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Results for “procrustes”

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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7 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Robust and optimal alignment of high-dimensional data using maximum likelihood estimation through a random sample consensus framework

Abstract Correcting spatial orientations of groups of high-dimensional data sets such that they are all in a consistent coordinate system is often a time-consuming and error-prone process. Automation of this process can be accomplished by using Generalized Procrustes Analysis to estimate the relative orientations among a population of high-dimensional data sets. A least squares Procrustes solution is applied through a maximum likelihood estimation and random sample consensus framework for robustness. The likelihood model is comprised of a mixture distribution where inliers are modeled using t -distribution and outliers from a uniform distribution. Applications will focus on a synthetic data set that emulates triaxial acceleration data and also real shock data from a population of triaxial accelerometers. Outliers represent either non-rigid body responses, environmental noise, and/or sensor and data acquisition issues. The intended application for the methodology is to robustly automate the rotation of populations of experimentally collected triaxial accelerometer data sets to a single global coordinate system.

LOSAC↗
NASA NTRS1999

30 Years of Wahba's Problem

This article discusses a problem proposed by Grace Wahba: Find the orthogonal matrix A with determinant +1 that minimizes the loss function L(A) is identical with the 1/2(summation from i( a(sub i) * absolute value of (b(sub i)- Ar(sub i))squared). where {b(sub i)} is a set of unit vectors measured in a spacecraft's body frame, {r(sub i)} e the corresponding unit vectors in a reference frame and {a(sub i) are non-negative weights). The orthogonal Procrustes problem is to find the orthogonal matrix A that is closest to B in the sense of the Fobenius norm, so that Wahba's Problem is equivalent to the orthogonal Procrustes problem with the provision that the determinant of A must be +1. The article reviews various solutions to this problem and the implementations of the various solutions.

Markley, F. Landis↗
DOE OSTI2024

Antarctic lake viromes reveal potential virus associated influences on nutrient cycling in ice-covered lakes

The McMurdo Dry Valleys (MDVs) of Antarctica are a mosaic of extreme habitats which are dominated by microbial life. The MDVs include glacial melt holes, streams, lakes, and soils, which are interconnected through the transfer of energy and flux of inorganic and organic material via wind and hydrology. For the first time, we provide new data on the viral community structure and function in the MDVs through metagenomics of the planktonic and benthic mat communities of Lakes Bonney and Fryxell. Viral taxonomic diversity was compared across lakes and ecological function was investigated by characterizing auxiliary metabolic genes (AMGs) and predicting viral hosts. Our data suggest that viral communities differed between the lakes and among sites: these differences were connected to microbial host communities. AMGs were associated with the potential augmentation of multiple biogeochemical processes in host, most notably with phosphorus acquisition, organic nitrogen acquisition, sulfur oxidation, and photosynthesis. Viral genome abundances containing AMGs differed between the lakes and microbial mats, indicating site specialization. Using procrustes analysis, we also identified significant coupling between viral and bacterial communities (p = 0.001). Finally, host predictions indicate viral host preference among the assembled viromes. Collectively, our data show that: (i) viruses are uniquely distributed through the McMurdo Dry Valley lakes, (ii) their AMGs can contribute to overcoming host nutrient limitation and, (iii) viral and bacterial MDV communities are tightly coupled.

Microbiology↗
NASA NTRS1989

Expansion and orthogonalization of measured modes for structure identification

The purpose was to investigate a new simultaneous expansion/orthogonalization method in comparison with two previously published expansion methods and a widely used orthogonalization technique. Each expansion method uses data from an analytical model of the structure to complete the estimate of the mode shape vectors. Berman and Nagy used Guyan expansion in their work with improving analytical models. In this method, modes are expanded one at a time, producing a set not orthogonal with respect to the mass matrix. Baruch and Bar Itzhack's optimal orthogonalization procedure was used to subsequently adjust the expanded modes. A second expansion technique was presented by O'Callahan, Avitabile, and Reimer and separately by Kammer. Again, modes are expanded individually and orthogonalized after expansion with the same optimal technique as above. Finally, a simultaneous expansion/orthogonalization method was developed from the orthogonal Procrustes problem of computational mathematics. In this method modes are optimally expanded as a set and orthogonal with respect to the mass matrix as a result. Two demonstation problems were selected for the comparison of the methods described. The first problem is an 8 degree of freedom spring-mass problem first presented by Kabe. Several conditions were examined for expansion method including the presence of errors in the measured data and in the analysis models. As a second demonstration problem, data from tests of laboratory scale model truss structures was expanded for system identification. Tests with a complete structure produced a correlated analysis model and the stiffness and mass matrices. Tests of various damaged configurations produced measured data for 6 modes at 14 dof locations.

Smith, Suzanne Weaver↗
NASA NTRS1990

Simultaneous expansion and orthogonalization of measured modes for structure identification

Tests of large structures on-orbit will be performed with measurements at a relatively few structure points. Values for the unmeasured degrees of freedom (dofs) can be estimated based on measured dofs and analytical model dynamic information. These 'expanded' mode shapes are useful for optimal-update identification and damage location as well as test/analysis correlation. A new method of expansion for test mode shape vectors is developed from the orthogonal Procrustes problem from computational linear algebra. A subspace defined by the set of measured dofs is compared to a subspace defined by mode shapes from an analytical model of the structure. The method simultaneously expands and orthogonalizes the mode shape vectors. Two demonstration problems are used to compare the new method to current expansion techniques. One demonstration uses test data from a laboratory scale-model truss structure. Performance of the new method is comparable or superior to that of the previous expansion methods which require separate orthogonalization.

Smith, Suzanne Weaver↗
NASA NTRS2000

Spacecraft Attitude Determination Methods

This document is presentation in viewgraph form, which outlines the methods of determining spacecraft attitude. The presentation reviews several parameterizations relating to spacecraft attitude, such as Euler's Theorem, Rodriques parameters, and Euler-Rodriques parameters or Quaternion. Onboard attitude determination is the norm, using either single frame or filtering methods. The presentation reviews several mathematical representations of attitude. The mechanisms for determining attitude on board the Hubble Space Telescope, the Tropical Rainfall and Measuring Mission and the Solar Anomalous and Magnetospheric Particle Explorer are reviewed. Wahba's problem, Procrustes Problem, and some solutions are also summarized.

Markley, F. Landis↗
NASA NTRS2003

Coordinated turn-and-reach movements. II. Planning in an external frame of reference

The preceding study demonstrated that normal subjects compensate for the additional interaction torques generated when a reaching movement is made during voluntary trunk rotation. The present paper assesses the influence of trunk rotation on finger trajectories and on interjoint coordination and determines whether simultaneous turn-and-reach movements are most simply described relative to a trunk-based or an external reference frame. Subjects reached to targets requiring different extents of arm joint and trunk rotation at a natural pace and quickly in normal lighting and in total darkness. We first examined whether the larger interaction torques generated during rapid turn-and-reach movements perturb finger trajectories and interjoint coordination and whether visual feedback plays a role in compensating for these torques. These issues were addressed using generalized Procrustes analysis (GPA), which attempts to overlap a group of configurations (e.g., joint trajectories) through translations and rotations in multi-dimensional space. We first used GPA to identify the mean intrinsic patterns of finger and joint trajectories (i.e., their average shape irrespective of location and orientation variability in the external and joint workspaces) from turn-and-reach movements performed in each experimental condition and then calculated their curvatures. We then quantified the discrepancy between each finger or joint trajectory and the intrinsic pattern both after GPA was applied individually to trajectories from a pair of experimental conditions and after GPA was applied to the same trajectories pooled together. For several subjects, joint trajectories but not finger trajectories were more curved in fast than slow movements. The curvature of both joint and finger trajectories of turn-and-reach movements was relatively unaffected by the vision conditions. Pooling across speed conditions significantly increased the discrepancy between joint but not finger trajectories for most subjects, indicating that subjects used different patterns of interjoint coordination in slow and fast movements while nevertheless preserving the shape of their finger trajectory. Higher movement speeds did not disrupt the arm joint rotations despite the larger interaction torques generated. Rather, subjects used the redundant degrees of freedom of the arm/trunk system to achieve similar finger trajectories with differing joint configurations. We examined finger movement patterns and velocity profiles to determine the frame of reference in which turn-and-reach movements could be most simply described. Finger trajectories of turn-and-reach movements had much larger curvatures and their velocity profiles were less smooth and less bell-like in trunk-based coordinates than in external coordinates. Taken together, these results support the conclusion that turn-and-reach movements are controlled in an external frame of reference.

NASA Discipline Neuroscience↗