor ocean currents

Information from a number of sources is synthesized, and an error budget is deduced giving the projected overall height uncertainty correction for a suggested next-generation high-precision radar altimeter. Uncertainties deriving from the wet and dry troposphere, clouds, and the ionosphere are reviewed. It is assumed that the next generation of precision altimeters will be dual-frequency (13.5 and 6 GHz) and will be designed to correct for the ionospheric error. The altimeter-carrying satellite will have a nadir pointing near coincident-beam dual-frequency microwave radiometer for mitigating the wet tropospheric uncertainty. Whereas there are a number of caveats, the combined uncertainty in the height correction due to the atmosphere for the suggested system should be nominally 3 cm rms compared with at least 6 cm associated with the Seasat-A mission. Improvements in height resolution of the kind discussed here are considered vital for future satellite missions designed to monitor ocean currents.

Goldhirsh, J.↗

NASA NTRS2010

Development of an Uncertainty Model for the National Transonic Facility

This paper introduces an uncertainty model being developed for the National Transonic Facility (NTF). The model uses a Monte Carlo technique to propagate standard uncertainties of measured values through the NTF data reduction equations to calculate the combined uncertainties of the key aerodynamic force and moment coefficients and freestream properties. The uncertainty propagation approach to assessing data variability is compared with ongoing data quality assessment activities at the NTF, notably check standard testing using statistical process control (SPC) techniques. It is shown that the two approaches are complementary and both are necessary tools for data quality assessment and improvement activities. The SPC approach is the final arbiter of variability in a facility. Its result encompasses variation due to people, processes, test equipment, and test article. The uncertainty propagation approach is limited mainly to the data reduction process. However, it is useful because it helps to assess the causes of variability seen in the data and consequently provides a basis for improvement. For example, it is shown that Mach number random uncertainty is dominated by static pressure variation over most of the dynamic pressure range tested. However, the random uncertainty in the drag coefficient is generally dominated by axial and normal force uncertainty with much less contribution from freestream conditions.

Walter, Joel A.↗

DOE OSTI2020

Measurement of properties of B$^0_\mathrm{s}\to\mu^+\mu^-$ decays and search for B$^0\to\mu^+\mu^-$ with the CMS experiment

Results are reported for the $ {\mathrm{B}}_{\mathrm{s}}^0 $→ μ$^{+}$μ$^{−}$ branching fraction and effective lifetime and from a search for the decay B$^{0}$→ μ$^{+}$μ$^{−}$. The analysis uses a data sample of proton-proton collisions accumulated by the CMS experiment in 2011, 2012, and 2016, with center-of-mass energies (integrated luminosities) of 7 TeV (5 fb$^{−1}$), 8 TeV (20 fb$^{−1}$), and 13 TeV (36 fb$^{−1}$). The branching fractions are determined by measuring event yields relative to B$^{+}$→ J/ψK$^{+}$ decays (with J/ψ → μ$^{+}$μ$^{−}$), which results in the reduction of many of the systematic uncertainties. The decay $ {\mathrm{B}}_{\mathrm{s}}^0 $→ μ$^{+}$μ$^{−}$ is observed with a significance of 5.6 standard deviations. The branching fraction is measured to be $ \mathrm{\mathcal{B}}\left({\mathrm{B}}_{\mathrm{s}}^0\to {\upmu}^{+}{\upmu}^{-}\right)=\left[2.9\pm 0.7\left(\exp \right)\pm 0.2\left(\mathrm{frag}\right)\right]\times {10}^{-9} $, where the first uncertainty combines the experimental statistical and systematic contributions, and the second is due to the uncertainty in the ratio of the $ {\mathrm{B}}_{\mathrm{s}}^0 $ and the B$^{+}$ fragmentation functions. No significant excess is observed for the decay B$^{0}$→ μ$^{+}$μ$^{−}$, and an upper limit of ℬ(B$^{0}$ → μ$^{+}$μ$^{−}$) < 3.6 × 10$^{−10}$ is obtained at 95% confidence level. The $ {\mathrm{B}}_{\mathrm{s}}^0 $→ μ+μ− effective lifetime is measured to be $ {\tau}_{\upmu^{+}{\upmu}^{-}}={1.70}_{-0.44}^{+0.61} $ ps. These results are consistent with standard model predictions.[graphic not available: see fulltext]

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS2016

On the Calculation of Uncertainty Statistics with Error Bounds for CFD Calculations Containing Random Parameters and Fields

This chapter discusses the ongoing development of combined uncertainty and error bound estimates for computational fluid dynamics (CFD) calculations subject to imposed random parameters and random fields. An objective of this work is the construction of computable error bound formulas for output uncertainty statistics that guide CFD practitioners in systematically determining how accurately CFD realizations should be approximated and how accurately uncertainty statistics should be approximated for output quantities of interest. Formal error bounds formulas for moment statistics that properly account for the presence of numerical errors in CFD calculations and numerical quadrature errors in the calculation of moment statistics have been previously presented in [8]. In this past work, hierarchical node-nested dense and sparse tensor product quadratures are used to calculate moment statistics integrals. In the present work, a framework has been developed that exploits the hierarchical structure of these quadratures in order to simplify the calculation of an estimate of the quadrature error needed in error bound formulas. When signed estimates of realization error are available, this signed error may also be used to estimate output quantity of interest probability densities as a means to assess the impact of realization error on these density estimates. Numerical results are presented for CFD problems with uncertainty to demonstrate the capabilities of this framework.

Uncertainty↗

NASA NTRS1999

SeaWiFS Postlaunch Technical Report Series: The SeaWiFS Solar Radiation-Based Calibration and the Transfer-to-Orbit Experiment - Volume 5

The solar radiation-based calibration (SRBC) of the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) was performed on 1 November 1993. Measurements were made outdoors in the courtyard of the instrument manufacturer. SeaWiFS viewed the solar irradiance reflected from the sensor's diffuser in the same manner as viewed on orbit. The calibration included measurements using a solar radiometer designed to determine the transmittances of principal atmospheric constituents. The primary uncertainties in the outdoor measurements are the transmission of the atmosphere and the reflectance of the diffuser. Their combined uncertainty is about 5 or 6%. The SRBC also requires knowledge of the extraterrestrial solar spectrum. Four solar models are used. When averaged over the responses of the SeaWiFS bands, the irradiance models agree at the 3.6% level, with the greatest difference for SeaWiFS band 8. The calibration coefficients from the SRBC are lower than those from the laboratory calibration of the instrument in 1997. For a representative solar model, the ratios of the SRBC coefficients to laboratory values average 0.962 with a standard deviation of 0.012. The greatest relative difference is 0.946 for band 8. These values are within the estimated uncertainties of the calibration measurements. For the transfer-to-orbit experiment, the measurements in the manufacturer's courtyard are used to predict the digital counts from the instrument on its first day on orbit (August 1, 1997). This experiment requires an estimate of the relative change in the diffuser response for the period between the launch of the instrument and its first solar measurements on orbit (September 9, 1997). In relative terms, the counts from the instrument on its first day on orbit averaged 1.3% higher than predicted, with a standard deviation of 1.2% and a greatest difference of 2.4% or band 7. The estimated uncertainty for the transfer-to-orbit experiment is about 3 or 4%.

Hooker, Stanford B.↗

NASA NTRS2019

Uncertainty Analysis of the CE-22 Advanced Nozzle Test Facility

This paper presents methods and results of a detailed measurement uncertainty analysis that was performed for the Advanced Nozzle Test Facility, CE-22, located at the NASA Glenn Research Center. Results for the uncertainty in thrust and flow coefficients, in addition to other variables of interest, are provided. Results are presented separately as random uncertainty (characterizing errors inherent to instrument or measurement environment, impacting repeatability), systematic uncertainty (capturing inaccuracies due to measurement process, calibration, installation effects or other sources which may introduce bias), and total combined uncertainty. The statistical methods and engineering judgments used to estimate elemental uncertainties are described. The analysis tool MANTUS (Measurement Analysis Tool for Uncertainty in Systems) was used to quantify instrumentation system uncertainty, and statistical analysis and engineering judgment were used to quantify other random and systematic uncertainty sources. The Monte Carlo method was used to propagate systematic and random elemental uncertainties to determine the uncertainties of various calculated variables of interest.

data quality↗