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Results for “homogeneous Poisson process”

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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9 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Convolutional Non-Homogeneous Poisson Process and its Application to Wildfire Ignition Risk Quantification for Power Delivery Networks

To quantify wildfire ignition risks on power delivery networks, the current practice predominantly relies on the empirically calculated fire danger indices, which may not well capture the effects of dynamically changing environmental factors. This article proposes a spatio-temporal point process model, known as the Convolutional Non-homogeneous Poisson Process (cNHPP), and applies the model to quantify wildfire ignition risks for power delivery networks. The proposed model captures both the current (i.e., instantaneous) and cumulative (i.e., historical) effects of key environmental processes (i.e., covariates) on wildfire risks, as well as the spatio-temporal dependency among different segments of the power delivery network. The computation and interpretation of the intensity function are thoroughly investigated. We apply the proposed approach to estimate wildfire ignition risks on major transmission lines in California, using historical fire data, meteorological and vegetation data obtained from the National Oceanic and Atmospheric Administration and National Aeronautics and Space Administration. Here, a comprehensive comparison study is performed to show the applicability and predictive capability of the proposed approach.

Non-homogeneous Poisson Process↗
DOE OSTI2021

A note on minimizing time assurance tests for repairable systems

We consider assurance testing for repairable systems when supplementary information is available in addition to the data collected in the assurance test. Here, the supplementary information is incorporated using a Bayesian inferential framework. Here we consider assurance testing for a homogeneous Poisson process. In this note we consider an alternative criterion that minimizes the test time while ensuring that the requirements on the producer's and consumer's risks are met. We illustrate the use of this alternative criterion with an example.

42 ENGINEERING↗
DOE OSTI2024

Quantile regression-enriched event modeling framework for dropout analysis in high-temperature superconductor manufacturing

High-temperature superconductor (HTS) tapes have shown promising characteristics of high critical current, which are prerequisites for applications in high-field magnets. Due to the unstable growth conditions in the HTS manufacturing process, however, the frequent occurrences of dropouts in the critical current impede the consistent performance of HTS tapes. To manufacture HTS tapes with large scale, high yield, and uniform performance, it is essential to develop novel data analysis approaches for modeling the dropouts and identifying the related important process parameters. Conventional methods for modeling recurrent events, such as the point process, require the extraction of events from quality measurements. As the critical current is a continuous process, it may not comprehensively represent the drop patterns by transforming the time-series measurements into a set of events. Here, to solve this issue, we develop a novel quantile regression-enriched event modeling (QREM) framework that integrates the non-homogeneous Poisson process for modeling the occurrence of dropouts and the quantile regression for capturing the drop patterns. By incorporating the feature selection and regularization, the proposed framework identifies a set of significant process parameters that can potentially cause the dropouts of HTS tapes. The proposed method is tested on real HTS tapes produced using an advanced manufacturing process, successfully identifying important parameters that influence dropout events including the substrate temperature and voltage. The results demonstrate that the proposed QREM method outperforms the standard point process in predicting the occurrence of dropouts.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

The Poisson tensor completion parametric estimator

We introduce the Poisson tensor completion (PTC) estimator that exploits inter-sample relationships to compute a low-rank Poisson tensor decomposition of the frequency histogram for samples of a multivariate distribution. Our crucial observation is that the histogram bins are an instance of a space partitioning of counts and thus can be identified with a spatial non-homogeneous Poisson process. The Poisson tensor decomposition leads to a completion of the mean measure over all bins—including those containing few to no samples—and leads to our proposed estimator. A Poisson tensor decomposition models the underlying distribution of the count data and guarantees non-negative estimated values obviating the need for additional constraints to ensure non-negativity. Furthermore, we demonstrate that our PTC estimator is a substantial improvement over standard histogram-based estimators for sub-Gaussian probability distributions because of the concentration of norm phenomenon.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Online Learning and Pricing for Service Systems with Reusable Resources

We consider a price-based revenue management problem with finite reusable resources over a finite time horizon T. Customers arrive following a price-dependent Poisson process, and each customer requests one unit of c homogeneous reusable resources. If there is an available unit, the customer gets served within a price-dependent exponentially distributed service time; otherwise, the customer waits in a queue until the next available unit. In this paper, we assume that the firm does not know how the arrival and service rates depend on posted prices, and thus it makes adaptive pricing decisions in each period based only on past observations to maximize the cumulative revenue. Given a discrete price set with cardinality P, we propose two online learning algorithms, termed batch upper confidence bound (BUCB) and batch Thompson sampling (BTS), and prove that the cumulative regret upper bound is O˜(√PT) , which matches the regret lower bound. In establishing the regret, we bound the transient system performance upon price changes via a novel coupling argument, and also generalize bandits to accommodate subexponential rewards. Here, we also extend our approach to models with balking and reneging customers and discuss a continuous price setting. Our numerical experiments demonstrate the efficacy of the proposed BUCB and BTS algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Change-point Detection and Image Segmentation for Time Series of Astrophysical Images

Many astrophysical phenomena are time-varying, in the sense that their intensity, energy spectrum, and/or the spatial distribution of the emission suddenly change. This paper develops a method for modeling a time series of images. Under the assumption that the arrival times of the photons follow a Poisson process, the data are binned into 4D grids of voxels (time, energy band, and x-y coordinates), and viewed as a time series of non-homogeneous Poisson images. The method assumes that at each time point, the corresponding multiband image stack is an unknown 3D piecewise constant function including Poisson noise. It also assumes that all image stacks between any two adjacent change points (in time domain) share the same unknown piecewise constant function. The proposed method is designed to estimate the number and the locations of all of the change points (in time domain), as well as all of the unknown piecewise constant functions between any pairs of the change points. The method applies the minimum description length principle to perform this task. A practical algorithm is also developed to solve the corresponding complicated optimization problem. Simulation experiments and applications to real data sets show that the proposed method enjoys very promising empirical properties. Applications to two real data sets, the XMM observation of a flaring star and an emerging solar coronal loop, illustrate the usage of the proposed method and the scientific insight gained from it.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Particle transport in Markov stochastic mixtures with spatial gradients

Markov geometries are a prototype class of stochastic media that are widely used to model complex disordered systems. In a series of recent works, we have shown that spatially homogeneous (but possibly non-isotropic) Poisson tessellations can be conveniently used in order to generate three-dimensional realizations of Markov media and thus characterize the features of particle transport e.g. in fragmented fuel elements following severe nuclear accidents or Rayleigh-Taylor turbulent mixing for inertial confinement fusion. In this paper we show that Poisson tessellations can be extended to take into account the presence of spatial gradients, which commonly occur in real-world applications due to material stratification. For this purpose, we will provide an explicit construction of spatially-non-homogeneous Poisson tessellations, fully characterize their statistical properties, and finally illustrate the behaviour of particle transport in such random media. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Transport in Stochastic Media with Random Chord Length Distributions

Thermal radiation transport computations in binary Markovian random mixtures rely almost exclusively on the Levermore-Pomraning (LP) model which is obtained by applying a heuristic closure to the ensemble averaged random medium transport equation. The validity of this model has been extensively tested by comparing numerical results over a broad parameter range (material types and mixing parameters) against benchmark solutions in planar geometry. The conditions under which the LP-model provides useful results and when it breaks down are now well established, but work to date has been largely restricted to homogeneous mixing statistics, i.e., the mean chord lengths of both materials are taken to be spatially constant. In recent work, this limitation was relaxed by allowing the mean chord lengths and, in a consistent fashion, the volume fractions in the LP-model to vary spatially and in a follow-up investigation benchmark solutions were obtained by ensemble averaging results over material realizations sampled from a nonhomogeneous Poisson process (NHPP). Numerical experiments in rod geometry with specifically linear and quadratic spatial dependence of chord lengths showed that the material averaged radiation intensities vary nonmonotonically with depth into the medium, in stark contrast to solutions obtained assuming uniform chord lengths. Moreover, depending on the local optical thickness and strength of scattering, the LP-model results showed locally more nuanced deviations from the benchmark solutions than was the case with constant chord lengths. These limited numerical investigations highlight the nontrivial qualitative and quantitative consequences of nonhomogeneous mixing statistics, in particular that closure approximations may not be uniformly valid or invalid over the problem domain.

42 ENGINEERING↗
DOE OSTI2023

11-th order of accuracy for numerical solution of 3-D Poisson equation with irregular interfaces on unfitted Cartesian meshes

For the first time the optimal local truncation error method (OLTEM) with 125-point stencils and unfitted Cartesian meshes has been developed in the general 3-D case for the Poisson equation for heterogeneous materials with smooth irregular interfaces. The 125-point stencils equations that are similar to those for quadratic finite elements are used for OLTEM. The interface conditions for OLTEM are imposed as constraints at a small number of interface points and do not require the introduction of additional unknowns, i.e., the sparse structure of global discrete equations of OLTEM is the same for homogeneous and heterogeneous materials. The stencils coefficients of OLTEM are calculated by the minimization of the local truncation error of the stencil equations. These derivations include the use of the Poisson equation for the relationship between the different spatial derivatives. Such a procedure provides the maximum possible accuracy of the discrete equations of OLTEM. In contrast to known numerical techniques with quadratic elements and third order of accuracy on conforming and unfitted meshes, OLTEM with the 125-point stencils provides 11-th order of accuracy, i.e., an extremely large increase in accuracy by 8 orders for similar stencils. The numerical results show that OLTEM yields much more accurate results than high-order finite elements with much wider stencils. The increased numerical accuracy of OLTEM leads to an extremely large increase in computational efficiency. Additionally, a new post-processing procedure with the 125-point stencil has been developed for the calculation of the spatial derivatives of the primary function. The post-processing procedure includes the minimization of the local truncation error and the use of the Poisson equation. It is demonstrated that the use of the partial differential equation (PDE) for the 125-point stencils improves the accuracy of the spatial derivatives by 6 orders compared to post-processing without the use of PDE as in existing numerical techniques. At an accuracy of 0.1% for the spatial derivatives, OLTEM reduces the number of degrees of freedom by 900 - 4∙10 6 times compared to quadratic finite elements. The developed post-processing procedure can be easily extended to unstructured meshes and can be independently used with existing post-processing techniques (e.g., with finite elements).

97 MATHEMATICS AND COMPUTING↗