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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2018

Narrowband Propagation Statistics of Aeronautical Mobile-Ground Links in the L- and C-Bands

To provide for the safe integration of unmanned aircraft systems (UAS) into the National Airspace System (NAS), command and control (C2) links must be highly reliable. Hence, protected aviation spectrum is required to support such links for UAS that are integrated into controlled non-segregated airspace. For air-ground (i.e., non-satellite) links, protected aviation spectrum to support C2 links is available in the 960-1164 MHz (L) and 5030-5091 MHz (C) bands. The performance of any C2 system is critically dependent upon the characteristics of the air-ground (AG) channel. Therefore, as part of its UAS Integration in the NAS (UAS in the NAS) project, the U.S. National Aeronautics and Space Administration (NASA) performed a series of air-ground propagation flight tests to collect AG channel data for model development and analysis of potential C2 communications links capable of providing the required reliability. NASA's Glenn Research Center (GRC) conducted an extensive air-ground channel propagation measurement campaign (at altitude) for frequencies in the 960-977 MHz and 5030-5091 MHz ranges, for seven different terrain environments. The measurements were conducted in 2013, and produced the largest set of AG channel data ever gathered to date. This data was subsequently processed to develop models for the AG channel. The statistics collected enabled the derivation of channel model parameters for both narrowband and wideband channels. In order to make the propagation data widely available, the resulting narrowband statistics were processed and submitted to the International Telecommunications Union Radiocommunication Sector (ITU-R) Study Group 3 Data Banks. Formats for data tables were developed, and tables of the aggregate narrowband propagation statistics for the seven ground site terrain environments were prepared, submitted to, and approved by, the ITU-R Study Group 3. This paper provides brief background on the measurement campaign, collection and processing of data, and development of the narrowband data tables. It further provides examples of the data and its use.

aircraft communications↗
NASA NTRS2019

Discovery of Activities via Statistical Clustering of Fixation Patterns

Human behavior often consists of a series of distinct activities, each characterized by a unique signature of visual behavior. This is true even in a restricted domain, such as piloting an aircraft, where patterns of visual signatures might represent activities like communicating, navigating, and monitoring. We propose a novel analysis method for gaze-tracking data, to perform blind discovery of these activities based on their behavioral signatures. The method is in some respects similar to recurrence analysis, but here we compare not individual fixations, but groups of fixations aggregated over a fixed time interval. The duration of this interval is a parameter that we will refer to as τ. We assume that the environment has been divided into a set of N different areas-of-interest (AOIs). For a given interval of time of duration τ, we compute the proportion of time spent fixating each AOI, resulting in an N-dimensional vector. These proportions can be converted to counts by multiplying by τ divided by the average fixation duration (another parameter that we fix at 280 milliseconds). We compare different intervals by computing the chi-square statistic. The p-value associated with the statistic is the likelihood of observing the data under the hypothesis that the data in the two intervals were generated by a single process with a single set of probabilities governing the fixation of each AOI. We have investigated the method using a set of 10 synthetic "activities," that sample 4 AOIs. Four of these activities visit 3 of the 4 AOIs, with equal probability; as there are four different ways to leave-one- out, there are four such activities. Similarly, there are six different activities that leave-two-out. Sequences of simulated behavior were generated by running each activity for 40 seconds, in sequence, for a total of 6.7 minutes. The figure to the right shows the matrix of chi-square statistics, using a value of 2.8 seconds for τ, corresponding to 10 fixations. Low values (dark) indicate poor evidence for activity differences, while high values (bright) indicate strong evidence. The dark squares along the main diagonal each correspond to the forty second intervals in which the activity was held constant; the 4x4 block at the lower left corresponds to the four leave-one-out activities, while the 6x6 block in the upper right corresponds to the leave-two-out activities. (The anti-diagonal pattern of white squares indicates those activity pairs that share no AOIs.) The chi-square values can be binarized by choosing a particular significance level; we are interested in grouping bins that represent the same activity, effectively accepting the null hypothesis. Therefore, we may adopt a relatively lax criterion; for example, choosing a p-value of 0.2 means that two behaviors that have only a 1-in-5 chance of being produced by a single activity might nevertheless be clustered together. We have explored several methods to perform clustering on the data and solving for the activity probabilities. Greedy methods begin by selecting the time bin that is similar to the most (or least) other bins, and then forming a cluster from it and all other non-discriminable bins. These methods show mediocre performance, as they do not take into account temporal contiguity. Preliminary results indicate that methods that "grow" clusters in time from seed points perform better.

activity analysis↗
NASA NTRS2019

Cellular Statistical Models of Broken Cloud Fields. Part IV: Effects of Pixel Size on Idealized Satellite Observations

In the fourth part of our “Cellular Statistical Models of Broken Cloud Fields” series we use the binary Markov processes framework for quantitative investigation of the effects of low resolution of idealized satellite observations on the statistics of the retrieved cloud masks. We assume that the cloud fields are Markovian and are characterized by the “actual” cloud fraction (CF) and scale length. We use two different models of observations: a simple discrete-point sampling and a more realistic “pixel” protocol. The latter is characterized by a state attribution function (SAF) which has the meaning of the probability that the pixel with a certain CF is declared cloudy in the observed cloud mask. The stochasticity of the SAF means that the cloud/clear attribution is not ideal and can be affected by external or unknown factors. We show that the observed cloud masks can be accurately described as Markov chains of pixels and use the master-matrix formalism (introduced in Part III of the series) for analytical computation of their parameters: the “observed” CF and scale length. This procedure allows us to establish a quantitative relationship (which is pixel-size dependent) between the actual and the observed cloud-field statistics. The feasibility of restoring the former from the latter is considered. The adequacy of our analytical approach to idealized observations is evaluated using numerical simulations. Comparison of the observed parameters of the simulated datasets with their theoretical expectations showed an agreement within 0.005 for the CF, while for the scale length it is within 1% in the sampling case and within 4% in the pixel case.

Mikhail D. Alexandrov↗
NASA NTRS2018

Discovery of Activities via Statistical Clustering of Fixation Patterns

Human behavior often consists of a series of distinct activities, each characterized by a unique pattern of interaction with the visual environment. This is true even in a restricted domain, such as a piloting an aircraft, where activities with distinct visual signatures might be things like communicating, navigating, and monitoring. We propose a novel analysis method for gaze-tracking data, to perform blind discovery of these hypothetical activities. The method is in some respects similar to recurrence analysis, but here we compare not individual fixations, but groups of fixations aggregated over a fixed time interval. The duration of this interval is a parameter that we will refer to as delta. We assume that the environment has been divided into a set of N different areas-of-interest (AOIs). For a given interval of time of duration delta, we compute the proportion of time spent fixating each AOI, resulting in an N-dimensional vector. These proportions can be converted to integer counts by multiplying by delta divided by the average fixation duration (another parameter that we fix at 280 milliseconds). We compare different intervals by computing the chi-square statistic. The p-value associated with the statistic is the likelihood of observing the data under the hypothesis that the data in the two intervals were generated by a single process with a single set of probabilities governing the fixation of each AOI. The method has been applied to approximately 100 hours of eye movement data collected from pilots in a high-fidelity B747 flight simulator, and the results have been compared to synthetic data in which the each activity is represented as first-order Markov process with random probabilities assigned to the AOIs. Randomly-generated synthetic activities can require thousands of fixations to be discriminated with statistical significance, while the human data can be clustered using averaging windows of some 10's of seconds, suggesting that the actual activities are much more narrowly focused than random Markov models.

activity analysis↗
NASA NTRS2019

Statistical Hypothesis Testing in Wavelet Analysis: Theoretical Developments and Applications to Indian Rainfall

Statistical hypothesis tests in wavelet analysis are methods that assess the degree to which a wavelet quantity(e.g., power and coherence) exceeds background noise. Commonly, a point-wise approach is adopted in which a wavelet quantity at every point in a wavelet spectrum is individually compared to the critical level of the point-wise test. However, because adjacent wavelet coefficients are correlated and wavelet spectra often contain many wavelet quantities, the point-wise test can produce many false positive results that occur in clusters or patches. To circumvent the point-wise test drawbacks, it is necessary to implement the recently developed area-wise, geometric, cumulative area-wise, and topological significance tests, which are reviewed and developed in this paper. To improve the computational efficiency of the cumulative area-wise test, a simplified version of the testing procedure is created based on the idea that its output is the mean of individual estimates of statistical significance calculated from the geometric test applied at a set of point-wise significance levels. Ideal examples are used to show that the geometric and cumulative area-wise tests are unable to differentiate wavelet spectral features arising from singularity-like structures from those associated with periodicities. A cumulative arc-wise test is therefore developed to strictly test for periodicities by using normalized arc length, which is defined as the number of points composing a cross section of a patch divided by the wavelet scale in question. A previously proposed topological significance test is formalized using persistent homology profiles (PHPs) measuring the number of patches and holes corresponding to the set of all point-wise significance values. Ideal examples show that the PHPs can be used to distinguish time series containing signal components from those that are purely noise. To demonstrate the practical uses of the existing and newly developed statistical methodologies, a first comprehensive wavelet analysis of Indian rainfall is also provided. An R software package has been written by the author to implement the various testing procedures.

Wind speed↗
NASA NTRS2019

A Global Model for Estimating Atmospheric Phase Scintillation Statistics

Since 2007, the National Aeronautics and Space Administration (NASA) has been collecting atmospheric phase turbulence data from various NASA ground stations throughout the world. The goal of these measurement campaigns has been to generate statistics to characterize the local site turbulence conditions and their impact on widely distributed ground based antenna arrays. This is of critical importance for the situation of uplink arraying, in which a priori knowledge of the fast varying turbulent conditions of water vapor in the troposphere may not be known, and will impact the power combining efficiency of ground based transmitting arrays. Therefore, the design of these type of systems will be dependent on the local climatology of the particular ground station site. Based on the 30+ station years of data collected characterizing atmospheric phase scintillation statistics at various sites, a global model is presented which attempts to predict the average phase statistics of a generic site based on local surface weather data, such as surface pressure, temperature, relative humidity, wind speed, and median wind direction. A model is proposed and based on a standard log power distribution similar to amplitude scintillation models trained on the existing data sets and shows reasonable accuracy against existing data sets.

propagation↗
NASA NTRSDate not supplied

Statistical learning framework for safety and failure analysis of a DNN-based autonomous aircraft system

Deep Neural Networks (DNNs) and Machine Learning technology is increasingly used for safety-critical applications in the Aerospace domain. To ensure safe operations, the DNN and the system must undergo rigorous verification and validation, including advanced statistical analyses. Performance and safety of the DNN and system behavior must not only be analyzed for the nominal case, but under numerous off-nominal and failure cases. In this paper we will describe how our statistical learning framework SYSAI can efficiently perform such analyses using the tool’s unique combination of advanced learning modeling and statistical analysis techniques. SYSAI can effectively explore the high-dimensional state and failure space of the system under test; geometrical shape detection of safety regions and boundaries support explainability of the results to the designer. In this paper, we report experiments and results obtained with a vision-based DNN control system (ACT) that is capable of autonomously steering an aircraft down a runway.

Yuning He↗
NASA NTRS2021

Truncated ARQ Statistical Link Analysis for Dynamic Links

The future deep space links are migrating towards higher frequency bands such as Ka band and optical. These links are susceptible to non Gaussian and non linear effects such as atmospheric turbulence, scintillation, antenna mis-pointing, jitter, etc. These dynamic links thus will experience various degrees of fading loss, and some of these link disruptions cannot be effectively mitigated by forward error correction coding and/or interleaving. One effective way to ensure reliable communication is by using Automatic Repeat Request (ARQ) protocol, where the receiver acknowledges to the transmitter whether or not a data unit is successfully received. If a data unit is not successfully received (such as after a pre-set time-out), the transmitter would then re-transmit the lost data unit to the receiver. In a previous paper, we derived a statistical link analysis method of finding the optimal operating Signal-to-Noise Ratio (SNR) and estimating the latency of an ARQ scheme. In a more recent paper, we demonstrated the above method using the SNR distribution constructed from the Ka-band (32 GHz) flight data. To simplify the discussion, we considered the academic approach that the ARQ scheme allows for an infinite number of retransmissions. In this paper, we consider the more practical case of a truncated ARQ scheme, where there is a limit on the number of retransmissions. We derive the error probability, the optimal SNR setting, and the latency statistics of the correctly received frames of the truncated ARQ schemes. We first discuss the truncated ARQ link analysis principles using the Gaussian assumption for SNR distribution with a large variance. Next, we demonstrate the statistical truncated ARQ link analysis using the SNR distribution constructed from the Ka-band flight data. The results in this paper can be applied in the design of reliable communication systems such as the Consultative Committee for Space Data System (CCSDS) File Transfer Protocol (CFTP) and the Delay Tolerant Network (DTN).

Morabito, David↗
NASA NTRS2022

Markovian Statistical Model of Cloud Optical Thickness. Part I: Theory and Examples

We present a generalization of the binary-value Markovian model previously used for statistical characterization of cloud masks to a continuous-value model describing 1D fields of cloud optical thickness (COT). This model has simple functional expressions and is specified by four parameters: the cloud fraction, the autocorrelation (scale) length, and the two parameters of the normalized probability density function of (non-zero) COT values (this PDF is assumed to have gamma-distribution form). Cloud masks derived from this model by separation between the values above and below some threshold in COT appear to have the same statistical properties as in binary-value model described in our previous publications. We demonstrate the ability of our model to generate examples of various cloud-field types by using it to statistically imitate actual cloud observations made by the Research Scanning Polarimeter (RSP) during two field experiments.

binary-value Markovian model↗
NASA NTRS2024

Interpretable Machine Learning for Molecular Biosignatures: a Novel Single-Sample Feature Importance Method That Is Sensitive To Statistical Interactions

Isotope ratio mass spectrometry (IRMS) of volatiles (e.g., CO 2 ) promises to be a powerful tool for potential biosignature detection for future missions to ocean worlds (OW) such as Europa and Enceladus. Machine learning (ML) methods for IRMS data could enable science autonomy by onboard prediction of seawater chemistry and biosignature presence. However, ML models are likely to be complex and involve statistical interactions between features (variables), which can make predictions seem opaque and enigmatic. For ML predictions as significant as extraterrestrial biosignatures, we must place extraordinary confidence in models. It is therefore essential that these models make interpretable predictions (i.e., human-understandable) and include false-prediction diagnostics. We achieve high accuracy and interpretability in ML biosignature and seawater chemistry models for OW through a nearest-neighbors feature selection tool that detects statistical interactions between predictors, constructs interaction networks for visualization of selected features working together to make a prediction, and reports single-sample feature importance scores for false-detection diagnostics. Here we develop a novel single-sample nearest-neighbors projected distance regression(ssNPDR) feature selection method that improves upon existing single-sample algorithms through the inclusion of statistical interactions while providing false-prediction diagnostics for ML models.

geochemistry↗
DOE OSTI2014

Feasibility Study on the Use of On-line Multivariate Statistical Process Control for Safeguards Applications in Natural Uranium Conversion Plants

The objective of this work was to determine the feasibility of using on-line multivariate statistical process control (MSPC) for safeguards applications in natural uranium conversion plants. Multivariate statistical process control is commonly used throughout industry for the detection of faults. For safeguards applications in uranium conversion plants, faults could include the diversion of intermediate products such as uranium dioxide, uranium tetrafluoride, and uranium hexafluoride. This study was limited to a 100 metric ton of uranium (MTU) per year natural uranium conversion plant (NUCP) using the wet solvent extraction method for the purification of uranium ore concentrate. A key component in the multivariate statistical methodology is the Principal Component Analysis (PCA) approach for the analysis of data, development of the base case model, and evaluation of future operations. The PCA approach was implemented through the use of singular value decomposition of the data matrix where the data matrix represents normal operation of the plant. Component mole balances were used to model each of the process units in the NUCP. However, this approach could be applied to any data set. The monitoring framework developed in this research could be used to determine whether or not a diversion of material has occurred at an NUCP as part of an International Atomic Energy Agency (IAEA) safeguards system. This approach can be used to identify the key monitoring locations, as well as locations where monitoring is unimportant. Detection limits at the key monitoring locations can also be established using this technique. Several faulty scenarios were developed to test the monitoring framework after the base case or normal operating conditions of the PCA model were established. In all of the scenarios, the monitoring framework was able to detect the fault. Overall this study was successful at meeting the stated objective.

Ladd-Lively, Jennifer L↗
DOE OSTI2015

Statistical Characterization of Medium-Duty Electric Vehicle Drive Cycles: Preprint

In an effort to help commercialize technologies for electric vehicles (EVs) through deployment and demonstration projects, the U.S. Department of Energy’s (DOE's) American Recovery and Reinvestment Act (ARRA) provided funding to participating U.S. companies to cover part of the cost of purchasing new EVs. Within the medium- and heavy-duty commercial vehicle segment, both Smith Electric Newton and and Navistar eStar vehicles qualified for such funding opportunities. In an effort to evaluate the performance characteristics of the new technologies deployed in these vehicles operating under real world conditions, data from Smith Electric and Navistar medium-duty EVs were collected, compiled, and analyzed by the National Renewable Energy Laboratory's (NREL) Fleet Test and Evaluation team over a period of 3 years. More than 430 Smith Newton EVs have provided data representing more than 150,000 days of operation. Similarly, data have been collected from more than 100 Navistar eStar EVs, resulting in a comparative total of more than 16,000 operating days. Combined, NREL has analyzed more than 6 million kilometers of driving and 4 million hours of charging data collected from commercially operating medium-duty electric vehicles in various configurations. In this paper, extensive duty-cycle statistical analyses are performed to examine and characterize common vehicle dynamics trends and relationships based on in-use field data. The results of these analyses statistically define the vehicle dynamic and kinematic requirements for each vehicle, aiding in the selection of representative chassis dynamometer test cycles and the development of custom drive cycles that emulate daily operation. In this paper, the methodology and accompanying results of the duty-cycle statistical analysis are presented and discussed. Results are presented in both graphical and tabular formats illustrating a number of key relationships between parameters observed within the data set that relate to medium duty EVs.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2015

Ideas for Effective Communication of Statistical Results

Effective presentation of statistical results to those with less statistical training, including managers and decision-makers requires planning, anticipation and thoughtful delivery. Here are several recommendations for effectively presenting statistical results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Statistical Characterization of Medium-Duty Electric Vehicle Drive Cycles

In an effort to help commercialize technologies for electric vehicles (EVs) through deployment and demonstration projects, the U.S. Department of Energy's (DOE's) American Recovery and Reinvestment Act (ARRA) provided funding to participating U.S. companies to cover part of the cost of purchasing new EVs. Within the medium- and heavy-duty commercial vehicle segment, both Smith Electric Newton and and Navistar eStar vehicles qualified for such funding opportunities. In an effort to evaluate the performance characteristics of the new technologies deployed in these vehicles operating under real world conditions, data from Smith Electric and Navistar medium-duty EVs were collected, compiled, and analyzed by the National Renewable Energy Laboratory's (NREL) Fleet Test and Evaluation team over a period of 3 years. More than 430 Smith Newton EVs have provided data representing more than 150,000 days of operation. Similarly, data have been collected from more than 100 Navistar eStar EVs, resulting in a comparative total of more than 16,000 operating days. Combined, NREL has analyzed more than 6 million kilometers of driving and 4 million hours of charging data collected from commercially operating medium-duty electric vehicles in various configurations. In this paper, extensive duty-cycle statistical analyses are performed to examine and characterize common vehicle dynamics trends and relationships based on in-use field data. The results of these analyses statistically define the vehicle dynamic and kinematic requirements for each vehicle, aiding in the selection of representative chassis dynamometer test cycles and the development of custom drive cycles that emulate daily operation. In this paper, the methodology and accompanying results of the duty-cycle statistical analysis are presented and discussed. Results are presented in both graphical and tabular formats illustrating a number of key relationships between parameters observed within the data set that relate to medium duty EVs.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2015

Statistical Techniques For Real-time Anomaly Detection Using Spark Over Multi-source VMware Performance Data

Anomaly detection refers to the identi cation of an irregular or unusual pat- tern which deviates from what is standard, normal, or expected. Such deviated patterns typically correspond to samples of interest and are assigned different labels in different domains, such as outliers, anomalies, exceptions, or malware. Detecting anomalies in fast, voluminous streams of data is a formidable chal- lenge. This paper presents a novel, generic, real-time distributed anomaly detection framework for heterogeneous streaming data where anomalies appear as a group. We have developed a distributed statistical approach to build a model and later use it to detect anomaly. As a case study, we investigate group anomaly de- tection for a VMware-based cloud data center, which maintains a large number of virtual machines (VMs). We have built our framework using Apache Spark to get higher throughput and lower data processing time on streaming data. We have developed a window-based statistical anomaly detection technique to detect anomalies that appear sporadically. We then relaxed this constraint with higher accuracy by implementing a cluster-based technique to detect sporadic and continuous anomalies. We conclude that our cluster-based technique out- performs other statistical techniques with higher accuracy and lower processing time.

Apache Spark↗
DOE OSTI2016

Statistical Sampling Plan for AGR-5/6/7 Fuel Materials

Kernels, coated particles, and compacts will be manufactured to predefined specifications for irradiation in the AGR 5/6/7 experiments. Many tests will be performed for quality assurance and most of these tests correspond to criteria that have to be met with 95% confidence, based on random samples. This report describes the statistical acceptance testing methods and gives minimum sample sizes for kernels to achieve 95% confidence. Coated particles and compacts will be addressed in revisions to this report. The methods used for sample size determination are described in detail in INL/EXT 05 00349, Statistical Methods Handbook for Advanced Gas Reactor Fuel Materials (Einerson 2005). The statistical approach is to collect a representative sample, apply an acceptance test to the sample, and accept or reject the product based on this test for each criterion. The criteria or “product specifications” are contained in SPC-1352, “AGR 5/6/7 Fuel Specification,” Revision 1 and are duplicated in this plan.

+↗
DOE OSTI2016

A Statistical Testing Approach for Quantifying Software Reliability; Application to an Example System

The U.S. Nuclear Regulatory Commission (NRC) encourages the use of probabilistic risk assessment (PRA) technology in all regulatory matters, to the extent supported by the state-of-the-art in PRA methods and data. Although much has been accomplished in the area of risk-informed regulation, risk assessment for digital systems has not been fully developed. The NRC established a plan for research on digital systems to identify and develop methods, analytical tools, and regulatory guidance for (1) including models of digital systems in the PRA's of nuclear power plants (NPPs), and, (2) incorporating digital systems in the NRC's risk-informed licensing and oversight activities. Under NRC's sponsorship, Brookhaven National Laboratory (BNL) explored approaches for addressing the failures of digital instrumentation and control (I and C) systems in the current NPP PRA framework. Specific areas investigated included PRA modeling digital hardware , development of a philosophical basis for defining software failure , and identification of desirable attributes of quantitative software reliability methods . Based on the earlier research, statistical testing is considered a promising method for quantifying software reliability. It is widely recognized that software failures are due to the triggering of pre-existing defects by the software's operational environment. Software defects can arise from errors made in user requirements or coding errors introduced during the developmental process. The software's operational environment includes factors such as the time history of digital system inputs, communication interfaces, the internal state of the digital system, and external conditions. Thus, software reliability is a function of both the number of pre-existing defects and the presence of a triggering condition caused by the manner in which the software is used. In this paper, we describe a statistical software-testing approach for quantifying software reliability and applied it to the loop-operating control system (LOCS) of an experimental loop of the Advanced Test Reactor (ATR) at Idaho National Laboratory (INL). The work involved collaboration between BNL and INL. The objectives of the study include: (1) Development of a statistical testing approach for estimating software failure probability on demand, the results of which are suitable for including in a probabilistic risk assessment (PRA); and, (2) Application of the approach to the LOCS to estimate its failure probability, and obtain insights into the feasibility, practicality, and usefulness of the estimation in models of digital systems for inclusion in nuclear power plants' PRAs. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

Effects of statistical uncertainty in activation calculations based on Monte Carlo radiation transport - 25353

This paper focuses on the analysis of the uncertainty in isotopic concentrations determined by Monte Carlo depletion calculations performed for the purposes of activation source calculations. In this work, we use repeated, statistically independent, Monte Carlo depletion calculations to examine the convergence behavior and statistical uncertainty in isotopic densities. Performing many, small, Monte Carlo depletion simulations and then recombining them is a useful approach and enables statistical analysis that can help ensure convergence. Convergence behavior is discussed in terms of stability of the mean, trends in the 95% confidence interval, and distributions of the isotopic densities. Just as in the more familiar Monte Carlo simulations of fluxes or reaction rates, convergence of isotopic densities may exhibit expected behavior such as stable means and 95% confidence intervals that decrease like N{sup -1/2} , or may exhibit poorly-converging behaviors. The most poorly-converging cases in this work were found to be for the products of high-energy threshold reactions. Finally, we examine the conditions under which uncertainty in the isotopic density can be determined from reaction rate uncertainty, and demonstrate the need for considering correlated variates in isotopic uncertainty propagation. Correlation between reaction rate tallies appears most important when the cross sections for the reactions and neutron energies considered are not strongly varying. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗