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Essential Statistical Concepts

Statistical methods are an essential element to making quality measurements, allowing the organization and interrogation of data in a structured way. This introductory chapter describes key concepts of measurement statistics that are used in many nondestructive assay (NDA) methods and is intended as a primer to the reading list provided in the reference section. (Croft and Burr 2016; Smith 1991; Smith 2013; Taylor 1997; Triola 2017). The textbooks by Triola on elementary statistics (Figure 1), Taylor, and Smith (2013) introduce uncertainty analysis in the physical sciences. Smith (1991) provides a rigorous introduction with examples to correlated variables. These texts collectively offer an excellent foundation for understanding essential statistical concepts.

97 MATHEMATICS AND COMPUTING↗

OzDES reverberation mapping program: Lag recovery reliability for 6-yr C iv analysis

ABSTRACT We present the statistical methods that have been developed to analyse the OzDES reverberation mapping sample. To perform this statistical analysis we have created a suite of customizable simulations that mimic the characteristics of each source in the OzDES sample. These characteristics include: the variability in the photometric and spectroscopic light curves, the measurement uncertainties, and the observational cadence. By simulating the sources in the OzDES sample that contain the C iv emission line, we developed a set of criteria that rank the reliability of a recovered time-lag depending on the agreement between different recovery methods, the magnitude of the uncertainties, and the rate at which false positives were found in the simulations. These criteria were applied to simulated light curves and these results used to estimate the quality of the resulting Radius–Luminosity relation. We grade the results using three quality levels (gold, silver, and bronze). The input slope of the R–L relation was recovered within 1σ for each of the three quality samples, with the gold standard having the lowest dispersion with a recovered a R–L relation slope of 0.454 ± 0.016 with an input slope of 0.47. Future work will apply these methods to the entire OzDES sample of 771 AGN.

79 ASTRONOMY AND ASTROPHYSICS↗

Verification and validation of residual stresses in composite structures

Process-induced residual stresses occur in composite structures composed of dissimilar materials. As these residual stresses could result in fracture, their consideration when designing composite parts is necessary. However, the experimental determination of residual stresses in prototype parts can be time and cost prohibitive. Alternatively, it is possible for computational tools to predict potential residual stresses. Therefore, the objectives of the presented work are to demonstrate an efficient method for simulating residual stresses in composite parts, as well as the potential value of statistical methods during analyses for which material properties are unknown. Specifically, a simplified residual stress modeling approach is implemented within Sandia National Laboratories’ SIERRA/SolidMechanics code. Concurrent with the model development, bi-material composite structures are designed and manufactured to exhibit significant residual stresses. Then, the presented modeling approach is rigorously verified and validated through simulations of the bi-material composite structures’ manufacturing processes, including a mesh convergence study, sensitivity analysis, and uncertainty quantification. The simulations’ final results show adequate agreement with the experimental measurements, indicating the validity of a simple modeling approach, as well as a necessity for the inclusion of material parameter uncertainty in the final residual stress predictions.

42 ENGINEERING↗

Subsurface Trend Analysis domains for the northern Gulf of Mexico

Geologic domains for the northern Gulf of Mexico derived using the Subsurface Trend Analysis (STA) method. The domains were postulated using geologic province, lithologic, and structural information and validated using statistical methods. Publication detailing the STA method: Rose, K., Bauer, J.R., and Mark-Moser, M. (2020) Subsurface trend analysis, a multi-variate geospatial approach for subsurface evaluation and uncertainty reduction, Interpretation, vol. 8, issue 1 https://library.seg.org/doi/abs/10.1190/int-2019-0019.1 Detailed discussion of domain formation and analysis: Mark-Moser, M., Miller, R., Bauer, J., Rose, K., and C. Disenhof. 2018, Analysis of Subsurface Reservoir Properties Using a Novel Geospatial Approach, Offshore Gulf of Mexico. NETL-TRS-2018 https://edx.netl.doe.gov/dataset/detailed-analysis-of-geospatial-trends-of-hydrocarbon-accumulations-offshore-gulf-of-mexico

geology↗

Data-Driver Interpretation of Ultradeep Azimuthal Propagation

We report the interpretation of geological features around the borehole stresses on the search of true earth model parameters. Different from the conventional logging-while-drilling (LWD) technologies, such as wireline induction and propagation resistivity tools, the azimuthal resistivity measurement acquires the ability of directional sensitivity. Within this decade, this type of tools has been greatly enhanced with over hundred feet depth-of-detection (DoD). To resolve the interpretation of geological features within 100 feet from the borehole, the multiple-layer structure must be considered. However, the traditional methods can never handle the highly nonlinear inverse problems especially facing on the complicated earth structure. Meanwhile, no justifiable uncertainty of inverse parameters can be provided. The statistical methods have been adopted to search for the global statistical distribution and uncertainties of earth model parameters. However, the most attempts are still stuck in non-uniqueness of the solutions since the structure of earth model has been predefined, where the number of layers is assumed, which introduces another ambiguity into the model interpretation. This paper develops a general trans-dimensional Bayesian methodology to solve non-linear inverse problem of earth layer resistivity and depth to the layer boundaries, from the interpretation of ultra-deep azimuthal resistivity measurements. The presented work is a data-driven approach to search out the multi-dimensional parameter spaces. Finally, the simulations tell that the algorithm can efficiently solve the earth model interpretation within a hundred feet from borehole, and examine the uncertainty of earth model parameters.

58 GEOSCIENCES↗

The Spiral Arm Segments of the Galaxy within 3 kpc from the Sun: A Statistical Approach

As can be reasonably expected, upcoming large-scale APOGEE, GAIA, GALAH, LAMOST, and WEAVE stellar spectroscopic surveys will yield rather noisy Galactic distributions of stars. In view of the possibility of employing these surveys, our aim is to present a statistical method to extract information about the spiral structure of the Galaxy from currently available data, and to demonstrate the effectiveness of this method. The model differs from previous works studying how objects are distributed in space in its calculation of the statistical significance of the hypothesis that some of the objects are actually concentrated in a spiral. A statistical analysis of the distribution of cold dust clumps within molecular clouds, H ii regions, Cepheid stars, and open clusters in the nearby Galactic disk within 3 kpc from the Sun is carried out. As an application of the method, we obtain distances between the Sun and the centers of the neighboring Sagittarius arm segment, the Orion arm segment in which the Sun is located, and the Perseus arm segment. Pitch angles of the logarithmic spiral segments and their widths are also estimated. The hypothesis that the collected objects accidentally form spirals is refuted with almost 100% statistical confidence. We show that these four independent distributions of young objects lead to essentially the same results. We also demonstrate that our newly deduced values of the mean distances and pitch angles for the segments are not too far from those found recently by Reid et al. using VLBI-based trigonometric parallaxes of massive star-forming regions.

79 ASTRONOMY AND ASTROPHYSICS↗

Acute stress reduces population-level metabolic and proteomic variation

Abstract Background Variation in omics data due to intrinsic biological stochasticity is often viewed as a challenging and undesirable feature of complex systems analyses. In fact, numerous statistical methods are utilized to minimize the variation among biological replicates. Results We demonstrate that the common statistics relative standard deviation (RSD) and coefficient of variation (CV), which are often used for quality control or part of a larger pipeline in omics analyses, can also be used as a metric of a physiological stress response. Using an approach we term Replicate Variation Analysis (RVA), we demonstrate that acute physiological stress leads to feature-wide canalization of CV profiles of metabolomes and proteomes across biological replicates. Canalization is the repression of variation between replicates, which increases phenotypic similarity. Multiple in-house mass spectrometry omics datasets in addition to publicly available data were analyzed to assess changes in CV profiles in plants, animals, and microorganisms. In addition, proteomics data sets were evaluated utilizing RVA to identify functionality of reduced CV proteins. Conclusions RVA provides a foundation for understanding omics level shifts that occur in response to cellular stress. This approach to data analysis helps characterize stress response and recovery, and could be deployed to detect populations under stress, monitor health status, and conduct environmental monitoring.

59 BASIC BIOLOGICAL SCIENCES↗

Hawaii Play Fairway Analysis: Lanai Resistivity and Density 3D Inversion Models

To prepare for its third phase, the Hawaii Play Fairway project conducted groundwater sampling and analyses in ten locations in the Hawaiian islands, magnetotelluric (MT) and gravity surveys, as well as calculations of 3D subsurface stress due to the weight of the rock underlying the topography of the volcano. The subsurface stresses were used to evaluate the potential for fracture-induced permeability. Inversions of the MT and gravity data produce 3D models of resistivity and density, respectively, on Lanai, across Haleakala's SW rift (Maui), and surrounding Mauna Kea (Hawaii Island). The project developed and applied a new method for incorporating depth information about resistivity, density, and potential for fracture-induced permeability into the statistical method for computing resource probability in these three focus areas. The project then incorporated the new groundwater results with the new geophysical results and the calculations of potential for fracture-induced permeability to produce updated maps of resource probability and confidence. These results were used to identify target sites for exploratory drilling. Spreadsheet information: Each sheet contains data for a particular depth in kilometers. Positive depths are above sea level, and negative below. For more information, go to the Hawaii Groundwater and Geothermal Resources Center website linked in the resources.

15 GEOTHERMAL ENERGY↗

Quantification and prediction of solidification textures under additive manufacturing conditions

Crystallographic textures are a major determinant of the macroscale anisotropic properties of polycrystalline metallic alloys produced in a wide range of additive manufacturing (AM) processes. Here, we introduce a statistical method that can accurately quantify the degree of orientational order of textures despite the large random fluctuations in the orientation of individual grains inherent in AM processes. The method, demonstrated for laser and resolidification of AlSi thin films, extends Z-scoring to a dynamical regime to assess the statistical significance of observed textures compared to randomly generated ones at different stages of solidification. We further show that, combined with phase-field modeling, this method can be used to infer fundamental anisotropic properties of the solid-liquid interface that are essential for texture prediction, and are compared here to the results of atomistic simulations. In addition, phase-field modeling reveals that, even at rapid AM solidification rates, the observed 〈110〉-dominated textures in the AlSi thin films are controlled predominantly by the anisotropy of the interface free-energy and sheds light on the physical mechanism of grain competition. These results significantly enhance both the existing tools for the quantification and prediction of AM crystallographic textures and our basic understanding of their formation.

36 MATERIALS SCIENCE↗

Markov Chain Monte Carlo Predictions of Neutron-rich Lanthanide Properties as a Probe of r -process Dynamics

Lanthanide element signatures are key to understanding many astrophysical observables, from merger kilonova light curves to stellar and solar abundances. To learn about the lanthanide element synthesis that enriched our solar system, we apply the statistical method of Markov Chain Monte Carlo to examine the nuclear masses capable of forming the r-process rare-earth abundance peak. We describe the physical constraints we implement with this statistical approach and demonstrate the use of the parallel chains method to explore the multidimensional parameter space. We apply our procedure to three moderately neutron-rich astrophysical outflows with distinct types of r-process dynamics. We show that the mass solutions found are dependent on outflow conditions and are related to the r-process path. We describe in detail the mechanism behind peak formation in each case. We then compare our mass predictions for neutron-rich neodymium and samarium isotopes to the latest experimental data from the CPT at CARIBU. Here, we find our mass predictions given outflows that undergo an extended (n,γ)⇌(γ,n) equilibrium to be those most compatible with both observational solar abundances and neutron-rich mass measurements.

79 ASTRONOMY AND ASTROPHYSICS↗

Bias Correction and Statistical Downscaling of Future Solar Irradiance Projections Using the NSRDB

Assessing renewable energy resources under future climate scenarios has been highlighted to understand potential impacts of future climate change in renewable generation on the power sector. Climate model projection has been recognized by the renewable energy community as a useful data set to analyze the impacts of future climate change on renewable resources. However, future climate projections generated from general circulation models (GCMs) contain inherent biases that need to be corrected for accurate analysis of future projections of climate variables. In addition, the coarse spatiotemporal resolution of GCMs needs to be improved for regional climate studies. In this work, we develop statistical methods to downscale future projections of global horizontal irradiance (GHI) in a computationally efficient way. Our approach builds statistical downscaling models that correct bias of climate projection of GHI and downscale the future GHI projection from daily-scale to hourly-scale. The National Solar Radiation Database (NSRDB) is used to calibrate the statistical models and validate the downscaled GHI projections across the contiguous United State (CONUS). Preliminary results show that the statistical approach efficiently downscales climate projections of GHI with a nBIAS of 3%, nMAE of 34 % and nRMSE of 46% calculated against NSRDB for CONUS. This study describes the implemented methodology and initial results as well as future research to create high-resolution climate data sets for solar energy applications.

analytical models↗

Predictive Battery Lifetime Modeling at NREL [Slides]

Battery lifetime models are used to extrapolate data from accelerated aging tests to simulate degradation in real-world applications such as electric vehicles and battery energy storage systems. Methods developed at NREL utilize both expert domain-knowledge and machine-learning to identify models, using statistical methods such as cross-validation and bootstrap resampling to interrogate model performance and quantify uncertainty. These models can be utilized in systems level simulations to predict battery performance or technoeconomic models to estimate the lifetime cost of battery systems.

25 ENERGY STORAGE↗

Detected Changes in Precipitation Extremes at Their Native Scales Derived from In Situ Measurements

Abstract The gridding of daily accumulated precipitation—especially extremes—from ground-based station observations is problematic due to the fractal nature of precipitation, and therefore estimates of long period return values and their changes based on such gridded daily datasets are generally underestimated. In this paper, we characterize high-resolution changes in observed extreme precipitation from 1950 to 2017 for the contiguous United States (CONUS) based on in situ measurements only. Our analysis utilizes spatial statistical methods that allow us to derive gridded estimates that do not smooth extreme daily measurements and are consistent with statistics from the original station data while increasing the resulting signal-to-noise ratio. Furthermore, we use a robust statistical technique to identify significant pointwise changes in the climatology of extreme precipitation while carefully controlling the rate of false positives. We present and discuss seasonal changes in the statistics of extreme precipitation: the largest and most spatially coherent pointwise changes are in fall (SON), with approximately 33% of CONUS exhibiting significant changes (in an absolute sense). Other seasons display very few meaningful pointwise changes (in either a relative or absolute sense), illustrating the difficulty in detecting pointwise changes in extreme precipitation based on in situ measurements. While our main result involves seasonal changes, we also present and discuss annual changes in the statistics of extreme precipitation. In this paper we only seek to detect changes over time and leave attribution of the underlying causes of these changes for future work.

54 ENVIRONMENTAL SCIENCES↗

Combining simulations and data with deep learning and uncertainty quantification for advanced energy modeling

A novel and modern framework for energy modeling is developed in this paper with a focus on nuclear energy modeling and simulation. The framework combines multiphysics simulations and real data, with validation by uncertainty quantification tasks and facilitation by machine and deep learning methods. The hybrid framework is built on the basis of a wide range of physical models, real data, mathematical and statistical methods, and artificial intelligence techniques. The framework is demonstrated in different applications, including quantifying uncertainties in computer simulations, multiphysics coupling, analysis of variance using machine learning surrogate models, deep learning of time series phenomena, and propagating parametric uncertainties of nuclear data. The applications demonstrated are oriented to nuclear engineering simulations, even though majority of the methods are applicable to other energy sources (eg, renewable). Efficient utilization of this framework is expected to yield a much better understanding of the physical phenomena analyzed as well as an improvement in the performance of the energy design/model under construction.

42 ENGINEERING↗

A comparison of methods for assessing power output in non-uniform onshore wind farms

Wind resource assessments are used to estimate a wind farm's power production during the planning process. It is important that these estimates are accurate, as they can impact financing agreements, transmission planning, and environmental targets. Here, we analyze the challenges in wind power estimation for onshore farms. Turbine wake effects are a strong determinant of farm power production. With given input wind conditions, wake losses typically cause downstream turbines to produce significantly less power than upstream turbines. These losses have been modeled extensively and are well understood under certain conditions. Most notably, validation of different model types has favored offshore farms. Models that capture the dynamics of offshore wind conditions do not necessarily perform equally as well for onshore wind farms. We analyze the capabilities of several different methods for estimating wind farm power production in 2 onshore farms with non-uniform layouts. We compare the Jensen model to a number of statistical models, to meteorological downscaling techniques, and to using no model at all. In conclusion, we show that the complexities of some onshore farms result in wind conditions that are not accurately modeled by the Jensen wake decay techniques and that statistical methods have some strong advantages in practice.

17 WIND ENERGY↗

UNDERSTANDING THE SEMI-PROBABILISTIC APPROACHES IN STRUCTURAL RELIABILITY USED TO SET DESIGN RELIABILITY TARGETS FOR GRAPHITE COMPONENTS USING ASME BPVC METHODS

Graphite is a quasi-brittle material, resulting in random variability in tensile strength distributions. To account for the random variability in strength, HHA-3000 of the ASME BPVC provides two semi-probabilistic methods for qualifying nuclear graphite components in the design stage, the simplified and full assessments. The full and simplified assessments apply statistical methods to engineering-based design problems. This is often referred to as reliability-based design. Reliability-based design (RBD) is a method to develop reliable designs by accounting for uncertainties and result in small chances of failure when also considering safety factors. RBDs provide reliability targets using semi-probabilistic approaches. RBD is implemented in ASME BPVC HHA-3000 for nuclear graphite components, but is not specific to that application. There has been much confusion around the methods implemented in ASME BPVC HHA-3000 for qualifying nuclear graphite components. To address the confusion, this paper takes a hierarchical approach. First, the general RBD framework is presented. Then, the semi-probabilistic methods and the underlying assumptions implemented in the assessments are presented. The semi-probabilistic methods are separated from the engineering modifications that have been made to the assessments. After building the framework and underlying assumptions, the specific methods in the full and simplified assessments are explained in three steps: inputs, methods, outputs. The methods are applied to an H-451 reflector block. Tensile strength properties for other graphite grades are provided.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Multivariate Analysis of the Influence of Process Parameters on Suspension Plasma-Sprayed Coatings

Suspension plasma spray (SPS) is far more complicated than conventional plasma spray and requires a deep knowledge about the influence of process parameters and their correlations. In this study, YSZ coatings were manufactured by SPS with six different process parameters such as plasma power, suspension mass load, original powder size, substrate surface topology, spray distance, and spray step. Afterwards, the porosity of as-prepared coatings was investigated by image method and X-ray transmission technique. A multivariate analysis on the collected experimental data was carried out by employing mathematical statistics methods. The results showed that: 1) Coating porosity has a negative correlation with plasma power and suspension mass load and a positive correlation with the original powder size, spray distance, spray step, and substrate roughness; 2) Spraying distance is the main factor affecting to coating porosity, followed by suspension mass load and substrate surface roughness, respectively. A linear model for porosity prediction was developed and was verified by experiments. The mechanism by which process parameters influence coating porosity is also discussed.

Zhao, Yongli↗

On the uncertainty of long-period return values of extreme daily precipitation

Methods for calculating return values of extreme precipitation and their uncertainty are compared using daily precipitation rates over the Western U.S. and Southwestern Canada from a large ensemble of climate model simulations. The roles of return-value estimation procedures and sample size in uncertainty are evaluated for various return periods. We compare two different generalized extreme value (GEV) parameter estimation techniques, namely L-moments and maximum likelihood (MLE), as well as empirical techniques. Even for very large datasets, confidence intervals calculated using GEV techniques are narrower than those calculated using empirical methods. Furthermore, the more efficient L-moments parameter estimation techniques result in narrower confidence intervals than MLE parameter estimation techniques at small sample sizes, but similar best estimates. It should be noted that we do not claim that either parameter fitting technique is better calibrated than the other to estimate long period return values. While a non-stationary MLE methodology is readily available to estimate GEV parameters, it is not for the L-moments method. Comparison of uncertainty quantification methods are found to yield significantly different estimates for small sample sizes but converge to similar results as sample size increases. Finally, practical recommendations about the length and size of climate model ensemble simulations and the choice of statistical methods to robustly estimate long period return values of extreme daily precipitation statistics and quantify their uncertainty.

54 ENVIRONMENTAL SCIENCES↗