Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Density estimation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Noise and error analysis and optimization in particle-based kinetic plasma simulations

In this paper we analyze the noise in macro-particle methods used in plasma physics and fluid dynamics, leading to approaches for minimizing the total error, focusing on electrostatic models in one dimension. We begin by describing kernel density estimation for continuous values of the spatial variable x, expressing the kernel in a form in which its shape and width are represented separately. The covariance matrix of the noise in the density is computed, first for uniform true density. The bandwidth of the covariance matrix C(x,y) is related to the width of the kernel. A feature that stands out is the presence of constant negative terms in the elements of the covariance matrix both on and off-diagonal. These negative correlations are related to the fact that the total number of particles is fixed at each time step; they also lead to the property ∫C(x,y)dy = 0. We investigate the effect of these negative correlations on the electric field computed by Gauss's law, finding that the noise in the electric field is related to a process called the Ornstein-Uhlenbeck bridge, leading to a covariance matrix of the electric field with variance significantly reduced relative to that of a Brownian process. For non-constant density, p(x), still with continuous x, we analyze the total error in the density estimation and discuss it in terms of bias-variance optimization (BVO). For some characteristic length l, determined by the density and its second derivative, and kernel width h, having too few particles within h leads to too much variance; for h that is large relative to l, there is too much smoothing of the density. The optimum between these two limits is found by BVO. For kernels of the same width, it is shown that this optimum (minimum) is weakly sensitive to the kernel shape. Next, we repeat the analysis for x discretized on a grid. In this case the charge deposition rule is determined by a particle shape. An important property to be respected in the discrete system is the exact preservation of total charge on the grid; this property is necessary to ensure that the electric field is equal at both ends, consistent with periodic boundary conditions. We find that if the particle shapes satisfy a partition of unity property, the particle charge deposited on the grid is conserved exactly. Further, if the particle shape is expressed as the convolution of a kernel with another kernel that satisfies the partition of unity, then the particle shape obeys the partition of unity. This property holds for kernels of arbitrary width, including widths that are not integer multiples of the grid spacing. Furthermore, we show results relaxing the approximations used to do BVO optimization analytically, by doing numerical computations of the total error as a function of the kernel width, on a grid in x. The comparison between numerical and analytical results shows good agreement over a range of particle shapes. We discuss the practical implications of our results, including the criteria for design and implementation of computationally efficient particle shapes that take advantage of the developed theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Graph-Augmented Normalizing Flows for Anomaly Detection of Multiple Time Series

Anomaly detection is a widely studied task for a broad variety of data types; among them, multiple time series appear frequently in applications, including for example, power grids and traffic networks. Detecting anomalies for multiple time series, however, is a challenging subject, owing to the intricate interdependencies among the constituent series. We hypothesize that anomalies occur in low density regions of a distribution and explore the use of normalizing flows for unsupervised anomaly detection, because of their superior quality in density estimation. Moreover, we propose a novel flow model by imposing a Bayesian network among constituent series. A Bayesian network is a directed acyclic graph (DAG) that models causal relationships; it factorizes the joint probability of the series into the product of easy-to-evaluate conditional probabilities. We call such a graph-augmented normalizing flow approach GANF and propose joint estimation of the DAG with flow parameters. We conduct extensive experiments on real-world datasets and demonstrate the effectiveness of GANF for density estimation, anomaly detection, and identification of time series distribution drift.

Dai, Enyan↗
DOE OSTI2024

Spatial patterns in occupancy and density of larval lampreys in freshwater habitats restored to a Stage 0 condition

Abstract We examined occupancy and density of larval lampreys ( Entosphenus tridentatus and Lampetra spp.) in two rivers in Oregon (USA) restored to a Stage 0 condition 1–5 years prior, using a multiscale occupancy model and a zero‐inflated Poisson mixture model. We sampled lampreys using backpack electrofishing in randomly distributed, paired, 1‐m 2 quadrats and recorded environmental data. Probabilities of occupancy and density were higher when water velocity was low, the substrate was noncompacted, and sediment was dominated by fines (<4 mm). At mean water depth (0.34 m) and velocity (0.09 m/s), estimated densities in occupied quadrats were 4.8 lampreys/m 2 (95%: 3.4–6.9) when the substrate was compacted, and fines were not dominant, and 21.1 lampreys/m 2 (95%: 17.7–25.3) when the substrate was noncompacted and fines were dominant. Probabilities of detecting occupancy in a 1‐m 2 quadrat sampled by backpack electrofishing were 0.76 (95%: 0.64–0.87) when captured after visual observation and 0.80 (95%: 0.71–0.88) with blind sweeps (i.e., constantly moving the net regardless of observation). The probability of capturing a single lamprey in a quadrat sampled by blind sweeps was 0.32 (95%: 0.27–0.37). Sampling in paired 1‐m 2 quadrats facilitated concurrent examination of patterns in occupancy and density while accounting for capture probability, which could aid temporal monitoring of restored habitats. To the best of our knowledge, this is the first study to document occupancy and estimate densities of larval lampreys in habitats that underwent valley floor restoration to Stage 0. We observed both lamprey genera within 5 years of restoration. Aquatic restoration that increases low‐velocity, noncompacted, fine sediment habitats could benefit lampreys.

Harris, Julianne E.↗
DOE OSTI2021

Next-Cycle Optimal Fuel Control for Cycle-to-Cycle Variability Reduction in EGR-Diluted Combustion

In this simulation study, cycle-to-cycle fuel control was used to reduce CCV by injecting additional fuel in operating conditions with sporadic misfires and partial burns. An optimal control policy was proposed that utilizes 1) a physics-based model that tracks in-cylinder gas composition and 2) a one-step-ahead prediction of the combustion efficiency based on a kernel density estimator. The optimal solution, however, presents a tradeoff between the reduction in combustion CCV and the increase in fuel injection quantity required to stabilize the charge. Such a tradeoff can be ad- just by a single parameter embedded in the cost function.

Maldonado, BryanP. [Oak Ridge National Lab. (ORNL)↗
DOE OSTI2023

A Multi-Fidelity Gaussian Process Regression Method for Probabilistic Wind Farm Power Curve Estimation

Accurate estimation of the power curve for wind turbines or wind farms is crucial to ensure their efficient operation and management. However, conventional methods for power curve estimation rely either on expensive and infrequent measurements or on low-quality numerical simulations. Moreover, the majority of previous studies on power curve estimation for wind turbines or wind farms focused on deterministic estimation, which provides a point estimate of the relationship between wind speed and power generation. Nevertheless, the deterministic approach fails to consider the inherent uncertainty associated with wind energy production resulting from varying turbine characteristics. This can lead to inaccurate power generation estimation and suboptimal decisions regarding energy management. In this paper, a kernel density estimation (KDE) based Multi-Fidelity Gaussian Process Regression (MFGPR) model is proposed to fuse theoretical power curve data and the ground true measurements to create a mapping of wind speed and wind power. By conducting a case study on an actual wind farm in China, the efficacy of the proposed MFGPR model was demonstrated in characterizing the variability of wind power. The probabilistic MFGPR model was also able to generate confidence intervals that encompassed the measured power, thereby improving the accuracy and confidence in wind power estimation or wind resource assessment. Overall, the proposed MFGPR model offers a reliable approach to integrate high-fidelity ground measurements and theoretical power curve data, resulting in precise wind resource assessment and power estimation.

Gaussian process regression↗
DOE OSTI2025

Reference Correlations for the Density and Viscosity of Molten Alkali and Alkaline Earth Fluoride Salts

While there is a significant body of literature pertaining to thermophysical property measurements of molten salts, there is often a wide degree of variability among independent measurements of the same compounds. As such, the scientific community benefits greatly from an unbiased, independent assessment of duplicate datasets, so that reference correlations which describe these thermophysical properties as functions of temperature can be determined and then commonly used by researchers, scientists, and engineers. With regard to molten fluoride compounds, a significant time has elapsed since density and viscosity reference correlations have been determined; Janz conducted the most recent effort, in 1988, to provide reference correlations for the densities and viscosities of molten fluoride compounds via the National Standard Reference Data System coordinated by the National Bureau of Standards. Since then, new data have been published for molten fluoride compounds, and a new precedent has surfaced for putting forth reference correlations that involve fitting to multiple primary datasets. In this work, reference correlations are put forth for molten alkali and alkaline earth fluoride compounds in an effort to provide updated, improved correlations for general use. For molten alkali fluoride densities, estimated uncertainties with a 95% confidence interval are summarized as follows: LiF (0.63%), NaF (0.48%), KF (0.76%), RbF (0.93%), and CsF (0.75%). For molten alkaline earth fluoride densities, an estimated uncertainty was not able to be quantified for BeF 2 because of limited data; however, estimated uncertainties with a 95% confidence interval are summarized as follows for the remaining alkaline earth fluorides: MgF 2 (1.5%), CaF 2 (0.92%), SrF 2 (1.6%), and BaF 2 (0.23%). For molten alkali fluoride viscosities, uncertainty was not able to be quantified for RbF and CsF because of limited data; however, estimated uncertainties with a 95% confidence interval are summarized as follows for the remaining alkali fluorides: LiF (4.4%), NaF (3.0%), and KF (4.0%). For molten alkaline earth fluoride viscosities, limited consistent data resulted in the recommendation of single datasets (from literature) that are deemed to be the most trustworthy based on the quality of the underlying experimental studies.

Birri, A. [Oak Ridge National Laboratory (ORNL), O↗
DOE OSTI2021

A Novel Data-based Stochastic Distribution Control for Non-Gaussian Stochastic Systems

In this note, we present a novel data-based approach to investigate the non-Gaussian stochastic distribution control problem. As the motivation of this note, the existing methods have been summarised regarding to the drawbacks, for example, neural network weights training for unknown stochastic distribution and so on. To overcome these disadvantages, a new transformation for dynamic probability density function is given by kernel density estimation using interpolation. Based upon this transformation, a representative model has been developed while the stochastic distribution control problem has been transformed into an optimisation problem. Then, data-based direct optimisation and identification-based indirect optimisation have been proposed. In addition, the convergences of the presented algorithms are analysed and the effectiveness of these algorithms has been evaluated by numerical examples. In summary, the contributions of this note are as follows: 1) a new data-based probability density function transformation is given; 2) the optimisation algorithms are given based on the presented model; and 3) a new research framework is demonstrated as the potential extensions to the existing stochastic distribution control.

42 ENGINEERING↗
DOE OSTI2022

A functional global sensitivity measure and efficient reliability sensitivity analysis with respect to statistical parameters

Sensitivity analysis and reliability assessment are two important aspects of structural and system safety. Epistemic uncertainty with respect to probabilistic model of input parameters due to lack of knowledge is present in many scarce-data applications and complicates the characterization of uncertainty in model response. In this article, we present two importance measures to evaluate the impact of distribution parameters on the probability distribution function (PDF) of the output and the failure probability. The epistemic uncertainty associated with the distribution parameters is modeled as random variables. Additionally, a modified extended polynomial chaos expansion (MEPCE) approach is introduced in which aleatory and epistemic random variables are modeled and propagated simultaneously while allowing the separate assessment for any single epistemic variable. A MEPCE-based kernel density estimation (KDE) construction provides a composite map from each epistemic variable to the response PDF. The functional global sensitivity index of the PDF with respect to the distribution parameters is thus derived, as a function of output, which is both more informative and more efficient than standard scalar sensitivity measures. Reliability sensitivity indices can be readily evaluated by integrating the global sensitivity index function over the failure zone. Three illustrative examples are used to demonstrate the proposed methodology.

42 ENGINEERING↗
DOE OSTI2022

Improved Data Interpretation through Identification of Time Series Periodicity Changes

Analysis and interpretation of time series data is easiest when the data values occur at uniform intervals in time, but actual data may have differing data sampling frequencies, such as monthly and daily readings. Applying data analysis techniques, such as smoothing, to such a data set may not give a representative result between time segments. The ability to automatically distinguish time segments of differing data frequency would provide a means for applying data analysis independently to each segment, though a suitable blending at segment boundaries would be required. A method for detecting frequency changes was developed and applied to Gaussian and median smoothing of hydraulic head data from groundwater wells at the U.S. Department of Energy Hanford Site in southeastern Washington state. The process identifies time segments of high-frequency (daily) or low-frequency (greater than daily) data using adjusted-bandwidth Gaussian kernel density estimation and a threshold value, which are further refined to address small blocks of low-frequency data within larger blocks of high-frequency data. User-selectable levels of smoothing are then applied independently to the time segments prior to combining the segment results for a single smoothed data set. This time segment identification approach provides effective low- and high-frequency data separation, which provides a method to apply data analysis independently to each time segment.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Conformal Hierarchical Simulation-Based Inference with Local Validity

Trustworthy and interpretable uncertainty quantification is a long-standing challenge in artificial intelligence. Simulation-based inference (SBI) comprises a broad swath of approaches for estimating latent parameters with uncertainties. Although flexible neural density estimators in SBI can be remark- ably expressive capturing highly structured, high-dimensional posteriors their credible regions can be badly mis-calibrated and are often only accompanied by heuristic coverage checks. We present the first SBI framework that delivers finite-sample local valid coverage guarantees that hold in the neighborhood of each observation. Our framework can couple any off-the-shelf hierarchical SBI engine with a confor- mal Bayesian post-processing step that operates on the posterior predictive density. A kernel-weighted conformity score adapts the conformal quantile to the local geometry of the data, yielding prediction sets that are simultaneously (i) marginally calibrated, (ii) locally valid, and (iii) hierarchical, handling global and observation-specific parameters in a single pass. Through experiments on synthetic data and benchmarks from neuroscience and physics, we show that our approach attains 1 − α coverage, where prior SBI methods under- or over-cover. Our approach also maintains a competitive, credible set size with minimal computational overhead. Finally, our approach can be used to make predictions on real data and give valid credible regions modulo weight-initialization-based model mis-specification.

Trivedi, Shubhendu [Fermilab]↗
DOE OSTI2020

Understanding Asteroid 16 Psyche’s composition through 3D impact crater modeling

Asteroid 16 Psyche is the largest M-type (metallic) Main Belt Asteroid (MBA). Radar albedo data indicate Psyche’s surface is rich in metallic content, but estimates for Psyche’s bulk structure vary widely, with bulk density estimates ranging from 1.4 ± 0.3 g/cm 3 to 4.5 ± 1.4 g/cm 3 and porosity estimates ranging from 30% to 70%. A forthcoming NASA discovery mission will visit Psyche. Narrowing the range of estimated compositions of Psyche prior to mission launch can help to determine the necessary tools for asteroid analysis. Psyche has two large impact structures in its Southern hemisphere, with estimated diameters from 50 km to 70 km and estimated depths up to 6.4 km. In this work, we present results from 2D and 3D hydrocode simulations of the largest of these impact structures. Through quantitative comparison of the simulated crater dimensions with measured values, our models suggest that Psyche is largely composed of porous, metallic material. In addition, to match the crater dimensions, our simulations indicate that the angle of impact was significantly altered from vertical by 45–60 degrees.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Multi-head physics-informed neural networks for learning functional priors and uncertainty quantification

In numerous applications, the integration of prior knowledge and historical information is essential, particularly for tasks requiring the solution of ordinary or partial differential equations (ODEs/PDEs) in data-sparse or noisy environments. For instance, achieving accurate solutions to time-dependent PDEs with limited initial condition measurements necessitates an effective strategy for embedding prior knowledge. Hard-parameter sharing architectures in neural networks (NNs) have demonstrated success in both traditional and scientific machine learning domains, facilitating the learning of informative representations. Here, in this study, we introduce a novel, yet efficient, method to enhance physics-informed neural networks (PINNs) by incorporating a multi-head structure that enables the learning of functional priors from both empirical data and governing physical laws. This prior information can then be used to address data sparsity and high-level noise in solving ODE/PDE problems with uncertainty quantification (UQ). The approach, termed Multi-Head PINN (MH-PINN), consists of a shared body NN and multiple head NNs, each corresponding to an individual PINN instance. Our framework for functional prior learning is carried out in two stages: (1) training the MH-PINNs to develop a shared body NN alongside multiple head NNs, and (2) employing these trained head NNs to estimate a prior distribution through a normalizing flow-based density estimator. The learned functional prior can then be applied as a regularization mechanism in deterministic contexts or as an informative prior within a Bayesian inference framework, aiding in the resolution of subsequent ODE/PDE tasks. We evaluate the efficacy of MH-PINNs across five benchmark problems, including a high-dimensional parametric PDE, all characterized by data sparsity or substantial noise levels. Our findings reveal that MH-PINNs deliver accurate solutions and robust UQ, demonstrating adaptability across a range of complex and challenging scenarios.

Bayesian inference↗
DOE OSTI2022

Non-Parametric Statistical Analysis of Current Waveforms through Power System Sensors

The protection, control, and monitoring of the power grid is not possible without accurate measurement devices. As the percentage of renewable energy sources penetrating the existing grid infrastructure increases, so do uncertainties surrounding their effects on the everyday operation of the power system. Many of these devices are sources of high-frequency transients. These transients may be useful for identifying certain events or behaviors otherwise not seen in traditional analysis techniques. Therefore, the ability of sensors to accurately capture these phenomena is paramount. In this work, two commercial-grade power system distribution sensors are investigated in terms of their ability to replicate high-frequency phenomena by studying their responses to three events: a current inrush, a microgrid “close-in”, and a fault on the terminals of a wind turbine. Kernel density estimation is used to derive the non-parametric probability density functions of these error distributions and their adequateness is quantified utilizing the commonly used root mean square error (RMSE) metric. It is demonstrated that both sensors exhibit characteristics in the high harmonic range that go against the assumption that measurement error is normally distributed.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Assessment of Molten Eutectic LiF-NaF-KF Density through Experimental Determination and Semiempirical Modeling

Molten salts have favorable material properties for use in high-temperature energy systems, including thermal energy storage systems, concentrating solar power plants, nuclear reactors, and various industrial manufacturing processes. Knowledge of chemical and thermophysical property data is essential for the design and optimization of these systems, yet data are often limited or uncertain for many candidate salts due to the difficulty of thermophysical property measurements at relevant temperatures (e.g., 500–900 °C). Here, the density of molten LiF-NaF-KF eutectic is reassessed through review of previous experimental data, new density measurements from 470 to 800 °C, and semiempirical modeling. Additionally, the density was measured using the displacement technique. Compositional and temperature-dependent density estimates were calculated with a multidimensional Redlich–Kister model. The results of the new experimental measurements agree within 2% of the modeled density of molten eutectic LiF-NaF-KF. The Redlich–Kister model’s prediction shows a near-ideal density behavior for the LiF-NaF-KF system and is promising for the estimation of off-eutectic LiF-NaK-KF densities. Finally, through review of the existing literature and comparison to new measurements, recommendations are made for the density of LiF-NaF-KF.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Measuring Young Stars in Space and Time. II. The Pre-main-sequence Stellar Content of N44

The Hubble Space Telescope survey Measuring Young Stars in Space and Time (MYSST) entails some of the deepest photometric observations of extragalactic star formation, capturing even the lowest-mass stars of the active star-forming complex N44 in the Large Magellanic Cloud. We employ the new MYSST stellar catalog to identify and characterize the content of young pre-main-sequence (PMS) stars across N44 and analyze the PMS clustering structure. To distinguish PMS stars from more evolved line of sight contaminants, a non-trivial task due to several effects that alter photometry, we utilize a machine-learning classification approach. This consists of training a support vector machine (SVM) and a random forest (RF) on a carefully selected subset of the MYSST data and categorize all observed stars as PMS or non-PMS. Combining SVM and RF predictions to retrieve the most robust set of PMS sources, we find ∼26,700 candidates with a PMS probability above 95% across N44. Employing a clustering approach based on a nearest neighbor surface density estimate, we identify 16 prominent PMS structures at 1σ significance above the mean density with sub-clusters persisting up to and beyond 3σ significance. The most active star-forming center, located at the western edge of N44's bubble, is a subcluster with an effective radius of ∼5.6 pc entailing more than 1100 PMS candidates. Furthermore, we confirm that almost all identified clusters coincide with known H ii regions and are close to or harbor massive young O stars or YSOs previously discovered by MUSE and Spitzer observations.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Simulation based inference with domain adaptation for strong gravitational lensing

Simulation based inference leverages machine learning to carry out Bayesian inference in systems with intractable likelihoods. However, transitioning a network trained on simulated data to real data runs the risk of encountering domain shift, leading to performance losses. We attempt to implement domain adaptation into the sbi neural posterior estimation framework using the Maximum Mean Discrepancy as an additional network loss, using masked autoregressive fow (MAF) as our density estimator. We test the network on a set of 400,000 simulated strong gravitational lensing images generated using deeplenstronomy. The source domain is defined as low noise whereas the target domain has a noise profile sampled from experimentally derived DES survey conditions. We find that SBI appears robust against small changes in the data with similar performance on source and target. Moreover, while DA does lead to performance improvements, they are marginal at 6% less inference error.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗