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48 records · Page 3

Inverse sequential procedures for the monitoring of time series

When one or more new values are added to a developing time series, they change its descriptive parameters (mean, variance, trend, coherence). A 'change index (CI)' is developed as a quantitative indicator that the changed parameters remain compatible with the existing 'base' data. CI formulate are derived, in terms of normalized likelihood ratios, for small samples from Poisson, Gaussian, and Chi-Square distributions, and for regression coefficients measuring linear or exponential trends. A substantial parameter change creates a rapid or abrupt CI decrease which persists when the length of the bases is changed. Except for a special Gaussian case, the CI has no simple explicit regions for tests of hypotheses. However, its design ensures that the series sampled need not conform strictly to the distribution form assumed for the parameter estimates. The use of the CI is illustrated with both constructed and observed data samples, processed with a Fortran code 'Sequitor'.

Radok, Uwe↗

Physics-Based Machine Learning Methods for U-235 Forensics Signatures

Signatures of low-intensity U-235 sources have been recently studied by utilizing a variety of machine learning (ML) classifiers using features derived from gamma spectral measurements collectedunder structured campaigns. Several ML classifiers, such as ensemble of tress and classification trees, revealed misleadingly-optimistic training error due to over-fitting, and furthermore,their performance is not directly relatable to the physical properties due to their data-driven, opaque designs. We present a regression-based ML method that first estimates the inverse distanceto the source and then utilizes a threshold to infer its presence, by representing the background as a source located at an infinite distance. For the inverse distance estimation, we study the ensembleof trees and Gaussian process regression methods, and a hyper parameter auto-tuning and selection method that employs five regression estimators. These methods avoid the over-fittingobserved in several ML classifiers, while providing the classification error nearly comparable to them based on independent test data. Their error is directly related to estimates of the inversephysical distance to source, and the precision of error determines the seperability property that determines the false alarm and missed detection rates. The property of monotonic decrease of thesource strength with increasing detector distance combined with Poisson distribution of measurements is utilized to analytically validate these methods by deriving the generalization equations ofunderlying regression methods.

Rao, Nageswara↗

Physics-Based Machine Learning Methods for U-235 Forensics Signatures

Signatures of low-intensity U-235 sources have been recently studied by utilizing a variety of machine learning (ML) classifiers using features derived from gamma spectral measurements collected under structured campaigns. Several ML classifiers, such as ensemble of tress and classification trees, revealed misleadingly-optimistic training error due to over-fitting, and furthermore, their performance is not directly relatable to the physical properties due to their data-driven, opaque designs. We present a regression-based ML method that first estimates the inverse distance to the source and then utilizes a threshold to infer its presence, by representing the background as a source located at an infinite distance. For the inverse distance estimation, we study the ensemble of trees and Gaussian process regression methods, and a hyper parameter auto-tuning and selection method that employs five regression estimators. These methods avoid the over-fitting observed in several ML classifiers, while providing the classification error nearly comparable to them based on independent test data. Their error is directly related to estimates of the inverse physical distance to source, and the precision of error determines the seperability property that determines the false alarm and missed detection rates. The property of monotonic decrease of the source strength with increasing detector distance combined with Poisson distribution of measurements is utilized to analytically validate these methods by deriving the generalization equations of underlying regression methods.

Rao, Nageswara↗

Simulation of Mechanical Fractionation of Chopped Whole-Plant Corn (WPC) Using Discrete Element Method (DEM)

Fractionating whole-plant corn (WPC) in a single-pass harvesting system requires studies on the WPC-to-equipment interaction for improved property control, as well as mechanical and air-driven separation processes compared to the traditional multi-pass grain and stover harvesting system. The discrete element method (DEM) technique has the potential to simulate WPC mechanical fractionation and support simulation-based design of WPC separation processes. In this study, methods to develop DEM particle models of WPC (kernel, cob, stalk, and husk) and their material properties for simulating mass fractionation using the ASABE standard mechanical shaker were proposed. Measurement was done on the axial dimensions (major, intermediate, and minor) and mass of each WPC type (mean sample size is 56), sampled from single-pass harvesting. Applying gaussian multivariate regression and bootstrapping re-sampling techniques, a DEM particle approximate to each WPC was developed. Sensitivity analysis of the DEM Young‘s modulus, Poisson‘s ratio, and interaction parameters of coefficient of restitution, coefficient of rolling friction, and coefficient of static friction on mass fraction was performed after 156 ASABE sieve-shaking DEM simulation runs, generated using Latin Hypercube Design (LHD) design of experiment (DOE) from 19 DEM material parameters. DEM simulation using Hertz-Mindlin with flexible bond contact laws and DOE optimized material properties successfully reproduced the mass fractions retained in ASABE sieves at 9.8% mean relative error and a coefficient of determination of R2 = 0.87. Here, the DEM methodology developed for mechanical WPC mass fractionation could be deployed to perform virtual design of feedstock handling equipment and performance analysis of mechanical fraction systems.

09 BIOMASS FUELS↗

Full-Field Strain Measurement Integrated with Two Dimension Regression Analysis to Evaluate the Bi-Modulus Elastic Properties of Isotropic and Transversely Isotropic Materials

Background: Measuring the physical properties of shale is critical for optimizing engineering activities such as geothermal energy generation and hydraulic fracturing. Shale is a transversely isotropic material. Furthermore, this material can also include micro and macro cracks at different locations and orientations that cause it to behave differently under tensile or compressive loading. Objective: In this work, a combined experimental–numerical approach is proposed to evaluate the bi-modulus elastic properties of isotropic and transversely isotropic materials. Methods: Full-field strain measurements for a circular disk under diametral compression are integrated with a regression analysis technique to evaluate the elastic properties of bi-modulus materials subjected to tensile and compressive loads using two loading configurations on the same specimen. Digital Image Correlation (DIC) is used to measure the full-field strains. Subsequently, in the case of an isotropic material, a linear least-squares approach is utilized to process the experimentally determined strains in conjunction with analytical expressions of the stress fields (in terms of far-field loading) to determine the elastic modulus E, the shear modulus G, and the Poisson’s ratio $v$. In the case of a transversely isotopic material, such as shale, a finite element model is implemented to determine the stress fields (again in terms of far-field loading), which is followed by repeating the previous regression analysis in an iterative process to estimate the elastic parameters. Results: The results show that the proposed technique successfully provides a complete set of elastic properties as a function of both the loading condition and the principal material directions. The technique is validated by measurements on a known isotropic material and then applied to determine the properties of shale. Conclusion: In this work, the proposed approach is successfully used to calculate the bi-modulus elastic response of poly(methyl meth- acrylate) (PMMA) and shale. As expected, PMMA exhibits an isotropic response with no bi-modulus effect, however, shale exhibits both transverse isotropy and a bi-modulus effect. Therefore, this approach holds promise for investigating the elastic properties of materials like rocks and fiber-reinforced composite laminates as functions of the principal material directions and the loading conditions.

42 ENGINEERING↗

Regularized Differentiation for Bioburden Density Estimation in Planetary Protection

In this paper, we propose and investigate the performance of two novel shrinkage estimators for bioburden density estimation in planetary protection. The estimators are based on the regularized differentiation of a cumulative count of colony forming units collected throughout the data collecting session or the life cycle of the entire mission. The regularized differentiation recasts the problem of bioburden density estimation as a linear least squares problem. The least squares problem is then solved through regularization techniques, such as truncated singular value decomposition and penalized least squares. The regularization is necessary to avoid noise amplification during the differentiation of noisy data. The two regularization estimators are compared with four other commonly used estimators to simultaneously evaluate the means of multivariable independent Poisson distributions: the maximum likelihood, noninformative Bayes estimator with Jeffreys prior, Empirical Bayes using conjugate gamma-Poisson model with gamma parameters selected by method of moments, and the Clevenson-Zidek estimator. It is shown through computer-simulated data that the regularized differentiation based on ridge regression has the smallest mean-squared error among all estimators. The analysis of shrinkage mechanism implemented by regularized differentiation is performed, and it is shown that the regularized differentiation amounts to performing a weighted averaging of all the samples. The weights are determined by the regularization parameter automatically selected by the L-curve technique. Since the method of least squares makes no distributional assumptions about the data, it presents an attractive technique for bioburden density estimation when there are concerns about the misspecification of the distributional model. The paper concludes with the analysis of the bioburden data collected during InSight mission and directions for future work.

97 - MATHEMATICS AND COMPUTING↗

Prediction of electric and magnetic fields from spectral data using machine learning algorithms for Doppler-free saturation spectroscopy diagnostics

The prediction of electric and magnetic field amplitudes from atomic spectral data is critical for plasma control in fusion devices such as tokamaks. Conventional approaches that rely on physics-based models are computationally expensive and unsuitable for real-time applications. In this work, we develop and benchmark three machine learning algorithms—simulation-based inference (SBI), fully connected neural networks (FCNN), and histogram-based gradient boosting regression (GBR-Hist)—to infer field intensities directly from Doppler-free saturation spectroscopy (DFSS) spectra. Synthetic datasets of spectra were generated using the EZSSS code and evaluated both with and without added Poisson noise to mimic experimental conditions. We find that SBI achieves the highest accuracy and robustness, FCNN provides a strong balance of accuracy and computational efficiency for real-time applications, and GBR-Hist offers the fastest inference but is more sensitive to noise. Furthermore, these results demonstrate the potential of machine learning to accelerate DFSS analysis and enhance its utility for plasma diagnostics and control.

Doppler-free saturation spectroscopy↗

Extracting the Galactic Center excess’ source-count distribution with neural nets

The two leading hypotheses for the Galactic Center excess (GCE) in the Fermi data are an unresolved population of faint millisecond pulsars (MSPs) and dark-matter (DM) annihilation. The dichotomy between these explanations is typically reflected by modeling them as two separate emission components. However, point sources (PSs) such as MSPs become statistically degenerate with smooth Poisson emission in the ultrafaint limit (formally where each source is expected to contribute much less than one photon on average), leading to an ambiguity that can render questions such as whether the emission is PS-like or Poissonian in nature ill defined. We present a conceptually new approach that describes the PS and Poisson emission in a unified manner and only afterwards derives constraints on the Poissonian component from the so obtained results. For the implementation of this approach, we leverage deep learning techniques, centered around a neural network-based method for histogram regression that expresses uncertainties in terms of quantiles. We demonstrate that our method is robust against a number of systematics that have plagued previous approaches, in particular DM/PS misattribution. In the Fermi data, we find a faint GCE described by a median source-count distribution (SCD) peaked at a flux of ~ 4 x 10 -11 counts cm -2 s -1 (corresponding to ~ 3-4 expected counts per PS), which would require N ~ $\mathscr{O}$(10 4 ) sources to explain the entire excess (median value N = 29,300 across the sky). Although faint, this SCD allows us to derive the constraint η ρ ≤ 66% for the Poissonian fraction of the GCE flux η ρ at 95% confidence, suggesting that a substantial amount of the GCE flux is due to PSs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

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↗

Treatment of singularities in cracked bodies

Three-dimensional finite-element analyses of middle-crack tension (M-T) and bend specimens subjected to mode I loadings were performed to study the stress singularity along the crack front. The specimen was modeled using 20-node isoparametric elements. The displacements and stresses from the analysis were used to estimate the power of singularities using a log-log regression analysis along the crack front. The analyses showed that finite-sized cracked bodies have two singular stress fields of the form rho = C sub o (theta, z) r to the -1/2 power + D sub o (theta, phi) R to the lambda rho power. The first term is the cylindrical singularity with the power -1/2 and is dominant over the middle 96 pct (for Poisson's ratio = 0.3) of the crack front and becomes nearly zero at the free surface. The second singularity is a vertex singularity with the vertex point located at the intersection of the crack front and the free surface. The second term is dominant at the free surface and becomes nearly zero away from the the boundary layer. The thickness of the boundary layer depends on Poisson's ratio of the material and is independent of the specimen type. The thickness of the boundary layer varied from 0 pct to about 5 pct of the total specimen thickness as Poisson's ratio varied from 0.0 to 0.45. Because there are two singular stress fields near the free surface, the strain energy release rate (G) is an appropriate parameter to measure the severity of the crack.

Shivakumar, K. N.↗

Treatment of singularities in cracked bodies

Three-dimensional finite-element analyses of middle-crack tension (M-T) and bend specimens subjected to mode I loadings were performed to study the stress singularity along the crack front. The specimen was modeled using 20-node isoparametric elements. The displacements and stresses from the analysis were used to estimate the power of singularities using a log-log regression analysis along the crack front. The analyses showed that finite-sized cracked bodies have two singular stress fields of the form rho = C sub o (theta, z) r to the -1/2 power + D sub o (theta, phi) R to the lambda rho power. The first term is the cylindrical singularity with the power -1/2 and is dominant over the middle 96 pct (for Poisson's ratio = 0.3) of the crack front and becomes nearly zero at the free surface. The second singularity is a vertex singularity with the vertex point located at the intersection of the crack front and the free surface. The second term is dominant at the free surface and becomes nearly zero away from the boundary layer. The thickness of the boundary layer depends on Poisson's ratio of the material and is independent of the specimen type. The thickness of the boundary layer varied from 0 pct to about 5 pct of the total specimen thickness as Poisson's ratio varied from 0.0 to 0.45. Because there are two singular stress fields near the free surface, the strain energy release rate (G) is an appropriate parameter to measure the severity of the crack.

Shivakumar, K. N.↗

Machine learning elastic constants of multi-component alloys

The present manuscript explores application of machine learning methods for determining elastic constants and other derived mechanical properties of multi-component alloys. Here, a number of machine learning models, including linear regression, neural network and random forest based models, are trained and tested on a dataset of binary alloys generated using density functional theory (DFT) calculations and spanning over a large number of elemental species in the periodic table. Starting with a wide range of simple and easily accessible compositionally-averaged elemental features, a correlation-based feature selection strategy was used to systematically down-select a set of most relevant features towards the prediction of the elasticity tensor components. The true predictive performance and the associated uncertainties of the models were established by testing on unseen data and bootstrapping, respectively. A single and pair-wise feature partial dependence analysis was performed to visualize the average property trends in the multi-dimensional feature space in order to further understand the achieved predictive performance. The utility of the trained model is further demonstrated by obtaining sufficiently accurate yet highly efficient approximations for bulk modulus, Young’s modulus, shear modulus and Poisson’s ratio for alloys beyond the binary space (i.e., two-component alloys) on which the model was originally trained. More importantly, we test and validate the predictive performance of the developed model directly against the experimentally measured elastic constants of technologically relevant multi-component alloys (such as, Ni- and Ti-based alloys). Finally, utility of such a data-enabled route is demonstrated by predicting the possible range of various elastic properties for vast composition space available within the five component Ni-Cr-Fe-Mo-W alloy system in a high-throughput manner.

36 MATERIALS SCIENCE↗