Search NASA⌕ Search

SEARCH · Search NASA

Results for “Geometric Transformation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 289 records · Page 16

Geometric aspects in digital analysis of Multi-Spectral Scanner (MSS) data

Present automated systems of interpretation which apply pattern recognition techniques on MSS data do not fully consider the geometry of the acquisition system. In an effort to improve the usefulness of the MSS data when digitally treated, geometric aspects are analyzed and discussed. Attempts to correct for scanner instabilities in position and orientation by affine and polynomial transformations, as well as by modified collinearity equations are described. Methods of accounting for panoramic and relief effects are also discussed. It is anticipated that reliable area as well as position determinations can be accomplished during the process of automatic interpretation. A concept for a unified approach to the treatment of remote sensing data, both metric and nonmetric is presented.

Mikhail, E. M.↗

Curved Finite Elements and Curve Approximation

The approximation of parameterized curves by segments of parabolas that pass through the endpoints of each curve segment arises naturally in all quadratic isoparametric transformations. While not as popular as cubics in curve design problems, the use of parabolas allows the introduction of a geometric measure of the discrepancy between given and approximating curves. The free parameters of the parabola may be used to optimize the fit, and constraints that prevent overspill and curve degeneracy are introduced. This leads to a constrained optimization problem in two varibles that can be solved quickly and reliably by a simple method that takes advantage of the special structure of the problem. For applications in the field of computer-aided design, the given curves are often cubic polynomials, and the coefficient may be calculated in closed form in terms of polynomial coefficients by using a symbolic machine language so that families of curves can be approximated with no further integration. For general curves, numerical quadrature may be used, as in the implementation where the Romberg quadrature is applied. The coefficient functions C sub 1 (gamma) and C sub 2 (gamma) are expanded as polynomials in gamma, so that for given A(s) and B(s) the integrations need only be done once. The method was used to find optimal constrained parabolic approximation to a wide variety of given curves.

Baart, M. L.↗

Role of geometric dynamic recrystallization in nanocrystalline alloys

Nanocrystalline and near-nano-grained metals are plagued with an overall lack of ductility and formability. This is in part due to their inability to support the dislocation mechanisms or undergo the same types of transformations that conventional coarse-grained metals access in order to increase their workability. Therefore, despite their advanced properties such as high strength, the manufacturing of such fine-grained metals, which exposes them to multi-axial states of stress in operations such as rolling, drawing, extrusion, forging, and bending, has not been possible. In this work, we address this limitation and highlight an important aspect of geometric dynamic recrystallization (GDRX) in nanocrystalline materials as a way to improve manufacturability. In particular, using two different alloy compositions and two different processing techniques, this study points to the fact that if nanocrystalline or near nano metals can be truly stabilized, they can repeatedly undergo the same types of processes that conventional coarse-grained metals endure, increasing both their formability and hence manufacturability. The results reveal that due to a large number of initial high-angle grain boundaries and large applied compressive strains, GDRX is activated in the absence of any discontinuous dynamic recrystallization (DDRX) or continuous dynamic recrystallization (CDRX). This is a unique aspect of stabilized nanocrystalline materials, as traditionally fine-grained metals are not microstructurally stable enough to accommodate such an event.

36 MATERIALS SCIENCE↗

Three-dimensional super line-localization in low signal-to-noise microscope images via prior-apprised unsupervised learning (PAUL)

Biological processes such as processive enzyme turnover and intracellular cargo tracking involve the dynamic motion of a small "article" along a curvilinear biopolymer track. To understand these processes that occur across multiple length and time scales, one must acquire both the trajectory of the particle and the position of the track along which it moves, possibly by combining high-resolution single-particle tracking with conventional microscopy. Yet, usually there is a significant resolution mismatch between these modalities: while the tracked particle is localized with a precision of 10 nm, the image of the surroundings is limited by optical difraction, with 200 nm lateral and 500 nm axial resolutions. Compared to the particle's trajectory, the surrounding curvilinear structure appears as a blurred and noisy image. This disparity in the spatial resolutions of the particle trajectory and the surrounding curvilinear structure image makes data reconstruction, as well as interpretation, particularly challenging. Analysis is further complicated when the curvilinear structures are oriented arbitrarily in 3D space. Here, we present a prior-apprised unsupervised learning (PAUL) approach to extract information from 3D images where the underlying features resemble a curved line such as a filament or microtubule. This three-stage framework starts with a Hessian-based feature enhancement, which is followed by feature registration, where local line segments are detected on repetitively sampled subimage tiles. In the final stage, statistical learning, segments are clustered based on their geometric relationships. Principal curves are then approximated from each segment group via statistical tools including principal component analysis, bootstrap and kernel transformation. This procedure is characterized on simulated images, where sub-voxel medium deviations from true curves have been achieved. The 3D PAUL approach has also been implemented for successful line localization in experimental 3D images of gold nanowires obtained using a multifocal microscope. Lastly, this work not only bridges the resolution gap between two microscopy modalities, but also allows us to conduct 3D super line-localization imaging experiments, without using super-resolution techniques.

42 ENGINEERING↗

Bi-resampled data study

The results of an experimental study conducted to determine the geometric and radiometric effects of double resampling (bi-resampling) performed on image data in the process of performing map projection transformations are reported.

Benner, R.↗

Development of computerized analysis for solid propellant combustion (ISAP-2)

This report is an improvement of ISAP-1, SRB Vorticity-Acoustic Coupled Instability Analysis, September 1986. Included in this report are the automatic generation of all input data for grid configuration, boundary conditions for coupled acoustic and vortical field calculations, transformation of all dimensions to a parametric form, resulting in flexibility for the user to define the size of the problem (geometric configurations) with reduction in storage (15 to 65%) and computer run-time (50 to 75%). Additional research is required for the following areas: (1) turbulence effects; (2) nonlinear wave oscillations; and (3) chemistry upon combustion instability.

Chung, T. J.↗

Application of Least-Squares Adjustment Technique to Geometric Camera Calibration and Photogrammetric Flow Visualization

Flow visualization produces data in the form of two-dimensional images. If the optical components of a camera system are perfect, the transformation equations between the two-dimensional image and the three-dimensional object space are linear and easy to solve. However, real camera lenses introduce nonlinear distortions that affect the accuracy of transformation unless proper corrections are applied. An iterative least-squares adjustment algorithm is developed to solve the nonlinear transformation equations incorporated with distortion corrections. Experimental applications demonstrate that a relative precision on the order of 40,000 is achievable without tedious laboratory calibrations of the camera.

Chen, Fang-Jenq↗

A Fourier transform method for Vsin i estimations under nonlinear Limb-Darkening laws

Star rotation offers us a large horizon for the study of many important physical issues pertaining to stellar evolution. Currently, four methods are widely used to infer rotation velocities, namely those related to line width calibrations, on the fitting of synthetic spectra, interferometry, and on Fourier transforms (FTs) of line profiles. Almost all of the estimations of stellar projected rotation velocities using the Fourier method in the literature have been addressed with the use of linear limb-darkening (LD) approximations during the evaluation of rotation profiles and their cosine FTs, which in certain cases, lead to discrepant velocity estimates. In this work, we introduce new mathematical expressions of rotation profiles and their Fourier cosine transforms assuming three nonlinear LD laws—quadratic, square-root, and logarithmic—and study their applications with and without gravity-darkening (GD) and geometrical flattening (GF) effects. Through an analysis of He I models in the visible range accounting for both limb and GD, we find out that, for classical models without rotationally driven effects, all the Vsin i values are too close to each other. On the other hand, taking into account GD and GF, the Vsin i obtained with the linear law result in Vsin i values that are systematically smaller than those obtained with the other laws. As a rule of thumb, we apply these expressions to the FT method to evaluate the projected rotation velocity of the emission B-type star Achernar (α Eri).

79 ASTRONOMY AND ASTROPHYSICS↗

A phase-field model for non-isothermal phase transformation and plasticity in polycrystalline yttria-stabilized tetragonal zirconia

Here we propose an elastoplastic phase-field (PF) model to investigate the mechanics of tetragonal-to-monoclinic phase transformation (TMPT) and elastoplastic deformation of polycrystalline yttria-stabilized tetragonal zirconia (YSTZ). A Landau polynomial with non-vanishing chemical energy at the equilibrium temperature is introduced to account for the actual formation energies of the phases. The effects of different grain orientations, latent heat, and temperature on TMPT and deformation mechanisms are considered. The suppressive transformation effects of the grain boundaries (GBs) is modeled using an inhomogeneous kinetic coefficient in the bulk and GBs. The simulation results for single crystals demonstrate the capability of the model to reproduce the orientation-dependent compressive deformation of YSTZ similar to atomistic simulations and micropillar experiments. The single crystal with [100] crystallographic orientation along the loading direction (SC[100]) displays both TMPT and plasticity, SC[101] experiences only phase transformation, while SC[001] undergoes only plastic yielding. The TMPT induced by compressive loading exhibits shape memory effect (SME) below the equilibrium transformation temperature and pseudoelasticity above it, while the critical transformation stress increases with increasing loading temperature. The irrecoverable plastic strain is found to trap a part of the monoclinic phase, which prevents a complete reverse transformation. The polycrystalline cases also display SME and PE at low and high temperatures, respectively. Due to the orientation differences between grains and the stress concentrations at geometric nonlinearities, plastic deformation occurs in polycrystalline YSTZ for an applied load less than the yield stress. The results suggest a possible limitation of plasticity and an improvement of the shape recovery of YSTZ if one can control the orientation of the grains and/or increase the density of stacking faults at the GBs during material processing.

36 MATERIALS SCIENCE↗

A FFT-based numerical implementation of mesoscale field dislocation mechanics: Application to two-phase laminates

In this study, we present an enhanced crystal plasticity elasto-viscoplastic fast Fourier transform (EVPFFT) formulation coupled with a phenomenological Mesoscale Field Dislocation Mechanics (MFDM) theory here named MFDM-EVPFFT formulation. In contrast with classic CP-EVPFFT, the model is able to tackle plastic flow and hardening due to polar dislocation density distributions or geometrically necessary dislocations (GNDs) in addition to statistically stored dislocations (SSDs). The model also considers GND mobility through a GND density evolution law numerically solved with a recently developed filtered spectral approach, which is here coupled with stress equilibrium. The discrete Fourier transform method combined with finite differences is applied to solve both lattice incompatibility and Lippmann-Schwinger equations in an augmented Lagrangian numerical scheme. Numerical results are presented for two-phase laminate composites with plastic channels and elastic second phase. It is shown that both GND densities and slip constraint at phase boundaries influence the overall and local hardening behavior. In contrast with the CP-EVPFFT formulation, a channel size effect is predicted on the shear flow stress with the present MFDM-EVPFFT formulation. The size effect originates from the progressive formation of continuous screw GND pile-ups from phase boundaries to the channel center. The effect of GND mean free path on local and global responses is also examined for the two-phase composite.

36 MATERIALS SCIENCE↗

Uncertainty Quantification Techniques for Population Density Estimates Derived from Sparse Open Source Data

The Population Density Tables (PDT) project at the Oak Ridge National Laboratory (www.ornl.gov) is developing population density estimates for specific human activities under normal patterns of life based largely on information available in open source. Currently, activity based density estimates are based on simple summary data statistics such as range and mean. Researchers are interested in improving activity estimation and uncertainty quantification by adopting a Bayesian framework that considers both data and sociocultural knowledge. Under a Bayesian approach knowledge about population density may be encoded through the process of expert elicitation. Due to the scale of the PDT effort which considers over 250 countries, spans 40 human activity categories, and includes numerous contributors, an elicitation tool is required that can be operationalized within an enterprise data collection and reporting system. Such a method would ideally require that the contributor have minimal statistical knowledge, require minimal input by a statistician or facilitator, consider human difficulties in expressing qualitative knowledge in a quantitative setting, and provide methods by which the contributor can appraise whether their understanding and associated uncertainty was well captured. This paper introduces an algorithm that transforms answers to simple, non-statistical questions into a bivariate Gaussian distribution as the prior for the Beta distribution. Based on geometric properties of the Beta distribution parameter feasibility space and the bivariate Gaussian distribution, an automated method for encoding is developed that responds to these challenging enterprise requirements. Though created within the context of population density, this approach may be applicable to a wide array of problem domains requiring informative priors for the Beta distribution.

Bayesian↗

Transformational part-count in layered octahedral-tetrahedral truss configurations

The number of component part (nodes, struts and panels) termed part count, is an important factor in the design, manufacture, and assembly of modular space structures. Part count expressions are presented for a variety of profiles derived from the layered octahedral-tetrahedral truss configuration. Referred to as the tetrahedral truss in the NASA projects, this specific geometry has been used in several missions. The general expressions presented here transforms to others as one profile changes to another. Such transformational part count relations provide a measure of flexibility and generality, and may be useful when dealing with a wider range of geometric configurations.

Lalvani, Haresh↗

Initial study of Schroedinger eigenmaps for spectral target detection

Spectral target detection refers to the process of searching for a specific material with a known spectrum over a large area containing materials with different spectral signatures. Traditional target detection methods in hyperspectral imagery (HSI) require assuming the data fit some statistical or geometric models and based on the model, to estimate parameters for defining a hypothesis test, where one class (i.e., target class) is chosen over the other classes (i.e., background class). Nonlinear manifold learning methods such as Laplacian eigenmaps (LE) have extensively shown their potential use in HSI processing, specifically in classification or segmentation. Recently, Schroedinger eigenmaps (SE), which is built upon LE, has been introduced as a semisupervised classification method. In SE, the former Laplacian operator is replaced by the Schroedinger operator. The Schroedinger operator includes by definition, a potential term V that steers the transformation in certain directions improving the separability between classes. In this regard, we propose a methodology for target detection that is not based on the traditional schemes and that does not need the estimation of statistical or geometric parameters. This method is based on SE, where the potential term V is taken into consideration to include the prior knowledge about the target class and use it to steer the transformation in directions where the target location in the new space is known and the separability between target and background is augmented. An initial study of how SE can be used in a target detection scheme for HSI is shown here. Inscene pixel and spectral signature detection approaches are presented. Finally, the HSI data used comprise various target panels for testing simultaneous detection of multiple objects with different complexities.

97 MATHEMATICS AND COMPUTING↗

Fiber-Coupled Substrate-Integrated Hollow Waveguides: An Innovative Approach to Mid-infrared Remote Gas Sensors

Here, in this study, an innovative approach based on fiberoptically coupled substrate-integrated hollow waveguide (iHWG) gas cells for the analysis of low sample volumes suitable for remote broad- and narrow-band mid-infrared (MIR; 2.5–20 μm) sensing applications is reported. The feasibility of remotely addressing iHWG gas cells, configured in a double-pass geometry via a reflector, by direct coupling to a 7-around-1 mid-infrared fiber bundle is demonstrated, facilitating low-level hydrocarbon gas analysis. For comparison studies, two iHWGs with substrate dimensions of 50 × 50 × 12 mm (L × W × H) and geometric channel lengths of 138 and 58.5 mm, serving as miniature light-guiding gas cells, were fiber-coupled to a Fourier transform infrared spectrometer enabling broadband MIR sensing. In addition to the fundamental feasibility of this concept, the achievable sensitivity toward several gaseous hydrocarbons and the reproducibility of assembling the fiber-iHWG interface were investigated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Real-time observation of nanoscale topological transitions in epitaxial PbTe/CdTe heterostructures

The almost completely immiscible PbTe/CdTe heterostructure has recently become a prototype system for self-organized quantum dot formation based on solid-state phase separation. Here, we study by real-time transmission electron microscopy the topological transformations of two-dimensional PbTe-epilayers into, first, a quasi-one-dimensional percolation network and subsequently into zero-dimensional quantum dots. Finally, the dot size distribution coarsens by Ostwald ripening. The whole transformation sequence occurs during all stages in the fully coherent solid state by bulk diffusion. A model based on the numerical solution of the Cahn-Hilliard equation reproduces all relevant morphological and dynamic aspects of the experiments, demonstrating that this standard continuum approach applies to coherent solids down to nanometer dimensions. As the Cahn-Hilliard equation does not depend on atomistic details, the observed morphological transformations are general features of the model. To confirm the topological nature of the observed shape transitions, we developed a parameter-free geometric model. This, together with the Cahn-Hilliard approach, is in qualitative agreement with the experiments.

36 MATERIALS SCIENCE↗

Implementation of an algorithm for cylindrical object identification using range data

One of the problems in 3-D object identification and localization is addressed. In robotic and navigation applications the vision system must be able to distinguish cylindrical or spherical objects as well as those of other geometric shapes. An algorithm was developed to identify cylindrical objects in an image when range data is used. The algorithm incorporates the Hough transform for line detection using edge points which emerge from a Sobel mask. Slices of the data are examined to locate arcs of circles using the normal equations of an over-determined linear system. Current efforts are devoted to testing the computer implementation of the algorithm. Refinements are expected to continue in order to accommodate cylinders in various positions. A technique is sought which is robust in the presence of noise and partial occlusions.

Bozeman, Sylvia T.↗

A multiblock grid generation technique applied to a jet engine configuration

Techniques are presented for quickly finding a multiblock grid for a 2D geometrically complex domain from geometrical boundary data. An automated technique for determining a block decomposition of the domain is explained. Techniques for representing this domain decomposition and transforming it are also presented. Further, a linear optimization method may be used to solve the equations which determine grid dimensions within the block decomposition. These algorithms automate many stages in the domain decomposition and grid formation process and limit the need for human intervention and inputs. They are demonstrated for the meridional or throughflow geometry of a bladed jet engine configuration.

Stewart, Mark E. M.↗

The Porous Microstructure Analysis (PuMA) software

The open-source Porous Microstructure Analysis (PuMA) software was implemented to offer an efficient framework for determining material characteristics from 3D microstructures. Its development was inspired by progress in X-ray microtomography, an imaging technology that captures the internal structure of materials in 3D, and even in a 4D temporal context. Over recent years, this method has transformed the domain of materials science due to its capability to non-destructively examine material microstructures while presenting digital data about their geometrical details. It has provided insights into materials relevant to several NASA missions, including heatshields, parachute fabrics, meteorites, and other advanced composites. PuMA, in its current version 3, delivers an array of features, spanning from basic geometric insights of a microstructure to intricate anisotropic thermo-elastic and chemical behavior. Specifically, the software evaluates morphological attributes (specific surface area, volume fractions, mean intercept lengths, orientation) and physical characteristics (conductivity, elasticity, permeability, and tortuosity). Additionally, it can model material degradation processes, such as oxidation and surface chemistry interactions. The software can generate synthetic microstructures, from straightforward geometrical designs to intricate woven and non-woven geometries. Coupling material generation and characterization enable parametric studies and sensitivity analysis to optimize the microstructural performance and inform design decisions and reliability assessment based on uncertainty quantification. A recent addition to PuMA includes the TomoSAM plugin, devised to incorporate the cutting-edge Segment Anything Model (SAM). SAM is a promptable deep learning model that can identify objects and create image masks in a zero-shot manner, based only on a few user clicks. The synergy between these tools aids in the segmentation of complex 3D datasets from tomography or other imaging techniques, which would otherwise require a laborious manual segmentation process.

Tomography↗