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NASA NTRSDate not supplied

Design Under Uncertainty for Conceptual Aircraft Design Leveraging Analytical Gradients

The purpose of this paper is to extend previously demonstrated methodologies for design under uncertainty, leveraging analytical gradients to higher fidelity analysis for use in conceptual aircraft design. Previous work developed methods to generate analytical derivatives through polynomial chaos expansion, eliminating the need to estimate derivatives via complex step or finite difference. In this research, the authors build upon the methods to include physics-based aircraft design codes for aircraft design under uncertainty. This extends the previous work’s case study, which employed analytical aerodynamics and Breguet range estimations for wing design, to a higher fidelity level. In addition, this work extends previous work on interface development between the Uncertainty Quantification with Polynomial Chaos Expansion (UQPCE) software and Model-Based Systems Analysis and Engineering (MBSA&E) frameworks. This paper will discuss the development work necessary to perform multidisciplinary design under uncertainty as well as demonstrate the mechanics of interfacing UQPCE and conceptual aircraft design tools such as NASA’s Aviary code. In a case study, a conceptual aircraft design under uncertainty was conducted and compared against a traditional deterministic design. When given information about the uncertainty space from UQPCE, the optimizer was able to shape the output distribution and produce a more robust design.

UQ↗

NASA NTRS1997

Estimating the Uncertainty in Passive-Microwave Rain-Retrievals

Current passive-microwave rain-retrieval methods are largely based on databases built off-line using cloud models. The vertical distribution of hydrometeors within the cloud has a large impact on upwelling brightness temperatures ([31,[5]). Thus, a forward radiative transfer model can predict off-line the radiance associated with different rain scenarios. To estimate the rain from measured brightness temperatures, one simply looks for the rain scenario whose associated radiances are closest to the measurements. To understand the uncertainties in this process, we first study the dependence of the simulated brightness temperatures on different hydrometeor size distribution (DSD) models. We then analyze the marginal and joint distributions of the radiances observed by the Tropical Rainfall Measuring Mission satellite and of those in the databases used in the TRMM rain retrievals. We finally calculate the covariances of the rain profiles and brightness temperatures in the TRMM passive-microwave database and derive a simple parametric model for the conditional uncertainty, given measured radiances. These results are used to characterize the uncertainty inherent in the passive-microwave retrieval.

Coppens, Dorothee↗

NASA NTRS2010

The Effect of Nondeterministic Parameters on Shock-Associated Noise Prediction Modeling

Engineering applications for aircraft noise prediction contain models for physical phenomenon that enable solutions to be computed quickly. These models contain parameters that have an uncertainty not accounted for in the solution. To include uncertainty in the solution, nondeterministic computational methods are applied. Using prediction models for supersonic jet broadband shock-associated noise, fixed model parameters are replaced by probability distributions to illustrate one of these methods. The results show the impact of using nondeterministic parameters both on estimating the model output uncertainty and on the model spectral level prediction. In addition, a global sensitivity analysis is used to determine the influence of the model parameters on the output, and to identify the parameters with the least influence on model output.

Dahl, Milo D.↗

NASA NTRS2011

Forward Modeling of Atmospheric Carbon Dioxide in GEOS-5: Uncertainties Related to Surface Fluxes and Sub-Grid Transport

Forward GEOS-5 AGCM simulations of CO2, with transport constrained by analyzed meteorology for 2009-2010, are examined. The CO2 distributions are evaluated using AIRS upper tropospheric CO2 and ACOS-GOSAT total column CO2 observations. Different combinations of surface C02 fluxes are used to generate ensembles of runs that span some uncertainty in surface emissions and uptake. The fluxes are specified in GEOS-5 from different inventories (fossil and biofuel), different data-constrained estimates of land biological emissions, and different data-constrained ocean-biology estimates. One set of fluxes is based on the established "Transcom" database and others are constructed using contemporary satellite observations to constrain land and ocean process models. Likewise, different approximations to sub-grid transport are employed, to construct an ensemble of CO2 distributions related to transport variability. This work is part of NASA's "Carbon Monitoring System Flux Pilot Project,"

Pawson, Steven↗

NASA NTRS1993

Probabilistic simulation of multi-scale composite behavior

A methodology is developed to computationally assess the probabilistic composite material properties at all composite scale levels due to the uncertainties in the constituent (fiber and matrix) properties and in the fabrication process variables. The methodology is computationally efficient for simulating the probability distributions of material properties. The sensitivity of the probabilistic composite material property to each random variable is determined. This information can be used to reduce undesirable uncertainties in material properties at the macro scale of the composite by reducing the uncertainties in the most influential random variables at the micro scale. This methodology was implemented into the computer code PICAN (Probabilistic Integrated Composite ANalyzer). The accuracy and efficiency of this methodology are demonstrated by simulating the uncertainties in the material properties of a typical laminate and comparing the results with the Monte Carlo simulation method. The experimental data of composite material properties at all scales fall within the scatters predicted by PICAN.

Liaw, D. G.↗

NASA NTRS2017

Variation in Coronal Activity from Solar Cycle 24 Minimum to Maximum Using Three-Dimensional Reconstructions of the Coronal Electron Density from STEREO/COR1

Three-dimensional electron density distributions in the solar corona are reconstructed for 100 Carrington rotations (CR 2054 - 2153) during 2007/03 - 2014/08 using the spherically symmetric method from polarized white-light observations with the inner coronagraph (COR1) onboard the twin Solar Terrestrial Relations Observatory (STEREO). These three-dimensional electron density distributions are validated by comparison with similar density models derived using other methods such as tomography and a magnetohydrodynamics (MHD) model as well as using data from the Solar and Heliospheric Observatory (SOHO)/Large Angle and Spectrometric Coronagraph (LASCO)-C2. Uncertainties in the estimated total mass of the global corona are analyzed based on differences between the density distributions for COR1-A and -B. Long-term variations of coronal activity in terms of the global and hemispheric average electron densities (equivalent to the total coronal mass) reveal a hemispheric asymmetry during the rising phase of Solar Cycle 24, with the northern hemisphere leading the southern hemisphere by a phase shift of 7 - 9 months. Using 14 CR (approx. equal to 13-month) running averages, the amplitudes of the variation in average electron density between Cycle 24 maximum and Cycle 23/24 minimum (called the modulation factors) are found to be in the range of 1.6 - 4.3. These modulation factors are latitudinally dependent, being largest in polar regions and smallest in the equatorial region. These modulation factors also show a hemispheric asymmetry: they are somewhat larger in the southern hemisphere. The wavelet analysis shows that the short-term quasi-periodic oscillations during the rising and maximum phases of Cycle 24 have a dominant period of 7 - 8 months. In addition, it is found that the radial distribution of the mean electron density for streamers at Cycle 24 maximum is only slightly larger (by approx. equal to 30%) than at cycle minimum.

Wang, Tongjiang↗

NASA NTRS1994

Some rules for polydimensional squeezing

The review of the following results is presented: For mixed state light of N-mode electromagnetic field described by Wigner function which has generic Gaussian form, the photon distribution function is obtained and expressed explicitly in terms of Hermite polynomials of 2N-variables. The momenta of this distribution are calculated and expressed as functions of matrix invariants of the dispersion matrix. The role of new uncertainty relation depending on photon state mixing parameter is elucidated. New sum rules for Hermite polynomials of several variables are found. The photon statistics of polymode even and odd coherent light and squeezed polymode Schroedinger cat light is given explicitly. Photon distribution for polymode squeezed number states expressed in terms of multivariable Hermite polynomials is discussed.

Manko, Vladimir I.↗

NASA NTRS2007

MODIS Aerosol Observations used to Constrain Dust Distributions and Lifecycle in the NASA GEOS-5 Model

Approximately 240 Tg of mineral dust aerosol are transported annually from Saharan Africa to the Atlantic Ocean. Dust affects the Earth radiation budget, and plays direct (through scattering and absorption of radiation) and indirect (through modification of cloud properties and environment) roles in climate. Deposition of dust to the surface provides an important nutrient source to terrestrial and oceanic ecosystems. Dust is additionally a contributor to adverse air quality. Among the tools toward understanding the lifecycle and impacts of mineral dust aerosols are numerical models. Important constraints on these models come from quantitative satellite observations, like those from the space-based Moderate Resolution Imaging Spectroradiometer (MODIS). In particular, Kauhan et al. [2005] used MODIS aerosol observations to infer transport and deposition fluxes of Saharan dust over the Atlantic, Caribbean, and Amazonian basins. Those observations are used here to constrain the transport of dust and its interannual variability simulated in the NASA GEOS-5 general circulation model and data assimilation system. Significant uncertainty exists in the MODIS-derived fluxes, however, due to uncertainty in the wind fields provided by meteorological analyses in this region. That same uncertainty in the wind fields is manifest in our GEOS-5 simulations of dust distributions. Here we use MODIS observations to investigate the seasonality and location of the Saharan dust plume and explore through sensitivity analysis of our model the meteorological controls on the dust distribution, including dust direct radiative effects and sub-gridscale source and sink processes.

Colarco, P.↗

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

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

Uncertainty Quantification↗

NASA NTRS2016

Probabilistic Damage Characterization Using the Computationally-Efficient Bayesian Approach

This work presents a computationally-ecient approach for damage determination that quanti es uncertainty in the provided diagnosis. Given strain sensor data that are polluted with measurement errors, Bayesian inference is used to estimate the location, size, and orientation of damage. This approach uses Bayes' Theorem to combine any prior knowledge an analyst may have about the nature of the damage with information provided implicitly by the strain sensor data to form a posterior probability distribution over possible damage states. The unknown damage parameters are then estimated based on samples drawn numerically from this distribution using a Markov Chain Monte Carlo (MCMC) sampling algorithm. Several modi cations are made to the traditional Bayesian inference approach to provide signi cant computational speedup. First, an ecient surrogate model is constructed using sparse grid interpolation to replace a costly nite element model that must otherwise be evaluated for each sample drawn with MCMC. Next, the standard Bayesian posterior distribution is modi ed using a weighted likelihood formulation, which is shown to improve the convergence of the sampling process. Finally, a robust MCMC algorithm, Delayed Rejection Adaptive Metropolis (DRAM), is adopted to sample the probability distribution more eciently. Numerical examples demonstrate that the proposed framework e ectively provides damage estimates with uncertainty quanti cation and can yield orders of magnitude speedup over standard Bayesian approaches.

Warner, James E.↗

NASA NTRSDate not supplied

Impacts of Aerosol and Cloud Variability on Satellite-Derived All-skies Direct Aerosol Radiative Effects (DARE) over the North and Southeast Atlantic

The Top-of-Atmosphere (TOA) Shortwave (SW) Direct Aerosol Radiative Effect (DARE) in all-sky conditions (i.e., aerosols in clear skies and aerosols above and below all types of clouds) is the global change in upwelling radiative flux due to aerosols. It is one of the strongest indicators of global climate change due to aerosols. SW DARE at TOA depends on the Earth’s surface albedo, cloud fraction, cloud optical properties, and aerosol optical properties, which are all challenging to accurately characterize from space. The overarching goals of our project are to provide state-of-the-art observational all-sky TOA SW DARE, along with guidance on which aerosol and/or cloud properties are the most important to measure, and at which spatio-temporal scales, for accurate DARE observations. We compute all-sky DARE based on state-of-the-art cloud and aerosol retrieval algorithms from CALIOP (Cloud–Aerosol Lidar with Orthogonal Polarization) and MODIS (Moderate Resolution Imaging spectroradiometer) satellite sensors, as well as aerosol intensive properties from MERRA-2 (Modern-Era Retrospective Analysis for Research and Applications, version 2) simulations over three specific regions of the Atlantic Ocean from 2012 to 2016. In this symposium, we present a characterization of the cloud and aerosol optical and physical properties and the observational TOA SW DARE along three individual satellite tracks in the Southeast Atlantic region -- on September 18 and 20, 2016 and August 13, 2017. We then quantify the impact of assuming homogeneous cloud or aerosol fields in space-based TOA SW DARE calculations. And, finally, the resulting space-based all-skies aerosol vertical distribution and DARE calculations are evaluated using remote sensing observations from coincident suborbital flights from the NASA ORACLES (the ObseRvations of Aerosols above CLouds and their intEractionS, ORACLES field campaign) field campaign. The NASA Atmospheric Observing System (AOS) mission addresses the NASA Aerosol, Cloud, Convection and Precipitation (ACCP) designated observables and proposes, as one of its aerosol objectives, to reduce uncertainties in estimates of global mean all-sky SW DARE at TOA. Well characterizing clouds, aerosol vertical distributions, aerosol types and associated all-skies DARE over the Atlantic Ocean will inform the AOS community on where, when, how, and how often the satellite retrievals should be performed to estimate DARE and reduce all-skies DARE uncertainties most accurately. These comprehensive characterizations will also identify the key regions and times when the AOS (or other ACCP-related) suborbital missions should be conducted to evaluate and improve the AOS space-based observations and retrievals.

aerosol↗

NASA NTRS2022

Development of a “Nature Run” for Observing System Simulation Experiments (OSSEs) for Snow Mission Development

Snow is a fundamental component of global and regional water budgets, particularly in mountainous areas and regions downstream that rely on snowmelt for water resources. Land surface models (LSMs) are commonly used to develop spatially distributed estimates of snow water equivalent (SWE) and runoff. However, LSMs are limited by uncertainties in model physics and parameters, among other factors. In this study, we describe the use of model calibration tools to improve snow simulations within the Noah-MP LSM as the first step in an observing system simulation experiment (OSSE). Noah-MP is calibrated against the University of Arizona (UA) SWE product over a western Colorado domain. With spatially varying calibrated parameters, we run calibrated and default Noah-MP simulations for water years 2010–20. By evaluating both simulations against the UA dataset, we show that calibration decreases domain averaged temporal RMSE and bias for snow depth from 0.15 to 0.13 m and from −0.036 to −0.0023 m, respectively, and improves the timing of snow ablation. Increased snow simulation performance also improves estimates of model-simulated runoff in four of six study basins, though only one has statistically significant improvement. Spatially distributed Noah-MP snow parameters perform better than default uniform values. We demonstrate that calibrating variables related to snow albedo calculations and rain–snow partitioning, among other processes, is a necessary step for creating a nature run that reasonably approximates true snow conditions for the OSSEs. Additionally, the inclusion of a snowfall scaling term can address biases in precipitation from meteorological forcing datasets, further improving the utility of LSMs for generating reliable spatiotemporal estimates of snow.

Melissa L. Wrzesien↗

NASA NTRS2000

Expected Utility Distributions for Flexible, Contingent Execution

This paper presents a method for using expected utility distributions in the execution of flexible, contingent plans. A utility distribution maps the possible start times of an action to the expected utility of the plan suffix starting with that action. The contingent plan encodes a tree of possible courses of action and includes flexible temporal constraints and resource constraints. When execution reaches a branch point, the eligible option with the highest expected utility at that point in time is selected. The utility distributions make this selection sensitive to the runtime context, yet still efficient. Our approach uses predictions of action duration uncertainty as well as expectations of resource usage and availability to determine when an action can execute and with what probability. Execution windows and probabilities inevitably change as execution proceeds, but such changes do not invalidate the cached utility distributions, thus, dynamic updating of utility information is minimized.

Bresina, John L.↗

NASA NTRS1999

Recent Development on O(+) - O Collision Frequency and Ionosphere-Thermosphere Coupling

The collision frequency between an oxygen atom and its singly charged ion controls the momentum transfer between the ionosphere and the thermosphere. There has been a long standing discrepancy, extending over a decade, between the theoretical and empirical determination of this frequency: the empirical value of this frequency exceeded the theoretical value by a factor of 1.7. Recent improvements in theory were obtained by using accurate oxygen ion-oxygen atom potential energy curves, and partial wave quantum mechanical calculations. We now have applied three independent statistical methods to the observational data, obtained at the MIT/Millstone Hill Observatory, consisting of two sets A and B. These methods give results consistent with each other, and together with the recent theoretical improvements, bring the ratio close to unity, as it should be. The three statistical methods lead to an average for the ratio of the empirical to the theoretical values equal to 0.98, with an uncertainty of +/-8%, resolving the old discrepancy between theory and observation. The Hines statistics, and the lognormal distribution statistics, both give lower and upper bounds for the Set A equal to 0.89 and 1.02, respectively. The related bounds for the Set B are 1.06 and 1.17. The average values of these bounds thus bracket the ideal value of the ratio which should be equal to unity. The main source of uncertainties are errors in the profile of the oxygen atom density, which is of the order of 11%. An alternative method to find the oxygen atom density is being suggested.

Omidvar, K.↗

NASA NTRS2002

Micro-Pulse Lidar Signals: Uncertainty Analysis

Micro-pulse lidar (MPL) systems are small, autonomous, eye-safe lidars used for continuous observations of the vertical distribution of cloud and aerosol layers. Since the construction of the first MPL in 1993, procedures have been developed to correct for various instrument effects present in MPL signals. The primary instrument effects include afterpulse, laser-detector cross-talk, and overlap, poor near-range (less than 6 km) focusing. The accurate correction of both afterpulse and overlap effects are required to study both clouds and aerosols. Furthermore, the outgoing energy of the laser pulses and the statistical uncertainty of the MPL detector must also be correctly determined in order to assess the accuracy of MPL observations. The uncertainties associated with the afterpulse, overlap, pulse energy, detector noise, and all remaining quantities affecting measured MPL signals, are determined in this study. The uncertainties are propagated through the entire MPL correction process to give a net uncertainty on the final corrected MPL signal. The results show that in the near range, the overlap uncertainty dominates. At altitudes above the overlap region, the dominant source of uncertainty is caused by uncertainty in the pulse energy. However, if the laser energy is low, then during mid-day, high solar background levels can significantly reduce the signal-to-noise of the detector. In such a case, the statistical uncertainty of the detector count rate becomes dominant at altitudes above the overlap region.

Welton, Ellsworth J.↗

NASA NTRS2018

Stochastic Reduced Order Models with Python (SROMPy)

Stochastic Reduced Order Models with Python (SROMPy) is a software package developed to enable user-friendly utilization of the stochastic reduced order model (SROM) approach for uncertainty quantification. A SROM is a low dimensional, discrete approximation to a random quantity that enables efficient and non-intrusive stochastic computations. With SROMPy, a user can easily generate a SROM to approximate a random variable or vector described by several different types of probability distributions using the Python programming language. Once a SROM is constructed, the software can be used to propagate uncertainty through a user-defined computational model to estimate statistics of a given quantity of interest. This report is meant to introduce the SROMPy module and brie y demonstrate its capabilities. A simple example of a spring-mass system with a random input is included to illustrate the practicality of the SROM approach to uncertainty quantification and relative ease of applying it with SROMPy. The example includes a comparison with a solution obtained using classical Monte Carlo simulation, demonstrating the similarities and advantages of using the SROM approach.

Warner, James E.↗

NASA NTRS2023

Do Citizen Science Intense Observation Periods Increase Data Usability? A Deep Dive of the NASA GLOBE Clouds Data Set With Satellite Comparisons

The Global Learning and Observations to Benefit the Environment (GLOBE) citizen science program has recently conducted a series of month-long intensive observation periods (IOPs), asking the public to submit daily reports on cloud and sky conditions from all regions of Earth. This provides a wealth of crowdsourced observations from the ground, which complements other conventional scientific cloud data. In addition, the GLOBE reports are matched in space and time with geostationary and low Earth orbit satellites, which allows for a straightforward comparison of cloud properties, and minimizes the biases associated with mismatched sampling between participants and satellites. The matched GLOBE dataset is used to calculate the mean observed cloud cover by atmospheric level both worldwide and by region. The overall magnitudes of cloud cover between the GLOBE participants and the matched satellites agree within 10%, which is notable given the distinctly different natures of the data sources. The mean vertical cloud profiles show GLOBE reporting more low-level clouds and fewer high-level clouds than satellites. The low cloud disagreement is likely related to satellites missing low clouds when high clouds block their view. Conversely, the high cloud disagreement is related primarily to cloud opacity, as satellites may miss some optically thin clouds. Monte Carlo testing shows the results to be robust, and the tripled amount of IOP data reduces uncertainty by half. These findings also highlight ways in which citizen science IOP data may be used to support scientific research while accounting for their unique properties. Plain Language Summary: Citizen science is becoming an increasingly prominent aspect of scientific research, and so it important to study how citizen science data can be used effectively. For example, The GLOBE Program has recently conducted a series of special data-collecting events, or “challenges”, which gathered large numbers of reports on cloud and sky conditions. Because NASA GLOBE Clouds matches the participant reports with cloud observations from satellites, we can use these data to get a combined view of clouds from above and below. When looking at the average cloud cover for different atmospheric levels across Earth, we find that the GLOBE participants and the satellites agree quite closely. This is a surprising and fascinating find, given how different in nature volunteer ground reports are to satellite measurements. However, there are some small but notable disagreements between GLOBE participants and satellites about the distribution of cloud cover at different levels. In addition, by testing the data for uncertainty, we show that the results from the GLOBE data are reliable, and that more public participation improves the reliability. So, by carefully designing the analysis methodology, and by testing for the uncertainty of the data, citizen science can make a meaningful contribution to scientific research.

J. Brant Dodson↗