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NASA NTRS1975

Multivariate Analysis, Retrieval, and Storage System (MARS). Volume 6: MARS System - A Sample Problem (Gross Weight of Subsonic Transports)

The Mars system is a tool for rapid prediction of aircraft or engine characteristics based on correlation-regression analysis of past designs stored in the data bases. An example of output obtained from the MARS system, which involves derivation of an expression for gross weight of subsonic transport aircraft in terms of nine independent variables is given. The need is illustrated for careful selection of correlation variables and for continual review of the resulting estimation equations. For Vol. 1, see N76-10089.

Hague, D. S.↗
NASA NTRS2011

Distributed Monitoring of the R(sup 2) Statistic for Linear Regression

The problem of monitoring a multivariate linear regression model is relevant in studying the evolving relationship between a set of input variables (features) and one or more dependent target variables. This problem becomes challenging for large scale data in a distributed computing environment when only a subset of instances is available at individual nodes and the local data changes frequently. Data centralization and periodic model recomputation can add high overhead to tasks like anomaly detection in such dynamic settings. Therefore, the goal is to develop techniques for monitoring and updating the model over the union of all nodes data in a communication-efficient fashion. Correctness guarantees on such techniques are also often highly desirable, especially in safety-critical application scenarios. In this paper we develop DReMo a distributed algorithm with very low resource overhead, for monitoring the quality of a regression model in terms of its coefficient of determination (R2 statistic). When the nodes collectively determine that R2 has dropped below a fixed threshold, the linear regression model is recomputed via a network-wide convergecast and the updated model is broadcast back to all nodes. We show empirically, using both synthetic and real data, that our proposed method is highly communication-efficient and scalable, and also provide theoretical guarantees on correctness.

Bhaduri, Kanishka↗
NASA NTRS2019

Numerical Reanalyses as a Gateway to Arctic Synthesis

Reanalyses are regularly gridded, retrospective depictions of the physical earth system, which are produced through the correction of a short-term forecast to available observations. In the Arctic, reanalyses are particularly well suited to marshal the sparse observing network to provide a plausible, multivariate representation of conditions. Atmospheric reanalyses such as MERRA-2 (NASA Modern-Era Retrospective analysis for Research and Applications, version 2) and ocean reanalyses such as SODA3 (Univ. Maryland Simple Ocean Data Assimilation version 3) are widely used in Arctic research for diagnostic studies of circulation, model evaluation, and as boundary conditions for a variety of process models. Here, we provide examples that illustrate the utility of reanalyses for providing information on the spatial and temporal scales of recent, rapid changes in the Arctic. Recent trends in Arctic surface temperatures, surface melt over Greenland and Arctic glaciers, and evolving freshwater conditions in the Arctic Ocean are examples where reanalyses can provide information that cannot easily be obtained via other means. These examples provide information on the scale, magnitude, and the uncertainty of recent Arctic change and provide a context for future scenarios. We further quantify uncertainties in key reanalyses variables and approaches for addressing these issues.

Arctic↗
NASA NTRS1988

A multivariate variational objective analysis-assimilation method. Part 1: Development of the basic model

The variational method of undetermined multipliers is used to derive a multivariate model for objective analysis. The model is intended for the assimilation of 3-D fields of rawinsonde height, temperature and wind, and mean level temperature observed by satellite into a dynamically consistent data set. Relative measurement errors are taken into account. The dynamic equations are the two nonlinear horizontal momentum equations, the hydrostatic equation, and an integrated continuity equation. The model Euler-Lagrange equations are eleven linear and/or nonlinear partial differential and/or algebraic equations. A cyclical solution sequence is described. Other model features include a nonlinear terrain-following vertical coordinate that eliminates truncation error in the pressure gradient terms of the horizontal momentum equations and easily accommodates satellite observed mean layer temperatures in the middle and upper troposphere. A projection of the pressure gradient onto equivalent pressure surfaces removes most of the adverse impacts of the lower coordinate surface on the variational adjustment.

Achtemeier, Gary L.↗
NASA NTRS1995

Reduction, analysis, and properties of electric current systems in solar active regions

The specific attraction and, in large part, the significance of solar magnetograms lie in the fact that they give the most important data on the electric currents and the nonpotentiality of active regions. Using the vector magnetograms from the Marshall Space Flight Center (MSFC), we employ a unique technique in the area of data analysis for resolving the 180 deg ambiguity in order to calculate the spatial structure of the vertical electric current density. The 180 deg ambiguity is resolved by applying concepts from the nonlinear multivariable optimization theory. The technique is shown to be of particular importance in very nonpotential active regions. The characterization of the vertical electric current density for a set of vector magnetograms using this method then gives the spatial scale, locations, and magnitude of these current systems. The method, which employs an intermediate parametric function which covers the magnetogram and which defines the local `preferred' direction, minimizes a specific functional of the observed transverse magnetic field. The specific functional that is successful is the integral of the square of the vertical current density. We find that the vertical electric current densities have common characteristics for the extended bipolar (beta) (gamma) (delta)-regions studied. The largest current systems have j(sub z)'s which maximizes around 30 mA/sq m and have a linear decreasing distribution to a diameter of 30 Mn.

Gary, G. Allen↗
NASA NTRS1995

Reduction, Analysis, and Properties of Electric Current Systems in Solar Active Regions

The specific attraction and, in large part, the significance of solar vector magnetograms lie in the fact that they give the most important data on the electric currents and the nonpotentiality of active regions. Using the vector magnetograms from the Marshall Space Flight Center (MSFC), we employ a unique technique in the area of data analysis for resolving the 180 degree ambiguity in order to calculate the spatial structure of the vertical electric current density. The 180 degree ambiguity is resolved by applying concepts from the nonlinear multivariable optimization theory. The technique is shown to be of particular importance in very nonpotential active regions. The characterization of the vertical electric current density for a set of vector magnetograms using this method then gives the spatial scale, locations, and magnitude of these current systems. The method, which employs an intermediate parametric function which covers the magnetogram and which defines the local "preferred" direction, minimizes a specific functional of the observed transverse magnetic field. The specific functional that is successful is the integral of the square of the vertical current density. We find that the vertical electric current densities have common characteristics for the extended bipolar beta gamma delta-regions studied. The largest current systems have j(sub z)'s which maximizes around 30 mA per square meter and have a linear decreasing distribution to a diameter of 30 Mm.

Gary, G. Allen↗
NASA NTRS1997

An Assessment of the Regional Distribution of the Oxygen-Isotope Ratio in Northeastern Canada

A compilation of mean values of the oxygen-isotope ratio relative to standard mean ocean Water for 22 sites representative of conditions in north-eastern Canada is complemented with data on mean annual surface temperature, latitude, surface elevation, and mean annual shortest distance to open ocean denoted by the 10% sea-ice concentration boundary. Stepwise regression analysis is used to develop a multivariate model suitable to infer the distribution of 6 1"0 in an area of complex topography and possibly mixed source of advected water vapor. The best model is produced by a run in the backward mode at the 95% confidence level in which only temperature, latitude and distance to the open ocean remain in the model (the correlation coefficient is 0.915, the adjusted coefficient of determination is 0.809, the root mean square residual is 1.62). This model is similar to the best 6180 predictive model derived elsewhere for Greenland, suggesting a common principal source of advected moisture.

Giovinetto, Mario B.↗
NASA NTRS2014

Real-Time Onboard Global Nonlinear Aerodynamic Modeling from Flight Data

Flight test and modeling techniques were developed to accurately identify global nonlinear aerodynamic models onboard an aircraft. The techniques were developed and demonstrated during piloted flight testing of an Aermacchi MB-326M Impala jet aircraft. Advanced piloting techniques and nonlinear modeling techniques based on fuzzy logic and multivariate orthogonal function methods were implemented with efficient onboard calculations and flight operations to achieve real-time maneuver monitoring and analysis, and near-real-time global nonlinear aerodynamic modeling and prediction validation testing in flight. Results demonstrated that global nonlinear aerodynamic models for a large portion of the flight envelope were identified rapidly and accurately using piloted flight test maneuvers during a single flight, with the final identified and validated models available before the aircraft landed.

Brandon, Jay M.↗
NASA NTRSDate not supplied

Toward The Development of Hailstorm Climatologies Derived From Reanalyses and Infared/Passive Microwave Satellite Imagers

Geostationary satellite imagers, such as those of the Geostationary Operational Environmental Satellite (GOES) and Meteosat series, provide both historical and near-real-time observations of cloud top patterns that are commonly associated with severe convection. Environmental conditions favorable for severe weather are thought to be represented well by reanalyses. Predicting exactly where convection and costly storm hazards like hail will occur using models or satellite imagery alone, however, is extremely challenging. The multivariate combination of satellite-observed cloud patterns with reanalysis environmental parameters, linked to United States Next Generation Weather Radar- (NEXRAD-) estimated Maximum Expected Size of Hail (MESH) using a deep neural network (DNN), enables estimation of potentially severe hail likelihood for any observed storm cell. These estimates are specifically designed to make hail likelihood distinctions based on satellite-indicated points of deep convection within environments favorable for storm development. We seek an approach that can be used to estimate climatological hailstorm frequency and risk throughout the historical satellite data record. This presentation demonstrates that statistical distributions of convective parameters from satellite and reanalysis show separation between non-severe/severe hailstorm classes for predictors including overshooting cloud top temperature and area characteristics, convective available potential energy, vertical wind shear, 500 hPa temperature, mid-level lapse rate, precipitable water, and convective inhibition. These complex, multivariate predictor relationships are exploited within a DNN to produce a hail likelihood metric with a critical success index of 0.504 and Heidke skill score of 0.403, which is exceptional among recent analogous hail studies. Furthermore, applications of the DNN to select case studies demonstrate good qualitative agreement between hail likelihood and MESH. These hail classifications are aggregated across an 11-year GOES-12/13 image database to derive a hail frequency and severity climatology, which denotes the Central Plains, the Midwest, and northwestern Mexico as being the most hail-prone regions within the domain studied. Opportunities for training and applying DNN-based hailstorm predictions to recently developed GOES-8/10/12/13/16 and Meteosat Second Generation convective storm detection and characterization climatologies over South America and South Africa, respectively, will also be presented.

Kristopher Bedka↗
NASA NTRS2019

Modeling and Simulation Techniques for the NASA SLS Service Module Panel Separation Event; from Loosely-Coupled Euler to Fully-Coupled 6-DOF, Time-Accurate, Navier-Stokes Methodologies

An aerodynamic database has been generated for use by the Orion Multi-Purpose Crew Vehicle (MPCV) Program to analyze Service Module (SM) panel jettison from the NASA SLS vehicle. The database is a combination of CFD data for the panel aerodynamic coefficients, and MATLAB code written to query the CFD data. The Cart3D inviscid CFD flow solver was used to generate the panel aerodynamic coefficients for static panel orientations and free stream conditions that can occur during the jettison event. The MATLAB code performs the multivariate interpolation to obtain aerodynamic coefficients. The MATLAB code uses input for SM panel parameters and returns the SM panel aerodynamic force and moment coefficients for use with a Six-Degree-of-Freedom (6-DOF) motion solver to model the jettison event. This paper examines the accuracy of the sequential-static database approach by modeling the panel jettison event with a fully-coupled, time-dependent, viscous, moving-body CFD simulation. The fully-coupled simulation is obtained using the Loci/Chem unstructured Navier-Stokes CFD solver. The results show that the fully-coupled approach agrees well with the loosely-coupled database/6-DOF approach, indicating that unsteady effects are minimal for the panel jettison event. These results suggest that the database/6-DOF approach is sufficient. In addition, this paper presents the development of an uncertainty model for use in Monte Carlo analysis of the panel jettison event. Here viscous CFD simulations are obtained with Loci/Chem and compared to the inviscid CFD forces and moments. An uncertainty model based on model-form error and numerical error is presented.

Hall, Leslie H.↗
NASA NTRS1972

Pole placement with constant gain output feedback

Given a linear time invariant multivariable system with m inputs and p outputs, it was shown that p closed loop poles of the system can be preassigned arbitrarily using constant gain output feedback provided (A circumflex, B circumflex) is controllable. These data show that if (A circumflex, B circumflex, C circumflex) is controllable and observable, and Rank B circumflex = m, Rank C circumflex = p, then max (m,p) poles of the system can be assigned arbitarily using constant gain output feedback. Further, it is shown that in some cases more than max (m,p) poles can be arbitrarily assigned. A least square design technique is outlined to approximate the desired pole locations when it is not possible to place all the poles.

Sridhar, B.↗
NASA NTRS1988

An adaptive identification and control scheme for large space structures

A unified identification and control scheme capable of achieving space at form performance objectives under nominal or failure conditions is described. Preliminary results are also presented, showing that the methodology offers much promise for effective robust control of large space structures. The control method is a multivariable, adaptive, output predictive controller called Model Predictive Control (MPC). MPC uses a state space model and input reference trajectories of set or tracking points to adaptively generate optimum commands. For a fixed model, MPC processes commands with great efficiency, and is also highly robust. A key feature of MPC is its ability to control either nonminimum phase or open loop unstable systems. As an output controller, MPC does not explicitly require full state feedback, as do most multivariable (e.g., Linear Quadratic) methods. Its features are very useful in LSS operations, as they allow non-collocated actuators and sensors. The identification scheme is based on canonical variate analysis (CVA) of input and output data. The CVA technique is particularly suited for the measurement and identification of structural dynamic processes - that is, unsteady transient or dynamically interacting processes such as between aerodynamics and structural deformation - from short, noisy data. CVA is structured so that the identification can be done in real or near real time, using computationally stable algorithms. Modeling LSS dynamics in 1-g laboratories has always been a major impediment not only to understanding their behavior in orbit, but also to controlling it. In cases where the theoretical model is not confirmed, current methods provide few clues concerning additional dynamical relationships that are not included in the theoretical models. CVA needs no a priori model data, or structure; all statistically significant dynamical states are determined using natural, entropy-based methods. Heretofore, a major limitation in applying adaptive controllers to LSS problems has been the requirement for accurate models. We feel that MPC coupled with the CVA identification scheme will resolve this limitation. The results are based on research performed under an SBIR grant, administered by the Air Force Office of Scientific Research.

Carroll, J. V.↗
NASA NTRS2004

Autonomous Propulsion System Technology Being Developed to Optimize Engine Performance Throughout the Lifecycle

The goal of the Autonomous Propulsion System Technology (APST) project is to reduce pilot workload under both normal and anomalous conditions. Ongoing work under APST develops and leverages technologies that provide autonomous engine monitoring, diagnosing, and controller adaptation functions, resulting in an integrated suite of algorithms that maintain the propulsion system's performance and safety throughout its life. Engine-to-engine performance variation occurs among new engines because of manufacturing tolerances and assembly practices. As an engine wears, the performance changes as operability limits are reached. In addition to these normal phenomena, other unanticipated events such as sensor failures, bird ingestion, or component faults may occur, affecting pilot workload as well as compromising safety. APST will adapt the controller as necessary to achieve optimal performance for a normal aging engine, and the safety net of APST algorithms will examine and interpret data from a variety of onboard sources to detect, isolate, and if possible, accommodate faults. Situations that cannot be accommodated within the faulted engine itself will be referred to a higher level vehicle management system. This system will have the authority to redistribute the faulted engine's functionality among other engines, or to replan the mission based on this new engine health information. Work is currently underway in the areas of adaptive control to compensate for engine degradation due to aging, data fusion for diagnostics and prognostics of specific sensor and component faults, and foreign object ingestion detection. In addition, a framework is being defined for integrating all the components of APST into a unified system. A multivariable, adaptive, multimode control algorithm has been developed that accommodates degradation-induced thrust disturbances during throttle transients. The baseline controller of the engine model currently being investigated has multiple control modes that are selected according to some performance or operational criteria. As the engine degrades, parameters shift from their nominal values. Thus, when a new control mode is swapped in, a variable that is being brought under control might have an excessive initial error. The new adaptive algorithm adjusts the controller gains on the basis of the level of degradation to minimize the disruptive influence of the large error on other variables and to recover the desired thrust response.

Litt, Jonathan S.↗
NASA NTRS2015

Background Noises Versus Intraseasonal Variation Signals: Small vs. Large Convective Cloud Objects From CERES Aqua Observations

During inactive phases of Madden-Julian Oscillation (MJO), there are plenty of deep but small convective systems and far fewer deep and large ones. During active phases of MJO, a manifestation of an increase in the occurrence of large and deep cloud clusters results from an amplification of large-scale motions by stronger convective heating. This study is designed to quantitatively examine the roles of small and large cloud clusters during the MJO life cycle. We analyze the cloud object data from Aqua CERES (Clouds and the Earth's Radiant Energy System) observations between July 2006 and June 2010 for tropical deep convective (DC) and cirrostratus (CS) cloud object types according to the real-time multivariate MJO index, which assigns the tropics to one of the eight MJO phases each day. The cloud object is a contiguous region of the earth with a single dominant cloud-system type. The criteria for defining these cloud types are overcast footprints and cloud top pressures less than 400 hPa, but DC has higher cloud optical depths (=10) than those of CS (<10). The size distributions, defined as the footprint numbers as a function of cloud object diameters, for particular MJO phases depart greatly from the combined (8-phase) distribution at large cloud-object diameters due to the reduced/increased numbers of cloud objects related to changes in the large-scale environments. The medium diameter corresponding to the combined distribution is determined and used to partition all cloud objects into "small" and "large" groups of a particular phase. The two groups corresponding to the combined distribution have nearly equal numbers of footprints. The medium diameters are 502 km for DC and 310 km for cirrostratus. The range of the variation between two extreme phases (typically, the most active and depressed phases) for the small group is 6-11% in terms of the numbers of cloud objects and the total footprint numbers. The corresponding range for the large group is 19-44%. In terms of the probability density functions of radiative and cloud physical properties, there are virtually no differences between the MJO phases for the small group, but there are significant differences for the large groups for both DC and CS types. These results suggest that the intreseasonal variation signals reside at the large cloud clusters while the small cloud clusters represent the background noises resulting from various types of the tropical waves with different wavenumbers and propagation speeds/directions.

Xu, Kuan-Man↗
NASA NTRS1974

Multivariate Analysis, Retrieval, and Storage System (MARS). Volume 1: MARS System and Analysis Techniques

A method for rapidly examining the probable applicability of weight estimating formulae to a specific aerospace vehicle design is presented. The Multivariate Analysis Retrieval and Storage System (MARS) is comprised of three computer programs which sequentially operate on the weight and geometry characteristics of past aerospace vehicles designs. Weight and geometric characteristics are stored in a set of data bases which are fully computerized. Additional data bases are readily added to the MARS system and/or the existing data bases may be easily expanded to include additional vehicles or vehicle characteristics.

Hague, D. S.↗
NASA NTRS1976

Feature combinations and the Bhattacharyya criterion

A procedure for calculating a kxn rank k matrix B for data compression using the Bhattacharyya bound on the probability of error and an iterative construction using Householder transformation was developed. Two sets of remotely sensed agricultural data are used to demonstrate the application of the procedure. The results of the applications gave some indication of the extent to which the Bhattacharyya bound on the probability of error is affected by such transformations for multivariate normal populations.

Decell, H. P., Jr.↗
NASA NTRS2022

Sea Level Rise and City-Level Climate Action

Background: Climate change is the greatest threat to global health in the 21st century. Rising sea levels are one particularly concerning manifestation of this and many of the world’s largest cities are vulnerable to sea level rise (SLR). Thus, urban climate adaptation and mitigation policies are increasingly important to protect population health. Objectives: This study aimed to determine whether being at risk of SLR was associated with city-level climate action. It also aimed to assess the wider drivers of climate action in cities, in order to guide ongoing efforts to motivate climate action, assess public health preparedness and identify research gaps. Methods: This is an ecological cross-sectional study using secondary data from CDP, the Urban Climate Change Research Network (UCCRN), World Bank, United Nations Cities and EM-DAT (Emergency Events Database). The study population consisted of 517 cities who participated in CDP’s 2019 Cities Survey. Multivariable logistic regression was utilized to assess the relationship between risk of SLR and city-level climate action, and secondly, to assess the wider determinants of city-level climate action. Results: There was evidence of crude associations between risk of SLR and three outcome variables representing city-level climate action. However, after adjusting for confounding variables, these crude associations disappeared. World region, national income status and urban population were shown to be stronger predictors of city-level climate action. Conclusion: It is concerning for population health that there is no association demonstrated between risk of SLR and climate action. This could indicate a lack of awareness of the risks posed by SLR within urban governance. To fulfil their health protection responsibilities, it is essential that public health professionals take a leading role in advocating for climate action.

sea level rise↗
NASA NTRS1976

Feature combinations and the divergence criterion

Classifying large quantities of multidimensional remotely sensed agricultural data requires efficient and effective classification techniques and the construction of certain transformations of a dimension reducing, information preserving nature. The construction of transformations that minimally degrade information (i.e., class separability) is described. Linear dimension reducing transformations for multivariate normal populations are presented. Information content is measured by divergence.

Decell, H. P., Jr.↗