Booster Separation Environment: Experiment and CFD Uncertainty Estimation Framework
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uncertainty quantification↗
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Recent Surface Reflectance Measurement Campaigns with Emphasis on Best Practices, SI Traceability and Uncertainty Estimation
A significant problem facing the optical satellite calibration community is limited knowledge of the uncertainties associated with fundamental measurements, such as surface reflectance, used to derive satellite radiometric calibration estimates. In addition, it is difficult to compare the capabilities of calibration teams around the globe, which leads to differences in the estimated calibration of optical satellite sensors. This paper reports on two recent field campaigns that were designed to isolate common uncertainties within and across calibration groups, particularly with respect to ground-based surface reflectance measurements. Initial results from these efforts suggest the uncertainties can be as low as 1.5% to 2.5%. In addition, methods for improving the cross-comparison of calibration teams are suggested that can potentially reduce the differences in the calibration estimates of optical satellite sensors.
reflectance measurements↗
An Efficient Deterministic Approach to Model-based Prediction Uncertainty Estimation
Prognostics deals with the prediction of the end of life (EOL) of a system. EOL is a random variable, due to the presence of process noise and uncertainty in the future inputs to the system. Prognostics algorithm must account for this inherent uncertainty. In addition, these algorithms never know exactly the state of the system at the desired time of prediction, or the exact model describing the future evolution of the system, accumulating additional uncertainty into the predicted EOL. Prediction algorithms that do not account for these sources of uncertainty are misrepresenting the EOL and can lead to poor decisions based on their results. In this paper, we explore the impact of uncertainty in the prediction problem. We develop a general model-based prediction algorithm that incorporates these sources of uncertainty, and propose a novel approach to efficiently handle uncertainty in the future input trajectories of a system by using the unscented transformation. Using this approach, we are not only able to reduce the computational load but also estimate the bounds of uncertainty in a deterministic manner, which can be useful to consider during decision-making. Using a lithium-ion battery as a case study, we perform several simulation-based experiments to explore these issues, and validate the overall approach using experimental data from a battery testbed.
Daigle, Matthew J.↗
Uncertainty Estimates for Sonic-Boom Pressure Signatures and Loudness Carpets
A non-intrusive uncertainty quantification method is applied to computational analysis of supersonic, low-boom aircraft. The mean and standard deviation statistics of the pressure waveforms and loudness metrics are evaluated through use of numerical quadrature. The probability density function (p.d.f.) of these outputs is evaluated via kernel density estimation. The simulations use an inviscid, embedded-boundary Cartesian-mesh flow solver in the nearfield combined with an augmented Burgers’ equation solver for propagation in the farfield. The results show that the p.d.f. of the waveform is bimodal at shocks, which makes the mean and standard deviation statistics inappropriate. Despite this limitation, we show that the moment statistics can provide effective assessment of discrepancies when comparing with experimental data. This is demonstrated by presenting uncertainty analysis of a wind-tunnel test and showing that we significantly improve the predictions when we include the test uncertainties in the simulation. Normal distributions are obtained for the ground signature and loudness metrics, which is primarily due to the careful shaping of the low-boom waveform. Separation of variables and error control are used to reduce computational cost. We demonstrate that this is an efficient approach in the sense of balancing numerical errors in the statistics quadrature with discretization errors in the solvers.
ARMD↗
Uncertainty estimates in geomagnetic field modeling
This paper presents an extension of the conventional uncertainty analysis which characterizes the sources of uncertainty in the coefficients of the geomagnetic field models. The new formalism accounts for the systematic errors introduced by the omission of such sources as the presence of crustal fields, the external fields, and the field from the truncated terms. The usefulness of this formalism depends on two critical conditions. The first of these is the knowledge of the statistical properties of the fields whose parameters are not solved in the analysis, i.e., the crustal field and the external field. The second critical point in the practical use of the method is the approximation used for the weight matrix.
Langel, R. A.↗
Remote sensing-based vegetation and soil moisture constraints reduce irrigation estimation uncertainty
Understanding the human water footprint and its impact on the hydrological cycle is essential to inform water management under climate change. Despite efforts in estimating irrigation water withdrawals in earth system models, uncertainties and discrepancies exist within and across modeling systems conditioned by model structure, irrigation parameterization, and the choice of input datasets. Achieving model reliability could be much more challenging for data-sparse regions, given limited access to ground truth for parameterization and validation. Here, we demonstrate the potential of utilizing remotely sensed vegetation and soil moisture observations in constraining irrigation estimation in the Noah-MP land surface model. Results indicate that the two constraints together can effectively reduce model sensitivity to the choice of irrigation parameterization by 7%–43%. It also improves the characterization of the spatial patterns of irrigation and its impact on evapotranspiration and surface soil moisture by correcting for vegetation conditions and irrigation timing. This study highlights the importance of utilizing remotely sensed soil moisture and vegetation measurements in detecting irrigation signals and correcting for vegetation growth. Integrating the two remote sensing datasets into the model provides an effective and less feature engineered approach to constraining the uncertainty of irrigation modeling. Such strategies can be potentially transferred to other modeling systems and applied to regions across the globe.
Wanshu Nie↗
Uncertainty Estimation Cheat Sheet for Probabilistic Risk Assessment
Quantitative results for aerospace engineering problems are influenced by many sources of uncertainty. Uncertainty analysis aims to make a technical contribution to decision-making through the quantification of uncertainties in the relevant variables as well as through the propagation of these uncertainties up to the result. Uncertainty can be thought of as a measure of the 'goodness' of a result and is typically represented as statistical dispersion. This paper will explain common measures of centrality and dispersion; and-with examples-will provide guidelines for how they may be estimated to ensure effective technical contributions to decision-making.
Britton, Paul↗
Accounting for Point Estimate Uncertainty in Space Systems Reliability and Risk Analysis
Understanding and accounting for uncertainty in risk analysis is a critical step in the management and communication of risk in engineered systems. The component and system-level analysis to determine the probability of a negative outcome and its consequence is often quantified by a point estimate. Many Program and Enterprise decisions involving technical concerns and issues rely on reliability engineering activities to produce quantified risk analysis to inform the decision making process. At NASA, it is common to use a Probabilistic Risk Analysis (PRA) to inform the overall risk to Loss of Mission or Loss of Crew that involves integration across all spacecraft subsystem fault trees to produce an overall probability of mission failure. The point estimate is an estimate of this overall probability and is an immediate result of a fault tree model. It is the result of a model where the probability of each event is taken to be equal to its mean. The value provides an approximation of the overall mean without running any uncertainty calculations (e.g., no sampling). Using only the point estimate can lead to a false sense of precision and the point estimate may not match the resulting mean when uncertainty is taken into consideration. This paper will explore five conditions that can cause the PRA model mean to diverge from the point estimate and will provide engineers and managers insight into the importance of understanding uncertainty in the elements of PRA models.
Paul J Collier↗
Overview of Combined Error and Uncertainty Estimates for CFD Problems
No abstract available
Posteriori↗
Uncertainty Estimates for Fitting Zernike Polynomials to Discrete Data
Zernike polynomials are a widely used metric in modern optical analysis. They conveniently represent surfaces as a series of weighted terms corresponding to various optical aberrations. Ideally, each term is independent of others in the series, but Zernike polynomials lose this property when working with sets of discrete data. This gives rise to uncertainty in each polynomial’s actual contribution and affects metrology and simulation estimates of their relative weights. Several factors influencing these estimates are the number and arrangement of sample locations, the method for calculating the weights, and the total number of Zernike terms used in the calculation. Discussed is the uncertainty associated with linear regression using random sampling. Other topics reviewed are complex Zernike polynomials and vector spaces of functions.
Zernike Polynomials↗
Trend Detection of Atmospheric Time Series: Incorporating Appropriate Uncertainty Estimates and Handling Extreme Events
This paper is aimed at atmospheric scientists without formal training in statistical theory. Its goal is to, 1) provide a critical review of the rationale for trend analysis of the time series typically encountered in the field of atmospheric chemistry; 2) describe a range of trend-detection methods; and 3) demonstrate effective means of conveying the results to a general audience. Trend detections in atmospheric chemical composition data are often challenged by a variety of sources of uncertainty, which often behave differently to other environmental phenomena such as temperature, precipitation rate, or stream flow, and may require specific methods depending on the science questions to be addressed. Some sources of uncertainty can be explicitly included in the model specification, such as autocorrelation and seasonality, but some inherent uncertainties are difficult to quantify, such as data heterogeneity and measurement uncertainty due to the combined effect of short- and long-term natural variability, instrumental stability, and aggregation of data from sparse sampling frequency. Failure to account for these uncertainties might result in an inappropriate inference of the trends and their estimation errors. On the other hand, the variation in extreme events might be interesting for different scientific questions, for example, the frequency of extremely high surface ozone events and their relevance to human health. In this study we aim to, 1) review trend detection methods for addressing different levels of data complexity in different chemical species; 2) demonstrate that the incorporation of scientifically interpretable covariates can outperform pure numerical curve fitting techniques in terms of uncertainty reduction and improved predictability; 3) illustrate the study of trends based on extreme quantiles that can provide insight beyond standard mean or median based trend estimates; and 4) present an advanced method of quantifying regional trends based on the inter-site correlations of multi-site data. All demonstrations are based on time series of observed trace gases relevant to atmospheric chemistry, but the methods can be applied to other environmental data sets.
Trace gas↗
Models of Wake-Vortex Spreading Mechanisms and Their Estimated Uncertainties
One of the primary constraints on the capacity of the nation's air transportation system is the landing capacity at its busiest airports. Many airports with nearly-simultaneous operations on closely-spaced parallel runways (i.e., as close as 750 ft (246m)) suffer a severe decrease in runway acceptance rate when weather conditions do not allow full utilization. The objective of a research program at NASA Ames Research Center is to develop the technologies needed for traffic management in the airport environment so that operations now allowed on closely-spaced parallel runways under Visual Meteorological Conditions can also be carried out under Instrument Meteorological Conditions. As part of this overall research objective, the study reported here has developed improved models for the various aerodynamic mechanisms that spread and transport wake vortices. The purpose of the study is to continue the development of relationships that increase the accuracy of estimates for the along-trail separation distances available before the vortex wake of a leading aircraft intrudes into the airspace of a following aircraft. Details of the models used and their uncertainties are presented in the appendices to the paper. Suggestions are made as to the theoretical and experimental research needed to increase the accuracy of and confidence level in the models presented and instrumentation required or more precise estimates of the motion and spread of vortex wakes. The improved wake models indicate that, if the following aircraft is upwind of the leading aircraft, the vortex wakes of the leading aircraft will not intrude into the airspace of the following aircraft for about 7s (based on pessimistic assumptions) for most atmospheric conditions. The wake-spreading models also indicate that longer time intervals before wake intrusion are available when atmospheric turbulence levels are mild or moderate. However, if the estimates for those time intervals are to be reliable, further study is necessary to develop the instrumentation and procedures needed to accurately define when the more benign atmospheric conditions exist.
Rossow, Vernon J.↗
Uncertainty Estimates of Psychoacoustic Thresholds Obtained from Group Tests
Adaptive psychoacoustic test methods, in which the next signal level depends on the response to the previous signal, are the most efficient for determining psychoacoustic thresholds of individual subjects. In many tests conducted in the NASA psychoacoustic labs, the goal is to determine thresholds representative of the general population. To do this economically, non-adaptive testing methods are used in which three or four subjects are tested at the same time with predetermined signal levels. This approach requires us to identify techniques for assessing the uncertainty in resulting group-average psychoacoustic thresholds. In this presentation we examine the Delta Method of frequentist statistics, the Generalized Linear Model (GLM), the Nonparametric Bootstrap, a frequentist method, and Markov Chain Monte Carlo Posterior Estimation and a Bayesian approach. Each technique is exercised on a manufactured, theoretical dataset and then on datasets from two psychoacoustics facilities at NASA. The Delta Method is the simplest to implement and accurate for the cases studied. The GLM is found to be the least robust, and the Bootstrap takes the longest to calculate. The Bayesian Posterior Estimate is the most versatile technique examined because it allows the inclusion of prior information.
Rathsam, Jonathan↗
Phase-Retrieval Uncertainty Estimation and Algorithm Comparison for the JWST-ISIM Test Campaign
Phase retrieval, the process of determining the exitpupil wavefront of an optical instrument from image-plane intensity measurements, is the baseline methodology for characterizing the wavefront for the suite of science instruments (SIs) in the Integrated Science Instrument Module (ISIM) for the James Webb Space Telescope (JWST). JWST is a large, infrared space telescope with a 6.5-meter diameter primary mirror. JWST is currently NASA's flagship mission and will be the premier space observatory of the next decade. ISIM contains four optical benches with nine unique instruments, including redundancies. ISIM was characterized at the Goddard Space Flight Center (GSFC) in Greenbelt, MD in a series of cryogenic vacuum tests using a telescope simulator. During these tests, phase-retrieval algorithms were used to characterize the instruments. The objective of this paper is to describe the Monte-Carlo simulations that were used to establish uncertainties (i.e., error bars) for the wavefronts of the various instruments in ISIM. Multiple retrieval algorithms were used in the analysis of ISIM phase-retrieval focus-sweep data, including an iterativetransform algorithm and a nonlinear optimization algorithm. These algorithms emphasize the recovery of numerous optical parameters, including low-order wavefront composition described by Zernike polynomial terms and high-order wavefront described by a point-by-point map, location of instrument best focus, focal ratio, exit-pupil amplitude, the morphology of any extended object, and optical jitter. The secondary objective of this paper is to report on the relative accuracies of these algorithms for the ISIM instrument tests, and a comparison of their computational complexity and their performance on central and graphical processing unit clusters. From a phase-retrieval perspective, the ISIM test campaign includes a variety of source illumination bandwidths, various image-plane sampling criteria above and below the Nyquist- Shannon critical sampling value, various extended object sizes, and several other impactful effects.
Design Analysis↗
Estimating uncertainty in daily weather interpolations: a Bayesian framework for developing climate surfaces
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Adam M. Wilson↗
Uncertainty estimation via preflight test procedures for a space stabilized inertial navigation system
Preflight operation and alignment of space stabilized inertial navigation system for vertical takeoff aircraft
Johansen, H. K.↗
Ozone perturbations by enhanced levels of CFCs, N2O, and CH4 A two-dimensional diabatic circulation study including uncertainty estimates
Observations made over the last few years suggest that the tropospheric concentrations of N2O, CH4, and O3 are increasing. Increases in the concentration of chlorofluorocarbons (CFCs) have been observed for some time. The present study is concerned with combined scenarios of future releases of N2O, CH4, and CFCs, which can affect the height profiles of ozone, while changes in latitudinal gradients of ozone may also be expected. Ozone perturbation calculations performed in the two-dimensional transport-chemistry model described by Stordal et al. (1985) are also presented, and the effects of increased levels of CFCs, N2O, and CH4 are examined. It is found that CH4 may be the most important ozone-perturbing trace species in connection with future tropospheric climatic impacts. A substantial increase in the tropospheric abundancy of CH4 could lead to large future ozone enhancements throughout the troposphere and lower stratosphere at middle and low latitudes.
Isaksen, I. S. A.↗
Employing Sensitivity Derivatives to Estimate Uncertainty Propagation in CFD
Two methods that exploit the availability of sensitivity derivatives are successfully employed to predict uncertainty propagation through Computational Fluid Dynamics (CFD) code for an inviscid airfoil problem. An approximate statistical second-moment method and a Sensitivity Derivative Enhanced Monte Carlo (SDEMC) method are successfully demonstrated on a two-dimensional problem. First- and second-order sensitivity derivatives of code output with respect to code input are obtained through an efficient incremental iterative approach. Given uncertainties in statistically independent, random, normally distributed flow parameters (input variables); these sensitivity derivatives enable one to formulate first- and second-order Taylor Series approximations for the mean and variance of CFD output quantities. Additionally, incorporation of the first-order sensitivity derivatives into the data reduction phase of a conventional Monte Carlo (MC) simulation allows for improved accuracy in determining the first moment of the CFD output. Both methods are compared to results generated using a conventional MC method. The methods that exploit the availability of sensitivity derivatives are found to be valid when considering small deviations from input mean values.
Putko, Michele M.↗