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All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

Multivariate Methods for Prediction of Geologic Sample Composition with Laser-Induced Breakdown Spectroscopy

Laser-induced breakdown spectroscopy (LIBS) uses pulses of laser light to ablate a material from the surface of a sample and produce an expanding plasma. The optical emission from the plasma produces a spectrum which can be used to classify target materials and estimate their composition. The ChemCam instrument on the Mars Science Laboratory (MSL) mission will use LIBS to rapidly analyze targets remotely, allowing more resource- and time-intensive in-situ analyses to be reserved for targets of particular interest. ChemCam will also be used to analyze samples that are not reachable by the rover's in-situ instruments. Due to these tactical and scientific roles, it is important that ChemCam-derived sample compositions are as accurate as possible. We have compared the results of partial least squares (PLS), multilayer perceptron (MLP) artificial neural networks (ANNs), and cascade correlation (CC) ANNs to determine which technique yields better estimates of quantitative element abundances in rock and mineral samples. The number of hidden nodes in the MLP ANNs was optimized using a genetic algorithm. The influence of two data preprocessing techniques were also investigated: genetic algorithm feature selection and averaging the spectra for each training sample prior to training the PLS and ANN algorithms. We used a ChemCam-like laboratory stand-off LIBS system to collect spectra of 30 pressed powder geostandards and a diverse suite of 196 geologic slab samples of known bulk composition. We tested the performance of PLS and ANNs on a subset of these samples, choosing to focus on silicate rocks and minerals with a loss on ignition of less than 2 percent. This resulted in a set of 22 pressed powder geostandards and 80 geologic samples. Four of the geostandards were used as a validation set and 18 were used as the training set for the algorithms. We found that PLS typically resulted in the lowest average absolute error in its predictions, but that the optimized MLP ANN and the CC ANN often gave results comparable to PLS. Averaging the spectra for each training sample and/or using feature selection to choose a small subset of wavelengths to use for predictions gave mixed results, with degraded performance in some cases and similar or slightly improved performance in other cases. However, training time was significantly reduced for both PLS and ANN methods by implementing feature selection, making this a potentially appealing method for initial, rapid-turn-around analyses necessary for Chemcam's tactical role on MSL. Choice of training samples has a strong influence on the accuracy of predictions. We are currently investigating the use of clustering algorithms (e.g. k-means, neural gas, etc.) to identify training sets that are spectrally similar to the unknown samples that are being predicted, and therefore result in improved predictions

Morris, Richard↗
NASA NTRS2010

Preliminary Multivariable Cost Model for Space Telescopes

Parametric cost models are routinely used to plan missions, compare concepts and justify technology investments. Previously, the authors published two single variable cost models based on 19 flight missions. The current paper presents the development of a multi-variable space telescopes cost model. The validity of previously published models are tested. Cost estimating relationships which are and are not significant cost drivers are identified. And, interrelationships between variables are explored

Stahl, H. Philip↗
NASA NTRS2009

A Multivariate Randomization Text of Association Applied to Cognitive Test Results

Randomization tests provide a conceptually simple, distribution-free way to implement significance testing. We have applied this method to the problem of evaluating the significance of the association among a number (k) of variables. The randomization method was the random re-ordering of k-1 of the variables. The criterion variable was the value of the largest eigenvalue of the correlation matrix.

Ahumada, Albert↗
NASA NTRS2011

Development of a Multivariable Parametric Cost Analysis for Space-Based Telescopes

Over the past 400 years, the telescope has proven to be a valuable tool in helping humankind understand the Universe around us. The images and data produced by telescopes have revolutionized planetary, solar, stellar, and galactic astronomy and have inspired a wide range of people, from the child who dreams about the images seen on NASA websites to the most highly trained scientist. Like all scientific endeavors, astronomical research must operate within the constraints imposed by budget limitations. Hence the importance of understanding cost: to find the balance between the dreams of scientists and the restrictions of the available budget. By logically analyzing the data we have collected for over thirty different telescopes from more than 200 different sources, statistical methods, such as plotting regressions and residuals, can be used to determine what drives the cost of telescopes to build and use a cost model for space-based telescopes. Previous cost models have focused their attention on ground-based telescopes due to limited data for space telescopes and the larger number and longer history of ground-based astronomy. Due to the increased availability of cost data from recent space-telescope construction, we have been able to produce and begin testing a comprehensive cost model for space telescopes, with guidance from the cost models for ground-based telescopes. By separating the variables that effect cost such as diameter, mass, wavelength, density, data rate, and number of instruments, we advance the goal to better understand the cost drivers of space telescopes.. The use of sophisticated mathematical techniques to improve the accuracy of cost models has the potential to help society make informed decisions about proposed scientific projects. An improved knowledge of cost will allow scientists to get the maximum value returned for the money given and create a harmony between the visions of scientists and the reality of a budget.

Dollinger, Courtnay↗
NASA NTRS2005

Self-Organizing-Map Program for Analyzing Multivariate Data

SOM_VIS is a computer program for analysis and display of multidimensional sets of Earth-image data typified by the data acquired by the Multi-angle Imaging Spectro-Radiometer [MISR (a spaceborne instrument)]. In SOM_VIS, an enhanced self-organizing-map (SOM) algorithm is first used to project a multidimensional set of data into a nonuniform three-dimensional lattice structure. The lattice structure is mapped to a color space to obtain a color map for an image. The Voronoi cell-refinement algorithm is used to map the SOM lattice structure to various levels of color resolution. The final result is a false-color image in which similar colors represent similar characteristics across all its data dimensions. SOM_VIS provides a control panel for selection of a subset of suitably preprocessed MISR radiance data, and a control panel for choosing parameters to run SOM training. SOM_VIS also includes a component for displaying the false-color SOM image, a color map for the trained SOM lattice, a plot showing an original input vector in 36 dimensions of a selected pixel from the SOM image, the SOM vector that represents the input vector, and the Euclidean distance between the two vectors.

Li, P. Peggy↗
NASA NTRS2012

Using Statistical Multivariable Models to Understand the Relationship Between Interplanetary Coronal Mass Ejecta and Magnetic Flux Ropes

In-situ measurements of interplanetary coronal mass ejections (ICMEs) display a wide range of properties. A distinct subset, "magnetic clouds" (MCs), are readily identifiable by a smooth rotation in an enhanced magnetic field, together with an unusually low solar wind proton temperature. In this study, we analyze Ulysses spacecraft measurements to systematically investigate five possible explanations for why some ICMEs are observed to be MCs and others are not: i) An observational selection effect; that is, all ICMEs do in fact contain MCs, but the trajectory of the spacecraft through the ICME determines whether the MC is actually encountered; ii) interactions of an erupting flux rope (PR) with itself or between neighboring FRs, which produce complex structures in which the coherent magnetic structure has been destroyed; iii) an evolutionary process, such as relaxation to a low plasma-beta state that leads to the formation of an MC; iv) the existence of two (or more) intrinsic initiation mechanisms, some of which produce MCs and some that do not; or v) MCs are just an easily identifiable limit in an otherwise corntinuous spectrum of structures. We apply quantitative statistical models to assess these ideas. In particular, we use the Akaike information criterion (AIC) to rank the candidate models and a Gaussian mixture model (GMM) to uncover any intrinsic clustering of the data. Using a logistic regression, we find that plasma-beta, CME width, and the ratio O(sup 7) / O(sup 6) are the most significant predictor variables for the presence of an MC. Moreover, the propensity for an event to be identified as an MC decreases with heliocentric distance. These results tend to refute ideas ii) and iii). GMM clustering analysis further identifies three distinct groups of ICMEs; two of which match (at the 86% level) with events independently identified as MCs, and a third that matches with non-MCs (68 % overlap), Thus, idea v) is not supported. Choosing between ideas i) and iv) is more challenging, since they may effectively be indistinguishable from one another by a single in-situ spacecraft. We offer some suggestions on how future studies may address this.

Riley, P.↗
NASA NTRS2013

A Framework for Robust Multivariable Optimization of Integrated Circuits in Space Applications

Application Specific Integrated Circuit (ASIC) design for space applications involves multiple challenges of maximizing performance, minimizing power and ensuring reliable operation in extreme environments. This is a complex multidimensional optimization problem which must be solved early in the development cycle of a system due to the time required for testing and qualification severely limiting opportunities to modify and iterate. Manual design techniques which generally involve simulation at one or a small number of corners with a very limited set of simultaneously variable parameters in order to make the problem tractable are inefficient and not guaranteed to achieve the best possible results within the performance envelope defined by the process and environmental requirements. What is required is a means to automate design parameter variation, allow the designer to specify operational constraints and performance goals, and to analyze the results in a way which facilitates identifying the tradeoffs defining the performance envelope over the full set of process and environmental corner cases. The system developed by the Mixed Signal ASIC Group (MSAG) at the Goddard Space Flight Center is implemented as framework of software modules, templates and function libraries. It integrates CAD tools and a mathematical computing environment, and can be customized for new circuit designs with only a modest amount of effort as most common tasks are already encapsulated. Customization is required for simulation test benches to determine performance metrics and for cost function computation. Templates provide a starting point for both while toolbox functions minimize the code required. Once a test bench has been coded to optimize a particular circuit, it is also used to verify the final design. The combination of test bench and cost function can then serve as a template for similar circuits or be re-used to migrate the design to different processes by re-running it with the new process specific device models. The system has been used in the design of time to digital converters for laser ranging and time-of-flight mass spectrometry to optimize analog, mixed signal and digital circuits such as charge sensitive amplifiers, comparators, delay elements, radiation tolerant dual interlocked (DICE) flip-flops and two of three voter gates.

DuMonthier, Jeffrey↗
NASA NTRS2013

An Alternative Flight Software Trigger Paradigm: Applying Multivariate Logistic Regression to Sense Trigger Conditions using Inaccurate or Scarce Information

In late 2014, NASA will fly the Orion capsule on a Delta IV-Heavy rocket for the Exploration Flight Test-1 (EFT-1) mission. For EFT-1, the Orion capsule will be flying with a new GPS receiver and new navigation software. Given the experimental nature of the flight, the flight software must be robust to the loss of GPS measurements. Once the high-speed entry is complete, the drogue parachutes must be deployed within the proper conditions to stabilize the vehicle prior to deploying the main parachutes. When GPS is available in nominal operations, the vehicle will deploy the drogue parachutes based on an altitude trigger. However, when GPS is unavailable, the navigated altitude errors become excessively large, driving the need for a backup barometric altimeter. In order to increase overall robustness, the vehicle also has an alternate method of triggering the drogue parachute deployment based on planet-relative velocity if both the GPS and the barometric altimeter fail. However, this velocity-based trigger results in large altitude errors relative to the targeted altitude. Motivated by this challenge, this paper demonstrates how logistic regression may be employed to automatically generate robust triggers based on statistical analysis. Logistic regression is used as a ground processor pre-flight to develop a classifier. The classifier would then be implemented in flight software and executed in real-time. This technique offers excellent performance even in the face of highly inaccurate measurements. Although the logistic regression-based trigger approach will not be implemented within EFT-1 flight software, the methodology can be carried forward for future missions and vehicles.

Smith, Kelly M.↗
NASA NTRS2013

Robust Multivariable Optimization and Performance Simulation for ASIC Design

Application-specific-integrated-circuit (ASIC) design for space applications involves multiple challenges of maximizing performance, minimizing power, and ensuring reliable operation in extreme environments. This is a complex multidimensional optimization problem, which must be solved early in the development cycle of a system due to the time required for testing and qualification severely limiting opportunities to modify and iterate. Manual design techniques, which generally involve simulation at one or a small number of corners with a very limited set of simultaneously variable parameters in order to make the problem tractable, are inefficient and not guaranteed to achieve the best possible results within the performance envelope defined by the process and environmental requirements. What is required is a means to automate design parameter variation, allow the designer to specify operational constraints and performance goals, and to analyze the results in a way that facilitates identifying the tradeoffs defining the performance envelope over the full set of process and environmental corner cases. The system developed by the Mixed Signal ASIC Group (MSAG) at the Goddard Space Flight Center is implemented as a framework of software modules, templates, and function libraries. It integrates CAD tools and a mathematical computing environment, and can be customized for new circuit designs with only a modest amount of effort as most common tasks are already encapsulated. Customization is required for simulation test benches to determine performance metrics and for cost function computation.

DuMonthier, Jeffrey↗
NASA NTRS2013

An Alternative Flight Software Trigger Paradigm: Applying Multivariate Logistic Regression to Sense Trigger Conditions Using Inaccurate or Scarce Information

In late 2014, NASA will fly the Orion capsule on a Delta IV-Heavy rocket for the Exploration Flight Test-1 (EFT-1) mission. For EFT-1, the Orion capsule will be flying with a new GPS receiver and new navigation software. Given the experimental nature of the flight, the flight software must be robust to the loss of GPS measurements. Once the high-speed entry is complete, the drogue parachutes must be deployed within the proper conditions to stabilize the vehicle prior to deploying the main parachutes. When GPS is available in nominal operations, the vehicle will deploy the drogue parachutes based on an altitude trigger. However, when GPS is unavailable, the navigated altitude errors become excessively large, driving the need for a backup barometric altimeter to improve altitude knowledge. In order to increase overall robustness, the vehicle also has an alternate method of triggering the parachute deployment sequence based on planet-relative velocity if both the GPS and the barometric altimeter fail. However, this backup trigger results in large altitude errors relative to the targeted altitude. Motivated by this challenge, this paper demonstrates how logistic regression may be employed to semi-automatically generate robust triggers based on statistical analysis. Logistic regression is used as a ground processor pre-flight to develop a statistical classifier. The classifier would then be implemented in flight software and executed in real-time. This technique offers improved performance even in the face of highly inaccurate measurements. Although the logistic regression-based trigger approach will not be implemented within EFT-1 flight software, the methodology can be carried forward for future missions and vehicles.

Smith, Kelly M.↗
NASA NTRS2013

An Alternative Flight Software Paradigm: Applying Multivariate Logistic Regression to Sense Trigger Conditions using Inaccurate or Scarce Information

In late 2014, NASA will fly the Orion capsule on a Delta IV-Heavy rocket for the Exploration Flight Test-1 (EFT-1) mission. For EFT-1, the Orion capsule will be flying with a new GPS receiver and new navigation software. Given the experimental nature of the flight, the flight software must be robust to the loss of GPS measurements. Once the high-speed entry is complete, the drogue parachutes must be deployed within the proper conditions to stabilize the vehicle prior to deploying the main parachutes. When GPS is available in nominal operations, the vehicle will deploy the drogue parachutes based on an altitude trigger. However, when GPS is unavailable, the navigated altitude errors become excessively large, driving the need for a backup barometric altimeter to improve altitude knowledge. In order to increase overall robustness, the vehicle also has an alternate method of triggering the parachute deployment sequence based on planet-relative velocity if both the GPS and the barometric altimeter fail. However, this backup trigger results in large altitude errors relative to the targeted altitude. Motivated by this challenge, this paper demonstrates how logistic regression may be employed to semi-automatically generate robust triggers based on statistical analysis. Logistic regression is used as a ground processor pre-flight to develop a statistical classifier. The classifier would then be implemented in flight software and executed in real-time. This technique offers improved performance even in the face of highly inaccurate measurements. Although the logistic regression-based trigger approach will not be implemented within EFT-1 flight software, the methodology can be carried forward for future missions and vehicles

Smith, Kelly↗
NASA NTRS2014

Multivariate Dynamical Modeling to Investigate Human Adaptation to Space Flight: Initial Concepts

The array of physiological changes that occur when humans venture into space for long periods presents a challenge to future exploration. The changes are conventionally investigated independently, but a complete understanding of adaptation requires a conceptual basis founded in intergrative physiology, aided by appropriate mathematical modeling. NASA is in the early stages of developing such an approach.

Shelhamer, Mark↗
NASA NTRS2014

Multivariate Dynamic Modeling to Investigate Human Adaptation to Space Flight: Initial Concepts

The array of physiological changes that occur when humans venture into space for long periods presents a challenge to future exploration. The changes are conventionally investigated independently, but a complete understanding of adaptation requires a conceptual basis founded in integrative physiology, aided by appropriate mathematical modeling. NASA is in the early stages of developing such an approach.

Shelhamer, Mark↗