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NASA NTRS1999

Comparing Parameter Estimation Techniques for an Electrical Power Transformer Oil Temperature Prediction Model

This paper examines various sources of error in MIT's improved top oil temperature rise over ambient temperature model and estimation process. The sources of error are the current parameter estimation technique, quantization noise, and post-processing of the transformer data. Results from this paper will show that an output error parameter estimation technique should be selected to replace the current least squares estimation technique. The output error technique obtained accurate predictions of transformer behavior, revealed the best error covariance, obtained consistent parameter estimates, and provided for valid and sensible parameters. This paper will also show that the output error technique should be used to minimize errors attributed to post-processing (decimation) of the transformer data. Models used in this paper are validated using data from a large transformer in service.

Morris, A. Terry↗

NASA NTRS2000

Estimating Long Term Surface Soil Moisture in the GCIP Area From Satellite Microwave Observations

Soil moisture is an important component of the water and energy balances of the Earth's surface. Furthermore, it has been identified as a parameter of significant potential for improving the accuracy of large-scale land surface-atmosphere interaction models. However, accurate estimates of surface soil moisture are often difficult to make, especially at large spatial scales. Soil moisture is a highly variable land surface parameter, and while point measurements are usually accurate, they are representative only of the immediate site which was sampled. Simple averaging of point values to obtain spatial means often leads to substantial errors. Since remotely sensed observations are already a spatially averaged or areally integrated value, they are ideally suited for measuring land surface parameters, and as such, are a logical input to regional or larger scale land process models. A nine-year database of surface soil moisture is being developed for the Central United States from satellite microwave observations. This region forms much of the GCIP study area, and contains most of the Mississippi, Rio Grande, and Red River drainages. Daytime and nighttime microwave brightness temperatures were observed at a frequency of 6.6 GHz, by the Scanning Multichannel Microwave Radiometer (SMMR), onboard the Nimbus 7 satellite. The life of the SMMR instrument spanned from Nov. 1978 to Aug. 1987. At 6.6 GHz, the instrument provided a spatial resolution of approximately 150 km, and an orbital frequency over any pixel-sized area of about 2 daytime and 2 nighttime passes per week. Ground measurements of surface soil moisture from various locations throughout the study area are used to calibrate the microwave observations. Because ground measurements are usually only single point values, and since the time of satellite coverage does not always coincide with the ground measurements, the soil moisture data were used to calibrate a regional water balance for the top 1, 5, and 10 cm surface layers in order to interpolate daily surface moisture values. Such a climate-based approach is often more appropriate for estimating large-area spatially averaged soil moisture because meteorological data are generally more spatially representative than isolated point measurements of soil moisture. Vegetation radiative transfer characteristics, such as the canopy transmissivity, were estimated from vegetation indices such as the Normalized Difference Vegetation Index (NDVI) and the 37 GHz Microwave Polarization Difference Index (MPDI). Passive microwave remote sensing presents the greatest potential for providing regular spatially representative estimates of surface soil moisture at global scales. Real time estimates should improve weather and climate modelling efforts, while the development of historical data sets will provide necessary information for simulation and validation of long-term climate and global change studies.

Owe, Manfred↗

NASA NTRS2000

Improving the Discipline of Cost Estimation and Analysis

The need to improve the quality and accuracy of cost estimates of proposed new aerospace systems has been widely recognized. The industry has done the best job of maintaining related capability with improvements in estimation methods and giving appropriate priority to the hiring and training of qualified analysts. Some parts of Government, and National Aeronautics and Space Administration (NASA) in particular, continue to need major improvements in this area. Recently, NASA recognized that its cost estimation and analysis capabilities had eroded to the point that the ability to provide timely, reliable estimates was impacting the confidence in planning man), program activities. As a result, this year the Agency established a lead role for cost estimation and analysis. The Independent Program Assessment Office located at the Langley Research Center was given this responsibility.

Piland, William M.↗

NASA NTRS2000

Estimation of Handling Qualities Parameters of the Tu-144 Supersonic Transport Aircraft from Flight Test Data

Low order equivalent system (LOES) models for the Tu-144 supersonic transport aircraft were identified from flight test data. The mathematical models were given in terms of transfer functions with a time delay by the military standard MIL-STD-1797A, "Flying Qualities of Piloted Aircraft," and the handling qualities were predicted from the estimated transfer function coefficients. The coefficients and the time delay in the transfer functions were estimated using a nonlinear equation error formulation in the frequency domain. Flight test data from pitch, roll, and yaw frequency sweeps at various flight conditions were used for parameter estimation. Flight test results are presented in terms of the estimated parameter values, their standard errors, and output fits in the time domain. Data from doublet maneuvers at the same flight conditions were used to assess the predictive capabilities of the identified models. The identified transfer function models fit the measured data well and demonstrated good prediction capabilities. The Tu-144 was predicted to be between level 2 and 3 for all longitudinal maneuvers and level I for all lateral maneuvers. High estimates of the equivalent time delay in the transfer function model caused the poor longitudinal rating.

Curry, Timothy J.↗

NASA NTRS2000

A Texture-Polarization Method for Estimating Convective/Stratiform Precipitation Area Coverage from Passive Microwave Radiometer Data

Observational and modeling studies have described the relationships between convective/stratiform rain proportion and the vertical distributions of vertical motion, latent heating, and moistening in mesoscale convective systems. Therefore, remote sensing techniques which can quantify the relative areal proportion of convective and stratiform, rainfall can provide useful information regarding the dynamic and thermodynamic processes in these systems. In the present study, two methods for deducing the convective/stratiform areal extent of precipitation from satellite passive microwave radiometer measurements are combined to yield an improved method. If sufficient microwave scattering by ice-phase precipitating hydrometeors is detected, the method relies mainly on the degree of polarization in oblique-view, 85.5 GHz radiances to estimate the area fraction of convective rain within the radiometer footprint. In situations where ice scattering is minimal, the method draws mostly on texture information in radiometer imagery at lower microwave frequencies to estimate the convective area fraction. Based upon observations of ten convective systems over ocean and nine systems over land, instantaneous 0.5 degree resolution estimates of convective area fraction from the Tropical Rainfall Measuring Mission Microwave Imager (TRMM TMI) are compared to nearly coincident estimates from the TRMM Precipitation Radar (TRMM PR). The TMI convective area fraction estimates are slightly low-biased with respect to the PR, with TMI-PR correlations of 0.78 and 0.84 over ocean and land backgrounds, respectively. TMI monthly-average convective area percentages in the tropics and subtropics from February 1998 exhibit the greatest values along the ITCZ and in continental regions of the summer (southern) hemisphere. Although convective area percentages. from the TMI are systematically lower than those from the PR, monthly rain patterns derived from the TMI and PR rain algorithms are very similar. TMI rain depths are significantly higher than corresponding rain depths from the PR in the ITCZ, but are similar in magnitude elsewhere.

Olson, William S.↗

NASA NTRS2000

Real-Time Parameter Estimation in the Frequency Domain

A method for real-time estimation of parameters in a linear dynamic state-space model was developed and studied. The application is aircraft dynamic model parameter estimation from measured data in flight. Equation error in the frequency domain was used with a recursive Fourier transform for the real-time data analysis. Linear and nonlinear simulation examples and flight test data from the F-18 High Alpha Research Vehicle were used to demonstrate that the technique produces accurate model parameter estimates with appropriate error bounds. Parameter estimates converged in less than one cycle of the dominant dynamic mode, using no a priori information, with control surface inputs measured in flight during ordinary piloted maneuvers. The real-time parameter estimation method has low computational requirements and could be implemented

Morelli, Eugene A.↗

NASA NTRS2001

Fast Quaternion Attitude Estimation from Two Vector Measurements

Many spacecraft attitude determination methods use exactly two vector measurements. The two vectors are typically the unit vector to the Sun and the Earth's magnetic field vector for coarse "sun-mag" attitude determination or unit vectors to two stars tracked by two star trackers for fine attitude determination. Existing closed-form attitude estimates based on Wahba's optimality criterion for two arbitrarily weighted observations are somewhat slow to evaluate. This paper presents two new fast quaternion attitude estimation algorithms using two vector observations, one optimal and one suboptimal. The suboptimal method gives the same estimate as the TRIAD algorithm, at reduced computational cost. Simulations show that the TRIAD estimate is almost as accurate as the optimal estimate in representative test scenarios.

Markley, F. Landis↗

NASA NTRS2001

Robust Fault Detection Using Robust Z1 Estimation and Fuzzy Logic

This research considers the application of robust Z(sub 1), estimation in conjunction with fuzzy logic to robust fault detection for an aircraft fight control system. It begins with the development of robust Z(sub 1) estimators based on multiplier theory and then develops a fixed threshold approach to fault detection (FD). It then considers the use of fuzzy logic for robust residual evaluation and FD. Due to modeling errors and unmeasurable disturbances, it is difficult to distinguish between the effects of an actual fault and those caused by uncertainty and disturbance. Hence, it is the aim of a robust FD system to be sensitive to faults while remaining insensitive to uncertainty and disturbances. While fixed thresholds only allow a decision on whether a fault has or has not occurred, it is more valuable to have the residual evaluation lead to a conclusion related to the degree of, or probability of, a fault. Fuzzy logic is a viable means of determining the degree of a fault and allows the introduction of human observations that may not be incorporated in the rigorous threshold theory. Hence, fuzzy logic can provide a more reliable and informative fault detection process. Using an aircraft flight control system, the results of FD using robust Z(sub 1) estimation with a fixed threshold are demonstrated. FD that combines robust Z(sub 1) estimation and fuzzy logic is also demonstrated. It is seen that combining the robust estimator with fuzzy logic proves to be advantageous in increasing the sensitivity to smaller faults while remaining insensitive to uncertainty and disturbances.

Curry, Tramone↗

NASA NTRS2003

Combined Radiometer-Radar Microphysical Profile Estimations with Emphasis on High Frequency Brightness Temperature Observations

Information about the vertical microphysical cloud structure is useful in many modeling and predictive practices. Radiometers and radars are used to observe hydrometeor properties. This paper describes an iterative retrieval algorithm that combines the use of airborne active and wideband (10 to 340 GHz) passive observations to estimate the vertical content and particle size distributions of liquid and frozen hydrometeors. The physically-based retrieval algorithm relies on the high frequencies (greater than 89 GHz) to provide details on the frozen hydrometeors. Neglecting the high frequencies yielded acceptable estimates of the liquid profiles, but the ice profiles were poorly retrieved. Airborne radar and radiometer observations from the third Convection and Moisture EXperiment (CAMEX-3) were used in the retrieval algorithm as constraints. Nadir profiles were estimated for a minute each of flight time (approximately 12.5 km along track) from an anvil, convection, and quasi- stratiform rain. The complex structure of the frozen hydrometeors required the most iterations for convergence for the anvil cloud type. The wideband observations were found to more than double the estimated frozen hydrometeor content as compared to retrievals using only 90-GHz and below. The convective and quasi-stratiform quickly reached convergence (minimized difference between observations and calculations using the estimated profiles). A qualitative validation using coincident in situ CAMEX-3 observations shows that the retrieved particle size distributions are well corroborated with independent measurements.

Gail Skofronick-Jackson↗

NASA NTRS1995

Brazil Fire Characterization and Burn Area Estimation Using the Airborne Infrared Disaster Assessment (AIRDAS) System

Remotely sensed estimations of regional and global emissions from biomass combustion have been used to characterize fire behavior, determine fire intensity, and estimate burn area. Highly temporal, low resolution satellite data have been used to calculate estimates of fire numbers and area burned. These estimates of fire activity and burned area have differed dramatically, resulting in a wide range of predictions on the ecological and environmental impacts of fires. As part of the Brazil/United States Fire Initiative, an aircraft campaign was initiated in 1992 and continued in 1994. This multi-aircraft campaign was designed to assist in the characterization of fire activity, document fire intensity and determine area burned over prescribed, agricultural and wildland fires in the savanna and forests of central Brazil. Using a unique, multispectral scanner (AIRDAS), designed specifically for fire characterization, a variety of fires and burned areas were flown with a high spatial and high thermal resolution scanner. The system was used to measure flame front size, rate of spread, ratio of smoldering to flaming fronts and fire intensity. In addition, long transects were flown to determine the size of burned areas within the cerrado and transitional ecosystems. The authors anticipate that the fire activity and burned area estimates reported here will lead to enhanced information for precise regional trace gas prediction.

Brass, J. A.↗

NASA NTRS1996

Adjustment of Sensor Locations During Thermal Property Parameter Estimation

The temperature dependent thermal properties of a material may be evaluated from transient temperature histories using nonlinear parameter estimation techniques. The usual approach is to minimize the sum of the squared errors between measured and calculated temperatures at specific locations in the body. Temperature measurements are usually made with thermocouples and it is customary to take thermocouple locations as known and fixed during parameter estimation computations. In fact, thermocouple locations are never known exactly. Location errors on the order of the thermocouple wire diameter are intrinsic to most common instrumentation procedures (e.g., inserting a thermocouple into a drilled hole) and additional errors can be expected for delicate materials, difficult installations, large thermocouple beads, etc.. Thermocouple location errors are especially significant when estimating thermal properties of low diffusively materials which can sustain large temperature gradients during testing. In the present work, a parameter estimation formulation is presented which allows for the direct inclusion of thermocouple positions into the primary parameter estimation procedure. It is straightforward to set bounds on thermocouple locations which exclude non-physical locations and are consistent with installation tolerances. Furthermore, bounds may be tightened to an extent consistent with any independent verification of thermocouple location, such as x-raying, and so the procedure is entirely consonant with experimental information. A mathematical outline of the procedure is given and its implementation is illustrated through numerical examples characteristic of light-weight, high-temperature ceramic insulation during transient heating. The efficacy and the errors associated with the procedure are discussed.

Milos, Frank S.↗

NASA NTRS2002

Finite Element A Posteriori Error Estimation for Heat Conduction

This research investigates residual-based a posteriori error estimates for finite element approximations of heat conduction in single-layer and multi-layered materials. The finite element approximation, based upon hierarchical modelling combined with p-version finite elements, is described with specific application to a two-dimensional, steady state, heat-conduction problem. Element error indicators are determined by solving an element equation for the error with the element residual as a source, and a global error estimate in the energy norm is computed by collecting the element contributions. Numerical results of the performance of the error estimate are presented by comparisons to the actual error. Two methods are discussed and compared for approximating the element boundary flux. The equilibrated flux method provides more accurate results for estimating the error than the average flux method. The error estimation is applied to multi-layered materials with a modification to the equilibrated flux method to approximate the discontinuous flux along a boundary at the material interfaces. A directional error indicator is developed which distinguishes between the hierarchical modeling error and the finite element error. Numerical results are presented for single-layered materials which show that the directional indicators accurately determine which contribution to the total error dominates.

Lang, Christapher G.↗

NASA NTRS2002

Linear Parameter Varying Control Synthesis for Actuator Failure, Based on Estimated Parameter

The design of a linear parameter varying (LPV) controller for an aircraft at actuator failure cases is presented. The controller synthesis for actuator failure cases is formulated into linear matrix inequality (LMI) optimizations based on an estimated failure parameter with pre-defined estimation error bounds. The inherent conservatism of an LPV control synthesis methodology is reduced using a scaling factor on the uncertainty block which represents estimated parameter uncertainties. The fault parameter is estimated using the two-stage Kalman filter. The simulation results of the designed LPV controller for a HiMXT (Highly Maneuverable Aircraft Technology) vehicle with the on-line estimator show that the desired performance and robustness objectives are achieved for actuator failure cases.

Shin, Jong-Yeob↗

NASA NTRS2003

Kalman Filtering with Inequality Constraints for Turbofan Engine Health Estimation

Kalman filters are often used to estimate the state variables of a dynamic system. However, in the application of Kalman filters some known signal information is often either ignored or dealt with heuristically. For instance, state variable constraints (which may be based on physical considerations) are often neglected because they do not fit easily into the structure of the Kalman filter. This paper develops two analytic methods of incorporating state variable inequality constraints in the Kalman filter. The first method is a general technique of using hard constraints to enforce inequalities on the state variable estimates. The resultant filter is a combination of a standard Kalman filter and a quadratic programming problem. The second method uses soft constraints to estimate state variables that are known to vary slowly with time. (Soft constraints are constraints that are required to be approximately satisfied rather than exactly satisfied.) The incorporation of state variable constraints increases the computational effort of the filter but significantly improves its estimation accuracy. The improvement is proven theoretically and shown via simulation results. The use of the algorithm is demonstrated on a linearized simulation of a turbofan engine to estimate health parameters. The turbofan engine model contains 16 state variables, 12 measurements, and 8 component health parameters. It is shown that the new algorithms provide improved performance in this example over unconstrained Kalman filtering.

Simon, Dan↗

NASA NTRS2003

On the Singularity in the Estimation of the Quaternion-of-Rotation

It has been claimed in the archival literature that the covariance matrix of a Kalman filter, which is designed to estimate the quaternion-of-rotation, is necessarily rank deficient because the normality constraint of the quaternion produces dependence between the quaternion elements. In reality, though, this phenomenon does not occur. The covariance matrix is not singular, and the filter is well behaved. Several simple examples are presented that demonstrate the regularity of the covariance matrix. First, estimation cases are presented where a relationship exists between the estimated variables, and yet the covariance matrix is not singular. Then the particular problem of quaternion estimation is analyzed. It is shown that the discrepancy stems from the fact that a functional relationship exists between the elements of the true quaternion but not between its estimated elements.

Bar-Itzhack, Itzhack Y.↗

NASA NTRS2001

Estimates of M2 Tidal Energy Dissipation from TOPEX/Poseidon Altimeter Data

Most of the tidal energy dissipation in the ocean occurs in shallow seas, as has long been recognized. However, recent work has suggested that a significant fraction of the dissipation, perhaps 1 TW or more, occurs in the deep ocean. This paper builds further evidence for that conclusion. More than 6 years of data from the TOPEX/Poseidon satellite altimeter are used to map the tidal dissipation rate throughout the world ocean. The dissipation rate is estimated as a balance between the rate of working by tidal forces and the energy flux divergence, computed using currents derived by least squares fitting of the altimeter data and the shallow water equations. Such calculations require dynamical assumptions, in particular about the nature of dissipation. To assess sensitivity of dissipation estimates to input assumptions, a large suite of tidal inversions based on a wide range of drag parameterizations and employing both real and synthetic altimeter data are compared. These experiments and Monte Carlo error fields from a generalized inverse model are used to establish error uncertainties for the dissipation estimates. Owing to the tight constraints on tidal elevation fields provided by the altimeter, area integrals of the energy balance are remarkably insensitive to required dynamical assumptions. Tidal energy dissipation is estimated for all major shallow seas (excluding individual polar seas) and compared with previous model and data-based estimates. Dissipation in the open ocean is significantly tnhanced around major bathymetric features, in a manner consistent with simple theories the generation of baroclinic tides.

Egbert, Gary D.↗

NASA NTRS2003

Estimates of Random Error in Satellite Rainfall Averages

Satellite rain estimates are most accurate when obtained with microwave instruments on low earth-orbiting satellites. Estimation of daily or monthly total areal rainfall, typically of interest to hydrologists and climate researchers, is made difficult, however, by the relatively poor coverage generally available from such satellites. Intermittent coverage by the satellites leads to random "sampling error" in the satellite products. The inexact information about hydrometeors inferred from microwave data also leads to random "retrieval errors" in the rain estimates. In this talk we will review approaches to quantitative estimation of the sampling error in area/time averages of satellite rain retrievals using ground-based observations, and methods of estimating rms random error, both sampling and retrieval, in averages using satellite measurements themselves.

Bell, Thomas L.↗

NASA NTRS2004

Multivariate Error Covariance Estimates by Monte-Carlo Simulation for Assimilation Studies in the Pacific Ocean

One of the most difficult aspects of ocean state estimation is the prescription of the model forecast error covariances. The paucity of ocean observations limits our ability to estimate the covariance structures from model-observation differences. In most practical applications, simple covariances are usually prescribed. Rarely are cross-covariances between different model variables used. Here a comparison is made between a univariate Optimal Interpolation (UOI) scheme and a multivariate OI algorithm (MvOI) in the assimilation of ocean temperature. In the UOI case only temperature is updated using a Gaussian covariance function and in the MvOI salinity, zonal and meridional velocities as well as temperature, are updated using an empirically estimated multivariate covariance matrix. Earlier studies have shown that a univariate OI has a detrimental effect on the salinity and velocity fields of the model. Apparently, in a sequential framework it is important to analyze temperature and salinity together. For the MvOI an estimation of the model error statistics is made by Monte-Carlo techniques from an ensemble of model integrations. An important advantage of using an ensemble of ocean states is that it provides a natural way to estimate cross-covariances between the fields of different physical variables constituting the model state vector, at the same time incorporating the model's dynamical and thermodynamical constraints as well as the effects of physical boundaries. Only temperature observations from the Tropical Atmosphere-Ocean array have been assimilated in this study. In order to investigate the efficacy of the multivariate scheme two data assimilation experiments are validated with a large independent set of recently published subsurface observations of salinity, zonal velocity and temperature. For reference, a third control run with no data assimilation is used to check how the data assimilation affects systematic model errors. While the performance of the UOI and MvOI is similar with respect to the temperature field, the salinity and velocity fields are greatly improved when multivariate correction is used, as evident from the analyses of the rms differences of these fields and independent observations. The MvOI assimilation is found to improve upon the control run in generating the water masses with properties close to the observed, while the UOI failed to maintain the temperature and salinity structure.

Borovikov, Anna↗