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NASA NTRS1995

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.↗

NASA NTRS1986

Information extraction from multivariate images

An overview of several multivariate image processing techniques is presented, with emphasis on techniques based upon the principal component transformation (PCT). Multiimages in various formats have a multivariate pixel value, associated with each pixel location, which has been scaled and quantized into a gray level vector, and the bivariate of the extent to which two images are correlated. The PCT of a multiimage decorrelates the multiimage to reduce its dimensionality and reveal its intercomponent dependencies if some off-diagonal elements are not small, and for the purposes of display the principal component images must be postprocessed into multiimage format. The principal component analysis of a multiimage is a statistical analysis based upon the PCT whose primary application is to determine the intrinsic component dimensionality of the multiimage. Computational considerations are also discussed.

Park, S. K.↗

NASA NTRS1994

Multivariate space - time analysis of PRE-STORM precipitation

This paper presents the methodologies and results of the multivariate modeling and two-dimensional spectral and correlation analysis of PRE-STORM rainfall gauge data. Estimated parameters of the models for the specific spatial averages clearly indicate the eastward and southeastward wave propagation of rainfall fluctuations. A relationship between the coefficients of the diffusion equation and the parameters of the stochastic model of rainfall fluctuations is derived that leads directly to the exclusive use of rainfall data to estimate advection speed (about 12 m/s) as well as other coefficients of the diffusion equation of the corresponding fields. The statistical methodology developed here can be used for confirmation of physical models by comparison of the corresponding second-moment statistics of the observed and simulated data, for generating multiple samples of any size, for solving the inverse problem of the hydrodynamic equations, and for application in some other areas of meteorological and climatological data analysis and modeling.

Polyak, Ilya↗

NASA NTRS1983

Longitudinal flying qualities criteria for single-pilot instrument flight operations

Modern estimation and control theory, flight testing, and statistical analysis were used to deduce flying qualities criteria for General Aviation Single Pilot Instrument Flight Rule (SPIFR) operations. The principal concern is that unsatisfactory aircraft dynamic response combined with high navigation/communication workload can produce problems of safety and efficiency. To alleviate these problems. The relative importance of these factors must be determined. This objective was achieved by flying SPIFR tasks with different aircraft dynamic configurations and assessing the effects of such variations under these conditions. The experimental results yielded quantitative indicators of pilot's performance and workload, and for each of them, multivariate regression was applied to evaluate several candidate flying qualities criteria.

Stengel, R. F.↗

NASA NTRS1986

Longitudinal flying qualitites criteria for single-pilot instrument flight operations

Modern estimation and control theory, flight testing, and statistical analysis were used to deduce flying qualities criteria for General Aviation Single Pilot Instrument Flight Rule (SPIFR) operations. The principal concern is that unsatisfactory aircraft dynamic response combined with high navigation/communication workload can produce problems of safety and efficiency. To alleviate these problems, the relative importance of these factors must be determined. This objective was achieved by flying SPIFR tasks with different aircraft dynamic configurations and assessing the effects of such variations under these conditions. The experimental results yielded quantitative indicators of pilot's performance and workload, and for each of them, multivariate regression was applied to evaluate several candidate flying qualities criteria.

Bar-Gill, A.↗

NASA NTRS1995

The second-moment climatology of the GATE rain rate data

The first part of this paper presents the description of the GARP (Global Atmospheric Research Program) Atlantic Tropical Experiment (GATE) 1 rain-rate data and its two-dimensional spectral and correlation characteristics, which has made it possible to accomplish the following: to show the concentration of a significant power along the frequency axis in the spatiotemporal spectra; to detect a diurnal cycle (which has a range of variation of about 3.4-5.4 mm/n) as one of the sources of bias in the rain statistics of satellite data; to study the distinction between the north-south and east-west transport of spatial rain-rate field and character of its anisotropy; to evaluate the scales of the distinction between second-moment estimates associated with ground and satellite samples; and to determine the appropriate spatial and temporal scales of simple linear stochastic models fitted to averaged rain-rate fields. The second part of this paper is devoted to an analysis of the diffusion of the rain rate by establishing a relationship between the parameters of the multivariate autoregressive model and the coefficients of a diffusion equation. This analysis led to the use of rain data to estimate the rain advection velocity as well as other coefficients of the diffusion equation of the corresponding field. The results obtained can be used for comparison with corresponding estimates of other sources of data (satellite, Tropical Oceans Global Atmosphere Coupled Ocean - Atmosphere Response Experiment (TOGA, COARE) or simulated by physical models), for generating multiple samples of any size, for solving the inverse problems of some of the hydrodynamic equations, and in some other areas of rain data analysis and modeling.

Polyak, Ilya↗

NASA NTRS1993

Space Shuttle Main Engine performance analysis

For a number of years, NASA has relied primarily upon periodically updated versions of Rocketdyne's power balance model (PBM) to provide space shuttle main engine (SSME) steady-state performance prediction. A recent computational study indicated that PBM predictions do not satisfy fundamental energy conservation principles. More recently, SSME test results provided by the Technology Test Bed (TTB) program have indicated significant discrepancies between PBM flow and temperature predictions and TTB observations. Results of these investigations have diminished confidence in the predictions provided by PBM, and motivated the development of new computational tools for supporting SSME performance analysis. A multivariate least squares regression algorithm was developed and implemented during this effort in order to efficiently characterize TTB data. This procedure, called the 'gains model,' was used to approximate the variation of SSME performance parameters such as flow rate, pressure, temperature, speed, and assorted hardware characteristics in terms of six assumed independent influences. These six influences were engine power level, mixture ratio, fuel inlet pressure and temperature, and oxidizer inlet pressure and temperature. A BFGS optimization algorithm provided the base procedure for determining regression coefficients for both linear and full quadratic approximations of parameter variation. Statistical information relative to data deviation from regression derived relations was also computed. A new strategy for integrating test data with theoretical performance prediction was also investigated. The current integration procedure employed by PBM treats test data as pristine and adjusts hardware characteristics in a heuristic manner to achieve engine balance. Within PBM, this integration procedure is called 'data reduction.' By contrast, the new data integration procedure, termed 'reconciliation,' uses mathematical optimization techniques, and requires both measurement and balance uncertainty estimates. The reconciler attempts to select operational parameters that minimize the difference between theoretical prediction and observation. Selected values are further constrained to fall within measurement uncertainty limits and to satisfy fundamental physical relations (mass conservation, energy conservation, pressure drop relations, etc.) within uncertainty estimates for all SSME subsystems. The parameter selection problem described above is a traditional nonlinear programming problem. The reconciler employs a mixed penalty method to determine optimum values of SSME operating parameters associated with this problem formulation.

Santi, L. Michael↗

NASA NTRS1986

Analysis/forecast experiments with a flow-dependent correlation function using FGGE data

The use of a flow-dependent correlation function to improve the accuracy of an optimum interpolation (OI) scheme is examined. The development of the correlation function for the OI analysis scheme used for numerical weather prediction is described. The scheme uses a multivariate surface analysis over the oceans to model the pressure-wind error cross-correlation and it has the ability to use an error correlation function that is flow- and geographically-dependent. A series of four-day data assimilation experiments, conducted from January 5-9, 1979, were used to investigate the effect of the different features of the OI scheme (error correlation) on forecast skill for the barotropic lows and highs. The skill of the OI was compared with that of a successive correlation method (SCM) of analysis. It is observed that the largest difference in the correlation statistics occurred in barotropic and baroclinic lows and highs. The comparison reveals that the OI forecasts were more accurate than the SCM forecasts.

Baker, W. E.↗

NASA NTRS2013

Analysis of Multivariate Experimental Data Using A Simplified Regression Model Search Algorithm

A new regression model search algorithm was developed that may be applied to both general multivariate experimental data sets and wind tunnel strain-gage balance calibration data. The algorithm is a simplified version of a more complex algorithm that was originally developed for the NASA Ames Balance Calibration Laboratory. The new algorithm performs regression model term reduction to prevent overfitting of data. It has the advantage that it needs only about one tenth of the original algorithm's CPU time for the completion of a regression model search. In addition, extensive testing showed that the prediction accuracy of math models obtained from the simplified algorithm is similar to the prediction accuracy of math models obtained from the original algorithm. The simplified algorithm, however, cannot guarantee that search constraints related to a set of statistical quality requirements are always satisfied in the optimized regression model. Therefore, the simplified algorithm is not intended to replace the original algorithm. Instead, it may be used to generate an alternate optimized regression model of experimental data whenever the application of the original search algorithm fails or requires too much CPU time. Data from a machine calibration of NASA's MK40 force balance is used to illustrate the application of the new search algorithm.

Ulbrich, Norbert M.↗

NASA NTRS2002

Using Clustering to Establish Climate Regimes from PCM Output

A multivariate statistical clustering technique--based on the k-means algorithm of Hartigan has been used to extract patterns of climatological significance from 200 years of general circulation model (GCM) output. Originally developed and implemented on a Beowulf-style parallel computer constructed by Hoffman and Hargrove from surplus commodity desktop PCs, the high performance parallel clustering algorithm was previously applied to the derivation of ecoregions from map stacks of 9 and 25 geophysical conditions or variables for the conterminous U.S. at a resolution of 1 sq km. Now applied both across space and through time, the clustering technique yields temporally-varying climate regimes predicted by transient runs of the Parallel Climate Model (PCM). Using a business-as-usual (BAU) scenario and clustering four fields of significance to the global water cycle (surface temperature, precipitation, soil moisture, and snow depth) from 1871 through 2098, the authors' analysis shows an increase in spatial area occupied by the cluster or climate regime which typifies desert regions (i.e., an increase in desertification) and a decrease in the spatial area occupied by the climate regime typifying winter-time high latitude perma-frost regions. The patterns of cluster changes have been analyzed to understand the predicted variability in the water cycle on global and continental scales. In addition, representative climate regimes were determined by taking three 10-year averages of the fields 100 years apart for northern hemisphere winter (December, January, and February) and summer (June, July, and August). The result is global maps of typical seasonal climate regimes for 100 years in the past, for the present, and for 100 years into the future. Using three-dimensional data or phase space representations of these climate regimes (i.e., the cluster centroids), the authors demonstrate the portion of this phase space occupied by the land surface at all points in space and time. Any single spot on the globe will exist in one of these climate regimes at any single point in time. By incrementing time, that same spot will trace out a trajectory or orbit between and among these climate regimes (or atmospheric states) in phase (or state) space. When a geographic region enters a state it never previously visited, a climatic change is said to have occurred. Tracing out the entire trajectory of a single spot on the globe yields a 'manifold' in state space representing the shape of its predicted climate occupancy. This sort of analysis enables a researcher to more easily grasp the multivariate behavior of the climate system.

Oglesby, Robert↗

NASA NTRS2002

On the Choice of Variable for Atmospheric Moisture Analysis

The implications of using different control variables for the analysis of moisture observations in a global atmospheric data assimilation system are investigated. A moisture analysis based on either mixing ratio or specific humidity is prone to large extrapolation errors, due to the high variability in space and time of these parameters and to the difficulties in modeling their error covariances. Using the logarithm of specific humidity does not alleviate these problems, and has the further disadvantage that very dry background estimates cannot be effectively corrected by observations. Relative humidity is a better choice from a statistical point of view, because this field is spatially and temporally more coherent and error statistics are therefore easier to obtain. If, however, the analysis is designed to preserve relative humidity in the absence of moisture observations, then the analyzed specific humidity field depends entirely on analyzed temperature changes. If the model has a cool bias in the stratosphere this will lead to an unstable accumulation of excess moisture there. A pseudo-relative humidity can be defined by scaling the mixing ratio by the background saturation mixing ratio. A univariate pseudo-relative humidity analysis will preserve the specific humidity field in the absence of moisture observations. A pseudorelative humidity analysis is shown to be equivalent to a mixing ratio analysis with flow-dependent covariances. In the presence of multivariate (temperature-moisture) observations it produces analyzed relative humidity values that are nearly identical to those produced by a relative humidity analysis. Based on a time series analysis of radiosonde observed-minus-background differences it appears to be more justifiable to neglect specific humidity-temperature correlations (in a univariate pseudo-relative humidity analysis) than to neglect relative humidity-temperature correlations (in a univariate relative humidity analysis). A pseudo-relative humidity analysis is easily implemented in an existing moisture analysis system, by simply scaling observed-minus background moisture residuals prior to solving the analysis equation, and rescaling the analyzed increments afterward.

Dee, Dick P.↗

NASA NTRS1994

Seasonal Patterns and Remote Spectral Estimation of Canopy Chemistry Across the Oregon Transect

We examined seasonal changes in canopy chemical concentrations and content in conifer forests growing along a climate gradient in western Oregon, as part of the Oregon Transect Ecosystem Research (OTTER) study. The chemical variables were related to seasonal patterns of growth and production. Statistical comparisons of chemical variables with data collected from two different airborne remote-sensing platforms were also carried out. Total nitrogen (N) concentrations in foliage varied significantly both seasonally and among sites; when expressed as content in the forest canopy, nitrogen varied to a much greater extent and was significantly related to aboveground net primary production (r = 0.99). Chlorophyll and free amino acid concentrations varied more strongly than did total N and may have reflected changes in physiological demands for N. Large variations in starch concentrations were measured from pre- to post-budbreak in all conifer sites. Examination of remote-sensing data from two different airborne instruments suggests the potential for remote measurement of some canopy chemicals. Multivariate analysis of high-resolution spectral data in the near infrared region indicated significant correlations between spectral signals and N concentration and canopy N content; the correlation with canopy N content was stronger and was probably associated in part with water absorption features of the forest canopy. The spectral bands that were significantly correlated with lignin concentration and content were similar to bands selected in the other laboratory and airborne studies; starch concentrations were not significantly related to spectral reflectance data. Strong relationships between the spectral position of specific reflectance features in the visible region and chlorophyll were also found.

Matson, Pamela↗

NASA NTRS1986

A variational assimilation method for satellite and conventional data: Development of basic model for diagnosis of cyclone systems

A three-dimensional diagnostic model for the assimilation of satellite and conventional meteorological data is developed with the variational method of undetermined multipliers. Gridded fields of data from different type, quality, location, and measurement source are weighted according to measurement accuracy and merged using least squares criteria so that the two nonlinear horizontal momentum equations, the hydrostatic equation, and an integrated continuity equation are satisfied. The model is used to compare multivariate variational objective analyses with and without satellite data with initial analyses and the observations through criteria that were determined by the dynamical constraints, the observations, and pattern recognition. It is also shown that the diagnoses of local tendencies of the horizontal velocity components are in good comparison with the observed patterns and tendencies calculated with unadjusted data. In addition, it is found that the day-night difference in TOVS biases are statistically different (95% confidence) at most levels. Also developed is a hybrid nonlinear sigma vertical coordinate that eliminates hydrostatic truncation error in the middle and upper troposphere and reduces truncation error in the lower troposphere. Finally, it is found that the technique used to grid the initial data causes boundary effects to intrude into the interior of the analysis a distance equal to the average separation between observations.

Achtemeier, G. L.↗

NASA NTRSDate not supplied

A Novel Machine Learning Method for Surface PM2.5 Estimations from Geostationary Satellites

Particulate matter (PM) with a diameter of less or equal to 2.5 μm, known as PM , affects human health as it penetrates the respiratory system. The Environmental Protection Agency (EPA) measures the atmospheric concentration of PM using air quality monitors stationed throughout the Continental United States (CONUS). Such measurements are points on a spatial domain and therefore, might not be representative of the air quality at nearby areas considering that the composition of the atmosphere is highly variable from place to place. Satellite based AOD permits a spatially uniform means of estimating PM and new geostationary satellites provide high temporal and spatial resolution estimation of AOD. However, the concentration of PM is non-linearly dependent on other atmospheric parameters that include relative humidity, temperature, and height of the planetary boundary layer. This information may be estimated at similar spatial and temporal resolutions as AOD from numerical modeling such as from the National Oceanic and Atmospheric Administration’s (NOAA) High Resolution Rapid Refresh (HRRR) model which resolves near real-time atmospheric conditions over the CONUS. The estimation of PM concentration is a multi-parametric problem that considers the effect of temporal dependencies among the different parameters. Deep learning approaches are appropriate for such complex estimation problems as they intrinsically capture relations among multiple non-linear parameters. This study compares deep-learning methods to traditional regression analysis to demonstrate the capabilities of these methods in predicting PM2.5 concentrations. Additionally, a novel ensemble learning approach is employed to identify scientific processes that could further improve the estimation of PM concentration. Utilizing Long Short-Term Memory (LSTM) neural networks, which are suitable for multivariate time series estimation problems as they are capable of learning long-term dependencies, individual models are created for each EPA station and trained on the aforementioned dataset collocated over each station. Individual station models are merged if the model's performance is improved by reducing the root mean squared error (RMSE) metric. This ensemble training method ultimately reduces the RMSE value. Evaluation of these results provide insights into physical processes and related observable parameters that may contribute to PM concentrations. Identified parameters evaluated to be statistically different between the merged and unmerged models are expected to improve overall performance. These new parameters are then utilized for reevaluation of the deep learning methods with an extreme gradient boosting model with an RMSE of 5.5 providing the best results.

George Priftis↗

NASA NTRS2022

Deriving Severe Hail Likelihood from Satellite Observations and Model Reanalysis Parameters using a Deep Neural Network

Geostationary satellite imagers, such as those of the Geostationary Operational Environmental Satellite (GOES) series, have been observing severe convection at 15–60-minute intervals for over 40 years. When properly assessed, such a data record can be valuable in efforts of estimating severe storm risk throughout the diurnal cycle based on automated detection of patterns consistently found atop severe storms. Furthermore, environmental conditions favorable for severe weather are well-known and are thought to be represented well by modern reanalysis products. Promoting resilience against such hazards on local and global scales is a chief goal the NASA Disasters program, which seeks to encourage use of satellite observations to mitigate risk. For instance, hail is the costliest severe weather hazard across the globe in terms of insured loss, but reporting inconsistencies for hail events globally make it difficult to develop models that can quantify the risk. Satellite observation and model reanalysis taken together have the potential to, with reasonable skill and specificity, characterize environmental conditions that are favorable for hazardous weather, and thereby enable creation of hazard climatologie. Such climatologies are particularly useful over regions without extensive radar networks or storm reporting. By mapping the multivariate combination of observed cloud features and reanalysis environmental parameters/indices to United States Next Generation Weather Radar (NEXRAD) radar-estimated Maximum Expected Size of Hail (MESH) by way of a deep neural network (DNN), estimates of likelihood for potentially severe hail can be produced. Such estimates are of greater complexity and efficiency than could be performed with previous multivariate or logistic regression analyses for observed points within convective systems. Statistical distributions of convective parameters from satellite and reanalysis are shown to highlight non-severe/severe class separation for well-known hailstorm predictors, e.g., overshooting cloud top characteristics, deep-layer wind shear, mid-level stability, helicity, and convective inhibition. These complex, multivariate predictor relationships are exploited within a DNN, which can efficiently produce a quantitative hail risk metric with better than 70% detection rate and under 30% false alarms. These hail classifications can then be aggregated across the satellite record to yield a hazard climatology for hail frequency and severity – knowledge of which is of particular interest to those who manage risk (e.g., insurers) and are seeking opportunities to identify hail-prone regions, particularly in developing nations. This NASA study uses satellite observations and model parameters in a DNN to perform climatological hailstorm analysis in support of catastrophe model development, with the hope of promoting risk resilience particularly in regions without adequate weather radar coverage.

Passive Remote Sensing↗

NASA NTRS2004

Neural network uncertainty assessment using Bayesian statistics: a remote sensing application

Neural network (NN) techniques have proved successful for many regression problems, in particular for remote sensing; however, uncertainty estimates are rarely provided. In this article, a Bayesian technique to evaluate uncertainties of the NN parameters (i.e., synaptic weights) is first presented. In contrast to more traditional approaches based on point estimation of the NN weights, we assess uncertainties on such estimates to monitor the robustness of the NN model. These theoretical developments are illustrated by applying them to the problem of retrieving surface skin temperature, microwave surface emissivities, and integrated water vapor content from a combined analysis of satellite microwave and infrared observations over land. The weight uncertainty estimates are then used to compute analytically the uncertainties in the network outputs (i.e., error bars and correlation structure of these errors). Such quantities are very important for evaluating any application of an NN model. The uncertainties on the NN Jacobians are then considered in the third part of this article. Used for regression fitting, NN models can be used effectively to represent highly nonlinear, multivariate functions. In this situation, most emphasis is put on estimating the output errors, but almost no attention has been given to errors associated with the internal structure of the regression model. The complex structure of dependency inside the NN is the essence of the model, and assessing its quality, coherency, and physical character makes all the difference between a blackbox model with small output errors and a reliable, robust, and physically coherent model. Such dependency structures are described to the first order by the NN Jacobians: they indicate the sensitivity of one output with respect to the inputs of the model for given input data. We use a Monte Carlo integration procedure to estimate the robustness of the NN Jacobians. A regularization strategy based on principal component analysis is proposed to suppress the multicollinearities in order to make these Jacobians robust and physically meaningful.

Neural Networks (Computer)↗

NASA NTRS2009

An Update on Mortality in the U.S. Astronaut Corps: 1959-2009

Although it has now been over 50 years since mankind first ventured into space, the long-term health impacts of human space flight remain largely unknown. Identifying factors that affect survival and prognosis among those who participate in space flight is vitally important, as the era of commercial space flight approaches and NASA prepares for missions to Mars. The Longitudinal Study of Astronaut Health is a prospective study designed to examine trends in astronaut morbidity and mortality. The purpose of this analysis was to describe and explore predictors of overall and cause-specific mortality among individuals selected for the U.S. astronaut corps. All U.S. astronauts (n=321), regardless of flight status, were included in this analysis. Death certificate searches were conducted to ascertain vital status and cause of death through April 2009. Data were collected from medical records and lifestyle questionnaires. Multivariable Cox regression modeling was used to calculate the mortality hazard associated with embarking on space flight, adjusted for sex, race, and age at selection. Between 1959 and 2009, there were 39 (12.1%) deaths. Of these deaths, 18 (42.2%) were due to occupational accidents; 7 (17.9%) were due to other accidents; 6 (15.4%) were attributable to cancer; 6 (15.4%) resulted from cardiovascular/circulatory diseases; and 2 (5.1%) were from other causes. Participation in space flight did not significantly increase mortality hazard over time (adjusted hazard ratio=0.57; 95% confidence interval=0.26-1.26. Because our results are based on a small sample size, future research that includes payload specialists, other space flight participants, and international crew members is warranted to maximize statistical power.

Amirian, E.↗

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.↗