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Results for “uncertainty analysis”

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NASA NTRS2013

The Challenges of Credible Thermal Protection System Reliability Quantification

The paper discusses several of the challenges associated with developing a credible reliability estimate for a human-rated crew capsule thermal protection system. The process of developing such a credible estimate is subject to the quantification, modeling and propagation of numerous uncertainties within a probabilistic analysis. The development of specific investment recommendations, to improve the reliability prediction, among various potential testing and programmatic options is then accomplished through Bayesian analysis.

Green, Lawrence L.↗

NASA NTRS2014

The Evolution of the Galaxy Rest-Frame Ultraviolet Luminosity Function Over the First Two Billion Years

We present a robust measurement and analysis of the rest-frame ultraviolet (UV) luminosity function at z = 4 to 8. We use deep Hubble Space Telescope imaging over the CANDELS/GOODS fields, the Hubble Ultra Deep Field and the Hubble Frontier Field deep parallel observations near the Abell 2744 and MACS J0416.1- 2403 clusters. The combination of these surveys provides an effective volume of 0.6-1.2 ×10(exp 6) Mpc(exp 3) over this epoch, allowing us to perform a robust search for bright (M(sub UV) less than −21) and faint (M(sub UV) = −18) galaxies. We select galaxies using a well-tested photometric redshift technique with careful screening of contaminants, finding a sample of 7446 galaxies at 3.5 less than z less than 8.5, with more than 1000 galaxies at z of approximately 6 - 8. We measure both a stepwise luminosity function for galaxies in our redshift samples, as well as a Schechter function, using a Markov Chain Monte Carlo analysis to measure robust uncertainties. At the faint end our UV luminosity functions agree with previous studies, yet we find a higher abundance of UV-bright galaxies at z of greater than or equal to 6. Our bestfit value of the characteristic magnitude M* is consistent with −21 at z of greater than or equal to 5, different than that inferred based on previous trends at lower redshift. At z = 8, a single power-law provides an equally good fit to the UV luminosity function, while at z = 6 and 7, an exponential cutoff at the bright-end is moderately preferred. We compare our luminosity functions to semi-analytical models, and find that the lack of evolution in M* is consistent with models where the impact of dust attenuation on the bright-end of the luminosity function decreases at higher redshift, though a decreasing impact of feedback may also be possible. We measure the evolution of the cosmic star-formation rate (SFR) density by integrating our observed luminosity functions to M(sub UV) = −17, correcting for dust attenuation, and find that the SFR density declines proportionally to (1 + z)((exp −4.3)(+/-)(0.5)) at z greater than 4, consistent with observations at z greater than or equal to 9. Our observed luminosity functions are consistent with a reionization history that starts at redshift of approximately greater than 10, completes at z greater than 6, and reaches a midpoint (x(sub HII) = 0.5) at 6.7 less than z less than 9.4. Finally, using a constant cumulative number density selection and an empirically derived rising star-formation history, our observations predict that the abundance of bright z = 9 galaxies is likely higher than previous constraints, though consistent with recent estimates of bright z similar to 10 galaxies.

Galaxy↗

NASA NTRS2017

Determining the Optimal Spectral Sampling Frequency and Uncertainty Thresholds for Hyperspectral Remote Sensing of Ocean Color

Using a modified geostatistical technique, empirical variograms were constructed from the first derivative of several diverse remote sensing reflectance and phytoplankton absorbance spectra to describe how data points are correlated with distance across the spectra. The maximum rate of information gain is measured as a function of the kurtosis associated with the Gaussian structure of the output, and is determined for discrete segments of spectra obtained from a variety of water types (turbid river filaments, coastal waters, shelf waters, a dense Microcystis bloom, and oligotrophic waters), as well as individual and mixed phytoplankton functional types (PFTs; diatoms, chlorophytes, cyanobacteria, coccolithophores). Results show that a continuous spectrum of 5 to 7 nm spectral resolution is optimal to resolve the variability across mixed reflectance and absorbance spectra. In addition, the impact of uncertainty on subsequent derivative analysis is assessed, showing that a limit of 3 Gaussian noise (SNR 66) is tolerated without smoothing the spectrum, and 13 (SNR 15) noise is tolerated with smoothing.

Noise in imaging systems↗

NASA NTRS2019

Hybrid Transportation System Integrated Trajectory Design and Optimization for Mars Landing Site Accessibility

NASA’s Mars Study Capability Team continues the agency’s efforts to study and refine the nation’s plan to field a sustainable human Mars campaign. One of the primary open issues left unanswered during previous analysis cycles was the uncertainty of the impact to the vehicle performance requirement to deliver crew and cargo to the same landing site across multiple mission opportunities. The Mars Study Capability Team has recently developed an integrated trajectory optimization and system closure model to solve the complex interplanetary trajectory optimization using both low-thrust and high-thrust maneuvers. This paper demonstrates the capability of this new integrated trajectory design and optimization method as it applies to the landing site accessibility problem for the Hybrid transportation architecture. The results showed that the current vehicle is capable of reaching up to +20 degree latitude and down to -20 degree latitude in every mission opportunity from 2033 to 2052. However, reaching latitudes beyond +/- 20 required more propellant than the spacecraft is currently designed to carry for many of the mission opportunities.

Chai, Patrick R.↗

NASA NTRS2022

MLtool: Universal Supervised Machine Learning Tool to Model Tabulated Data

Machine Learning (ML) is a subfield of Artificial Intelligence that gives computers the ability to learn from past data without being explicitly programmed. The predictive capabilities of ML models have already been used to facilitate several scientific breakthroughs. However, the practical application of ML is often limited due to the gaps in technical knowledge of its users. The common issue faced by many scientific researchers is the inability to choose the appropriate ML pipelines that are needed to treat real-world data, which is often sparse and noisy. To solve this problem, we have developed an automated Machine Learning tool (MLtool) that includes a set of ML algorithms and approaches to aid scientific researchers. The current version of MLtool is implemented as an object-oriented Python code that is easily extensible. It includes 44 different regression algorithms used to model data. MLtool helps users select the best model for their data, based on the scoring metrics used. Besides regression algorithms, MLtool also includes a suite of pre- and post-processing techniques such as missing value imputation, categorical variable encoding, input feature normalization, uncertainty quantification, exploratory data analysis (EDA), etc. MLtool was tested on several publicly available multi-dimensional data sets and was found capable of making accurate predictions.

Machine learning↗

NASA NTRSDate not supplied

Envisioning the Future of International Earth Observations Collaboration: Area and Map Accuracy Estimation by Sampling

- Maps have errors, sometimes a lot of errors ⇒ obtaining information directly from map problematic; any use of the map will benefit from information about errors/uncertainty - IPCC: unbiasedness and uncertainty - By randomly drawing a sample from the study area, observing reference conditions at drawn locations, and constructing estimators – easily estimate areas and map accuracy ± uncertainty - Sampling design and analysis, relatively easy – collecting reference observations is not. Cloud-based solutions, e.g. AREA2, Collect Earth Online, facilitate the collection of reference observations - More research and guidance needed!

Pontus Olofsson↗

NASA NTRS2022

MLtool Python Code

Machine Learning↗

NASA NTRSDate not supplied

Aerothermal Analysis and Thermal Protection System Design of the Mars Sample Retrieval Lander [SRL].

Mars Sample Retrieval Lander, part of the Mars Sample Return (MSR) mission, is being designed to land the heaviest payload yet, to the surface of Mars. SRL is being designed to carry the Lander, Sample Transfer System, Mars Acent Vehicle, and two Sample Recovery Helicopters. Compared to MSL and Mars 2020, SRL has a significantly higher ballistic coefficient, and flies at a higher lift/drag configuration. While the SRL heatshield is very similar to that of MSL and M2020, the backshell is very different, so as to accommode the payload. SRL is shielded by the same TPS materials as MSL and Mars 2020, with changes to design reflecting the SRL configuration and ConOPS. The aerothermal analysis and TPS design methodology of SRL relies on the successes of MSL and Mars 2020, and the lessons learned from MEDLI and MEDLI2. However, the constraints on mass require us to revisit all of our prediction models and analysis assumptions, in an attempt to reduce conservatism and TPS mass. MSL and Mars 2020 reconstruction, and detailed comparisons against MEDLI/MEDLI2 data are being used to justify our analysis approach and refine uncertainties and margins.

Mars↗

NASA NTRSDate not supplied

Reduction of Aircraft Noise Uncertainty for a Notional Supersonic Business Jet

NASA supported a study by the International Civil Aviation Organization on the environmental impact of adding supersonic aircraft to the existing global fleet by designing a notional 55-tonne supersonic business jet. The aircraft is referred to as the Supersonic Technology Concept Aeroplane (STCA) and has been used in a multitude of studies over the past few years. One of the many studies on this aircraft was the noise produced by the STCA during landing and take-off (LTO) operations. The LTO noise for the STCA was assessed using contemporary noise prediction tools that have been primarily developed for and utilized by subsonic aircraft, resulting in a high level of uncertainty for the STCA noise predictions. NASA has recently been conducting research and developing tools to reduce the uncertainty for airport noise predictions of supersonic aircraft. The initial focus of the uncertainty reduction was on the jet and inlet-radiated fan noise produced by supersonic engine systems since these sources are dominant during take-off and landing operations for supersonic jets. The results of these efforts are discussed and applied to the STCA model to update the airport noise predictions and associated uncertainty metrics. It is shown that by using new noise source prediction models, the overall system-level cumulative noise uncertainty of the study vehicle is reduced from a standard deviation of 7.8 EPNdB to 2.0 EPNdB.

uncertainty↗

NASA NTRS2020

How Long Is Too Long? Variogram Analysis of AERONET Data to Aid Aerosol Validation and Intercomparison Studies

Geophysical data sets derived from satellite sensors, ground/airborne instrumentation, and computational models are often compared against each other. A common example is the validation of satellite aerosol optical depth (AOD) retrievals against measurements from Aerosol Robotic Network (AERONET) Sun photometers. Spatiotemporal mismatch between data set sampling means that uncaptured variation in the underlying geophysical field introduces apparent disagreement into such comparisons, known as representation or collocation matchup uncertainty. This study uses variogram analysis of AERONET data to estimate temporal mismatch uncertainties and decorrelation time scales for the global AERONET record. As well as total AOD, the fine‐ and coarse‐mode AODs, Ångström Exponent (AE), and fine‐mode fraction (FMF) of AOD are analyzed. Globally, a time difference of 30 min typically induces from 0.011–0.035 variation in AOD. For total, fine, and coarse AODs the typical time to decorrelation is around 2–10 days. For AE and FMF it is 3–33 days; that is, aerosol systems often persist significantly longer than individual events in them. Biomass burning regions tend to show the largest and fastest subdaily AOD variability and also longest times to decorrelation. Some sites show significant season‐to‐season variations in behavior. These results can be used to inform site‐specific time collocation thresholds for aerosol validation analyses and account for temporal variation when estimating data set uncertainty. They also have implications for comparisons between different satellite products or models, data aggregation, and time series analyses. Results are provided on a site‐by‐site basis to facilitate use by other researchers.

satellite↗

NASA NTRS2018

Multifidelity Uncertainty Quantification of a Commercial Supersonic Transport

The objective of this work was to develop a multifidelity uncertainty quantification approach for efficient analysis of a commercial supersonic transport concept. An approach based on point-collocation, non-intrusive polynomial chaos was formulated in which a low-fidelity model could be corrected using multiple higher-fidelity models. The formulation and methodology also allows for the addition of uncertainty sources not present in the lower fidelity models. To demonstrate the applicability and potential computational savings of the multifidelity polynomial chaos approach, two model problems were explored. The first was a supersonic airfoil with three levels of modeling fidelity, each capturing a gradual increase in modeling of the underlying flow physics. As much as 50% computational cost reduction was observed using the mutlifidelity approach, while predicting nearly the same amount of uncertainty in drag. The second problem was a commercial supersonic transport. This model had three levels of fidelity that included two different modeling approaches and the addition of physics between the fidelity levels. Results of this analysis yielded nearly a 70% computational savings to predict a comparable amount of uncertainty in ground noise. Both problems illustrate the applicability and significant computational savings of the multifidelity method for efficient and accurate uncertainty quantification.

Thomas K. West IV↗

NASA NTRS2009

Bounded Linear Stability Analysis - A Time Delay Margin Estimation Approach for Adaptive Control

This paper presents a method for estimating time delay margin for model-reference adaptive control of systems with almost linear structured uncertainty. The bounded linear stability analysis method seeks to represent the conventional model-reference adaptive law by a locally bounded linear approximation within a small time window using the comparison lemma. The locally bounded linear approximation of the combined adaptive system is cast in a form of an input-time-delay differential equation over a small time window. The time delay margin of this system represents a local stability measure and is computed analytically by a matrix measure method, which provides a simple analytical technique for estimating an upper bound of time delay margin. Based on simulation results for a scalar model-reference adaptive control system, both the bounded linear stability method and the matrix measure method are seen to provide a reasonably accurate and yet not too conservative time delay margin estimation.

Nguyen, Nhan T.↗

NASA NTRS2012

Robustness Analysis and Optimally Robust Control Design via Sum-of-Squares

A control analysis and design framework is proposed for systems subject to parametric uncertainty. The underlying strategies are based on sum-of-squares (SOS) polynomial analysis and nonlinear optimization to design an optimally robust controller. The approach determines a maximum uncertainty range for which the closed-loop system satisfies a set of stability and performance requirements. These requirements, de ned as inequality constraints on several metrics, are restricted to polynomial functions of the uncertainty. To quantify robustness, SOS analysis is used to prove that the closed-loop system complies with the requirements for a given uncertainty range. The maximum uncertainty range, calculated by assessing a sequence of increasingly larger ranges, serves as a robustness metric for the closed-loop system. To optimize the control design, nonlinear optimization is used to enlarge the maximum uncertainty range by tuning the controller gains. Hence, the resulting controller is optimally robust to parametric uncertainty. This approach balances the robustness margins corresponding to each requirement in order to maximize the aggregate system robustness. The proposed framework is applied to a simple linear short-period aircraft model with uncertain aerodynamic coefficients.

Dorobantu, Andrei↗

NASA NTRS2004

Application of Non-Deterministic Methods to Assess Modeling Uncertainties for Reinforced Carbon-Carbon Debris Impacts

The Space Shuttle Columbia Accident Investigation Board (CAIB) made several recommendations for improving the NASA Space Shuttle Program. An extensive experimental and analytical program has been developed to address two recommendations related to structural impact analysis. The objective of the present work is to demonstrate the application of probabilistic analysis to assess the effect of uncertainties on debris impacts on Space Shuttle Reinforced Carbon-Carbon (RCC) panels. The probabilistic analysis is used to identify the material modeling parameters controlling the uncertainty. A comparison of the finite element results with limited experimental data provided confidence that the simulations were adequately representing the global response of the material. Five input parameters were identified as significantly controlling the response.

Lyle, Karen H.↗

NASA NTRS2006

Closed-Loop Evaluation of an Integrated Failure Identification and Fault Tolerant Control System for a Transport Aircraft

Formal robustness analysis of aircraft control upset prevention and recovery systems could play an important role in their validation and ultimate certification. Such systems developed for failure detection, identification, and reconfiguration, as well as upset recovery, need to be evaluated over broad regions of the flight envelope or under extreme flight conditions, and should include various sources of uncertainty. To apply formal robustness analysis, formulation of linear fractional transformation (LFT) models of complex parameter-dependent systems is required, which represent system uncertainty due to parameter uncertainty and actuator faults. This paper describes a detailed LFT model formulation procedure from the nonlinear model of a transport aircraft by using a preliminary LFT modeling software tool developed at the NASA Langley Research Center, which utilizes a matrix-based computational approach. The closed-loop system is evaluated over the entire flight envelope based on the generated LFT model which can cover nonlinear dynamics. The robustness analysis results of the closed-loop fault tolerant control system of a transport aircraft are presented. A reliable flight envelope (safe flight regime) is also calculated from the robust performance analysis results, over which the closed-loop system can achieve the desired performance of command tracking and failure detection.

Shin, Jong-Yeob↗

NASA NTRSDate not supplied

Uncertainty Estimation for SMAP Level-1 Brightness Temperature Assimilation at Different Timescales

In this study, we assimilate Soil Moisture Active Passive (SMAP) mission brightness temperature (Tb) observations into NASA’s Catchment Land Surface Model using an Ensemble Kalman filter to update surface and root-zone soil moisture simulations. Different time series components of the Tb observations are assimilated including anomalies, inter-annual variations, and high-frequency variations. To optimize the weights that the data assimilation (DA) puts on the observations, the ratio between the un-certainties of modeled and observed Tb is approximated using modeled and observed soil moisture uncertainties estimated using triple collocation analysis. Results are compared to a benchmark experiment that mimics the operational SMAP Level-4 algorithm, which assimilates Tb observations using a spatially-constant 4 Kelvin (K) observation uncertainty. All DA experiments exhibit notable skill improvements in most regions. Improvements are greatest for the inter-annual variations in the simulations of both surface and root-zone soil moisture (mean improvements in terms of Pearson correlation (-) are 0.08 and 0.06, respectively). Anomaly simulations improve similarly (0.07), and improvements in the high-frequency variations are only observed for sur-face soil moisture simulations (0.06). Strikingly, however, no notable difference in skill—neither improvement nor deterioration—is observed between the experiments that use optimized observation uncertainty parameters and the 4 K benchmark experiment. We show, analytically, that this may be explained by the presence of large observation operator errors, which have the potential to render post-update uncertainty insensitive to inaccuracies in the Kalman gain.

Alexander Gruber↗

NASA NTRS1998

Robust Flutter Margin Analysis that Incorporates Flight Data

An approach for computing worst-case flutter margins has been formulated in a robust stability framework. Uncertainty operators are included with a linear model to describe modeling errors and flight variations. The structured singular value, mu, computes a stability margin that directly accounts for these uncertainties. This approach introduces a new method of computing flutter margins and an associated new parameter for describing these margins. The mu margins are robust margins that indicate worst-case stability estimates with respect to the defined uncertainty. Worst-case flutter margins are computed for the F/A-18 Systems Research Aircraft using uncertainty sets generated by flight data analysis. The robust margins demonstrate flight conditions for flutter may lie closer to the flight envelope than previously estimated by p-k analysis.

Lind, Rick↗

NASA NTRS1991

Collisional cascading - The limits of population growth in low earth orbit

Random collisions between made-made objects in earth orbit will lead to a significant source of orbital debris, but there are a number of uncertainties in these models, and additional analysis and data are required to fully characterize the future environment. However, the nature of these uncertainties are such that while the future environment is uncertain, the fact that collisions will control the future environment is less uncertain. The data that already exist is sufficient to show that cascading collisions will control the future debris environment with no, or very minor increases in the current low-earth-orbit population. Two populations control this process: explosion fragments and expended rocket bodies and payloads. Practices are already changing to limit explosions in low earth orbit; it is necessary to begin limiting the number of expended rocket bodies and payloads in orbit.

Kessler, Donald J.↗