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NASA NTRS2013

Analysis of Multivariate Experimental Data Using A Simplified Regression Model Search Algorithm

A new regression model search algorithm was developed in 2011 that may be used to analyze both general multivariate experimental data sets and wind tunnel strain-gage balance calibration data. The new algorithm is a simplified version of a more complex search algorithm that was originally developed at the NASA Ames Balance Calibration Laboratory. The new algorithm has the advantage that it needs only about one tenth of the original algorithm's CPU time for the completion of a search. In addition, extensive testing showed that the prediction accuracy of math models obtained from the simplified algorithm is similar to the prediction accuracy of math models obtained from the original algorithm. The simplified algorithm, however, cannot guarantee that search constraints related to a set of statistical quality requirements are always satisfied in the optimized regression models. Therefore, the simplified search algorithm is not intended to replace the original search algorithm. Instead, it may be used to generate an alternate optimized regression model of experimental data whenever the application of the original search algorithm either fails or requires too much CPU time. Data from a machine calibration of NASA's MK40 force balance is used to illustrate the application of the new regression model search algorithm.

multivariate experimental data↗

NASA NTRS2013

Analysis of Multivariate Experimental Data Using A Simplified Regression Model Search Algorithm

A new regression model search algorithm was developed that may be applied to both general multivariate experimental data sets and wind tunnel strain-gage balance calibration data. The algorithm is a simplified version of a more complex algorithm that was originally developed for the NASA Ames Balance Calibration Laboratory. The new algorithm performs regression model term reduction to prevent overfitting of data. It has the advantage that it needs only about one tenth of the original algorithm's CPU time for the completion of a regression model search. In addition, extensive testing showed that the prediction accuracy of math models obtained from the simplified algorithm is similar to the prediction accuracy of math models obtained from the original algorithm. The simplified algorithm, however, cannot guarantee that search constraints related to a set of statistical quality requirements are always satisfied in the optimized regression model. Therefore, the simplified algorithm is not intended to replace the original algorithm. Instead, it may be used to generate an alternate optimized regression model of experimental data whenever the application of the original search algorithm fails or requires too much CPU time. Data from a machine calibration of NASA's MK40 force balance is used to illustrate the application of the new search algorithm.

Ulbrich, Norbert M.↗

NASA NTRS1993

Designing reduced-order linear multivariable controllers using experimentally derived plant data

An iterative numerical algorithm for simultaneously improving multiple performance and stability robustness criteria for multivariable feedback systems is developed. The unsatisfied design criteria are improved by updating the free parameters of an initial, stabilizing controller's state-space matrices. Analytical expressions for the gradients of the design criteria are employed to determine a parameter correction that improves all of the feasible, unsatisfied design criteria at each iteration. A controller design is performed using the algorithm with experimentally derived data from a large space structure test facility. Experimental results of the controller's performance at the facility are presented.

Frazier, W. G.↗

NASA NTRS2009

Regression Model Optimization for the Analysis of Experimental Data

A candidate math model search algorithm was developed at Ames Research Center that determines a recommended math model for the multivariate regression analysis of experimental data. The search algorithm is applicable to classical regression analysis problems as well as wind tunnel strain gage balance calibration analysis applications. The algorithm compares the predictive capability of different regression models using the standard deviation of the PRESS residuals of the responses as a search metric. This search metric is minimized during the search. Singular value decomposition is used during the search to reject math models that lead to a singular solution of the regression analysis problem. Two threshold dependent constraints are also applied. The first constraint rejects math models with insignificant terms. The second constraint rejects math models with near-linear dependencies between terms. The math term hierarchy rule may also be applied as an optional constraint during or after the candidate math model search. The final term selection of the recommended math model depends on the regressor and response values of the data set, the user s function class combination choice, the user s constraint selections, and the result of the search metric minimization. A frequently used regression analysis example from the literature is used to illustrate the application of the search algorithm to experimental data.

Ulbrich, N.↗

NASA NTRS1976

Multivariate normality

Sets of experimentally determined or routinely observed data provide information about the past, present and, hopefully, future sets of similarly produced data. An infinite set of statistical models exists which may be used to describe the data sets. The normal distribution is one model. If it serves at all, it serves well. If a data set, or a transformation of the set, representative of a larger population can be described by the normal distribution, then valid statistical inferences can be drawn. There are several tests which may be applied to a data set to determine whether the univariate normal model adequately describes the set. The chi-square test based on Pearson's work in the late nineteenth and early twentieth centuries is often used. Like all tests, it has some weaknesses which are discussed in elementary texts. Extension of the chi-square test to the multivariate normal model is provided. Tables and graphs permit easier application of the test in the higher dimensions. Several examples, using recorded data, illustrate the procedures. Tests of maximum absolute differences, mean sum of squares of residuals, runs and changes of sign are included in these tests. Dimensions one through five with selected sample sizes 11 to 101 are used to illustrate the statistical tests developed.

Crutcher, H. L.↗

NASA NTRS2013

Statistical Analyses of Raw Material Data for MTM45-1/CF7442A-36% RW: CMH Cure Cycle

This report describes statistical characterization of physical properties of the composite material system MTM45-1/CF7442A, which has been tested and is currently being considered for use on spacecraft structures. This composite system is made of 6K plain weave graphite fibers in a highly toughened resin system. This report summarizes the distribution types and statistical details of the tests and the conditions for the experimental data generated. These distributions will be used in multivariate regression analyses to help determine material and design allowables for similar material systems and to establish a procedure for other material systems. Additionally, these distributions will be used in future probabilistic analyses of spacecraft structures. The specific properties that are characterized are the ultimate strength, modulus, and Poisson􀂶s ratio by using a commercially available statistical package. Results are displayed using graphical and semigraphical methods and are included in the accompanying appendixes.

Coroneos, Rula↗

NASA NTRS1981

A model of the human observer and decision maker

The decision process is described in terms of classical sequential decision theory by considering the hypothesis that an abnormal condition has occurred by means of a generalized likelihood ratio test. For this, a sufficient statistic is provided by the innovation sequence which is the result of the perception an information processing submodel of the human observer. On the basis of only two model parameters, the model predicts the decision speed/accuracy trade-off and various attentional characteristics. A preliminary test of the model for single variable failure detection tasks resulted in a very good fit of the experimental data. In a formal validation program, a variety of multivariable failure detection tasks was investigated and the predictive capability of the model was demonstrated.

Wewerinke, P. H.↗

NASA NTRS2001

Response Surface Modeling Using Multivariate Orthogonal Functions

A nonlinear modeling technique was used to characterize response surfaces for non-dimensional longitudinal aerodynamic force and moment coefficients, based on wind tunnel data from a commercial jet transport model. Data were collected using two experimental procedures - one based on modem design of experiments (MDOE), and one using a classical one factor at a time (OFAT) approach. The nonlinear modeling technique used multivariate orthogonal functions generated from the independent variable data as modeling functions in a least squares context to characterize the response surfaces. Model terms were selected automatically using a prediction error metric. Prediction error bounds computed from the modeling data alone were found to be- a good measure of actual prediction error for prediction points within the inference space. Root-mean-square model fit error and prediction error were less than 4 percent of the mean response value in all cases. Efficacy and prediction performance of the response surface models identified from both MDOE and OFAT experiments were investigated.

Morelli, Eugene A.↗

DOE OSTI2025

MethodOpt: a Shiny-based graphical user interface for multivariate optimization of sampling and analytical instrumentation

Method optimization is an important step in producing useful data in various experimental settings involving the use of sampling and analytical instrumentation, such as gas-chromatography mass-spectrometry or other analytical techniques. However, traditional optimization techniques often lack the sophistication of more modern optimization techniques developed in areas of applied mathematics. A graphical user interface has been developed that implements a multivariate, multi-objective optimization technique for spectra-generating sampling and analytical instrumentation, which saves substantial time and resources compared to the more traditional approaches to method development.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS2010

Molybdenum Valence in Basaltic Silicate Melts

The moderately siderophile element molybdenum has been used as an indicator in planetary differentiation processes, and is particularly relevant to core formation [for example, 1-6]. However, models that apply experimental data to an equilibrium differentiation scenario infer the oxidation state of molybdenum from solubility data or from multivariable coefficients from metal-silicate partitioning data [1,3,7]. Partitioning behavior of molybdenum, a multivalent element with a transition near the J02 of interest for core formation (~IW-2) will be sensitive to changes in JO2 of the system and silicate melt structure. In a silicate melt, Mo can occur in either 4+ or 6+ valence state, and Mo6+ can be either octahedrally or tetrahedrally coordinated. Here we present first XANES measurements of Mo valence in basaltic run products at a range of P, T, and JO2 and further quantify the valence transition of Mo.

Danielson, L. R.↗

NASA NTRS2011

Molybdenum Valence in Basaltic Silicate Melts: Effects of Temperature and Pressure

The metal-silicate partitioning behavior of molybdenum has been used as a test for equilibrium core formation hypotheses [for example, 1-6]. However, current models that apply experimental data to equilibrium core-mantle differentiation infer the oxidation state of molybdenum from solubility data or from multivariable coefficients from metal-silicate partitioning data [1,3,7]. Molybdenum, a multi-valent element with a valence transition near the fO2 of interest for core formation (approx.IW-2) will be sensitive to changes in fO2 of the system and silicate melt structure. In a silicate melt, Mo can occur in either 4+ or 6+ valence state, and Mo(6+) can be either octahedrally or tetrahedrally coordinated. Here we present X-ray absorption near edge structure (XANES) measurements of Mo valence in basaltic run products at a range of P, T, and fO2 and further quantify the valence transition of Mo.

Danielson, L. R.↗

DOE OSTI2025

Intrinsic Kinetics of Polyethylene Terephthalate Pyrolysis via Micropyrolysis and Multivariate Chromatographic Analysis

This study provides an in-depth investigation of the primary decomposition of polyethylene terephthalate (PET) via pyrolysis, employing an experimental-analytic workflow that integrates design of experiments (DoE), micropyrolysis coupled with comprehensive two-dimensional gas chromatography (GC×GC), and multivariate data analysis to verify intrinsic kinetic conditions and elucidate evolving product distributions for mapping key reaction pathways. Peaks that could not be identified using commercial spectral libraries were assigned using Mass Frontier simulations, enabling the identification of divinyl terephthalate, ethyl vinyl terephthalate, and 2-(benzoyloxy)ethyl vinyl terephthalate. A polar×polar (non-orthogonal) column set tailored for the detection of carboxylic acids enhanced the quantification of benzoic acid, 4-vinylbenzoic acid, 4-ethylbenzoic acid, and methylbenzoic acid by up to 6-fold relative to an orthogonal column combination (non-polar×mid-polar). Moreover, pyrolysis variables were systematically evaluated using a Box- Behnken design (BBD), encompassing pyrolysis temperature (500−600 °C), sample weight (50−150 μg), and carrier gas flow rate (100−300 mL min −1 ). Among these, pyrolysis temperature was the only statistically significant factor influencing product yields, ranging from 58.78 to 84.26 wt %. In contrast, neither the sample weight nor the carrier gas flow rate had a significant effect on product yields within the evaluated experimental space. At 600 °C, the major pyrolysis products were benzoic acid (up to 20.20 ± 1.46 wt %) and CO 2 (up to 21.28 ± 1.46 wt %), which can be produced through decarboxylation reactions. These findings underscore the critical importance of selecting appropriate analytical columns for the accurate quantification of heteroatomcontaining products such as carboxylic acids, which may otherwise be underestimated or undetected due to their reactivity with the stationary phase of non-polar and mid-polar columns, as well as other GC components. They also highlight the importance of selecting pyrolysis conditions for investigating the primary decomposition of PET under an isothermal kinetically limited regime.

aromatic compounds↗

DOE OSTI2025

Investigating Kinetic Mechanisms of Soot Formation in Plasma Pyrolysis of Methane via Active Learning (Final Technical Report)

Plasma pyrolysis of methane is an effective route for zero-carbon hydrogen production. Yet, soot generated from pyrolysis of hydrocarbons is detrimental to the climate and human health. There is ample experimental and theoretical evidence that suggests polycyclic aromatic hydrocarbons (PAHs) are the molecular precursors to soot particles. The reaction pathways of PAH formation are intricately dependent on a multitude of process parameters, whose kinetic mechanisms are not well-understood in plasma pyrolysis. This project aims to leverage advances in the kinetic modeling of soot formation in combustion, as well as in surrogate modeling and active learning, to systematically investigate the effects of process parameter on the kinetics of PAH formation in plasma pyrolysis of methane. To this end, we propose to use the PAH formation kinetics model developed by the PPPL/PU group based on the well-established ABF and HACA mechanisms, coupled with low-temperature plasma models. We will develop an active learning (AL) framework based on Bayesian optimization to systematically and data-efficiently explore the complex and multivariable parameter space of plasma pyrolysis in order to quantify the effects of plasma and feed parameters on the ABF and HACA kinetic pathways. AL is the branch of machine learning concerned with systematically querying samples from a system (experimental or computational) to train a data-driven model that maps design parameters to a performance criterion. We will use the data generated via AL to perform global sensitivity analysis, combined with uncertainty quantification, to elucidate the impact of different reaction pathways on minimizing formation of soot precursors. This study will result in an improved understanding of kinetics of PAH formation in plasma pyrolysis and can pave the way for more advanced mechanistic studies (e.g., soot nucleation mechanisms). Additionally, the findings will be useful for establishing practical strategies for increasing the pyrolysis efficiency and producing high-grade carbon for synthesis of nanomaterials.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2002

Development of a Generic Creep-Fatigue Life Prediction Model

The objective of this research proposal is to further compile creep-fatigue data of steel alloys and superalloys used in military aircraft engines and/or rocket engines and to develop a statistical multivariate equation. The newly derived model will be a probabilistic fit to all the data compiled from various sources. Attempts will be made to procure the creep-fatigue data from NASA Glenn Research Center and other sources to further develop life prediction models for specific alloy groups. In a previous effort [1-3], a bank of creep-fatigue data has been compiled and tabulated under a range of known test parameters. These test parameters are called independent variables, namely; total strain range, strain rate, hold time, and temperature. The present research attempts to use these variables to develop a multivariate equation, which will be a probabilistic equation fitting a large database. The data predicted by the new model will be analyzed using the normal distribution fits, the closer the predicted lives are with the experimental lives (normal line 1 to 1 fit) the better the prediction. This will be evaluated in terms of a coefficient of correlation, R 2 as well. A multivariate equation developed earlier [3] has the following form, where S, R, T, and H have specific meaning discussed later.

Goswami, Tarun↗

DOE OSTI2026

QProR: An Efficient Framework for Quantity-of-Interest Based Progressive Retrieval with Guaranteed Error Control

Scientific applications generate an unprecedented volume of data, overwhelming the network and file systems’ bandwidth and posing challenges for efficient and scalable data retrieval and analysis. Progressive data compression offers a promising solution by enabling on-demand retrieval at reduced size. However, existing progressive methods either fail to bound the errors in essential quantities of interest (QoIs) derived from raw data or suffer from suboptimal retrieval efficiency. In this work, we propose QProR, an efficient QoI-based progressive framework that optimizes progressive retrieval for target QoIs. Our key contributions include: (1) a systematic framework that integrates error-controlled lossy compressors with bitplane encoding while decoupling the two processes for high flexibility and adaptability; (2) a novel weighted bitplane encoding method which incorperates QoI knowledge into data refactoring to enhance retrieval efficiency; (3) an optimized retrieval strategy that accounts for the varying impacts of different variables on multivariate QoIs; (4) comprehensive evaluations using six real-world datasets from multiple scientific applications and thorough comparisons against state of the arts. Experimental results demonstrate that QProR achieves up to 80.38% reduction in the retrieval size under the same requested QoI error tolerance, when compared with the best-performing existing methods. When transferring 384 GB of scientific data to remote sites, QProR delivers up to 1.68 × speedup in the end-to-end data transfer performance.

Li, Wenbo [University of Kentucky]↗

DOE OSTI2025

Sensitive Detection of Structural Differences using a Statistical Framework for Comparative Crystallography

Chemical and conformational changes underlie the functional cycles of proteins. Comparative crystallography can reveal these changes over time, over ligands, and over chemical and physical perturbations in atomic detail. A key difficulty, however, is that the resulting observations must be placed on the same scale by correcting for experimental factors. We recently introduced a Bayesian framework for correcting (scaling) X-ray diffraction data by combining deep learning with statistical priors informed by crystallographic theory. To scale comparative crystallography data, we here combine this framework with a multivariate statistical theory of comparative crystallography. By doing so, we find strong improvements in the detection of protein dynamics, element-specific anomalous signal, and the binding of drug fragments.

Hekstra, Doeke R. [Harvard Univ., Cambridge, MA (U↗

DOE OSTI2025

Uncertainty quantification of a physics-informed model based on sparse identification of a Thermal Energy Distribution System

Integrated energy systems (IES)s are crucial for enhancing the economy and efficiency of power generation sources (e.g., nuclear energy) necessary to unleash American energy dominance. These systems can be integrated with thermal energy storage (TES) and intermittent renewable energies to optimize overall energy use, peak-load regulation, and demand-side responses. However, the stabilization of energy generation, transport, and utilization introduces operational complexities that exceed the challenges of managing each sub-component individually. Currently, though IESs rely on human operators for efficiency and stability, reducing human error risk and enhancing performance through automation is highly desirable. Recent advances at Idaho National Laboratory have demonstrated successful control of the Thermal Energy Distributed System (TEDS). However, the automatic control system depends on a deterministic Sparse Identification of Nonlinear Dynamics with Control (SINDyC) model, which are trained based on simulation data from physics-based simulations. Because of uncertainties in physics-based simulation, SINDyC model results in large discrepancies against experimental data and cannot be reliably used in automatic control. In this paper, we present an innovative approach to address these discrepancies by quantifying uncertainties and developing a more robust model. We first generated trajectories by using first-principles physics codes to encapsulate the experiment. Next, we trained thousands of models by randomly sampling these trajectories. We then collapsed all those models into one probabilistic SINDyC by fitting a multivariate Gaussian distribution onto the resulting coefficient’s distribution. Despite its simplicity, our approach successfully produced 95% confidence intervals that captured the experimental trajectories. It even did so with a higher probability and better U-pooling score across six of the seven relevant quantities of interest (QoIs), as compared to other classical approaches. In conclusion, ongoing research is focusing on generating new experimental trajectories to validate this approach, and on employing Bayesian calibration to refine parametric uncertainties and guide future model development efforts.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Optimizing high energy density sulfur cathodes: A multivariate approach to electrode formulation and processing

Lithium-sulfur (Li-S) batteries involve complex solid-liquid-solid phase transformations during both discharging and charging processes, where cathode materials, formulation, and structure play a crucial role. Here, a design of experiments (DoE) methodology and an empirical model are developed to systematically explore the interactions and trade-offs among cathode factors and process variables, and to obtain generalizable effects estimates for the multivariate system. Compared to the conventional one-factor-at-a-time (OFAT) approach, this work demonstrates advantages in both efficiency and accuracy by allowing the data to guide future research and decisions. Further, an optimized cathode formulation and processing parameters are predicted and validated experimentally, achieving over 1000 mAh g -1 in discharge capacity and improved cycling under practical lean electrolyte (4 µL mg -1 S) and high S-loading cathodes (>4 mg cm -2 ) conditions. The optimized cathode was scaled up and assembled into Li-S pouch cells, achieving 316 Wh kg -1 in cell-level energy, proving that the comprehensive and rigorous framework for optimizing complex systems with DoE leads to improved performance in a practical pouch cell system.

25 ENERGY STORAGE↗