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NASA NTRS2019

Continuously Improving Parametric Modeling with Historical Data on the ICESat-2 Mission

This paper delves into the details of the Joint Confidence Level (JCL) process performed for the Ice, Cloud, and Land Elevation Satellite (ICESat)-2 mission and how past performance was incorporated into subsequent JCL models to enable the project to continuously analyze potential slips to their launch readiness date (LRD). One year prior to the mission Preliminary Review (mPDR), the JCL model development process began. The first model was well received at the mPDR, held on October 10, 2012, and the input received by the Standing Review Board was incorporated into the model for the official data drop for key decision point (KDP)-C. The 70% JCL results of the October 2012 mPDR model forecast an LRD of February 2017 and associated cost of $830M. This result in 2012 immediately highlighted potential challenges with the project-planned LRD of July 2016. The year following the mPDR, the project had sustained a oneyear slip in the LRD due to problematic systems engineering requirement issues which impacted all project subsystems. This slip moved the project planned LRD from July 2016 to July 2017, an additional 5 months beyond the 2012 model’s 70% JCL result for the LRD of February 2017. As the project was quickly approaching the mission Critical Design Review (mCDR), the need for reliable JCL results increased significantly. The project held discussions on the JCL modeling process and focused on the input uncertainty distributions. Specifically, to identify the uncertainty distributions that the 2012 mPDR model would have needed to produce a 70% LRD result of July 2017. This led the project to compare multiple uncertainty distributions, and ultimately spurred the project to utilize uncertainty distributions that incorporated project past performance and historical data to forecast potential LRD slips. The revised results, created in 2014 and utilizing the new uncertainty distributions, showed that with 70% confidence, the ICESat-2 mission would launch in August 2018 with a cost of $1,044M. Today, ICESat-2 is scheduled to launch on September 15, 2018 with a project management (PM) agreement value of $1,056M. This illustrates how a JCL model can be continuously improved to produce valuable results for a project, even in cases of LRD delays. The primary reason for the ICESat-2 LRD delay is due to a laser failure on the primary instrument. Laser failure was one of the highest risk and uncertainty drivers within the JCL model. The project placed the most risk in this area of the model, and the model further identified the laser as the top risk driver and contributor to the LRD result. This further illustrates how a JCL can be used to predict and quantify possible issues on new technology missions.

Krygiel, Joseph↗

NASA NTRS2011

Probabilistic Analysis of a Composite Crew Module

An approach for conducting reliability-based analysis (RBA) of a Composite Crew Module (CCM) is presented. The goal is to identify and quantify the benefits of probabilistic design methods for the CCM and future space vehicles. The coarse finite element model from a previous NASA Engineering and Safety Center (NESC) project is used as the baseline deterministic analysis model to evaluate the performance of the CCM using a strength-based failure index. The first step in the probabilistic analysis process is the determination of the uncertainty distributions for key parameters in the model. Analytical data from water landing simulations are used to develop an uncertainty distribution, but such data were unavailable for other load cases. The uncertainty distributions for the other load scale factors and the strength allowables are generated based on assumed coefficients of variation. Probability of first-ply failure is estimated using three methods: the first order reliability method (FORM), Monte Carlo simulation, and conditional sampling. Results for the three methods were consistent. The reliability is shown to be driven by first ply failure in one region of the CCM at the high altitude abort load set. The final predicted probability of failure is on the order of 10-11 due to the conservative nature of the factors of safety on the deterministic loads.

FROM↗

NASA NTRS2016

A Review of Recent Updates of Sea-Level Projections at Global and Regional Scales

Sea-level change (SLC) is a much-studied topic in the area of climate research, integrating a range of climate science disciplines, and is expected to impact coastal communities around the world. As a result, this field is rapidly moving, and the knowledge and understanding of processes contributing to SLC is increasing. Here, we discuss noteworthy recent developments in the projection of SLC contributions and in the global mean and regional sea-level projections. For the Greenland Ice Sheet contribution to SLC, earlier estimates have been confirmed in recent research, but part of the source of this contribution has shifted from dynamics to surface melting. New insights into dynamic discharge processes and the onset of marine ice sheet instability increase the projected range for the Antarctic contribution by the end of the century. The contribution from both ice sheets is projected to increase further in the coming centuries to millennia. Recent updates of the global glacier outline database and new global glacier models have led to slightly lower projections for the glacier contribution to SLC (7-17 cm by 2100), but still project the glaciers to be an important contribution. For global mean sea-level projections, the focus has shifted to better estimating the uncertainty distributions of the projection time series, which may not necessarily follow a normal distribution. Instead, recent studies use skewed distributions with longer tails to higher uncertainties. Regional projections have been used to study regional uncertainty distributions, and regional projections are increasingly being applied to specific regions, countries, and coastal areas.

glaciers↗

NASA NTRS2021

Expected Collision Rates for Tracked Satellites

This analysis estimates collision risks between tracked satellites based on the statistically expected collision rate _Nc and number of collisions Nc, which are closely related to the collision probability Pc. For isolated encounters, Nc equals Pc. For multi-encounter interactions, Nc can exceed Pc and is significantly easier to approximate semi-analytically. Estimating Nc requires integrating the collision rate over time throughout an interaction, with each required _Nc value calculated as a statistical expectation value based on the uncertainty distributions of initial orbital states. The uncertainty distributions are estimated from orbit determination analyses of satellite trajectory measurements. The formulation accounts for the nonlinear orbital motion of the satellites, and derives Nc and _Nc expressions for Monte Carlo simulations as well as semi-analytical approximations for single- and multi-encounter interactions.

Collision Rates↗

NASA NTRS1993

Positive phase space distributions and uncertainty relations

In contrast to a widespread belief, Wigner's theorem allows the construction of true joint probabilities in phase space for distributions describing the object system as well as for distributions depending on the measurement apparatus. The fundamental role of Heisenberg's uncertainty relations in Schroedinger form (including correlations) is pointed out for these two possible interpretations of joint probability distributions. Hence, in order that a multivariate normal probability distribution in phase space may correspond to a Wigner distribution of a pure or a mixed state, it is necessary and sufficient that Heisenberg's uncertainty relation in Schroedinger form should be satisfied.

Kruger, Jan↗

NASA NTRS2016

The Near-Earth Meteoroid Flux, Speed Distribution, and Uncertainty

Meteoroids are known to pose a threat to spacecraft; they can puncture components, disturb spacecraft attitude, and possibly create secondary electrical effects. Accurate environment models are therefore critical for mitigating meteoroid-related risks. While there are several meteoroid environment models available for assessing spacecraft risk, the uncertainties associated with these models are not well understood. Because meteoroid properties are derived from indirect observations such as meteors and impact craters, the uncertainty in the meteoroid flux is potentially quite large. We combine existing meteoroid flux measurements with new radar and optical meteor data to improve our characterization of the meteoroid flux onto the Earth and its velocity distribution. We use data extracted from the NASA all-sky network, the Canadian Automated Meteor Observatory, and the Canadian Meteor Orbit Radar. We improve our characterization of the observed meteoroid speed distribution by incorporating modern descriptions of the ionization efficiency (e.g., Thomas et al., 2016). We also present estimates of the uncertainties associated with our meteoroid flux distribution. Finally, we discuss the implications for spacecraft. Our model is constrained by the cratering rate on the space-facing surface of LDEF, and thus the risk posed to spacecraft by meteoroid-induced physical damage is the least uncertain component of our model. Other sources of risk, however, may vary. For instance, a lower average meteoroid speed would require a higher meteoroid mass flux in order to match the LDEF crater counts, leading to higher predicted rates of attitude disturbances.

Moorhead, Althea↗

NASA NTRS2007

Managing Uncertainty Due to a Fundamental Error Source Arising from Scatterer Distribution Complexity in Radar Remote Sensing of Precipitation

The assumption that cloud and rain drops are spatially distributed according to a Poisson distribution within a scattering volume probed by a radar being used to estimate precipitation has represented bedrock theory in establishing 'rules of the game' for pulse averaging--the process needed to beat down noise to an acceptable level in the measurement of radar reflectivity factor. Based on relatively recent observations of 'realistic' spatial distributions of hydrometeor scatterers in a cloudy atmosphere motivates a renewed examination of the consequences of using a too simplified assumption underlying volume scattering--particularly in regards to the standard pulse averaging rule. Our investigation addresses two extremes, simple to complex, insofar as allowed for complexities in an underlying scatterer distribution. It is demonstrated that as the spatial distribution ranges from Poisson (a narrow distribution) to multi-fractal (much broader distribution), uncertainty in a measurement increases if the rule for pulse averaging goes unchanged from its Poisson distribution reference county. [A bounded cascade is used for the multi-fractal distribution, a regularly observed distribution vis-a-vis cloud liquid water content.] The resultant measurement uncertainty leads to a fundamental source of error in the estimation of rain rate from radar measurements, one that has been disregarded since the early 1950s when radar sets first began to be used for rainfall measuring. It is shown how this source of error can be 'managed'--under the assumption that number of data analysis experiments would be carried out, experiments involving pulse-by-pulse measurements obtained from a radar set modified to output individual pulses of reflectivity factor. For practical applications, a new parameter called normalized k-sample intensity invariance is developed to enable defining the required pulse average count according to a preferred degree of uncertainty.

Smith, Eric A.↗

NASA NTRS2004

Uncertainties in estimates of the risks of late effects from space radiation

Methods used to project risks in low-Earth orbit are of questionable merit for exploration missions because of the limited radiobiology data and knowledge of galactic cosmic ray (GCR) heavy ions, which causes estimates of the risk of late effects to be highly uncertain. Risk projections involve a product of many biological and physical factors, each of which has a differential range of uncertainty due to lack of data and knowledge. Using the linear-additivity model for radiation risks, we use Monte-Carlo sampling from subjective uncertainty distributions in each factor to obtain an estimate of the overall uncertainty in risk projections. The resulting methodology is applied to several human space exploration mission scenarios including a deep space outpost and Mars missions of duration of 360, 660, and 1000 days. The major results are the quantification of the uncertainties in current risk estimates, the identification of factors that dominate risk projection uncertainties, and the development of a method to quantify candidate approaches to reduce uncertainties or mitigate risks. The large uncertainties in GCR risk projections lead to probability distributions of risk that mask any potential risk reduction using the "optimization" of shielding materials or configurations. In contrast, the design of shielding optimization approaches for solar particle events and trapped protons can be made at this time and promising technologies can be shown to have merit using our approach. The methods used also make it possible to express risk management objectives in terms of quantitative metrics, e.g., the number of days in space without exceeding a given risk level within well-defined confidence limits. Published by Elsevier Ltd on behalf of COSPAR.

Non-NASA Center↗

NASA NTRS2016

Lessons from Climate Modeling on the Design and Use of Ensembles for Crop Modeling

Working with ensembles of crop models is a recent but important development in crop modeling which promises to lead to better uncertainty estimates for model projections and predictions, better predictions using the ensemble mean or median, and closer collaboration within the modeling community. There are numerous open questions about the best way to create and analyze such ensembles. Much can be learned from the field of climate modeling, given its much longer experience with ensembles. We draw on that experience to identify questions and make propositions that should help make ensemble modeling with crop models more rigorous and informative. The propositions include defining criteria for acceptance of models in a crop MME, exploring criteria for evaluating the degree of relatedness of models in a MME, studying the effect of number of models in the ensemble, development of a statistical model of model sampling, creation of a repository for MME results, studies of possible differential weighting of models in an ensemble, creation of single model ensembles based on sampling from the uncertainty distribution of parameter values or inputs specifically oriented toward uncertainty estimation, the creation of super ensembles that sample more than one source of uncertainty, the analysis of super ensemble results to obtain information on total uncertainty and the separate contributions of different sources of uncertainty and finally further investigation of the use of the multi-model mean or median as a predictor.

Model ensembles↗

NASA NTRS2002

Uncertainties in Estimates of the Risks of Late Effects from Space Radiation

The health risks faced by astronauts from space radiation include cancer, cataracts, hereditary effects, and non-cancer morbidity and mortality risks related to the diseases of the old age. Methods used to project risks in low-Earth orbit are of questionable merit for exploration missions because of the limited radiobiology data and knowledge of galactic cosmic ray (GCR) heavy ions, which causes estimates of the risk of late effects to be highly uncertain. Risk projections involve a product of many biological and physical factors, each of which has a differential range of uncertainty due to lack of data and knowledge. Within the linear-additivity model, we use Monte-Carlo sampling from subjective uncertainty distributions in each factor to obtain a Maximum Likelihood estimate of the overall uncertainty in risk projections. The resulting methodology is applied to several human space exploration mission scenarios including ISS, lunar station, deep space outpost, and Mar's missions of duration of 360, 660, and 1000 days. The major results are the quantification of the uncertainties in current risk estimates, the identification of factors that dominate risk projection uncertainties, and the development of a method to quantify candidate approaches to reduce uncertainties or mitigate risks. The large uncertainties in GCR risk projections lead to probability distributions of risk that mask any potential risk reduction using the "optimization" of shielding materials or configurations. In contrast, the design of shielding optimization approaches for solar particle events and trapped protons can be made at this time, and promising technologies can be shown to have merit using our approach. The methods used also make it possible to express risk management objectives in terms of quantitative objective's, i.e., the number of days in space without exceeding a given risk level within well defined confidence limits.

Cucinotta, F. A.↗

NASA NTRS2017

Methods for Probabilistic Uncertainty Analysis and Bayesian Analysis with Examples of Statistically Analyzing Data to Revise MMOD Risk Estimates and Compare Models

Probabilistic methods are presented for characterizing and quantifying uncertainties in models and model predictions. Techniques are given for constructing specific uncertainty distributions based on available information. Alternative techniques are given for propagating uncertainties in model inputs to obtain the uncertainty in the model result or prediction. Bayesian techniques are also described for utilizing data and information to update and revise model results and predictions. The focus is on applications with numerous specific examples given. The use of data to revise Micrometeoroid and Orbital Debris (MMOD) risk prediction models are among the examples given.

Risk↗

NASA NTRSDate not supplied

It Depends - An Overview of Probabilistic Risk Analysis Concepts

How do you understand the data and assumptions in your probabilistic analysis? The PRA analyst needs to understand the data and input assumptions to effectively communicate the system/mission's risks. The decision maker also needs to understand conservatisms and how to interpret uncertainty in the PRA results. Properties such as assumptions on the distributions, uncertainty, use of test data, and common cause modeling can be the subject of much discussion, but often are the leading drivers of a risk profile.

risk assessment↗

NASA NTRSDate not supplied

Proposed Reliability-Based Damage Tolerance Guidelines for Space Systems

Deterministic damage tolerance guidelines for highly reusable and efficiently designed launch systems can be challenging to meet and result in overly conservative assessments for tightly controlled manufacturing processes. Deterministic approaches may be unconservative when the structure is workmanship sensitive and there is a wide spread in fracture properties. Reliability-based damage tolerance assessments targeting a component reliability over the service life commensurate to mission risk posture is a promising alternative. Low production rates, short fleets, and lack of standards or guidance has slowed down widespread adoption of this method. Guidance for the robust application of reliability-based damage tolerance for space systems are proposed. These guidelines cover the treatment of uncertainty in damage tolerance analysis, the collection of data to develop probabilistic distributions, uncertainty propagation methods, and types of hardware.

Reliability-Based Damage Tolerance↗

NASA NTRS1985

Flight-Stability Extremes Calculated From the Uncertainty Ellipse

Tangents and normals to ellipse derived for situations with two correlated aerodynamic force or moment variables having normally (Gaussian) distributed uncertainty. Although transformations and vector calculations tedious when done by hand, equations in closed form and give rapid results when performed by computers or programable desk calculators. Probability extremes of ratios and magnitude obtained directly, without repeated table lookup or other complication.

Dominik, D. F.↗

NASA NTRS2019

Fast-Time Simulation for Evaluating the Impact of Estimated Flight Ready Time Uncertainty on Surface Metering

NASA has been developing and demonstrating new concepts and technologies for Integrated Arrival, Departure, and Surface (IADS) traffic management capabilities under the Airspace Technology Demonstration 2 (ATD-2) project. One of the IADS capabilities in the ATD-2 project is surface metering enabled by a tactical surface scheduler to provide controllers with the pushback advisories for departures at gates. The tactical surface scheduler uses the estimated flight ready times provided by airlines, called Earliest Off-Block Times (EOBTs), as input to calculate the target off-block times for pushback advisories. However, the EOBTs are often inaccurate and deviate from the actual flight ready times, which may reduce the benefits of surface metering. In this paper, a linear regression model is developed to model the EOBT uncertainty distribution over time based on actual EOBT data collected at Charlotte airport. This EOBT model is integrated with a tactical surface scheduler and a fast-time simulation tool. To evaluate the impact of the EOBT accuracy on airport surface operations, fast-time simulations are implemented for selected traffic scenarios under different levels of modelled EOBT accuracy. The simulation results show that the EOBT uncertainty affects several performance metrics related to the surface metering, such as gate hold, taxi time reduction, and target takeoff time predictability, which in turn influences ATD-2's scheduler performance.

tactical surface scheduler↗

NASA NTRS2019

Fast-Time Simulation for Evaluating the Impact of Estimated Flight Ready Time Uncertainty on Surface Metering

tactical surface scheduler↗

NASA NTRS1977

Ku-band antenna acquisition and tracking performance study, volume 4

The results pertaining to the tradeoff analysis and performance of the Ku-band shuttle antenna pointing and signal acquisition system are presented. The square, hexagonal and spiral antenna trajectories were investigated assuming the TDRS postulated uncertainty region and a flexible statistical model for the location of the TDRS within the uncertainty volume. The scanning trajectories, shuttle/TDRS signal parameters and dynamics, and three signal acquisition algorithms were integrated into a hardware simulation. The hardware simulation is quite flexible in that it allows for the evaluation of signal acquisition performance for an arbitrary (programmable) antenna pattern, a large range of C/N sub O's, various TDRS/shuttle a priori uncertainty distributions, and three distinct signal search algorithms.

Huang, T. C.↗

NASA NTRS1990

An extragalactic reference frame from DSN VLBI measurements - 1989

Assessment of the impact of recent improvements Deep Space Network (DSN) instrumentation, as well as of joint data analyses, provide a prognosis for the accuracy level to be expected in future realizations of an inertial radio reference frame. Intercontinental dual-frequency radio interferometric measurements during 68 sessions (including two recent sessions employing Mark III instrumentation) from 1978 to 1989 using NASA's DSN stations in California, Spain, and Australia give 8900 pairs of delay and delay-rate observations. Analysis yields a catalog of positions of 200 extragalactic radio sources north of -45 deg declination. The resulting source-position formal uncertainty distributions peak below 1 milliarcsecond, with 75 percent being smaller than 2 mas. Comparison with independent measurements shows some evidence for systematic errors at the milliarcsecond level.

Sovers, O. J.↗