Results for “error estimation” — Page 25

NASA NTRS2020

Cramer-Rao Lower Bound for SoOp-R-Based Root-Zone Soil Moisture Remote Sensing

Signals of opportunity (SoOp) reflectometry (SoOp-R) is a maturing field for geophysical remote sensing as evidenced by the growing number of airborne and spaceborne experiments. As this approach receives more attention, it is worth analyzing SoOp-R’s capabilities to retrieve subsurface soil moisture (SM) by leveraging communication and navigation satellite transmitters. In this research, the CRLB is used to identify the effects of variable SoOp-R parameters on the best achievable estimation error for root-zone soil moisture (RZSM). This study investigates the use of multiple frequency, polarization, and incidence angle measurement configurations on a two-layered dielectric profile. The results also detail the effects of variable SM conditions on the capability of SoOp-R systems to predict subsurface SM. The most prevalent observation is the importance of using at least two frequencies to limit uncertainties from subsurface SM estimates. If at least two frequencies are used, the CRLB of a profile is retrievable within the root-zone depending on the surface SM content as well as the number of independent measurements of the profile. For a depth of 30 cm, it is observed that a CRLB corresponding to 4% RZSM estimation accuracy is achievable with as few as 2 dual-frequency-based SoOp-R measurements. For this depth, increasing number of measurements provided by polarization and incidence angle allow for sensing of increasingly wet SM profile structures. This study, overall, details a methodology by which SoOp-R receiver system can be designed to achieve a desired CRLB using a trade-off study between the available measurements and SM profile.

Signals of Opportunity (SoOp)↗

NASA NTRS1996

Coherent Lidar Design and Performance Verification

This final report summarizes the investigative results from the 3 complete years of funding and corresponding publications are listed. The first year saw the verification of beam alignment for coherent Doppler lidar in space by using the surface return. The second year saw the analysis and computerized simulation of using heterodyne efficiency as an absolute measure of performance of coherent Doppler lidar. A new method was proposed to determine the estimation error for Doppler lidar wind measurements without the need for an independent wind measurement. Coherent Doppler lidar signal covariance, including wind shear and turbulence, was derived and calculated for typical atmospheric conditions. The effects of wind turbulence defined by Kolmogorov spatial statistics were investigated theoretically and with simulations. The third year saw the performance of coherent Doppler lidar in the weak signal regime determined by computer simulations using the best velocity estimators. Improved algorithms for extracting the performance of velocity estimators with wind turbulence included were also produced.

Frehlich, Rod↗

NASA NTRS1978

Kalman filter divergence and aircraft motion estimators

Kalman filters designed for many aerospace systems turn out to be unsatisfactory. The estimate errors become large compared to the errors predicted by the theory ('divergence'). One of the principal causes of this failure is that the system model contains states or modes that are undisturbed by the modeled process noise, and are neutrally stable (NS). One cure for such problems is periodic restarting of a time-varying Kalman filter. Other cures include minimum variance observers with eigenvalue constraints, added noise, pole-shifting, and destabilization. Several examples are given, including effective time-invariant estimators for the longitudinal and lateral motions of an airplane where several NS modes are undisturbed by wind gusts. An interpretation of these estimators as a 'strapdown IMU' without accelerometers, gimbaled gyros, or servos is given.

Bryson, A. E., Jr.↗

NASA NTRS1990

Consistency and convergence for numerical radiation conditions

The problem of imposing radiation conditions at artificial boundaries for the numerical simulation of wave propagation is considered. Emphasis is on the behavior and analysis of the error which results from the restriction of the domain. The theory of error estimation is briefly outlined for boundary conditions. Use is made of the asymptotic analysis of propagating wave groups to derive and analyze boundary operators. For dissipative problems this leads to local, accurate conditions, but falls short in the hyperbolic case. A numerical experiment on the solution of the wave equation with cylindrical symmetry is described. A unified presentation of a number of conditions which have been proposed in the literature is given and the time dependence of the error which results from their use is displayed. The results are in qualitative agreement with theoretical considerations. It was found, however, that for this model problem it is particularly difficult to force the error to decay rapidly in time.

Hagstrom, Thomas↗

NASA NTRS2014

Numerical Simulations For the F-16XL Aircraft Configuration

Numerical simulations of flow around the F-16XL are presented as a contribution to the Cranked Arrow Wing Aerodynamic Project International II (CAWAPI-II). The NASA Tetrahedral Unstructured Software System (TetrUSS) is used to perform numerical simulations. This CFD suite, developed and maintained by NASA Langley Research Center, includes an unstructured grid generation program called VGRID, a postprocessor named POSTGRID, and the flow solver USM3D. The CRISP CFD package is utilized to provide error estimates and grid adaption for verification of USM3D results. A subsonic high angle-of-attack case flight condition (FC) 25 is computed and analyzed. Three turbulence models are used in the calculations: the one-equation Spalart-Allmaras (SA), the two-equation shear stress transport (SST) and the kε turbulence models. Computational results, and surface static pressure profiles are presented and compared with flight data. Solution verification is performed using formal grid refinement studies, the solution of Error Transport Equations, and adaptive mesh refinement. The current study shows that the USM3D solver coupled with CRISP CFD can be used in an engineering environment in predicting vortex-flow physics on a complex configuration at flight Reynolds numbers.

Elmiligui, Alaa A.↗

DOE OSTI2024

On the Training and Generalization of Deep Operator Networks

Here, we present a novel training method for deep operator networks (DeepONets), one of the most popular neural network models for operators. DeepONets are constructed by two subnetworks, namely the branch and trunk networks. Typically, the two subnetworks are trained simultaneously, which amounts to solving a complex optimization problem in a high dimensional space. In addition, the nonconvex and nonlinear nature makes training very challenging. To tackle such a challenge, we propose a two-step training method that trains the trunk network first and then sequentially trains the branch network. The core mechanism is motivated by the divide-and-conquer paradigm and is the decomposition of the entire complex training task into two subtasks with reduced complexity. Therein the Gram–Schmidt orthonormalization process is introduced which significantly improves stability and generalization ability. On the theoretical side, we establish a generalization error estimate in terms of the number of training data, the width of DeepONets, and the number of input and output sensors. Numerical examples are presented to demonstrate the effectiveness of the two-step training method, including Darcy flow in heterogeneous porous media.

deep operator networks↗

NASA NTRS1988

Flood basalt eruptions, comet showers, and mass extinction events

A chronology of initiation dates of the major continental flood basalt episodes has been established from compilation of published K-Ar and Ar-Ar ages of basaltic flows and related basic intrusions. The dating is therefore independent of the biostratigraphic and paleomagnetic time scales, and the estimated errors of the inititation dates are approximately + or - 4 pct. There are 11 distinct episodes of continental flood basalts known during the past 250 Myr. The data show that flood basalt episodes are generally relatively brief geologic events, with intermittent eruptions during peak output periods lasting ony 2 to 3 Myr or less. Statistical analyses suggest that these episodes may have occurred quasi-periodically with a mean cycle time of 32 + or - 1 Myr. The initiation dates of the flood basalts are close to the estimated dates of marine mass extinctions and impact-crater clusters. Although a purely internal forcing might be argued for the flood basalt volcanism, quasi-periodic comet impacts may be the trigger for both the flood basalts and the extinctions. Impact cratering models suggest that large-body impactors lead to deep initial cratering, and therefore may cause mantle disturbances and initiate mantle plume activity. The flood basalt episodes commonly mark the initiation or jump of a mantle hotspot, and are often followed by continental rifting and separation. Evidence from dynamical studies of impacts, occurrences of craters and hotspots, and the geochemistry of boundary layers is synthesized to provide a possible model of impact-generated volcanism. Flood basalt eruptions may themselves have severe effects on climate, and possibly on life. Impacts might, as a result, have led to mass extinctions through direct atmospheric disturbances, and/or indirectly through prolonged flood basalt volcanism.

Rampino, Michael R.↗

DOE OSTI2024

Error and Correction Analysis for the FFA@CEBAF Energy Upgrade

An energy upgrade design for the Continuous Electron Beam Accelerator Facility (CEBAF) is under development, using fixed field alternating gradient (FFA) return arcs to recirculate electron beam up to an additional five times through the accelerating structures at CEBAF. A necessary component of any large accelerator is a beam steering and optical correction system. Small environmental changes and system errors can lower beam quality or even shut down the machine; and in pursuit of the scientific mission of JLab, high quality electron beams must be delivered to the experimental halls on a predictable schedule. Correction in the novel FFA arcs of the current upgrade design is complicated by several factors. These complexities inform the choice of correction algorithm structure and parameter values. A baseline algorithm in addition to diagnostic and correction hardware configuration is presented. The effect of this correction protocol is shown with respect to estimated errors, and several possible extensions of the algorithm are discussed. This work presents an important proof of concept for the FFA@CEBAF design effort, and provides a functional correction strategy which may be simply adjusted and optimized for future design changes.

Coxe, Alex [Old Dominion Univ., Norfolk, VA (Unite↗

NASA NTRS2021

Trend Detection of Atmospheric Time Series: Incorporating Appropriate Uncertainty Estimates and Handling Extreme Events

This paper is aimed at atmospheric scientists without formal training in statistical theory. Its goal is to, 1) provide a critical review of the rationale for trend analysis of the time series typically encountered in the field of atmospheric chemistry; 2) describe a range of trend-detection methods; and 3) demonstrate effective means of conveying the results to a general audience. Trend detections in atmospheric chemical composition data are often challenged by a variety of sources of uncertainty, which often behave differently to other environmental phenomena such as temperature, precipitation rate, or stream flow, and may require specific methods depending on the science questions to be addressed. Some sources of uncertainty can be explicitly included in the model specification, such as autocorrelation and seasonality, but some inherent uncertainties are difficult to quantify, such as data heterogeneity and measurement uncertainty due to the combined effect of short- and long-term natural variability, instrumental stability, and aggregation of data from sparse sampling frequency. Failure to account for these uncertainties might result in an inappropriate inference of the trends and their estimation errors. On the other hand, the variation in extreme events might be interesting for different scientific questions, for example, the frequency of extremely high surface ozone events and their relevance to human health. In this study we aim to, 1) review trend detection methods for addressing different levels of data complexity in different chemical species; 2) demonstrate that the incorporation of scientifically interpretable covariates can outperform pure numerical curve fitting techniques in terms of uncertainty reduction and improved predictability; 3) illustrate the study of trends based on extreme quantiles that can provide insight beyond standard mean or median based trend estimates; and 4) present an advanced method of quantifying regional trends based on the inter-site correlations of multi-site data. All demonstrations are based on time series of observed trace gases relevant to atmospheric chemistry, but the methods can be applied to other environmental data sets.

Trace gas↗

NASA NTRS1986

Interaction of the equatorial midnight pressure bulge and thermospheric zonal winds

The zonal component of the thermospheric neutral wind in the equatorial region is found to flow eastward all night, having a minimum near midnight. The data, obtained by Spencer et al. on the Dynamics Explorer-2 (DE-2) satellite, and reported more recently by Wharton et al., indicate that the minimum feature is significant. The minimum is illustrated by a 4th order Fourier series fit to the data points reported by Wharton et al. A table gives the amplitudes and phases of the four harmonic components used with the estimated error for each amplitude. It is asked whether this behavior is due to the local passage of the equatorial midnight pressure bulge associated with the midnight temperature anomaly. If so, it is to be expected that other data characterizing the midnight temperature anomaly should show consistency with this observation, especially in view of the large changes observed in the zonal velocity in the midnight sector. Consistency in momentum conservation may be checked using available data from previous independent experiments. Such data, taken under similar conditions of solar activity, was substituted into the momentum equation and found to be consistent using a priori estimates of the effect of viscosity.

Herrero, F. A.↗

NASA NTRS2006

Parallel Estimation and Control Architectures for Deep-Space Formation Flying Spacecraft

The formation flying of precisely controlled spacecraft in deep space can be used to implement optical instruments capable of imaging planets in other solar systems. The distance of the formation from Earth necessitates a significant level of autonomy and each spacecraft must base its actions on its estimates of the location and velocity of the other spacecraft. Precise coordination and control is the key requirement in such missions and the flow of information between spacecraft must be carefully designed. Doing this in an efficient and optimal manner requires novel techniques for the design of the on-board estimators. The use of standard Kalman filter-based designs can lead to unanticipated dynamics--which we refer to as disagreement dynamics--in the estimators' errors. We show how communication amongst the spacecraft can be designed in order to control all of the dynamics within the formation. We present several results relating the topology of the communication network to the resulting closed-loop control dynamics of the formation. The consequences for the design of the control, communication and coordination are discussed.

distributed control↗

NASA NTRS2015

Sensor Selection for Aircraft Engine Performance Estimation and Gas Path Fault Diagnostics

This paper presents analytical techniques for aiding system designers in making aircraft engine health management sensor selection decisions. The presented techniques, which are based on linear estimation and probability theory, are tailored for gas turbine engine performance estimation and gas path fault diagnostics applications. They enable quantification of the performance estimation and diagnostic accuracy offered by different candidate sensor suites. For performance estimation, sensor selection metrics are presented for two types of estimators including a Kalman filter and a maximum a posteriori estimator. For each type of performance estimator, sensor selection is based on minimizing the theoretical sum of squared estimation errors in health parameters representing performance deterioration in the major rotating modules of the engine. For gas path fault diagnostics, the sensor selection metric is set up to maximize correct classification rate for a diagnostic strategy that performs fault classification by identifying the fault type that most closely matches the observed measurement signature in a weighted least squares sense. Results from the application of the sensor selection metrics to a linear engine model are presented and discussed. Given a baseline sensor suite and a candidate list of optional sensors, an exhaustive search is performed to determine the optimal sensor suites for performance estimation and fault diagnostics. For any given sensor suite, Monte Carlo simulation results are found to exhibit good agreement with theoretical predictions of estimation and diagnostic accuracies.

Gas Turbine Engines↗

NASA NTRS2015

Sensor Selection for Aircraft Engine Performance Estimation and Gas Path Fault Diagnostics

This paper presents analytical techniques for aiding system designers in making aircraft engine health management sensor selection decisions. The presented techniques, which are based on linear estimation and probability theory, are tailored for gas turbine engine performance estimation and gas path fault diagnostics applications. They enable quantification of the performance estimation and diagnostic accuracy offered by different candidate sensor suites. For performance estimation, sensor selection metrics are presented for two types of estimators including a Kalman filter and a maximum a posteriori estimator. For each type of performance estimator, sensor selection is based on minimizing the theoretical sum of squared estimation errors in health parameters representing performance deterioration in the major rotating modules of the engine. For gas path fault diagnostics, the sensor selection metric is set up to maximize correct classification rate for a diagnostic strategy that performs fault classification by identifying the fault type that most closely matches the observed measurement signature in a weighted least squares sense. Results from the application of the sensor selection metrics to a linear engine model are presented and discussed. Given a baseline sensor suite and a candidate list of optional sensors, an exhaustive search is performed to determine the optimal sensor suites for performance estimation and fault diagnostics. For any given sensor suite, Monte Carlo simulation results are found to exhibit good agreement with theoretical predictions of estimation and diagnostic accuracies.

Gas Turbine Engines↗

NASA NTRS2016

Sensor Selection for Aircraft Engine Performance Estimation and Gas Path Fault Diagnostics

This paper presents analytical techniques for aiding system designers in making aircraft engine health management sensor selection decisions. The presented techniques, which are based on linear estimation and probability theory, are tailored for gas turbine engine performance estimation and gas path fault diagnostics applications. They enable quantification of the performance estimation and diagnostic accuracy offered by different candidate sensor suites. For performance estimation, sensor selection metrics are presented for two types of estimators including a Kalman filter and a maximum a posteriori estimator. For each type of performance estimator, sensor selection is based on minimizing the theoretical sum of squared estimation errors in health parameters representing performance deterioration in the major rotating modules of the engine. For gas path fault diagnostics, the sensor selection metric is set up to maximize correct classification rate for a diagnostic strategy that performs fault classification by identifying the fault type that most closely matches the observed measurement signature in a weighted least squares sense. Results from the application of the sensor selection metrics to a linear engine model are presented and discussed. Given a baseline sensor suite and a candidate list of optional sensors, an exhaustive search is performed to determine the optimal sensor suites for performance estimation and fault diagnostics. For any given sensor suite, Monte Carlo simulation results are found to exhibit good agreement with theoretical predictions of estimation and diagnostic accuracies.

Diagnosis↗

NASA NTRS2019

Adjoint-Based Anisotropic Mesh Adaptation for a Stabilized Finite-Element Flow Solver

An adjoint solver is implemented in the FUN3D stabilized finite-element flow solver. The adjoint solution is used to generate anisotropic, adapted meshes to control error in scalar out- put functionals, such as lift or drag coefficient. The inviscid and turbulent adjoints are verified with a finite-difference derivative approximation and can be used in design optimization in addition to mesh adaptation. The adjoint capability represents an extension of previous research using the FUN3D stabilized finite-element capability with metric-based mesh adaptation and interpolation-based error estimates to generate highly anisotropic adapted meshes for turbulent flows. In the present work, a metric-based approach is again utilized, where the adjoint and the primal solutions both contribute to the generation of a metric tensor field that is subsequently used to produce the required anisotropic mesh for each adaptation cycle. Adaptive results are then shown for an inviscid supersonic flow over a diamond airfoil, inviscid transonic flow over the ONERA M6 wing, and viscous laminar flow over the NACA 0012 airfoil, all using drag force as the output functional. Adjoint-based adaptation is compared with a multiscale solution-based approach that controls the L norm of Mach number interpolation error to demonstrate the effectiveness and effciency of the adjoint-based adaptive mesh technology.

Balan, Aravind↗

NASA NTRS2007

The Impact of Atmospheric InfraRed Sounder (AIRS) Profiles on Short-term Weather Forecasts

The Atmospheric Infrared Sounder (AIRS), together with the Advanced Microwave Sounding Unit (AMSU), represents one of the most advanced spacebased atmospheric sounding systems. The combined AlRS/AMSU system provides radiance measurements used to retrieve temperature profiles with an accuracy of 1 K over 1 km layers under both clear and partly cloudy conditions, while the accuracy of the derived humidity profiles is 15% in 2 km layers. Critical to the successful use of AIRS profiles for weather and climate studies is the use of profile quality indicators and error estimates provided with each profile Aside form monitoring changes in Earth's climate, one of the objectives of AIRS is to provide sounding information of sufficient accuracy such that the assimilation of the new observations, especially in data sparse region, will lead to an improvement in weather forecasts. The purpose of this paper is to describe a procedure to optimally assimilate highresolution AIRS profile data in a regional analysis/forecast model. The paper will focus on the impact of AIRS profiles on a rapidly developing east coast storm and will also discuss preliminary results for a 30-day forecast period, simulating a quasi-operation environment. Temperature and moisture profiles were obtained from the prototype version 5.0 EOS science team retrieval algorithm which includes explicit error information for each profile. The error profile information was used to select the highest quality temperature and moisture data for every profile location and pressure level for assimilation into the ARPS Data Analysis System (ADAS). The AIRS-enhanced analyses were used as initial fields for the Weather Research and Forecast (WRF) system used by the SPORT project for regional weather forecast studies. The ADASWRF system will be run on CONUS domain with an emphasis on the east coast. The preliminary assessment of the impact of the AIRS profiles will focus on quality control issues associated with AIRS, intelligent use of the quality indicators, and forecast verification.

Chou, Shih-Hung↗

NASA NTRS1990

Dynamical reference frames in the planetary and earth-moon systems

Estimates of the accuracies of the ephemerides are reviewed using data for planetary and lunar systems to determine the efficacy of the inherent dynamical reference frame. The varied observational data are listed and given with special attention given to ephemeris improvements. The importance of ranging data is discussed with respect to the inner four planets and the moon, and the discrepancy of 1 arcsec/century between mean motions determined by optical observations versus ranging data is addressed. The Viking mission data provide inertial mean motions for the earth and Mars of 0.003 arcsec/century which will deteriorate to 0.01 arcsec after about 10 years. Uncertainties for other planets and the moon are found to correspond to approximately the same level of degradation. In general the data measurements and error estimates are improving the ephemerides, although refitting the data cannot account for changes in mean motion.

Standish, E. M.↗

NASA NTRS2009

Guaranteeing Failsafe Operation of Extended-Scene Shack-Hartmann Wavefront Sensor Algorithm

A Shack-Hartmann sensor (SHS) is an optical instrument consisting of a lenslet array and a camera. It is widely used for wavefront sensing in optical testing and astronomical adaptive optics. The camera is placed at the focal point of the lenslet array and points at a star or any other point source. The image captured is an array of spot images. When the wavefront error at the lenslet array changes, the position of each spot measurably shifts from its original position. Determining the shifts of the spot images from their reference points shows the extent of the wavefront error. An adaptive cross-correlation (ACC) algorithm has been developed to use scenes as well as point sources for wavefront error detection. Qualifying an extended scene image is often not an easy task due to changing conditions in scene content, illumination level, background, Poisson noise, read-out noise, dark current, sampling format, and field of view. The proposed new technique based on ACC algorithm analyzes the effects of these conditions on the performance of the ACC algorithm and determines the viability of an extended scene image. If it is viable, then it can be used for error correction; if it is not, the image fails and will not be further processed. By potentially testing for a wide variety of conditions, the algorithm s accuracy can be virtually guaranteed. In a typical application, the ACC algorithm finds image shifts of more than 500 Shack-Hartmann camera sub-images relative to a reference sub -image or cell when performing one wavefront sensing iteration. In the proposed new technique, a pair of test and reference cells is selected from the same frame, preferably from two well-separated locations. The test cell is shifted by an integer number of pixels, say, for example, from m= -5 to 5 along the x-direction by choosing a different area on the same sub-image, and the shifts are estimated using the ACC algorithm. The same is done in the y-direction. If the resulting shift estimate errors are less than a pre-determined threshold (e.g., 0.03 pixel), the image is accepted. Otherwise, it is rejected.

Sidick, Erikin↗