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DOE OSTI2020

Application of Detectability Analysis for Power System Dynamic State Estimation

To guide the measurement placement and selection for dynamic state estimation in power systems, it is important to determine the existence of an observer that can estimate the dynamic states. Past studies have been focused on observability analysis, which determines whether the initial states can be uniquely determined. In this paper, detectability analysis is proposed to determine whether the current states can be estimated as time involving. Through the proposed detectability analysis, the states of an unobservable system can be categorized into the detectable states and undetectable states. It is shown that if the eigenvalues corresponding to the unobservable states are stable, the states are detectable and their estimates will converge to the true ones asymptotically. The study can be used to guide measurement placement and selection.

Detectability, dynamic state estimation↗

DOE OSTI2019

A Game-Theoretic Data-Driven Approach for Pseudo-Measurement Generation in Distribution System State Estimation

In this paper, we present an efficient computational framework with the purpose of generating weighted pseudo-measurements to improve the quality of distribution system state estimation (DSSE) and provide observability with advanced metering infrastructure (AMI) against unobservable customers and missing data. The proposed technique is based on a game-theoretic expansion of relevance vector machines (RVMs). This platform is able to estimate the nodal power consumption and quantify its uncertainty while reducing the prohibitive computational burden of model training for large AMI datasets. To achieve this objective, the large training set is decomposed and distributed among multiple parallel learning entities. The resulting estimations from the parallel RVMs are then combined using a game-theoretic model based on the idea of repeated games with vector payoff. It is observed that through this approach and by exploiting the seasonal changes in customers’ behavior the accuracy of pseudo-measurements can be considerably improved, while introducing robustness against bad training data samples. The proposed pseudo-measurement generation model is integrated into a DSSE using a closed-loop information system, which takes advantage of a branch current state estimator (BCSE) to further improve the performance of the designed machine learning framework. This method has been tested on a practical distribution feeder model with smart meter data for verification.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2019

A Fully Computable A Posteriori Error Estimate for the Stokes Equations on Polytopal Meshes

Here in this paper, we present a simple a posteriori error estimate for the weak Galerkin finite element method for the Stokes equation. This residual type estimator can be applied to general meshes such as polytopal mesh or meshes with hanging nodes. The reliability and efficiency of the estimator are proved in this paper. Five numerical tests demonstrate the effectiveness and flexibility of the adaptive mesh refinement guided by the designed error estimator.

finite element methods↗

DOE OSTI2018

Trip Energy Estimation Methodology and Model Based on Real-World Driving Data for Green-Routing Applications

A data-informed model to predict energy use for a proposed vehicle trip has been developed in this paper. The methodology leverages roughly one million miles of real-world driving data to generate the estimation model. Driving is categorized at the sub-trip level by average speed, road gradient, and road network geometry, then aggregated by category. An average energy consumption rate is determined for each category, creating an energy rate look-up table. Proposed vehicle trips are then categorized in the same manner, and estimated energy rates are appended from the look-up table. The methodology is robust and applicable to a wide range of driving data. The model has been trained on vehicle travel profiles from the Transportation Secure Data Center at the National Renewable Energy Laboratory and validated against on-road fuel consumption data from testing in Phoenix, Arizona. When compared against the detailed on-road conventional vehicle fuel consumption test data, the energy estimation model accurately predicted which route would consume less fuel over a dozen different tests. When compared against a larger set of real-world origin-destination pairs, it is estimated that implementing the present methodology should accurately select the route that consumes the least fuel 90% of the time. The model results can be used to inform control strategies in routing tools, such as change in departure time, alternate routing, and alternate destinations to reduce energy consumption. This work provides a highly extensible framework that allows the model to be tuned to a specific driver or vehicle type.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2021

Evaluation of residual gas fraction estimation methods for cycle-to-cycle combustion variability analysis and modeling

Cycle-to-cycle combustion variability in spark-ignition engines during normal operation is mainly caused by random perturbations of the in-cylinder conditions such as the flow velocity field, homogeneity of the air-fuel distribution, spark energy discharge, and turbulence intensity of the flame front. Such perturbations translate into the variability of the energy released observed at the end of the combustion process. During normal operating conditions, the cycle-to-cycle variability (CCV) of the energy release behaves as random uncorrelated noise. However, during diluted combustion, in either the form of exhaust gas recirculation (EGR) or excess air (lean operation), the CCV tends to increase as dilution increases. Moreover, when the ignition limit is reached at high dilution levels, the combustion CCV is exacerbated by sporadic occurrences of incomplete combustion events, and the uncorrelation assumption no longer holds. The low or null energy released by partial burns and misfires has an impact on the following combustion event due to the residual gas that carries burned and unburned gases, which contributes to the deterministic coupling between engine cycles. Many residual gas fraction estimation methods, however, only address the nominal case where complete combustion occurs and combustion events are uncorrelated. Here we evaluate the efficacy of such methods on capturing the effects of partial burns and misfires on the residual gas estimate for high-EGR operation. The advantages and disadvantages of each method are discussed based on their ability to generate cycle-to-cycle estimates. Finally, a comparison between the different estimation techniques is presented based on their usefulness for control-oriented modeling.

42 ENGINEERING↗

DOE OSTI2026

Estimating CO 2 fluxes through integrating spatial and temporal input layers via deep learning algorithms

Background Accurate estimation of net ecosystem exchange of CO 2 fluxes (Fc) is essential for understanding carbon cycle processes and assessing ecosystem carbon budgets. However, conventional modeling approaches often emphasize temporal dynamics while overlooking the pronounced spatial heterogeneity within the footprint of eddy covariance (EC) towers, potentially limiting predictive accuracy and interpretability of Fc estimates. To address this challenge, we developed a spatiotemporal model that integrates high-resolution footprint-weighted spatial information with sequential environmental drivers. Results The integrated model combines a deeper graph convolutional network to characterize fine-scale spatial variability within EC footprints and a gated recurrent unit network to capture temporal dependencies in biophysical conditions. Using multi-year flux tower observations, remote sensing vegetation indices and footprint modeling, we evaluate the proposed method across three land cover types. This spatiotemporal model consistently outperforms temporal-only and spatial-only baselines, achieving the highest overall accuracy (R 2 = 0.9569) and the lowest RMSE (1.8128 μmol m −2 s −1 ) and MAE (1.1939 μmol m −2 s −1 ). Performance gains are particularly evident in ecosystems with strong vegetation heterogeneity, where spatial structure substantially modulates Fc variability. Conclusions This study demonstrates the importance of joint modeling spatial heterogeneity and temporal dynamics for improving Fc estimation and provides a robust method for advancing footprint-based Fc estimates across diverse ecosystems, supporting refined assessments of terrestrial carbon fluxes, and enhancing scientific foundations for carbon studies.

CO2 flux estimate↗

DOE OSTI2021

Lung Cancer in the Mayak Workers Cohort: Risk Estimation and Uncertainty Analysis

The workers at the Mayak nuclear facility near Ozyorsk, Russia are a primary source of information about exposure to radiation at low-dose rates, since they were subject to protracted exposures to external gamma rays and to internal exposures from plutonium inhalation. Here we re-examine lung cancer mortality rates and assess the effects of external gamma and internal plutonium exposures using recently developed Monte Carlo dosimetry systems. Using individual lagged mean annual lung doses computed from the dose realizations, we fit excess relative risk (ERR) models to the lung cancer mortality data for the Mayak Workers Cohort using risk-modeling software. We then used the corrected information matrix (CIM) approach to widen the confidence intervals of ERR by taking into account the uncertainty in doses represented by multiple realizations from the Monte Carlo dosimetry systems. Findings of this work revealed that there were 930 lung cancer deaths during follow-up. Plutonium lung doses (but not gamma doses) were generally higher in the new dosimetry systems than those used in the previous analysis. This led to a reduction in the risk per unit dose compared to prior estimates. The estimated ERR/Gy for external gamma-ray exposure was 0.19 (95% CI: 0.07 to 0.31) for both sexes combined, while the ERR/Gy for internal exposures based on mean plutonium doses were 3.5 (95% CI: 2.3 to 4.6) and 8.9 (95% CI: 3.4 to 14) for males and females at attained age 60. Accounting for uncertainty in dose had little effect on the confidence intervals for the ERR associated with gamma-ray exposure, but had a marked impact on confidence intervals, particularly the upper bounds, for the effect of plutonium exposure [adjusted 95% CIs: 1.5 to 8.9 for males and 2.7 to 28 for females]. In conclusion, lung cancer rates increased significantly with both external gamma-ray and internal plutonium exposures. Accounting for the effects of dose uncertainty markedly increased the width of the confidence intervals for the plutonium dose response but had little impact on the external gamma dose effect estimate. Adjusting risk estimate confidence intervals using CIM provides a solution to the important problem of dose uncertainty. This work demonstrates, for the first time, that it is possible and practical to use our recently developed CIM method to make such adjustments in a large cohort study.

uncertainty, radiation risk estimation, Mayak Prod↗

DOE OSTI2023

Calibrating Constant Elasticity of Substitution Technologies to Bottom-up Cost Estimates

We propose a method for calibrating an industry-level technology to engineering (bottom-up) estimates with a particular focus on abatement opportunities. As a demonstration, substitution elasticities across inputs are adjusted in the nested cost function for the electricity sector to best fit a target marginal abatement cost (MAC) curve derived from engineering assessments of available technologies. Elasticities are optimized over an entire relevant range of the MAC, whereas current techniques use local point estimates under little or no abatement. In the context of fitting to a given MAC we evaluate alternative nesting structures and find that, while complexity in nesting improves the fit, even relatively simple nesting structures can reasonably approximate the target MAC. In our example, focused on the electricity sector, we find standard elasticities adopted in top-down models moderately overstate abatement costs relative to the engineering targets. In our preferred specification the most important adjustment is to escalate the substitution elasticity between energy and value-added inputs. This is consistent with an argument that the current set of point estimates fail to properly account for new capital-based technologies. These conclusions, however, are sensitive to our assumption about output-intensity abatement and consumer price responsiveness, both of which are not delineated in engineering estimates.

abatement cost↗

DOE OSTI2013

Residual a posteriori error estimation of a mimetic/virtual element method

A posteriori error estimation and adaptivity are very useful in the context of the mimetic finite difference method due to the flexibility of the meshes to which this family of numerical schemes can be applied. Nevertheless, developing error estimators for mimetic methods is not a straightforward task due to the lack of knowledge of the basis functions. This issue is tackled by the virtual element method recently introduced in [4], which can be interpreted as a Galerkin reformulation of the mimetic finite difference method. In the new virtual element setting, we develop a residual based a posteriori error estimator that immediately applies to its mimetic counterpart. For such estimator we prove the reliability and we show the numerical performance when it is combined with an adaptive strategy for the mesh refinement. For the lowest-regular approximation we also developed an hp-adaptive strategy based on the comparison between the numerical solution on a base mesh and on a reference mesh.

a posteriori error estimation↗

DOE OSTI2023

Pragmatic Uncertainty Quantification and Propagation in Inverse Estimation of Structural Dynamics Parameters given Material Property Uncertainties and Limited Sensor Data

In this report we demonstrate some relatively simple and inexpensive methods to effectively account for various sources of epistemic lack-of-knowledge type uncertainty in inverse problems. The demonstration problem involves inverse estimation of six parameters of a bolted joint that attaches a kettlebell shaped object to a thick plate. The parameters are efficiently inverted in a modal-based model calibration using gradient-based optimization. Two material properties of the kettlebell are treated as uncertain to within given epistemic uncertainty bounds. We apply and test interval and sparse-sample probabilistic approaches to account for uncertainty in the estimated parameters (and various scalar functionals of the parameters as generic quantities of interest, QOIs) due to uncertainties in the material properties. We also investigate the error effects of limited numbers of vibration sensors (accelerometers) on the kettlebell and plate, and therefore abbreviated excitation/response information in the parameter inversions. We propose and demonstrate a Leave-K-Sensors-Out “cross-prediction” UQ approach to estimate related uncertainties on the parameters and QOI functionals. We indicate how uncertainties from material properties and limited sensors are treated in a combined manner. The economical combined UQ approach involves just three to five samples (i.e. three to five inverse simulations), with no added complication or error/uncertainty from use of surrogate models for affordability. Finally, we describe a related economical UQ approach for handling potential parameter solution non-uniqueness and numerical optimization related precision uncertainties in the estimated parameter values. Indicated further research is identified.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Maximum Likelihood Estimation: Some Basics

The maximum likelihood estimation is a general estimation procedure. It is often compared to estimation procedures like the ordinary least squares regression or generalized method of moments, to name a few. We discuss some basics about the maximum likelihood estimation, its advantages and disadvantages, and provide an example application to a gamma distribution function.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Maximum Likelihood Estimation: Some Basics

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Multi-Area Distribution System State Estimation Using Decentralized Physics-Aware Neural Networks

The development of active distribution grids requires more accurate and lower computational cost state estimation. In this paper, the authors investigate a decentralized learning-based distribution system state estimation (DSSE) approach for large distribution grids. The proposed approach decomposes the feeder-level DSSE into subarea-level estimation problems that can be solved independently. The proposed method is decentralized pruned physics-aware neural network (D-P2N2). The physical grid topology is used to parsimoniously design the connections between different hidden layers of the D-P2N2. Monte Carlo simulations based on one-year of load consumption data collected from smart meters for a three-phase distribution system power flow are developed to generate the measurement and voltage state data. The IEEE 123-node system is selected as the test network to benchmark the proposed algorithm against the classic weighted least squares and state-of-the-art learning-based DSSE approaches. Numerical results show that the D-P2N2 outperforms the state-of-the-art methods in terms of estimation accuracy and computational efficiency.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Secure State Estimation with Asynchronous Measurements for Coordinated Cyber Attack Detection in Active Distribution Systems

Coordinated cyber attacks tamper with measurement data to disrupt the situational awareness of active distribution systems. Various sensors report measurements asynchronously at different rates, which introduces challenges during state estimation. In addition, this forces cyber intruders to exert greater effort to compromise multiple communication channels and launch coordinated attacks. Therefore, multi-channel and asynchronous measurements could be harnessed to develop more secure cyber defense strategies. In this paper, a prediction-correction-based multi-rate observer is designed to exploit the value of asynchronous measurements for the detection of coordinated false data injection (FDI) attacks. First, a time-function-dependent prediction-correction strategy is proposed to adjust the sampling interval for each sensor’s measurement. Then, an observer is designed based on the trade-off between estimation error and the optimal period of the most recent sampling instant, with the convergence of estimation error with the maximum permitted sampling interval. Moreover, the conditions for exponential stability are developed using the Lyapunov–Krasovskii functional technique. Next, a coordinated FDI attack detection strategy is developed based on the dual nonlinear minimization problem. The proposed attack detection and secure state estimation strategies are tested on the IEEE 13-node system. Simulation results show that these schemes are effective in enhancing attack detection based on asynchronous measurements or compromised data.

asynchronous measurements↗

DOE OSTI2026

Deep nonparametric estimation of operators between infinite dimensional spaces

Learning operators between infinitely dimensional spaces is an important learning task arising in machine learning, imaging science, mathematical modeling and simulations, etc. This paper studies the nonparametric estimation of Lipschitz operators using deep neural networks. Non-asymptotic upper bounds are derived for the generalization error of the empirical risk minimizer over a properly chosen network class. Under the assumption that the target operator exhibits a low dimensional structure, our error bounds decay as the training sample size increases, with an attractive fast rate depending on the intrinsic dimension in our estimation. Our assumptions cover most scenarios in real applications and our results give rise to fast rates by exploiting low dimensional structures of data in operator estimation. We also investigate the influence of network structures (e.g., network width, depth, and sparsity) on the generalization error of the neural network estimator and propose a general suggestion on the choice of network structures to maximize the learning efficiency quantitatively.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Adaptive stratified importance sampling: hybridization of extrapolation and importance sampling Monte Carlo methods for estimation of wind turbine extreme loads

Wind turbine extreme load estimation is especially difficult because turbulent inflow drives nonlinear turbine physics and control strategies; thus there can be huge differences in turbine response to essentially equivalent environmental conditions. The two main current approaches, extrapolation and Monte Carlo sampling, are both unsatisfying: extrapolation-based methods are dangerous because by definition they make predictions outside the range of available data, but Monte Carlo methods converge too slowly to routinely reach the desired 50-year return period estimates. Thus a search for a better method is warranted. We introduce an adaptive stratified importance sampling approach that allows for treating the choice of environmental conditions at which to run simulations as a stochastic optimization problem that minimizes the variance of unbiased estimates of extreme loads. Furthermore, the framework, built on the traditional bin-based approach used in extrapolation methods, provides a close connection between sampling and extrapolation, and thus allows the solution of the stochastic optimization (i.e., the optimal distribution of simulations in different wind speed bins) to guide and recalibrate the extrapolation. Results show that indeed this is a promising approach, as the variance of both the Monte Carlo and extrapolation estimates are reduced quickly by the adaptive procedure. We conclude, however, that due to the extreme response variability in turbine loads to the same environmental conditions, our method and any similar method quickly reaches its fundamental limits, and that therefore our efforts going forward are best spent elucidating the underlying causes of the response variability.

17 WIND ENERGY↗

NASA NTRS2006

Spacecraft inertia estimation via constrained least squares

This paper presents a new formulation for spacecraft inertia estimation from test data. Specifically, the inertia estimation problem is formulated as a constrained least squares minimization problem with explicit bounds on the inertia matrix incorporated as LMIs [linear matrix inequalities). The resulting minimization problem is a semidefinite optimization that can be solved efficiently with guaranteed convergence to the global optimum by readily available algorithms. This method is applied to data collected from a robotic testbed consisting of a freely rotating body. The results show that the constrained least squares approach produces more accurate estimates of the inertia matrix than standard unconstrained least squares estimation methods.

inertia estimation↗

NASA NTRS2005

Optimal Estimation of Clock Values and Trends from Finite Data

We show how to solve two problems of optimal linear estimation from a finite set of phase data. Clock noise is modeled as a stochastic process with stationary dth increments. The covariance properties of such a process are contained in the generalized autocovariance function (GACV). We set up two principles for optimal estimation: with the help of the GACV, these principles lead to a set of linear equations for the regression coefficients and some auxiliary parameters. The mean square errors of the estimators are easily calculated. The method can be used to check the results of other methods and to find good suboptimal estimators based on a small subset of the available data.

stationary increments↗