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NASA NTRS2006

Adapting Covariance Propagation to Account for the Presence of Modeled and Unmodeled Maneuvers

This paper explores techniques that can be used to adapt the standard linearized propagation of an orbital covariance matrix to the case where there is a maneuver and an associated execution uncertainty. A Monte Carlo technique is used to construct a final orbital covariance matrix for a 'propagate-burn-propagate' process that takes into account initial state uncertainty and execution uncertainties in the maneuver magnitude. This final orbital covariance matrix is regarded as 'truth' and comparisons between it and three methods using modified linearized covariance propagation are made. The first method accounts for the maneuver by modeling its nominal effect within the state transition matrix but excludes the execution uncertainty by omitting a process noise matrix from the computation. In the second method, the maneuver is not modeled but the uncertainty in its magnitude is accounted for by the inclusion of a process noise matrix. In the third method, which is essentially a hybrid of the first two, the nominal portion of the maneuver is included via the state transition matrix while a process noise matrix is used to account for the magnitude uncertainty. Since this method also correctly accounts for the presence of the maneuver in the nominal orbit, it is the best method for applications involving the computation of times of closest approach and the corresponding probability of collision, Pc. However, applications for the two other methods exist and are briefly discussed. Despite the fact that the process model ('propagate-burn-propagate') that was studied was very simple - point-mass gravitational effects due to the Earth combined with an impulsive delta-V in the velocity direction for the maneuver - generalizations to more complex scenarios, including high fidelity force models, finite duration maneuvers, and maneuver pointing errors, are straightforward and are discussed in the conclusion.

Schiff, Conrad↗

NASA NTRS2010

Impact of Damping Uncertainty on SEA Model Response Variance

Statistical Energy Analysis (SEA) is commonly used to predict high-frequency vibroacoustic levels. This statistical approach provides the mean response over an ensemble of random subsystems that share the same gross system properties such as density, size, and damping. Recently, techniques have been developed to predict the ensemble variance as well as the mean response. However these techniques do not account for uncertainties in the system properties. In the present paper uncertainty in the damping loss factor is propagated through SEA to obtain more realistic prediction bounds that account for both ensemble and damping variance. The analysis is performed on a floor-equipped cylindrical test article that resembles an aircraft fuselage. Realistic bounds on the damping loss factor are determined from measurements acquired on the sidewall of the test article. The analysis demonstrates that uncertainties in damping have the potential to significantly impact the mean and variance of the predicted response.

Schiller, Noah↗

NASA NTRS2014

Uncertainty Quantification and Certification Prediction of Low-Boom Supersonic Aircraft Configurations

The primary objective of this work was to develop and demonstrate a process for accurate and efficient uncertainty quantification and certification prediction of low-boom, supersonic, transport aircraft. High-fidelity computational fluid dynamics models of multiple low-boom configurations were investigated including the Lockheed Martin SEEB-ALR body of revolution, the NASA 69 Delta Wing, and the Lockheed Martin 1021-01 configuration. A nonintrusive polynomial chaos surrogate modeling approach was used for reduced computational cost of propagating mixed, inherent (aleatory) and model-form (epistemic) uncertainty from both the computation fluid dynamics model and the near-field to ground level propagation model. A methodology has also been introduced to quantify the plausibility of a design to pass a certification under uncertainty. Results of this study include the analysis of each of the three configurations of interest under inviscid and fully turbulent flow assumptions. A comparison of the uncertainty outputs and sensitivity analyses between the configurations is also given. The results of this study illustrate the flexibility and robustness of the developed framework as a tool for uncertainty quantification and certification prediction of low-boom, supersonic aircraft.

West, Thomas K., IV↗

NASA NTRS2015

Calibration of Predictor Models Using Multiple Validation Experiments

This paper presents a framework for calibrating computational models using data from several and possibly dissimilar validation experiments. The offset between model predictions and observations, which might be caused by measurement noise, model-form uncertainty, and numerical error, drives the process by which uncertainty in the models parameters is characterized. The resulting description of uncertainty along with the computational model constitute a predictor model. Two types of predictor models are studied: Interval Predictor Models (IPMs) and Random Predictor Models (RPMs). IPMs use sets to characterize uncertainty, whereas RPMs use random vectors. The propagation of a set through a model makes the response an interval valued function of the state, whereas the propagation of a random vector yields a random process. Optimization-based strategies for calculating both types of predictor models are proposed. Whereas the formulations used to calculate IPMs target solutions leading to the interval value function of minimal spread containing all observations, those for RPMs seek to maximize the models' ability to reproduce the distribution of observations. Regarding RPMs, we choose a structure for the random vector (i.e., the assignment of probability to points in the parameter space) solely dependent on the prediction error. As such, the probabilistic description of uncertainty is not a subjective assignment of belief, nor is it expected to asymptotically converge to a fixed value, but instead it casts the model's ability to reproduce the experimental data. This framework enables evaluating the spread and distribution of the predicted response of target applications depending on the same parameters beyond the validation domain.

Crespo, Luis G.↗

NASA NTRS2003

Reducing Design Risk Using Robust Design Methods: A Dual Response Surface Approach

Space transportation system conceptual design is a multidisciplinary process containing considerable element of risk. Risk here is defined as the variability in the estimated (output) performance characteristic of interest resulting from the uncertainties in the values of several disciplinary design and/or operational parameters. Uncertainties from one discipline (and/or subsystem) may propagate to another, through linking parameters and the final system output may have a significant accumulation of risk. This variability can result in significant deviations from the expected performance. Therefore, an estimate of variability (which is called design risk in this study) together with the expected performance characteristic value (e.g. mean empty weight) is necessary for multidisciplinary optimization for a robust design. Robust design in this study is defined as a solution that minimizes variability subject to a constraint on mean performance characteristics. Even though multidisciplinary design optimization has gained wide attention and applications, the treatment of uncertainties to quantify and analyze design risk has received little attention. This research effort explores the dual response surface approach to quantify variability (risk) in critical performance characteristics (such as weight) during conceptual design.

Unal, Resit↗

NASA NTRS2001

Accuracy of Pressure Sensitive Paint

Uncertainty in pressure sensitive paint (PSP) measurement is investigated from a standpoint of system modeling. A functional relation between the imaging system output and luminescent emission from PSP is obtained based on studies of radiative energy transports in PSP and photodetector response to luminescence. This relation provides insights into physical origins of various elemental error sources and allows estimate of the total PSP measurement uncertainty contributed by the elemental errors. The elemental errors and their sensitivity coefficients in the error propagation equation are evaluated. Useful formulas are given for the minimum pressure uncertainty that PSP can possibly achieve and the upper bounds of the elemental errors to meet required pressure accuracy. An instructive example of a Joukowsky airfoil in subsonic flows is given to illustrate uncertainty estimates in PSP measurements.

Liu, Tianshu↗

NASA NTRS1980

A cosmic-ray age based on the abundance of Be-10

The paper discusses a measurement of the isotopic composition of galactic cosmic-ray beryllium made with high resolution aboard the ISEE 3 spacecraft. The isotope fractions of Be-7, Be-9, and Be-10 were determined; the abundance of the radioactive isotope Be-10 is used to deduce the cosmic-ray confinement time of 8,400,000/yr and an interstellar gas density of 0.33 atoms/cu cm in the confinement volume. Errors in the propagation model parameters which result in comparable uncertainties are discussed.

Wiedenbeck, M. E.↗

NASA NTRS1991

A measurement of the cosmic-ray H-2 and He-3 spectra and H-2/He-4 and He-3/He-4 ratios in 1989

The energy spectra of H-2 and H-3 nuclei up to energies of 450 and 800 MeV nucleon, respectively, were measured during a balloon flight of the NASA/NMSU Balloon Borne Magnet Facility on September 5, 1989. These isotopes were cleanly resolved from the more abundant H-1 and He-4 using a measurement of rigidity versus velocity as measured in a high-resolution scintillation counter. After correction for atmospheric secondaries the measured H-2/He-4 and He-3/He-4 ratios are both consistent with the production expected if H-1 and He-4 have the same path length in the galaxy as heavier cosmic-ray nuclei such as C and Fe, to within about 20 percent. Solar modulation effects play an important role in this uncertainty. This result favors a generally similar propagation history, along with similar types of sources for H-1 and He-4 and the heavier cosmic-ray nuclei.

Webber, W. R.↗

NASA NTRS2011

Wallops' Low Elevation Link Analysis for the Constellation Launch/Ascent Links

Prior to the redirection of the Constellation Program, the Wallops 11.3-meter ground station was tasked to support the Orion's Dissimilar Voice (DV) link and the Ares's Development Flight Instrument (DFI) link. Detailed analysis of the launch trajectories indicates that during the launch and ascent operation, the critical events of Orion-Ares main engine cut off (MECO) and Separation occur at low elevation angle. We worked with engineers from both Wallops Flight Facility (WFF) and Johnson Space Center (JSC) to perform an intensive measurement and link analysis campaign on the DV and DFI links. The main results were as follows: (1) The DV links have more than 3 dB margin at MECO and Separation. (2) The DFI links have 0 dB margin at Separation during certain weather condition in summer season. (3) Tropospheric scintillation loss is the major impairment at low elevation angle. (4) The current scintillation models in the Recommendation ITU-R P.618 (Propagation data and prediction methods required for the design of Earth-space telecommunication systems), which are based on limited experimental and theoretical work, exhibit idiosyncratic behaviors. We developed an improved model based on the measurements of recent Shuttle mission launch and ascent links and the ITU propagation data. (5) Due to the attitude uncertainty of the Orion-Ares stack, the high dynamics of the launch and ascent trajectory, and the irregularity of the Orion and Ares antenna patterns, we employed new link analysis approach to model the spacecraft antenna gain. In this paper we discuss the details of the aforementioned results.

Cheung, Kar-Ming↗

NASA NTRS2019

Uncertainty in Soil Moisture Retrievals: an Ensemble Approach Using SMOS L-Band Microwave Data

The uncertainty of soil moisture (SM) retrievals from satellite brightness temperature (TB) observations depends primarily on the choice of radiative transfer model (RTM) parameters, prior SM information and TB inputs. This paper studies the sensitivity of several (quasi-)operational and experimental SM retrieval products from the Soil Moisture Ocean Salinity (SMOS) mission to these choices at 11 reference sites, located in 7 watersheds across the United States (US). Different literature-based RTM parameter sets cause large biases between retrievals. Whereas typical RTM parameter sets are calibrated for SM retrievals, it is shown that a parameter set carefully optimized for TB forward modeling can also be used for retrieving SM. It is also shown that the inclusion of dynamic prior SM estimates in a Bayesian retrieval scheme can strongly improve SM retrievals, regardless of the choice of RTM parameters, and that the use of multi-angular and multi-polarization TB does not necessarily lead to superior retrievals compared to retrievals based on TB data at a single incidence angle and polarization. The second part of this paper evaluates ensemble uncertainty metrics for SM retrievals obtained by propagating a wide range of RTM parameters through the RTM. As expected for bounded variables, the spread in the ensemble SM retrievals is smallest for wet and dry SM values and highest for intermediate SM values. After removal of the strong long-term mean bias associated with the RTM parameter values for individual ensemble members, the remaining anomaly ensemble SM spread of 0.037 cu m/cu m approximates the actual time series unbiased root-mean-square-difference of 0.042 cu m/cu m between ensemble mean retrievals and in situ reference data across the reference sites. However, the temporal variability in the anomaly ensemble spread reveals higher-order biases in the retrieval error, which should be accounted for when characterizing retrieval error.

Jan Quets↗

NASA NTRS2019

Risk Estimation of Threatening Asteroids

When faced with the question of designing an asteroid deflection mission or with the decision of launching it, significant uncertainties are present in the asteroid’s physical properties, and its orbit solution. The success of the deflection mission relies heavily on these aspects. For example, a heavier than expected asteroid will reduce the imparted deflection DV. So will a larger porosity value by reducing the beta factor [1]. Here, we present a new capability that estimates asteroid impact risk under consideration of these uncertainties. The new method samples the uncertainty space along multiple dimensions, performs a predetermined deflection, propagates the deflected samples to the Earth, models the impact damage, and estimates the overall risk outcome. The work builds on the Probabilistic Asteroid Impact Risk (PAIR) assessment tool [2] by including orbital uncertainty and deflection capabilities. We demonstrate this risk estimation approach for threatening asteroids using the example of the fictitious impactor 2019 PDC. Such analysis provides a quantitative basis for the work of decision makers and disaster managers. It may further find application in areas such as mitigation mission planning where projected post-mitigation risk can be compared to premitigation levels as a means of cost-benefit analysis formitigation options.

Rumpf, Clemens↗

NASA NTRSDate not supplied

Towards an Optimal Estimation Retrieval of Cirrus Cloud Optical and Microphysical Properties Using Hyperspectral Shortwave Instruments and A Fast Radiative Transfer Algorithm

Cirrus cloud retrieval products (here, cloud optical depth, effective particle size, and cloud top height) are important inputs into numerical weather and climate models. Uncertainties in such retrieval products, as a matter of course, propagate downstream, impacting model calculations. Improvements in high-quality global cirrus cloud optical and microphysical data products from satellite observations are needed to understand and reduce retrieval uncertainties. Hyperspectral instruments produce high-resolution and information-dense radiance spectra, thus offering the opportunity to reduce uncertainties in retrieval products. An optimal estimation-based cirrus cloud optical and microphysical product retrieval is under development for the NASA Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) and the Earth Surface Mineral Dust Source Investigation (EMIT) instruments, and the forthcoming Climate Absolute Radiance and Refractivity Observatory Pathfinder (CLARREO-Pathfinder). The spectral coverage of all three instruments includes the ultraviolet, visible, and near-infrared. In this study a very fast radiative transfer model, the Principal Component-based Radiative Transfer Model in the solar spectral region (PCRTM-Solar), is used for forward modeling computations. This will reduce the computational burden in the forward radiance and Jacobian calculations as the cost function is minimized, enabling the entire AVIRIS, EMIT, and CLARREO-Pathfinder spectral range to be used in the optimal estimation framework. Using the entire spectrum will maximize the information content, resulting in a more robust and more accurate retrieval. As a first step, the retrieval is being designed for single layer ice clouds over open ocean water. Preliminary results will be shown.

Jeffrey Mast↗

NASA NTRSDate not supplied

Towards an Optimal Estimation Retrieval of Cirrus Cloud Optical and Microphysical Properties Using Hyperspectral Shortwave Instruments and A Fast Radiative Transfer Algorithm

Cirrus cloud retrieval products (here, cloud optical depth, effective particle size, and cloud top height) are important inputs into numerical weather and climate models. Uncertainties in such retrieval products, as a matter of course, propagate downstream, impacting model calculations. Improvements in high-quality global cirrus cloud optical and microphysical data products from satellite observations are needed to understand and reduce retrieval uncertainties. Hyperspectral shortwave instruments produce high-resolution and information-dense spectra, thus offering the opportunity to reduce uncertainties in retrieval products. We are in the process of developing a retrieval that uses the very fast Principal Component Radiative Transfer Model in the solar spectral region (PCRTM-Solar) in the forward model calculations. This retrieval will use measured reflectances from the NASA Earth Surface Mineral Dust Source Investigation (EMIT) and the forthcoming Climate Absolute Radiance and Refractivity Observatory Pathfinder (CLARREO-Pathfinder) instruments. In this manuscript we present progress towards a reference retrieval employing a widely used, verified, accurate, yet computationally slower radiative transfer modeling technique. The reference retrieval, while too slow for using the complete hyperspectral measurement, will allow us to study the behavior of retrieval products and help us verify results from our in-development fast retrieval. Both retrievals will use the optimal estimation retrieval framework. In this manuscript we present results from an uncertainty analysis considering three uncertainty sources for a cirrus cloud retrieval in the form of error covariance matrices: reflectance uncertainty due to water vapor, the reflectance uncertainty due to ice crystal scattering assumptions, and the instrument measurement uncertainty. Results show that the uncertainty due to habit selection is the largest, while that due to water vapor is at most 0.6% relative to channel reflectance. As a first step, the retrieval is being designed for single layer ice clouds over open ocean water.

Cirrus cloud↗

NASA NTRS2004

The Precision and Accuracy of AIRS Level 1B Radiances for Climate Studies

We investigate uncertainties in the Atmospheric Infrared Sounder (AIRS) radiances based on in-flight and preflight calibration algorithms and observations. The global coverage and spectra1 resolution ((lamda)/(Delta)(lamda) ~ 1200) of AIRS enable it to produce a data set that can be used as a climate data record over the lifetime of the instrument. Therefore, we examine the effects of the uncertainties in the calibration and the detector stability on future climate studies. The uncertainties of the parameters that go into the AIRS radiometric calibration are propagated to estimate the accuracy of the radiances and any climate data record created from AIRS measurements. The calculated radiance uncertainties are consistent with observations. Algorithm enhancements may be able to reduce the radiance uncertainties by as much as 7%. We find that the orbital variation of the gain contributes a brightness temperature bias of < 0.01 K.

climate↗

NASA NTRS2006

Convective Weather Forecast Quality Metrics for Air Traffic Management Decision-Making

Since numerical weather prediction models are unable to accurately forecast the severity and the location of the storm cells several hours into the future when compared with observation data, there has been a growing interest in probabilistic description of convective weather. The classical approach for generating uncertainty bounds consists of integrating the state equations and covariance propagation equations forward in time. This step is readily recognized as the process update step of the Kalman Filter algorithm. The second well known method, known as the Monte Carlo method, consists of generating output samples by driving the forecast algorithm with input samples selected from distributions. The statistical properties of the distributions of the output samples are then used for defining the uncertainty bounds of the output variables. This method is computationally expensive for a complex model compared to the covariance propagation method. The main advantage of the Monte Carlo method is that a complex non-linear model can be easily handled. Recently, a few different methods for probabilistic forecasting have appeared in the literature. A method for computing probability of convection in a region using forecast data is described in Ref. 5. Probability at a grid location is computed as the fraction of grid points, within a box of specified dimensions around the grid location, with forecast convection precipitation exceeding a specified threshold. The main limitation of this method is that the results are dependent on the chosen dimensions of the box. The examples presented Ref. 5 show that this process is equivalent to low-pass filtering of the forecast data with a finite support spatial filter. References 6 and 7 describe the technique for computing percentage coverage within a 92 x 92 square-kilometer box and assigning the value to the center 4 x 4 square-kilometer box. This technique is same as that described in Ref. 5. Characterizing the forecast, following the process described in Refs. 5 through 7, in terms of percentage coverage or confidence level is notionally sound compared to characterizing in terms of probabilities because the probability of the forecast being correct can only be determined using actual observations. References 5 through 7 only use the forecast data and not the observations. The method for computing the probability of detection, false alarm ratio and several forecast quality metrics (Skill Scores) using both the forecast and observation data are given in Ref. 2. This paper extends the statistical verification method in Ref. 2 to determine co-occurrence probabilities. The method consists of computing the probability that a severe weather cell (grid location) is detected in the observation data in the neighborhood of the severe weather cell in the forecast data. Probabilities of occurrence at the grid location and in its neighborhood with higher severity, and with lower severity in the observation data compared to that in the forecast data are examined. The method proposed in Refs. 5 through 7 is used for computing the probability that a certain number of cells in the neighborhood of severe weather cells in the forecast data are seen as severe weather cells in the observation data. Finally, the probability of existence of gaps in the observation data in the neighborhood of severe weather cells in forecast data is computed. Gaps are defined as openings between severe weather cells through which an aircraft can safely fly to its intended destination. The rest of the paper is organized as follows. Section II summarizes the statistical verification method described in Ref. 2. The extension of this method for computing the co-occurrence probabilities in discussed in Section HI. Numerical examples using NCWF forecast data and NCWD observation data are presented in Section III to elucidate the characteristics of the co-occurrence probabilities. This section also discusses the procedure for computing throbabilities that the severity of convection in the observation data will be higher or lower in the neighborhood of grid locations compared to that indicated at the grid locations in the forecast data. The probability of coverage of neighborhood grid cells is also described via examples in this section. Section IV discusses the gap detection algorithm and presents a numerical example to illustrate the method. The locations of the detected gaps in the observation data are used along with the locations of convective weather cells in the forecast data to determine the probability of existence of gaps in the neighborhood of these cells. Finally, the paper is concluded in Section V.

Chatterji, Gano B.↗

NASA NTRS2017

Assessment of the Gaussian Covariance Approximation over an Earth-Asteroid Encounter Period

In assessing the risk an asteroid may pose to the Earth, the asteroids state is often predicted for many years, often decades. Only by accounting for the asteroids initial state uncertainty can a measure of the risk be calculated. With the asteroids state uncertainty growing as a function of the initial velocity uncertainty, orbit velocity at the last state update, and the time from the last update to the epoch of interest, the asteroids position uncertainties can grow to many times the size of the Earth when propagated to the encounter risk corridor. This paper examines the merits of propagating the asteroids state covariance as an analytical matrix. The results of this study help to bound the efficacy of applying different metrics for assessing the risk an asteroid poses to the Earth. Additionally, this work identifies a criterion for when different covariance propagation methods are needed to continue predictions after an Earth-encounter period.

uncertainty characterization↗

NASA NTRS1985

Measurement of neutrino oscillations in MACRO experiment

The possibility of investigating neutrino oscillations in the proposed MACRO experiment are considered. Its sensitivity taking into account the theoretical uncertainties coming from flux calculations, geomagnetic effects and propagation through matter, and the experimental limitations.

Musser, J.↗

NASA NTRS2020

Improving Rain/No-Rain Detection Skill by Merging Precipitation Estimates from Different Sources

Rain/no-rain detection error is a key source of uncertainty in regional and global precipitation products that propagates into offline hydrological and land surface modeling simulations. Such detection error is difficult to evaluate and/or filter without access to high-quality reference precipitation datasets. For cases where such access is not available, this study proposes a novel approach for improved rain/no-rain detection. Based on categorical triple collocation (CTC) and a probabilistic framework, a weighted merging algorithm (CTC-M) is developed to combine noisy, but independent, precipitation products into an optimal binary rain/no-rain time series. Compared with commonly used approaches that directly apply the best parent product for rain/no-rain detection, the superiority of CTC-M is demonstrated analytically and numerically using spatially dense precipitation measurements over Europe. Our analysis also suggests that CTC-M is tolerant to a range of cross-correlated rain/no-rain detection errors and detection biases of the parent products. As a result, CTC-M will benefit global precipitation estimation by improving the representation of precipitation occurrence in gauge-based and multisource merged precipitation products.

Jianzhi Dong↗