Introduction to Uncertainty Quantification for Modeling and Simulation
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Systems engineers often make use of cost Rules ofThumb in order to estimate cost during early phases of projectformulation. These Rules of Thumb typically take the form ofa sequence of percentages over which a total cost is allocatedacross NASA WBS elements. Rules of Thumb can then be usedto extrapolate cost from one or more known WBS elements tothe remaining unknown WBS elements, assisting early projectformulation architecture studies (such as those in JPL’s Team Xand A Team).A number of issues can arise when generating and using costRules of Thumb. For example, many records of project costsconsist of incomplete data. Typical methods of dealing withincomplete cost allocation data include (a) ignoring missionswith incomplete data, or (b) taking averages of the non-zero percentagesacross missions, but both of these methods can result inbiased estimates if the existence of incomplete data correlateswith total mission cost or any particular WBS element. Anothercommon example is cost reported in one or more incorrect WBSelements. This is especially prevalent in smaller missions whereit is more common for engineers to perform tasks that fall underthe purview of multiple WBS elements.Furthermore, a Rule of Thumb estimate is typically reported asa point estimate; there is no reported uncertainty around thepercentages used to generate an allocation. Even in the rarecase in which confidence intervals around mean percentages areprovided, there may be positive or negative correlations betweenWBS elements which can skew estimates.Here we attempt to address these problems by formulatingprobabilistic Rules of Thumb in which a distribution of allocationschemes, rather than a single allocation scheme, is generated.We use a bootstrap imputation method to simultaneouslyaccount for uncertainty in the missing data while using allavailable information contained in the dataset. The imputeddatasets are then input into a multivariate Bayesian modelwhich accounts for correlations between WBS elements andproperly accounts for uncertainty in the final Rule of Thumbpercentages and predictions. We describe the mathematicalmodel and provides snippets of R code utilizing the brms(Bayesian Regression Models using Stan) package. To illustratethis model, we generate a Bayesian Level 2 WBS Cost Rule ofThumb for MIDEX (Medium-Class Explorers) missions withdata extracted from NASA’s CADRe. We then compare thismethod’s performance with the classical Rule of Thumb method.
The Low-Earth Orbit Flight Test of an Inflatable Decelerator (LOFTID) was a flight demonstration of the Hypersonic Inflatable Aerodynamic Decelerator (HIAD) technology, which has the potential to enable delivery of heavy payloads to Mars, Venus, and Titan, as well as return to Earth. Unlike rigid aeroshells that are constrained by the diameter of the launch vehicle shroud, inflatable aeroshells can be deployed to a much larger drag area, thus allowing a more massive spacecraft to begin its deceleration at higher altitudes and experience less heating. On November 10, 2022, the LOFTID reentry vehicle launched aboard a United Launch Alliance Atlas V rocket to low-Earth orbit. The aeroshell was inflated to its full 6-meter diameter, and the vehicle then successfully re-entered the atmosphere, landing in the Pacific Ocean. The aeroshell was composed of seven tori bound together by high strength straps to create a 70-degree half-angle sphere-cone, and the forebody was covered with a flexible thermal protection system (FTPS) (Fig. 1). The centerbody of the vehicle housed six visual cameras. Each camera was made up of 1920 x 1080 pixels and had a field-of-view (FOV) of 85.4° x 55.6°, resulting in a resolution of less than 0.1" at all locations on the aftbody side of the aeroshell. The approximate locations of the cameras and their associated FOVs is shown in Fig. 2. The high loads experienced during flight resulted in the cone of the aeroshell deflecting. This behavior was seen during the static load testing of the aeroshell in May 2021, in which loads ranging from 1,000 to 20,000 lbf were applied, and deflections of up to ~1.7° were observed. The LOFTID team was interested in estimating the deflection of the aeroshell during the its entry into Earth's atmosphere. Before launch, 1"-diameter black circles were drawn on select structural straps for tracking with the visual cameras; the change in position of these features could then be used to calculate aeroshell deflection angle.
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The Low-Earth Orbit Flight Test of an Inflatable Decelerator (LOFTID) was a flight demonstration of the Hypersonic Inflatable Aerodynamic Decelerator (HIAD) technology, which has the potential to enable delivery of heavy payloads to Mars, Venus, and Titan, as well as return to Earth. Unlike rigid aeroshells that are constrained by the diameter of the launch vehicle shroud, inflatable aeroshells can be deployed to a much larger drag area, thus allowing a more massive spacecraft to begin its deceleration at higher altitudes and experience less heating. On November 10, 2022, the LOFTID reentry vehicle launched aboard a United Launch Alliance Atlas V rocket to low-Earth orbit. The aeroshell was inflated to its full 6-meter diameter, and the vehicle then successfully re-entered the atmosphere, landing in the Pacific Ocean. The aeroshell was composed of seven tori bound together by high strength straps to create a 70-degree half-angle sphere-cone, and the forebody was covered with a flexible thermal protection system (FTPS) (Fig. 1). The centerbody of the vehicle housed six visual cameras. Each camera was made up of 1920 x 1080 pixels and had a field-of-view (FOV) of 85.4° x 55.6°, resulting in a resolution of less than 0.1" at all locations on the aftbody side of the aeroshell. The approximate locations of the cameras and their associated FOVs is shown in Fig. 2. The high loads experienced during flight resulted in the cone of the aeroshell deflecting. This behavior was seen during the static load testing of the aeroshell in May 2021, in which loads ranging from 1,000 to 20,000 lbf were applied, and deflections of up to ~1.7° were observed. The LOFTID team was interested in estimating the deflection of the aeroshell during the its entry into Earth's atmosphere. Before launch, 1"-diameter black circles were drawn on select structural straps for tracking with the visual cameras; the change in position of these features could then be used to calculate aeroshell deflection angle.
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Traditionally, mission planners have used a heuristic and qualitative approach to design medical systems based on prior experience however this approach may result in high variability and implicit bias to design and could put missions and crewmembers at risk. The Informing Mission Planning through Analysis of Complex Tradespaces (IMPACT) tool is a probabilistic risk assessment tool designed by NASA to model medical risk in long duration missions outside of low earth orbit (LEO). This tool can quantify risk metrics such as risk of crewmember death, loss of crew task time, and the need for medical evacuation to better inform and augment the more traditional approach to medical system design. The risk metric of Return to Definitive Care (RTDC) represents the likelihood of requiring medical evacuation and has been difficult to quantify in a reliable and standardized manner. Initial development of the RTDC metric was constrained due to the complexity of a medical evacuation decision and the lack of prior spaceflight data and this presentation will discuss the review and improvement process used to increase model accuracy and fidelity.
Long-term increases in Arctic river discharge have been well documented, and observations in the six largest Arctic rivers show strong positive correlations between dissolved organic carbon (DOC) concentration, river discharge, and chromophoric dissolved organic matter (CDOM) content. Here, observations of DOC and CDOM collected from 2009-2019 by the Arctic Great Rivers Observatory were used to estimate chromophoric DOC (CDOC) concentrations in the Kolyma, Lena, Mackenzie, Ob’, Yenisey, and Yukon Rivers. All rivers but the Mackenzie showed significant positive correlations between annual watershed runoff and the proportion of the DOC that is chromophoric. Historical estimates of DOC and CDOC export were calculated for 1982-2019 by extrapolating the DOC and CDOC concentration – discharge relationships from 2009-2019 as a hindcast modeled estimate. For the six rivers combined, modeled DOC and CDOC export increased, but CDOC increased faster than total DOC. The Lena and Ob’ Rivers showed significant increases in DOC export individually, with annual trends of 39.1 and 20.4 Gg C yr -1 respectively. November-April (winter) DOC and CDOC export increased in all rivers but the Yenisey, with the hindcast winter Kolyma export increasing by more than 20% per decade. There were no significant trends in discharge or associated DOC and CDOC fluxes during the observational period from 2009-2019; only when hindcasted values driven by changes in river discharge were analyzed did trends in DOC and CDOC emerge. This demonstrates how shifting seasonal distributions and increases in discharge can drive changes in DOC and CDOC concentrations and export, independent of other environmental factors.
NASA's development of advanced 3D woven carbon composites, such as HEEET and 3MDCP, represents a significant leap in materials designed to endure extreme atmospheric entry conditions. However, the internal complexity of these materials introduces a variety of structures and novel defect types. Traditional characterization methods rely on labor-intensive, manual examination of X-ray CT scans, demanding considerable time and expertise. This process, while thorough, is not sustainable for large-scale analysis and defect tracking. Addressing this critical challenge, this presentation introduces an innovative suite of automated tools and analytical techniques, pioneered by the Mars Sample Return (MSR) Earth Entry System (EES) Thermal Protection System (TPS) project. These advancements offer a more efficient and accurate approach for quantifying CT data and characterizing the defects of 3D woven composites.
The solidification velocity in a model nickel-alloy single crystal during laser spot melting was recently characterized using synchrotron X-ray imaging. The measured solidification velocity was found to exceed the absolute stability threshold predicted by the Kurz-Giovanola-Trivedi (KGT) model. The discrepancies between the model and experiments motivate the further assessment of accurate material properties. This work quantifies the impact material property uncertainty has on model predictions of the absolute stability threshold velocities. Properties from the literature are reviewed and compared to those calculated using computational thermodynamics to provide uncertainty estimates on input properties to the KGT model. Global sensitivity analysis is used to quantify the influence of each uncertain input property on the predicted threshold velocity. This work supports the understanding of the nickel-alloy solidification during powder bed fusion additive manufacturing and identifies the solidification material properties that are the most important to assess from first-principles computations and experiments.
The ability of atom probe tomography (APT) to interrogate small sample volumes with high efficiency makes it uniquely useful in the study of small mineral grains or domains. Although it is frequently employed in the analysis of geological materials, particularly in the characterization of nanoscale chemical heterogeneities, the degree of quantitative accuracy achieved by APT can be difficult to determine.
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The goal of our project is to integrate diverse global and local air quality data sources using the cloud computing platform of Google Earth Engine to provide synthesized estimates and forecasts of air quality at a local scale but with a global scope freely accessible by air quality managers worldwide, facilitating their decision-making processes.
At NASA, the Crew Health and Performance (CHP) system represents the span of countermeasures, capabilities, interventions, and tested processes and procedures that in combination work to mitigate the human component of spaceflight mission risk. Across the varying NASA mental models of the CHP system, the different functionalities needed to meet human flight systems standards can be broken down into specific categories (i.e. medical capability, environmental health, behavioral health). These categories can be further broken down into specific subgroups generally associated with the CHP functionalities meant to mitigate or buy down individual human system risks. Taking a similar development approach we seek to leverage dynamic probabilistic risk assessment as a means to quantify and relatively assess the human risk state within the crew health and performance domain. By utilizing existing tools as integrators, we propose a rapid development strategy for incorporating research and operational data that represent the influence of the CHP system functionalities, in order to provide order of magnitudes estimates of the influence on most human system risks outcomes. The model system utilizes a modest cumulative risk approach and that limits the scope to primary paths of influence between the CHP functionalities and human system risks, thus enabling quick prototypes of the integrative effects of CHP functional combinations to solicit valuable feedback from stakeholders and customers on the data, relationship, and structure of the integration.
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Interest in novel aircraft configurations has continued to grow in response to increasing demand for improved fuel efficiency. One such configuration of interest is the Transonic Truss-Braced Wing (TTBW). Because the improvement of the TTBW comes from increased efficiency during cruise, it offers increasing returns as the mission distance increases. As a result, there is often a crossover point which represents the minimum mission range where the TTBW will offer a fuel burn reduction relative to a similar Tube and Wing aircraft with similar component technology levels. Aircraft rarely fly missions at their maximum range, so it is important to investigate not only the maximum benefit, but also the most likely benefit. Design decisions and analysis assumptions that significantly impact this crossover point include whether to put fuel in body tanks, how weight build-up estimation is calibrated, engine technology selection, and flight Mach number. This study, conducted under NASA’s Sustainable Flight Demonstration project and inspired by differing assumptions made by different research teams, details the impacts of changing these design decisions and assumptions.
Interest in novel aircraft configurations has continued to grow in response to increasing demand for improved fuel efficiency. One such configuration of interest is the Transonic Truss-Braced Wing (TTBW). Because the improvement of the TTBW comes from increased efficiency during cruise, it offers increasing returns as the mission distance increases. As a result, there is often a crossover point which represents the minimum mission range where the TTBW will offer a fuel burn reduction relative to a similar Tube and Wing aircraft with similar component technology levels. Aircraft rarely fly missions at their maximum range, so it is important to investigate not only the maximum benefit, but also the most likely benefit. Design decisions and analysis assumptions that significantly impact this crossover point include whether to put fuel in body tanks, how weight build-up estimation is calibrated, engine technology selection, and flight Mach number. This study, conducted under NASA’s Sustainable Flight Demonstration project and inspired by differing assumptions made by different research teams, details the impacts of changing these design decisions and assumptions.