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At least 811 records · Page 45

A review of privacy in energy applications

As the distribution system continues to experience an increase in distributed energy resource (DER) and electric vehicle (EV) penetration, so does the need for new solutions that can help grid operators manage and leverage their capabilities. This will undoubtedly lead to new operational schemes and business opportunities that will transform the traditional consumer into a prosumer who will be more actively engaged in grid operations. Although the field is still under active development, many of the potential use cases presented in literature or industry are built upon edge computing, two-way communications, and other innovative computational constructs to attain their goals. However, at their core, many use cases assume a great level of data access to aid with the decision-making process, an assumption that may need to be revised to ensure fair and equitable operational processes are maintained. This may be particularly true as edge resources are predicted to participate in retail-side, many-to-many, or peer-to-peer markets and thus may lead to financial impacts if data access considerations are ignored. The need to revise data access mechanisms can be further justified by the introduction of new participants into the operational process, who do not have the same level of trust, nor the incentives to focus on energy delivery as their primary objective. At the same time, more consumers are becoming aware of their own data, and the potential impacts of its abuse. To help solution developers better understand these risks, this report has been developed to offer an initial introduction to the topic of privacy. This is achieved by 1) Highlighting the need for privacy-aware solutions; 2) Encouraging system designers to be inquisitive about the status quo; 3) Documenting the existing threat space; 4) Presenting and evaluating tools that may be helpful towards enabling better privacy postures; and 5) Making recommendations to encourage the adoption of better practices. From a technical perspective, the report focuses on evaluating two potential techniques by applying them to the Transactive Energy Space. Based on the obtained results, it can be established that differential privacy (DP) methods may have limited applicability when highly correlated, time-series data records need to be protected. However, DP may be a powerful tool when it is used to aggregate and analyze mid-size and large-size data sets in a more traditional statistical environment. The second tool under evaluation is threshold cryptography, which can guarantee complete secrecy (and thus privacy) but requires the establishment of key management procedures and dedicated communication channels for key coordination. Therefore, due to its increased computational overhead, the use of threshold cryptography must be weighted using a cost/benefit analysis on a per-application basis.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Data-driven Stellar Models

We developed a data-driven model to map stellar parameters ( T eff , log g , and [Fe/H]) accurately and precisely to broadband stellar photometry. This model must, and does, simultaneously constrain the passband-specific dust reddening vector in the Milky Way, R. The model uses a neural network to learn the (de-reddened) absolute magnitude in one band and colors across many bands, given stellar parameters from spectroscopic surveys and parallax constraints from Gaia. To demonstrate the effectiveness of this approach, we train our model on a data set with spectroscopic parameters from LAMOST, APOGEE, and GALAH, Gaia parallaxes, and optical and near-infrared photometry from Gaia, Pan-STARRS 1, Two Micron All Sky Survey and Wide-field Infrared Survey Explorer. Testing the model on these data sets leads to an excellent fit and a precise—and by construction—accurate prediction of the color–magnitude diagrams in many bands. This flexible approach rigorously links spectroscopic and photometric surveys, and also results in an improved, T eff -dependent R. As such, it provides a simple and accurate method for predicting photometry in stellar evolutionary models. Our model will form a basis to infer stellar properties, distances, and dust extinction from photometric data, which should be of great use in 3D mapping of the Milky Way. Our trained model can be obtained at doi:10.5281/zenodo.3902382.

79 ASTRONOMY AND ASTROPHYSICS↗

BETO 2021 Peer Review: 2.1.0.100 - Biochemical Platform Analysis

The objective of this project is to perform techno-economic analysis (TEA) to guide Biochemical Platform efforts, utilizing models for purposes of setting future R&D targets and tracking performance progress against those targets. Outcomes of our work are leveraged by BETO to guide program plans, as well as by other NREL/partner projects to quantify the impact of research on key technology barriers and to prioritize future efforts. This project provides high impact and relevance through establishing “bottom-up” TEA models as a basis for understanding the technical feasibility to meet “top-down” BETO cost targets. By providing a framework to translate technical performance to cost reductions in a biorefinery, our TEA models may be leveraged to maximize the efficiency of research funding towards the most economically impactful priorities, ultimately in support of BETO’s 2030 fuel cost targets below $2.5/GGE. In order to mitigate a key risk/challenge to this project in overly-constraining our analyses to a singular technology focus or TEA metric, our approach continuously re-assesses opportunities for better optimization and alternative technology pathway options, while maintaining close interaction with other BETO analysis partners. We have made numerous recent accomplishments rooted around identifying and working with the researchers to solve key technical and TEA/LCA challenges, reflected through notable improvements in State-of-Technology (SOT) updates over prior benchmarks.

biochemical↗

Kinetics-Informed Neural Networks

Chemical kinetics and reaction engineering consists of the phenomenological framework for the disentanglement of reaction mechanisms, optimization of reaction performance and the rational design of chemical processes. Here, we utilize feed-forward artificial neural networks as basis functions to solve ordinary differential equations (ODEs) constrained by differential algebraic equations (DAEs) that describe microkinetic models (MKMs). We present an algebraic framework for the mathematical description and classification of reaction networks, types of elementary reaction, and chemical species. Under this framework, we demonstrate that the simultaneous training of neural nets and kinetic model parameters in a regularized multi-objective optimization setting leads to the solution of the inverse problem through the estimation of kinetic parameters from synthetic experimental data. We analyze a set of scenarios to establish the extent to which kinetic parameters can be retrieved from transient kinetic data, and assess the robustness of the methodology with respect to statistical noise. Furthermore, this approach to inverse kinetic ODEs can assist in the elucidation of reaction mechanisms based on transient data.

36 MATERIALS SCIENCE↗

Holographic wavefront sensors

A brief historical review of the first designs of holographic wavefront sensors (WFS’s) and the concepts lying in their basis is presented. The main directions in the development of these sensors are highlighted and considered. One of these directions implies a two-stage transition from the use of several separate measuring channels with holograms filtering only one Zernike mode: first to the use of one channel with a multiplexed hologram filtering several first Zernike modes, and then to filtering the entire set of Zernike modes with the aid of one combined multiplexed hologram. Another line of research in this field (related to the first one) is the optimisation of the filter hologram structure in order to reduce cross-modulation interferences, increase multiplexing level, etc. One more line of research implements principles of dynamic holography by introducing spatial light modulators into the WFS composition. Hence, the advantages of time multiplexing of holograms can be used. The approach developed by G. Andersen’s team, aimed at adapting the holographic WFS design for operation as an element of adaptive optical system with a zonal corrector, as well as an approach implying development of hybrid holographic sensors, are considered separately. The results of the authors’ studies of holographic WFS’s with application of the methods of Fourier holography (i.e., holography of focused beams, in particular, using diffuse scatterers in a hologram recording channel) are also reported. (paper)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Coupled Neutronic and Thermal Hydraulic Analysis of a Natural Circulation Based Small Modular Reactor (SMR) Using VERA-CS

As part of the work supported by a US Department of Energy (DOE) Office of Nuclear Energy Gateway for Accelerated Innovation in Nuclear FY 2020 Voucher, Holtec International subsidiary SMR LLC (hereinafter referred to as Holtec) and Oak Ridge National Laboratory entered into a cooperative research and development agreement (CRADA) to develop coupled multiphysics core models of the Holtec developed small modular reactor (SMR), SMR-160. The scope of the 1 year project was to use the DOE–developed tool set, VERA, to analyze several aspects of a representative SMR-160 core design. The goals of the project were to perform the code-to-code benchmarking and to provide Holtec with a confirmatory calculations to compare against the results with the codes used in the SMR-160 design, identify and resolve areas of discrepancy between the two models to give Holtec a basis for selecting certain tool and model options, and develop a workflow so that the VERA model could be adapted easily to any future changes in the design of the SMR-160 core. The work proceeded in four phases: 1. Developing the initial VERA model based on Holtec-provided core design information; 2. Comparing VERA results with Holtec-provided calculations for the first five cycles; 3. Developing a VERA transient model based on the prior model; and 4. Training Holtec personnel on VERA and hand-off the developed models. This report summarizes at a high level the completed tasks. Details of the tasks and results are reserved for the full report, which will not be publicly released for 5 years per the terms of the CRADA. The report is titled “Coupled Neutronic and Thermal Hydraulic Analysis of a Natural Circulation Based Small Modular Reactor (SMR) using VERA-CS” and has the ORNL technical report number ORNL/TM 2021/2303 (NFE-20-08305)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Non-DNA radiosensitive targets that initiate persistent behavioral deficits in rats exposed to space radiation

Predicting future CNS risks for astronauts during deep-space missions will rely substantially on ground-based rodent data with space-relevant ions and behaviors. For rats, the accumulated evidence indicates that less densely ionizing radiation, such as 4 He and 12 C ions, induce behavior deficits at lower doses than densely ionizing ions, such as 48 Ti and 56 Fe. However, this observation conflicts with standard somatic radiobiology, in which densely ionizing ions are generally more effective than less densely ionizing ions, and where the DNA/nucleus is the accepted target for radiation-induced tumorigenesis, cytogenetic aberrations, genetic mutations, and reproductive cell death. To gain deeper insight into the subcellular nature of the radiation targets for behavior risks, we compared the effects of dose, fluence, and linear energy transfer (LET) of 4 He and 56 Fe particles using existing datasets for four distinct behavioral outcomes in rats: elevated plus maze (EPM-anxiety), novel object recognition (NOR-memory), operant responding (OR-response to environmental stimuli), and attentional set-shifting (ATSET-cognitive flexibility). We confirmed that less densely ionizing particles (except protons) showed ~100-fold lower threshold doses than densely ionizing particles for behavioral deficits (0.1–1 cGy for 4 He vs. 15–100 cGy for 56 Fe). However, when analyzed by fluence the behavioral responses converged, indicating that 4 He and 56 Fe were equally effective on a per-track basis. When analyzed by LET, there were ~100-fold differences in the LET for maximum effectiveness for behavioral deficits and DNA endpoints (~1 vs ~100 keV/μm, respectively). These unique features of radiation-induced behavioral deficits (high sensitivity to particles in the 1-keV/μm range, insensitivity to protons in the 0.2 keV/μm range, and isofluence dependence for particles with LET>1 keV/μm) provide evidence in support of a new hypothesis of sub-micron sized radiosensitive targets for behavioral effects consistent with the thickness of plasma membranes and/or small subcellular structures, smaller than a whole synapse. Like our behavior findings, mouse immature oocyte killing which is known to have a plasma membrane target was also better explained by fluence, rather than dose. In contrast, fluence analyses for DNA/nuclear endpoints in somatic cells (e.g., tumor induction, chromosome aberrations) showed opposite results, suggesting that behavior targets are not DNA. Our findings raise questions regarding the identity of subcellular targets and the multi-cellular functional unit for behavior risks, low-dose susceptibility, and generalizability from rat to other species and astronauts.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗

Spatial imaging of proton via leading-twist nonskewed GPDs with basis light-front quantization

The internal image of the proton is unveiled by examining the generalized parton distributions (GPDs) at zero skewness, within the basis light-front quantized environment. Several distributions emerge when a quark is sampled with different currents depending upon the helicity arrangements of the active quark and the proton target. We investigate six of the eight leading-twist proton GPDs of the valence quarks, the helicity conserving distributions ( H , E , H ˜ ) and the helicity nonconserving ( H T , E T , H ˜ T ) distributions at skewness set to zero ( ζ = 0 ). We consider purely transverse momentum transfer and, hence, obtain results describe only the proton’s two-dimensional structure in the transverse plane. We present the Mellin moments of these distribution functions, where the first moment produces a form factor and the second Mellin moments help extract the information on partonic contributions to the hadronic angular momentum. We compare our results for the Mellin moments with those from lattice QCD and other approaches where available. We also present the GPDs in transverse position space. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

Numerical Evidence for Many-Body Localization in Two and Three Dimensions

Disorder and interactions can lead to the breakdown of statistical mechanics in certain quantum systems, a phenomenon known as many-body localization (MBL). Much of the phenomenology of MBL emerges from the existence of localized-bits, or l-bits, a set of conserved quantities that are spatially localized and binary (i.e., possess only ±1 eigenvalues). While MBL and l-bits are known to exist in one-dimensional systems, their existence in dimensions greater than one is a key open question. To tackle this question, we develop an algorithm that can find approximate binary l-bits in arbitrary dimensions by adaptively generating a basis of operators in which to represent the l-bit. We use the algorithm to study four models: the one-, two-, and three-dimensional disordered Heisenberg models and the two-dimensional disordered hard-core Bose-Hubbard model. For all four of the models studied, our algorithm finds high-quality l-bits at large disorder strength and rapid qualitative changes in the distributions of l-bits in particular ranges of disorder strengths, suggesting the existence of MBL transitions. Furthermore, these transitions in the one-dimensional Heisenberg model and two-dimensional Bose-Hubbard model coincide well with past estimates of the critical disorder strengths in these models which further validates the evidence of MBL-like behavior in the other two and three-dimensional models we examine. In addition to finding MBL-like behavior in higher dimensions, our algorithm can be used to probe MBL in various geometries and dimensionality.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Module-Level Thermal Interface Material Degradation in HALT

Abstract In this study, thermal interface material (TIM) degradation is driven through highly accelerated life test (HALT) using temperature cycling with a prescribed vibrational acceleration for two commercially available materials having thermal conductivities of 6.0 and 8.5 W/m K. HALT specimens were prepared by applying TIM through a 4-mil stencil over AlSiC baseplates in the shape of those used in Wolfspeed CAS325M12HM2 power electronics modules. Baseplates were mounted onto aluminum carrier blocks with embedded thermocouples to characterize the thermal resistance across the baseplate and TIM layer. Thermal dissipation into the top of the baseplates was provided by a custom heating block, which mimics the size and placement of the die junctions in CAS325 modules, applying power loads of 200, 300, and 400 W. After initial characterization, samples were transferred to the HALT chamber with one set of samples exposed to temperature cycling only (TCO) and the other temperature cycling and vibration (TCV). Both sample sets were cycled between temperature extremes of −40 °C and 180 °C with vibrations applied at a peak acceleration of 3.21 Grms. After hundreds of cycles, samples were reevaluated to assess changes in thermal resistance to provide an accelerated measure of TIM degradation. This allows for reliability prediction of useful lifetime (illustrated in a solar inverter case study herein), as well as to provide a basis for developing an accelerated testing method to related temperature cycling to faster methods of degradation. Such techniques provide a means to develop maintenance schedules for power modules for ensuring sufficient thermal performance over the operating lifetime.

Engineering↗

Multiclass Classification Using Bayesian Multivariate Adaptive Regression Splines

We present a new Bayesian model for the problem of multiclass classification. In this model, the probabilities of class membership of a given observation are determined by the mean of a latent Gaussian distribution. The mean functions of this latent distribution consist of combinations of highly flexible basis functions of the inputs: multivariate adaptive regression splines (MARS), first developed for multiple regression. We use reversible jump Markov chain Monte Carlo to make inference on the classification model, including the number of basis functions. We compare the probabilistic classification performance of our proposed approach to existing methods on simulated and benchmark data, and compare uncertainty estimates on simulated data. Our proposed method compares favorably with existing Bayesian and frequentist multiclass classification methods in out-of-sample probabilistic classification, and uncertainty estimation of these probabilistic classifications. We examine the fit of the proposed method to a data set of hurricane storm surge levels near Delaware Bay, US, and conclude that sea level rise is a key contributor to damage delivered by storm surge.

97 MATHEMATICS AND COMPUTING↗

pdas-experiments

SAND2025-04589O pdas-experiments automates computational experiments of fluid flow simulations. It uses the pressio-demoapps-schwarz package as a basis to break down complex simulations into smaller, manageable parts. This application is an extension of the Sandia Pressio software which uses domain decomposition to work with complex simulations more efficiently. Users can test different simulation setups, while keeping a detailed record of their experiments so they can be reproduced later. The software includes a C++ program that runs individual experiments based on user-defined settings in a YAML file, as well as a Python script that can manage multiple simulations at once. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Tezaur, Irina [Sandia National Lab. (SNL-CA), Live↗

Implement and Test 3D Mortar Contact in BISON

We leverage the extension of the generation of mortar segment meshes to three dimensions in MOOSE’s framework to extend thermomechanical modeling capabilities to problems with three dimensions. A modular approach to gap heat transfer physics using the mortar finite element method was created and documented, mechanical contact was extended to three dimensions—including frictional behavior, performance and ease of use were improved, and steps towards scalability of solid mechanics problems involving contact were taken. Many of these new developments are demonstrated in the simulation of 3D light-water reactor (LWR) problems, where the thermomechanical interface problem is solved using the mortar finite element method. Usage of the mortar framework has improved convergence in 2D problems and has enabled employing friction in 3D problems, of which we show results of a short, local stack of 3D pellets. Consequently, the benefits of mortar in terms of solution convergence and quality are extended to three dimensions. Section 2 discusses fundamental developments that enabled the simulation of practical mortar problems in three dimensions and other general improvements, including the reduction of the derivative container size, the modification of dual basis computations when edge dropping (lack of secondary element projection) takes place, the improvement of conditioning when employing the VCP in-edge dropping conditions, and code usability and quality improvements. These latter code enhancements include the migration of tests using “old” mortar contact constraints to using dual mortar with a semi-smooth Newton solution strategy and the reuse of lower dimensional domains for straightforwardly setting up a mortar thermomechanical LWR problem, i.e. the MOOSE action is employed for mechanical contact and the thermal LWR action is employed to capture the gas conductance, contact, and radiation components of gap heat transfer physics. Independently of the mortar LWR thermal action, we developed a modular approach to gap heat transfer that resides in MOOSE and can be leveraged, e.g., in metallic fuel problems. This approach, whose code design based on MOOSE’s user objects to model specific physics was proposed by the maintenance activity, is detailed in Section 3. Based on the dual mortar finite element method, the frictional contact constraints were extended to three dimensions. A block sheared in two directions in and out of contact with a rigid plane is employed in Section 4 to show the way the approach handles changes in frictional states (e.g. stick to slip) within a competitive number of Newton iterations. Equations and numerical results on the use of the VCP with Cartesian Lagrange multipliers, whose combination enables their direct condensation, are described in Section 5.3. Two-dimensional and three-dimensional BISON LWR simulations are discussed in Section 6. Particularly, a stack of five eccentric pellets with a surface defect is simulated and the effect of pellet-cladding friction is assessed. Finally, conclusions are outlined in Section 7.

42 ENGINEERING↗

Is SMEFT enough?

There are two canonical approaches to treating the Standard Model as an Effective Field Theory (EFT): Standard Model EFT (SMEFT), expressed in the electroweak symmetric phase utilizing the Higgs doublet, and Higgs EFT (HEFT), expressed in the broken phase utilizing the physical Higgs boson and an independent set of Goldstone bosons. HEFT encompasses SMEFT, so understanding whether SMEFT is sufficient motivates identifying UV theories that require HEFT as their low energy limit. This distinction is complicated by field redefinitions that obscure the naive differences between the two EFTs. By reformulating the question in a geometric language, we derive concrete criteria that can be used to distinguish SMEFT from HEFT independent of the chosen field basis. We highlight two cases where perturbative new physics must be matched onto HEFT: ( i ) the new particles derive all of their mass from electroweak symmetry breaking, and ( ii ) there are additional sources of electroweak symmetry breaking. Additionally, HEFT has a broader practical application: it can provide a more convergent parametrization when new physics lies near the weak scale. The ubiquity of models requiring HEFT suggests that SMEFT is not enough.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Recognition Method of Vehicle Cluster Situation Based on Set Pair Logic considering Driver’s Cognition

The recognition of vehicle cluster situations is one of the critical technologies of advanced driving, such as intelligent driving and automated driving. The accurate recognition of vehicle cluster situations is helpful for behavior decision‐making safe and efficient. In order to accurately and objectively identify the vehicle cluster situation, a vehicle cluster situation model is proposed based on the interval number of set pair logic. The proposed model can express the traffic environment’s knowledge considering each vehicle’s characteristics, grouping relationships, and traffic flow characteristics in the target vehicle’s interest region. A recognition method of vehicle cluster situation is designed to infer the traffic environment and driving conditions based on the connection number of set pair logic. In the proposed model, the uncertainty of the driver’s cognition is fully considered. In the recognition method, the relative uncertainty and relative certainty of driver’s cognition, traffic information, and vehicle cluster situation are fully considered. The verification results show that the proposed recognition method of vehicle cluster situations can realize accurate and objective recognition. The proposed anthropomorphic recognition method could provide a basis for vehicle autonomous behavior decision‐making.

Liu, Shijie↗

Project: Corbomite - Product: ConsoleWorks REACT

TDi Technologies presents ConsoleWorks REACT, an advanced platform designed to tackle the complexities of cyber and operational risk assessment. This comprehensive solution goes beyond asset-focused approaches by considering the impact of both assets and people have on the security and operation of critical infrastructure, specifically targeting preventing gird mis-operation by evaluating real-time human interaction or commands with critical assets. The hypothesis suggests that by integrating the assessment of user commands into the overall risk assessment process, organizations can make more informed decisions, prioritize resources effectively, and respond promptly to potential threats. This hypothesis forms the basis for the development of a proactive and holistic risk management approach that is more comprehensive and context aware than traditional models which only look at assets, patch levels, configuration and threat intel by collecting that information off the network vs directly from the asset, human, and human interaction all in real-time. ConsoleWorks' unique man-in-the-middle architecture is a key feature that sets it apart in the cybersecurity landscape. This architecture enables the real-time observation, enforcement, and commands or interaction risk transparency of user interaction with critical infrastructure to be risk mitigated and audited as they are aggregated with device and human risk factors for a more comprehensive risk threat score across a device or group of devices. This architecture allows ConsoleWorks to act as a secure intermediary between users and critical assets, monitoring all interactions and ensuring that only authorized commands are sent to the asset to be executed. This not only enhances security but also provides a comprehensive audit trail of all user activities, contributing to compliance efforts and facilitating incident investigation and risk management. By integrating this unique architecture with our comprehensive risk assessment methodology, ConsoleWorks REACT provides a powerful solution for managing cyber and operational risks, enabling organizations to maintain a robust security posture and effectively mitigate potential threats. To that end, the primary objective of this project was to research and develop a robust solution that enables the energy industry to mitigate the risks associated with human actions that can compromise the security or operations of assets critical to energy delivery, generation, transmission and operation. ConsoleWorks REACT plays a pivotal role in achieving this goal by leveraging its unique capabilities to monitor and track all user activity. Through its Zero Trust approach, which emphasizes continuous verification, the platform ensures secure access to assets and serves as the centralized human response and notification platform for addressing cyber and operational issues.

97 MATHEMATICS AND COMPUTING↗

The Adjoint Petrov–Galerkin method for non-linear model reduction

Here, we formulate a new projection-based reduced-order modeling technique for non-linear dynamical systems. The proposed technique, which we refer to as the Adjoint Petrov–Galerkin (APG) method, is derived by decomposing the generalized coordinates of a dynamical system into a resolved coarse-scale set and an unresolved fine-scale set. A Markovian finite memory assumption within the Mori–Zwanzig formalism is then used to develop a reduced-order representation of the coarse scales. This procedure leads to a closed reduced-order model that displays commonalities with the adjoint stabilization method used in finite elements. The formulation is shown to be equivalent to a Petrov–Galerkin method with a non-linear, time-varying test basis, thus sharing some similarities with the Least-Squares Petrov–Galerkin method. Theoretical analysis examining a priori error bounds and computational cost is presented. Numerical experiments on the compressible Navier–Stokes equations demonstrate that the proposed method can lead to improvements in numerical accuracy, robustness, and computational efficiency over the Galerkin method on problems of practical interest. Improvements in numerical accuracy and computational efficiency over the Least-Squares Petrov–Galerkin method are observed in most cases.

42 ENGINEERING↗

Practical Guide to Chemometric Analysis of Optical Spectroscopic Data

The methodology and mathematical treatment of several classic multivariate methods for the analysis of spectroscopic data is demonstrated in a straightforward way that can be used as a basis for teaching an undergraduate introductory course on chemometric analysis. The multivariate techniques of classical least squares (CLS), principal component regression (PCR), and partial least squares (PLS), as well as the univariate Beer’s law method have been described and compared, building students’ understanding by starting with the univariate method and progressing step by step into the multivariate methods. Equations for the production of regression vectors from training set spectral data is described and their use demonstrated for the prediction of constituent concentrations on a separate validation set of spectra. Extreme care is taken to ensure consistency in variable formatting of data matrices. This provides a key foundation to understanding how spectral data are manipulated using these different mathematical approaches for building quantitative regression models. Each method is applied to a real-world data set, and the results are discussed to show students the types of information that can be gleaned from each method. A training set comprised of 20 infrared absorbance spectra containing 3 constituents (benzene, polystyrene, and gasoline) of known composition are used to demonstrate the matrix operations for each regression method. A separate set of 12 real-world napalm samples (containing benzene, polystyrene and gasoline) are used as a validation set to demonstrate the ability to utilize the regression models on an unknown dataset. A toolbox (PNNL Chemometric Toolbox) written in MATLAB language is supplied in the Supplemental Information file and can be used as a companion for understanding the development and deployment of the chemometric algorithms described in this paper. The datasets of the infrared spectra are also supplied, allowing users to build and inspect the chemometric models on their own. Finally, the Toolbox includes scripts to assist users in loading their own datasets into MATLAB and performing CLS, PCR, and PLS on their data.

Upper-Division Undergraduate, Analytical Chemistry↗