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NASA NTRS1994

A statistical analysis of the dependency of closure assumptions in cumulus parameterization on the horizontal resolution

Simulated data from the UCLA cumulus ensemble model are used to investigate the quasi-universal validity of closure assumptions used in existing cumulus parameterizations. A closure assumption is quasi-universally valid if it is sensitive neither to convective cloud regimes nor to horizontal resolutions of large-scale/mesoscale models. The dependency of three types of closure assumptions, as classified by Arakawa and Chen, on the horizontal resolution is addressed in this study. Type I is the constraint on the coupling of the time tendencies of large-scale temperature and water vapor mixing ratio. Type II is the constraint on the coupling of cumulus heating and cumulus drying. Type III is a direct constraint on the intensity of a cumulus ensemble. The macroscopic behavior of simulated cumulus convection is first compared with the observed behavior in view of Type I and Type II closure assumptions using 'quick-look' and canonical correlation analyses. It is found that they are statistically similar to each other. The three types of closure assumptions are further examined with simulated data averaged over selected subdomain sizes ranging from 64 to 512 km. It is found that the dependency of Type I and Type II closure assumptions on the horizontal resolution is very weak and that Type III closure assumption is somewhat dependent upon the horizontal resolution. The influences of convective and mesoscale processes on the closure assumptions are also addressed by comparing the structures of canonical components with the corresponding vertical profiles in the convective and stratiform regions of cumulus ensembles analyzed directly from simulated data. The implication of these results for cumulus parameterization is discussed.

Xu, Kuan-Man↗

NASA NTRS1993

The helical decomposition and the instability assumption

Direct numerical simulations show that the triadic transfer function T(k,p,q) peaks sharply when q (or p) is much smaller than k. The triadic transfer function T(k,p,q) gives the rate of energy input into wave number k from all interactions with modes of wave number p and q, where k, p, q form a triangle. This observation was thought to suggest that energy is cascaded downscale through non-local interactions with local transfer and that there was a strong connection between large and small scales. Both suggestions were in contradiction with the classical Kolmogorov picture of the energy cascade. The helical decomposition was found useful in distinguishing between kinematically independent interactions. That analysis has gone beyond the question of non-local interaction with local transfer. In particular, an assumption about the statistical direction of triadic energy transfer in any kinematically independent interaction was introduced (the instability assumption). That assumption is not necessary for the conclusions about non-local interactions with local transfer recalled above. In the case of turbulence under rapid rotation, the instability assumption leads to the prediction that energy is transferred in spectral space from the poles of the rotation axis toward the equator. The instability assumption is thought to be of general validity for any type of triad interactions (e.g. internal waves). The helical decomposition and the instability assumption offer detailed information about the homogeneous statistical dynamics of the Navier-Stokes equations. The objective was to explore the validity of the instability assumption and to study the contributions of the various types of helical interactions to the energy cascade and the subgrid-scale eddy-viscosity. This was done in the context of spectral closures of the Direct Interaction or Quasi-Normal type.

Waleffe, Fabian A.↗

NASA NTRS1990

Effects of simplifying assumptions on optimal trajectory estimation for a high-performance aircraft

When analyzing the performance of an aircraft, certain simplifying assumptions, which decrease the complexity of the problem, can often be made. The degree of accuracy required in the solution may determine the extent to which these simplifying assumptions are incorporated. A complex model may yield more accurate results if it describes the real situation more thoroughly. However, a complex model usually involves more computation time, makes the analysis more difficult, and often requires more information to do the analysis. Therefore, to choose the simplifying assumptions intelligently, it is important to know what effects the assumptions may have on the calculated performance of a vehicle. Several simplifying assumptions are examined, the effects of simplified models to those of the more complex ones are compared, and conclusions are drawn about the impact of these assumptions on flight envelope generation and optimal trajectory calculation. Models which affect an aircraft are analyzed, but the implications of simplifying the model of the aircraft itself are not studied. The examples are atmospheric models, gravitational models, different models for equations of motion, and constraint conditions.

Kern, Lura E.↗

NASA NTRS2011

Sensitivity of C-Band Polarimetric Radar-Based Drop Size Distribution Measurements to Maximum Diameter Assumptions

The estimation of rain drop size distribution (DSD) parameters from polarimetric radar observations is accomplished by first establishing a relationship between differential reflectivity (Z(sub dr)) and the central tendency of the rain DSD such as the median volume diameter (D0). Since Z(sub dr) does not provide a direct measurement of DSD central tendency, the relationship is typically derived empirically from rain drop and radar scattering models (e.g., D0 = F[Z (sub dr)] ). Past studies have explored the general sensitivity of these models to temperature, radar wavelength, the drop shape vs. size relation, and DSD variability. Much progress has been made in recent years in measuring the drop shape and DSD variability using surface-based disdrometers, such as the 2D Video disdrometer (2DVD), and documenting their impact on polarimetric radar techniques. In addition to measuring drop shape, another advantage of the 2DVD over earlier impact type disdrometers is its ability to resolve drop diameters in excess of 5 mm. Despite this improvement, the sampling limitations of a disdrometer, including the 2DVD, make it very difficult to adequately measure the maximum drop diameter (D(sub max)) present in a typical radar resolution volume. As a result, D(sub max) must still be assumed in the drop and radar models from which D0 = F[Z(sub dr)] is derived. Since scattering resonance at C-band wavelengths begins to occur in drop diameters larger than about 5 mm, modeled C-band radar parameters, particularly Z(sub dr), can be sensitive to D(sub max) assumptions. In past C-band radar studies, a variety of D(sub max) assumptions have been made, including the actual disdrometer estimate of D(sub max) during a typical sampling period (e.g., 1-3 minutes), D(sub max) = C (where C is constant at values from 5 to 8 mm), and D(sub max) = M*D0 (where the constant multiple, M, is fixed at values ranging from 2.5 to 3.5). The overall objective of this NASA Global Precipitation Measurement Mission (GPM/PMM Science Team)-funded study is to document the sensitivity of DSD measurements, including estimates of D0, from C-band Z(sub dr) and reflectivity to this range of D(sub max) assumptions. For this study, GPM Ground Validation 2DVD's were operated under the scanning domain of the UAHuntsville ARMOR C-band dual-polarimetric radar. Approximately 7500 minutes of DSD data were collected and processed to create gamma size distribution parameters using a truncated method of moments approach. After creating the gamma parameter datasets the DSD's were then used as input to a T-matrix model for computation of polarimetric radar moments at C-band. All necessary model parameterizations, such as temperature, drop shape, and drop fall mode, were fixed at typically accepted values while the D(sub max) assumption was allowed to vary in sensitivity tests. By hypothesizing a DSD model with D(sub max) (fit) from which the empirical fit to D0 = F[Z(sub dr)] was derived via non-linear least squares regression and a separate reference DSD model with D(sub max) (truth), bias and standard error in D0 retrievals were estimated in the presence of Z(sub dr) measurement error and hypothesized mismatch in D(sub max) assumptions. Although the normalized standard error for D0 = F[Z(sub dr)r] can increase slightly (as much as from 11% to 16% for all 7500 DSDs) when the D(sub max) (fit) does not match D(sub max) (truth), the primary impact of uncertainty in D(sub max) is a potential increase in normalized bias error in D0 (from 0% to as much as 10% over all 7500 DSDs, depending on the extent of the mismatch between D(sub max) (fit) and D(sub max) (truth)). For DSDs characterized by large Z(sub dr) (Z(sub dr) > 1.5 to 2.0 dB), the normalized bias error for D0 estimation at C-band is sometimes unacceptably large (> 10%), again depending on the extent of the hypothesized D(sub max) mismatch. Modeled errors in D0 retrievals from Z(sub dr) at C-band are demonstrated in detail and comparedo similar modeled retrieval errors at S-band and X-band where the sensitivity to D(sub max) is expected to be less. The impact of D(sub max) assumptions to the retrieval of other DSD parameters such as Nw, the liquid water content normalized intercept parameter, are also explored. Likely implications for DSD retrievals using C-band polarimetric radar for GPM are assessed by considering current community knowledge regarding D(sub max) and quantifying the statistical distribution of Z(sub dr) from ARMOR over a large variety of meteorological conditions. Based on these results and the prevalence of C-band polarimetric radars worldwide, a call for more emphasis on constraining our observational estimate of D(sub max) within a typical radar resolution volume is made

Carey, Lawrence D.↗

NASA NTRS1998

Why is it Doing That? - Assumptions about the FMS

In the glass cockpit, it's not uncommon to hear exclamations such as "why is it doing that?". Sometimes pilots ask "what were they thinking when they set it this way?" or "why doesn't it tell me what it's going to do next?". Pilots may hold a conceptual model of the automation that is the result of fleet lore, which may or may not be consistent with what the engineers had in mind. But what did the engineers have in mind? In this study, we present some of the underlying assumptions surrounding the glass cockpit. Engineers and designers make assumptions about the nature of the flight task; at the other end, instructor and line pilots make assumptions about how the automation works and how it was intended to be used. These underlying assumptions are seldom recognized or acknowledged, This study is an attempt to explicitly arti culate such assumptions to better inform design and training developments. This work is part of a larger project to support training strategies for automation.

Feary, Michael↗

NASA NTRS1994

Further evidence for the EPNT assumption

We recently proved a theorem extending the Greenberger-Horne-Zeilinger (GHZ) Theorem from multi-particle systems to two-particle systems. This proof depended upon an auxiliary assumption, the EPNT assumption (Emptiness of Paths Not Taken). According to this assumption, if there exists an Einstein-Rosen-Podolsky (EPR) element of reality that determines that a path is empty, then there can be no entity associated with the wave that travels this path (pilot-waves, empty waves, etc.) and reports information to the amplitude, when the paths recombine. We produce some further evidence in support of this assumption, which is certainly true in quantum theory. The alternative is that such a pilot-wave theory would have to violate EPR locality.

Greenberger, Daniel M.↗

NASA NTRSDate not supplied

Sensitivity of Hybrid NEP-Chemical Vehicle Mass to Assumptions for Crewed Opposition-Class Mars Missions

This research illustrates the impact of different technology choices and their associated performance on overall sizing for a hybrid Nuclear Electric Propulsion (NEP) and chemical crewed Mars transportation vehicle. A set of models for the trajectory and vehicle mass, power system specific mass(α), and power conversion performance enable the analysis. Vehicle mass required to close the mission is calculated as a function of α and specific impulse (Isp) for multiple choices of high-level assumptions including system alpha vs. power scaling and electric thruster type. System alpha is built up and compared for multiple cases of technology assumptions. A Brayton cycle model is used to illustrate the alpha sensitivities to assumptions in cycle design such as peak operating temperature and component performance. The analysis illustrates how technology performance sensitivities affect the alpha and thus vehicle sizing for a range of mission and technology assumptions.

Matthew Duchek↗

NASA NTRSDate not supplied

Logistics Rates and Assumptions for Future Human Spaceflight Missions Beyond LEO

As NASA prepares for future human spaceflight missions with extended crew duration in destinations beyond low Earth orbit (LEO), the Agency has focused itself on understanding the drivers to sustainably support human life beyond Earth’s atmosphere. Future missions to deep space, the lunar surface, and eventually the Martian surface pose new challenges in ensuring the crew is sufficiently supplied with all necessary materials. To mitigate the risk of not delivering sufficient consumables and logistics for human spaceflight missions, NASA has examined past human space mission data and developed metabolic modeling to determine estimates for the crew consumption rates of fluids, solid consumables, and additional equipment needed. This paper is a compilation of guidelines, rates, and assumptions necessary to evaluate the logistics needs for future human exploration conceptual missions beyond LEO, providing a starting point and resource of information regarding usage rates and overall logistics supply planning for crewed exploration missions. Logistics represent all equipment and supplies not installed as part of the vehicle that are needed to support mission activities. Logistics can be further divided into specific categories, including consumables, maintenance items, spares, utilization, outfitting, as well as any packaging required. This paper will also provide use case examples of logistics needs to support human missions in deep space, including a conceptual lunar surface mission. The paper provides information necessary to calculate the mass and volume of known logistics for conceptual future human exploration missions beyond LEO. The assumptions in the paper are updated versions of previous assumptions made by the Agency and were derived from a number of sources, including International Space Station (ISS) historical usage and resupply rates, the Life Support Baseline Values and Assumptions Document (BVAD) 2022, Human Integration Design Handbook (HIDH) 2014, and data gathered from NASA human spaceflight programs and projects. The primary goal of the paper is to establish a set of consistent reference rates that multiple teams and groups can utilize to conduct logistics analysis and compare cases. This methodology is for initial estimates of conceptual human missions and does not take the place of detailed analysis for programs, nor does it provide requirements for programs.

Human Spaceflight↗

NASA NTRSDate not supplied

Logistics Rates and Assumptions for Future Human Spaceflight Missions Beyond LEO

Human Spaceflight↗

NASA NTRSDate not supplied

Assumption Generation for the Verification of Learning-Enabled Autonomous Systems

Providing safety guarantees for autonomous systems is difficultas these systems operate in complex environments that require the use of learning-enabled components, such as deep neural networks (DNNs) for visual perception. DNNs are hard to analyze due to their size (they can have thousands or millions of parameters), lack of formal specifications (DNNs are typically learnt from labeled data, in the absence of any formal or informal requirements), and sensitivity to small changes in the environment. We present an assume-guarantee style compositional approach for the formal verification of system-level safety properties of such autonomous systems. Our insight is that we can analyze the system in the absence of the DNN perception components by automatically synthesizing assumptions on the DNN behaviour that guarantee the satisfaction of the required safety properties. The synthesized assumptions are the weakest in the sense that they characterize the output sequences of all the possible DNNs that, plugged into the autonomous system, guarantee the required safety properties. The assumptions can be leveraged as run-time monitors over a deployed DNN to guarantee the safety of the overall system; they can also be mined to extract local specifications for use during training and testing of DNNs. We illustrate our approach on a case study taken from the autonomous airplanes domain that uses a complex DNN for perception

Autonomous systems↗

NASA NTRS1977

A note on the assumption of quasiequilibrium in semiconductor junction devices

It is shown that the quasi-equilibrium theory for p-n junctions, as originally proposed by Shockley (1949), does not apply under conditions involving an application of comparatively low external voltages. A numerical example indicates that the quasi-equilibrium assumption must be discarded as soon as the voltage is increased beyond a certain critical value, although the system may still be in a low-level injection regime. It is currently not known which set of simplifying assumptions may replace the quasi-equilibrium assumptions. Possible analytic simplification relations applicable to moderate or high injection levels can, perhaps, be based on an approach considered by Mari (1968) and Choo (1971, 1972).

Von Roos, O.↗

NASA NTRS1980

Effects of various assumptions on the calculated liquid fraction in isentropic saturated equilibrium expansions

The saturated equilibrium expansion approximation for two phase flow often involves ideal-gas and latent-heat assumptions to simplify the solution procedure. This approach is well documented by Wegener and Mack and works best at low pressures where deviations from ideal-gas behavior are small. A thermodynamic expression for liquid mass fraction that is decoupled from the equations of fluid mechanics is used to compare the effects of the various assumptions on nitrogen-gas saturated equilibrium expansion flow starting at 8.81 atm, 2.99 atm, and 0.45 atm, which are conditions representative of transonic cryogenic wind tunnels. For the highest pressure case, the entire set of ideal-gas and latent-heat assumptions are shown to be in error by 62 percent for the values of heat capacity and latent heat. An approximation of the exact, real-gas expression is also developed using a constant, two phase isentropic expansion coefficient which results in an error of only 2 percent for the high pressure case.

Bursik, J. W.↗

NASA NTRS1987

Closure assumptions in the cumulus parameterization problem

While concentrating on the thermodynamical aspects of parameterizing deep cumulus clouds, some of the existing schemes are reviewed with an emphasis on their closure assumptions. It is shown that the closure assumptions in these schemes are some combination of four types. It is emphasized that observations should be used more extensively than in the past to directly verify and improve closure assumptions and to assess the limit of parameterizability. As an example, results from an analysis of the macroscopic behavior of moist convection are presented. The results suggest that cumulus clouds are basically parameterizable, in spite of the existence of mesoscale organization.

Arakawa, Akio↗

NASA NTRS1986

Some implications of the isotropic momentarily frozen assumptions for the SPAN-MAT program

Potential tests using turbulence velocity histories measured in the SPAN-MAT Program are outlined to determine validity of the homogeneous, momentarily frozen assumptions for the vertical turbulence velocity component and the homogeneous, isotropic, momentarily frozen assumptions for the horizontal turbulence velocity components. In addition, methods are reviewed for prediction of the crosscorrelation function between any two spatially separated turbulence velocity components using the homogeneous, isotropic, momentarily frozen assumptions and measurements of the transverse and longitudinal turbulence velocity components.

Mark, W. D.↗

NASA NTRS2002

Influence of 2D Finite Element Modeling Assumptions on Debonding Prediction for Composite Skin-stiffener Specimens Subjected to Tension and Bending

The influence of two-dimensional finite element modeling assumptions on the debonding prediction for skin-stiffener specimens was investigated. Geometrically nonlinear finite element analyses using two-dimensional plane-stress and plane strain elements as well as three different generalized plane strain type approaches were performed. The computed deflections, skin and flange strains, transverse tensile stresses and energy release rates were compared to results obtained from three-dimensional simulations. The study showed that for strains and energy release rate computations the generalized plane strain assumptions yielded results closest to the full three-dimensional analysis. For computed transverse tensile stresses the plane stress assumption gave the best agreement. Based on this study it is recommended that results from plane stress and plane strain models be used as upper and lower bounds. The results from generalized plane strain models fall between the results obtained from plane stress and plane strain models. Two-dimensional models may also be used to qualitatively evaluate the stress distribution in a ply and the variation of energy release rates and mixed mode ratios with lamination length. For more accurate predictions, however, a three-dimensional analysis is required.

Krueger, Ronald↗

NASA NTRS2002

Learning Assumptions for Compositional Verification

Compositional verification is a promising approach to addressing the state explosion problem associated with model checking. One compositional technique advocates proving properties of a system by checking properties of its components in an assume-guarantee style. However, the application of this technique is difficult because it involves non-trivial human input. This paper presents a novel framework for performing assume-guarantee reasoning in an incremental and fully automated fashion. To check a component against a property, our approach generates assumptions that the environment needs to satisfy for the property to hold. These assumptions are then discharged on the rest of the system. Assumptions are computed by a learning algorithm. They are initially approximate, but become gradually more precise by means of counterexamples obtained by model checking the component and its environment, alternately. This iterative process may at any stage conclude that the property is either true or false in the system. We have implemented our approach in the LTSA tool and applied it to the analysis of a NASA system.

Cobleigh, Jamieson M.↗

NASA NTRS2004

Assume-Guarantee Verification of Source Code with Design-Level Assumptions

Model checking is an automated technique that can be used to determine whether a system satisfies certain required properties. To address the 'state explosion' problem associated with this technique, we propose to integrate assume-guarantee verification at different phases of system development. During design, developers build abstract behavioral models of the system components and use them to establish key properties of the system. To increase the scalability of model checking at this level, we have developed techniques that automatically decompose the verification task by generating component assumptions for the properties to hold. The design-level artifacts are subsequently used to guide the implementation of the system, but also to enable more efficient reasoning at the source code-level. In particular we propose to use design-level assumptions to similarly decompose the verification of the actual system implementation. We demonstrate our approach on a significant NASA application, where design-level models were used to identify; and correct a safety property violation, and design-level assumptions allowed us to check successfully that the property was presented by the implementation.

Giannakopoulou, Dimitra↗

NASA NTRS2004

Comparison of 2D Finite Element Modeling Assumptions with Results From 3D Analysis for Composite Skin-Stiffener Debonding

The influence of two-dimensional finite element modeling assumptions on the debonding prediction for skin-stiffener specimens was investigated. Geometrically nonlinear finite element analyses using two-dimensional plane-stress and plane-strain elements as well as three different generalized plane strain type approaches were performed. The computed skin and flange strains, transverse tensile stresses and energy release rates were compared to results obtained from three-dimensional simulations. The study showed that for strains and energy release rate computations the generalized plane strain assumptions yielded results closest to the full three-dimensional analysis. For computed transverse tensile stresses the plane stress assumption gave the best agreement. Based on this study it is recommended that results from plane stress and plane strain models be used as upper and lower bounds. The results from generalized plane strain models fall between the results obtained from plane stress and plane strain models. Two-dimensional models may also be used to qualitatively evaluate the stress distribution in a ply and the variation of energy release rates and mixed mode ratios with delamination length. For more accurate predictions, however, a three-dimensional analysis is required.

Krueger, Ronald↗