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Results for “functional Principal Component Analysis”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Analysis of Electric Vehicle Charging Behavior Patterns with Function Principal Component Analysis Approach

This manuscript focused on analyzing electric vehicles’ (EV) charging behavior patterns with a functional data analysis (FDA) approach, with the goal of providing theoretical support to the EV infrastructure planning and regulation, as well as the power grid load management. 5-year real-world charging log data from a total of 455 charging stations in Kansas City, Missouri, was used. The focuses were placed on analyzing the daily usage occupancy variability, daily energy consumption variability, and station-level usage variability. Compared with the traditional discrete-based analysis models, the proposed FDA modeling approach had unique advantages in preserving the smooth function behavior of the data, bringing more flexibility in the modeling process with little required assumptions or background knowledge on independent variables, as well as the capability of handling time series data with different lengths or sizes. In addition to the patterns revealed in the EV charging station’s occupancy and energy consumption, the differences between EV driver’s charging time and parking time were analyzed and called for the needs for parking regulation and enforcement. The different usage patterns observed at charging stations located on different land-use types were also analyzed.

Engineering↗
DOE OSTI2021

Optical Variability of ICRF3 Quasars in the Pan-STARRS 3Pi Survey with Functional Principal Component Analysis

We make use of individual (epoch) detection data from the Pan-STARRS “3π” survey for 2863 optical ICRF3 counterparts in the five wavelength bands g, r, i, z, and y, published as part of the Data Release 2. A dedicated method based on the Functional Principal Component Analysis is developed for these sparse and irregularly sampled data. With certain regularization and normalization constraints, it allows us to obtain uniform and compatible estimates of the variability amplitudes and average magnitudes between the passbands and objects. We find that the starting assumption of affinity of the light curves for a given object at different wavelengths is violated for several percent of the sample. The distributions of rms variability amplitudes are strongly skewed toward small values, peaking at ∼0.1 mag with tails stretching to 2 mag. Statistically, the lowest variability is found for the r band and the largest for the reddest y band. A small “brighter-redder” effect is present, with amplitudes in y greater than amplitudes in g in 57% of the sample. The variability versus redshift dependence shows a strong decline with z toward redshift 3, which we interpret as the time dilation of the dominant time frequencies. The colors of radio-loud ICRF3 quasars are correlated with redshift in a complicated, wavy pattern governed by the emergence of brightest emission lines within the five passbands.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Functional Principal Component Analysis of Radio–Optical Reference Frame Tie

The Gaia optical reference frame is intrinsically undefined with respect to global orientation and spin, so it needs to be anchored in the radio-based International Celestial Reference Frame (ICRF) to provide a referenced and quasi-inertial celestial coordinate system. The link between the two fundamental frames is realized through two samples of distant extragalactic sources, mostly active galactic nuclei and quasars, but only the smaller sample of radio-loud ICRF sources with optical counterparts is available to determine the mutual orientation. The robustness of this link can be mathematically formulated in the framework of functional principal component analysis using a set of vector spherical harmonics to represent the differences in celestial positions of the common objects. The weakest eigenvectors are computed, which describe the greatest deficiency of the link. The deficient or poorly determined terms are specific vector fields on the sphere that carry the largest errors of absolute astrometry using Gaia in reference to the ICRF. This analysis provides guidelines for the future development of the ICRF maximizing the accuracy of the link over the entire celestial sphere. A measure of the robustness of a least-squares solution, which can be applied to any linear model fitting problem, is introduced to help discriminate between reference frame tie models of different degrees.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

A geometric approach for computing tolerance bounds for elastic functional data

We design an approach for constructing tolerance bounds for functional data with random warping variability. In particular, we define a generative, probabilistic model for the amplitude and phase components of such observations, which parsimoniously characterizes variability in the baseline data. Based on the proposed model, we define two different types of tolerance bounds that are able to measure both types of variability, and as a result, identify when the data has gone beyond the bounds of amplitude and/or phase. The first functional tolerance bounds are computed via a bootstrap procedure on the geometric space of amplitude and phase functions. The second functional tolerance bounds utilize functional Principal Component Analysis to construct a tolerance factor. Our report is motivated by two main applications: process control and disease monitoring. The problem of statistical analysis and modeling of functional data in process control is important in determining when a production has moved beyond a baseline. Moreover, in biomedical applications, doctors use long, approximately periodic signals (such as the electrocardiogram) to diagnose and monitor diseases. In this context, it is desirable to identify abnormalities in these signals. We additionally consider a simulated example to assess our approach and compare it to two existing methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Elastic functional changepoint detection of climate impacts from localized sources

Detecting changepoints in functional data has become an important problem as interest in monitoring of climate phenomenon has increased, where the data is functional in nature. Here, the observed data often contains both amplitude (y-axis) and phase (x-axis) variability. If not accounted for properly, true changepoints may be undetected, and the estimated underlying mean change functions will be incorrect. In this article, an elastic functional changepoint method is developed which properly accounts for these types of variability. The method can detect amplitude and phase changepoints which current methods in the literature do not, as they focus solely on the amplitude changepoint. This method can easily be implemented using the functions directly or can be computed via functional principal component analysis to ease the computational burden. We apply the method and its nonelastic competitors to both simulated data and observed data to show its efficiency in handling data with phase variation with both amplitude and phase changepoints. We use the method to evaluate potential changes in stratospheric temperature due to the eruption of Mt. Pinatubo in the Philippines in June 1991. Using an epidemic changepoint model, we find evidence of a increase in stratospheric temperature during a period that contains the immediate aftermath of Mt. Pinatubo, with most detected changepoints occurring in the tropics as expected.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Bounding uncertainty in functional data: A case study

Functional data are fast becoming a preeminent source of information across a wide range of industries. A particularly challenging aspect of functional data is bounding uncertainty. In this unique case study, we present our attempts at creating bounding functions for selected applications at Sandia National Laboratories (SNL). The first attempt involved a simple extension of functional principal component analysis (fPCA) to incorporate covariates. Though this method was straightforward, the extension was plagued by poor coverage accuracy for the bounding curve. This led to a second attempt utilizing elastic methodology which yielded more accurate coverage at the cost of more complexity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Covariate Dependent Sparse Functional Data Analysis

This study proposes a method to incorporate covariate information into sparse functional data analysis. The method aims at cases where each subject has a limited number of longitudinal measurements and is associated with static covariates. This research is motivated by several use cases in practice. One representative example is void swelling, a nuclear-specific material degradation mechanism. Void swelling is affected by many covariates, including alloy composition and irradiation type. How to accurately model the complicated joint effects of such covariates on the swelling process is the key to mitigating the effect of swelling and ensuring safe operation. Unlike most of the existing methods, the proposed method can handle high-dimensional covariates with the informative covariate identification procedure and sparse and irregularly spaced measurements, that is, does not require complete or dense observations. The main innovation of the proposed method is that we model the variation coming from covariates and the variation left conditioned on covariates, such that the functional principal component analysis and Gaussian process can be conducted in a unified manner. Further, we also propose a systematic approach to identify important covariates in the hypothesis testing context. The methodology is demonstrated on applications in nuclear engineering and healthcare and simulation studies.

42 ENGINEERING↗
DOE OSTI2025

Explainable Machine Learning for Functional Data

Black-box machine learning models are recognized as useful tools for prediction applications, but the algorithmic complexity of some models causes interpretation challenges. Explainability methods have been proposed to provide insight into these models, but there is little research focused on supervised modeling with functional data inputs. We argue that, especially in applications of high consequence, it is important to explicitly model the functional dependence in a black-box analysis to not obscure or misrepresent patterns in explanations. As such, we propose the V ariable importance E xplainable E lastic S hape A nalysis (VEESA) pipeline for training supervised machine learning models with functional inputs. The pipeline is an analysis process that includes the data preprocessing, modeling, and post-hoc explanations. The preprocessing is done using elastic functional principal components analysis, which accounts for vertical and horizontal variability in functional data and, ultimately, allows for explanations in the original data space that identify the important functional variability without bias due to correlated variables. Here, we demonstrate the pipeline on two high-consequence applications: explosives classification for national security and inkjet printer identification in forensic science. The applications exhibit the VEESA pipeline’s ability to provide an understanding of the characteristics of the functional data useful for prediction. Code for implementing the pipeline is available in the veesa R package (and supplemental python code).

Elastic Shape Analysis↗
DOE OSTI2023

VEESA R package

SAND2024-04584O R package for applying the VEESA pipeline method is a technique used for explainable machine learning with functional data. The VEESA pipeline makes use of the elastic-shape analysis framework for functional data. It also implements functional principal component analysis and permutation feature importance. 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.

Tucker, James↗
DOE OSTI2022

Functional Data Analysis for Extracting the Intrinsic Dimensionality of Spectra: Application to Chemical Homogeneity in the Open Cluster M67

High-resolution spectroscopic surveys of the Milky Way have entered the Big Data regime and have opened avenues for solving outstanding questions in Galactic archeology. However, exploiting their full potential is limited by complex systematics, whose characterization has not received much attention in modern spectroscopic analyses. In this work, we present a novel method to disentangle the component of spectral data space intrinsic to the stars from that due to systematics. Using functional principal component analysis on a sample of 18,933 giant spectra from APOGEE, we find that the intrinsic structure above the level of observational uncertainties requires ≈10 functional principal components (FPCs). Our FPCs can reduce the dimensionality of spectra, remove systematics, and impute masked wavelengths, thereby enabling accurate studies of stellar populations. To demonstrate the applicability of our FPCs, we use them to infer stellar parameters and abundances of 28 giants in the open cluster M67. We employ Sequential Neural Likelihood, a simulation-based Bayesian inference method that learns likelihood functions using neural density estimators, to incorporate non-Gaussian effects in spectral likelihoods. By hierarchically combining the inferred abundances, we limit the spread of the following elements in M67: Fe ≲ 0.02 dex; C ≲ 0.03 dex; O, Mg, Si, Ni ≲ 0.04 dex; Ca ≲ 0.05 dex; N, Al ≲ 0.07 dex (at 68% confidence). Our constraints suggest a lack of self-pollution by core-collapse supernovae in M67, which has promising implications for the future of chemical tagging to understand the star formation history and dynamical evolution of the Milky Way.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

High-Throughput Field Plant Phenotyping: A Self-Supervised Sequential CNN Method to Segment Overlapping Plants

High-throughput plant phenotyping—the use of imaging and remote sensing to record plant growth dynamics—is becoming more widely used. The first step in this process is typically plant segmentation, which requires a well-labeled training dataset to enable accurate segmentation of overlapping plants. However, preparing such training data is both time and labor intensive. To solve this problem, we propose a plant image processing pipeline using a self-supervised sequential convolutional neural network method for in-field phenotyping systems. This first step uses plant pixels from greenhouse images to segment nonoverlapping in-field plants in an early growth stage and then applies the segmentation results from those early-stage images as training data for the separation of plants at later growth stages. The proposed pipeline is efficient and self-supervising in the sense that no human-labeled data are needed. We then combine this approach with functional principal components analysis to reveal the relationship between the growth dynamics of plants and genotypes. We show that the proposed pipeline can accurately separate the pixels of foreground plants and estimate their heights when foreground and background plants overlap and can thus be used to efficiently assess the impact of treatments and genotypes on plant growth in a field environment by computer vision techniques. This approach should be useful for answering important scientific questions in the area of high-throughput phenotyping.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

System and method for automated extraction of high resolution structural dynamics from video

A method for extracting vibrational modes of a structure includes: receiving a plurality of video frames, each of the video frames including a plurality of pixels; decomposing each of the video frames on a plurality of spatial scales in accordance with complex steerable pyramid filters to obtain a filter response for each of the spatial scales; computing a plurality of local phases of the pixels of each frame; removing a temporal mean from each frame to obtain a plurality of factored vibration motion functions; performing principal component analysis on the factored vibration motion functions to obtain principal components; blind source separating the principal components to compute a plurality of modal coordinates; computing frequency and damping ratios in accordance with the modal coordinates; and outputting the computed frequency and damping ratios.

42 ENGINEERING↗
DOE OSTI2022

Seeking regularity from irregularity: unveiling the synthesis–nanomorphology relationships of heterogeneous nanomaterials using unsupervised machine learning

Nanoscale morphology of functional materials determines their chemical and physical properties. However, despite increasing use of transmission electron microscopy (TEM) to directly image nanomorphology, it remains challenging to quantify the information embedded in TEM data sets, and to use nanomorphology to link synthesis and processing conditions to properties. We develop an automated, descriptor-free analysis workflow for TEM data that utilizes convolutional neural networks and unsupervised learning to quantify and classify nanomorphology, and thereby reveal synthesis–nanomorphology relationships in three different systems. While TEM records nanomorphology readily in two-dimensional (2D) images or three-dimensional (3D) tomograms, we advance the analysis of these images by identifying and applying a universal shape fingerprint function to characterize nanomorphology. After dimensionality reduction through principal component analysis, this function then serves as the input for morphology grouping through unsupervised learning. We demonstrate the wide applicability of our workflow to both 2D and 3D TEM data sets, and to both inorganic and organic nanomaterials, including tetrahedral gold nanoparticles mixed with irregularly shaped impurities, hybrid polymer-patched gold nanoprisms, and polyamide membranes with irregular and heterogeneous 3D crumple structures. In each of these systems, unsupervised nanomorphology grouping identifies both the diversity and the similarity of the nanomaterial across different synthesis conditions, revealing how synthetic parameters guide nanomorphology development. Our work opens possibilities for enhancing synthesis of nanomaterials through artificial intelligence and for understanding and controlling complex nanomorphology, both for 2D systems and in the far less explored case of 3D structures, such as those with embedded voids or hidden interfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Augmenting machine learning of Grad–Shafranov equilibrium reconstruction with Green's functions

This work presents a method for predicting plasma equilibria in tokamak fusion experiments and reactors. The approach involves representing the plasma current as a linear combination of basis functions using principal component analysis of plasma toroidal current densities (J t ) from the EFIT-AI equilibrium database. Then utilizing EFIT's Green's function tables, basis functions are created for the poloidal flux (ψ) and diagnostics generated from the toroidal current (J t ). Similar to the idea of a physics-informed neural network (NN), this physically enforces consistency between ψ, J t , and the synthetic diagnostics. First, the predictive capability of a least squares technique to minimize the error on the synthetic diagnostics is employed. The results show that the method achieves high accuracy in predicting ψ and moderate accuracy in predicting J t with median R 2 = 0.9993 and R 2 = 0.978, respectively. A comprehensive NN using a network architecture search is also employed to predict the coefficients of the basis functions. The NN demonstrates significantly better performance compared to the least squares method with median R 2 = 0.9997 and 0.9916 for J t and ψ, respectively. The robustness of the method is evaluated by handling missing or incorrect data through the least squares filling of missing data, which shows that the NN prediction remains strong even with a reduced number of diagnostics. Additionally, the method is tested on plasmas outside of the training range showing reasonable results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Principal Component Analysis for Extremes and Application to U.S. Precipitation

Here, we propose a method for analyzing extremal behavior through the lens of a most efficient basis of vectors. The method is analogous to principal component analysis, but is based on methods from extreme value analysis. Specifically, rather than decomposing a covariance or correlation matrix, we obtain our basis vectors by performing an eigendecomposition of a matrix that describes pairwise extremal dependence. We apply the method to precipitation observations over the contiguous United States. We find that the time series of large coefficients associated with the leading eigenvector shows very strong evidence of a positive trend, and there is evidence that large coefficients of other eigenvectors have relationships with El Niño–Southern Oscillation.

54 ENVIRONMENTAL SCIENCES↗