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DOE OSTI2022

Kernel learning backward SDE filter for data assimilation

In this paper, we develop a kernel learning backward SDE filter method to estimate the state of a stochastic dynamical system based on its partial noisy observations. A system of forward backward stochastic differential equations is used to propagate the state of the target dynamical model, and Bayesian inference is applied to incorporate the observational information. Further, to characterize the dynamical model in the entire state space, we introduce a kernel learning method to learn a continuous global approximation for the conditional probability density function of the target state by using discrete approximated density values as training data. Numerical experiments demonstrate that the kernel learning backward SDE is highly effective.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2006

Calibration of the EU Oxybarometer for Nakhlites

Martian meteorites have various characteristics, which are direct clues to understanding the petrogenesis of Mars rocks. The variation in oxidation state among the Martian meteorites must have important implications for redox conditions of the Martian crust/mantle and overall differentiation on Mars. Wadhwa [1] and Herd et al. [2] reported that Martian basalts were formed under a range of oxidation states, suggesting complex petrogenesis processes. The nakhlites, which have rather different characteristics from basaltic shergottites, may give us additional clues to Martian petrogenesis. The oxidation states of meteorites are usually described by the oxygen fugacity (fO2) under which the meteorites crystallized. One of the methods to estimate the oxygen fugacity is the depth of Eu anomaly. Eu(2+)/Eu(3+) is determined by the oxygen fugacity and partitioning is different for Eu(2+) and Eu(3+). Therefore, the depth of Eu anomaly in a mineral is a function of the oxygen fugacity and the Eu2+/Eu3+ in the melt from which the mineral crystallized. This method has some advantages over another major method, the two-oxide oxybarometer [3], which can more easily be affected by subsolidus processes. The Eu oxybarometer can analyze the cores of the earliest formed crystals in Martian meteorites, which means it can give us a better indication of the oxygen fugacity of the parent melt. The calibration of the Eu oxybarometer has been done with the basaltic shergottites before [4]. However, it has never been applied to nakhlites (Oe et al. [5] measured the depth of Eu anomaly in the synthetic pyroxene only at QFM). Partition coefficients are strongly affected by phase compositions, especially pyroxene Ca content and melt Al content [e.g., 5,6]. The composition of nakhlite pyroxene is rather different from basaltic shergottite pyroxene. Thus, there may be problems in applying the Eu oxybarometer calibration for the basaltic shergottites [7] to nakhlites. Thus, we report in this abstract preliminary results of our experimental calibration of the depth of Eu anomaly in pyroxene vs. oxygen fugacity for nakhlites.

Makishima, J.↗

DOE OSTI2021

Efficient Estimation of Pauli Observables by Derandomization

In this work, we consider the problem of jointly estimating expectation values of many Pauli observables, a crucial subroutine in variational quantum algorithms. Starting with randomized measurements, we propose an efficient derandomization procedure that iteratively replaces random single-qubit measurements by fixed Pauli measurements; the resulting deterministic measurement procedure is guaranteed to perform at least as well as the randomized one. In particular, for estimating any L low-weight Pauli observables, a deterministic measurement on only of order log(L) copies of a quantum state suffices. In some cases, for example, when some of the Pauli observables have high weight, the derandomized procedure is substantially better than the randomized one. Specifically, numerical experiments highlight the advantages of our derandomized protocol over various previous methods for estimating the ground-state energies of small molecules.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRSDate not supplied

Joint Acceptance Attenuation Factor of Integrated Pressure with Unsteady Pressure-Sensitive Paint Measurements

The Unsteady Pressure-Sensitive Paint (uPSP) is widely used to measure the surface pressure of scaled models in wind tunnel tests. Compared to the conventional pressure transducers, uPSP has the advantage of high spatial resolution. With multiple high-speed Complementary Metal Oxide Superconductor (CMOS) cameras, the uPSP data collected with the camera pixels are mapped to the surface grid of the scaled model and converted to pressure. The shot noise is the dominant component of the noise in the uPSP measurement. The integrated pressure is usually computed on the grid nodes of a user-defined patch. The effect of shot noise is reduced in the integrated pressure on the patch; however, the measurement of the aerodynamic pressure may also be attenuated by the decorrelation of the flow pressure field being measured. This paper discusses the Joint Acceptance Attenuation Factor (JAAF) of the integrated pressure with uPSP measurements. The JAAF, a function of frequency, is defined as the ratio of the Power Spectral Density (PSD) of the integrated aerodynamic pressure on the patch to the average PSD of the aerodynamic pressure on the grid nodes of the patch. In this paper, the JAAF is investigated for the integrated pressure on rectangular patches, whose edges are defined in the direction along the streamline or across the streamline. Based on the assumption that the surface pressure field can be described by the Corcos model, the closed-form formulas to compute the JAAFs of the integrated pressure on the discrete grid nodes of a rectangular patch and over the continuous area of a rectangular patch are derived respectively. It is shown that the JAAF of the integrated pressure over the continuous area of a rectangular patch is the limit of that on discrete nodes of the rectangular patch when the number of nodes in each row or column goes to infinity. The closed-form formulas of the JAAF derived in this paper, with estimated parameters of the model, are verified with the measurements of the uPSP and the conventional pressure transducer collected in the Space Launch System Ascent Unsteady Aerodynamics Test at NASA Ames Research Center in November 2017. The closed-form formulas of the JAAF of the integrated pressure on the rectangular patches, based on the Corcos model, provide an efficient method to estimate the attenuation of integration by the decorrelation of the flow pressure field and set references for the comparison of the spectrum of the integrated uPSP measurements and the conventional pressure transducer measurements. The work described in this paper is a part of NASA’s development of a new state-of-the-art uPSP capability in production wind tunnels. Funding was provided by the NASA Aerosciences Evaluation and Test Capabilities Portfolio Office.

acoustics↗

NASA NTRSDate not supplied

Joint Acceptance Attenuation Factor of Integrated Pressure with Unsteady Pressure-Sensitive Paint Measurements

acoustics↗

NASA NTRS2013

Measuring and Estimating Normalized Contrast in Infrared Flash Thermography

Infrared flash thermography (IRFT) is used to detect void-like flaws in a test object. The IRFT technique involves heating up the part surface using a flash of flash lamps. The post-flash evolution of the part surface temperature is sensed by an IR camera in terms of pixel intensity of image pixels. The IR technique involves recording of the IR video image data and analysis of the data using the normalized pixel intensity and temperature contrast analysis method for characterization of void-like flaws for depth and width. This work introduces a new definition of the normalized IR pixel intensity contrast and normalized surface temperature contrast. A procedure is provided to compute the pixel intensity contrast from the camera pixel intensity evolution data. The pixel intensity contrast and the corresponding surface temperature contrast differ but are related. This work provides a method to estimate the temperature evolution and the normalized temperature contrast from the measured pixel intensity evolution data and some additional measurements during data acquisition.

Koshti, Ajay M.↗

NASA NTRS1980

A direct method for synthesizing low-order optimal feedback control laws with application to flutter suppression

A direct method of synthesizing a low-order optimal feedback control law for a high order system is presented. A nonlinear programming algorithm is employed to search for the control law design variables that minimize a performance index defined by a weighted sum of mean square steady state responses and control inputs. The controller is shown to be equivalent to a partial state estimator. The method is applied to the problem of active flutter suppression. Numerical results are presented for a 20th order system representing an aeroelastic wind-tunnel wing model. Low-order controllers (fourth and sixth order) are compared with a full order (20th order) optimal controller and found to provide near optimal performance with adequate stability margins.

Mukhopadhyay, V.↗

NASA NTRS2006

A Time Series Approach for Soil Moisture Estimation

Soil moisture is a key parameter in understanding the global water cycle and in predicting natural hazards. Polarimetric radar measurements have been used for estimating soil moisture of bare surfaces. In order to estimate soil moisture accurately, the surface roughness effect must be compensated properly. In addition, these algorithms will not produce accurate results for vegetated surfaces. It is difficult to retrieve soil moisture of a vegetated surface since the radar backscattering cross section is sensitive to the vegetation structure and environmental conditions such as the ground slope. Therefore, it is necessary to develop a method to estimate the effect of the surface roughness and vegetation reliably. One way to remove the roughness effect and the vegetation contamination is to take advantage of the temporal variation of soil moisture. In order to understand the global hydrologic cycle, it is desirable to measure soil moisture with one- to two-days revisit. Using these frequent measurements, a time series approach can be implemented to improve the soil moisture retrieval accuracy.

soil moisture↗

NASA NTRS2013

Interpreting SBUV Smoothing Errors: an Example Using the Quasi-biennial Oscillation

The Solar Backscattered Ultraviolet (SBUV) observing system consists of a series of instruments that have been measuring both total ozone and the ozone profile since 1970. SBUV measures the profile in the upper stratosphere with a resolution that is adequate to resolve most of the important features of that region. In the lower stratosphere the limited vertical resolution of the SBUV system means that there are components of the profile variability that SBUV cannot measure. The smoothing error, as defined in the optimal estimation retrieval method, describes the components of the profile variability that the SBUV observing system cannot measure. In this paper we provide a simple visual interpretation of the SBUV smoothing error by comparing SBUV ozone anomalies in the lower tropical stratosphere associated with the quasi-biennial oscillation (QBO) to anomalies obtained from the Aura Microwave Limb Sounder (MLS). We describe a methodology for estimating the SBUV smoothing error for monthly zonal mean (mzm) profiles. We construct covariance matrices that describe the statistics of the inter-annual ozone variability using a 6 yr record of Aura MLS and ozonesonde data. We find that the smoothing error is of the order of 1percent between 10 and 1 hPa, increasing up to 15-20 percent in the troposphere and up to 5 percent in the mesosphere. The smoothing error for total ozone columns is small, mostly less than 0.5 percent. We demonstrate that by merging the partial ozone columns from several layers in the lower stratosphere/troposphere into one thick layer, we can minimize the smoothing error. We recommend using the following layer combinations to reduce the smoothing error to about 1 percent: surface to 25 hPa (16 hPa) outside (inside) of the narrow equatorial zone 20 S-20 N.

ozone profile retrievals↗

NASA NTRS2004

Fast Computation of Frequency Response of Cavity-Backed Apertures Using MBPE in Conjunction with Hybrid FEM/MoM Technique

The hybrid Finite Element Method(FEM)/Method of Moments(MoM) technique has become popular over the last few years due to its flexibility to handle arbitrarily shaped objects with complex materials. One of the disadvantages of this technique, however, is the computational cost involved in obtaining solutions over a frequency range as computations are repeated for each frequency. In this paper, the application of Model Based Parameter Estimation (MBPE) method[1] with the hybrid FEM/MoM technique is presented for fast computation of frequency response of cavity-backed apertures[2,3]. In MBPE, the electric field is expanded in a rational function of two polynomials. The coefficients of the rational function are obtained using the frequency-derivatives of the integro-differential equation formed by the hybrid FEM/MoM technique. Using the rational function approximation, the electric field is calculated at different frequencies from which the frequency response is obtained.

Reddy, C. J.↗

DOE OSTI2021

Mechanical Loads on Spent Nuclear Fuel in the General 30 cm Package Drop Scenario

The U.S. Department of Energy Office of Nuclear Energy (DOE-NE) Spent Fuel and Waste Science & Technology (SFWST) research program is guided by the high-level goal of closing prioritized knowledge gaps related to spent nuclear fuel (SNF) storage and transportation, which are summarized by Saltzstein et al. (2020). One of the high-priority knowledge gaps is the identification and quantification of mechanical loads that are expected to affect SNF during normal conditions of transportation and storage to inform the range of physical SNF test programs. This report uses modeling and analysis methods to estimate the mechanical loads on spent nuclear fuel (SNF) in the general 30 cm package drop scenario. The drop scenario assumes impact limiters are in place in the transportation configuration and the impact surface is perfectly rigid. The goal of this analysis is to consider the universe of potential mechanical loading conditions that can happen to SNF and present the results in a manner that is useful for materials testing, decision making, and regulatory rule making purposes. This study uses validated finite element models and methods to perform a broad parametric study of key variables that can affect the mechanical loads on SNF during a hypothetical package free drop scenario. Physical drop test data from a cask and fuel assembly drop test campaign is the basis for model validation. Additionally, the results of the parametric study are used to inform a damage model, which uses multiple nonlinear regression to estimate the relationships between input variables and output response. The parametric finite element analyses consider thousands of input variable combinations, while the damage model estimates millions of combinations. The breadth of this study provides confidence that the potential range of mechanical loads that SNF might experience during the general 30 cm package drop scenario are characterized well enough to consider this knowledge gap closed. While this report documents the overall peak values calculated in this study, the 95 th percentile values, the histograms, and the observed trends are equally important. This study covered a large range of SNF temperatures, room temperature to 300°C, and burnups, 10 GWd/MTU to 62 GWd/MTU. Each temperature and burnup combination has a different cladding yield strain, so it is more meaningful to summarize the calculated cladding strain response as its factor of safety, which is defined relative to the yield strain. The factor of safety is calculated as the yield strain divided by the peak cladding strain. A factor of safety greater than unity indicates that the cladding remains below yield, whereas a value less than unity is indicative of plastic deformation. In all cases of this study a safety factor over 1.0 was calculated, although in the most limiting case at 300°C the safety factor was only 1.01, which suggests that yielding could occur when additional loads like rod internal pressure are included. When the temperature is restricted to 200°C the limiting safety factor increases to 1.28, which has significant margin to accommodate internal pressure and potential local cladding defects that could cause a local stress concentration. An important trend in the calculated fuel rod mechanical loads is that the 2 nd highest loaded fuel rod in an assembly tends to be significantly lower than the highest loaded rod. The implication is that even if one rod in an assembly experiences a failure the loads would have to be significantly higher to cause two or more rods to fail.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Landsat 8 monitoring of multi-depth suspended sediment concentrations in Lake Erie’s Maumee River using machine learning

Satellite remote sensing has been widely used to map suspended sediment concentration (SSC) in waterbodies. However, due to the complexity of sediment-water interactions, it has been difficult to derive linear and non-linear regression equations to reliably predict SSC, especially when trying to estimate depth of integrated sediment. Herein, this study uses Landsat 8 OLI (Operational Land Imager) sensor to map SSC within the Maumee River in Ohio, USA, at multiple depth intervals (15, 61, 91, and 182 cm). Simple linear least squares regression (LLSR), and three common machine learning models: random forest (RF), support vector regression (SVR), and model averaged neural network (MANN) were used to estimate SSC at the depth intervals. All machine learning models significantly outperformed LLSR while RF performed the best. In both RF and MANN, R2 (coefficient of determination) increases with depth with a maximum R2 of 0.89 and 0.83, respectively, at a depth of 0–182 cm. The results show that machine learning models can implement nonlinear relationships that produce better predictions than traditional linear regression methods in estimating depth integrated SSC, especially when samples are limited.

47 OTHER INSTRUMENTATION↗

DOE OSTI2017

Chapter 10: Peak Demand and Time-Differentiated Energy Savings Cross-Cutting Protocol. The Uniform Methods Project: Methods for Determining Energy Efficiency Savings for Specific Measures

Savings from electric energy efficiency measures and programs are often expressed in terms of annual energy and presented as kilowatt-hours per year (kWh/year). However, for a full assessment of the value of these savings, it is usually necessary to consider the measure or program's impact on peak demand as well as time-differentiated energy savings. This cross-cutting protocol describes methods for estimating the peak demand and time-differentiated energy impacts of measures implemented through energy efficiency programs.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2018

A Practical Approach to Sizing Neural Networks

Most approaches to machine learning experiments currently involve tedious hyperparameter tuning. This article first shows how to practically estimate the maximum size of a neural network given a training data set. We present four easily applicable rules to analytically determine the capacity of neural network architectures. The rules are derived based on MacKay’s information theoretic model of supervised machine learning [22]. This allows the comparison of the efficiency of different architectures independently of a task. Second, we introduce and experimentally validate a heuristic method to estimate the neural network capacity requirement for a given dataset and labeling. This allows an estimate of the required size of a neural network for a given problem. We conclude the article with a discussion on the consequences of sizing the network wrongly, which includes both increased computation effort for training as well as reduced generalization capability.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Estimating the Ultraviolet Emission of M Dwarfs with Exoplanets from Ca ii and Hα

M dwarf stars are excellent candidates around which to search for exoplanets, including temperate, Earth-sized planets. To evaluate the photochemistry of the planetary atmosphere, it is essential to characterize the UV spectral energy distribution of the planet’s host star. This wavelength regime is important because molecules in the planetary atmosphere such as oxygen and ozone have highly wavelength-dependent absorption cross sections that peak in the UV (900–3200 Å). We seek to provide a broadly applicable method of estimating the UV emission of an M dwarf, without direct UV data, by identifying a relationship between noncontemporaneous optical and UV observations. Our work uses the largest sample of M dwarf star far- and near-UV observations yet assembled. We evaluate three commonly observed optical chromospheric activity indices—Hα equivalent widths and log{sub 10} L Hα /L bol , and the Mount Wilson Ca ii H&K S and R HK ' indices—using optical spectra from the HARPS, UVES, and HIRES archives and new HIRES spectra. Archival and new Hubble Space Telescope COS and STIS spectra are used to measure line fluxes for the brightest chromospheric and transition region emission lines between 1200 and 2800 Å. Our results show a correlation between UV emission-line luminosity normalized to the stellar bolometric luminosity and Ca ii R HK ' with standard deviations of 0.31–0.61 dex (factors of ~2–4) about the best-fit lines. We also find correlations between normalized UV line luminosity and Hα log 10 L Hα /L bol and the S index. These relationships allow one to estimate the average UV emission from M0 to M9 dwarfs when UV data are not available.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2020

Estimating the Ultraviolet Emission of M Dwarfs with Exoplanets from Ca ii and Hα

M dwarf stars are excellent candidates around which to search for exoplanets, including temperate, Earth-sized planets. To evaluate the photochemistry of the planetary atmosphere, it is essential to characterize the UV spectral energy distribution of the planet's host star. This wavelength regime is important because molecules in the planetary atmosphere such as oxygen and ozone have highly wavelength-dependent absorption cross sections that peak in the UV (900–3200 Å). We seek to provide a broadly applicable method of estimating the UV emission of an M dwarf, without direct UV data, by identifying a relationship between noncontemporaneous optical and UV observations. Our work uses the largest sample of M dwarf star far- and near-UV observations yet assembled. We evaluate three commonly observed optical chromospheric activity indices—Hα equivalent widths and log(10) L(Hα)/L(bol), and the Mount Wilson Ca ii H&K S and R'(HK) indices—using optical spectra from the HARPS, UVES, and HIRES archives and new HIRES spectra. Archival and new Hubble Space Telescope COS and STIS spectra are used to measure line fluxes for the brightest chromospheric and transition region emission lines between 1200 and 2800 Å. Our results show a correlation between UV emission-line luminosity normalized to the stellar bolometric luminosity and Ca ii R'(HK) with standard deviations of 0.31–0.61 dex (factors of ∼2–4) about the best-fit lines. We also find correlations between normalized UV line luminosity and Hα log(10) L(Hα)/L(bol) and the S index. These relationships allow one to estimate the average UV emission from M0 to M9 dwarfs when UV data are not available.

Katherine Melbourne↗

DOE OSTI2020

A Hybrid Framework Combining Model-Based and Data-Driven Methods for Hierarchical Decentralized Robust Dynamic State Estimation

This paper combines model-based and data-driven methods to develop a hierarchical, decentralized, robust dynamic state estimator (DSE). A two-level hierarchy is proposed, where the lower level consists of robust, model-based, decentralized DSEs. The state estimates sent from the lower level are received at the upper level, where they are filtered by a robust data-driven DSE after a principled sparse selection. This selection allows us to shrink the dimension of the problem at the upper level and hence significantly speed up the computational time. The proposed hybrid framework does not depend on the centralized infrastructure of the control centers; thus it can be completely embedded into the wide-area measurement systems. This feature will ultimately facilitate the placement of hierarchical decentralized control schemes at the phasor data concentrator locations. Also, the network model is not necessary; thus, a topology processor is not required. Finally, there is no assumption on the dynamics of the electric loads. The proposed framework is tested on the 2,000-bus synthetic Texas system, and shown to be capable of reconstructing the dynamic states of the generators with high accuracy, and of forecasting in the advent of missing data.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2026

Compact representation and long-time extrapolation of real-time data for quantum systems using the ESPRIT algorithm

Representing real-time data as a sum of complex exponentials provides a compact form that enables both denoising and extrapolation. As a fully data-driven method, the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm is agnostic to the underlying physical equations, making it broadly applicable to various observables and experimental or numerical setups. In this work, we consider applications of the ESPRIT algorithm primarily to extend real-time dynamical data from simulations of quantum systems. We evaluate ESPRIT's performance in the presence of noise and compare it to other extrapolation methods. We demonstrate its ability to extract information from short-time dynamics to reliably predict long-time behavior and determine the minimum time interval required for accurate results. We discuss how this insight can be leveraged in numerical methods that propagate quantum systems in time, and we show how ESPRIT can predict infinite-time values of dynamical observables, offering a purely data-driven approach to characterizing quantum phases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗