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At least 883 records · Page 49
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Breast dose in mammography is about 30% lower when realistic heterogeneous glandular distributions are considered

Purpose: Current dosimetry methods in mammography assume that the breast is comprised of a homogeneous mixture of glandular and adipose tissues. Three-dimensional (3D) dedicated breast CT (bCT) data sets were used previously to assess the complex anatomical structure within the breast, characterizing the statistical distribution of glandular tissue in the breast. The purpose of this work was to investigate the effect of bCT-derived heterogeneous glandular distributions on dosimetry in mammography. Methods: bCT-derived breast diameters, volumes, and 3D fibroglandular distributions were used to design realistic compressed breast models comprised of heterogeneous distributions of glandular tissue. The bCT-derived glandular distributions were fit to biGaussian functions and used as probability density maps to assign the density distributions within compressed breast models. The MCNPX 2.6.0 Monte Carlo code was used to estimate monoenergetic normalized mean glandular dose “DgN(E)” values in mammography geometry. The DgN(E) values were then weighted by typical mammography x-ray spectra to determine polyenergetic DgN (pDgN) coefficients for heterogeneous (pDgN{sub hetero}) and homogeneous (pDgN{sub homo}) cases. The dependence of estimated pDgN values on phantom size, volumetric glandular fraction (VGF), x-ray technique factors, and location of the heterogeneous glandular distributions was investigated. Results: The pDgN{sub hetero} coefficients were on average 35.3% (SD, 4.1) and 24.2% (SD, 3.0) lower than the pDgN{sub homo} coefficients for the Mo–Mo and W–Rh x-ray spectra, respectively, across all phantom sizes and VGFs when the glandular distributions were centered within the breast phantom in the coronal plane. At constant breast size, increasing VGF from 7.3% to 19.1% lead to a reduction in pDgN{sub hetero} relative to pDgN{sub homo} of 23.6%–27.4% for a W–Rh spectrum. Displacement of the glandular distribution, at a distance equal to 10% of the compressed breast width in the superior and inferior directions, resulted in a 37.3% and a −26.6% change in the pDgN{sub hetero} coefficient, respectively, relative to the centered distribution for the Mo–Mo spectrum. Lateral displacement of the glandular distribution, at a distance equal to 10% of the compressed breast width, resulted in a 1.5% change in the pDgN{sub hetero} coefficient relative to the centered distribution for the W–Rh spectrum. Conclusions: Introducing bCT-derived heterogeneous glandular distributions into mammography phantom design resulted in decreased glandular dose relative to the widely used homogeneous assumption. A homogeneous distribution overestimates the amount of glandular tissue near the entrant surface of the breast, where dose deposition is exponentially higher. While these findings are based on clinically measured distributions of glandular tissue using a large cohort of women, future work is required to improve the classification of glandular distributions based on breast size and overall glandular fraction.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Distribution Development for the RDX Regional Model at Los Alamos National Laboratory - 20385

Representing uncertainty in model inputs often means finding a balance between uncertainty and physical reality. Developing wide distributions may seem conservative in principle, but this approach may lead to unrealistic model results. Characterizing the current state of knowledge of stochastic inputs presents many challenges, especially if the data available are limited or have limited relevance to the site. Relationships among these inputs may also be important to represent but are typically complex or difficult to define. Often special adjustments must be made to account for reduced credibility in particular data. If parameters are strongly related to one another, a correlation structure may be developed for input to the model. Other techniques such as regression models may be used to incorporate relationships between the information available and the desired parameters. The process of developing distributions must consider details of the model in terms of what the distribution is meant to represent. This paper uses the example of a probabilistic fate and transport model for hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) in the regional aquifer at Los Alamos National Laboratory (LANL). For many parameters, a single draw is applied to all space and time over which the model is run, for a single iteration. This simplification is often made for many reasons, and can often be beneficial, but also adds additional complexity in the distribution development process. Defining the distributional goals as they relate to the modeling process is an important step, which should take place prior to evaluation of the data. Usually, the distributions developed are meant to characterize the average value of the parameter over the spatial and temporal domain of the model. Distribution development requires consideration of many sources of information on the parameter where available, ideally from multiple references. Examples of different sources include data from different references but also from different conditions, measurement methods, or experimental types. Depending on these conditions and the reliability or relevance of particular references, different sources of data may each contribute valuable information but have varying relevance to the site. In these cases, weighting data unequally is a useful way to incorporate this information. As an example, aqueous dispersivity data are available for a variety of rock types. Only a few values are available for the desired rock type, and this is not enough to develop a distribution. Therefore, dispersivity values from other rock types are included in distribution development but are down-weighted such that the best data have the most influence on the distribution developed. In another case, K{sub d} distributions in the model are meant to represent a known composition of multiple soil types. Data from these materials are weighted accordingly to develop a distribution for the weighted average K{sub d} across soil types. Other cases include varying reliability of different sources, and weighting data according to the confidence in these sources. In some cases, input parameters are correlated with one another. An example is advective porosity, which is positively correlated with total porosity and must be less than total porosity. Paired data with both parameters must exist to discern the relationship between the two parameters and if it is necessary to build a correlation structure into the model. In general, correlated parameters may be represented in the model by a multivariate distribution, or perhaps more desirably, capturing the correlation within the developed distributions which may be treated as independent from one another. In the example of porosity, this can be done by transforming advective porosity into a proportion of total porosity which may be drawn independently from the distribution of total porosity. This paper explores how complex data and correlations can be incorporated to meet the distributional goals of the model, using the RDX regional model as a detailed example. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2018

Scale Mixtures of Frechet Distributions as Asymptotic Approximations of Extreme Precipitation

This paper is a further development of the results of [20] where, based on the negative binomial model for the duration of wet periods measured in days [16], an asymptotic approximation was proposed for the distribution of the maximum daily precipitation volume within a wet period. This approximation has the form of a scale mixture of the Fr´echet distribution with the gamma mixing distribution and coincides with the distribution of a positive power of a random variable having the Snedecor–Fisher distribution. Here we extend this result to the mth extremes, m ∈ ℕ, and sample quantiles. The proof of this result is based on the representation of the negative binomial distribution as a mixed geometric (and hence, mixed Poisson) distribution [17] and limit theorems for extreme order statistics in samples with random sizes having mixed Poisson distributions [10]. Some analytic properties of the obtained limit distribution are described. In particular, it is demonstrated that under certain conditions the limit distribution of the maximum precipitation is mixed exponential and hence, is infinitely divisible. It is shown that under the same conditions this limit distribution can be represented as a scale mixture of stable or Weibull or Pareto or folded normal laws. The corresponding product representations for the limit random variable can be used for its computer simulation. The results of fitting this distribution to real data are presented illustrating high adequacy of the proposed model. It is also shown that the limit distribution of sample quantiles is the well-known Student distribution. Several methods are proposed for the estimation of the parameters of the asymptotic distributions. The obtained mixture representations for the limit laws and the corresponding asymptotic approximations provide better insight into the nature of mixed probability (“Bayesian”) models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

2012 Market Report on U.S. Wind Technologies in Distributed Applications

At the end of 2012, U.S. wind turbines in distributed applications reached a 10-year cumulative installed capacity of more than 812 MW from more than 69,000 units across all 50 states. In 2012 alone, nearly 3,800 wind turbines totaling 175 MW of distributed wind capacity were documented in 40 states and in the U.S. Virgin Islands, with 138 MW using utility-scale turbines (i.e., greater than 1 MW in size), 19 MW using mid-size turbines (i.e., 101 kW to 1 MW in size), and 18.4 MW using small turbines (i.e., up to 100 kW in size). Distributed wind is defined in terms of technology application based on a wind project’s location relative to end-use and power-distribution infrastructure, rather than on technology size or project size. Distributed wind systems are either connected on the customer side of the meter (to meet the onsite load) or directly to distribution or micro grids (to support grid operations or offset large loads nearby). Estimated capacity-weighted average costs for 2012 U.S. distributed wind installations was $\$$2,540/kW for utility-scale wind turbines, $\$$2,810/kW for mid-sized wind turbines, and $\$$6,960/kW for newly manufactured (domestic and imported) small wind turbines. An emerging trend observed in 2012 was an increased use of refurbished turbines. The estimated capacity-weighted average cost of refurbished small wind turbines installed in 2012 was $\$$4,080/kW. As a result of multiple projects using utility-scale turbines, Iowa deployed the most new overall distributed wind capacity, 37 MW, in 2012. Nevada deployed the most small wind capacity in 2012, with nearly 8 MW of small wind turbines installed in distributed applications. In the case of mid-size turbines, Ohio led all states in 2012 with 4.9 MW installed in distributed applications. State and federal policies and incentives continued to play a substantial role in the development of distributed wind projects. In 2012, U.S. Treasury Section 1603 payments and grants and loans from the U.S. Department of Agriculture’s Rural Energy for America Program were the main sources of federal funding for distributed wind projects. State and local funding varied across the country, from rebates to loans, tax credits, and other incentives. Reducing utility bills and hedging against potentially rising electricity rates remain drivers of distributed wind installations. In 2012, other drivers included taking advantage of the expiring U.S. Treasury Section 1603 program and a prosperous year for farmers. While 2012 saw a large addition of distributed wind capacity, considerable barriers and challenges remain, such as a weak domestic economy, inconsistent state incentives, and very competitive solar photovoltaic and natural gas prices. The industry remains committed to improving the distributed wind marketplace by advancing the third-party certification process and introducing alternative financing models, such as third-party power purchase agreements and lease-to-own agreements more typical in the solar photovoltaic market. Continued growth is expected in 2013.

distributed wind↗
DOE OSTI2014

Oxygen distribution in tumors: A qualitative analysis and modeling study providing a novel Monte Carlo approach

Purpose: To construct a Monte Carlo (MC)-based simulation model for analyzing the dependence of tumor oxygen distribution on different variables related to tumor vasculature [blood velocity, vessel-to-vessel proximity (vessel proximity), and inflowing oxygen partial pressure (pO{sub 2})]. Methods: A voxel-based tissue model containing parallel capillaries with square cross-sections (sides of 10 μm) was constructed. Green's function was used for diffusion calculations and Michaelis-Menten's kinetics to manage oxygen consumption. The model was tuned to approximately reproduce the oxygenational status of a renal carcinoma; the depth oxygenation curves (DOC) were fitted with an analytical expression to facilitate rapid MC simulations of tumor oxygen distribution. DOCs were simulated with three variables at three settings each (blood velocity, vessel proximity, and inflowing pO{sub 2}), which resulted in 27 combinations of conditions. To create a model that simulated variable oxygen distributions, the oxygen tension at a specific point was randomly sampled with trilinear interpolation in the dataset from the first simulation. Six correlations between blood velocity, vessel proximity, and inflowing pO{sub 2} were hypothesized. Variable models with correlated parameters were compared to each other and to a nonvariable, DOC-based model to evaluate the differences in simulated oxygen distributions and tumor radiosensitivities for different tumor sizes. Results: For tumors with radii ranging from 5 to 30 mm, the nonvariable DOC model tended to generate normal or log-normal oxygen distributions, with a cut-off at zero. The pO{sub 2} distributions simulated with the six-variable DOC models were quite different from the distributions generated with the nonvariable DOC model; in the former case the variable models simulated oxygen distributions that were more similar to in vivo results found in the literature. For larger tumors, the oxygen distributions became truncated in the lower end, due to anoxia, but smaller tumors showed undisturbed oxygen distributions. The six different models with correlated parameters generated three classes of oxygen distributions. The first was a hypothetical, negative covariance between vessel proximity and pO{sub 2} (VPO-C scenario); the second was a hypothetical positive covariance between vessel proximity and pO{sub 2} (VPO+C scenario); and the third was the hypothesis of no correlation between vessel proximity and pO{sub 2} (UP scenario). The VPO-C scenario produced a distinctly different oxygen distribution than the two other scenarios. The shape of the VPO-C scenario was similar to that of the nonvariable DOC model, and the larger the tumor, the greater the similarity between the two models. For all simulations, the mean oxygen tension decreased and the hypoxic fraction increased with tumor size. The absorbed dose required for definitive tumor control was highest for the VPO+C scenario, followed by the UP and VPO-C scenarios. Conclusions: A novel MC algorithm was presented which simulated oxygen distributions and radiation response for various biological parameter values. The analysis showed that the VPO-C scenario generated a clearly different oxygen distribution from the VPO+C scenario; the former exhibited a lower hypoxic fraction and higher radiosensitivity. In future studies, this modeling approach might be valuable for qualitative analyses of factors that affect oxygen distribution as well as analyses of specific experimental and clinical situations.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1955

Spatial Burnout in Water Reactors with Nonuniform Startup Distributions of Uranium and Boron

Spatial burnout calculations have been made of two types of water moderated cylindrical reactor using boron as a burnable poison to increase reactor life. Specific reactors studied were a version of the Submarine Advanced Reactor (sAR) and a supercritical water reactor (SCW) . Burnout characteristics such as reactivity excursion, neutron-flux and heat-generation distributions, and uranium and boron distributions have been determined for core lives corresponding to a burnup of approximately 7 kilograms of fully enriched uranium. All reactivity calculations have been based on the actual nonuniform distribution of absorbers existing during intervals of core life. Spatial burnout of uranium and boron and spatial build-up of fission products and equilibrium xenon have been- considered. Calculations were performed on the NACA nuclear reactor simulator using two-group diff'usion theory. The following reactor burnout characteristics have been demonstrated: 1. A significantly lower excursion in reactivity during core life may be obtained by nonuniform rather than uniform startup distribution of uranium. Results for SCW with uranium distributed to provide constant radial heat generation and a core life corresponding to a uranium burnup of 7 kilograms indicated a maximum excursion in reactivity of 2.5 percent. This compared to a maximum excursion of 4.2 percent obtained for the same core life when w'anium was uniformly distributed at startup. Boron was incorporated uniformly in these cores at startup. 2. It is possible to approach constant radial heat generation during the life of a cylindrical core by means of startup nonuniform radial and axial distributions of uranium and boron. Results for SCW with nonuniform radial distribution of uranium to provide constant radial heat generation at startup and with boron for longevity indicate relatively small departures from the initially constant radial heat generation distribution during core life. Results for SAR with a sinusoidal distribution rather than uniform axial distributions of boron indicate significant improvements in axial heat generation distribution during the greater part of core life. 3. Uranium investments for cylindrical reactors with nonuniform radial uranium distributions which provide constant radial heat generation per unit core volume are somewhat higher than for reactors with uniform uranium concentration at startup. On the other hand, uranium investments for reactors with axial boron distributions which approach constant axial heat generation are somewhat smaller than for reactors with uniform boron distributions at startup.

Fox, Thomas A.↗
DOE OSTI2013

Application of activity pencil beam algorithm using measured distribution data of positron emitter nuclei for therapeutic SOBP proton beam

Purpose: Recently, much research on imaging the clinical proton-irradiated volume using positron emitter nuclei based on target nuclear fragment reaction has been carried out. The purpose of this study is to develop an activity pencil beam (APB) algorithm for a simulation system for proton-activated positron-emitting imaging in clinical proton therapy using spread-out Bragg peak (SOBP) beams.Methods: The target nuclei of activity distribution calculations are {sup 12}C nuclei, {sup 16}O nuclei, and {sup 40}Ca nuclei, which are the main elements in a human body. Depth activity distributions with SOBP beam irradiations were obtained from the material information of ridge filter (RF) and depth activity distributions of compounds of the three target nuclei measured by BOLPs-RGp (beam ON-LINE PET system mounted on a rotating gantry port) with mono-energetic Bragg peak (MONO) beam irradiations. The calculated data of depth activity distributions with SOBP beam irradiations were sorted in terms of kind of nucleus, energy of proton beam, SOBP width, and thickness of fine degrader (FD), which were verified. The calculated depth activity distributions with SOBP beam irradiations were compared with the measured ones. APB kernels were made from the calculated depth activity distributions with SOBP beam irradiations to construct a simulation system using the APB algorithm for SOBP beams.Results: The depth activity distributions were prepared using the material information of RF and the measured depth activity distributions with MONO beam irradiations for clinical therapy using SOBP beams. With the SOBP width widening, the distal fall-offs of depth activity distributions and the difference from the depth dose distributions were large. The shapes of the calculated depth activity distributions nearly agreed with those of the measured ones upon comparison between the two. The APB kernels of SOBP beams were prepared by making use of the data on depth activity distributions with SOBP beam irradiations that were made from the depth activity distributions with MONO beam irradiations and sorted in terms of energy, SOBP width, and thickness of FD. The data on APB kernels of SOBP beams were determined as installment data for the simulation system using the APB algorithm for SOBP beam irradiations.Conclusions: A method of obtaining the depth activity distributions and the APB algorithm for clinical use of SOBP beams have been developed. It is suggested that the simulation system for imaging the clinical irradiated volume with the APB algorithm can be used in clinical proton therapy using SOBP beams by preparing and investigating the data on APB kernels of SOBP beams.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2016

Therapeutic analysis of high-dose-rate {sup 192}Ir vaginal cuff brachytherapy for endometrial cancer using a cylindrical target volume model and varied cancer cell distributions

Purpose: To evaluate high-dose-rate (HDR) vaginal cuff brachytherapy (VCBT) in the treatment of endometrial cancer in a cylindrical target volume with either a varied or a constant cancer cell distributions using the linear quadratic (LQ) model. Methods: A Monte Carlo (MC) technique was used to calculate the 3D dose distribution of HDR VCBT over a variety of cylinder diameters and treatment lengths. A treatment planning system (TPS) was used to make plans for the various cylinder diameters, treatment lengths, and prescriptions using the clinical protocol. The dwell times obtained from the TPS were fed into MC. The LQ model was used to evaluate the therapeutic outcome of two brachytherapy regimens prescribed either at 0.5 cm depth (5.5 Gy × 4 fractions) or at the vaginal mucosal surface (8.8 Gy × 4 fractions) for the treatment of endometrial cancer. An experimentally determined endometrial cancer cell distribution, which showed a varied and resembled a half-Gaussian distribution, was used in radiobiology modeling. The equivalent uniform dose (EUD) to cancer cells was calculated for each treatment scenario. The therapeutic ratio (TR) was defined by comparing VCBT with a uniform dose radiotherapy plan in term of normal cell survival at the same level of cancer cell killing. Calculations of clinical impact were run twice assuming two different types of cancer cell density distributions in the cylindrical target volume: (1) a half-Gaussian or (2) a uniform distribution. Results: EUDs were weakly dependent on cylinder size, treatment length, and the prescription depth, but strongly dependent on the cancer cell distribution. TRs were strongly dependent on the cylinder size, treatment length, types of the cancer cell distributions, and the sensitivity of normal tissue. With a half-Gaussian distribution of cancer cells which populated at the vaginal mucosa the most, the EUDs were between 6.9 Gy × 4 and 7.8 Gy × 4, the TRs were in the range from (5.0){sup 4} to (13.4){sup 4} for the radiosensitive normal tissue depending on the cylinder size, treatment lengths, prescription depth, and dose as well. However, for a uniform cancer cell distribution, the EUDs were between 6.3 Gy × 4 and 7.1 Gy × 4, and the TRs were found to be between (1.4){sup 4} and (1.7){sup 4}. For the uniformly interspersed cancer and radio-resistant normal cells, the TRs were less than 1. The two VCBT prescription regimens were found to be equivalent in terms of EUDs and TRs. Conclusions: HDR VCBT strongly favors cylindrical target volume with the cancer cell distribution following its dosimetric trend. Assuming a half-Gaussian distribution of cancer cells, the HDR VCBT provides a considerable radiobiological advantage over the external beam radiotherapy (EBRT) in terms of sparing more normal tissues while maintaining the same level of cancer cell killing. But for the uniform cancer cell distribution and radio-resistant normal tissue, the radiobiology outcome of the HDR VCBT does not show an advantage over the EBRT. This study strongly suggests that radiation therapy design should consider the cancer cell distribution inside the target volume in addition to the shape of target.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2022

Introducing the 9500 Node Distribution Test System to Support Advanced Power Applications: An Operations-Focused Approach

The 9500 Node Test System is a representative section of distribution power system model developed as a part of the GridAPPS-D™ project, an effort funded by DOE as a part of the Grid Modernization Lab Consortium (GMLC) program. The test system was developed to fulfill a growing need to represent the rapidly evolving state of electric distribution systems by combining elements of legacy infrastructure systems, modern feeder topologies, and an anticipated future with smart grid technologies. It also provides a network model capable of supporting the simulation of operational scenarios such as the ones in a utility distribution control center. This test system allows the evaluation of the performance of advanced power applications in real-time, such as one that simulates the operations of an Advanced Distribution Management Systems (ADMS), Distributed Energy Resource Management Systems (DERMS), etc. in a Distribution control center. This model is an extension of the widely used IEEE 8500 Node Test Feeder and is currently being validated to become an IEEE test case to help increase adoption and widespread usage among both academia and industry. It is a full-size model representative of a section of a utility’s distribution system with multiple feeders fed from different substations. The model includes multiple distribution circuits, a sub-transmission system, multiple substations, behind the meter customer rooftop photovoltaics (PV), and multiple utility-scale distributed energy resources. To enable accurate simulations of operational scenarios, the 9500 Node Test System is designed to support procedure-based operations, with the ability to realistically demonstrate switching operations, feeder reconfiguration, adjustment of volt-var control equipment, dispatch of distributed generation, and response to planned and unplanned outages. The 9500 Node Test System includes three radial distribution feeders with 12.3 MVA of average load, consisting of both medium voltage and low voltage equipment each supplied by a different distribution substation. The three distribution feeders are connected to each other through Normally-Open switches which can be closed when needed to simulate restoration scenarios due to a fault. One feeder represents today’s grid with low penetration of customer-side renewables. The second represents a potential future grid with microgrids and 100% renewable penetration. The third has no customer generation resources, a district steam plant, and a utility-scale solar farm. The three diverse circuits were created to allow the simulation of both today’s situation as well as potential future scenarios. All three feeders have customers connected by low-voltage secondary triplex lines. This test system meets all requirements outlined in the report for creating a simulation environment that would enable discussion between key technical stakeholders as well as having the potential to accelerate operational application development and their subsequent testing and integration. The new model is a possible representation of what we believe the distribution grid may look like in the future: a high penetration of renewables, reconfigurable radial and mesh topology, numerous DERs, islanded microgrids, and significantly increased data and measurement density. The system supports both the solution of existing and newer algorithms but also enables the evaluation of applications in a realistic operational environment defined by task oriented procedural steps that represent the interaction between the control center operator and field personnel.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Data assimilation for burnup distribution of PWR with three-dimensional variational algorithm and artificial neutral network

In this paper, a data-assimilation method has been proposed and applied for the burnup distribution of PWR. The burnup distribution is significant to the safety and economy of the reactor, as it is essential for the fuel-reloading design and optimization. Due to the burnup distribution cannot be measured directly during the reactor operation, the numerical simulation is widely applied to determine the burnup distribution. However, there is a deviation between the numerical simulation and the actual core due to some unavoidable factors, such as component manufacturing deviation, uneven flow distribution and so on. These differences would induce the errors to the simulation values of power distributions and hence to the burnup distribution. To address this problem, a data-assimilation method for the burnup distribution has been proposed with the application of power-distribution measurements. In our research, the three-dimensional variational (3DVAR) algorithm was applied for burnup-distribution calibration and the artificial neutral network (ANN) was applied to establish the relation between power distribution and corresponding burnup distribution. As engineering verification, the proposed data-assimilation method has been applied to the CNP1000 PWR operated in China. The numerical results indicated that the burnup-distribution errors can be reduced notably, as the maximum value of relative errors for power distribution can be reduced from 5.35% to 3.96%. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
NASA NTRS2004

Probability Distribution Estimated From the Minimum, Maximum, and Most Likely Values: Applied to Turbine Inlet Temperature Uncertainty

Modern engineering design practices are tending more toward the treatment of design parameters as random variables as opposed to fixed, or deterministic, values. The probabilistic design approach attempts to account for the uncertainty in design parameters by representing them as a distribution of values rather than as a single value. The motivations for this effort include preventing excessive overdesign as well as assessing and assuring reliability, both of which are important for aerospace applications. However, the determination of the probability distribution is a fundamental problem in reliability analysis. A random variable is often defined by the parameters of the theoretical distribution function that gives the best fit to experimental data. In many cases the distribution must be assumed from very limited information or data. Often the types of information that are available or reasonably estimated are the minimum, maximum, and most likely values of the design parameter. For these situations the beta distribution model is very convenient because the parameters that define the distribution can be easily determined from these three pieces of information. Widely used in the field of operations research, the beta model is very flexible and is also useful for estimating the mean and standard deviation of a random variable given only the aforementioned three values. However, an assumption is required to determine the four parameters of the beta distribution from only these three pieces of information (some of the more common distributions, like the normal, lognormal, gamma, and Weibull distributions, have two or three parameters). The conventional method assumes that the standard deviation is a certain fraction of the range. The beta parameters are then determined by solving a set of equations simultaneously. A new method developed in-house at the NASA Glenn Research Center assumes a value for one of the beta shape parameters based on an analogy with the normal distribution (ref.1). This new approach allows for a very simple and direct algebraic solution without restricting the standard deviation. The beta parameters obtained by the new method are comparable to the conventional method (and identical when the distribution is symmetrical). However, the proposed method generally produces a less peaked distribution with a slightly larger standard deviation (up to 7 percent) than the conventional method in cases where the distribution is asymmetric or skewed. The beta distribution model has now been implemented into the Fast Probability Integration (FPI) module used in the NESSUS computer code for probabilistic analyses of structures (ref. 2).

Holland, Frederic A., Jr.↗
DOE OSTI2019

Scaling Input Distributions for Probabilistic Models - 19472

It is important to address scaling issues when building models to support risk-based decisions for radioactive waste disposal sites. Currently, probabilistic risk assessment and probabilistic performance assessment models are run for multiple realizations where each realization uses one value from each input distribution over the entire modeled time. The input distributions represent the current state of knowledge in the mean of the input variable over the spatial region of interest and over the time period of the model run. This paper focuses on the time factor in input distribution scaling because it presents more serious conceptual and distributional challenges than the spatial factor. One of the challenges in temporal scaling is the effect of non-linearity on propagation of distribution uncertainty through to uncertainty in results. Radioactive waste disposal models tend to have both linear and non-linear components in their models. Dose assessment calculations are typically represented by linear models, while contaminant transport models have linear and non-linear components. In principle, temporal scaling of input parameter distributions for a linear model is straightforward, but scaling of input distributions for non-linear models is not. This paper uses examples to investigate the effects of input distribution temporal scaling on simple linear and non-linear models. Different scaling scenarios were investigated by comparing three analysis tools: analytical mathematical representations, statistical software programming, and GoldSim Monte Carlo simulation software. R statistical software is an open source statistical programming language often used for statistical analyses and graphical representation of data. GoldSim is a robust probabilistic dynamic modeling platform used in performance assessment modeling of radioactive waste sites. A simple linear model, a quadratic model and a multiplicative model were the cases explored for each of these tools. For the three analysis tools considered and with each of the scaling cases, 1,000 realizations were implemented from distributions of the random variables of interest. This is a sufficient number of realizations for simple models to capture the model space. An annual temporal resolution of a 100-year simulation period was chosen for all models and analysis tools. The effects of temporal scaling were demonstrated by investigating two different options for time scaling. Option 1 was set up so that the input distributions represented the expected value on an annual time scale, and a new value from that distribution was chosen every year (at every time step which equaled a year) for 100 years. In Option 2, the input distributions were scaled to represent the expected mean value of the input variable over the 100 years of simulation, and one value from that distribution was chosen for the entire elapsed time. Results show agreement across the three analysis tools. As expected, the linear models have identical results for the two different scaling Options, and the non-linear models diverge in the results for different time scale implementation. The implications of this work point to the need for careful consideration of input distribution temporal scaling. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

Coordinated operation of pumped-storage hydropower with power and water distribution systems

Small pumped-storage hydropower (PSH) units have gained popularity as distributed energy storage options that can provide flexibility to the operation of power distribution systems. Optimal operation of small PSH units is not only dependent on the energy storage provided to power distribution system, but also on the inflow and outflow of water from and to the water distribution system. Here, in this context, this paper develops an optimization model for coordinated operation of PSH units with power and water distribution systems. The proposed model optimizes the operation of water tanks, variable-speed pumps and PSH in pumping and generating modes to minimize the operation cost of power distribution system, while respecting the power flow constraints of power distribution and hydraulic constraints of water distribution system. Appropriate electricity tariffs are implemented to avoid additional expenses in water distribution system that can be enforced by its coordinated operation in favor of power distribution system. The proposed model is implemented on a 33-bus and a 123-bus test power distribution system connected to a 16-node test water distribution system. Results demonstrate the effectiveness of proposed model in tapping PSH flexibility to reduce the operation cost of power and water distribution systems, while meeting the power and water demands.

13 HYDRO ENERGY↗
DOE OSTI2022

Layered Coordination Architecture for Resilient Restoration of Power Distribution Systems

The current practices for restoring critical services in the distribution system during a disaster, align with the traditional centralized ideology of distribution systems operations. A central processor evaluates the distribution system after a disruption and attains a restoration plan. However, the centralized operational paradigm is susceptible to single-point failures, requires full situational awareness of the distribution system, and poses scalability challenges for large multifeeder distribution systems. This motivates a distributed decision-making paradigm where multiple agents solve smaller subproblems and jointly coordinate their individual decisions to achieve the global/network-level objective. Toward this goal, we propose a layered architecture for distributed algorithms for resilience and a two-stage distributed algorithm for distribution system restoration. The proposed distributed decision-making framework enables the bottom-up restoration of the distribution system using all available resources, including distributed generation, while only requiring local awareness and limited communications with neighboring connected regions. The proposed framework is robust to single-point failures, enables autonomy using distributed algorithms, and had reduced computational cost compared to centralized optimization solutions.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2011

On the Use of the Beta Distribution in Probabilistic Resource Assessments

The triangular distribution is a popular choice when it comes to modeling bounded continuous random variables. Its wide acceptance derives mostly from its simple analytic properties and the ease with which modelers can specify its three parameters through the extremes and the mode. On the negative side, hardly any real process follows a triangular distribution, which from the outset puts at a disadvantage any model employing triangular distributions. At a time when numerical techniques such as the Monte Carlo method are displacing analytic approaches in stochastic resource assessments, easy specification remains the most attractive characteristic of the triangular distribution. The beta distribution is another continuous distribution defined within a finite interval offering wider flexibility in style of variation, thus allowing consideration of models in which the random variables closely follow the observed or expected styles of variation. Despite its more complex definition, generation of values following a beta distribution is as straightforward as generating values following a triangular distribution, leaving the selection of parameters as the main impediment to practically considering beta distributions. This contribution intends to promote the acceptance of the beta distribution by explaining its properties and offering several suggestions to facilitate the specification of its two shape parameters. In general, given the same distributional parameters, use of the beta distributions in stochastic modeling may yield significantly different results, yet better estimates, than the triangular distribution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Ion-cyclotron instability in plasmas described by product-bi-kappa distributions

The dispersion relation for parallel propagating waves in the ion-cyclotron branch is investigated numerically by considering that the velocity distribution of the ion population is a function of type product-bi-kappa. We investigate the effects of the non-thermal features and of the anisotropy associated with this type of distribution on the ion-cyclotron instability, as well as the influence of different forms of the electron distribution, by considering Maxwellian distributions, bi-kappa distributions, and product-bi-kappa distributions. The cases of ions described by either Maxwellian or bi-kappa distributions are also considered, for comparison. The results of the numerical analysis show that the increase in the non-thermal character associated with the anisotropic kappa distributions for ions contributes to enhance the instability as compared to that obtained in the Maxwellian case, in magnitude and in wave number range, with more significant enhancement for the case of ion product-bi-kappa distributions than for the case of ion bi-kappa distributions. It is also shown that the ion-cyclotron instability is decreased if the electrons are described by product-bi-kappa distributions, while electrons described by bi-kappa distributions lead to growth rates which are very similar to those obtained considering a Maxwellian distribution for the electron population.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2011

THE POSTERIOR DISTRIBUTION OF sin(i) VALUES FOR EXOPLANETS WITH M{sub T} sin(i) DETERMINED FROM RADIAL VELOCITY DATA

Radial velocity (RV) observations of an exoplanet system giving a value of M{sub T} sin(i) condition (i.e., give information about) not only the planet's true mass M{sub T} but also the value of sin(i) for that system (where i is the orbital inclination angle). Thus, the value of sin(i) for a system with any particular observed value of M{sub T} sin(i) cannot be assumed to be drawn randomly from a distribution corresponding to an isotropic i distribution, i.e., the presumptive prior distribution. Rather, the posterior distribution from which it is drawn depends on the intrinsic distribution of M{sub T} for the exoplanet population being studied. We give a simple Bayesian derivation of this relationship and apply it to several 'toy models' for the intrinsic distribution of M{sub T} , on which we have significant information from available RV data in some mass ranges but little or none in others. The results show that the effect can be an important one. For example, even for simple power-law distributions of M{sub T} , the median value of sin(i) in an observed RV sample can vary between 0.860 and 0.023 (as compared to the 0.866 value for an isotropic i distribution) for indices of the power law in the range between -2 and +1, respectively. Over the same range of indices, the 95% confidence interval on M{sub T} varies from 1.0001-2.405 ({alpha} = -2) to 1.13-94.34 ({alpha} = +2) times larger than M{sub T} sin(i) due to sin(i) uncertainty alone. More complex, but still simple and plausible, distributions of M{sub T} yield more complicated and somewhat unintuitive posterior sin(i) distributions. In particular, if the M{sub T} distribution contains any characteristic mass scale M{sub c} , the posterior sin(i) distribution will depend on the ratio of M{sub T} sin(i) to M{sub c} , often in a non-trivial way. Our qualitative conclusion is that RV studies of exoplanets, both individual objects and statistical samples, should regard the sin(i) factor as more than a 'numerical constant of order unity' with simple and well-understood statistical properties. We argue that reports of M{sub T} sin(i) determinations should be accompanied by a statement of the corresponding confidence bounds on M{sub T} at, say, the 95% level based on an explicitly stated assumed form of the true M{sub T} distribution in order to reflect more accurately the mass uncertainties associated with RV studies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

On the Path to SunShot - Emerging Issues and Challenges with Integrating High Levels of Solar into the Distribution System

Wide use of advanced inverters could double the electricity-distribution system’s hosting capacity for distributed PV at low costs—from about 170 GW to 350 GW (see Palmintier et al. 2016). At the distribution system level, increased variable generation due to high penetrations of distributed PV (typically rooftop and smaller ground-mounted systems) could challenge the management of distribution voltage, potentially increase wear and tear on electromechanical utility equipment, and complicate the configuration of circuit-breakers and other protection systems—all of which could increase costs, limit further PV deployment, or both. However, improved analysis of distribution system hosting capacity—the amount of distributed PV that can be interconnected without changing the existing infrastructure or prematurely wearing out equipment—has overturned previous rule-of-thumb assumptions such as the idea that distributed PV penetrations higher than 15% require detailed impact studies. For example, new analysis suggests that the hosting capacity for distributed PV could rise from approximately 170 GW using traditional inverters to about 350 GW with the use of advanced inverters for voltage management, and it could be even higher using accessible and low-cost strategies such as careful siting of PV systems within a distribution feeder and additional minor changes in distribution operations. Also critical to facilitating distributed PV deployment is the improvement of interconnection processes, associated standards and codes, and compensation mechanisms so they embrace PV’s contributions to system-wide operations. Ultimately SunShot-level PV deployment will require unprecedented coordination of the historically separate distribution and transmission systems along with incorporation of energy storage and “virtual storage,” which exploits improved management of electric vehicle charging, building energy systems, and other large loads. Additional analysis and innovation are neede

14 SOLAR ENERGY↗