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All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Credible Computations: Standard and Uncertainty

The discipline of computational fluid dynamics (CFD) is at a crossroad. Most of the significant advances related to computational methods have taken place. The emphasis is now shifting from methods to results. Significant efforts are made in applying CFD to solve design problems. The value of CFD results in design depends on the credibility of computed results for the intended use. The process of establishing credibility requires a standard so that there is a consistency and uniformity in this process and in the interpretation of its outcome. The key element for establishing the credibility is the quantification of uncertainty. This paper presents salient features of a proposed standard and a procedure for determining the uncertainty. A customer of CFD products - computer codes and computed results - expects the following: A computer code in terms of its logic, numerics, and fluid dynamics and the results generated by this code are in compliance with specified requirements. This expectation is fulfilling by verification and validation of these requirements. The verification process assesses whether the problem is solved correctly and the validation process determines whether the right problem is solved. Standards for these processes are recommended. There is always some uncertainty, even if one uses validated models and verified computed results. The value of this uncertainty is important in the design process. This value is obtained by conducting a sensitivity-uncertainty analysis. Sensitivity analysis is generally defined as the procedure for determining the sensitivities of output parameters to input parameters. This analysis is a necessary step in the uncertainty analysis, and the results of this analysis highlight which computed quantities and integrated quantities in computations need to be determined accurately and which quantities do not require such attention. Uncertainty analysis is generally defined as the analysis of the effect of the uncertainties involved in all stages of a process on the final responses. There are two approaches for conducting the uncertainty analysis: experimental and computational. These analyses and approaches are briefly described.

Mehta, Unmeel B.↗
NASA NTRSDate not supplied

Application of Framework for Estimating Performance and Associated Uncertainty for Modified Aircraft Configurations Using NASA's X-57 Maxwell

A framework to estimate the performance and associated uncertainty of modified configurations of certified aircraft is applied to the X-57 Maxwell aircraft. In previous theoretical studies, the framework was shown to predict performance and uncertainty bounds accurately. The X-57 Maxwell is an experimental aircraft designed to demonstrate the benefits of distributed electric propulsion through a series of four incremental modifications to a Tecnam P2006T aircraft. The available models and data are first shown to be within the application domain of the framework. We then apply the framework to two X-57 Maxwell modifications. We compare the estimated performance and associated uncertainties against the airworthiness criteria. The results indicate that the framework is a promising tool for the certification by analysis workflow. We expect the framework to reduce and supplement the flight testing required to show compliance to airworthiness certification criteria for a modified configuration.

Uncertainty Quantification↗
NASA NTRSDate not supplied

Empirical Noise Modeling of Internally Mixed Exhaust Systems

There appear to be no non-proprietary methods to predict the noise of internally mixed exhaust systems, and no guidance for how to adapt known jet noise models for these configurations. This paper surveys literature and historical databases acquired at NASA Glenn's Aero-Acoustic Propulsion Lab to give such guidance. The core premise is that an exhaust system with well-designed mixer produces noise that is to first approximation the same as a fully-mixed jet flow. Refinement of what is meant by a “fully mixed jet” can lead to more accurate prediction of the main jet noise. Additional noise is often generated within the nozzle, typically at high frequencies, whose source mechanism(s) are not obvious. However, a noise prediction method can be established that captures some aspects of the excess noise and provide an estimate of the total jet noise. Explorations of source mechanisms associated with the internal mixer have led to a new noise model which includes the effects of having an external plug nozzle, a feature desirable for near-term supersonic aircraft. Statistical analysis of historical data is provided to estimate the uncertainty in using this method given the variations found that cannot be directly computed without detailed mixer geometry.

Noise Prediction↗
NASA NTRSDate not supplied

Empirical Noise Modeling of Internally Mixed Exhaust Systems

There appears to be no non-proprietary methods to predict the noise of internally mixed exhaust systems, and no guidance for how to adapt known jet noise models for these configurations. This paper surveys literature and historical databases acquired at NASA Glenn's Aero-Acoustic Propulsion Lab to give such guidance. The core premise is that an exhaust system with well-designed mixer produces noise that is to first approximation the same as a fully-mixed jet flow. Refinement of what is meant by a “fully mixed jet” can lead to more accurate prediction of the main jet noise. Additional noise is often generated within the nozzle, typically at high frequencies, whose source mechanism(s) are not obvious. However, a noise prediction method can be established that captures some aspects of the excess noise and provide an estimate of the total jet noise. Explorations of source mechanisms associated with the internal mixer have led to a new noise model which includes the effects of having an external plug nozzle, a feature desirable for near-term supersonic aircraft. Statistical analysis of historical data is provided to estimate the uncertainty in using this method given the variations found that cannot be directly computed without detailed mixer geometry.

Noise Prediction↗
NASA NTRS2013

Remaining Useful Life Estimation in Prognosis: An Uncertainty Propagation Problem

The estimation of remaining useful life is significant in the context of prognostics and health monitoring, and the prediction of remaining useful life is essential for online operations and decision-making. However, it is challenging to accurately predict the remaining useful life in practical aerospace applications due to the presence of various uncertainties that affect prognostic calculations, and in turn, render the remaining useful life prediction uncertain. It is challenging to identify and characterize the various sources of uncertainty in prognosis, understand how each of these sources of uncertainty affect the uncertainty in the remaining useful life prediction, and thereby compute the overall uncertainty in the remaining useful life prediction. In order to achieve these goals, this paper proposes that the task of estimating the remaining useful life must be approached as an uncertainty propagation problem. In this context, uncertainty propagation methods which are available in the literature are reviewed, and their applicability to prognostics and health monitoring are discussed.

Uncertainty Quantification↗
NASA NTRSDate not supplied

CONUS and Global Carbon Consumption Database for Wildland Fire

Fire plays a significant role on both national and global scales, profoundly impacting landscapes shaped by human activity as well as wildlands. Even though fire can be devastating, wildland fire is a natural and integral force on our landscapes. Fires can also serve to reduce fuels to mitigate wildfire risk and maintain healthy ecosystem functions. However, the smoke produced by fires, regardless of their size or purpose, can pose adverse effects on human health when inhaled downwind. Understanding the influence of smoke on air quality and human well-being necessitates the quantification of emissions that fires release into the atmosphere. In response to this need, we have developed a carbon consumption database for the Continental United States (CONUS) and are developing a global carbon consumption database, both of which are directly link to distinct fuels within various fire danger categories. Fuel Characteristic Classification System (FCCS) fuels are used to parameterize biomass, and consumption is broken down into five Fire Danger categories (Low, Moderate, High, Very High, Extreme), for both ‘new’ and ‘residual’ burning scenarios. Residual burned area is defined as burning in areas that have recently burned. We implemented the FCCS 30-meter CONUS fuelbed dataset during the 2019 Fire Influence on Regional to Global Environments and Air Quality (FIREX-AQ) campaign to estimate daily carbon emissions. Our emissions estimates were rigorously compared against in-situ measurements of CO2, CO, and black carbon aerosols, revealing a robust agreement between the two datasets. The 300-meter global database builds upon the foundations of the Pettinari, M. Lucrecia (2015) Global Fuelbed database, a global fuel map with standardized FCCS biomass parameters. These products can serve as valuable tools when used in conjunction with burned area data to rapidly and accurately estimate carbon consumed and released into the atmosphere.

FCCS↗
NASA NTRSDate not supplied

Applicability of a Framework for Estimating Performance and Associated Uncertainty for Modified Aircraft Configurations

As improvements are made to the accuracy and reliability of modeling and simulation techniques, certification by analysis becomes a more attractive alternative compared to traditional aircraft flight testing. Certification by analysis is especially cost-effective when one considers modifications to a previously certified aircraft. However, it is important that the models and methods used are applicable and accurate throughout the intended use domain. A framework for estimating the performance and associated uncertainty was introduced in an earlier paper. The factors and limitations of this framework for estimating the performance and associated model form uncertainty are explored to determine the range of applicability of the framework, particularly with respect to model form, process and sensor noise, and quality of available flight test data. This paper focuses on the general limitations and applicability of the framework and not the applicability of the individual methods to a range of modified configurations, which requires a large number of modified configurations and is an area for future work. The effects of these factors on the performance and uncertainty results are demonstrated using NASA’s Generic Transport Model aircraft.

uncertainty quantification↗
NASA NTRS2012

Top-down Estimate of Dust Emissions Through Integration of MODIS and MISR Aerosol Retrievals With the Geos-chem Adjoint Model

Predicting the influences of dust on atmospheric composition, climate, and human health requires accurate knowledge of dust emissions, but large uncertainties persist in quantifying mineral sources. This study presents a new method for combined use of satellite-measured radiances and inverse modeling to spatially constrain the amount and location of dust emissions. The technique is illustrated with a case study in May 2008; the dust emissions in Taklimakan and Gobi deserts are spatially optimized using the GEOSChem chemical transport model and its adjoint constrained by aerosol optical depth (AOD) that are derived over the downwind dark-surface region in China from MODIS (Moderate Resolution Imaging Spectroradiometer) reflectance with the aerosol single scattering properties consistent with GEOS-chem. The adjoint inverse modeling yields an overall 51% decrease in prior dust emissions estimated by GEOS-Chem over the Taklimakan-Gobi area, with more significant reductions south of the Gobi Desert. The model simulation with optimized dust emissions shows much better agreement with independent observations from MISR (Multi-angle Imaging SpectroRadiometer) AOD and MODIS Deep Blue AOD over the dust source region and surface PM10 concentrations. The technique of this study can be applied to global multi-sensor remote sensing data for constraining dust emissions at various temporal and spatial scales, and hence improving the quantification of dust effects on climate, air quality, and human health.

MODIS aerosol retrievals↗
NASA NTRS2000

Validation of real-time three-dimensional echocardiography for quantifying left ventricular volumes in the presence of a left ventricular aneurysm: in vitro and in vivo studies

OBJECTIVES: To validate the accuracy of real-time three-dimensional echocardiography (RT3DE) for quantifying aneurysmal left ventricular (LV) volumes. BACKGROUND: Conventional two-dimensional echocardiography (2DE) has limitations when applied for quantification of LV volumes in patients with LV aneurysms. METHODS: Seven aneurysmal balloons, 15 sheep (5 with chronic LV aneurysms and 10 without LV aneurysms) during 60 different hemodynamic conditions and 29 patients (13 with chronic LV aneurysms and 16 with normal LV) underwent RT3DE and 2DE. Electromagnetic flow meters and magnetic resonance imaging (MRI) served as reference standards in the animals and in the patients, respectively. Rotated apical six-plane method with multiplanar Simpson's rule and apical biplane Simpson's rule were used to determine LV volumes by RT3DE and 2DE, respectively. RESULTS: Both RT3DE and 2DE correlated well with actual volumes for aneurysmal balloons. However, a significantly smaller mean difference (MD) was found between RT3DE and actual volumes (-7 ml for RT3DE vs. 22 ml for 2DE, p = 0.0002). Excellent correlation and agreement between RT3DE and electromagnetic flow meters for LV stroke volumes for animals with aneurysms were observed, while 2DE showed lesser correlation and agreement (r = 0.97, MD = -1.0 ml vs. r = 0.76, MD = 4.4 ml). In patients with LV aneurysms, better correlation and agreement between RT3DE and MRI for LV volumes were obtained (r = 0.99, MD = -28 ml) than between 2DE and MRI (r = 0.91, MD = -49 ml). CONCLUSIONS: For geometrically asymmetric LVs associated with ventricular aneurysms, RT3DE can accurately quantify LV volumes.

NASA Discipline Cardiopulmonary↗
NASA NTRS2022

Global Dust Cycle and Direct Radiative Effect in E3SM Version 1: Impact of Increasing Model Resolution

Quantification of dust aerosols in Earth System Models (ESMs) has important implications for water cycle and biogeochemistry studies. This study examines the global life cycle and direct radiative effects (DREs) of dust in the U.S. Department of Energy's Energy Exascale Earth System Model version 1 (E3SMv1), and the impact of increasing model resolution both horizontally and vertically. The default 1° E3SMv1 captures the spatial and temporal variability in the observed dust aerosol optical depth (DAOD) reasonably well, but overpredicts dust absorption in the shortwave (SW). Simulations underestimate the dust vertical and long-range transport, compared with the satellite dust extinction profiles. After updating dust refractive indices and correcting for a bias in partitioning size-segregated emissions, both SW cooling and longwave (LW) warming of dust simulated by E3SMv1 are increased and agree better with other recent studies. The estimated net dust DRE of −0.42 Wm−2 represents a stronger cooling effect than the observationally based estimate −0.2 Wm−2 (−0.48 to +0.2), due to a smaller LW warming. Constrained by a global mean DAOD, model sensitivity studies of increasing horizontal and vertical resolution show strong influences on the simulated global dust burden and lifetime primarily through the change of dust dry deposition rate; there are also remarkable differences in simulated spatial distributions of DAOD, DRE, and deposition fluxes. Thus, constraining the global DAOD is insufficient for accurate representation of dust climate effects, especially in transitioning to higher- or variable-resolution ESMs. Better observational constraints of dust vertical profiles, dry deposition, size, and LW properties are needed.

dust aerosol↗
NASA NTRS2021

Post-Landing Major Element Quantification Using SuperCam Laser Induced Breakdown Spectroscopy

The SuperCam instrument on the PerseveranceMars 2020 rover uses a pulsed 1064 nm laser to ablate targets at a distance and conduct laser induced breakdown spectroscopy (LIBS) by analyzing the light from the resulting plasma. SuperCam LIBS spectra are preprocessed to remove ambient light, noise, and the continuum signal present in LIBS observations. Prior to quantification, spectra are masked to remove noisier spectrometer regions andspectra are normalized to minimize signal fluctuations and effectsof target distance.In some cases, the spectra are also standardized or binned prior to quantification. To determine quantitative elemental compositionsof diverse geologic materials at Jezero crater, Mars, we use a suite of 1198 laboratory spectra of 334 well-characterized reference samples. The samples were selected to span a wide range of compositions and include typical silicate rocks, pure minerals (e.g.,silicates, sulfates, carbonates, oxides),more unusual compositions (e.g.,Mn oreand sodalite), andreplicates of the sintered SuperCam calibration targets (SCCTs) onboardthe rover. For each major element (SiO2, TiO2, Al2O3, FeOT, MgO, CaO, Na2O, K2O), the database was subdivided into five“folds” with similar distributions of the element of interest. One fold was held out as an independent test set, and the remaining fourfolds were used to optimize multivariate regression models relating the spectrum to the composition. We considered a variety of models, and selected several for further investigation for each element, based primarily on the root mean squared error of prediction (RMSEP) on the test set, when analyzed at 3m. In cases with several models of comparable performance at 3 m, we incorporated the SCCT performance at different distances to choose the preferred model. Shortly after landing on Mars and collecting initial spectra of geologic targets, we selected one model per element. Subsequently, with additional data from geologic targets, some models were revised to ensure results that are more consistent with geochemical constraints. The calibration discussed here is a snapshot of an ongoing effort to deliver the most accurate chemical compositions with SuperCam LIBS.

Mars 2020↗
NASA NTRS1999

A Quantitative Study of Oxygen as a Metabolic Regulator

An acute reduction in oxygen (O2) delivery to a tissue is generally associated with a decrease in phosphocreatine, increases in ADP, NADH/NAD, and inorganic phosphate, increased rates of glycolysis and lactate production, and reduced rates of pyruvate and fatty acid oxidation. However, given the complexity of the human bioenergetic system and its components, it is difficult to determine quantitatively how cellular metabolic processes interact to maintain ATP homeostasis during stress (e.g., hypoxia, ischemia, and exercise). Of special interest is the determination of mechanisms relating tissue oxygenation to observed metabolic responses at the tissue, organ, and whole body levels and the quantification of how changes in tissue O2 availability affect the pathways of ATP synthesis and the metabolites that control these pathways. In this study, we extend a previously developed mathematical model of human bioenergetics to provide a physicochemical framework that permits quantitative understanding of O2 as a metabolic regulator. Specifically, the enhancement permits studying the effects of variations in tissue oxygenation and in parameters controlling the rate of cellular respiration on glycolysis, lactate production, and pyruvate oxidation. The whole body is described as a bioenergetic system consisting of metabolically distinct tissue/organ subsystems that exchange materials with the blood. In order to study the dynamic response of each subsystem to stimuli, we solve the ordinary differential equations describing the temporal evolution of metabolite levels, given the initial concentrations. The solver used in the present study is the packaged code LSODE, as implemented in the NASA Lewis kinetics and sensitivity analysis code, LSENS. A major advantage of LSENS is the efficient procedures supporting systematic sensitivity analysis, which provides the basic methods for studying parameter sensitivities (i.e., changes in model behavior due to parameter variation). Sensitivity analysis establishes relationships between model predictions and problem parameters (i.e., initial concentrations, rate coefficients, etc). It helps determine the effects of uncertainties or changes in these input parameters on the predictions, which ultimately are compared with experimental observations in order to validate the model. Sensitivity analysis can identify parameters that must be determined accurately because of their large effect on the model predictions and parameters that need not be known with great precision because they have little or no effect on the solution. This capability may prove to be important in optimizing the design of experiments, thereby reducing the use of animals. This approach can be applied to study the metabolic effects of reduced oxygen delivery to cardiac muscle due to local myocardial ischemia and the effects of acute hypoxia on brain metabolism. Other important applications of sensitivity analysis include identification of quantitatively relevant pathways and biochemical species within an overall mechanism, when examining the effects of a genetic anomaly or pathological state on energetic system components and whole system behavior.

Radhakrishnan, Krishnan↗
NASA NTRS2020

Uncertainty Quantification of Global Net Methane Emissions From Terrestrial Ecosystems Using a Mechanistically Based Biogeochemistry Model

Quantification of methane (CH4) emissions from wetlands and its sinks from uplands is still fraught with large uncertainties. Here, a methane biogeochemistry model was revised, parameterized, and verified for various wetland ecosystems across the globe. The model was then extrapolated to the global scale to quantify the uncertainty induced from four different types of uncertainty sources including parameterization, wetland type distribution, wetland area distribution, and meteorological input. We found that global wetland emissions are 212 ± 62 and 212 ± 32 Tg CH4 year−1 (1Tg = 1012 g) due to uncertain parameters and wetland type distribution, respectively, during 2000–2012. Using two wetland distribution data sets and three sets of climate data, the model simulations indicated that the global wetland emissions range from 186 to 212 CH4 year−1 for the same period. The parameters were the most significant uncertainty source. After combining the global methane consumption in the range of −34 to −46 Tg CH4 year−1, we estimated that the global net land methane emissions are 149–176 Tg CH4 year−1 due to uncertain wetland distribution and meteorological input. Spatially, the northeast United States and Amazon were two hotspots of methane emission, while consumption hotspots were in the Eastern United States and eastern China. During 1950–2016, both wetland emissions and upland consumption increased during El Niño events and decreased during La Niña events. This study highlights the need for more in situ methane flux data, more accurate wetland type, and area distribution information to better constrain the model uncertainty.

wetland methane emission↗
NASA NTRSDate not supplied

End-To-End Uncertainty Quantification with Analytical Derivatives for Design Under Uncertainty

Uncertainty quantification (UQ) is a rapidly growing and evolving discipline, especially within the aerospace community. Performing analysis with UQ can provide decision makers with a wealth of information about a candidate design. However, the value of UQ is fully realized when the information gained during UQ analysis is leveraged in a feedback loop of a design optimization process, often referred to as design under uncertainty. Although design under uncertainty can be a powerful risk mitigation technique, there are a number of roadblocks that prevent its implementation. Two primary factors are computational costs and added complexity of the analysis. High fidelity simulations on the order tens of uncertain variables quickly become computationally infeasible. Also, implementing UQ into an existing multidisciplinary design and optimization (MDO) process often requires extensive knowledge of the UQ methods and careful treatment of the problem formulation. The objective of this work is to address these two primary roadblocks and enable practitioners to efficiently perform design under uncertainty with limited knowledge of the UQ discipline. Methods outlined in this paper demonstrate MDO incorporating UQ into the design process, leveraging an analytic derivative tool chain through the entire optimization. The proposed approach leverages machine learning techniques to generate a differentiable confidence interval output from polynomial chaos models. This technique, coupled with the incorporation of analytical derivatives through the Polynomial Chaos Expansion (PCE) process, eliminates the need to estimate derivatives which are usually obtained from finite difference, complex step, or similar methods. Developing a differentiable confidence interval allows mixed uncertainty problems (both epistemic and aleatory) to be modeled. Without such modeling, these problems cannot accurately predict objective functions containing statistical quantities such as mean and variance. The addition of analytic derivatives to a polynomial chaos-based UQ method decreases the computational costs of performing design under uncertainty by orders of magnitude in comparison with methods such as complex step. The method and codes developed are modular in nature and are a drop-in solution for design under uncertainty within existing MDO problems. A low-fidelity analytical multidisciplinary optimization under uncertainty for a wing design in OpenMDAO is detailed in this paper. This demonstration case will include both objective functions and constraints which are influenced by uncertain parameters.

Ben D Phillips↗
NASA NTRSDate not supplied

End-To-End Uncertainty Quantification with Analytical Derivatives for Design Under Uncertainty

Uncertainty quantification (UQ) is a rapidly growing and evolving discipline, especially within the aerospace community. Performing analysis with UQ can provide decision makers with a wealth of information about a candidate design. However, the value of UQ is fully realized when the information gained during UQ analysis is leveraged in a feedback loop of a design optimization process, often referred to as design under uncertainty. Although design under uncertainty can be a powerful risk mitigation technique, there are a number of roadblocks that prevent its implementation. Two primary factors are computational costs and added complexity of the analysis. High fidelity simulations on the order tens of uncertain variables quickly become computationally infeasible. Also, implementing UQ into an existing multidisciplinary design and optimization (MDO) process often requires extensive knowledge of the UQ methods and careful treatment of the problem formulation. The objective of this work is to address these two primary roadblocks and enable practitioners to efficiently perform design under uncertainty with limited knowledge of the UQ discipline. Methods outlined in this paper demonstrate MDO incorporating UQ into the design process, leveraging an analytic derivative tool chain through the entire optimization. The proposed approach leverages machine learning techniques to generate a differentiable confidence interval output from polynomial chaos models. This technique, coupled with the incorporation of analytical derivatives through the Polynomial Chaos Expansion (PCE) process, eliminates the need to estimate derivatives which are usually obtained from finite difference, complex step, or similar methods. Developing a differentiable confidence interval allows mixed uncertainty problems (both epistemic and aleatory) to be modeled. Without such modeling, these problems cannot accurately predict objective functions containing statistical quantities such as mean and variance. The addition of analytic derivatives to a polynomial chaos-based UQ method decreases the computational costs of performing design under uncertainty by orders of magnitude in comparison with methods such as complex step. The method and codes developed are modular in nature and are a drop-in solution for design under uncertainty within existing MDO problems. A low-fidelity analytical multidisciplinary optimization under uncertainty for a wing design in OpenMDAO is detailed in this paper. This demonstration case will include both objective functions and constraints which are influenced by uncertain parameters.

Ben Phillips↗
NASA NTRS2019

Health Management and Prognostics for Electric Aircraft Powertrain

W and c Any air borne vehicle needs incorporating safety as key parameter of measure, and inclusion of autonomy raises the critical need for safety under autonomous operations. Management of faults and component degradation is key as complexity in autonomous operations grow over the period of time. Therefore, in addition to basic operational requirements, an autonomous electric vehicle should be able to make accurate estimates of its current system health and take the correct decisions to complete its mission successfully. Real-time safety and state-awareness tools are therefore essential for the vehicle to be able to reach its destination in a safe and successful manner. The need for safety assurance and health management capabilities is particularly relevant for aircraft electric propulsion systems, which are relatively new and with limited historical to learn. They are critical systems requiring high power density along with reliability, resilience, efficient management of weight, and operational costs. A model- based fault diagnosis and prognostics approach of complex critical systems can successfully accomplish the safety and state awareness goal for such electric propulsion systems, enabling autonomous decision making capability for safe and efficient operation. To identify critical components in the system a Qualitative Bayesian approach using FMECA is implemented. This requires the assessment of some quantities representing the state of the electric unmanned aerial systems (e-UAS), as well as look-ahead forecasts of such states during the entire flight, presented in form of safety metrics (SM). In-service data and performance data gathered from degraded components sup- ports diagnostic and prognostic methods for these systems, but this data can be difficult to obtain as weight and packaging restrictions reduce redundancy and instrumentation on-board the vehicle. Therefore, an model-based framework should be capable or operating with limited data. In addition to data scarcity, the variability of such complex critical systems re- quires the model-based framework to reason in the presence of uncertainty, such as sensor noise, and modeling imperfections. Quantification of errors and uncertainties in the measured states and quantities is therefore a fundamental step for a precise estimation of such SMs; un-modeled uncertainty may result in erroneous state assessment and un- reliable predictions of future states of e-UAVs. Typical, centralized model-based schemes suffer from inherent disadvantages such as computational complexity, single point of failure, and scalability issues, and therefore may fail in such a complex scenario. This paper presents a methodology for developing a system level diagnostics and prognostics approach using a Qualitative Bayesian FMECA approach along with a formal uncertainty management framework for an e-UAS. In this work we demonstrate the efficacy of the framework to predict effects of sub-system level degradation on vehicle operation incorporating uncertainty management to predict future behavior under different operating conditions.

Kulkarni, Chetan↗
NASA NTRS2024

Development of a Data Fusion Methodology for Lineload Aerodynamic Databases for a Launch Vehicle during Liftoff and Transition

The need for databases for the distributed loading on launch vehicles during the early portion of flight necessitates the use of expensive computational flows in regimes where wake effects dominate. While also being expensive, this is a regime that computational tools tend to historically have problems simulating accurately. To help tackle this problem, a method of data fusion to combine computational results to wind tunnel derived force and moment data is developed. Using this method, significant reduction in computational costs and increases in confidence of the final product is possible and has been used to generate several databases for the Space Launch System (SLS) at NASA. While the full details of database generation are not part of this work, the crucial method at its core is developed here. Two SLS geometries are used throughout the work to demonstrate the techniques. These are two of the larger geometries and represent both planned crewed missions to the Moon as well as potential cargo missions to deep space. The method uses principal component analysis (PCA) to generate a reduced ordered model (ROM) to help fill in the full parameter space. Other similar techniques are explored, but were not found to have a significant result on the predictions of the ROM. Because the full number of components are kept to generate the model, this lack of difference is expected. This method is then extended to ensure that predicted surfaces match trusted force and moment data derived from wind tunnel testing. This extension is done by setting up a constrained optimization problem in order to minimize the deviation from the surface resolved computational data while still integrating to the desired values. When generating the constrained optimization problem, a weighting factor to balance these competing needs is introduced. The work compares previously introduced weighting terms from similar work to the proposed terms and shows that the previously used terms do not have as desirable behavior in this flow regime. This method is then expanded by developing a technique to incorporate uncertainty quantification into the developed data fusion methodology. This expansion takes a two pronged approach. One examines transferring the uncertainties in the force and moment database and characterizes how those adjustments change the predicted lineloads. The second looks at model form error and looks how rebuilding the model using slightly different data changes the predictions. These two terms are then combined in order to create an uncertainty model that takes both effects into account. The limitations of the proposed methods is then discussed as well as possible techniques to address these shortcomings.

Launch Vehicles↗
NASA NTRSDate not supplied

Probabilistic Calibration of Expensive Models using Efficiently Trained Surrogates

Calibration of computational models in the presence of uncertainty is often cast as a Bayesian inference problem and solved via sampling methods, e.g., Markov chain Monte Carlo. When the computational model is expensive, this task becomes intractable due to the large number of samples required to accurately estimate the posterior distribution of the calibration parameters. A popular solution to this problem is to use machine learning to develop a faster-to-evaluate, lower-fidelity substitute for the original model to serve as a surrogate while solving the inference problem. Although considered an offline cost, generating training data to construct this surrogate model can still be an expensive task in practice. An active learning algorithm is presented that focuses training on improving surrogate accuracy specifically in and around the bulk of the posterior distribution, as this is where the model is exercised during calibration. Candidate samples are drawn from families of distributions related to an approximation of the posterior. The sample maximizing predictive variance is then selected for evaluation by the original computational model, yielding a label for the training point. Iterating this approach increases efficiency relative to space filling designs (e.g., Latin hypercube sampling) by avoiding low probability points. Practical considerations are discussed, including the benefits of using a sequential Monte Carlo sampling approach, convergence heuristics, and the importance of both exploration and exploitation given that the true posterior is unknown a priori.

uncertainty quantification↗