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NASA NTRS2011

Chance-Constrained Guidance With Non-Convex Constraints

Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of failure) is below a user-specified bound known as the risk bound. An example problem is to drive a car to a destination as fast as possible while limiting the probability of an accident to 10(exp -7). This framework allows users to trade conservatism against performance by choosing the risk bound. The more risk the user accepts, the better performance they can expect.

FROM↗

NASA NTRS2023

Evaluation of a Regional Crop Model Implementation for Sub-National Yield Assessments in Kenya

CONTEXT: Cropping system models can be used to both assess regional food security and to monitor and predict agricultural drought. Agriculture in Kenya is extremely important to both the economy and food security of the country. OBJECTIVE: This study evaluated a regional implementation of a widely used crop model, the Decision Support System for Agrotechnology Transfer (DSSAT), within a coupled modeling framework, the Regional Hydrologic Extremes Assessment System (RHEAS), over Kenya. The goal of this study was to assess the ability of RHEAS to simulate the annual variability of maize yields at the county level and evaluate the uncertainty inherent in the model and inputs. METHODS: The RHEAS system implements a stochastic ensemble approach to account for field scale variabilities in crop management practices and underlying soil and weather conditions. Satellite-derived datasets were used to evaluate the land surface component of the system and seasonally disaggregated yield for 5 years was used to assess the performance of the cropping system model. RESULTS AND CONCLUSIONS: The median correlation between RHEAS and satellite-derived soil moisture and evapotranspiration estimates were 0.78, and 0.51, respectively, indicating that the model is able to capture the key drivers of the hydrological budget. Overall, RHEAS simulated yearly yield variations with a median correlation of 0.7 with reported yields, with the best performance in the short rains season. However, across both seasons, the RHEAS model was positively biased on the order of ~1.6 MT/ha. The overall median unbiased RMSE was 0.66 MT/ha. The RHEAS system shows skill at simulating extreme departures in anomalies, and a majority of the time (62.5%) the reported yields fall within the interquartile range of the simulations. SIGNIFICANCE: One of the most important areas of improvement for the next generation of agricultural data and models is to better understand and communicate the inherent uncertainties. This is especially critical in data-limited regions. Here we present a modeling system and its implementation that begins to address these concerns. We demonstrate the ability to simulate broad trends in yields at the county level for sub-annual yields with skills that commensurate previous national/annual level studies.

Crop model↗

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 NTRS1982

Computation of the intervals of uncertainties about the parameters found for identification

A modeling method to calculate the intervals of uncertainty for parameters found by identification is described. The region of confidence and the general approach to the calculation of these intervals are discussed. The general subprograms for determination of dimensions are described. They provide the organizational charts for the subprograms, the tests carried out and the listings of the different subprograms.

Mereau, P.↗

NASA NTRS2023

Modeling Dust Mineralogical Composition: Sensitivity to Soil Mineralogy Atlases and Their Expected Climate Impacts

Soil dust aerosols are a key component of the climate system, as they interact with short- and long-wave radiation, alter cloud formation processes, affect atmospheric chemistry and play a role in biogeochemical cycles by providing nutrient inputs such as iron and phosphorus. The influence of dust on these processes depends on its physicochemical properties, which, far from being homogeneous, are shaped by its regionally varying mineral composition. The relative amount of minerals in dust depends on the source region and shows a large geographical variability. However, many state-of-the-art Earth system models (ESMs), upon which climate analyses and projections rely, still consider dust mineralogy to be invariant. The explicit representation of minerals in ESMs is more hindered by our limited knowledge of the global soil composition along with the resulting size-resolved airborne mineralogy than by computational constraints. In this work we introduce an explicit mineralogy representation within the state-of-the-art Multiscale Online Nonhydrostatic AtmospheRe CHemistry (MONARCH) model. We review and compare two existing soil mineralogy datasets, which remain a source of uncertainty for dust mineralogy modeling and provide an evaluation of multiannual simulations against available mineralogy observations. Soil mineralogy datasets are based on measurements performed after wet sieving, which breaks the aggregates found in the parent soil. Our model predicts the emitted particle size distribution (PSD) in terms of its constituent minerals based on brittle fragmentation theory (BFT), which reconstructs the emitted mineral aggregates destroyed by wet sieving. Our simulations broadly reproduce the most abundant mineral fractions independently of the soil composition data used. Feldspars and calcite are highly sensitive to the soil mineralogy map, mainly due to the different assumptions made in each soil dataset to extrapolate a handful of soil measurements to arid and semi-arid regions worldwide. For the least abundant or more difficult-to-determine minerals, such as iron oxides, uncertainties in soil mineralogy yield differences in annual mean aerosol mass fractions of up to ∼ 100 %. Although BFT restores coarse aggregates including phyllosilicates that usually break during soil analysis, we still identify an overestimation of coarse quartz mass fractions (above 2 µm in diameter). In a dedicated experiment, we estimate the fraction of dust with undetermined composition as given by a soil map, which makes up ∼ 10 % of the emitted dust mass at the global scale and can be regionally larger. Changes in the underlying soil mineralogy impact our estimates of climate-relevant variables, particularly affecting the regional variability of the single-scattering albedo at solar wavelengths or the total iron deposited over oceans. All in all, this assessment represents a baseline for future model experiments including new mineralogical maps constrained by high-quality spaceborne hyperspectral measurements, such as those arising from the NASA Earth Surface Mineral Dust Source Investigation (EMIT) mission.

Soil dust↗

NASA NTRS2004

Bayesian Approach to the Joint Inversion of Gravity and Magnetic Data, with Application to the Ismenius Area of Mars

This viewgraph presentation reviews a Bayesian approach to the inversion of gravity and magnetic data with specific application to the Ismenius Area of Mars. Many inverse problems encountered in geophysics and planetary science are well known to be non-unique (i.e. inversion of gravity the density structure of a body). In hopes of reducing the non-uniqueness of solutions, there has been interest in the joint analysis of data. An example is the joint inversion of gravity and magnetic data, with the assumption that the same physical anomalies generate both the observed magnetic and gravitational anomalies. In this talk, we formulate the joint analysis of different types of data in a Bayesian framework and apply the formalism to the inference of the density and remanent magnetization structure for a local region in the Ismenius area of Mars. The Bayesian approach allows prior information or constraints in the solutions to be incorporated in the inversion, with the "best" solutions those whose forward predictions most closely match the data while remaining consistent with assumed constraints. The application of this framework to the inversion of gravity and magnetic data on Mars reveals two typical challenges - the forward predictions of the data have a linear dependence on some of the quantities of interest, and non-linear dependence on others (termed the "linear" and "non-linear" variables, respectively). For observations with Gaussian noise, a Bayesian approach to inversion for "linear" variables reduces to a linear filtering problem, with an explicitly computable "error" matrix. However, for models whose forward predictions have non-linear dependencies, inference is no longer given by such a simple linear problem, and moreover, the uncertainty in the solution is no longer completely specified by a computable "error matrix". It is therefore important to develop methods for sampling from the full Bayesian posterior to provide a complete and statistically consistent picture of model uncertainty, and what has been learned from observations. We will discuss advanced numerical techniques, including Monte Carlo Markov

data analysis↗

NASA NTRS1994

Feedback control laws for highly maneuverable aircraft

During the first half of the year, the investigators concentrated their efforts on completing the design of control laws for the longitudinal axis of the HARV. During the second half of the year they concentrated on the synthesis of control laws for the lateral-directional axes. The longitudinal control law design efforts can be briefly summarized as follows. Longitudinal control laws were developed for the HARV using mu synthesis design techniques coupled with dynamic inversion. An inner loop dynamic inversion controller was used to simplify the system dynamics by eliminating the aerodynamic nonlinearities and inertial cross coupling. Models of the errors resulting from uncertainties in the principal longitudinal aerodynamic terms were developed and included in the model of the HARV with the inner loop dynamic inversion controller. This resulted in an inner loop transfer function model which was an integrator with the modeling errors characterized as uncertainties in gain and phase. Outer loop controllers were then designed using mu synthesis to provide robustness to these modeling errors and give desired response to pilot inputs. Both pitch rate and angle of attack command following systems were designed. The following tasks have been accomplished for the lateral-directional controllers: inner and outer loop dynamic inversion controllers have been designed; an error model based on a linearized perturbation model of the inner loop system was derived; controllers for the inner loop system have been designed, using classical techniques, that control roll rate and Dutch roll response; the inner loop dynamic inversion and classical controllers have been implemented on the six degree of freedom simulation; and lateral-directional control allocation scheme has been developed based on minimizing required control effort.

Garrard, William L.↗

NASA NTRS1983

Radiation protection for manned space activities

The Earth's natural radiation environment poses a hazard to manned space activities directly through biological effects and indirectly through effects on materials and electronics. The following standard practices are indicated that address: (1) environment models for all radiation species including uncertainties and temporal variations; (2) upper bound and nominal quality factors for biological radiation effects that include dose, dose rate, critical organ, and linear energy transfer variations; (3) particle transport and shielding methodology including system and man modeling and uncertainty analysis; (4) mission planning that includes active dosimetry, minimizes exposure during extravehicular activities, subjects every mission to a radiation review, and specifies operational procedures for forecasting, recognizing, and dealing with large solar flaes.

Jordan, T. M.↗

NASA NTRS1994

Modeling tropical Pacific sea surface temperature with satellite-derived solar radiative forcing

Two independent datasets for the solar radiation at the surface derived from satellites are compared. The data derived from the Earth Radiation Budget Experiment (ERBE) is for the net solar radiation at the surface whereas the International Satellite Cloud Climatology Project (ISCCP) data is for the downward flux only and was corrected with a space- and time-varying albedo. The ISCCP net flux is at all times higher than the ERBE flux. The difference can be divided into an offset that decreases with latitude and another component that correlates with high tropical cloud cover. With this latter exception the two datasets provide spatial patterns of solar flux that are very similar. A tropical Pacific Ocean model is forced with these two datasets and observed climatological winds. The upward heat flux is parameterized taking into account separately the longwave radiative, latent, and sensible heat fluxes. Best fit values for the uncertain parameters are found using an optimization procedure that seeks to minimize the difference between model and observed SST by varying the parameters within a reasonable range of uncertainty. The SST field the model produces with the best fit parameters is the best the model can do. If the differences between the model and data are larger than can be accounted for by remaining uncertainties in the heat flux parameterization and forcing data then the ocean model must be held to be at fault. Using this method of analysis, a fundamental model fault is identified. Inadequate treatment of mixed layer/entrainment processes in upwelling regions of the eastern tropical Pacific leads to a large and seasonally varying error in the model SST. Elsewhere the model SST is insufficiently different from observed to be able to identify model errors.

Seager, Richard↗

NASA NTRS2010

Simulations of Aerosol Microphysics in the NASA GEOS-5 Model

Aerosol-cloud-chemistry interactions have potentially large but uncertain impacts on Earth's climate. One path to addressing these uncertainties is to construct models that incorporate various components of the Earth system and to test these models against data. To that end, we have previously incorporated the Goddard Chemistry, Aerosol, Radiation, and Transport (GOCART) module online in the NASA Goddard Earth Observing System model (GEOS-5). GEOS-5 provides a platform for Earth system modeling, incorporating atmospheric and ocean general circulation models, a land surface model, a data assimilation system, and treatments of atmospheric chemistry and hydrologic cycle. Including GOCART online in this framework has provided a path for interactive aerosol-climate studies; however, GOCART only tracks the mass of aerosols as external mixtures and does not include the detailed treatments of aerosol size distribution and composition (internal mixtures) needed for aerosol-cloud-chemistry-climate studies. To address that need we have incorporated the Community Aerosol and Radiation Model for Atmospheres (CARMA) online in GEOS-5. CARMA is a sectional aerosol-cloud microphysical model, capable of treating both aerosol size and composition explicitly be resolving the aerosol distribution into a variable number of size and composition groupings. Here we present first simulations of dust, sea salt, and smoke aerosols in GEOS-5 as treated by CARMA. These simulations are compared to available aerosol satellite, ground, and aircraft data and as well compared to the simulated distributions in our current GOCART based system.

Colarco, Peter↗

NASA NTRS1972

Preliminary study of the application of the Timation 3 satellite to earth physics

The Timation 3 is a timing and navigation satellite originally planned for launch in December 1972 into a circular orbit at 98 deg inclination 14,000 km altitude with gravity gradient stabilization. An error analysis indicates a satellite position uncertainty of about one meter, 80 percent of which is attributable to the assumed gravity model errors. The remaining uncertainties have a period equal to that of the satellites and can be filtered out yielding an effective uncertainty of about 10 cm in the study of phenomena having different periodicities. The accomplishment of these results depends on a careful consideration of solar radiation pressure taking account of the spacecraft reflecting properties and variations in the presentation area. Consideration is also given to the displacement of the laser reflectors from the center of mass of the spacecraft and to the dynamic coupling of any libration in attitude with the orbital motion. The results indicate that a good set of well distribution laser observations of Timation 3 could yield determinations of polar motion, sea floor spreading, solid earth tides, and earth rotation at the 10 cm level.

Carpenter, L.↗

NASA NTRS2004

Finite Element Modeling Used to Study Stress Distribution on the Foot

A method to study the stress distribution inside the forefoot during walking was developed at the Cleveland Clinic Foundation by a researcher from the NASA Glenn Research Center. In this method, a semiautomated process was outlined to create a three-dimensional, patient-specific, finite element model (FEM) of the forefoot using magnetic resonance images (MRI). The images were processed in Matlab using the k-nearest neighbor (k-NN) classification algorithm and Sobel edge detection to separate the different tissue types: bone, skin, fat, and muscle. This information was used to create curves and surfaces that were exported to an FEM preprocessor known as Truegrid. In Truegrid, eight-noded or brick elements were created by using surface mapping. The FEM was processed and postprocessed in Abaqus. Material properties of the models were obtained from past experiments such as fat pad confined compression, skin axial and biaxial tests, muscle in vivo compressive tests, and reference literature (bone properties). Nonlinear (hyperelastic) material models were used for the skin (epidermis and dermis), fat, and muscles; and a linear elastic model was used for the bones. Muscle activation during walking yielded uncertainties in the muscle material model since contracted muscles are stiffer than relaxed muscles. These uncertainties were resolved by performing a sensitivity analysis of the muscle material properties. The original properties were multiplied by arbitrary factors of 2, 3, 0.5, and 0.33. The strain and stress distributions, as well as the locations of peak values, were similar in all cases. The peak contact pressure P obtained for each case varied with respect to the applied factor f as follows:

Morales, Nelson↗

NASA NTRS2022

Use of Machine Learning to Reduce Uncertainties in Particle Number Concentration and Aerosol Indirect Radiative Forcing Predicted by Climate Models

The radiative forcing of anthropogenic aerosols associated with aerosol–cloud interactions (RF(sub aci)) remains the largest source of uncertainty in climate prediction. The calculation of particle number concentration (PNC), one of the critical parameters affecting RF(sub aci), is generally simplified in climate models. Here we employ outputs from long-term (30-years) simulations of a global size-resolved (sectional) aerosol microphysics model and a machine-learning tool to develop a Random Forest Regression Model (RFRM) for PNC. We have implemented the PNC RFRM in GISS-ModelE2.1 with a mass-based One-Moment Aerosol module, which is one of CMIP6 models. Compared to the default setting, the GISS-ModelE2.1 simulation based on RFRM reduces the changes of cloud droplet number concentration associated with anthropogenic emissions, and decreases the RF(sub aci) from −1.46 W⋅m(exp −2) to −1.11 W⋅m(exp −2). This work highlights a promising approach based on machine learning to reduce uncertainties of climate models in predicting PNC and RF(sub aci) without compromising their computing efficiency.

Radiative forcing↗

NASA NTRS1997

Internal Physical Features of a Land Surface Model Employing a Tangent Linear Model

The Earth's land surface, including its biomass, is an integral part of the Earth's weather and climate system. Land surface heterogeneity, such as the type and amount of vegetative covering., has a profound effect on local weather variability and therefore on regional variations of the global climate. Surface conditions affect local weather and climate through a number of mechanisms. First, they determine the re-distribution of the net radiative energy received at the surface, through the atmosphere, from the sun. A certain fraction of this energy increases the surface ground temperature, another warms the near-surface atmosphere, and the rest evaporates surface water, which in turn creates clouds and causes precipitation. Second, they determine how much rainfall and snowmelt can be stored in the soil and how much instead runs off into waterways. Finally, surface conditions influence the near-surface concentration and distribution of greenhouse gases such as carbon dioxide. The processes through which these mechanisms interact with the atmosphere can be modeled mathematically, to within some degree of uncertainty, on the basis of underlying physical principles. Such a land surface model provides predictive capability for surface variables including ground temperature, surface humidity, and soil moisture and temperature. This information is important for agriculture and industry, as well as for addressing fundamental scientific questions concerning global and local climate change. In this study we apply a methodology known as tangent linear modeling to help us understand more deeply, the behavior of the Mosaic land surface model, a model that has been developed over the past several years at NASA/GSFC. This methodology allows us to examine, directly and quantitatively, the dependence of prediction errors in land surface variables upon different vegetation conditions. The work also highlights the importance of accurate soil moisture information. Although surface variables are predicted imperfectly due to inherent uncertainties in the modeling process, our study suggests how satellite observations can be combined with the model, through land surface data assimilation, to improve their prediction.

Yang, Runhua↗

NASA NTRS2011

NASA System Safety Handbook: System Safety Framework and Concepts for Implementation - Volume 1

System safety assessment is defined in NPR 8715.3C, NASA General Safety Program Requirements as a disciplined, systematic approach to the analysis of risks resulting from hazards that can affect humans, the environment, and mission assets. Achievement of the highest practicable degree of system safety is one of NASA's highest priorities. Traditionally, system safety assessment at NASA and elsewhere has focused on the application of a set of safety analysis tools to identify safety risks and formulate effective controls.1 Familiar tools used for this purpose include various forms of hazard analyses, failure modes and effects analyses, and probabilistic safety assessment (commonly also referred to as probabilistic risk assessment (PRA)). In the past, it has been assumed that to show that a system is safe, it is sufficient to provide assurance that the process for identifying the hazards has been as comprehensive as possible and that each identified hazard has one or more associated controls. The NASA Aerospace Safety Advisory Panel (ASAP) has made several statements in its annual reports supporting a more holistic approach. In 2006, it recommended that "... a comprehensive risk assessment, communication and acceptance process be implemented to ensure that overall launch risk is considered in an integrated and consistent manner." In 2009, it advocated for "... a process for using a risk-informed design approach to produce a design that is optimally and sufficiently safe." As a rationale for the latter advocacy, it stated that "... the ASAP applauds switching to a performance-based approach because it emphasizes early risk identification to guide designs, thus enabling creative design approaches that might be more efficient, safer, or both." For purposes of this preface, it is worth mentioning three areas where the handbook emphasizes a more holistic type of thinking. First, the handbook takes the position that it is important to not just focus on risk on an individual basis but to consider measures of aggregate safety risk and to ensure wherever possible that there be quantitative measures for evaluating how effective the controls are in reducing these aggregate risks. The term aggregate risk, when used in this handbook, refers to the accumulation of risks from individual scenarios that lead to a shortfall in safety performance at a high level: e.g., an excessively high probability of loss of crew, loss of mission, planetary contamination, etc. Without aggregated quantitative measures such as these, it is not reasonable to expect that safety has been optimized with respect to other technical and programmatic objectives. At the same time, it is fully recognized that not all sources of risk are amenable to precise quantitative analysis and that the use of qualitative approaches and bounding estimates may be appropriate for those risk sources. Second, the handbook stresses the necessity of developing confidence that the controls derived for the purpose of achieving system safety not only handle risks that have been identified and properly characterized but also provide a general, more holistic means for protecting against unidentified or uncharacterized risks. For example, while it is not possible to be assured that all credible causes of risk have been identified, there are defenses that can provide protection against broad categories of risks and thereby increase the chances that individual causes are contained. Third, the handbook strives at all times to treat uncertainties as an integral aspect of risk and as a part of making decisions. The term "uncertainty" here does not refer to an actuarial type of data analysis, but rather to a characterization of our state of knowledge regarding results from logical and physical models that approximate reality. Uncertainty analysis finds how the output parameters of the models are related to plausible variations in the input parameters and in the modeling assumptions. The evaluation of unrtainties represents a method of probabilistic thinking wherein the analyst and decision makers recognize possible outcomes other than the outcome perceived to be "most likely." Without this type of analysis, it is not possible to determine the worth of an analysis product as a basis for making decisions related to safety and mission success. In line with these considerations the handbook does not take a hazard-analysis-centric approach to system safety. Hazard analysis remains a useful tool to facilitate brainstorming but does not substitute for a more holistic approach geared to a comprehensive identification and understanding of individual risk issues and their contributions to aggregate safety risks. The handbook strives to emphasize the importance of identifying the most critical scenarios that contribute to the risk of not meeting the agreed-upon safety objectives and requirements using all appropriate tools (including but not limited to hazard analysis). Thereafter, emphasis shifts to identifying the risk drivers that cause these scenarios to be critical and ensuring that there are controls directed toward preventing or mitigating the risk drivers. To address these and other areas, the handbook advocates a proactive, analytic-deliberative, risk-informed approach to system safety, enabling the integration of system safety activities with systems engineering and risk management processes. It emphasizes how one can systematically provide the necessary evidence to substantiate the claim that a system is safe to within an acceptable risk tolerance, and that safety has been achieved in a cost-effective manner. The methodology discussed in this handbook is part of a systems engineering process and is intended to be integral to the system safety practices being conducted by the NASA safety and mission assurance and systems engineering organizations. The handbook posits that to conclude that a system is adequately safe, it is necessary to consider a set of safety claims that derive from the safety objectives of the organization. The safety claims are developed from a hierarchy of safety objectives and are therefore hierarchical themselves. Assurance that all the claims are true within acceptable risk tolerance limits implies that all of the safety objectives have been satisfied, and therefore that the system is safe. The acceptable risk tolerance limits are provided by the authority who must make the decision whether or not to proceed to the next step in the life cycle. These tolerances are therefore referred to as the decision maker's risk tolerances. In general, the safety claims address two fundamental facets of safety: 1) whether required safety thresholds or goals have been achieved, and 2) whether the safety risk is as low as possible within reasonable impacts on cost, schedule, and performance. The latter facet includes consideration of controls that are collective in nature (i.e., apply generically to broad categories of risks) and thereby provide protection against unidentified or uncharacterized risks.

Dezfuli, Homayoon↗

NASA NTRS2006

Software Development Cost Estimation Executive Summary

Identify simple fully validated cost models that provide estimation uncertainty with cost estimate. Based on COCOMO variable set. Use machine learning techniques to determine: a) Minimum number of cost drivers required for NASA domain based cost models; b) Minimum number of data records required and c) Estimation Uncertainty. Build a repository of software cost estimation information. Coordinating tool development and data collection with: a) Tasks funded by PA&E Cost Analysis; b) IV&V Effort Estimation Task and c) NASA SEPG activities.

data mining↗

NASA NTRSDate not supplied

Comparison of Entry Descent and Landing Aerodynamic Databases with Uncertainty Quantification Developed Using Machine Learning Techniques

When developing the aerodynamic databases for use in trajectory simulations, it is important to develop a system of metrics to qualify which aerodynamic models are best to use. Since aerodynamics are just one input into trajectory simulations, the results of these simulations do not reflect on the quality of the aerodynamic database used. This means that aerodynamic database comparisons must be done offline. While traditional metrics that focus on mean/nominal predictions are a good first step, more robust estimates of the prediction interval become important as more focused uncertainty models are developed. We explore the limitations of evaluating aerodynamic models based purely on nominal-centered response surfaces. Before elaborating and evaluating metrics based on distributed models, the value of evaluating prediction interval and confidence interval are discussed to conclude that prediction intervals are more relevant to the use of trajectory analysis. Several metrics to evaluate the prediction interval are introduced with a focus on the standard calibration metric. Finally, we compare candidate models using both mean and distributed metrics. A finalized candidate model developed using state of the art machine learning methods is compared to a baseline model developed using traditional aerodynamic database modeling techniques.

Aerodynamic Database↗

NASA NTRS1989

A variational approach to understanding white dwarf evolution

A variational approach is used to map out the effects that uncertainties in the theoretical model parameters have upon the derived ages near the observed cutoff in the white dwarf luminosity function. Two representative sequences are assessed, simulating a white dwarf with a 50/50 C/O mixture in the core and an outer helium layer and a white dwarf with a C/O convective overshooting profile. The differential effects that the variation of selected model input quantities has on the ages are reported, and it is concluded that internal theoretical uncertainties are small and getting smaller with time, and the results underscore the power of using the observed white dwarf luminosity function for studying the history of star formation in the Galaxy.

Wood, M. A.↗