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DOE OSTI2016

Asteroid models from photometry and complementary data sources

I discuss inversion methods for asteroid shape and spin reconstruction with photometry (lightcurves) and complementary data sources such as adaptive optics or other images, occultation timings, interferometry, and range-Doppler radar data. These are essentially different sampling modes (generalized projections) of plane-of-sky images. An important concept in this approach is the optimal weighting of the various data modes. The maximum compatibility estimate, a multi-modal generalization of the maximum likelihood estimate, can be used for this purpose. I discuss the fundamental properties of lightcurve inversion by examining the two-dimensional case that, though not usable in our three-dimensional world, is simple to analyze, and it shares essentially the same uniqueness and stability properties as the 3-D case. After this, I review the main aspects of 3-D shape representations, lightcurve inversion, and the inclusion of complementary data.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2011

SPIN VECTOR AND SHAPE OF (6070) RHEINLAND AND THEIR IMPLICATIONS

Main belt asteroids (6070) Rheinland and (54827) 2001 NQ8 belong to a small population of couples of bodies that reside in very similar heliocentric orbits. Vokrouhlicky and Nesvorny promoted the term 'asteroid pairs', pointing out their common origin within the past tens to hundreds of kyr. Previous attempts to reconstruct the initial configuration of Rheinland and 2001 NQ8 at the time of their separation have led to the prediction that Rheinland's rotation should be retrograde. Here, we report extensive photometric observations of this asteroid and use the light curve inversion technique to directly determine its rotation state and shape. We confirm the retrograde sense of rotation of Rheinland, with obliquity value constrained to be {>=}140{sup 0}. The ecliptic longitude of the pole position is not well constrained as yet. The asymmetric behavior of Rheinland's light curve reflects a sharp, near-planar edge in our convex shape representation of this asteroid. Our calibrated observations in the red filter also allow us to determine H{sub R} = 13.68 {+-} 0.05 and G = 0.31 {+-} 0.05 values of the H-G system. With the characteristic color index V - R = 0.49 {+-} 0.05 for S-type asteroids, we thus obtain H = 14.17 {+-} 0.07 for the absolute magnitude of (6070) Rheinland. This is a significantly larger value than previously obtained from analysis of astrometric survey observations. We next use the obliquity constraint for Rheinland to eliminate some degree of uncertainty in the past propagation of its orbit. This is because the sign of the past secular change of its semimajor axis due to the Yarkovsky effect is now constrained. The determination of the rotation state of the secondary component, asteroid (54827) 2001 NQ8, is the key element in further constraining the age of the pair and its formation process.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Aerodynamic Sensitivities over Separable Shape Tensors

Here, we present a comprehensive aerodynamic sensitivity analysis of airfoil parameterization informed by separable shape tensors. This parameterization approach uniquely benefits the design process by isolating various well-studied shape characteristics, such as airfoil thickness, and providing a well-regulated low-dimensional parameter domain for aerodynamic designs. Exploring the aerodynamic sensitivities of this novel parameterization can provide valuable insights for more robust designs and future manufacturing efforts. We construct a data-driven parameter space of airfoils using principal geodesic analysis of separable shape tensors informed by a curated database containing almost 20,000 suitable engineering airfoils. Analyzing the shape reconstruction error and the maximum mean discrepancy between joint distributions of aerodynamic quantities, we study the dimensionality of the learned parameter space. This simple numerical experiment demonstrates a dramatic dimension reduction that retains design effectiveness and promotes regularity of the shape representations. Finally, we generate new airfoils and use the HAM2D Reynolds-averaged Navier–Stokes solver to predict lift, drag, and moment coefficients. We compute multiple sensitivity metrics to quantify and assert the consistency of parameter influence on the aerodynamic quantities. We also explore low-dimensional polynomial ridge approximations to motivate physical intuitions and offer explanations of the approximated sensitivities.

17 WIND ENERGY↗

NASA NTRS1991

Tactile discrimination and representations of texture, shape, and softness

We present here some of the salient results on the tactual discriminabilities of human subjects obtained through psychophysical experiments, and the associated peripheral neural codes obtained through electrophysiological recordings from monkey single nerve fibers. Humans can detect the presence of a 2 micron high single dot on a smooth glass plate stroked on the skin, based on the responses of Meissner type rapidly adapting fibers (RAs). They can also detect a 0.06 micron high grating on the plate, owing to the response of Pacinian corpuscle fibers. Among all the possible representations of the shapes of objects, the surface curvature distribution seems to be the most relevant for tactile sensing. Slowly adapting fibers respond to both the change and rate of change of curvature of the skin surface at the most sensitive spot in their receptive fields, whereas RAs respond only to the rate of change of curvature. Human discriminability of compliance of objects depends on whether the object has a deformable or rigid surface. When the surface is deformable, the spatial pressure distribution within the contact region is dependent on object compliance, and hence information from cutaneous mechanoreceptors is sufficient for discrimination of subtle differences in compliance. When the surface is rigid, kinesthetic information is necessary for discrimination, and the discriminability is much poorer than that for objects with deformable surfaces.

Srinivasan, M. A.↗

DOE OSTI2016

Learning Weight Uncertainty with Stochastic Gradient MCMC for Shape Classification

Learning the representation of shape cues in 2D & 3D objects for recognition is a fundamental task in computer vision. Deep neural networks (DNNs) have shown promising performance on this task. Due to the large variability of shapes, accurate recognition relies on good estimates of model uncertainty, ignored in traditional training of DNNs, typically learned via stochastic optimization. This paper leverages recent advances in stochastic gradient Markov Chain Monte Carlo (SG-MCMC) to learn weight uncertainty in DNNs. It yields principled Bayesian interpretations for the commonly used Dropout/DropConnect techniques and incorporates them into the SG-MCMC framework. Extensive experiments on 2D & 3D shape datasets and various DNN models demonstrate the superiority of the proposed approach over stochastic optimization. Our approach yields higher recognition accuracy when used in conjunction with Dropout and Batch-Normalization.

convolutional neural network↗

DOE OSTI2016

A unified free-form representation applied to the shape optimization of the hohlraum with octahedral 6 laser entrance holes

The hohlraum is very crucial for indirect laser driven Inertial Confinement Fusion. Usually, its shape is designed as sphere, cylinder, or rugby with some kind of fixed functions, such as ellipse or parabola. Recently, a spherical hohlraum with octahedral 6 laser entrance holes (LEHs) has been presented with high flux symmetry [Lan et al., Phys. Plasmas 21, 010704 (2014); 21, 052704 (2014)]. However, there is only one shape parameter, i.e., the hohlraum to capsule radius ratio, being optimized. In this paper, we build the hohlraum with octahedral 6LEHs with a unified free-form representation, in which, by varying additional shape parameters: (1) available hohlraum shapes can be uniformly and accurately represented, (2) it can be used to understand why the spherical hohlraum has higher flux symmetry, (3) it allows us to obtain a feasible shape design field satisfying flux symmetry constraints, and (4) a synthetically optimized hohlraum can be obtained with a tradeoff of flux symmetry and other hohlraum performance. Finally, the hohlraum with octahedral 6LEHs is modeled, analyzed, and then optimized based on the unified free-form representation. The results show that a feasible shape design field with flux asymmetry no more than 1% can be obtained, and over the feasible design field, the spherical hohlraum is validated to have the highest flux symmetry, and a synthetically optimal hohlraum can be found with closing flux symmetry but larger volume between laser spots and centrally located capsule.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

A symbolic framework to obtain mid-fidelity models of flexible multibody systems with application to horizontal-axis wind turbines

Abstract. The article presents a symbolic framework (also called computer algebra program) that is used to obtain, in symbolic mathematical form, the linear and nonlinear equations of motion of a mid-fidelity multibody system including rigid and flexible bodies. Our approach is based on Kane's method and a nonlinear shape function representation for flexible bodies. The shape function approach does not represent the state of the art for flexible multibody dynamics but is an effective trade-off to obtain mid-fidelity models with few degrees of freedom, taking advantage of the separation of space and time. The method yields compact symbolic equations of motion with implicit account of the constraints. The general and automatic framework facilitates the creation and manipulation of models with various levels of complexity by adding or removing degrees of freedom. The symbolic treatment allows for analytical gradients and linearized equations of motion. The linear and nonlinear equations can be exported to Python code or dedicated software. There are multiple applications, such as time domain simulation, stability analyses, frequency domain analyses, advanced controller design, state observers, and digital twins. In this article, we describe the method we used to systematically generate the equations of motion of multibody systems and present the implementation of the framework using the Python package SymPy. We apply the framework to generate illustrative land-based and offshore wind turbine models. We compare our results with OpenFAST simulations and discuss the advantages and limitations of the method. The Python implementation is provided as an open-source project.

Branlard, Emmanuel (ORCID:0000000277506128)↗

DOE OSTI2023

Off-axis representation of hyperbolic mirror shapes for X-ray beamlines

Mirror-centered, closed-form expressions for hyperbolic surfaces used in X-ray beamlines have been derived. Hyperbolic mirrors create a virtual focus or source point and can be used to lengthen or shorten the effective focal distance of a compound optical system. The derivations here express off-axis segments of a hyperbolic surface in terms of the real and virtual focal distances and the incident glancing angle at the center of the mirror. Conventional mathematical expressions of hyperbolic shapes describe the surfaces in Cartesian or polar coordinates centered on an axis of symmetry, necessitating cumbersome rotation and translation to mirror-centered coordinates. The representation presented here, with zero slope and the origin at the central point, is most convenient for modeling, metrology, aberration correction, and general surface analysis of off-axis configurations. The direct derivation avoids the need for nested coordinate transforms. A series expansion provides a helpful approximation; the coefficients of the implicit equation are also provided.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2011

Exact solution for a noncentral electric dipole ring-shaped potential in the tridiagonal representation

The Schroedinger equation with noncentral electric dipole ring-shaped potential is investigated by working in a complete square integrable basis that supports an infinite tridiagonal matrix representation of the wave operator. The three-term recursion relations for the expansion coefficients of both the angular and radial wavefunctions are presented. The discrete spectrum for the bound states is obtained by the diagonalization of the radial recursion relation. Some potential applications of this system in different fields are discussed.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Separable shape tensors for aerodynamic design

Airfoil shape design is a classical problem in engineering and manufacturing. In this work, we combine principled physics-based considerations for the shape design problem with modern computational techniques using a data-driven approach. Modern and traditional analyses of two-dimensional (2D) and three-dimensional (3D) aerodynamic shapes reveal a flow-based sensitivity to specific deformations that can be represented generally by affine transformations (rotation, scaling, shearing, and translation). We present a novel representation of shapes that decouples affine-style deformations over a submanifold and a product submanifold principally of the Grassmannian. As an analytic generative model, the separable representation, informed by a database of physically relevant airfoils, offers: (i) a rich set of novel 2D airfoil deformations not previously captured in the data, (ii) an improved low-dimensional parameter domain for inferential statistics informing design/manufacturing, and (iii) consistent 3D blade representation and perturbation over a sequence of nominal 2D shapes.

42 ENGINEERING↗

DOE OSTI2023

G2Aero: A Python package for separable shape tensors

G2Aero is a Python package for the design and deformation of discrete planar curves and tubular surfaces using a geometric data-driven approach. G2Aero utilizes a topology of product manifolds: the Grassmannian, $\mathcal{G}$($\mathcal{n}$, 2) - the set of 2-dimensional subspaces in $\mathbb{R}$ $\mathcal{n}$ - and the symmetric positive-definite (SPD) manifold, $\mathcal{S}^{2}_{++}$ - the set of 2x2 SPD matrices. The package provides a novel framework for representing separable deformations to shapes, which consist of stretching, scaling, rotating, and translating - also known as affine deformations - and a set of complementary deformations - which we refer to as undulation-type deformations. We focus on airfoil and blade design applications to emphasize the utility of the methods in an environment where the separation of affine and undulation-type deformations is critical. Notable functionalities of the framework for blade design include: 1) generating novel 2D (airfoil) shapes informed by a database of physically relevant airfoils, 2) building 3D blades by interpolating sequences of 2D airfoil cross-sections, and 3) generating blades with consistent perturbations along the blade span. We discuss the framework and provide examples in the context of wind energy applications, specifically wind turbine blade design. Figure 1 shows the wire frame obtained by interpolating airfoils defining the IEA 15-MW wind turbine blade and applying affine transformations corresponding to twist, chordal scaling, and bending. This, and all other figures in the paper, can be reproduced following examples and referencing supporting documentation provided in the G2Aero package.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2007

Validation and Determination of Ice Water Content - Radar Reflectivity Relationships during CRYSTAL-FACE: Flight Requirements for Future Comparisons

In order for clouds to be more accurately represented in global circulation models (GCM), there is need for improved understanding of the properties of ice such as the total water in ice clouds, called ice water content (IWC), ice particle sizes and their shapes. Improved representation of clouds in models will enable GCMs to better predict for example, how changes in emissions of pollutants affect cloud formation and evolution, upper tropospheric water vapor, and the radiative budget of the atmosphere that is crucial for climate change studies. An extensive cloud measurement campaign called CRYSTAL-FACE was conducted during Summer 2002 using instrumented aircraft and a variety of instruments to measure properties of ice clouds. This paper deals with the measurement of IWC using the Harvard water vapor and total water instruments on the NASA WB-57 high-altitude aircraft. The IWC is measured directly by these instruments at the altitude of the WB-57, and it is compared with remote measurements from the Goddard Cloud Radar System (CRS) on the NASA ER-2. CRS measures vertical profiles of radar reflectivity from which IWC can be estimated at the WB-57 altitude. The IWC measurements obtained from the Harvard instruments and CRS were found to be within 20-30% of each other. Part of this difference was attributed to errors associated with comparing two measurements that are not collocated in time an space since both aircraft were not in identical locations. This study provides some credibility to the Harvard and CRS-derived IWC measurements that are in general difficult to validate except through consistency checks using different measurement approaches.

Sayres, D. S.↗

NASA NTRS2008

A Faceted Shape Model Approach to Altimetry and Velocimetry for Irregularly Shaped Bodies

Range and velocity sensors based on lidar or radar with multiple beams are often used to measure the altitude and velocity, respectively, of a spacecraft above a targetbody. A difficulty that arises when navigating about small bodies such as asteroids or comets, is that the notion of altitude is largely obscured by the irregular shape of the target surface. This paper develops a method to incorporate the multibeam altimeter and Doppler velocimeter measurements into the on-board spacecraft state estimator by using information from a faceted shape model representation of the target body surface.

state estimation↗

DOE OSTI2020

Development of a Convolutional Neural Network Classifier for Data Starved Spectra - 20199

The Institute for Clean Energy Technology (ICET) at Mississippi State University is exploring the utility of machine learning in augmenting its mobile radiation surveying platforms, which are currently being developed as means to survey depleted uranium contaminated areas in support of remediation and decommissioning efforts. Mobile survey platforms provide a means to efficiently scan large areas of interest while reducing human exposure to radiation and other hazards. The survey platforms can also be used for scanning for any gamma emitting isotope in addition to depleted uranium. The spectral data that the platforms collect may be data starved with relatively low counts and poorly defined spectral features depending on the speed of the platforms and scintillation detector selection. Such data-starved spectra are difficult to use for isotope identification, requiring advanced knowledge of the possible radionuclides that could be present and environmental factors that could attenuate signals or introduce background noise. These factors in combination with the volume of survey data increases the time it takes to perform analysis of survey data when the source type is unknown. There are a number of algorithms in the field of machine learning that can be used to classify data that would be challenging and time-consuming for a human to identify. Supervised machine learning algorithms train models based on extensive amounts of human-labeled training data. Once sufficiently trained, these models can be used to quickly make high-fidelity predictions on new data. Convolutional neural networks are machine learning algorithms that excel in learning representations of 'shapes'. They do this by taking numerical input data and convolving them with spatial feature detectors referred to as filters. These filters are incrementally adjusted to reduce the prediction error on the data during the backpropagation step of training. Discussed in this paper is the development of a convolutional neural network classifier (CNNC) that can utilize spectral survey data for source discrimination and isotope identification. Bench-top laboratory experiments data using LaBr{sub 3}(Ce) scintillation detectors were used to train and evaluate the performance of the developed CNNC. The CNNC is capable of discriminating a variety of gamma emitting source types, differentiating different forms of uranium (depleted vs. natural), and estimating the amount of uranium for a known geometry. The discussed CNNC may be useful in scenarios where survey systems are deployed in situations where hazardous radioactive material maybe present, but the type is unknown. When used in remediation applications the CNNC can be used to screen-out false positives, helping reduce remediation costs. (authors)

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2016

PERIODIC ORBIT FAMILIES IN THE GRAVITATIONAL FIELD OF IRREGULAR-SHAPED BODIES

The discovery of binary and triple asteroids in addition to the execution of space missions to minor celestial bodies in the past several years have focused increasing attention on periodic orbits around irregular-shaped celestial bodies. In the present work, we adopt a polyhedron shape model for providing an accurate representation of irregular-shaped bodies and employ the model to calculate their corresponding gravitational and effective potentials. We also investigate the characteristics of periodic orbit families and the continuation of periodic orbits. We prove a fact, which provides a conserved quantity that permits restricting the number of periodic orbits in a fixed energy curved surface about an irregular-shaped body. The collisions of Floquet multipliers are maintained during the continuation of periodic orbits around the comet 1P/Halley. Multiple bifurcations in the periodic orbit families about irregular-shaped bodies are also discussed. Three bifurcations in the periodic orbit family have been found around the asteroid 216 Kleopatra, which include two real saddle bifurcations and one period-doubling bifurcation.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

Comment on “Shape transition of unstrained flattest single-walled carbon nanotubes under pressure” [J. Appl. Phys. 115, 044512 (2014)]

Recently, Mu et al. [J. Appl. Phys. 115, 044512 (2014)] have developed an analytic approach to describe some special shapes of a single-wall carbon nanotube (SWCNT) under hydrostatic pressure. These authors have found approximate analytic expressions for the parametric equations of the tube cross section profile and its curvature at the convex-to-concave transition pressure using a shell-like 2D continuum model describing the shapes of such nanotubes. In this comment, we provide additional insight into this problem taking into account the exact analytic representation of the shapes that a SWCNT attains when subjected to hydrostatic pressure according to the very same continuum model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Method for simultaneous characterization and expansion of reference libraries for small molecule identification

A variational autoencoder (VAE) has been developed to learn a continuous numerical, or latent, representation of molecular structure to expand reference libraries for small molecule identification. The VAE has been extended to include a chemical property decoder, trained as a multitask network, to shape the latent representation such that it assembles according to desired chemical properties. The approach is unique in its application to metabolomics and small molecule identification, focused on properties that are obtained from experimental measurements (m/z, CCS) paired with its training paradigm, which involves a cascade of transfer learning iterations. First, molecular representation is learned from a large dataset of structures with m/z labels. Next, in silico property values are used to continue training. Finally, the network is further refined by being trained with the experimental data. The trained network is used to predict chemical properties directly from structure and generate candidate structures with desired chemical properties. The network is extensible to other training data and molecular representations, and for use with other analytical platforms, for both chemical property and feature prediction as well as molecular structure generation.

Colby, Sean M.↗

DOE OSTI2020

Deep learning to generate in silico chemical property libraries and candidate molecules for small molecule identification in complex samples

Comprehensive and unambiguous identification of small molecules in complex samples will revolutionize our understanding of the role of metabolites in biological systems. Existing and emerging technologies have enabled measurement of chemical properties of molecules in complex mixtures and, in concert, are sensitive enough to resolve even stereoisomers. Despite these experimental advances, small molecule identification is inhibited by (i) chemical reference libraries (e.g. mass spectra, collision cross section, and other measurable property libraries) representing <1% of known molecules, limiting the number of possible identifications, and (ii) the lack of a method to generate candidate matches directly from experimental features (i.e. without a library). To this end, we developed a variational autoencoder (VAE) to learn a continuous numerical, or latent, representation of molecular structure to expand reference libraries for small molecule identification. We extended the VAE to include a chemical property decoder, trained as a multitask network, in order to shape the latent representation such that it assembles according to desired chemical properties. The approach is unique in its application to metabolomics and small molecule identification, with its focus on properties that can be obtained from experimental measurements (m/z, CCS) paired with its training paradigm, which involved a cascade of transfer learning iterations. First, molecular representation is learned from a large dataset of structures with m/z labels. Next, in silico property values are used to continue training, as experimental property data is limited. Finally, the network is further refined by being trained with the experimental data. This allows the network to learn as much as possible at each stage, enabling success with progressively smaller datasets without overfitting. Once trained, the network can be used to predict chemical properties directly from structure, as well as generate candidate structures with desired chemical properties. Our approach is orders of magnitude faster than first-principles simulation for CCS property prediction. Additionally, the ability to generate novel molecules along manifolds, defined by chemical property analogues, positions DarkChem as highly useful in a number of application areas, including metabolomics and small molecule identification, drug discovery and design, chemical forensics, and beyond.

Colby, Sean M.↗