Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Uncertainties”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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

At least 631 records · Page 35
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Kinetic model development and Bayesian uncertainty quantification for the complete reduction of Fe-based oxygen carriers with CH 4 , CO, and H 2 for chemical looping combustion

In this work, three kinetic models are developed and calibrated for the complete multi-step reduction of an Fe-based oxygen carrier (OC) particle with CH 4 , CO, and H 2 , using data from thermogravimetric analysis. The complete reduction rate profiles exhibit complex dynamics whose trajectory is significantly different depending on the reducing gas. A Bayesian model building and parameter estimation framework is applied for simultaneous parameter and model structure uncertainty quantification. The final models show excellent agreement between model predictions and calibration data, as well as new data not used for calibration (for the reduction of the OC with CH 4 ). Parameter uncertainty is quantified by determining joint posterior distribution, and model structure uncertainty is addressed by incorporating Gaussian process stochastic functions (represented by Bayesian smoothing splines) into the kinetic models. The final kinetic models with discrepancy functions are readily employable in equation-oriented simulation and optimization platforms.

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

Application of Markov Chain Monte Carlo Methods for Uncertainty Quantification in Inverse Transport Problems

Determination of the components of a radioactive source/shield system using the system’s radiation signature is of great importance in homeland security, material safeguards, and waste management. Although significant progress has been made toward solving this inverse transport problem in recent years, work remains to be done to quantify the uncertainty in reconstructed results. In this article we apply two Markov chain Monte Carlo (MCMC) approaches, the delayed rejection adaptive metropolis (DRAM) and differential evolution adaptive metropolis (DREAM) methods, to solve inverse problems and quantify uncertainty. The DRAM method uses delayed rejection combined with global adaptation of the proposal covariance matrix. Furthermore, the DREAM method hybridizes MCMC sampling with the differential evolution (DE) algorithm. In numerical test cases, the DRAM and DREAM methods are shown to be superior to a first-order inverse Hessian approach for problems with noisy data and multiple unknown quantities, with DREAM converging to the posterior distribution more quickly than DRAM. The DREAM and DRAM results indicate that a full posterior distribution is required to quantify uncertainty in many inverse transport problems.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
DOE OSTI2026

An Analysis of Future Wind Energy Resources and Cost Uncertainties Across the United States

Wind power is a growing source of energy generation that relies on complex global atmospheric and earth system processes. There has been evidence of reductions in average wind speeds over land in North America since the 1980s, and several models project that average wind speeds will continue to decrease. Concurrently, the cost of wind energy systems in the United States has been decreasing since around 2010, a trend also projected to continue. There is considerable uncertainty in these future projections, with quantitative estimates of future wind resource and system costs varying widely. To study this, we run wind energy models with possible future system costs, turbine designs, and meteorological inputs from multiple downscaled earth system models over the contiguous United States. Changes in mean annual energy production from 2000-2019 to 2040-2059 can be as high as +10% in South Texas or as low as -20% in Iowa. Larger turbines and moderate reductions in system costs can offset the largest projected decreases in wind resource, but much uncertainty remains in the extent to which wind resources will change and to what extent system costs can be reduced. An analysis of variance shows, in several states in the Midwest, uncertainty in future wind resources can influence the cost of wind energy nearly as much as uncertainty in future system costs.

17 WIND ENERGY↗
DOE OSTI2022

A Bayesian Approach for In-Situ Stress Prediction and Uncertainty Quantification for Subsurface Engineering

Many subsurface engineering applications require accurate knowledge of the in-situ state of stress for their safe design and operation. Existing methods to meet this need primarily include field measurements for estimating one or more of the principal stresses from a borehole, or optimization methods for constructing a 3D geomechanical model in terms of geophysical measurements. These methods, however, often contain considerable uncertainty in estimating the state of stress. Here, in this paper, we build on a Bayesian approach to quantify uncertainty in stress estimations for subsurface engineering applications. This approach can provide an estimate of the 3D distribution of stress throughout the volume of interest and provide an estimate of the uncertainty arising from the stress measurement, the rheology parameters, and a paucity of measurements. The value of this approach is demonstrated using stress measurements from the In Salah carbon storage site, which was one of the world’s first industrial carbon capture and storage projects. This demonstration shows the application of this Bayesian approach for estimating the initial state of stress for In Salah and quantifying the uncertainty in the estimated stress. Also, an assessment of a maximum injection pressure to prevent geomechanical risks from CO 2 injection pressures is provided in terms of the probability distribution of the minimum principal stress quantified by the approach. With the In Salah case study, this paper demonstrates that using the Bayesian approach can provide additional insights for site explorations and/or project operations to make informed-site decisions for subsurface engineering applications.

58 GEOSCIENCES↗
DOE OSTI2025

Uncertainty quantification for nuclear forensics with population analyses

Although neural networks offer cutting-edge predictive power, their deployment in high-consequence nuclear forensic applications is limited, partly because of their black-box nature. Incorporating robust uncertainty quantification methods into the predictive frameworks of neural networks is progress towards their future deployment in such scenarios. This work integrates uncertainty quantification into neural networks for nuclear reactor core-average burnup estimation from simulated environmental samples. We test two regimes (homogeneous and heterogeneous events) on DeepSets and Set Transformer architectures, we find both quantify predictive uncertainty effectively, but Set Transformer excels in partitioning latent events, offering superior predictive power and more informative uncertainty estimates.

Hatton, Conner [ORNL] (ORCID:0009000804970959)↗
DOE OSTI2021

Gap-filling eddy covariance methane fluxes: Comparison of machine learning model predictions and uncertainties at FLUXNET-CH4 wetlands

Time series of methane fluxes measured by eddy-covariance require gap-filling to estimate annual emissions. Gap-filling methane fluxes is challenging because of high variability and complex responses to multiple drivers. To date, there is no widely established gap-filling standard for methane, with regards both to the best model algorithms and predictors. In this study, we address the need for standardization by synthesizing results of gap-filling methods applied at 17 wetland sites spanning boreal to tropical regions including all major wetlands classes and two rice paddies. We introduce new procedures for: 1) creating realistic artificial gap scenarios, 2) training and evaluating gap-filling models without overstating performance, and 3) predicting half-hourly methane fluxes and annual emissions with robust uncertainty estimates. We tested a conventional method (marginal distribution sampling) and four machine learning algorithms - penalized linear regression, artificial neural networks, random forests, and boosted decision trees - and four predictor sets, including temporal, meteorological, ecosystem carbon and energy flux, and soil predictors. We find that the conventional method can achieve similar median performance to the machine learning models but is worse than the best machine learning models and relatively insensitive to predictor choices. Of the machine learning models, decision tree algorithms performed the best in cross-validation experiments, even with a baseline predictor set, and artificial neural networks showed comparable performance when using all predictors. Soil temperature was frequently the most important predictor whilst water table depth was important at sites with substantial water table fluctuations, highlighting the value of data on soil conditions. Raw gap-filling uncertainties from the machine learning models were underestimated and we propose a method to calibrate uncertainties to observations. Finally, we gap-fill and provide summary evaluation metrics for all 81 sites in the FLUXNET-CH4 community dataset and publicly release the python code for model development, evaluation, and uncertainty estimation.

42 ENGINEERING↗
DOE OSTI2024

Finite elements for Matérn-type random fields: Uncertainty in computational mechanics and design optimization

This work highlights an approach for incorporating realistic uncertainties into scientific computing workflows based on finite elements, focusing on prevalent applications in computational mechanics and design optimization. We leverage Matérn-type Gaussian random fields (GRFs) generated using the SPDE method to model aleatoric uncertainties, including environmental influences, variating material properties, and geometric ambiguities. Our focus lies on delivering practical GRF realizations that accurately capture imperfections and variations and understanding how they impact the predictions of computational models as well as the shape and topology of optimized designs. Here we describe a numerical algorithm based on solving a generalized SPDE to sample GRFs on arbitrary meshed domains. The algorithm leverages established techniques and integrates seamlessly with the open-source finite element library MFEM and associated scientific computing workflows, like those found in industrial and national laboratory settings. Our solver scales efficiently for large-scale problems and supports various domain types, including surfaces and embedded manifolds. We showcase its versatility through biomechanics and topology optimization applications, emphasizing the potential to influence these domains. The flexibility and efficiency of SPDE-based GRF generation empowers us to run large-scale optimization problems on 2D and 3D domains, including finding optimized designs on embedded surfaces, and to generate design features and topologies beyond the reach of conventional techniques. Moreover, these capabilities allow us to model and quantify geometric uncertainties on reconstructed submanifolds, such as the interpolated surfaces of cerebral aneurysms provided by postprocessing CT scans. In addition to offering benefits in these specific domains, the proposed techniques transcend specific applications and generalize to arbitrary forward and backward problems in uncertainty quantification involving finite elements.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A multistage distributionally robust optimization approach to water allocation under climate uncertainty

This paper investigates a Multistage Distributionally Robust Optimization (MDRO) approach to water allocation under climate uncertainty. The MDRO is formed by creating sets of conditional distributions (called conditional ambiguity sets) on a finite scenario tree. The distributions in the conditional ambiguity sets remain close to a nominal conditional distribution according a ø-divergence (e.g., Kullback-Leibler divergence, Hellinger distance, Burg entropy, etc.). Here, the paper discusses a decomposition algorithm to solve the resulting MDRO with ø-divergences, which uses the dual formulation and solves only linear subproblems instead of convex ones. Some properties of the algorithm such as generating feasible policies and valid upper/lower bounds are established. The paper then applies the modeling and solution techniques to allocate water in a rapidly-developing area of Tucson, Arizona. Tucson, like many arid and semi-arid regions around the world, faces considerable uncertainty in its ability to provide water for its citizens in the future. The primary sources of uncertainty in the Tucson region include (1) unpredictable population growth, (2) the availability of water from the Colorado River, and (3) the effects of climate variability on water consumption. This paper integrates forecasts for all these sources of uncertainty into a single optimization model for robust and sustainable water allocation. Then, it uses this model to analyze the value of constructing additional treatment facilities to reduce future water shortages. The results indicate that the MDRO approach can be very valuable for water managers by providing insights to minimize their risks and help them plan for the future.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Uncertainty analysis for techno-economic and life-cycle assessment of wet waste hydrothermal liquefaction with centralized upgrading to produce fuel blendstocks

Wet waste hydrothermal liquefaction is a promising technology for producing transportation fuels with much lower greenhouse gases emissions than petroleum-based fuels. However, its techno-economic and life cycle assessment are primarily based on laboratory scale testing data, subject to considerable uncertainties, and even bias, due to knowledge gaps. Here, a preliminary uncertainty analysis of key economic measures was conducted based on the 2019 state-of-technology model for biocrude production. Building on the preliminary analysis, this work presents a comprehensive uncertainty analysis in both economic and environmental measures of the entire supply chain of wet waste hydrothermal liquefaction to fuel blendstocks including biocrude upgrading based on the 2021 state-of-technology model. The analysis includes the most recent developments in hydrothermal liquefaction and biocrude upgrading technologies and Monte Carlo simulation based on an integrated model system including an improved reactor yield model, reduced-order process model, discounted cash flow economic model and simplified life-cycle assessment model. The estimated biocrude yield ranges from 42.2% to 52.4% with a median of 47.3%. The estimated fuel yield ranges from 34.7% to 42.7% with a median of 38.7%. The estimated minimum fuel selling price ranges from $\$ $2.28/gge to $\$ $3.45/gge with a median of $\$ $2.80/gge. Relative to petroleum-derived diesel, the estimated reduction in supply chain greenhouse gas emissions ranges from 73.4% to 81.8% with a median of 77.7%. Compared to the 2019 state-of-technology analysis, a significant improvement in biocrude selectivity and economic measures and reduction in uncertainties were achieved due to the incorporation of additional continuous experimental data sets, technology development and de-risking, and improvement in model accuracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

High-resolution modeling of indoor radon exposure with uncertainty quantification in Utah

Indoor radon accounts for 37% of population-level exposure to ionizing radiation in the United States. However, radon metrics are typically reported at coarse spatial scales, potentially obscuring meaningful local variation. We developed a high-resolution modeling framework to estimate indoor radon concentrations across Utah while explicitly quantifying predictive uncertainty. A total of 19,497 residential radon measurements collected between 2006 and 2017 were combined with environmental and housing characteristics and analyzed using a geospatial neural network that accommodates spatial dependence and nonlinear associations. Predictions were generated on a uniform hexagonal grid at 0.73 km2 resolution (H3 level 8). Out-of-sample predictions aggregated to the H3 level 8 grid showed good agreement with observed concentrations (Pearson r=0.64), while household-level predictions exhibited more moderate agreement (r=0.45). The model produced well-calibrated uncertainty estimates, with 24.1% of held-out observations exceeding the predicted 75th-percentile threshold. Maps of predicted radon concentrations and the probability of exceeding the U.S. EPA action level of 148 Bq/m3 (4 pCi/L) revealed substantial fine-scale spatial heterogeneity that was not apparent in conventional coarse-resolution summaries, with greater local variability observed in densely monitored urban counties than in sparsely sampled regions. High-resolution radon models that explicitly quantify uncertainty provide a useful framework for characterizing the spatial distribution of indoor radon and identifying areas of elevated exceedance risk. These findings highlight the value of fine-scale monitoring data and uncertainty-aware modeling approaches for radon exposure assessment, environmental risk characterization, and radon-related health research.

Wu, Yunhan [ORNL] (ORCID:0000000178842994)↗
DOE OSTI2026

Uncertainty quantification for Joule heating processes in fibrous pore-resolved media

Joule heating (JH) is an energy-efficient and sustainable technique for heating materials. Its application for industrial heating, particularly, has been gaining attention due to its potential for increasing the yield of various chemical products. The process involves the use of heating elements (materials that are highly conductive electrically and thermally) to heat up other materials or substances. These conductors, however, can exhbit varying degrees of uncertainty due to non-linearities in their temperature-dependent properties, which could result in variable material behavior. In this work, we carry out uncertainty quantification (UQ) at the pore scale to describe the uncertainty of such materials. In so doing, we applied the non-intrusive polynomial chaos expansion (PCE) technique to quantify the uncertainty within the system. The steady state Joule heating equation was solved numerically at the pore scale mimicking conditions within a heating chamber for propane dehydrogenation, and various electro-thermal profiles were obtained. We also examined the effect of the number of sampling points (20 – 100) and order of the PCE coefficients (2 – 5) on the accuracy of the temperature evaluations. The results were then benchmarked with the standard Monte Carlo (MC) method. The average temperature of the 4th-order global PCE showed good agreement with the MC results (which were positively skewed). Orders greater than 4 gave an underestimation of the temperatures while predictions for the peak temperature improved as the number of sampling points increased.

Fagbemi, Samuel [ORNL] (ORCID:0000000236995025)↗
DOE OSTI2026

Uncertainty quantification for competing failure mechanisms in unidirectionally reinforced carbon–carbon composites

Microstructure-informed finite element models play a key role in the carbon–carbon composite design process. Variability in manufacturing process parameters and experimental limitations introduce model parameter uncertainty. This study quantifies the effect of model parameter uncertainty on transverse tensile fracture behavior and proposes a methodology to predict the failure mode based on competing microscale damage mechanisms. Finite element simulations incorporate fiber–matrix interface debonding with cohesive zones and matrix damage with a smeared crack band approach in a unidirectional carbon–carbon composite. Results from a variance-based global sensitivity analysis identifies interfacial and matrix damage parameters as the primary source of variability in fracture behavior. Sobol’ indices indicate that matrix and cohesive zone strengths contribute 94% of the variance in the effective ultimate stress. A local analysis elucidates the relationship between these constituent strength parameters and failure mode by estimating the probability of cohesive, matrix, and mixed-mode dominated failure. Based on the results for 4000 simulations, 93% exhibit mixed-mode or interfacial dominated failure, which underscores the crucial role of fiber–matrix interface debonding in the transverse tensile failure of carbon–carbon composites. These uncertainty quantification results facilitate more efficient model calibration and provide a framework for microstructure-informed failure predictions in the face of manufacturing-induced uncertainty.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Unrecognized Sources of Uncertainties ( USU ) in Experimental Nuclear Data

Evaluated nuclear data uncertainties reported in the literature or archived in data libraries are often perceived as unrealistic, most often because they are thought to be too small. The impact of this issue in applied nuclear science has been discussed widely in recent years. Commonly suggested causes are: poor estimates of specific error components, neglect of uncertainty correlations, and overlooked known error sources. However, instances have been reported where very careful, objective assessments of all known error sources have been made with realistic error magnitudes and correlations provided, yet the resulting evaluated uncertainties still appear to be inconsistent with observed scatter of predicted mean values. These discrepancies might be attributed to significant unrecognized sources of uncertainty ( USU ) that limit the accuracy to which these physical quantities can be determined. The objective of our work reported herein has been to develop qualitative and quantitative procedures for revealing and including USU estimates in nuclear data evaluations involving experimental input data. This paper identifies several specific clues that can be explored by evaluators in identifying the existence of USU . It then describes numerical procedures we have introduced to generate quantitative estimates of USU magnitudes. Key requirements for these procedures to be viable are that sufficient numbers of data points be available, for statistical reasons, and that additional supporting information about the measurements be provided by the experimenters. Several realistic examples are described here to illustrate these procedures and demonstrate their outcomes and limitations. Our work strongly supports the view that USU is an important issue in nuclear data evaluation, with significant consequences for applications, and that this topic warrants further investigation by the nuclear science community.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Sensitivity of the simulation of passive neutron emission from UF 6 cylinders to the uncertainties in both 19 F(α,n) energy spectrum and thick target yield of 234 U in UF 6

Interest in safeguards verification measurements using passive thermal neutron counting to assay 235 U content in large 30B UF 6 canisters has grown in recent years. Here, the prohibitively high cost and impracticality of using reference 30B calibration cylinders extensively will likely make accurate simulations of increasing interest. Accuracy of the simulated response will define the confidence in the predicted response and the extent to which simulations can reasonably be relied upon. With 234 U driven 19 F(α, n) reactions being the main neutron source in low enriched UF 6 the uncertainties of the 19 F(α, n) energy spectrum and the thick target yield of 234 U in UF 6 propagate into the uncertainty in the predicted response and represent a major influence of basic nuclear data. Here sensitivity of the simulated total (Singles) and coincidence (Doubles) count rates are assessed for the Passive Neutron Enrichment Meter using six potential 19 F(α, n) neutron energy spectra over a range of enrichments and material distributions. The results indicate that variations in the Singles and Doubles due to simulated (α, n) neutron spectrum are less than 1.5% for this set of simulated neutron spectra, with dependence varying inversely with enrichment. Singles uncertainty is only slightly less than that of the thick target 19 F(α, n) yield corresponding to the primary neutron source, whereas the 19 F(α, n) yield dependence of the Doubles is reduced by the non-negligible 238 U(SF) coincident neutron emissions. Based on available thick target 19 F(α, n) yield estimates the uncertainty is on the order of 5%, establishing this as the main nuclear data limitation when simulating thermal neutron detectors response for 30B UF 6 storage cylinders. Based on these findings, it appears that the measurement and evaluation of the thick target 19 F(α, n) yield for uranium hexafluoride is due.

19F(α,n) neutron spectrum↗
DOE OSTI2020

Uncertainty analysis of PIV measurements in bubbly flows considering sampling and bubble effects with ray optics modeling

In this report, a modeling-based approach is developed to investigate the external sources of uncertainty in particle image velocimetry (PIV) measurements for two-phase bubbly flows. Primarily relied on ray optics modeling, this study focuses on the uncertainty in PIV measurements due to bubble-induced light distortion. In addition, the uncertainty due to sampling is also considered through synthetic PIV images generated from Monte Carlo sampling. Based on a PIV-planar laser induced florescence (PLIF) measurement system, three case studies are performed and discussed, considering respectively the sampling effect, bubble effect, and the combination of these two effects. These case studies confirm the validity of the ray optics modeling in obtaining accurate particle images through a benchmark test. Furthermore, it is also found that the bubble effect could significantly influence the particle images. On the other hand, the result of the case study with synthetic PIV images indicates that the bubble effect on particle images can be minimized by removing “outliers” in the obtained velocity vector field through a multi-pass post-processing procedure. However, the uncertainty of the velocity measurements will still increase.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

On the uncertainty of estimating photovoltaic soiling using nearby soiling data

The accumulation of dust on the surface of photovoltaic modules can reduce their performance and affect the cost competitiveness of this technology. This phenomenon is known as soiling and can be mitigated through appropriate corrective and/or preventive actions. In order to maximize its effectiveness, it is important to plan the soiling mitigation strategy even before the PV system is operational. This is typically done through a nearest neighbor approach, by estimating soiling using data from the nearest operational photovoltaic system. This work focuses on understanding the uncertainty related to this practice. For this purpose, the semi-variance function is used to study the dissimilarity between the soiling losses of two locations in California depending on their distance. The results show that, when the soiling loss at a nearby system is used to estimate soiling of a site, the uncertainty can be approximated to increase linearly at a rate of 0.08-0.10%/km up to 60 or 80 km. After this distance, the use of a nearest neighbor approach is no longer justified, as it produces an uncertainty as big as the average soiling loss of the sites in the dataset used in this study. In some conditions, uncertainties > 0% are found also for sites located within 25 km, meaning that even close-by systems might soil differently.

14 SOLAR ENERGY↗
DOE OSTI2025

Optimization problems governed by systems of PDEs with uncertainties

This paper reviews current theoretical and numerical approaches to optimization problems governed by partial differential equations (PDEs) that depend on random variables or random fields. Such problems arise in many engineering, science, economics and societal decision-making tasks. This paper focuses on problems in which the governing PDEs are parametrized by the random variables/fields, and the decisions are made at the beginning and are not revised once uncertainty is revealed. Examples of such problems are presented to motivate the topic of this paper, and to illustrate the impact of different ways to model uncertainty in the formulations of the optimization problem and their impact on the solution. A linear–quadratic elliptic optimal control problem is used to provide a detailed discussion of the set-up for the risk-neutral optimization problem formulation, study the existence and characterization of its solution, and survey numerical methods for computing it. Different ways to model uncertainty in the PDE-constrained optimization problem are surveyed in an abstract setting, including risk measures, distributionally robust optimization formulations, probabilistic functions and chance constraints, and stochastic orders. Furthermore, approximation-based optimization approaches and stochastic methods for the solution of the large-scale PDE-constrained optimization problems under uncertainty are described. Some possible future research directions are outlined.

Heinkenschloss, Matthias [Rice Univ., Houston, TX ↗
DOE OSTI2020

Lightning Interferometry Uncertainty, Beam Steering Interferometry, and Evidence of Lightning Being Ignited by a Cosmic Ray Shower

Abstract We present an uncertainty analysis on correlation‐based time delay estimate, the basis for broadband lightning interferometry. A normal interferometry would yield much higher uncertainties than the theoretically predicted lower bound due to finite correlation window lengths. However, if the signals are aligned in time, the uncertainties approach the lower bound and can be used to indicate the interferometric uncertainties. Based on this, we introduce a beam steering interferometry technique. It first estimates a direction centroid for the lightning sources with a normal interferometry and computes the time delays among the signals. It then shifts the raw data with the time delays to align the signals roughly in time and reprocess the aligned signals. It finally pushes the reprocessed results to their correct positions, based on the time delays estimated in the first step. We apply this technique on a fast positive breakdown (FPB) process that started a normal intracloud lightning. The FPB process is shown to have a much more complex structure and development than a normal interferometry would provide. More importantly, from both interferometric and polarization analyses, the FPB appears to be ignited by a cosmic ray shower (CRS). We estimate the radio frequency strength and frequency content related to a presumed CRS in a thunderstorm electric field and find that they are in agreement with the observations. We examine the electric field effect of the CRS front and find that it could raise the field above the threshold for positive breakdown and is capable of igniting the FPB (and the lightning).

Shao, Xuan‐Min↗