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NASA NTRS1976

Feasibility of Coherent and Incoherent Backscatter Experiments from the AMPS Laboratory. Technical Section

A computer program simulated the spectrum which resulted when a radar signal was transmitted into the ionosphere for a finite time and received for an equal finite interval. The spectrum derived from this signal is statistical in nature because the signal is scattered from the ionosphere, which is statistical in nature. Many estimates of any property of the ionosphere can be made. Their average value will approach the average property of the ionosphere which is being measured. Due to the statistical nature of the spectrum itself, the estimators will vary about this average. The square root of the variance about this average is called the standard deviation, an estimate of the error which exists in any particular radar measurement. In order to determine the feasibility of the space shuttle radar, the magnitude of these errors for measurements of physical interest must be understood.

Mozer, F. S.↗

DOE OSTI2017

Evaluation of a Class of Simple and Effective Uncertainty Methods for Sparse Samples of Random Variables and Functions

When very few samples of a random quantity are available from a source distribution of unknown shape, it is usually not possible to accurately infer the exact distribution from which the data samples come. Under-estimation of important quantities such as response variance and failure probabilities can result. For many engineering purposes, including design and risk analysis, we attempt to avoid under-estimation with a strategy to conservatively estimate (bound) these types of quantities -- without being overly conservative -- when only a few samples of a random quantity are available from model predictions or replicate experiments. This report examines a class of related sparse-data uncertainty representation and inference approaches that are relatively simple, inexpensive, and effective. Tradeoffs between the methods' conservatism, reliability, and risk versus number of data samples (cost) are quantified with multi-attribute metrics use d to assess method performance for conservative estimation of two representative quantities: central 95% of response; and 10 -4 probability of exceeding a response threshold in a tail of the distribution. Each method's performance is characterized with 10,000 random trials on a large number of diverse and challenging distributions. The best method and number of samples to use in a given circumstance depends on the uncertainty quantity to be estimated, the PDF character, and the desired reliability of bounding the true value. On the basis of this large data base and study, a strategy is proposed for selecting the method and number of samples for attaining reasonable credibility levels in bounding these types of quantities when sparse samples of random variables or functions are available from experiments or simulations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Towards a Robust Sampling Approach: A Computational Review and Design

As pointed out in several other works, the estimation of the reliability of the electrical grid can not be conducted without the estimation of the stochastic phenomena of electicity demand and electricity production by variable renewable sources. Therefore, sampling procedures have become integral in the design of engineering structures and analysis. Commonly referred to as Monte Carlo uncertainty analysis or integration, the general objective of these procedures is to establish specifics about the uncertainty of an output characteristic of such an engineering system, given uncertainty about its input characteristics. These sampling procedures are applied in a context in which establishing such specifics cannot be performed through other means. Variance-reduction techniques are designed to lessen the variability among estimators to estimate statistics of those output uncertainties. Importance-sampling techniques, on the other hand, are designed to reduce the number of samples needed to estimate a particular statistic—e.g., a tail probability. The combination of these approaches can reduce the computational burden considerably for a particular estimator and statistic. Importance sampling—geared and designed as it is toward improving a particular estimator—suffers, unfortunately, from the unintended consequence of reducing the performance of other estimators in terms of their variance. The objective of this paper is to offer an alternative sampling procedure where this variance does not grow unacceptably large for a suite of estimators. Moreover, it is anticipated that, with additional knowledge of how an engineering output characteristic responds to its input characteristics, tuning parameters of the input’s sampling procedure can be set to improve the output characteristic’s estimation. This work proves the effectiveness of the suggested alternative approach. Such positive outcome will lead to a decrease of the computational burden of performing stochastic optimization of integrated energy systems (e.g., components dispatch, and portfolio composition). In particular, capturing the contribution to the overall system cost of rare and unlikely events and patterns of the electricity demand and production will become less computationally expensive. This is due to the fact that the approach demonstrated here will allow the sampling of those rare occurrences more frequently without misrepresenting their probabilistic impacts.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2014

Kalman filter data assimilation: Targeting observations and parameter estimation

This paper studies the effect of targeted observations on state and parameter estimates determined with Kalman filter data assimilation (DA) techniques. We first provide an analytical result demonstrating that targeting observations within the Kalman filter for a linear model can significantly reduce state estimation error as opposed to fixed or randomly located observations. We next conduct observing system simulation experiments for a chaotic model of meteorological interest, where we demonstrate that the local ensemble transform Kalman filter (LETKF) with targeted observations based on largest ensemble variance is skillful in providing more accurate state estimates than the LETKF with randomly located observations. Additionally, we find that a hybrid ensemble Kalman filter parameter estimation method accurately updates model parameters within the targeted observation context to further improve state estimation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1986

A comparison of SIR-B directional ocean wave spectra with aircraft scanning radar spectra

Directional ocean wave spectra derived from Shuttle Imaging Radar-B (SIR-B) L-band imagery collected off the coast of Southern Chile on 11 and 12 October 1984 were compared with independent spectral estimates from two airborne scanning radars. In sea states with significant wave heights ranging from 3 to 5 meters, the SIR-B-derived sspectra at 18 deg and 25 deg off nadir yielded reasonable estimates of wavelengths, directions, and spectral shapes for all wave systems encountered, including a purely azimuth-traveling system. A SIR-B image intensity variance spectrum containing predominantly range-traveling waves closely resembles an independent aircraft estimate of the slope variance spectrum. The prediction of a U.S. Navy global spectral ocean wave model on 11 October 1984 exhibited no significant bias in dominant wave number but contained a directional bias of about 30 deg with respect to the mean of the aircraft and spacecraft estimates.

Beal, R. C.↗

DOE OSTI2019

A Bayesian Approach to Real-Time Dynamic Parameter Estimation Using Phasor Measurement Unit Measurement

Here, we develop a polynomial-chaos-expansion (PCE)-based approach for decentralized dynamic parameter estimation through Bayesian inference. Using this approach, the non-Gaussian distribution of the inverted parameters is obtained. More specifically, we first represent the decentralized generator model with the PCE-based surrogate. This surrogate allows us to efficiently evaluate the time-consuming dynamic solver at parameter values through Metropolis-Hastings (M-H)-based Markov chain Monte Carlo (MCMC). Then, we propose a two-stage hybrid Markov chain Monte Carlo (MCMC) to recover a posteriori distribution of the decentralized generator model parameters. In the first stage, we use the gradient-enhanced Langevin MCMC algorithm to characterize an intermediate posterior parameter distribution. This algorithm is computationally scalable to the high-dimensional parameter space. Based on the intermediate posterior distribution, during the second stage, we use the adaptive MCMC algorithm to fine-tune the strong correlations between the parameters. Finally, the fully recovered a posterior distribution is obtained in the end. The simulation results show that the proposed PCE-based hybrid MCMC algorithm can accurately and efficiently estimate the high-dimensional generator dynamic model parameters with full probabilistic distribution provided.

42 ENGINEERING↗

DOE OSTI2019

Geometric Estimation of Multivariate Dependency

This paper proposes a geometric estimator of dependency between a pair of multivariate random variables. The proposed estimator of dependency is based on a randomly permuted geometric graph (the minimal spanning tree) over the two multivariate samples. This estimator converges to a quantity that we call the geometric mutual information (GMI), which is equivalent to the Henze–Penrose divergence. between the joint distribution of the multivariate samples and the product of the marginals. The GMI has many of the same properties as standard MI but can be estimated from empirical data without density estimation; making it scalable to large datasets. The proposed empirical estimator of GMI is simple to implement, involving the construction of an minimal spanning tree (MST) spanning over both the original data and a randomly permuted version of this data. We establish asymptotic convergence of the estimator and convergence rates of the bias and variance for smooth multivariate density functions belonging to a Hölder class. We demonstrate the advantages of our proposed geometric dependency estimator in a series of experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Estimation of Body Fat Percentage for Clinical Pharmacokinetic Studies in Children

Obesity is a prevalent childhood condition and the degree of adiposity appears likely to be an important covariate in the pharmacokinetics (PKs) of many drugs. We undertook these studies to facilitate the evaluation and, where appropriate, quantification of the covariate effect of body fat percentage (BF%) on PK parameters in children. We examined two large databases to determine the values and variabilities of BF% in children with healthy body weights and in those with obesity, comparing the accuracy and precision of BF% estimation by both clinical methods and demographically derived techniques. Additionally, we conducted simulation studies to evaluate the utility of the several methods for application in clinical trials. BF% was correlated with body mass index (BMI), but was highly variable among both children with healthy body weights and those with obesity. Bio‐impedance and several demographically derived techniques produced mean estimates of BF% that differed from dual x‐ray absorptiometry by < 1% (accuracy) and a SD of 5% or less (precision). Simulation studies confirmed that when the differences in precision among the several methods were small compared with unexplained between‐subject variability of a PK parameter, the techniques were of similar value in assessing the contribution of BF%, if any, as a covariate for that PK parameter. The combination of sex and obesity stage explained 68% of the variance of BF% with BMI. The estimation of BF% from sex and obesity stage can routinely be applied to PK clinical trials to evaluate the contribution of BF% as a potential covariate.

Green, Thomas P.↗

DOE OSTI2017

Disconnected Diagrams in Lattice QCD

In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called \disconnected diagrams" and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagrams is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei. The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix elements of the nucleon at two different values of the lattice spacing. Finally, we employ these algorithms to do a high-precision study of strange sigma terms in light nuclei; to our knowledge this is the first calculation of its kind from Lattice QCD.

Gambhir, Arjun↗

NASA NTRS1982

Missing observations in multiyear rotation sampling designs

Because Multiyear estimation of at-harvest stratum crop proportions is more efficient than single year estimation, the behavior of multiyear estimators in the presence of missing acquisitions was studied. Only the (worst) case when a segment proportion cannot be estimated for the entire year is considered. The effect of these missing segments on the variance of the at-harvest stratum crop proportion estimator is considered when missing segments are not replaced, and when missing segments are replaced by segments not sampled in previous years. The principle recommendations are to replace missing segments according to some specified strategy, and to use a sequential procedure for selecting a sampling design; i.e., choose an optimal two year design and then, based on the observed two year design after segment losses have been taken into account, choose the best possible three year design having the observed two year parent design.

Gbur, E. E.↗

DOE OSTI2023

O’Hare Airport Short-Term Ground Transportation Modal Demand Forecast Using Gaussian Processes

Here, the principal objective of this study is to analyze the spatial and temporal variation of ground transportation airport demand and provide demand forecast to inform planning capability and explore alternatives for investments to accommodate airport growth. Because of its good adaptability and strong generalization ability for dealing with high-dimensional input, small-sample, and nonlinear spatial data, Gaussian process (GP) regression is used to provide forecast estimates using data from transportation network company (TNC) trips and urban rail passengers at Chicago's O'Hare International Airport. TNC airport trips differ significantly, with three times more distance, more than twice the travel time, and half of the share requests compared with nonairport trips. This highlights the need for separate demand models. Hourly analysis of the rail service indicates that this is likely heavily used by airport workers, whereas TNC services focus on travelers because of variations in the peak demand hours. Heteroscedastic GP regression is implemented because of differences in trip variance between night and day hours. Estimates are given for weekdays and weekend trips, and the 95% confidence intervals are calculated. The introduction of flight schedule information into the models shows marginal improvements in their performance. However, fitting a GP regression becomes computationally expensive with increased sample size and the introduction of spatial components. Transportation planners and policymakers can use the results and methods implemented in this study to optimize transportation assets and provide long-range simulations of the current and future conditions in the area.

42 ENGINEERING↗

DOE OSTI2016

A New CE TSUNAMI-3D Capability for Calculating Undersampling Metrics and Biases

This study investigates the viability of several statistical metrics for predicting the undersampling biases in continuous-energy (CE) Monte Carlo transport simulation tally estimates. Undersampling is a phenomenon in which a Monte Carlo simulation fails to use enough particles per generation to adequately sample fission points in all regions of a problem, resulting in biases in tally estimates that are much larger than the statistical uncertainties, potentially leading to erroneous conclusions regarding system performance and safety. Previous work found that biases due to undersampling could be as large as several hundred per cent mille (pcm) for eigenvalue estimates and up to tens or hundreds of percent for flux tally estimates. This paper documents the encapsulation of undersampling metrics within CE TSUNAMI-3D in the SCALE code system and examines the correlation between the various undersampling metric scores and the magnitude of various undersampling biases. Of the metrics examined, the RHW metric, the Tally Entropy metric, and the uncertainty in the scores for these metrics produce scores that correlated well with the fraction of the undersampling biases in various eigenvalue, flux, and energy-integrated reaction rate tallies in an infinitely reflected model of a PWR fuel assembly. The average number of nonzero scores per generation encountered by a tally was also found to show promise at predicting the magnitude of undersampling biases, and it also found use in detecting and filtering extremely undersampled tallies in the application of the other metrics. Future work will strengthen these conclusions by improving the degree of convergence for the examined tally and undersampling bias estimates, apply these metrics to a more broad variety of systems, and investigate variance reduction approaches for mitigating undersampling in Monte Carlo tally estimates. (authors)

42 ENGINEERING↗

DOE OSTI2016

Variance components in confocal scanning laser tomography measurements of neuro‐retinal rim area and the effect of repeated measurements on the power to detect loss over time

Abstract Purpose To estimate the variation in measurements of neuro‐retinal rim area (NRA) determined by confocal scanning laser tomography and consequences for clinical follow‐up. Methods Altogether, 24 healthy subjects were randomized on –320 μ m, Moorfields and Standard NRA plane strategies. Additionally, NRA was measured in 32 glaucoma subjects. Variance components for subjects, visits and measurements were estimated with analysis of variance. Sample sizes required to detect a 6.0 × 10 −2 mm 2 NRA change were estimated assuming a significance level of 0.05 and a power of 0.8. Consequences for independent group, and paired comparison design, respectively, were analysed. Further, precision in estimates within subjects over time was investigated. Results The variation of NRA among subjects was considerably larger than the variation among visits and measurements. For glaucoma subjects, the variation among visits and measurements were of the same order but larger than in healthy subjects. It was found that independent group comparisons require inconveniently large sample sizes. Within‐subject paired comparisons over time require sample sizes of below 15 subjects. The estimated variations for glaucoma subjects imply that 54 months of follow‐up is required for detection of change from baseline. Conclusions The variance for subjects is substantial in relation to those for visits and measurements. Cross‐sectional independent group comparisons of levels of NRA are unsuitable, due to considerable subject variation. Levels of NRA differences within subjects between visits can be estimated with acceptable precision. Neuro‐retinal rim area (NRA) measurement can be used for long‐term follow‐up of glaucoma progression.

Sandberg Melin, Camilla↗

DOE OSTI2017

A novel approach to the bias-variance problem in bump hunting

This study explores various data-driven methods for performing background-model selection, and for assigning uncertainty on the signal-strength estimator that arises due to the choice of background model. The performance of these methods is evaluated in the context of several realistic example problems. Furthermore, a novel strategy is proposed that greatly simplifies the process of performing a bump hunt when little is assumed to be known about the background. This new approach is shown to greatly reduce the potential bias in the signal-strength estimator, without degrading the sensitivity by increasing the variance, and to produce confidence intervals with valid coverage properties.

47 OTHER INSTRUMENTATION↗

NASA NTRS2017

Remediating Non-Positive Definite State Covariances for Collision Probability Estimation

The NASA Conjunction Assessment Risk Analysis team estimates the probability of collision (Pc) for a set of Earth-orbiting satellites. The Pc estimation software processes satellite position+velocity states and their associated covariance matri-ces. On occasion, the software encounters non-positive definite (NPD) state co-variances, which can adversely affect or prevent the Pc estimation process. Inter-polation inaccuracies appear to account for the majority of such covariances, alt-hough other mechanisms contribute also. This paper investigates the origin of NPD state covariance matrices, three different methods for remediating these co-variances when and if necessary, and the associated effects on the Pc estimation process.

Hall, Doyle T.↗

DOE OSTI2022

Real-Time Distribution System State Estimation with Asynchronous Measurements

We report state estimation is a fundamental task in power systems. Although distribution systems are increasingly equipped with sensing devices and smart meters, measurements are typically reported at different rates and asynchronously; these aspects pose severe strains on workhorse state estimation algorithms, which are designed to process batches of data collected in a synchronous manner from all the measurement units. In this paper, we develop a novel state estimation algorithm to continuously update the estimate of the state based on measurements received in an asynchronous manner from measurement units. The synthesis of the algorithm hinges on a proximal-point type method, implemented in an online fashion, and capable of processing measurements received sequentially from sensors. A performance analysis is presented by providing bounds on the estimation error in terms of the mean and variance that hold at each iteration and asymptotically. The scheme is also compared with a more traditional Weighted Least Squares estimator that compensates for the lack of measurement data by using, as pseudo measurements, the measurement retrieved during a certain time window. Numerical simulations on the IEEE 37-bus feeder corroborate the analytical findings.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Toward quantum Monte Carlo forces on heavier ions: Scaling properties

Quantum Monte Carlo (QMC) forces have been studied extensively in recent decades because of their importance with spectroscopic observables and geometry optimization. Here, we benchmark the accuracy and computational cost of QMC forces. The zero-variance zero-bias (ZVZB) force estimator is used in standard variational and diffusion Monte Carlo simulations with mean-field based trial wavefunctions and atomic pseudopotentials. Statistical force uncertainties are obtained with a recently developed regression technique for heavy tailed QMC data [P. Lopez Rios and G. J. Conduit, Phys. Rev. E 99, 063312 (2019)]. By considering selected atoms and dimers with elements ranging from H to Zn (1 ≤ Z eff ≤ 20), we assess the accuracy and the computational cost of ZVZB forces as the effective pseudopotential valence charge, Z eff , increases. We find that the costs of QMC energies and forces approximately follow simple power laws in Zeff. The force uncertainty grows more rapidly, leading to a best case cost scaling relationship of approximately Z e ff 6.5 ( 3 ) for diffusion Monte Carlo. We find that the accessible system size at fixed computational cost scales as Z e ff − 2 , insensitive to model assumptions or the use of the “space warp” variance-reduction technique. Our results predict the practical cost of obtaining forces for a range of materials, such as transition metal oxides where QMC forces have yet to be applied, and underscore the importance of further developing force variance-reduction techniques, particularly for atoms with high Z eff .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Quantifying uncertainty for deep learning based forecasting and flow-reconstruction using neural architecture search ensembles

Classical problems in computational physics such as data-driven forecasting and signal reconstruction from sparse sensors have recently seen an explosion in deep neural network (DNN) based algorithmic approaches. However, most DNN models do not provide uncertainty estimates, which are crucial for establishing the trustworthiness of these techniques in downstream decision making tasks and scenarios. In recent years, ensemble-based methods have achieved significant success for the uncertainty quantification in DNNs on a number of benchmark problems. However, their performance on real-world applications remains under-explored. In this work, we present an automated approach to DNN discovery and demonstrate how this may also be utilized for ensemble-based uncertainty quantification. Specifically, we propose the use of a scalable neural and hyperparameter architecture search for discovering an ensemble of DNN models for complex dynamical systems. We highlight how the proposed method not only discovers high-performing neural network ensembles for our tasks, but also quantifies uncertainty seamlessly. This is achieved by using genetic algorithms and Bayesian optimization for sampling the search space of neural network architectures and hyperparameters. Subsequently, a model selection approach is used to identify candidate models for an ensemble set construction. Afterwards, a variance decomposition approach is used to estimate the uncertainty of the predictions from the ensemble. We demonstrate the feasibility of this framework for two tasks — forecasting from historical data and flow reconstruction from sparse sensors for the sea-surface temperature. In conclusion, we demonstrate superior performance from the ensemble in contrast with individual high-performing models and other benchmarks.

Deep ensembles↗