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At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Assessment of Rainfall Estimates Using a Standard Z-R Relationship and the Probability Matching Method Applied to Composite Radar Data in Central Florida

Precipitation estimates from radar systems are a crucial component of many hydrometeorological applications, from flash flood forecasting to regional water budget studies. For analyses on large spatial scales and long timescales, it is frequently necessary to use composite reflectivities from a network of radar systems. Such composite products are useful for regional or national studies, but introduce a set of difficulties not encountered when using single radars. For instance, each contributing radar has its own calibration and scanning characteristics, but radar identification may not be retained in the compositing procedure. As a result, range effects on signal return cannot be taken into account. This paper assesses the accuracy with which composite radar imagery can be used to estimate precipitation in the convective environment of Florida during the summer of 1991. Results using Z = 30OR(sup 1.4) (WSR-88D default Z-R relationship) are compared with those obtained using the probability matching method (PMM). Rainfall derived from the power law Z-R was found to he highly biased (+90%-l10%) compared to rain gauge measurements for various temporal and spatial integrations. Application of a 36.5-dBZ reflectivity threshold (determined via the PMM) was found to improve the performance of the power law Z-R, reducing the biases substantially to 20%-33%. Correlations between precipitation estimates obtained with either Z-R relationship and mean gauge values are much higher for areal averages than for point locations. Precipitation estimates from the PMM are an improvement over those obtained using the power law in that biases and root-mean-square errors are much lower. The minimum timescale for application of the PMM with the composite radar dataset was found to be several days for area-average precipitation. The minimum spatial scale is harder to quantify, although it is concluded that it is less than 350 sq km. Implications relevant to the WSR-88D system are discussed.

Crosson, William L.↗
DOE OSTI2025

Covariance-Free Bifidelity Control Variates Importance Sampling for Rare Event Reliability Analysis

Multifidelity modeling has been steadily gaining attention as a tool to address the problem of exorbitant model evaluation costs that makes the estimation of failure probabilities a significant computational challenge for complex real-world problems, particularly when failure is a rare event. To implement multifidelity modeling, estimators that efficiently combine information from multiple models/sources are necessary. In past works, the variance reduction techniques of control variates (CV) and importance sampling (IS) have been leveraged for this task. In this paper, we present the CVIS framework—a creative take on a coupled CV and IS estimator for bifidelity reliability analysis. The framework addresses some of the practical challenges of the CV method by using an estimator for the control variate mean and sidestepping the need to estimate the covariance between the original estimator and the control variate through a clever choice for the tuning constant. Furthermore, the task of selecting an efficient IS distribution is also considered, with a view towards maximally leveraging the bifidelity structure and maintaining expressivity. Additionally, a diagnostic is provided that indicates both the efficiency of the algorithm as well as the relative predictive quality of the models utilized. Finally, the behavior and performance of the framework is explored through analytical and numerical examples.

Markov chain Monte Carlo↗
DOE OSTI2022

Advanced Laboratory and Field Arrays: Debris Modeling, Detection,& Mitigation (Task 1)

The statement of project objectives for this task was: develop tools, methods and models to assess, and mitigate the risk of damage to MHK infrastructure from woody debris. Develop the capability to detect woody debris using sonar and/or physical methods for purposes of characterizing debris statistics in river (at UAF’s Tanana River Test Site) and near-shore wave (at Yakutat, AK) environments and to activate debris mitigation measures. Develop debris impact risk maps and tables using statistics on debris size, geometry, type, prevalence, mobility and location. Improve and apply the COUPi discrete element method (DEM) to develop models of debris movement and impact on MHK infrastructure to evaluate risk of damage, and interference, to operations from debris. The proposed final deliverable for the task was a set of tools or techniques for providing estimates of the probability of debris impact, and resulting impact forces, on MHK infrastructure as a function of debris size, type, wave regime, and current velocity. Such estimates are required to assess damage risks to operational MHK infrastructure.

13 HYDRO ENERGY↗
NASA NTRS1983

The mass of the Oort cloud

The total mass of comets in the Oort cloud is calculated. The distribution of cometary masses is found based on the observed distribution of cometary magnitudes corrected for observational selection effects by Everhart (1967), and a derived relationship between brightness and nucleus mass. A cloud population of 1.4 trillion comets brighter than an absolute magnitude of 11 as found by Weissman (1982) is used. The estimated total mass is 1.9 earth masses. The probable error in the estimate is about one order of magnitude. Most of the mass of the Oort cloud is concentrated in the size range of the observed long-period comets. The mass estimate is consistent with either cometary formation among the outer planets, or in satellite fragments of the primordial solar nebula.

Weissman, P. R.↗
NASA NTRS2001

A New Fine-Scale, Quasi-Global Combined Precipitation Estimate Based on TRMM

A TRMM-based 3-hourly precipitation algorithm is currently under development, with the goal of producing 0.25 deg x 0.25 deg, 3-hourly gridded estimates for the period January 1999 to the present over the latitude band +/-50 deg. [Extension to higher latitudes will be undertaken next]. TMI precipitation estimates are used to calibrate SSM/I estimates, and AMSR, when available. Then a merger of the microwave estimates is used to create a calibrated IR estimate in a Probability-Matched-Threshold approach. The microwave and IR estimates are next combined at the individual 3-hour level. Early results will be shown, including typical tropical and extratropical storm evolution and examples of the diurnal cycle. Major issues will be discussed, including the choice of IR algorithm, the approach to merging the IR and microwave estimates, and extension to the GPCP One-Degree Daily product (for which the authors are responsible). The work described here provides one approach to using data from the future NASA Global Precipitation Measurement program, which is designed to provide full global coverage by low-orbit passive microwave satellites every three hours beginning around 2007.

Huffman, George J.↗
DOE OSTI2024

Impact of solar geoengineering on temperature-attributable mortality

Decisions about solar geoengineering (SG) entail risk–risk tradeoffs between the direct risks of SG and SG’s ability to reduce climate risks. Quantitative comparisons between these risks are needed to inform public policy. We evaluate idealized SG’s effectiveness in reducing deaths from warming using two climate models and an econometric analysis of temperature-attributable mortality. We find SG’s impact on temperature-attributable mortality is uneven with decreases for hotter, poorer regions and increases in cooler, richer regions. Relative to no SG, global mortality is reduced by over 400,000 deaths annually [90% CI: (−1.2 million,2.7 million)] for cooling of 1 °C from 2.5 °C above preindustrial in 2080. We find no evidence that mortality reduction achieved by SG is smaller than the reduction from equivalent cooling by emissions reductions. Combining our estimates with existing estimates of sulphate aerosol injection direct mortality risk from air quality and UV-attributable cancer enables the first quantitative risk-risk comparison of SG. We estimate with 61% probability that the mortality benefits of cooling outweigh these direct SG risks. We find the benefits outweigh these risks by 13 times for our central estimates, or 4 deaths per 100,000 per 1 °C per year [90% CI: (−11,23)]. This is not a comprehensive evaluation of the risk–risk tradeoffs around SG, yet by comparing some of the most consequential impacts on human welfare it is a useful first step. While these findings are robust to a variety of alternative assumptions, considerable uncertainties remain and require further investigation.

Harding, Anthony (ORCID:0000000262898253)↗
NASA NTRS2005

An Improved Analysis of Forest Carbon Dynamics using Data Assimilation

There are two broad approaches to quantifying landscape C dynamics - by measuring changes in C stocks over time, or by measuring fluxes of C directly. However, these data may be patchy, and have gaps or biases. An alternative approach to generating C budgets has been to use process-based models, constructed to simulate the key processes involved in C exchange. However, the process of model building is arguably subjective, and parameters may be poorly defined. This paper demonstrates why data assimilation (DA) techniques - which combine stock and flux observations with a dynamic model - improve estimates of, and provide insights into, ecosystem carbon (C) exchanges. We use an ensemble Kalman filter (EnKF) to link a series of measurements with a simple box model of C transformations. Measurements were collected at a young ponderosa pine stand in central Oregon over a 3-year period, and include eddy flux and soil C02 efflux data, litterfall collections, stem surveys, root and soil cores, and leaf area index data. The simple C model is a mass balance model with nine unknown parameters, tracking changes in C storage among five pools; foliar, wood and fine root pools in vegetation, and also fresh litter and soil organic matter (SOM) plus coarse woody debris pools. We nested the EnKF within an optimization routine to generate estimates from the data of the unknown parameters and the five initial conditions for the pools. The efficacy of the DA process can be judged by comparing the probability distributions of estimates produced with the EnKF analysis vs. those produced with reduced data or model alone. Using the model alone, estimated net ecosystem exchange of C (NEE)= -251 f 197g Cm-2 over the 3 years, compared with an estimate of -419 f 29gCm-2 when all observations were assimilated into the model. The uncertainty on daily measurements of NEE via eddy fluxes was estimated at 0.5gCm-2 day-1, but the uncertainty on assimilated estimates averaged 0.47 g Cm-2 day-1, and only exceeded 0.5gC m-2 day-1 on days where neither eddy flux nor soil efflux data were available. In generating C budgets, the assimilation process reduced the uncertainties associated with using data or model alone and the forecasts of NEE were statistically unbiased estimates. The results of the analysis emphasize the importance of time series as constraints. Occasional, rare measurements of stocks have limited use in constraining the estimates of other components of the C cycle. Long time series are particularly crucial for improving the analysis of pools with long time constants, such as SOM, woody biomass, and woody debris. Long-running forest stem surveys, and tree ring data, offer a rich resource that could be assimilated to provide an important constraint on C cycling of slow pools. For extending estimates of NEE across regions, DA can play a further important role, by assimilating remote-sensing data into the analysis of C cycles. We show, via sensitivity analysis, how assimilating an estimate of photosynthesis - which might be provided indirectly by remotely sensed data - improves the analysis of NEE.

Williams, Mathew↗
NASA NTRS2006

Exploration Health Risks: Probabilistic Risk Assessment

Maintenance of human health on long-duration exploration missions is a primary challenge to mission designers. Indeed, human health risks are currently the largest risk contributors to the risks of evacuation or loss of the crew on long-duration International Space Station missions. We describe a quantitative assessment of the relative probabilities of occurrence of the individual risks to human safety and efficiency during space flight to augment qualitative assessments used in this field to date. Quantitative probabilistic risk assessments will allow program managers to focus resources on those human health risks most likely to occur with undesirable consequences. Truly quantitative assessments are common, even expected, in the engineering and actuarial spheres, but that capability is just emerging in some arenas of life sciences research, such as identifying and minimize the hazards to astronauts during future space exploration missions. Our expectation is that these results can be used to inform NASA mission design trade studies in the near future with the objective of preventing the higher among the human health risks. We identify and discuss statistical techniques to provide this risk quantification based on relevant sets of astronaut biomedical data from short and long duration space flights as well as relevant analog populations. We outline critical assumptions made in the calculations and discuss the rationale for these. Our efforts to date have focussed on quantifying the probabilities of medical risks that are qualitatively perceived as relatively high risks of radiation sickness, cardiac dysrhythmias, medically significant renal stone formation due to increased calcium mobilization, decompression sickness as a result of EVA (extravehicular activity), and bone fracture due to loss of bone mineral density. We present these quantitative probabilities in order-of-magnitude comparison format so that relative risk can be gauged. We address the effects of conservative and nonconservative assumptions on the probability results. We discuss the methods necessary to assess mission risks once exploration mission scenarios are characterized. Preliminary efforts have produced results that are commensurate with earlier qualitative estimates of risk probabilities in this and other operational contexts, indicating that our approach may be usefully applied in support of the development of human health and performance standards for long-duration space exploration missions. This approach will also enable mission-specific probabilistic risk assessments for space exploration missions.

Rhatigan, Jennifer↗
NASA NTRS2002

Iridium and Spherules in Late Eocene Impact Deposits

We have been independently examining the Ir (FTK) and spherule (SL) contents of recently discovered late Eocene impact deposits from the south Atlantic and western Indian oceans. These include ODP Sites 1090 [14,15], 709 [lo], and 699 [Liu in prep.]. Iridium abundances at these sites are within the typical range reported for late Eocene deposits, with peak concentrations between 100 and 1000 pg/g. In Table 1 we present estimated net Ir fluences (in ng Ir/cm ) for these and nine other sites. Although there are fewer sites than the K/T boundary, the average of 9 ng Ir/cm2 is probably a good estimate of the late Eocene global flux. This is enough Ir for a 6 km comet (assuming 250 ng/g Ir, p=1.5), is sufficient to produce the Popigai or Chesapeake Bay structures, and is 16% of the flux estimated for the K/T boundary (55 ng/cm2 [ 161). Figure 1 shows the relative abundances of Ir, glassy microtektites and cpx-bearing spherules in sediments from Sites 699 and 1090, which are separated by only 3100 km. Although these two sites have similar Ir anomalies, the abundances of spherules are quite different. Site 1090 has well-defined peaks for both types of spherules, with a peak of 562 cpx spheruledg, while Site 699 contains only a few glassy microtektites and no cpx spherules. While the different abundances of spherules may reflect a heterogeneous distribution of spherules on the Earth s surface, an equally likely cause of this difference may be differential preservation of spherules in the sediment. recovered are only a trace residue of the initial impact deposit. Earlier work found 0.22 ng/g Ir in glassy microtektites from Site 689 [17], an insufficient concentration to support 0.16 ng/g in the bulk sediment at this site. We measured 15 ng/g Ir in a group of 95 cpx spherules from Site 1090 with sizes from 63 to -200 pm, a set typical of the size distribution at this site. Although this is a significant concentration it also cannot support the Ir peak. We presently lack quantitative data on the mass concentration of cpx spherules in Site 1090 sediments, but it is certainly <1 mg/g in The impact record in the late Eocene is very different from that at the Cretaceous-Tertiary In contrast, the late Eocene probably experienced multiple impact events.

Kyte, F. T.↗
DOE OSTI2022

Radiative transition probabilities of neutral and singly ionized Europium estimated by laser-induced breakdown spectroscopy (LIBS)

Laser-induced breakdown spectroscopy (LIBS) is a versatile technique for compositional analysis for solids, liquids, or gasses. LIBS is an asset for the quantitative or qualitative analysis of resource limited materials like actinides and rare earths because it is quasi-nondestructive. Two Eu 2 O 3 pellets were synthesized to be a test and validation set, respectively. Spectral lines identified from the National Institute of Standards and Technology database with fundamental data reported were used to form Saha-Boltzmann plots. The Saha-Boltzmann plots were used to determine the plasma temperatures and electron densities of the laser-induced plasmas for both samples. These Saha-Boltzmann plots were then used to calculate previously unreported transition probabilities associated with identified peaks. Additionally, the transition probabilities presented in this paper provide the capability for calibration free LIBS to be performed more readily on europium samples and the spectroscopic analysis of stellar bodies. Eight previously unreported transition probabilities are presented in this paper; five for Eu I and three for Eu II. The transition probabilities for Eu I ranged from 0.172 to 7.38 × 10 7 s -1 and those for Eu II ranged from 1.56 to 6.75 × 10 7 s -1 .

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Estimation of sensor measurement errors in reactor coolant systems using multi-sensor fusion

A nuclear power plant is typically instrumented with a variety of sensors to continually monitor its variables, and their sensor’s measurements may be used to assess the plant state and initiate safety actions, if needed. Errors in sensor measurements, due to factors such as calibration drifts, critically affect such state assessments. Here, we address a problem of estimating sensor errors using physics-informed machine learning methods that use measurements collected under known plant conditions. For a given sensor, we propose an information fusion method that uses measurements from other sensors to estimate its output assuming it is error-free and provides its difference from an actual measurement as an error estimate. We present the ensemble of trees and support vector machine fusers, and evaluate their performance using measurements collected over an emulated test loop of a pressurized water reactor. The plant variables are related to each other through the underlying physical laws under inertial constraints that place bounds on their derivatives, which analytically justify the applicability of machine learning methods for computing these fusers. Under twenty scenarios, we assess their sensor error estimates for pressure sensors of the heat exchanger of a reactor’s primary coolant system. Multiple types of errors are captured by both fusers under externally induced calibration drifts, blockages, minor leaks and air gaps in sensing lines, and electromagnetic interference; the root mean square error of the estimation of error is under 2.2% percent of the maximum measurement. We present generalization equations, in the framework of statistical learning theory, for these methods that characterize the confidence probability that the estimation error is bounded by a specified parameter in future test scenarios.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Performance evaluation of cosmic ray muon trajectory estimation algorithms

Muons, being elementary particles with minimal interaction with nuclear materials and abundant at sea level, have sparked interest in utilizing them for imaging various applications, such as mining [Borselli et al., Sci. Rep. 12, 22329 (2022)], volcano imaging [Nagamine et al., Nucl. Instrum. Meth. A, 356, 585(1995)], and underground tunnel detection [Guardincerri et al., Pure Appl. Geophys. 174, 2133 (2017)]. Recently, their use in nuclear nonproliferation and safeguard verification has gained attention, particularly in cargo screening for nuclear waste smuggling [Baesso et al., J. Instrum. 9, C10041 (2014)], source localization [L. J. Schultz et al., Nucl. Instrum. Meth. A 519, 687 (2004)], and locating nuclear fuel debris in reactors [Borozdin et al., Phys. Rev. Let. 109, 152501 (2012)]. However, the resolution of muon image reconstruction techniques is limited due to multiple Coulomb scattering (MCS) within the target object. To achieve robust muon tomography, it is crucial to develop efficient and flexible physics-based algorithms that can model the MCS process accurately and estimate the most probable trajectory of muons as they pass through the target object. To address this limitation, in this study, a novel algorithmic approach utilizing the Bayesian probability theory and Gaussian approximation of MCS is chosen. Different energy levels, materials, and target sizes were considered in the evaluations. The results demonstrate that the Generalized Muon Trajectory Estimation (GMTE) algorithm offers significant improvements over currently used algorithms. Across all test scenarios, the GMTE algorithm demonstrated ~50% and 38% increase in precision compared to Straight Line Path (SLP) and Point of Closest Approach (PoCA) algorithms, respectively. Furthermore, it exhibited 10%–35% and 10%–15% increases in muon flux utilization for high and medium Z materials, respectively, compared to the PoCA algorithm. In conclusion, the extensive simulations confirm the enhanced performance and efficiency of the GMTE algorithm, offering improved resolution and reduced measurement time for cosmic ray muon imaging compared to the current SLP and PoCA algorithms.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1993

Quality metrics for sensor images

Methods are needed for evaluating the quality of augmented visual displays (AVID). Computational quality metrics will help summarize, interpolate, and extrapolate the results of human performance tests with displays. The FLM Vision group at NASA Ames has been developing computational models of visual processing and using them to develop computational metrics for similar problems. For example, display modeling systems use metrics for comparing proposed displays, halftoning optimizing methods use metrics to evaluate the difference between the halftone and the original, and image compression methods minimize the predicted visibility of compression artifacts. The visual discrimination models take as input two arbitrary images A and B and compute an estimate of the probability that a human observer will report that A is different from B. If A is an image that one desires to display and B is the actual displayed image, such an estimate can be regarded as an image quality metric reflecting how well B approximates A. There are additional complexities associated with the problem of evaluating the quality of radar and IR enhanced displays for AVID tasks. One important problem is the question of whether intruding obstacles are detectable in such displays. Although the discrimination model can handle detection situations by making B the original image A plus the intrusion, this detection model makes the inappropriate assumption that the observer knows where the intrusion will be. Effects of signal uncertainty need to be added to our models. A pilot needs to make decisions rapidly. The models need to predict not just the probability of a correct decision, but the probability of a correct decision by the time the decision needs to be made. That is, the models need to predict latency as well as accuracy. Luce and Green have generated models for auditory detection latencies. Similar models are needed for visual detection. Most image quality models are designed for static imagery. Watson has been developing a general spatial-temporal vision model to optimize video compression techniques. These models need to be adapted and calibrated for AVID applications.

Ahumada, AL↗
NASA NTRS2007

Predicting the Earth encounters of (99942) Apophis

Arecibo delay-Doppler measurements of (99942) Apophis in 2005 and 2006 resulted in a five standard-deviation trajectory correction to the optically predicted close approach distance to Earth in 2029. The radar measurements reduced the volume of the statistical uncertainty region entering the encounter to 7.3% of the pre-radar solution, but increased the trajectory uncertainty growth rate across the encounter by 800% due to the closer predicted approach to the Earth. A small estimated Earth impact probability remained for 2036. With standard-deviation plane-of-sky position uncertainties for 2007-2010 already less than 0.2 arcsec, the best near-term ground-based optical astrometry can only weakly affect the trajectory estimate. While the potential for impact in 2036 will likely be excluded in 2013 (if not 2011) using ground-based optical measurements, approximations within the Standard Dynamical Model (SDM) used to estimate and predict the trajectory from the current era are sufficient to obscure the difference between a predicted impact and a miss in 2036 by altering the dynamics leading into the 2029 encounter. Normal impact probability assessments based on the SDM become problematic without knowledge of the object's physical properties; impact could be excluded while the actual dynamics still permit it. Calibrated position uncertainty intervals are developed to compensate for this by characterizing the minimum and maximum effect of physical parameters on the trajectory. Uncertainty in accelerations related to solar radiation can cause between 82 and 4720 Earth-radii of trajectory change relative to the SDM by 2036. If an actionable hazard exists, alteration by 2-10% of Apophis' total absorption of solar radiation in 2018 could be sufficient to produce a six standard-deviation trajectory change by 2036 given physical characterization; even a 0.5% change could produce a trajectory shift of one Earth-radius by 2036 for all possible spin-poles and likely masses. Planetary ephemeris uncertainties are the next greatest source of systematic error, causing up to 23 Earth-radii of uncertainty. The SDM Earth point-mass assumption introduces an additional 2.9 Earth-radii of prediction error by 2036. Unmodeled asteroid perturbations produce as much as 2.3 Earth-radii of error. We find no future small-body encounters likely to yield an Apophis mass determination prior to 2029. However, asteroid (144898) 2004 VD17, itself having a statistical Earth impact in 2102, will probably encounter Apophis at 6.7 lunar distances in 2034, their uncertainty regions coming as close as 1.6 lunar distances near the center of both SDM probability distributions.

Orbit determination↗
DOE OSTI2022

Regional Characteristics of Observable Foreshocks

Abstract Measures of foreshock occurrence are systematically examined using earthquake catalogs for eight regions (Italy, southern California, northern California, Costa Rica, Onshore Japan, Alaska, Turkey, and Greece) after imposing a magnitude ≥3.0 completeness level. Foreshocks are identified using three approaches: a magnitude-dependent space + fixed-time windowing method, a nearest-neighbor clustering method, and a modified magnitude-dependent space + variable-time windowing method. The method with fixed-time windows systematically yields higher counts of foreshocks than the other two clustering methods. We find similar counts of foreshocks across the three methods when the magnitude aperture is equalized by including only earthquakes in the magnitude range M*−2≤ M< M*, in which M* is the mainshock magnitude. For most of the catalogs (excluding Italy and southern California), the measured b-values of the foreshocks of all region-specific mainshocks are lower by 0.1–0.2 than b-values of respective aftershocks. Allowing for variable-time windows results in relatively high probabilities of having at least one foreshock in Italy (∼43%–56%), compared to other regional catalogs. Foreshock probabilities decrease to 14%–41% for regions such as Turkey, Greece, and Costa Rica. Similar trends are found when requiring at least five foreshocks in a sequence to be considered. Estimates of foreshock probabilities for each mainshock are method dependent; however, consistent regional trends exist regardless of method, with regions such as Italy and southern California producing more observable foreshocks than Turkey and Greece. Some regions with relatively high background seismicity have comparatively low probabilities of detectable foreshock activity when using methods that account for variable background, possibly due to depletion of near-failure fault conditions by background activity.

Geochemistry & Geophysics↗
NASA NTRS1980

Limits on the possible intrinsic magnetic field of Venus

Magnetic field measurements obtained by the Pioneer Venus orbiter at low altitudes in the solar wind wake region are examined for possible surface-correlated features and any possible intrinsic magnetic moment. The field variations observed in the wake do not resemble those expected for a solar wind interaction with even a weak intrinsic magnetic field. Little orbit-to-orbit persistence of features is found in the magnetic records. The magnetic field measurements in the wake are averaged in 10 deg x 10 deg bins to minimize the effects of external field sources. In these 37 bins, the average fields appear to be randomly oriented and consistent with zero mean in the region mapped. Using these 37 averaged vector fields, a maximum intrinsic magnetic dipole moment is obtained of 4.3 + or - 2.0 x 10 to the 21st G cu cm, approximately an order of magnitude less than previous estimates. It is noted that a more conservative estimate of the probable error of the mean is 5.5 x 10 to the 21st G cu cm. The Pioneer Venus measurements are thus consistent with zero planetary moment. The present measurements are found to be far below estimates made on the basis of angular momentum, the so-called magnetic Bode's law, and far below the dynamo scaling law of Busse.

Russell, C. T.↗
DOE OSTI2021

An extended polynomial chaos expansion for PDF characterization and variation with aleatory and epistemic uncertainties

This paper presents an extended polynomial chaos formalism for epistemic uncertainties and a new framework for evaluating sensitivities and variations of output probability density functions (PDF) to uncertainty in probabilistic models of input variables. An ”extended” polynomial chaos expansion (PCE) approach is developed that accounts for both aleatory and epistemic uncertainties, modeled as random variables, thus allowing a unified treatment of both types of uncertainty. We explore in particular epistemic uncertainty associated with the choice of prior probabilistic models for input parameters. A PCE-based Kernel Density (KDE) construction provides a composite map from the PCE coefficients and germ to the PDF of quantities of interest (QoI). Here, the sensitivities of these PDF with respect to the input parameters are then evaluated. Input parameters of the probabilistic models are considered. By sampling over the epistemic random variable, a family of PDFs is generated and the failure probability is itself estimated as a random variable with its own PCE. Integrating epistemic uncertainties within the PCE framework results in a computationally efficient paradigm for propagation and sensitivity evaluation. Two typical illustrative examples are used to demonstrate the proposed approach.

Aleatory uncertainty↗
NASA NTRS1992

Statistical plant set estimation using Schroeder-phased multisinusoidal input design

A frequency domain method is developed for plant set estimation. The estimation of a plant 'set' rather than a point estimate is required to support many methods of modern robust control design. The approach here is based on using a Schroeder-phased multisinusoid input design which has the special property of placing input energy only at the discrete frequency points used in the computation. A detailed analysis of the statistical properties of the frequency domain estimator is given, leading to exact expressions for the probability distribution of the estimation error, and many important properties. It is shown that, for any nominal parametric plant estimate, one can use these results to construct an overbound on the additive uncertainty to any prescribed statistical confidence. The 'soft' bound thus obtained can be used to replace 'hard' bounds presently used in many robust control analysis and synthesis methods.

Bayard, D. S.↗