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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

nautilus : boosting Bayesian importance nested sampling with deep learning

ABSTRACT We introduce a novel approach to boost the efficiency of the importance nested sampling (INS) technique for Bayesian posterior and evidence estimation using deep learning. Unlike rejection-based sampling methods such as vanilla nested sampling (NS) or Markov chain Monte Carlo (MCMC) algorithms, importance sampling techniques can use all likelihood evaluations for posterior and evidence estimation. However, for efficient importance sampling, one needs proposal distributions that closely mimic the posterior distributions. We show how to combine INS with deep learning via neural network regression to accomplish this task. We also introduce nautilus, a reference open-source python implementation of this technique for Bayesian posterior and evidence estimation. We compare nautilus against popular NS and MCMC packages, including emcee, dynesty, ultranest, and pocomc, on a variety of challenging synthetic problems and real-world applications in exoplanet detection, galaxy SED fitting and cosmology. In all applications, the sampling efficiency of nautilus is substantially higher than that of all other samplers, often by more than an order of magnitude. Simultaneously, nautilus delivers highly accurate results and needs fewer likelihood evaluations than all other samplers tested. We also show that nautilus has good scaling with the dimensionality of the likelihood and is easily parallelizable to many CPUs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Search for the NΔ resonance in the 𝛾𝑑 → 𝑑𝜋 +𝜋 − reaction

A dibaryon which is an object with baryon number B = 2 has been studied for a long time. Dyson and Xuong classified non-strangeness dibaryon states based on SU(6) symmetries in 1960?s. In the framework, the deuteron is classified as one of the sextet states of dibaryons. Although dibaryon have been an interesting subject of research for a long time, most of the experimental studies up to the early 2000?s were unsuccessful. The CELCIUS/WASA collaboration reported this state via the double-pionic fusion reaction (?= ! 3c0c0) in 2009. Thereafter, the WASA-at-COSY collaboration revealed properties of the isoscaler resonance state via the ?= ! 3c0c0 reaction in 2011. The dibaryon resonance state with isospin ? = 0 and spin ( = 3 thought to be a ?03 which was predicted by Dyson and Xuong at 2.35 GeV?22 with a configuration of ??. The reported mass and width of that state were 2?37 GeV?22 and 0?07 GeV?22, espectively. The mass was ?0?08 GeV?22 smaller than that of 2?, the width was narrower than that of single ?. This surprising result made dibaryon study come back into the limelight. ?12 is one of the dibaryon states classified by Dyson and Xuong with isospin ? = 1, spin ( = 2. This state can be regarded as an s-wave #? resonance. ?12 is an interesting state from the point of view of the possibilities of existence as an internal structure of ?03 and contribution to many-body effects in nuclei. Though there were some experimental clues and theoretical studies of this state, it was unclear whether the obtained experimental results represented a real resonance or not due to the difficulty of separation from kinematical effects. Very recently, the FOREST group at Tohoku University reported a photoproduced isovector dibaryon state at mass of 2.14 GeV?22 in the 3c0 invariant mass spectra of the W3 ! 3c0c0 reaction. The most probable ?% configuration was 2¸ although they didn?t exclude the possibility of ?% = 1¸ or 3?. They separated the dibaryon production process from conventional pion production process for the first time using angular distribution of deuteron. We investigated the W3 ! 3c¸c? reaction for study of a possible #? dibaryon state using a deuterium target at the Research Center for Electron Photon Science, Tohoku University, Japan. In the experiment, ?3 ? 1012 tagged photon beam at energies ranging from 0.8 to 1.1 GeV was impinged to the liquid deuterium target (?520 mg?cm2) and the charged particles in the final state: deuteron, c¸, and c?, were detected by a magnetic spectrometer with a large solid angle named NKS2. NKS2 had capabilities of reconstructing momentum of charged particles, multi-track analysis, and ??c separation. We performed two different analyses named 2-track analysis and 3-track analysis. The 2-track (3-track) analysis was for events in which two (three) particles of 3c¸c? in the final state, including deuteron, were detected by NKS2. In the 3-track and 2-track analysis, ?2000? ?15000 events were identified as the W3 ! 3c¸c? reaction events, respectively. The 2-track analysis with higher statistics was mainly used to derive the cross sections, and the 3-track analysis was used to check the consistency of the 2-track analysis. In this thesis, we have shown the total cross section, the differential cross sections of the W3 ! 3c¸c? reaction in the region of jC j ¡ 0?15 GeV2. This is the world?s first measurement of this reaction in this energy region. Dibaryon resonance structures were observed below the #? threshold in the differential cross section of the invariant mass of 3c?. The mass and width of the structure were consistent with these of ?12 measured by the W3 ! 3c0c0 reaction. The mechanism of the production process was discussed based on the angular distribution of emitted deuteron.

Toyama, Yuichi↗
DOE OSTI2021

Comparative Assessment of Data-driven Process Models in Health Information Technology

Process mining for conformance analysis consists of comparing a reference process model against a data-driven process model generated via log files from information technology systems. However, in the absence of a complete reference process model, we found no suggested approaches in the literature to address the need for evaluating process conformance among different healthcare facilities to assess standardization of care. Our goal is to find similarities and dissimilarities in data-driven process models among US Veterans Health Administration (VHA) facilities that can be indicative of patient safety issues. Our hypothesis was that the analysis would not produce statistically significant differences in outcome. We present a unique implementation of conformance analysis in process mining that consists of combining process mining, process mapping and statistical metrics. We illustrate our approach by applying it to the analysis of two clinical radiology order process models generated from healthcare data provided by two similar facilities in the VHA. The comparative assessment showed that about 70% of the orders completed successfully and 30% were not completed due to policy and duplications. Our analysis found a good statistical correlation between both facilities, as the Spearman’s correlation coefficient between facilities for the frequency of cases per total hours was 0.87879, for the frequency of cases by state transition was 0.79702 and for the throughput time per state transition was 0.63582. Additional statistical analyses using the Mann-Whitney U test and the root mean square error both produced values that were not significant. The foregoing approach validated our hypothesis by demonstrating a good statistical correlation of data describing the flow of clinical radiology orders absent a credible reference model. Finding good agreement between both facilities was important in confirming that the clinical orders flow in a similar manner, suggesting standardization of care.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Advanced data analysis in inertial confinement fusion and high energy density physics

Bayesian analysis enables flexible and rigorous definition of statistical model assumptions with well-characterized propagation of uncertainties and resulting inferences for single-shot, repeated, or even cross-platform data. This approach has a strong history of application to a variety of problems in physical sciences ranging from inference of particle mass from multi-source high-energy particle data to analysis of black-hole characteristics from gravitational wave observations. The recent adoption of Bayesian statistics for analysis and design of high-energy density physics (HEDP) and inertial confinement fusion (ICF) experiments has provided invaluable gains in expert understanding and experiment performance. In this Review, we discuss the basic theory and practical application of the Bayesian statistics framework. We highlight a variety of studies from the HEDP and ICF literature, demonstrating the power of this technique. Due to the computational complexity of multi-physics models needed to analyze HEDP and ICF experiments, Bayesian inference is often not computationally tractable. Two sections are devoted to a review of statistical approximations, efficient inference algorithms, and data-driven methods, such as deep-learning and dimensionality reduction, which play a significant role in enabling use of the Bayesian framework. We provide additional discussion of various applications of Bayesian and machine learning methods that appear to be sparse in the HEDP and ICF literature constituting possible next steps for the community. We conclude by highlighting community needs, the resolution of which will improve trust in data-driven methods that have proven critical for accelerating the design and discovery cycle in many application areas.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

STAT7 v1.2 User Guide: The STAT7 Code for Statistical Propagation of Uncertainties in Steady-State Thermal Hydraulics Analysis of Plate-Fueled Reactors

The STAT7 software was developed to perform steady-state, single-phase thermal hydraulics analysis of plate-fueled reactors based on statistical propagation of uncertainties. Application of the software is for non-power research and test reactors, including conversion to low-enriched uranium fuel of U.S. High-Performance Research Reactors such as Massachusetts Institute of Technology Research Reactor. Since it can be necessary to repeat analysis during fuel reloading, STAT7 accommodates flexibility in analyzing many realistic aspects of reactor fuel management. STAT7 uses a Monte Carlo approach to model uncertainty in common fuel fabrication parameters and other key reactor operating parameters required for thermal hydraulics analyses of research and test reactors. These safety calculations are ultimately intended to protect against high fuel plate temperatures due to critical heat flux, or onset of flow instability. STAT7 supports water properties based on the IAPWS-IF97 functions (The International Association for the Properties of Water and Steam Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam) in addition to the fit functions. STAT7 predicts axial profiles of fuel, cladding, and coolant temperature along a lateral stripe that runs the full length of the fuel plate from the bottom to the top. STAT7 can simultaneously analyze all of the axial nodes of all of the fuel plates and all of the coolant channels for one latera stripe of a fuel element. Power splits are calculated for each axial node of each plate to determine how much of the power goes out each face of the plate. By running STAT7 multiple times, full core analysis can be performed by analyzing the margin to onset of nucleate boiling and onset of flow instability for each axial node of each stripe of each plate of each fuel element in the core.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

A Bayesian approach to strong lens finding in the era of wide-area surveys

ABSTRACT The arrival of the Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST), Euclid-Wide and Roman wide-area sensitive surveys will herald a new era in strong lens science in which the number of strong lenses known is expected to rise from $\mathcal {O}(10^3)$ to $\mathcal {O}(10^5)$. However, current lens-finding methods still require time-consuming follow-up visual inspection by strong lens experts to remove false positives which is only set to increase with these surveys. In this work, we demonstrate a range of methods to produce calibrated probabilities to help determine the veracity of any given lens candidate. To do this we use the classifications from citizen science and multiple neural networks for galaxies selected from the Hyper Suprime-Cam survey. Our methodology is not restricted to particular classifier types and could be applied to any strong lens classifier which produces quantitative scores. Using these calibrated probabilities, we generate an ensemble classifier, combining citizen science, and neural network lens finders. We find such an ensemble can provide improved classification over the individual classifiers. We find a false-positive rate of 10−3 can be achieved with a completeness of 46 per cent, compared to 34 per cent for the best individual classifier. Given the large number of galaxy–galaxy strong lenses anticipated in LSST, such improvement would still produce significant numbers of false positives, in which case using calibrated probabilities will be essential for population analysis of large populations of lenses and to help prioritize candidates for follow-up.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Detection of the significant impact of source clustering on higher order statistics with DES Year 3 weak gravitational lensing data

We measure the impact of source galaxy clustering on higher order summary statistics of weak gravitational lensing data. By comparing simulated data with galaxies that either trace or do not trace the underlying density field, we show that this effect can exceed measurement uncertainties for common higher order statistics for certain analysis choices. We evaluate the impact on different weak lensing observables, finding that third moments and wavelet phase harmonics are more affected than peak count statistics. Using Dark Energy Survey (DES) Year 3 (Y3) data, we construct null tests for the source-clustering-free case, finding a p-value of p = 4 × 10 −3 (2.6σ) using third-order map moments and p = 3 × 10 −11 (6.5σ) using wavelet phase harmonics. The impact of source clustering on cosmological inference can be either included in the model or minimized through ad hoc procedures (e.g. scale cuts). We verify that the procedures adopted in existing DES Y3 cosmological analyses were sufficient to render this effect negligible. Failing to account for source clustering can significantly impact cosmological inference from higher order gravitational lensing statistics, e.g. higher order N-point functions, wavelet-moment observables, and deep learning or field-level summary statistics of weak lensing maps.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

PISCES two-detector covariance matrix fit for the NOvA Experiment

NOvA is a long-baseline neutrino oscillation experiment with two functionally identical detectors: a Near Detector (ND) at Fermilab, placed 1 km from the neutrino source, and a Far Detector (FD) located 810 km away from the ND in Minnesota. NOvA's primary physics goals are the precise measurements of neutrino oscillation parameters $\theta_{23}$ and $\Delta m^2_{32}$ , determine the neutrino mass ordering, and constrain the value of $\delta_{CP}$, via the study of muon neutrino to electron neutrino oscillation. In the standard NOvA three-flavor analysis, oscillation parameters are extracted using an extrapolation technique in which the ND data constrain the FD prediction through a ratio method. While this allows for systematic uncertainties sharing the same effects in both detectors to cancel, it remains an FD-only fit and does not fully leverage the constraining power of the high-statistics ND. This analysis proposes a simultaneous ND+FD fit using the PISCES method. PISCES (Parameter Inference with Systematic Covariance and Exact Statistics) is a framework designed to support complex configurations such as a joint ND+FD fit. This allows PISCES to take full advantage of the ND data to directly constrain systematic uncertainties across all samples. In PISCES, systematic uncertainties are encoded in a fractional covariance matrix, and statistical uncertainties are handled with a Poisson likelihood, making the approach well suited for low-statistics samples. For interpretability, we further use a Newton–Raphson + PCA method to recover per-systematic pulls from the covariance formulation. This poster presents the full PISCES joint ND+FD fit for the NOvA three-flavor analysis, describes its implementation and evaluates its performance through extensive robustness tests and fake data studies. It also provides a comparison between the PISCES joint ND+FD results and the standard NOvA extrapolation method.

Rajaoalisoa, Miriama [Cincinnati U.] (ORCID:000000↗
DOE OSTI2023

Quantifying the impact of operating temperature on cracking in battery electrodes, using super-resolution of microscopy images and stereology

There are numerous factors that can have an impact on the degradation behavior of batteries, such as the number of recharge cycles or the charge rate. Here, we investigate the influence of operating temperature on the structural degradation of the microstructure in lithium-ion positive electrodes. For that purpose, the microstructure is characterized for cathodes which have been cycled for 200 cycles under 6C (10-minute) charging at different operating temperatures, namely, 20°C, 30°C, 40°C, and 50°C. For each operating condition scanning electron microscopy (SEM) images of cross-sectioned Li x Ni 0.5 Mn 0.3 Co 0.2 O 2 (NMC532) electrodes have been analyzed, to determine structural descriptors such as global particle porosity, crack size/length/width distribution, and porosity and specific surface area distribution of individual particles. Additionally, a stereological method has been deployed to investigate the local particle porosity as a function of distance to the particle center. Results show that particle porosity increases with increasing cycling temperature. Particle porosity is greatest at the particle center and decreases along the particle radius to the exterior. Particle surface area is similar across the four cycling-temperature aging conditions.

25 ENERGY STORAGE↗
DOE OSTI2022

Analysis of Loss-of-Offsite-Power Events: 2021 Update

Loss-of-offsite power (LOOP) can have a negative impact on a nuclear power plant’s ability to achieve and maintain safe shutdown conditions. LOOP event frequencies and times required for subsequent restoration of offsite power are important inputs to plant probabilistic risk assessments. This report presents a statistical and engineering analysis of LOOP frequencies and durations at U.S. commercial nuclear power plants. The data used in this study were based on the operating experience during calendar years 1987–2021, while the most recent 15-year data (i.e., from 2007–2021) were used for most analyses in this report. LOOP events during critical operation that did not result in a reactor trip are not included. Frequencies and durations were determined for four LOOP event categories: plant-centered, switchyard-centered, grid-related, and weather-related. These categories (and the All-LOOPs group which contains all LOOPs without regarding of the four categories) could be further grouped by whether a LOOP event occurred during critical operation, during shutdown operation, or during all operations. The following decreasing trends in the LOOP occurrence rates were identified for the most recent 10-year period (2012–2021): All-LOOPs during critical operation, switchyard-centered LOOPs during critical operation, and grid-related LOOPs during critical operation. Adverse trends in LOOP durations continue for switchyard-centered LOOPs during all operations, All-LOOPs during all operations, and All-LOOPs during shutdown operation for the 1997–2021 period. Statistical tests show the LOOP counts for the period of 2007–2021 are not uniformly distributed across the 12 months, and variation among the months exists for grid-related LOOPs during all operations, All-LOOPs during all operations, and All-LOOPs during critical operation. The engineering analysis of LOOP data showed for the period of 2007–2021, the equipment failure events were dominated by failures of relay and other; human errors have been less frequent and occurred primarily in maintenance and switching; and weather were dominated by tornadoes then by lightning and hurricane. Weather was the cause for 45% of LOOPs for the last fifteen years (2007– 2021) but only for 20% of LOOPs for the previous 20 years (1987–2006) .

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Analysis of Loss-of-Offsite-Power Events: Update

Loss-of-offsite power (LOOP) can have a negative impact on a nuclear power plant’s ability to achieve and maintain safe shutdown conditions. LOOP event frequencies and times required for subsequent restoration of offsite power are important inputs to plant probabilistic risk assessments. This report presents a statistical and engineering analysis of LOOP frequencies and durations at U.S. commercial nuclear power plants. The data used in this study were based on the operating experience during calendar years 1987–2020, while the most recent 15-year data (i.e., from 2006–2020) were used for most analyses in this report. LOOP events during critical operation that did not result in a reactor trip are not included. Frequencies and durations were determined for four LOOP event categories: plant-centered, switchyard-centered, grid-related, and weather related. Highly significant decreasing trends in the LOOP occurrence rates were identified for All-LOOPs during critical operation (p-value = 0.001) and switchyard-centered LOOPs during critical operation (p-value = 0.002) for the most recent 10-year period (2011–2020). Adverse trends in LOOP durations continue for switchyard-centered LOOPs (p-value = 0.005), All-LOOPs (p-value = 0.019), as well as All-LOOPs during shutdown operation (p-value = 0.003). Statistical tests show the LOOP counts are not uniformly distributed across the 12 months, and variation among the months exists for plant-centered LOOPs (p-value = 0.028), grid-related LOOPs (p-value = 0.021), All-LOOPs (p-value = 0.003), and All-LOOPs during critical operation (p-value = 0.008). The engineering analysis of LOOP data showed for the period of 2006–2020, the equipment failure events were dominated by failures of circuits and relay; human errors have been less frequent and occurred primarily in maintenance; and weather events were dominated by tornadoes and lightning.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

First test of the consistency relation for the large-scale structure using the anisotropic three-point correlation function of BOSS DR12 galaxies

ABSTRACT We present, for the first time, an observational test of the consistency relation for the large-scale structure (LSS) of the Universe through a joint analysis of the anisotropic two- and three-point correlation functions (2PCF and 3PCF) of galaxies. We parameterize the breakdown of the LSS consistency relation in the squeezed limit by Es, which represents the ratio of the coefficients of the shift terms in the second-order density and velocity fluctuations. Es ≠ 1 is a sufficient condition under which the LSS consistency relation is violated. A novel aspect of this work is that we constrain Es by obtaining information about the non-linear velocity field from the quadrupole component of the 3PCF without taking the squeezed limit. Using the galaxy catalogues in the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12, we obtain $E_{\rm s} = -0.92_{-3.26}^{+3.13}$, indicating that there is no violation of the LSS consistency relation in our analysis within the statistical errors. Our parameterization is general enough that our constraint can be applied to a wide range of theories, such as multicomponent fluids, modified gravity theories, and their associated galaxy bias effects. Our analysis opens a new observational window to test the fundamental physics using the anisotropic higher-order correlation functions of galaxy clustering.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Dark Energy Survey Year 3 Results: Cosmological constraints from second- and third-order shear statistics

Here, we present a cosmological analysis of the third-order aperture mass statistic using Dark Energy Survey Year 3 (DES Y3) data. We perform a complete tomographic measurement of the three-point correlation function of the Y3 weak lensing shape catalog with the four fiducial source redshift bins. Building upon our companion methodology paper, we apply a pipeline that combines the two-point function ξ ± with the mass aperture skewness statistic ⟨ M ap 3 ⟩ , which is an efficient compression of the full shear three-point function. We use a suite of simulated shear maps to obtain a joint covariance matrix. By jointly analyzing ξ ± and ⟨ M ap 3 ⟩ measured from DES Y3 data with a Λ CDM model, we find S 8 = 0.780 ± 0.015 and Ω m = 0.26 6 - 0.040 + 0.039 , yielding 111% of figure-of-merit improvement in the Ω m - S 8 plane relative to ξ ± alone, consistent with expectations from simulated likelihood analyses. With a w CDM model, we find S 8 = 0.74 9 - 0.026 + 0.027 and w 0 = - 1.39 ± 0.31 , which gives an improvement of 22% on the joint S 8 - w 0 constraint. Our results are consistent with w 0 = - 1 . Our new constraints are compared to CMB data from the Planck satellite, and we find that with the inclusion of ⟨ M ap 3 ⟩ the existing tension between the datasets is at the level of 2.3 σ . We show that the third-order statistic enables us to self-calibrate the mean photometric redshift uncertainty parameter of the highest redshift bin with little degradation in the figure of merit. Our results demonstrate the constraining power of higher-order lensing statistics and establish ⟨ M ap 3 ⟩ as a practical observable for joint analyses in current and future surveys.

Gomes, R. C. H. [University of Pennsylvania] (ORCI↗
DOE OSTI2024

The relationship between stress, anxiety and eating behavior among Chinese students: a cross-sectional study

Background The expansion of higher education and the growing number of college students have led to increased awareness of mental health issues such as stress, anxiety, and eating disorders. In China, the educational system and cultural expectations contribute to the stress experienced by college students. This study aims to clarify the role of anxiety as a mediator in the relationship between stress and eating behaviors among Chinese college students. Methods This study utilized data from the 2021 Psychology and Behavior Investigation of Chinese Residents, which included 1,672 college students under the age of 25. The analysis methods comprised descriptive statistics, t -tests, Pearson correlation analyses, and mediation effect analysis. Results The findings indicate that Chinese college students experience high levels of stress, with long-term stress slightly exceeding short-term stress. Both types of stress were positively correlated with increased anxiety and the adoption of unhealthy eating behaviors. Anxiety was identified as a significant mediator, accounting for 28.3% of the relationship between long-term stress and eating behavior (95% CI = 0.058–0.183). The mediation effect of short-term stress on eating behavior through anxiety was also significant, explaining 61.4% of the total effect (95% CI = 0.185–0.327). Conclusion The study underscores the importance of stress management and mental health services for college students. It recommends a comprehensive approach to reducing external pressures, managing anxiety, and promoting healthy eating behaviors among college students. Suggestions include expanding employment opportunities, providing career guidance, enhancing campus and societal support for holistic development, strengthening mental health services, leveraging artificial intelligence technologies, educating on healthy lifestyles, and implementing targeted health promotion programs.

Chai, Yulin↗
DOE OSTI2020

Energy Intensity Baselining and Tracking Guidance

Each company joining the U.S. Department of Energy’s (DOE’s) Better Buildings, Better Plants Program (Better Plants) commits to establishing an energy consumption and energy intensity (EI) baseline and to tracking its energy performance over a 10-year period against that baseline. The baseline must reflect a company’s energy consumption over a 12-month period, covering all its U.S.-based operations. Energy consumption is calculated by fuel type in terms of primary energy (also known as source energy). EI is broadly defined as the amount of energy consumed per unit of output produced. For this guidance document and for the program, the term energy performance represents an evaluation of a facility’s capacity to use energy efficiently. Metrics used to assess a facility’s energy performance can include EI, energy consumption, improvements in EI, etc. Establishing an energy baseline and tracking system is a critical first step in effectively managing energy use. Developing a baseline can help a company understand energy use within the corporation and give it a point of comparison to evaluate future efforts to improve energy performance. It can also support efforts to validate a company’s energy management activities, improve comparative analyses when using benchmarks, and help in predicting future energy needs. In addition, a company that normalizes its performance data can determine highly defensible measures of energy savings generated through implemented energy efficiency projects. Establishing a baseline and tracking energy performance is also a requirement for ISO 50001 certification. Although basic energy data can be collected through utility bills, most manufacturers will have to perform additional analyses to develop accurate and robust energy baselines and tracking systems. Energy is consumed in many ways within the manufacturing sector and can come from multiple sources. Energy is sometimes generated and sold to other parties or captured and reused on-site. External events can exert a significant impact on a facility or company’s energy use independent of any purposeful efforts to improve energy efficiency. Operational changes, such as production shifts—which may be inevitable for some companies over the 10-year period covered by the program—can also make a big difference in energy use. Since Better Plants asks companies to account for all their U.S.-based operations, mergers, acquisitions, and divestitures can also have significant implications for a company’s energy metrics. This document aims to demystify the sometimes complex baselining process. It devotes special attention to the task of normalizing and adjusting energy consumption to account for external factors, such as weather and production changes. A key recommendation is that companies use regression analysis to normalize their energy consumption data whenever possible. Regression analysis is a statistical technique that estimates the dependence of a variable (i.e., energy use in the context of Better Plants) on one or more independent variables such as ambient temperature, while controlling for the influence of other variables at the same time. A properly developed regression analysis can provide a reliable estimate of energy savings resulting from energy improvement strategies and projects by accounting for the effects of variables such as annual production levels and weather. DOE has developed a companion Energy Performance Indicator software tool (EnPI) to simplify the baselining process. This tool can run regression models, calculate changes in EI at the facility level, and automatically compile facility-level data into a corporate-wide metric. Note that although the relevant equations used to calculate EI are provided in this document, the EnPI tool will automatically perform most calculations for the user. Additionally, Better Plants Partners (Partners) can call on their Technical Account Manager (TAM) to help them establish a baseline and assist with the necessary calculations to track progress.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗