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NASA NTRS2016

Source Data Applicability Impacts on Epistemic Uncertainty for Launch Vehicle Fault Tree Models

Launch vehicle systems are designed and developed using both heritage and new hardware. Design modifications to the heritage hardware to fit new functional system requirements can impact the applicability of heritage reliability data. Risk estimates for newly designed systems must be developed from generic data sources such as commercially available reliability databases using reliability prediction methodologies, such as those addressed in MIL-HDBK-217F. Failure estimates must be converted from the generic environment to the specific operating environment of the system where it is used. In addition, some qualification of applicability for the data source to the current system should be made. Characterizing data applicability under these circumstances is crucial to developing model estimations that support confident decisions on design changes and trade studies. This paper will demonstrate a data-source applicability classification method for assigning uncertainty to a target vehicle based on the source and operating environment of the originating data. The source applicability is determined using heuristic guidelines while translation of operating environments is accomplished by applying statistical methods to MIL-HDK-217F tables. The paper will provide a case study example by translating Ground Benign (GB) and Ground Mobile (GM) to the Airborne Uninhabited Fighter (AUF) environment for three electronic components often found in space launch vehicle control systems. The classification method will be followed by uncertainty-importance routines to assess the need to for more applicable data to reduce uncertainty.

Al Hassan, Mohammad↗
NASA NTRS2016

Crop Model Improvement Reduces the Uncertainty of the Response to Temperature of Multi-Model Ensembles

To improve climate change impact estimates and to quantify their uncertainty, multi-model ensembles (MMEs) have been suggested. Model improvements can improve the accuracy of simulations and reduce the uncertainty of climate change impact assessments. Furthermore, they can reduce the number of models needed in a MME. Herein, 15 wheat growth models of a larger MME were improved through re-parameterization and/or incorporating or modifying heat stress effects on phenology, leaf growth and senescence, biomass growth, and grain number and size using detailed field experimental data from the USDA Hot Serial Cereal experiment (calibration data set). Simulation results from before and after model improvement were then evaluated with independent field experiments from a CIMMYT worldwide field trial network (evaluation data set). Model improvements decreased the variation (10th to 90th model ensemble percentile range) of grain yields simulated by the MME on average by 39% in the calibration data set and by 26% in the independent evaluation data set for crops grown in mean seasonal temperatures greater than 24 C. MME mean squared error in simulating grain yield decreased by 37%. A reduction in MME uncertainty range by 27% increased MME prediction skills by 47%. Results suggest that the mean level of variation observed in field experiments and used as a benchmark can be reached with half the number of models in the MME. Improving crop models is therefore important to increase the certainty of model-based impact assessments and allow more practical, i.e. smaller MMEs to be used effectively.

damage assessment↗
NASA NTRS2016

Exploiting Measurement Uncertainty Estimation in Evaluation of GOES-R ABI Image Navigation Accuracy Using Image Registration Techniques

In evaluating GOES-R Advanced Baseline Imager (ABI) image navigation quality, upsampled sub-images of ABI images are translated against downsampled Landsat 8 images of localized, high contrast earth scenes to determine the translations in the East-West and North-South directions that provide maximum correlation. The native Landsat resolution is much finer than that of ABI, and Landsat navigation accuracy is much better than ABI required navigation accuracy and expected performance. Therefore, Landsat images are considered to provide ground truth for comparison with ABI images, and the translations of ABI sub-images that produce maximum correlation with Landsat localized images are interpreted as ABI navigation errors. The measured local navigation errors from registration of numerous sub-images with the Landsat images are averaged to provide a statistically reliable measurement of the overall navigation error of the ABI image. The dispersion of the local navigation errors is also of great interest, since ABI navigation requirements are specified as bounds on the 99.73rd percentile of the magnitudes of per pixel navigation errors. However, the measurement uncertainty inherent in the use of image registration techniques tends to broaden the dispersion in measured local navigation errors, masking the true navigation performance of the ABI system. We have devised a novel and simple method for estimating the magnitude of the measurement uncertainty in registration error for any pair of images of the same earth scene. We use these measurement uncertainty estimates to filter out the higher quality measurements of local navigation error for inclusion in statistics. In so doing, we substantially reduce the dispersion in measured local navigation errors, thereby better approximating the true navigation performance of the ABI system.

navigation performance↗
NASA NTRS2016

The Near-Earth Meteoroid Flux, Speed Distribution, and Uncertainty

Meteoroids are known to pose a threat to spacecraft; they can puncture components, disturb spacecraft attitude, and possibly create secondary electrical effects. Accurate environment models are therefore critical for mitigating meteoroid-related risks. While there are several meteoroid environment models available for assessing spacecraft risk, the uncertainties associated with these models are not well understood. Because meteoroid properties are derived from indirect observations such as meteors and impact craters, the uncertainty in the meteoroid flux is potentially quite large. We combine existing meteoroid flux measurements with new radar and optical meteor data to improve our characterization of the meteoroid flux onto the Earth and its velocity distribution. We use data extracted from the NASA all-sky network, the Canadian Automated Meteor Observatory, and the Canadian Meteor Orbit Radar. We improve our characterization of the observed meteoroid speed distribution by incorporating modern descriptions of the ionization efficiency (e.g., Thomas et al., 2016). We also present estimates of the uncertainties associated with our meteoroid flux distribution. Finally, we discuss the implications for spacecraft. Our model is constrained by the cratering rate on the space-facing surface of LDEF, and thus the risk posed to spacecraft by meteoroid-induced physical damage is the least uncertain component of our model. Other sources of risk, however, may vary. For instance, a lower average meteoroid speed would require a higher meteoroid mass flux in order to match the LDEF crater counts, leading to higher predicted rates of attitude disturbances.

Moorhead, Althea↗
NASA NTRS2016

Reducing Multisensor Satellite Monthly Mean Aerosol Optical Depth Uncertainty: 1. Objective Assessment of Current AERONET Locations

Various space-based sensors have been designed and corresponding algorithms developed to retrieve aerosol optical depth (AOD), the very basic aerosol optical property, yet considerable disagreement still exists across these different satellite data sets. Surface-based observations aim to provide ground truth for validating satellite data; hence, their deployment locations should preferably contain as much spatial information as possible, i.e., high spatial representativeness. Using a novel Ensemble Kalman Filter (EnKF)- based approach, we objectively evaluate the spatial representativeness of current Aerosol Robotic Network (AERONET) sites. Multisensor monthly mean AOD data sets from Moderate Resolution Imaging Spectroradiometer, Multiangle Imaging Spectroradiometer, Sea-viewing Wide Field-of-view Sensor, Ozone Monitoring Instrument, and Polarization and Anisotropy of Reflectances for Atmospheric Sciences coupled with Observations from a Lidar are combined into a 605-member ensemble, and AERONET data are considered as the observations to be assimilated into this ensemble using the EnKF. The assessment is made by comparing the analysis error variance (that has been constrained by ground-based measurements), with the background error variance (based on satellite data alone). Results show that the total uncertainty is reduced by approximately 27% on average and could reach above 50% over certain places. The uncertainty reduction pattern also has distinct seasonal patterns, corresponding to the spatial distribution of seasonally varying aerosol types, such as dust in the spring for Northern Hemisphere and biomass burning in the fall for Southern Hemisphere. Dust and biomass burning sites have the highest spatial representativeness, rural and oceanic sites can also represent moderate spatial information, whereas the representativeness of urban sites is relatively localized. A spatial score ranging from 1 to 3 is assigned to each AERONET site based on the uncertainty reduction, indicating its representativeness level.

aerosol optical depth↗
NASA NTRS2019

Uncertainties in the Geostationary Ocean Color Imager (GOCI) Remote Sensing Reflectance for Assessing Diurnal Variability of Biogeochemical Processes

Short-term (sub-diurnal) biological and biogeochemical processes cannot be fully captured by the current suite of polar-orbiting satellite ocean color sensors, as their temporal resolution is limited to potentially one clear image per day. Geostationary sensors, such as the Geostationary Ocean Color Imager (GOCI) from the Republic of Korea, allow the study of these short-term processes because their orbit permit the collection of multiple images throughout each day for any area within the sensor’s field of regard. Assessing the capability to detect sub-diurnal changes in in-water properties caused by physical and biogeochemical processes characteristic of open ocean and coastal ocean ecosystems, however, requires an understanding of the uncertainties introduced by the instrument and/or geophysical retrieval algorithms. This work presents a study of the uncertainties during the daytime period for an ocean region with characteristically low-productivity with the assumption that only small and undetectable changes occur in the in-water properties due to biogeochemical processes during the daytime period. The complete GOCI mission data were processed using NASA’s SeaDAS/l2gen package. The assumption of homogeneity of the study region was tested using three-day sequences and diurnal statistics. This assumption was found to hold based on the minimal diurnal and day-to-day variability in GOCI data products. Relative differences with respect to the midday value were calculated for each hourly observation of the day in order to investigate what time of the day the variability is greater. Also, the influence of the solar zenith angle in the retrieval of remote sensing reflectances and derived products was examined. Finally, we determined that the uncertainties in water-leaving “remote-sensing” reflectance (Rrs) for the 412,443, 490, 555, 660 and 680 nm bands on GOCI are 8.05 x 10(exp -4), 5.49 x 10(exp -4), 4.48 x 10(exp -4), 2.51 x 10(exp -4), 8.83 x 10(exp -5), and 1.36 x 10(exp -4)/sr, respectively, and 1.09 x 10(exp -2)/cu.mgm for the chlorophyll-a concentration (Chl-a), 2.09 x 10(exp -3)/m for the absorption coefficient of chromophoric dissolved organic matter at 412 nm (a(sub g) (412)), and 3.7 mg/cu.m for particulate organic carbon (POC). These R(sub rs) values can be considered the threshold values for detectable changes of the in-water properties due to biological, physical or biogeochemical processes from GOCI.

Concha, Javier↗
NASA NTRS2019

Uncertainty of Observation Impact Estimation in an Adjoint Model Investigated with an Observing System Simulation Experiment

Adjoint models are often used to estimate the impact of different observations on short-term forecast skill. A common difficulty with the evaluation of short term forecast quality is the choice of verification fields. The use of self-analysis fields for verification is typical but incestuous, and introduces uncertainty due to biases and errors in the analysis field. In this study, an observing system simulation experiment (OSSE) is used to explore the uncertainty in adjoint model estimations of observation impact. The availability of the true state for verification in the OSSE framework in the form of the Nature Run allows calculation of the observation impact without the uncertainties present in self-analysis verification. These impact estimates are compared to estimates calculated using self-analysis verification. The Global Earth Observing System version 5 (GEOS-5) forecast model with Gridpoint Statistical Interpolation (GSI) is used with the National Aeronautics and Space Administration Global Modeling and Assimilation Office (NASA/GMAO) OSSE capability. The adjoint model includes moist processes, with total wet energy selected as the norm for evaluation of observation impacts. The results show that there are measurable but small discrepancies in the adjoint model estimation of observation impact. In general, observations of temperature and winds tend to have overestimated impacts with self-analysis verification, while observations of humidity and moisture-affected observations tend to have underestimated impacts. The small magnitude of the differences in impact estimates supports the robustness of the adjoint method of estimating observation impacts.

N C Prive↗
NASA NTRS2019

Scheduling and Airport Taxiway Path Planning Under Uncertainty

Congestion and uncertainty on the airport surface are major constraints to the available capacity of the air transport system. This project is to study the problem of planning and scheduling airport surface movement at large airports. Specifically, we focus on the departure time scheduling and taxiway path planning of multiple aircraft under uncertainty. We also developed a simulation tool that is capable of simulating aircraft movement along the taxiway and possible uncertainty during the movement.

Li, Jiaoyang↗
NASA NTRS2017

Data Assimilation and Uncertainties in Early Solar Cycle Predictions

Stochastic nature of solar activity variations together with our limited knowledge of the dynamo mechanism and subsurface dynamics causes uncertainty in predictions of the solar cycle. For improving the physics-­‐based predictions we can take advantage of the mathematical data assimilation approach that allows us to take into account both, observational errors and model uncertainties, and provide estimates of the next solar cycle along with prediction uncertainties. In this study we use the Parker's migratory dynamo model together with the equation of magnetic helicity balance, which reproduces main properties of the sunspot cycles and allow us to minimize discrepancies between the observed global activity variations and the model solution. The test simulation runs show that a reliable prediction can be obtained for two phases of preceding solar cycle: 1) if the polar field reversals shortly after the solar maxima (strong toroidal field and weak poloidal field), and 2) during the solar minima (strongest poloidal and weak toroidal fields). The early estimate of Cycle 25 obtained by this method shows that this cycle will start in 2019 – 2020, reach the maximum in 2023 – 2024, and that the mean sunspot number at the maximum will be about 90 (for the v2.0 sunspot number series).

Data Assimilation↗
NASA NTRS2019

CLARREO Pathfinder/VIIRS Intercalibration: Quantifying the Polarization Effects on Reflectance and the Intercalibration Uncertainty

Atmospheric scattering and surface polarization affect radiance measurements of polarization-sensitive instruments on orbit. Neglecting the polarization effects may lead to an inaccurate radiance/reflectance determination and underestimated radiance/reflectance uncertainty. Of the two instruments, CERES and VIIRS, slated to be intercalibrated by the CLARREO Pathfinder(CPF), the latter is known to be sensitive to polarization. The Pathfinder mission is tasked with accurately determining the uncertainty contribution of polarization and will provide the bench mark for the determination of the polarization correction factor for polarization-sensitive instruments. In this article, we show the formalism necessary to correct the reflectance for sensitivity to polarization after the CLARREO Pathfinder/VIIRS intercalibration, as well as the associated polarization uncertainty contribution to the overall intercalibrated reflectance error. To illustrate its usage, the formalism is applied to three dominant scene types.

Goldin, Daniel↗
NASA NTRS2006

Conflict Detection Using Variable Four-Dimensional Uncertainty Bounds to Control Missed Alerts

Decision-support tools for maintaining pairwise aircraft separation rely on conflict detection to alert the operator when the predicted trajectories of aircraft will result in a loss of separation. But aircraft frequently do not follow their predicted trajectories exactly. This can cause missed alerts and the failure of strategic separation procedures. We present a technique for modeling a bounded region of uncertainty around a four-dimensional predicted trajectory and an algorithm for detecting conflicts between trajectories modeled in this way that avoids missed alerts as long as the aircraft remain within the specified regions of uncertainty. In addition, we present an algorithm for detecting the intrusion of a trajectory modeled in this way into an area hazard modeled as a polygonal region. The size of the region of uncertainty can vary along the trajectory continually and independently in the along-path, cross-track, and vertical dimensions, providing an opportunity to reduce the likelihood of false alerts while protecting against typical prediction errors. The algorithm has been implemented in the Autonomous Operations Planner, a NASA Langley prototype decision support tool for airborne self-separation.

Karr, David A.↗
NASA NTRSDate not supplied

Probing Sensitivity of Discharge Characteristics to Model Selection using Uncertainty Quantification in an aprotic Li-Oxygen Battery

Currently, there are several models in the literature, such as kinetic models, microstructural models, and mass transport models that describe a Li-air battery's discharge behavior. Many of these models are calibrated and tested at low current densities and cannot be easily transferred to high current densities. Even at low current densities, there is no quantitative method for a researcher to choose a reaction kinetic model such as classical Butler-Volmer and its derivatives, and modified Marcus-Hush-Chidsey, a resistance model for lithium peroxide such as electron transport via tunneling or linear resistivity, a surface coverage model (lithium peroxide growth) such as partial coverage or full coverage, and mass transport model (discussed in Ref. [1]). Also, it is time-consuming to test different models at high current density (1C) due to a lack of well-tested models and well-calibrated model parameters. For this presentation, we will develop an analytical model, which acts as a surrogate model for a sophisticated finite element model to predict discharge time and discharge voltage. Next, we use an uncertainty quantifying technique called reduced-order stochastic optimization [2, 3] to determine the uncertainty in model parameters for rate kinetics, lithium peroxide resistivity, and parasitic resistance. Finally, a finite element simulation is performed to determine the error introduced by the surrogate model and its influence on the uncertainty in the model parameters.

M Mehta↗
NASA NTRS2019

Ephemeris refinement of 21 hot Jupiter exoplanets with high timing uncertainties

Transit events of extrasolar planets offer a wealth of information for planetary characterization. However, for many known targets, the uncertainty of their predicted transit windows prohibits an accurate scheduling of follow-up observations. In this work, we refine the ephemerides of 21 hot Jupiter exoplanets with the largest timing uncertainties. We collected 120 professional and amateur transit light curves of the targets of interest, observed with a range of telescopes of 0.3 m–2.2 m, and analyzed them along with the timing information of the planets discovery papers. In the case of WASP-117b, we measured a timing deviation compared to the known ephemeris of about 3.5 h, and for HAT-P-29b and HAT-P-31bthe deviation amounted to about 2 h and more. For all targets, the new ephemeris predicts transit timings with uncertainties of less than 6 min in the year 2018 and less than 13 min until 2025. Thus, our results allow for an accurate scheduling of follow-up observations in the next decade.

photometric↗
NASA NTRS2020

How emissions uncertainty influences the distribution and radiative impacts of smoke from fires in North America

Fires and the aerosols that they emit impact air quality, health, and climate, but the abundance and properties of carbonaceous aerosol (both black carbon and organic carbon) from biomass burning (BB) remain uncertain and poorly constrained. We aim to explore the uncertainties associated with fire emissions and their air quality and radiative impacts from underlying dry matter consumed and emissions factors. To investigate this, we compare model simulations from a global chemical transport model, GEOS-Chem, driven by a variety of fire emission inventories with surface and airborne observations of black carbon (BC) and organic aerosol (OA) concentrations and satellite-derived aerosol optical depth (AOD). We focus on two fire-detection-based and/or burned-area-based (FD-BA) inventories using burned area and active fire counts, respectively, i.e., the Global Fire Emissions Database version 4 (GFED4s) with small fires and the Fire INventory from NCAR version 1.5 (FINN1.5), and two fire radiative power (FRP)-based approaches, i.e., the Quick Fire Emission Dataset version 2.4 (QFED2.4) and the Global Fire Assimilation System version 1.2 (GFAS1.2). We show that, across the inventories, emissions of BB aerosol (BBA) differ by a factor of 4 to 7 over North America and that dry matter differences, not emissions factors, drive this spread. We find that simulations driven by QFED2.4 generally overestimate BC and, to a lesser extent, OA concentrations observations from two fire-influenced aircraft campaigns in North America (ARCTAS and DC3) and from the Interagency Monitoring of Protected Visual Environments (IMPROVE) network, while simulations driven by FINN1.5 substantially underestimate concentrations. The GFED4s and GFAS1.2-driven simulations provide the best agreement with OA and BC mass concentrations at the surface (IMPROVE), BC observed aloft (DC3 and ARCTAS), and AOD observed by MODIS over North America. We also show that a sensitivity simulation including an enhanced source of secondary organic aerosol (SOA) from fires, based on the NOAA Fire Lab 2016 experiments, produces substantial additional OA; however, the spread in the primary emissions estimates implies that this magnitude of SOA can be neither confirmed nor ruled out when comparing the simulations against the observations explored here. Given the substantial uncertainty in fire emissions, as represented by these four emission inventories, we find a sizeable range in 2012 annual BBA PM2.5 population-weighted exposure over Canada and the contiguous US (0.5 to 1.6 µg/cu. m). We also show that the range in the estimated global direct radiative effect of carbonaceous aerosol from fires (−0.11 to −0.048 W/sq. m) is large and comparable to the direct radiative forcing of OA (−0.09 W/sq. m) estimated in the Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change (IPCC). Our analysis suggests that fire emissions uncertainty challenges our ability to accurately characterize the impact of smoke on air quality and climate.

North America↗
NASA NTRS2020

Prelaunch Radiometric Calibration and Uncertainty Analysis of Landsat Thermal Infrared Sensor 2

The Thermal Infrared Sensor-2 (TIRS-2) that will be onboard Landsat 9 has undergone a prelaunch testing campaign to characterize its radiometric, spectral, and spatial performances and demonstrate compliance to its requirements. This work reviews the key elements of the instrument-level radiometric testing using an SI-traceable source to derive its uncertainties. Those arising from on-orbit calibration using the TIRS-2 onboard blackbody are also discussed. We use a Monte Carlo approach to propagate the uncertainties through a nonlinear calibration equation and address both random and systematic uncertainty terms. Achieving the required performance demonstrates the instrument's potential for enhancing our understanding of the Earth's environment.

Aaron Pearlman↗
NASA NTRSDate not supplied

Probabilistic Blast Damage Modeling Uncertainties and Sensitivities

Blast overpressure is the predominant source of ground damage posed by potentially hazardous asteroid strikes. Estimates of the extent, severity, and likelihoods of potential blast damage regions will be one of the key metrics needed to mount civil defense or disaster response plans in the face of an impending impact. However, there are many inherent sources of uncertainty in evaluating the damage, both in characterizing the properties of the incoming object and in the approaches used to model the entry/impact and resulting damage, which make it difficult to produce a single ‘accurate’ or ‘best guess’ prediction of ground damage. The current 2021 PDC hypothetical impact scenario poses a particular challenge due to its short warning time. The need for rapid disaster response to prepare for an immanent impact, combined with lack of observational opportunities to refine basic knowledge about the object’s basic size and properties, make understanding the range and relative likelihood of consequences particularly critical. The potential damage caused by these blasts can be evaluated using a range of modeling and simulation approaches and levels of fidelity. Fast-running engineering-level models can be used to run large numbers of probabilistically sampled cases covering wide variations of uncertain properties or parameters. High-fidelity simulations, on the other hand, can capture more detailed/accurate blast physics, but can only be performed for a small selection of specific cases, requiring many assumptions to be made about the initial object and its unpredictable entry/breakup characteristics. In order to provide a more complete picture of the potential threat for effective disaster response, both types of analysis need to be employed together. In this approach, high-fidelity simulations are used to refine and anchor engineering models, and the probabilistic engineering models are used to evaluate broad parameters spaces and guide selection of the most pertinent simulation cases for a given scenario. This presentation expands upon the probabilistic asteroid impact risk assessments being performed as part of the 2021 PDC hypothetical impact exercise, focusing on key aspects of blast damage modeling uncertainties and sensitivities. We review the current modeling and simulation approaches employed in the current assessment, compare the relative levels of uncertainty stemming from each main element of the problem (i.e., knowledge of the asteroid properties, modeling of the atmospheric entry/breakup and airburst, and estimates of the ground damage from the resulting blasts waves), and highlight any notable trends and sensitivities for the current scenario case.

SMD↗
NASA NTRS2019

Tropospheric Ozone Assessment Report: Tropospheric Ozone From 1877 to 2016, Observed Levels, Trends and Uncertainties

From the earliest observations of ozone in the lower atmosphere in the 19th century, both measurement methods and the portion of the globe observed have evolved and changed. These methods have different uncertainties and biases, and the data records differ with respect to coverage (space and time), information content, and representativeness. In this study, various ozone measurement methods and ozone datasets are reviewed and selected for inclusion in the historical record of background ozone levels, based on relationship of the measurement technique to the modern UV absorption standard, absence of interfering pollutants, representativeness of the well-mixed boundary layer and expert judgement of their credibility. There are significant uncertainties with the 19th and early 20th-century measurements related to interference of other gases. Spectroscopic methods applied before 1960 have likely underestimated ozone by as much as 11% at the surface and by about 24% in the free troposphere, due to the use of differing ozone absorption coefficients. There is no unambiguous evidence in the measurement record back to 1896 that typical mid-latitude background surface ozone values were below about 20 nmol mol–1, but there is robust evidence for increases in the temperate and polar regions of the northern hemisphere of 30–70%, with large uncertainty, between the period of historic observations, 1896–1975, and the modern period (1990–2014). Independent historical observations from balloons and aircraft indicate similar changes in the free troposphere. Changes in the southern hemisphere are much less. Regional representativeness of the available observations remains a potential source of large errors, which are difficult to quantify. The great majority of validation and intercomparison studies of free tropospheric ozone measurement methods use ECC ozonesondes as reference. Compared to UV-absorption measurements they show a modest (~1–5% ±5%) high bias in the troposphere, but no evidence of a change with time. Umkehr, lidar, and FTIR methods all show modest low biases relative to ECCs, and so, using ECC sondes as a transfer standard, all appear to agree to within one standard deviation with the modern UV-absorption standard. Other sonde types show an increase of 5–20% in sensitivity to tropospheric ozone from 1970–1995. Biases and standard deviations of satellite retrieval comparisons are often 2–3 times larger than those of other free tropospheric measurements. The lack of information on temporal changes of bias for satellite measurements of tropospheric ozone is an area of concern for long-term trend studies.

UV absorption standard↗
NASA NTRSDate not supplied

Uncertainty Estimates for Sonic-Boom Pressure Signatures and Loudness Carpets

A non-intrusive uncertainty quantification method is applied to computational analysis of supersonic, low-boom aircraft. The mean and standard deviation statistics of the pressure waveforms and loudness metrics are evaluated through use of numerical quadrature. The probability density function (p.d.f.) of these outputs is evaluated via kernel density estimation. The simulations use an inviscid, embedded-boundary Cartesian-mesh flow solver in the nearfield combined with an augmented Burgers’ equation solver for propagation in the farfield. The results show that the p.d.f. of the waveform is bimodal at shocks, which makes the mean and standard deviation statistics inappropriate. Despite this limitation, we show that the moment statistics can provide effective assessment of discrepancies when comparing with experimental data. This is demonstrated by presenting uncertainty analysis of a wind-tunnel test and showing that we significantly improve the predictions when we include the test uncertainties in the simulation. Normal distributions are obtained for the ground signature and loudness metrics, which is primarily due to the careful shaping of the low-boom waveform. Separation of variables and error control are used to reduce computational cost. We demonstrate that this is an efficient approach in the sense of balancing numerical errors in the statistics quadrature with discretization errors in the solvers.

ARMD↗