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Results for “uncertainty quantification and propagation”

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DOE OSTI2023

Estimating Travel Energy Consumption Uncertainty Based on Inferred Travel Mode and Sensed Travel Length

To properly inform transport policy and infrastructure changes, transportation related metrics need both measured values and uncertainties of those values. Travel monitoring smartphone apps can record people's travel behavior, but trip data quality is limited by sensor errors, user labeling rates and the accuracy of inference algorithms used for travel diary creation. We discuss the use of phone app recorded travel diary data to estimate energy consumption, and propose the use of propagation of variance to find error bars for such estimates. We define energy consumption for one trip as trip length times the energy intensity per distance unit of the travel mode used. We characterize trip length errors with relative error and inferred trip mode errors with confusion matrix columns. The resulting variances of each measurement are then propagated to the final calculated energy consumption. We tested our uncertainty methods on a dataset that used phone app data combined with prompted recall, consisting of 92,234 labeled trips for over 500,000 miles. Accounting for uncertainty using expected energy intensities and variance propagation gives a dataset-wide aggregate energy consumption percent error of about 8%, within one standard deviation from the truth. Future work could involve applying similar methods to other travel diary based metrics.

ADVANCED PROPULSION SYSTEMS,ENERGY PLANNING, POLIC↗

DOE OSTI2024

Probabilistic projections of the Amery Ice Shelf catchment, Antarctica, under conditions of high ice-shelf basal melt

Abstract. Antarctica's Lambert Glacier drains about one-sixth of the ice from the East Antarctic Ice Sheet and is considered stable due to the strong buttressing provided by the Amery Ice Shelf. While previous projections of the sea-level contribution from this sector of the ice sheet have predicted significant mass loss only with near-complete removal of the ice shelf, the ocean warming necessary for this was deemed unlikely. Recent climate projections through 2300 indicate that sufficient ocean warming is a distinct possibility after 2100. This work explores the impact of parametric uncertainty on projections of the response of the Lambert–Amery system (hereafter “the Amery sector”) to abrupt ocean warming through Bayesian calibration of a perturbed-parameter ice-sheet model ensemble. We address the computational cost of uncertainty quantification for ice-sheet model projections via statistical emulation, which employs surrogate models for fast and inexpensive parameter space exploration while retaining critical features of the high-fidelity simulations. To this end, we build Gaussian process (GP) emulators from simulations of the Amery sector at a medium resolution (4–20 km mesh) using the Model for Prediction Across Scales (MPAS)-Albany Land Ice (MALI) model. We consider six input parameters that control basal friction, ice stiffness, calving, and ice-shelf basal melting. From these, we generate 200 perturbed input parameter initializations using space filling Sobol sampling. For our end-to-end probabilistic modeling workflow, we first train emulators on the simulation ensemble and then calibrate the input parameters using observations of the mass balance, grounding line movement, and calving front movement with priors assigned via expert knowledge. Next, we use MALI to project a subset of simulations to 2300 using ocean and atmosphere forcings from a climate model for both low- and high-greenhouse-gas-emission scenarios. From these simulation outputs, we build multivariate emulators by combining GP regression with principal component dimension reduction to emulate multivariate sea-level contribution time series data from the MALI simulations. We then use these emulators to propagate uncertainty from model input parameters to predictions of glacier mass loss through 2300, demonstrating that the calibrated posterior distributions have both greater mass loss and reduced variance compared to the uncalibrated prior distributions. Parametric uncertainty is large enough through about 2130 that the two projections under different emission scenarios are indistinguishable from one another. However, after rapid ocean warming in the first half of the 22nd century, the projections become statistically distinct within decades. Overall, this study demonstrates an efficient Bayesian calibration and uncertainty propagation workflow for ice-sheet model projections and identifies the potential for large sea-level rise contributions from the Amery sector of the Antarctic Ice Sheet after 2100 under high-greenhouse-gas-emission scenarios.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Machine learning enhanced predictions of ICRF heating: Overcoming numerical limitations via data curation

In this work, we present the development of robust surrogate models for Ion Cyclotron Range of Frequencies (ICRF) and High-Harmonic Fast Wave (HHFW) heating predictions in fusion plasmas. Building upon our previous efforts to achieve real-time capable models, we identify the cause of the outliers found using TORIC in certain HHFW heating scenarios. The outliers are observed to be spurious ion Bernstein wave (IBW)-like modes caused by a wavelength control algorithm designed to address challenging scenarios with high perpendicular wavenumbers. The effect arises from the modulation in the perpendicular susceptibility, which can induce sign reversal and IBW-like propagation for scenarios featuring normalized ion Larmor radius λ i ≫ 1. We use TORIC with this algorithm disabled to generate a novel HHFW-NSTX database that is free of outliers. Surrogate models trained on this database, including Random Forest Regressor (RFR), Multi-Layer Perceptrons, and Gaussian Process Regressors (GPR), demonstrate the ability to accurately predict HHFW heating profiles, with regression scores of R 2 ∈[0.93−0.99]. Additionally we demonstrate that it is possible to generalize predictions beyond training data by the use of both RFR and GPR models, enabling the prediction of scenarios previously limited to the original model. GPR models also provide uncertainty quantification, offering insights into model confidence. This work introduces a comprehensive Verification, Validation, and Uncertainty Quantification methodology for surrogate modeling, applicable not only to ICRF heating but also to other RF heating challenges and fusion physics problems. Beyond accelerated inference, these models show effective extrapolation capabilities, providing an alternative for addressing numerical challenges.

Artificial neural networks↗

DOE OSTI2020

Uncertainty quantification of an empirical shell-model interaction using principal component analysis

Recent investigations have emphasized the importance of uncertainty quantification (UQ) in nuclear theory. Here, we carry out UQ for configuration-interaction shell-model calculations in the 1$\textit{s}$–0$\textit{d}$ valence space, investigating the sensitivity of observables to perturbations in the 66 parameters (matrix elements) of a high-quality empirical interaction. The large parameter space makes computing the corresponding Hessian numerically costly, so we compare a cost-effective approximation, using the Feynman-Hellmann theorem, to the full Hessian and find it works well. Diagonalizing the Hessian yields the principal components of the interaction: linear combinations of parameters ordered by sensitivity. This approximately decoupled distribution of parameters facilitates theoretical uncertainty propagation onto structure observables: electromagnetic transitions, Gamow-Teller decays, and dark matter-nucleus scattering matrix elements.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Impact of fission yield covariance matrices on decay heat uncertainty quantification with the DARWIN2 package

Although fission yields are strongly correlated, correlations between them are usually not taken into account when performing decay heat uncertainty calculations with the CEA DARWIN2 package due to the lack of reference covariance matrices associated to the JEFF-3.1.1 evaluation. However, covariance matrices for {sup 235}U and {sup 239}Pu thermal fission yields have been produced recently by the subgroup 37 of OECD/NEA Working Party on International Nuclear Data Evaluation Cooperation (WPEC). The study presented in this paper evaluates the effect of those covariances on the decay heat uncertainty calculation, both on fission burst experiments and on integral decay heat measurements that are part of the DARWIN2 experimental validation database. Although some differences are observed, partly due to the variety of models used to produce the matrices, the propagation of fission yield covariances always leads to a reduction of the decay heat uncertainty for cooling time above 10 seconds, indicating that not taking them into account is a conservative hypothesis from a safety point of view. Nevertheless, the strong impact of those covariances on the decay heat uncertainty also highlights the need of documented and consistent fission yield uncertainties and correlation data. On top of that, all the covariance matrices used for this study represent the correlation between the physical model parameters, but none of them includes the experimental correlations. An evaluation of the experimental correlations would also be of strong interest for decay heat uncertainty calculations. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Improving Trustworthiness of Data-Driven Power Grid Contingency Analysis With Bayesian Residual Graph Neural Networks

The evolving energy landscape requires novel tools to efficiently perform contingency analysis and reliability assessment of power grids, potentially in real-time. The high computational cost of traditional power flow solvers limits their applicability in practice. Machine learning (ML) surrogates such as deep neural networks (NNs) accelerate power flow solvers computations, enabling high-order contingency analysis and real-time decision-making by learning highly nonlinear functions and integrating grid topology via graph architectures. However, (graph) NNs lack predictive power away from training data and do not provide predictive confidence estimates. Here, we present a Bayesian residual graph NN that integrates knowledge from low-fidelity data via residual training and embeds granular quantification of uncertainties, improving trustworthiness critical for high-consequence decision-making. Applying Bayesian concepts to NNs is challenging due to the high-dimensionality of both the parameter space, complicating derivation of a meaningful prior, and the output space in large grid systems, requiring enhanced techniques to assess the predicted high-dimensional uncertainties. Our contributions include: (1) Deriving a prior for fully connected and graph NNs that leverages low-fidelity data to guide mean predictions and appropriately control prior predictive uncertainty. (2) Integrating this prior within an ensembling with anchoring scheme for efficient approximate posterior inference. (3) Deriving enhanced metrics to assess accuracy of both the mean and uncertainty predictions in high dimensions, appropriately accounting for correlations propagated through graph layers. The resulting Bayesian residual graph NN is tested on a contingency analysis task for 14-bus and 118-bus grids.

24 - POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Advanced Graphite Creep Uncertainty Analysis

Radiation damage estimation is an important component of the post irradiation analysis of the Advanced Graphite Creep (AGC) experiment. It depends primarily on the fast fluence, which is determined using well established methods of spectral adjustment. These are based on best estimates from models such as Monte Carlo N-Particle (MCNP), input cross-sections, and measured activities from flux wires in the experiment. Each of these parameters can propagate uncertainties which will affect the uncertainty in the calculated dose levels for AGC, or any experiment irradiated within a reactor. While the methods of propagating uncertainty are well-established, the final uncertainty estimates they provide are only as good as the estimates of uncertainty in the inputs on which they are based. The purpose of this work is to outline some deficiencies in the ways these input uncertainties are presently estimated, and to outline a methodology by which they can be improved. The fast fluence and radiation damage received by graphite specimens irradiated in the Advanced Graphite Creep (AGC) experiments is presently estimated using spectral adjustment methods that are based on both flux wire activity measurements, and MCNP model predictions. This work describes an ongoing effort to quantify and propagate uncertainties in inputs to the spectral adjustment process, and thereby quantify the resultant error in radiation damage (dpa) estimates. The effort is multi-faceted, and we consider the impacts of both the set of flux wires selected, and the counting process. An expanded set of flux wires is identified that provides a more comprehensive data set on the fast spectrum. To address the counting process itself, a series of round-robin measurements in several reactor metrology laboratories across the Department of Energy (DOE) complex and nuclear industry are being undertaken to refine the American Society for Testing and Materials (ASTM) standards for flux wire measurements. To address the contribution of uncertainty in the MCNP model predictions, an uncertainty quantification (UQ) tool has been developed that statistically samples the model input parameters, runs a series of cases, and assimilates the results to provide an overall uncertainty. The impact of the MCNP UQ tool results is demonstrated by re-analyzing previous AGC flux wire and irradiation data. While the expanded flux wire set obviously cannot be added to these experiments retroactively, plans for future graphite irradiations are outlined.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

On the Statistical Uncertainty of Monte Carlo-Calculated Scattering Sensitivities

Sensitivity coefficients calculated with Monte Carlo codes are widely used for nuclear data uncertainty quantification in the modeling and simulation of complex 3D reactor systems. This study systematically compares sensitivity coefficients and associated statistical uncertainties for the multiplication factor and fuel temperature reactivity across multiple Monte Carlo codes (SCALE/KENO, SCALE/Shift, MCNP, and Serpent) using simple models representing light-water reactors and advanced reactor concepts. For multiplication factor sensitivities, statistical uncertainties are generally acceptable, although scattering sensitivities show significantly larger statistical uncertainties than, for example, fission and capture reactions. Fuel temperature reactivity sensitivities show significantly larger statistical uncertainties across all reactions. Elastic scattering sensitivities are the most problematic: all Monte Carlo codes fail to resolve energy-dependent coefficients, and they produce dramatically different energy-collapsed values. Critically, the use of these sensitivity coefficients in nuclear data uncertainty propagation leads to reduced statistical uncertainties in individual uncertainty contributions. This can lead to the masking of unusable sensitivity coefficients and producing misleading uncertainty results. The findings of this study show that new or enhanced methods are needed to improve Monte Carlo elastic scattering sensitivity calculations. Additionally, this study shows the relevance of verifying sensitivity coefficients through direct perturbation calculations for individual nuclide reactions, instead of only for total cross sections as commonly done.

Bostelmann, Rike [ORNL] (ORCID:0000000165968088)↗

DOE OSTI2021

Uncertainty quantification for Multiphase-CFD simulations of bubbly flows: a machine learning-based Bayesian approach supported by high-resolution experiments

In this paper, we developed a machine learning-based Bayesian approach to inversely quantify and reduce the uncertainties of multiphase computational fluid dynamics (MCFD) simulations for bubbly flows. The proposed approach is supported by high-resolution two-phase flow measurements, including those by double-sensor conductivity probes, high-speed imaging, and particle image velocimetry. Local distributions of key physical quantities of interest (QoIs), including the void fraction and phasic velocities, are obtained to support the Bayesian inference. In the process, the epistemic uncertainties of the closure relations are inversely quantified while the aleatory uncertainties from stochastic fluctuations of the system are evaluated based on experimental uncertainty analysis. The combined uncertainties are then propagated through the MCFD solver to obtain uncertainties of the QoIs, based on which probability-boxes are constructed for validation. The proposed approach relies on three machine learning methods: feedforward neural networks and principal component analysis for surrogate modeling, and Gaussian processes for model form uncertainty modeling. The whole process is implemented within the framework of an open-source deep learning library PyTorch with graphics processing unit (GPU) acceleration, thus ensuring the efficiency of the computation. The results demonstrate that with the support of high-resolution data, the uncertainties of MCFD simulations can be significantly reduced. The proposed approach has the potential for other applications that involve numerical models with empirical parameters.

42 ENGINEERING↗

DOE OSTI2026

ECLEIRS: Exact conservation law embedded identification of reduced states for parameterized nonlinear conservation laws from sparse and noisy data

Multi-query applications such as parameter estimation, uncertainty quantification and design optimization for parameterized partial differential equation (PDE) systems are expensive. While reduced/latent state dynamics approaches for parameterized PDEs offer a viable alternative, these approaches rely on high-quality data and struggle with highly sparse spatiotemporal noisy measurements typically obtained from experiments. Furthermore, there is no guarantee that these models satisfy governing physical conservation laws. In this article, we propose a reduced state dynamics approach, referred to as ECLEIRS, that embeds exact conservation in the solution and flux representation by utilizing a space-time divergence-free neural network formulation. We compare ECLEIRS with other reduced state dynamics approaches, those that do not enforce any physical constraints and those with physics-informed loss functions, for three shock-propagation problems: 1-D advection, 1-D Burgers and 2-D Euler equations. In conclusion, the numerical experiments conducted in this study demonstrate that ECLEIRS provides the most accurate prediction of dynamics for unseen parameters even in the presence of highly sparse and noisy data.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Experimental uncertainty quantification using templates of expected measurement uncertainties for fast neutron-induced total, capture, and scattering cross sections

Careful experimental uncertainty quantification (UQ) is key for developing trustworthy evaluated nuclear data. Templates to account for missing or under-reported experimental uncertainties were recently developed by the covariance committee of Cross Section Evaluation Working Group (CSEWG). In this work, we illustrate the practical application and limitations of these templates for selected neutron-induced reactions, including (n, tot), (n, γ), and (n, xn) in the fast energy range, to illustrate their use in data analyses for nuclear data evaluations. We show that while the templates provide consistent framework, proper implementation still requires detailed knowledge of experimental conditions and careful treatment of nonlinear effects in cross section derivation. Case studies highlight how template-assisted UQ improves consistency with previous evaluations such as ENDF/B and reveals open challenges in propagating uncertainties across different energy regimes. The main contribution of this paper is to connect formal template recommendations with their use in practical evaluation workflows, clarifying both their benefits and current limitations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Status, Challenges, and Plans for Consistent Modeling and Evaluation of Fission Data: Nubar, PFNS, and FPY [Slides]

This presentation discusses the importance of consistent evaluations for fission observables. Currently, prompt fission quantities (e.g., neutron multiplicity, neutron energy spectrum, and fission product yields) are evaluated independently of one another, either with separate models or data-only/non-model evaluations (few – if any – shared model inputs) and inconsistencies can arise in evaluated data (e.g. NSE 190, 258 (2018)). They have found that consistent, model-based evaluations lead to more physical constraints on free parameters in the model, more robust predictions for other observables and other isotopes, that there are correlations between the uncertainties on different observables, and that uncertainties can be propagated to unmeasured quantities. They are working on developing models to the point where fission observables are calculated at the quality needed for an evaluation. They are striving to consistently calculate fission observables, such as $\bar{v}$, PFNS, and FPY, to a quality suitable for an evaluation. Current evaluations for fission observables use separate models for each observable (with minimal shared input) or are purely data driven. LANL models, such as the Monte Carlo CGMF and deterministic BeoH, have different strengths; the similar fission fragment initial conditions and decay models leads to consistency between the two codes (FPY can be connected to $\bar{v}$ and PFNS, even when calculated by different codes). Work is underway by Lovell to optimize the models and Neudecker is working to perform detailed uncertainty quantification. The PFNS, in particular, presents a significant challenge.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

(Doublon) Benchmarking of Different Inverse Point Kinetics Implementations for an Autocorrected Reactimeter Algorithm

In November 2017, the Transient Reactor Test Facility returned to operation. Since that time, many transient test series have been completed, such as the Transient Heatsink Overpower Response capsule (THOR), the Transient Water Irradiation System for TREAT (TWIST), and Sirius. Each has provided valuable data for materials performance and reactor safety that can be applied in future designs. During each experimental series, detector count rates provided important information on the core behavior during transients. However, a limitation of these data is that variations in the neutron distribution during experiments can cause errors when attempting to infer reactivity evolution from detector signals. Neutron physics codes can be used to compute the flux shape variations. However, this is a poor solution when the experimental data is used for code verification, validation and uncertainty quantification. Indeed, if the output of the code is used both as a reference and to correct what the reference is compared to, the circular dependency limits the quality of the verification, validation and uncertainty quantification approach. To overcome this problem, the autocorrected reactimeter algorithm (ACRA) has been developed. This approach infers a time-dependent reactivity evolution by testing different spatial corrections and selecting the one that minimizes reactivity variations when the core is in a frozen configuration (i.e., when there is no variation in parameters affecting reactivity). However, the scope of this method was limited to transients where there were negligible thermal feedback. Indeed, the core is never in a frozen configuration when the fuel temperature varies during the whole transient. This is our motivation for developing an improved version of the ACRA that does not require frozen configurations. To develop this new algorithm, we need a precise and unbiased implementation of the inverse point kinetic equations (IPKEs) as any error in the reactivity evaluation will be propagated into the choice of the optimal spatial correction. Indeed, the previous reactimeter algorithm would use approximations, such as a negligible flux amplitude derivative, to focus on rapidity. For the numerical validation of ACRA, we aim at absolute error under for reactivity derived from signals similar to the one of this study. In this summary, we test eight different IPKE implementations. Each will process a mockup signal built for this study, similar to those that the future ACRA will process. Each reactivity output will be compared to the reference reactivity that has been used to generate the mockup signal. The implementation minimizing the difference with the reference reactivity will be used in the development of a new ACRA formulation.

73 - NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Koopman-Based Approach to Nonintrusive Reduced Order Modeling: Application to Aerodynamic Shape Optimization and Uncertainty Propagation

A methodology for nonintrusive projection-based nonlinear model reduction originally presented by Renganathan et al. is further extended here toward parametric systems with a focus on application to aerospace design. Specifically, the method is extended to address static systems with parametric geometry (that deforms the mesh) in addition to parametric freestream boundary conditions. The main idea is to first perform a transformation on the governing equations such that it is lifted to a higher-dimensional but linear underdetermined system. This enables one to extract the system matrices easily as compared to that of the original nonlinear system. The underdetermined system is closed with a set of model-dependent nonlinear constraints upon which the model reduction is finally performed. The methodology is validated on the subsonic and transonic inviscid flows past the NACA0012 and the RAE2822 airfoils with parametrized shapes. The utility of the approach is further demonstrated by applying it to two common problems in aerospace design, namely, derivative-free global optimization and parametric uncertainty quantification with Monte Carlo sampling. Overall, the methodology is shown to achieve accuracy up to 5% and computational speedup of two to three orders of magnitude relative to the full order model. Comparison against another nonintrusive model reduction method revealed that the proposed approach is more robust, accurate, and retains the consistency between the state variables.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Uncertainty Propagation from Experiment Measurements to Modeling Approaches: A Case for SMR Steam Entrainment Testing

To license new and advanced reactor designs, regulators must be convinced that their unique safety cases—relative to existing large scale reactors—have been adequately addressed by the designed reactor protection systems. In water cooled small modular reactors (SMRs), droplet entrainment in steam flow has significant implications on the progression of accident scenarios due to its compact design features, which requires representative test data applicable to SMR designs. Computer code, modeling and simulation (M&S) tools and models require adequate verification, assessment, and qualification. This includes M&S results validation against scaled empirical data within allowable uncertainty bands to gain regulatory approvals during the various stages of reactor system design, demonstration, and commercialization. However, measurement uncertainty within the empirical datasets and test data applicability ranges requires careful consideration of M&S inputs (i.e., boundary conditions, and initial conditions), and verification and validation efforts. This study focuses on uncertainty quantification in designing scaled test facilities for SMR applications with appropriate measurements and a standard data-reduction method to estimate thermal hydraulics characteristics parameters that incorporate physics phenomena of interest. In addition, this study supports the evaluation model development and assessment process using M&S that interfaces with advanced computing tools and digital twin capabilities. This will allow synchronization between experiment and modeling approaches for droplet entrainment testing and analysis, improving diagnostics, prognostics, and decision-making to accelerate regulatory approval.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2020

A generalized approximate control variate framework for multifidelity uncertainty quantification

We describe and analyze a variance reduction approach for Monte Carlo (MC) sampling that accelerates the estimation of statistics of computationally expensive simulation models using an ensemble of models with lower cost. These lower cost models — which are typically lower fidelity with unknown statistics — are used to reduce the variance in statistical estimators relative to a MC estimator with equivalent cost. We derive the conditions under which our proposed approximate control variate framework recovers existing multifidelity variance reduction schemes as special cases. We demonstrate that existing recursive/nested strategies are suboptimal because they use the additional low-fidelity models only to efficiently estimate the unknown mean of the first low-fidelity model. As a result, they cannot achieve variance reduction beyond that of a control variate estimator that uses a single low-fidelity model with known mean. However, there often exists about an order-of-magnitude gap between the maximum achievable variance reduction using all low-fidelity models and that achieved by a single low-fidelity model with known mean. We show that our proposed approach can exploit this gap to achieve greater variance reduction by using non-recursive sampling schemes. The proposed strategy reduces the total cost of accurately estimating statistics, especially in cases where only low-fidelity simulation models are accessible for additional evaluations. Several analytic examples and an example with a hyperbolic PDE describing elastic wave propagation in heterogeneous media are used to illustrate the main features of the methodology.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Evaluation of average leaf inclination angle quantified by indirect optical instruments in crop fields

Average leaf inclination angle ($\overline{θ}$ L ) is an important canopy structure variable that influences light regime, photosynthesis, and evapotranspiration of plants. $\overline{θ}$ L can be measured through direct methods (e.g., protractor), which are labor-intensive and time-consuming, or through indirect optical instruments, which are more efficient than the direct methods. However, uncertainties of different indirect optical instruments for quantifying $\overline{θ}$ L remain largely unquantified. In this study, we evaluated and compared the performances of three major indirect optical instruments: (1) LAI-2200, (2) 30°-tilted camera, and (3) digital hemispherical photography (DHP), in different crop fields over a growing season, benchmarked with direct measurements. LAI-2200 and 30°-tilted camera showed higher agreement with direct $\overline{θ}$ measurements (R 2 = 0.54, RMSE = 7.37°; R 2 = 0.58, RMSE = 8.08°) than DHP (R 2 = 0.14, RMSE = 13.96°). Different performances of indirect optical instruments could be attributed to the accuracy of gap fraction measurement and the performance of the $\overline{θ}$ L quantification algorithms. When using the LAI-2200 algorithm, larger gap fraction gradients over view zenith angles led to larger $\overline{θ}$ L values, and smaller gap fraction gradients led to smaller $\overline{θ}$ L values. Such error propagation was larger in sparse canopy than in dense canopy. The Wilson G function of the LAI-2200 algorithm performed better in estimating $\overline{θ}$ L than the G function based on the ellipsoidal LAD function used by the CAN_EYE algorithm. We also proposed a modification of the LAI-2200 algorithm, which further improved the performance of LAI-2200 and 30°-tilted cameras in estimating $\overline{θ}$ L . We envision that the low-cost 30°-tilted cameras provide a promising sensor solution to continuously monitor canopy structure for various ecosystems.

30°-tilted camera↗

DOE OSTI2022

Robust two-colour pyrometry uncertainty analysis to acquire spatially-resolved measurements

Two-colour pyrometry (2CP) has been used over several decades to study engine-relevant combustion processes, but results are generally regarded as qualitative or semi-quantitative. In many current 2CP systems, large measurement errors are introduced by parallax because the two measured wavelengths are not from the same line of sight. Here this work presents a spatially-resolved 2CP system with the objective of quantifying and reducing measurement uncertainty. An optical setup that eliminates parallax in 2CP is used together with pixel-by-pixel calibration of the camera sensor to increase measurement accuracy. Primary uncertainty terms are identified, and an error propagation analysis is performed to compute uncertainties in the final results of soot temperature, soot concentration parameter, KL, and soot mass. These methodologies are applied to investigate an auto-igniting fuel spray in a constant pressure flow rig at diesel-like conditions of high ambient pressure and temperature. Results show bias uncertainty of around 200 K (≈10%) for temperature and about 40%–60% for KL. High uncertainty was found to occur on the diffusion flame front where both optical thickness and soot concentrations are small. However, these uncertain measurement zones with relatively low soot concentrations contribute minimally to the total soot mass present in the reacting jet during the temporal evolution of the flame.

42 ENGINEERING↗