Ranking problems in multivariate normal /statistical/ populations Final report, 1 Jul. 1966 - 30 Jun. 1967
Theory and solutions for ranking problems in multivariate normal statistical populations
STATISTICAL ANALYSIS↗
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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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Conic sectors for sampled-data feedback systems
The conic-sector analysis of the closed-loop stability and robustness of a multivariable-analog-system controller based on sampled-data feedback compensation is investigated. Conic sectors and sampled-data feedback systems are defined, and the existence of a conic sector containing a sampled-data operator is established mathematically. An example is presented to prove that the conic sector is computable and gives sufficient conditions of closed-loop stability. A procedure for determining sampled-data-operator gain is also derived.
Thompson, P. M.↗
Analysis of fault-tolerant neurocontrol architectures
The fault-tolerance of analog parallel distributed implementations of a multivariable aircraft neurocontroller is analyzed by simulating weight and neuron failures in a simplified scheme of analog processing based on the functional architecture of the ETANN chip (Electrically Trainable Artificial Neural Network). The neural information processing is found to be only partially distributed throughout the set of weights of the neurocontroller synthesized with the backpropagation algorithm. Although the degree of distribution of the neural processing, and consequently the fault-tolerance of the neurocontroller, could be enhanced using Locally Distributed Weight and Neuron Approaches, a satisfactory level of fault-tolerance could only be obtained by retraining the degrated VLSI neurocontroller. The possibility of maintaining neurocontrol performance and stability in the presence of single weight of neuron failures was demonstrated through an automated retraining procedure of the neurocontroller based on a pre-programmed choice and sequence of the training parameters.
Troudet, T.↗
Partial Least Squares and Neural Networks for Quantitative Calibration of Laser-induced Breakdown Spectroscopy (LIBs) of Geologic Samples
The ChemCam instrument [1] on the Mars Science Laboratory (MSL) rover will be used to obtain the chemical composition of surface targets within 7 m of the rover using Laser Induced Breakdown Spectroscopy (LIBS). ChemCam analyzes atomic emission spectra (240-800 nm) from a plasma created by a pulsed Nd:KGW 1067 nm laser. The LIBS spectra can be used in a semiquantitative way to rapidly classify targets (e.g., basalt, andesite, carbonate, sulfate, etc.) and in a quantitative way to estimate their major and minor element chemical compositions. Quantitative chemical analysis from LIBS spectra is complicated by a number of factors, including chemical matrix effects [2]. Recent work has shown promising results using multivariate techniques such as partial least squares (PLS) regression and artificial neural networks (ANN) to predict elemental abundances in samples [e.g. 2-6]. To develop, refine, and evaluate analysis schemes for LIBS spectra of geologic materials, we collected spectra of a diverse set of well-characterized natural geologic samples and are comparing the predictive abilities of PLS, cascade correlation ANN (CC-ANN) and multilayer perceptron ANN (MLP-ANN) analysis procedures.
Anderson, R. B.↗
Chemistry imaging and distribution analysis of rare earth elements in coal using LIBS and LA-ICP-MS instruments
Currently, demand for rare earth elements (REEs) increased significantly. Coal is actively evaluated as potential economic sources for extraction of REEs. Here, in this work, laser-induced breakdown spectroscopy (LIBS) was evaluated for rapid estimation of REEs content and their distribution in the natural coal samples. The results were compared with similar laser ablation–inductively coupled plasma–mass spectrometry (LA-ICP-MS) measurements. Thirteen coal samples (nine standard samples and five natural samples) were used in this study. Powder samples were pressed into pellets while coal chunks were directly ablated for data recording. Pellets of the powder standard samples were used to optimize the data acquisition system and then data recorded with this optimized system was used to identify the proper data acquisition and analysis models. After establishing the proper data acquisition system and analysis model using the standard samples, natural coal samples in powder form and their chunks were utilized to record LIBS and LA-ICP-MS spectra. Multivariate calibration models were developed using four of the natural samples, which were evaluated by predicting the REE content in the fifth sample. Principal component analysis was performed on the LIBS data obtained from the natural samples and it classified all the samples with high accuracy. Two-dimensional (2D) elemental mapping on coal chunk samples was also performed using both LIBS and LA-ICP-MS to study the distribution of REEs in the samples. The resulting elemental images and their correlations can be used to infer mineral distributions.
01 COAL, LIGNITE, AND PEAT↗
Dynamics and control of forward swept wing aircraft
Aspects of non-zero differential game theory with application to multivariable control synthesis and optimal linear control law design using optimum parameter sensitivity analysis are discussed.
Schmidt, D. K.↗
Variable Order and Distributed Order Fractional Operators
Many physical processes appear to exhibit fractional order behavior that may vary with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. This paper develops the concept of variable and distributed order fractional operators. Definitions based on the Riemann-Liouville definitions are introduced and behavior of the operators is studied. Several time domain definitions that assign different arguments to the order q in the Riemann-Liouville definition are introduced. For each of these definitions various characteristics are determined. These include: time invariance of the operator, operator initialization, physical realization, linearity, operational transforms. and memory characteristics of the defining kernels. A measure (m2) for memory retentiveness of the order history is introduced. A generalized linear argument for the order q allows the concept of "tailored" variable order fractional operators whose a, memory may be chosen for a particular application. Memory retentiveness (m2) and order dynamic behavior are investigated and applications are shown. The concept of distributed order operators where the order of the time based operator depends on an additional independent (spatial) variable is also forwarded. Several definitions and their Laplace transforms are developed, analysis methods with these operators are demonstrated, and examples shown. Finally operators of multivariable and distributed order are defined in their various applications are outlined.
Lorenzo, Carl F.↗
Nonparametric analysis of Minnesota spruce and aspen tree data and LANDSAT data
The application of nonparametric methods in data-intensive problems faced by NASA is described. The theoretical development of efficient multivariate density estimators and the novel use of color graphics workstations are reviewed. The use of nonparametric density estimates for data representation and for Bayesian classification are described and illustrated. Progress in building a data analysis system in a workstation environment is reviewed and preliminary runs presented.
Scott, D. W.↗
Using foreground/background analysis to determine leaf and canopy chemistry
Spectral Mixture Analysis (SMA) has become a well established procedure for analyzing imaging spectrometry data, however, the technique is relatively insensitive to minor sources of spectral variation (e.g., discriminating stressed from unstressed vegetation and variations in canopy chemistry). Other statistical approaches have been tried e.g., stepwise multiple linear regression analysis to predict canopy chemistry. Grossman et al. reported that SMLR is sensitive to measurement error and that the prediction of minor chemical components are not independent of patterns observed in more dominant spectral components like water. Further, they observed that the relationships were strongly dependent on the mode of expressing reflectance (R, -log R) and whether chemistry was expressed on a weight (g/g) or are basis (g/sq m). Thus, alternative multivariate techniques need to be examined. Smith et al. reported a revised SMA that they termed Foreground/Background Analysis (FBA) that permits directing the analysis along any axis of variance by identifying vectors through the n-dimensional spectral volume orthonormal to each other. Here, we report an application of the FBA technique for the detection of canopy chemistry using a modified form of the analysis.
Pinzon, J. E.↗
Accelerating Multivariate Functional Approximation Computation with Domain Decomposition Techniques⋆
Modeling large datasets through Multivariate Functional Approximations (MFA) provide an elegant way to handle many visualization and scientific analysis workflows. The process necessitates scalable data partitioning methods to compute MFA representations efficiently without compromising the accuracy or continuity of the reconstructed solution. We propose a domain -decomposed method for computing the MFA with B -spline bases, which reduces the total work per task and uses a restricted Additive Schwarz (RAS) method to converge the control point data degrees -of -freedom along subdomain boundaries. We provide an in-depth analysis of the parallel approach with domain decomposition solvers, aiming to minimize local subdomain error residuals and recover high -order continuity at subdomain interfaces with appropriate choices of knot overlaps. The communication cost, determined by the overlap regions in the RAS implementation, is optimized to recover the numerical error profile of the single subdomain case. Our proposed method stands in contrast to previous methods, which typically only recover either C 0 or at best C 1 continuity for arbitrary B -spline degree expansions, or those that require post -processing to blend discontinuities in the reconstructed data. We demonstrate the effectiveness of our approach using analytical and real -world datasets in 1D, 2D, and 3D through both strong and weak scaling studies. The performance results indicate that the overall cost of computing the approximation is directly proportional to the underlying nearest -neighbor communication implementation, and is only weakly dependent on the overlap region size that determines the size of the messages. This finding underscores the efficiency and scalability of our proposed method, making it a promising solution for handling large datasets in scientific workflows.
additive Schwarz solvers↗
Functional Groups Based on Leaf Physiology: Are they Spatially and Temporally Robust?
The functional grouping hypothesis, which suggests that complexity in function can be simplified by grouping species with similar responses, was tested in the Florida scrub habitat. Functional groups were identified based on how species in fire maintained FL scrub function in terms of carbon, water and nitrogen dynamics. The suite of physiologic parameters measured to determine function included both instantaneous gas exchange measurements obtained from photosynthetic light response curves and integrated measures of function. Using cluster analysis, five distinct physiologically-based functional groups were identified. Using non-parametric multivariate analyses, it was determined that these five groupings were not altered by plot differences or by the three different management regimes; prescribed burn, mechanically treated and burn, and fire-suppressed. The physiological groupings also remained robust between the two years 1999 and 2000. In order for these groupings to be of use for scaling ecosystem processes, there needs to be an easy-to-measure morphological indicator of function. Life form classifications were able to depict the physiological groupings more adequately than either specific leaf area or leaf thickness. THe ability of life forms to depict the groupings was improved by separating the parasitic Ximenia americana from the shrub category.
Foster, Tammy E.↗
Visualization for Insight and Data Analysis in Energy Research
This talk explores how advanced visualization technologies are transforming analytical reasoning and knowledge discovery in energy research, drawing on recent work at the National Laboratory of the Rockies' Computational Science Center. Through a series of scientific case studies, we demonstrate how immersive and high-resolution visualization environments enable scientists and engineers to identify previously unseen patterns and features - insights that often remain hidden in traditional desktop-based analysis. By embedding richer information into interactive analytics tools, these approaches support the exploration of complex, multivariate parameter spaces, where interaction itself catalyzes understanding. Beyond capability, we emphasize the critical role of visualization design grounded in perception and cognition, showing how visual encodings directly influence analytical outcomes. Spanning applications from materials science to integrated energy systems, these visualization approaches accelerate innovation and improve decision-making by enabling deeper, more reliable insight into increasingly complex energy data.
97 MATHEMATICS AND COMPUTING↗
LinkWinds: An Approach to Visual Data Analysis
The Linked Windows Interactive Data System (LinkWinds) is a prototype visual data exploration and analysis system resulting from a NASA/JPL program of research into graphical methods for rapidly accessing, displaying and analyzing large multivariate multidisciplinary datasets. It is an integrated multi-application execution environment allowing the dynamic interconnection of multiple windows containing visual displays and/or controls through a data-linking paradigm. This paradigm, which results in a system much like a graphical spreadsheet, is not only a powerful method for organizing large amounts of data for analysis, but provides a highly intuitive, easy to learn user interface on top of the traditional graphical user interface.
Jacobson, Allan S.↗
Astronaut Preflight Cardiovascular Variables Associated with Vascular Compliance are Highly Correlated with Post-Flight Eye Outcome Measures in the Visual Impairment Intracranial Pressure (VIIP) Syndrome Following Long Duration Spaceflight
The detection of the first VIIP case occurred in 2005, and adequate eye outcome measures were available for 31 (67.4%) of the 46 long duration US crewmembers who had flown on the ISS since its first crewed mission in 2000. Therefore, this analysis is limited to a subgroup (22 males and 9 females). A "cardiovascular profile" for each astronaut was compiled by examining twelve individual parameters; eleven of these were preflight variables: systolic blood pressure, pulse pressure, body mass index, percentage body fat, LDL, HDL, triglycerides, use of anti‐lipid medication, fasting serum glucose, and maximal oxygen uptake in ml/kg. Each of these variables was averaged across three preflight annual physical exams. Astronaut age prior to the long duration mission, and inflight salt intake was also included in the analysis. The group of cardiovascular variables for each crew member was compared with seven VIIP eye outcome variables collected during the immediate post‐flight period: anterior-posterior axial length of the globe measured by ultrasound and optical biometry; optic nerve sheath diameter, optic nerve diameter, and optic nerve to sheath ratio‐ each measured by ultrasound and magnetic resonance imaging (MRI), intraocular pressure (IOP), change in manifest refraction, mean retinal nerve fiber layer (RNFL) on optical coherence tomography (OCT), and RNFL of the inferior and superior retinal quadrants. Since most of the VIIP eye outcome measures were added sequentially beginning in 2005, as knowledge of the syndrome improved, data were unavailable for 22.0% of the outcome measurements. To address the missing data, we employed multivariate multiple imputation techniques with predictive mean matching methods to accumulate 200 separate imputed datasets for analysis. We were able to impute data for the 22.0% of missing VIIP eye outcomes. We then applied Rubin's rules for collapsing the statistical results across our 200 multiply imputed data sets to assess the canonical correlation between the eye outcomes and the twelve astronaut cardiovascular variables available for all 31 subjects. Results: A highly significant canonical correlation was observed among the canonical solutions (p<.00001), with an average best canonical correlation of.97. The results suggest a strong association between astronauts' measures of cardiovascular health and the seven eye outcomes of the VIIP syndrome used in this analysis. Furthermore, the "joint test" revealed a significant difference in cardiovascular profile between male and female astronauts (Prob > F = 0.00001). Overall, female astronauts demonstrated a significantly healthier cardiovascular status. Individually, the female astronauts had significantly healthier profiles on seven of twelve cardiovascular variables than the men (p values ranging from <0.0001 to <0.05). Male astronauts did not demonstrate significantly healthier values on any of the twelve cardiovascular variables measured
Otto, Christian↗
A computer analysis of ERTS data of the Lake Gregory area of South Australia with particular emphasis on its role in terrain classification for engineering
A digital computer and multivariate statistical techniques were used to analyze 4-band multispectral data. A representation of the original data for each of the four bands allows a certain degree of terrain interpretation; however, variations in appearance of sites within and between bands, without additional criteria for deciding which representation should be preferred, create difficulties for classification. Investigation of the video data groups produced by principal components analysis and cluster analysis techniques shows that effective correlations with classifications of terrain produced by conventional methods could be carried out. The analyses also highlighted underlying relationships between the various elements. The approach used allows large areas (185 cm by 185 cm) to be classified into fundamental units within a matter of hours and can be applied to those parts of the Earth where facilities for conventional studies are poor or lacking.
Lodwick, G. D.↗
Reflectance of vegetation, soil, and water
There are no author-identified significant results in this report. This report deals with the selection of the best channels from the 24-channel aircraft data to represent crop and soil conditions. A three-step procedure has been developed that involves using univariate statistics and an F-ratio test to indicate the best 14 channels. From the 14, the 10 best channels are selected by a multivariate stochastic process. The third step involves the pattern recognition procedures developed in the data analysis plan. Indications are that the procedures in use are satsifactory and will extract the desired information from the data.
Wiegand, C. L.↗
Techniques for assessment of flexible space structure control performance
Several multivariable concepts are presently applied to both the open-loop and closed-loop analysis of a wrap-rib antenna space structure. After evaluating the alternative placements of sensors and actuators by means of controllability, observability, and transmission-zero concepts, the linear quadratic gaussian/loop transfer recovery method is used to synthesize a control law for suppression of the transient vibrations that are typically encountered during maneuvers. The integration of these techniques and associated computer programs into a larger spacecraft design system is also discussed.
Rowell, Lawrence F.↗
Technology Assessments within NASA's Integrated Technology Assessment Center
NASA's Advanced Space Transportation Program (ASTP) founded the Integrated Technology Assessment Center (ITAC) to provide a comprehensive, systematic approach to identify long-term technology needs, to quantify payoffs for technology investments, and to assess the progress of ASTP-sponsored technology programs in the hypersonics/Earth-to-orbit area. To accomplish these goals, the ITAC has assembled an experienced team representing a broad sector of the aerospace community and developed a systematic assessment process complete with supporting tools. In the ITAC approach, concepts for transportation systems are first selected based on relevance to the ASTP. Models of these concepts are then developed and data on advanced technologies are collected. Projections of key technology characteristics with respect to the specific concepts of interest are made. Both the models and technology projections are then fed into the ITAC's probabilistic systems analysis framework. The probabilistic outputs are weighed against metrics of interest to ASTP and a multivariate decision making process is used to provide inputs for technology prioritization within the ASTP. At present, the ITAC program is working to evaluate a variety of technologies for three two-stage hypersonic vehicle concepts. Concepts include an all rocket, vertical take off-horizontal landing (VTHL) system, a horizontal take-off-horizontal landing (HTHL) RBCC-propelled first stage/all rocket second stage system, and an HTHL turbine-based first stage/all rocket second stage system. This paper will provide a status update of the ITAC program including current results and plans.
Taylor, J. L.↗