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Viewgraphs on a distributed system for visualizing and analyzing multivariate and multidisciplinary data are presented. Topics covered include: program objectives; and the linked windows interactive data system (LinkWinds).
Grand tours are a class of methods for visualizing multivariate data, or any finite set of points in n-space. The idea is to create an animation of data projections by moving a 2-dimensional projection plane through n-space. The path of planes used in the animation is chosen so that it becomes dense, that is, it comes arbitrarily close to any plane. One of the original inspirations for the grand tour was the experience of trying to comprehend an abstract sculpture in a museum. One tends to walk around the sculpture, viewing it from many different angles. A useful class of grand tours is based on the idea of continuously interpolating an infinite sequence of randomly chosen planes. Visiting randomly (more precisely: uniformly) distributed planes guarantees denseness of the interpolating path. In computer implementations, 2-dimensional orthogonal projections are specified by two 1-dimensional projections which map to the horizontal and vertical screen dimensions, respectively. Hence, a grand tour is specified by a path of pairs of orthonormal projection vectors. This paper describes an interpolation scheme for smoothly connecting two pairs of orthonormal vectors, and thus for constructing interpolating grand tours. The scheme is optimal in the sense that connecting paths are geodesics in a natural Riemannian geometry.
THe Linked Windows Interactive Data System (LinkWinds) is being developed with NASA support. The objective of this proposal is to adapt and apply that system in a complex network environment containing elements to be found by scientists working multidisciplinary teams on very large scale and distributed data sets. The proposed three year program will develop specific visualization and analysis tools, to be exercised locally and remotely in the LinkWinds environment, to demonstrate visual data analysis, interdisciplinary data analysis and cooperative and interactive televisualization and analysis of data by geographically separated science teams. These demonstrators will involve at least two science disciplines with the aim of producing publishable results.
The Linked Windows Interactive Data System (Link Winds) is being developed with NASA support. The objective of this proposal is to adapt and apply that system in a complex network environment containing elements to be found by scientists working multidisciplinary teams on very large scale and distributed data sets. The proposed three year program will develop specific visualization and analysis tools, to be exercised locally and remotely in the Link Winds environment, to demonstrate visual data analysis, interdisciplinary data analysis and cooperative and interactive televisualization and analysis of data by geographically separated science teams. These demonstrations will involve at least two science disciplines with the aim of producing publishable results.
Multivariable manual compensatory tracking experiments were carried out in order to determine typical strategies of the human operator and conditions for improvement of his performance if one of the visual displays of the tracking errors is supplemented by an auditory feedback. Because the tracking error of the system which is only visually displayed is found to decrease, but not in general that of the auditorally supported system, it was concluded that the auditory feedback unloads the visual system of the operator who can then concentrate on the remaining exclusively visual displays.
In previous papers we've shown how a well known data compression algorithm called Entropy-constrained Vector Quantization ( can be modified to reduce the size and complexity of very large, satellite data sets. In this paper, we descuss how to visualize and understand the content of such reduced data sets.
We present a study of the visualization of 3-D second order tensor fields and matrix data. The general problem of visualizing unsymmetric real or complex Hermitian second order tensor fields can be reduced to the simultaneous visualization of a real and symmetric second order tensor field and a real vector field. As opposed to the discrete iconic techniques commonly used in multivariate data visualization, the emphasis is on exploiting the mathematical properties of tensor fields in order to facilitate their visualization and to produce a continuous representation of the data. We focus on interactively sensing and exploring real and symmetric second order tensor data by generalizing the vector notion of streamline to the tensor concept of hyperstreamline. We stress the importance of a structural analysis of the data field analogous to the techniques of vector field topology extraction in order to obtain a unique and objective representation of second order tensor fields.
Advanced manufacturing creates increasingly complex objects with material compositions that are often difficult to characterize by a single modality. Our collaborating domain scientists are going beyond traditional methods by employing both X-ray and neutron computed tomography to obtain complementary representations expected to better resolve material boundaries. However, the use of two modalities creates its own challenges for visualization, requiring either complex adjustments of bimodal transfer functions or the need for multiple views. Together with experts in nondestructive evaluation, we designed a novel interactive bimodal visualization approach to create a combined view of the co-registered X-ray and neutron acquisitions of industrial objects. Using an automatic topological segmentation of the bivariate histogram of X-ray and neutron values as a starting point, the system provides a simple yet effective interface to easily create, explore, and adjust a bimodal visualization. Here, we propose a widget with simple brushing interactions that enables the user to quickly correct the segmented histogram results. Our semiautomated system enables domain experts to intuitively explore large bimodal datasets without the need for either advanced segmentation algorithms or knowledge of visualization techniques. We demonstrate our approach using synthetic examples, industrial phantom objects created to stress bimodal scanning techniques, and real-world objects, and we discuss expert feedback.
Detecting and analyzing complex patterns in multivariate time-series data is crucial for decision-making in urban and environmental system operations. However, challenges arise from the high dimensionality, intricate complexity, and interconnected nature of complex patterns, which hinder the understanding of their underlying physical processes. Existing AI methods often face limitations in interpretability, computational efficiency, and scalability, reducing their applicability in real-world scenarios. This paper proposes a novel visual analytics framework that integrates two generative AI models, Temporal Fusion Transformer (TFT) and Variational Autoencoders (VAEs), to reduce complex patterns into lower-dimensional latent spaces and visualize them in 2D using dimensionality reduction techniques such as PCA, t-SNE, and UMAP with DBSCAN. These visualizations, presented through coordinated and interactive views and tailored glyphs, enable intuitive exploration of complex multivariate temporal patterns, identifying patterns’ similarities and uncover their potential correlations for a better interpretability of the AI outputs. The framework is demonstrated through a case study on power grid signal data, where it identifies multi-label grid event signatures, including faults and anomalies with diverse root causes. Additionally, novel metrics and visualizations are introduced to validate the models and assess the performance, efficiency, and consistency of latent maps generated by VAE, which have been utilized in prior studies for latent space cartography and used as a benchmark in this study, and the emerging TFT architecture under various configurations. These analyses provide actionable insights for model parameter tuning and reliability improvements. Comparative results highlight that TFT achieves shorter run times and superior scalability to diverse time-series data shapes compared to VAE. This work advances fault diagnosis in multivariate time series, fostering explainable AI to support critical system operations.
Texture-based correspondence display is a methodology to display corresponding data elements in visual representations of complex multidimensional, multivariate data. Texture is utilized as a persistent medium to contain a visual representation model and as a means to create multiple renditions of data where color is used to identify correspondence. Corresponding data elements are displayed over a variety of visual metaphors in a normal rendering process without adding extraneous linking metadata creation and maintenance. The effectiveness of visual representation for understanding data is extended to the expression of the visual representation model in texture.
The Integrated Data Visualization and Virtual Reality Tool (IDVVRT) Phase II effort was for the design and development of an innovative Data Visualization Environment Tool (DVET) for NASA engineers and scientists, enabling them to visualize complex multidimensional and multivariate data in a virtual environment. The objectives of the project were to: (1) demonstrate the transfer and manipulation of standard engineering data in a virtual world; (2) demonstrate the effects of design and changes using finite element analysis tools; and (3) determine the training and engineering design and analysis effectiveness of the visualization system.
Space Policy Directive-1 has led to NASA partnerships with commercial entities on procurement which includes the development of the Human Landing System (HLS) [1]. With the goal of delivering human crew to the lunar surface by 2024, system uncertainties become an important obstacle to the maturation of multiple new, driving technologies and mission concepts of the HLS program. As unmitigated uncertainties have previously led to failed development programs, these risks and their impacts must be understood and handled to ensure program success [2]. Sources of uncertainty include novel engine designs and configurations, increased reliance on cryogenic fluid management(CFM), and refueling technologies—which propagate as high-level performance metrics such as overall propellant mass and engine performance. Also, the occurrence of operational uncertainties—e.g. launch conditions or need to abort during the mission—can cause cascading effects on the rest of the mission that are difficult to definitively quantify, and are outside the scope of control. These concrete examples and other occurrences can be categorized as either epistemic or aleatory uncertainties.Epistemic uncertainty arises due to a lack of knowledge and can be alleviated with design and program maturation. Aleatory uncertainty is due to the inherent randomness of the system and cannot be directly reduced, unlike epistemic uncertainty. Robust design and probabilistic methods can compensate for aleatory effects. A taxonomy of uncertainty is referred to for this work [3]. In this paper, a probabilistic methodology to handle uncertainties has been demonstrated on a three-element HLS concept [1, 4], which allows tracking of current best estimates of the concept and assessment of concept design robustness against uncertainties. A sample case has been completed for this abstract, and an expansion on the methodology will be included in the final paper. This methodology has two key parts: first, the creation of a dynamic architecture model of a three-element HLS concept; and second, its use with surrogate modeling and range estimating techniques to capture and propagate uncertainties. This abstract will cover the basics of the approach used, and further details and justifications will be in the final paper.The mission profile associated with this three-element concept (Fig 1) was modeled as a set of mission events that facilitated mass changes, idles, or spacecraft maneuvers. The mission profile scope starts with each element’s NRHO orbit insertion and aggregation and ends at post-sortie rendezvous with Orion. More detail on the mission profile will be in the final paper. The DYnamic Rocket EQuation Tool (DYREQT), a space systems synthesis and sizing framework used by NASA, was used as the physics framework to model the HLS architecture for applying the probabilistic methodology [5, 6]. Specifically, a parametric representation of the lander, ascent, and transfer elements and the mission profile of each element was established, with vehicle and mission parameters available as inputs to allow for a dynamic model. Each vehicle stage was modeled with high-level performance metrics, using Isp and propellant mass fraction (PMF) to remain parametric. For the probabilistic analysis, uncertainties of interest within the HLS concept were enumerated and represented as parameters within the DYREQT model as inputs for vehicle stages or mission profile events. These parameters were frozen at their nominal values for the purposes of baselining architecture performance and sizing the vehicle appropriately based on reference documentation [1]. Range estimating—a probabilistic method that combines Monte Carlo sampling, focus on critical parameters, and heuristics to assess risk and opportunities—is traditionally used with Mass Equipment Lists (MELs), but has been adapted with operational parameters as well as vehicle parameters in theDYREQT model to capture mission uncertainty alongside vehicle uncertainty [7, 3]. This method was selected due to its application and insight on a system from a bottom-up perspective, independence from historical rules of thumb, and ability to generate sensitivities based on design decisions and uncertainties. As a sample case for the abstract, the boiloff rates of the vehicle elements and the loiter times during the mission (simulating launch time variations and changing window of opportunities) were used with range estimating to provide preliminary results. To perform the range estimation portion of this methodology (depicted in Fig. 3, further details in final paper), the DYREQT model was sampled using a Design of Experiments (DoE) to efficiently explore the architecture design space with respect to the sample set of uncertainty parameters; 5,000 cases via Latin Hypercube Sampling were computed on the DYREQT architecture model. Then, the results were used to create surrogate models, multivariate regressions that can visualize hypercube trends in the design space, of the architecture with respect to the uncertainty parameters. Range estimating was applied to the surrogates instead of the actual models, which saves computational expense due to the bulk of cases needed for the Monte Carlo simulation as part of range estimating. Uncertainty parameters were sampled independently from triangular distributions using the DoE ranges as ‘min’ and ‘max’, and the nominal value as ‘most likely’. Based engineering intuition, some uncertainty parameters are correlated—e.g. if the main propellant has a high boil-off rate, the oxidizer should follow suit as both are related to CFM technology.While a Monte Carlo simulation samples all inputs as independent, the results would show model correlations; thus, it is efficient to sample the inputs as correlated. Using a correlation matrix constructed for the uncertainty parameters, previously independent samples were transformed to perform a Correlated Monte Carlo. A table for the DoE ranges and probability distribution parameters is shown in Table 1, and more details on Correlated Monte Carlo Simulations will be discussed in the final paper. The model’s resulting DoE showed that multivariate polynomial equations fit via least squares method captured its behavior accurately for the sample case. For the Correlated Monte Carlo Simulation, a positive correlation between fuel and oxidizer boiloff rates was used as a demonstration. 10,000 cases were computed with the surrogates and the launched masses for each vehicle element was collated. The results can be displayed in a probability density function (PDF), showing the impact of the uncertainty parameters chosen. Integrating the PDFs will yield a cumulative distribution function (CDF) that shows the cumulative probability of a given value on the x-axis. For the sample case, the elements’ launch mass margin was calculated and represented in as CDFs, as a demonstrated representation of figures of merit for the HLS concept. For the lander and ascent elements, the NRHO mass insertion limit is 16t; the transfer element has a limit of 30t [1]. It can be seen with Figure 2 that this probabilistic methodology can provide insight into mass margin with respect to the uncertainties being modeled. Currently, the results show that the lander (descent) vehicle element has the most restrictive design space; it is the only element to show a 10% probability of negative margin. Further analysis on the Monte Carlo results will show sensitivities for driving constraints and parameters for architecture feasibility, which can lead to establishing potential mission rules.The combination of range estimating with a parametric architecture model for HLS demonstrated the capability of this probabilistic methodology in a sample case. As the HLS development progresses, this methodology has the potential for keeping current best estimates of architecture performance for awarded concepts due to the flexibility in DYREQT’s modeling framework and its parametric nature. Concept maturation and increased epistemic knowledge can be injected into the model probabilistic modeling, and thus continue to track probability of mission success.
The NASA Ames hyperwall is a display system designed to facilitate the visualization of sets of multivariate and multidimensional data like those generated in complex engineering and scientific computations. The hyperwall includes a 77 matrix of computer-driven flat-panel video display units, each presenting an image of 1,280 1,024 pixels. The term hyperwall reflects the fact that this system is a more capable successor to prior computer-driven multiple-flat-panel display systems known by names that include the generic term powerwall and the trade names PowerWall and Powerwall. Each of the 49 flat-panel displays is driven by a rack-mounted, dual-central-processing- unit, workstation-class personal computer equipped with a hig-hperformance graphical-display circuit card and with a hard-disk drive having a storage capacity of 100 GB. Each such computer is a slave node in a master/ slave computing/data-communication system (see Figure 1). The computer that acts as the master node is similar to the slave-node computers, except that it runs the master portion of the system software and is equipped with a keyboard and mouse for control by a human operator. The system utilizes commercially available master/slave software along with custom software that enables the human controller to interact simultaneously with any number of selected slave nodes. In a powerwall, a single rendering task is spread across multiple processors and then the multiple outputs are tiled into one seamless super-display. It must be noted that the hyperwall concept subsumes the powerwall concept in that a single scene could be rendered as a mosaic image on the hyperwall. However, the hyperwall offers a wider set of capabilities to serve a different purpose: The hyperwall concept is one of (1) simultaneously displaying multiple different but related images, and (2) providing means for composing and controlling such sets of images. In place of elaborate software or hardware crossbar switches, the hyperwall concept substitutes reliance on the human visual system for integration, synthesis, and discrimination of patterns in complex and high-dimensional data spaces represented by the multiple displayed images. The variety of multidimensional data sets that can be displayed on the hyperwall is practically unlimited. For example, Figure 2 shows a hyperwall display of surface pressures and streamlines from a computational simulation of airflow about an aerospacecraft at various Mach numbers and angles of attack. In this display, Mach numbers increase from left to right and angles of attack increase from bottom to top. That is, all images in the same column represent simulations at the same Mach number, while all images in the same row represent simulations at the same angle of attack. The same viewing transformations and the same mapping from surface pressure to colors were used in generating all the images.
Unmitigated uncertainties are known to have previously led to failed development programs; in order to combat these uncertainties, risks and their impacts must be understood and handled to ensure program success. In this paper, a probabilistic methodology to handle uncertainties is demonstrated on a three-element Human Landing System (HLS) concept, which allows tracking of current best estimates of the vehicle’s performance and assessment of its robustness against uncertainties. This methodology has two key parts: first, the creation of a dynamic architecture model of a three-element HLS concept; and second, its use with surrogate modeling and range estimating techniques to capture and propagate uncertainties. The DYnamic Rocket EQuation Tool (DYREQT), a space systems synthesis and sizing framework used by NASA, was used as to model the HLS architecture. For the probabilistic analysis, uncertainties of interest within the HLS concept were enumerated and represented as parameters within the DYREQT model as inputs for vehicle stages or mission profile events. Range estimating — a probabilistic method that combines Monte Carlo sampling, focus on critical parameters, and heuristics to assess risk and opportunities — is then adapted with operational parameters as well as vehicle parameters in the DYREQT model to capture mission uncertainty alongside vehicle uncertainty. To perform the range estimation portion of this methodology, the DYREQT model was sampled using a Design of Experiments (DoE) to efficiently explore the architecture design space with respect to the set of uncertainty parameters. Then, the results were used to create surrogate models, multivariate regressions that can visualize hypercube trends in the design space, of the architecture with respect to the uncertainty parameters. Using a correlation matrix constructed for the uncertainty parameters, previously independent samples were transformed to perform a Correlated Monte Carlo on the surrogate models. This probabilistic methodology was proved to provide insight into the underlying uncertainties of the three-element HLS architecture.
Unmitigated uncertainties are known to have previously led to failed development programs; in order to combat these uncertainties, risks and their impacts must be understood and handled to ensure program success. In this paper, a probabilistic methodology to handle uncertainties is demonstrated on a three-element Human Landing System (HLS) concept, which allows tracking of current best estimates of the vehicle’s performance and assessment of its robustness against uncertainties. This methodology has two key parts: first, the creation of a dynamic architecture model of a three-element HLS concept; and second, its use with surrogate modeling and range estimating techniques to capture and propagate uncertainties. The DYnamic Rocket EQuation Tool (DYREQT), a space systems synthesis and sizing framework used by NASA, was used as to model the HLS architecture. For the probabilistic analysis, uncertainties of interest within the HLS concept were enumerated and represented as parameters within the DYREQT model as inputs for vehicle stages or mission profile events. Range estimating — a probabilistic method that combines Monte Carlo sampling, focus on critical parameters, and heuristics to assess risk and opportunities — is then adapted with operational parameters as well as vehicle parameters in the DYREQT model to capture mission uncertainty alongside vehicle uncertainty. To perform the range estimation portion of this methodology, the DYREQT model was sampled using a Design of Experiments (DoE) to efficiently explore the architecture design space with respect to the set of uncertainty parameters. Then, the results were used to create surrogate models, multivariate regressions that can visualize hypercube trends in the design space, of the architecture with respect to the uncertainty parameters. Using a correlation matrix constructed for the uncertainty parameters, previously independent samples were transformed to perform a Correlated Monte Carlo on the surrogate models. This probabilistic methodology was proved to provide insight into the underlying uncertainties of the three-element HLS architecture.
Equicontrollability and its application to the linear time-invariant model-following problem are discussed. The problem is presented in the form of two systems, the plant and the model. The requirement is to find a controller to apply to the plant so that the resultant compensated plant behaves, in an input-output sense, the same as the model. All systems are assumed to be linear and time-invariant. The basic approach is to find suitable equicontrollable realizations of the plant and model and to utilize feedback so as to produce a controller of minimal state dimension. The concept of equicontrollability is a generalization of control canonical (phase variable) form applied to multivariable systems. It allows one to visualize clearly the effects of feedback and to pinpoint the parameters of a multivariable system which are invariant under feedback. The basic contributions are the development of equicontrollable form; solution of the model-following problem in an entirely algorithmic way, suitable for computer programming; and resolution of questions on system decoupling.
Multivariate descriptors of sway were used to test whether altered sensory conditions result not only in changes in amount of sway but also in postural coordination. Eigenvalues and directions of eigenvectors of the covariance of shnk and hip angles were used as a set of multivariate descriptors. These quantities were measured in 14 healthy adult subjects performing the Sensory Organization test, which disrupts visual and somatosensory information used for spatial orientation. Multivariate analysis of variance and discriminant analysis showed that resulting sway changes were at least bivariate in character, with visual and somatosensory conditions producing distinct changes in postural coordination. The most significant changes were found when somatosensory information was disrupted by sway-referencing of the support surface (P = 3.2 x 10(-10)). The resulting covariance measurements showed that subjects not only swayed more but also used increased hip motion analogous to the hip strategy. Disruption of vision, by either closing the eyes or sway-referencing the visual surround, also resulted in altered sway (P = 1.7 x 10(-10)), with proportionately more motion of the center of mass than with platform sway-referencing. As shown by discriminant analysis, an optimal univariate measure could explain at most 90% of the behavior due to altered sensory conditions. The remaining 10%, while smaller, are highly significant changes in posture control that depend on sensory conditions. The results imply that normal postural coordination of the trunk and legs requires both somatosensory and visual information and that each sensory modality makes a unique contribution to posture control. Descending postural commands are multivariate in nature, and the motion at each joint is affected uniquely by input from multiple sensors.
This paper describes by example a strategy for plotting and interacting with data in multiple metric spaces. The example system was designed for use with time-varying computational fluid dynamics (CFD) datasets, but the methodology is directly applicable to other types of field data. The central objects embodied by the tool are {\em portraits}, which show the data in various coordinate systems, while preserving their spatial connectivity and temporal variability. The coordinates are derived in various ways from the field data, and an important feature is that new and derived portraits can be created interactively. The primary operations supported by the tool are brushing and linking: the user can select a subset of a given portrait, and this subset is highlighted in all portraits. The user can combine highlighted subsets from an arbitrary number of portraits with the usual logical operators, thereby indicating where an arbitrarily complex set of conditions holds. The system is useful for exploratory visualization and feature detection in multivariate data.