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At least 235 records · Page 13

The arbitrary-order virtual element method for linear elastodynamics models. Convergence, stability and dispersion-dissipation analysis.

We design the conforming virtual element method for the numerical approximation of the two dimensional elastodynamics problem. We prove stability and convergence of the semi-discrete approximation and derive optimal error estimates under $\textit{h}$-refinement in both the energy and the $L^2$ norms, and optimal error estimates under $\textit{p}$-refinement in the energy norm. The performance of the proposed virtual element method is assessed on a set of different computational meshes, including non-convex cells up to order four in the h-refinement setting. Exponential convergence is also experimentally observed under p-refinement. Finally, we present a dispersion-dissipation analysis for both the semi-discrete and fully-discrete schemes, showing that polygonal meshes behave as classical simplicial/quadrilateral grids in terms of dispersion-dissipation properties.

97 MATHEMATICS AND COMPUTING↗

Improved Temperature Sounding and Quality Control Methodology Using AIRS/AMSU Data: The AIRS Science Team Version 5 Retrieval Algorithm

This paper describes the AIRS Science Team Version 5 retrieval algorithm in terms of its three most significant improvements over the methodology used in the AIRS Science Team Version 4 retrieval algorithm. Improved physics in Version 5 allows for use of AIRS clear column radiances in the entire 4.3 micron CO2 absorption band in the retrieval of temperature profiles T(p) during both day and night. Tropospheric sounding 15 micron CO2 observations are now used primarily in the generation of clear column radiances .R(sub i) for all channels. This new approach allows for the generation of more accurate values of .R(sub i) and T(p) under most cloud conditions. Secondly, Version 5 contains a new methodology to provide accurate case-by-case error estimates for retrieved geophysical parameters and for channel-by-channel clear column radiances. Thresholds of these error estimates are used in a new approach for Quality Control. Finally, Version 5 also contains for the first time an approach to provide AIRS soundings in partially cloudy conditions that does not require use of any microwave data. This new AIRS Only sounding methodology, referred to as AIRS Version 5 AO, was developed as a backup to AIRS Version 5 should the AMSU-A instrument fail. Results are shown comparing the relative performance of the AIRS Version 4, Version 5, and Version 5 AO for the single day, January 25, 2003. The Goddard DISC is now generating and distributing products derived using the AIRS Science Team Version 5 retrieval algorithm. This paper also described the Quality Control flags contained in the DISC AIRS/AMSU retrieval products and their intended use for scientific research purposes.

Susskind, Joel↗

Improved Determination of Surface and Atmospheric Temperatures Using Only Shortwave AIRS Channels: The AIRS Version 6 Retrieval Algorithm

AIRS was launched on EOS Aqua on May 4, 2002 together with ASMU-A and HSB to form a next generation polar orbiting infrared and microwave atmosphere sounding system (Pagano et al 2003). The theoretical approach used to analyze AIRS/AMSU/HSB data in the presence of clouds in the AIRS Science Team Version 3 at-launch algorithm, and that used in the Version 4 post-launch algorithm, have been published previously. Significant theoretical and practical improvements have been made in the analysis of AIRS/AMSU data since the Version 4 algorithm. Most of these have already been incorporated in the AIRS Science Team Version 5 algorithm (Susskind et al 2010), now being used operationally at the Goddard DISC. The AIRS Version 5 retrieval algorithm contains three significant improvements over Version 4. Improved physics in Version 5 allowed for use of AIRS clear column radiances (R(sub i)) in the entire 4.3 micron CO2 absorption band in the retrieval of temperature profiles T(p) during both day and night. Tropospheric sounding 15 micron CO2 observations were used primarily in the generation of clear column radiances (R(sub i)) for all channels. This new approach allowed for the generation of accurate Quality Controlled values of R(sub i) and T(p) under more stressing cloud conditions. Secondly, Version 5 contained a new methodology to provide accurate case-by-case error estimates for retrieved geophysical parameters and for channel-by-channel clear column radiances. Thresholds of these error estimates are used in a new approach for Quality Control. Finally, Version 5 contained for the first time an approach to provide AIRS soundings in partially cloudy conditions that does not require use of any microwave data. This new AIRS Only sounding methodology was developed as a backup to AIRS Version 5 should the AMSU-A instrument fail. Susskind et al 2010 shows that Version 5 AIRS Only sounding are only slightly degraded from the AIRS/AMSU soundings, even at large fractional cloud cover.

Susskind, Joel↗

Reduced Order Modeling conditioned on monitored features for response and error bounds estimation in engineered systems

Reduced Order Models (ROMs) form essential tools across engineering domains by virtue of their function as surrogates for computationally intensive digital twinning simulators. Although purely data-driven methods are available for ROM construction, schemes that allow to retain a portion of the physics tend to enhance the interpretability and generalization of ROMs. However, physics-based techniques can adversely scale when dealing with nonlinear systems that feature parametric dependencies. This study introduces a generative physics-based ROM that is suited for nonlinear systems with parametric dependencies and is additionally able to provide numerical error bounds associated with the respective estimates. A main contribution of this work is the conditioning of these parametric ROMs to features that can be derived from monitoring measurements, feasibly in an online fashion. This is contrary to most existing ROM schemes, which remain restricted to the prescription of the physics-based, and usually a priori unknown, system parameters. Our work utilizes conditional Variational Autoencoders to continuously map the required reduction bases to a feature vector extracted from limited output measurements, while additionally allowing for a probabilistic assessment of the ROM-estimated Quantities of Interest. An auxiliary task using a neural network-based parametrization of suitable probability distributions is introduced to re-establish the link with physical model parameters. We verify the proposed scheme on a series of simulated case studies incorporating effects of geometric and material nonlinearity under parametric dependencies related to system properties and input load characteristics.

Conditional VAEs↗

Improved AIRS/AMSU Surface and Atmospheric Soundings Under Partial Cloud Cover Using an AIRS Only Cloud Clearing Approach

AIRS was launched on EOS Aqua on May 4,2002, together with AMSU-A and HSB, to form a next generation polar orbiting infrared and microwave atmospheric sounding system. This paper describes the latest scientific advances made in the AIRS Science Team Version 5.0 retrieval algorithm. Starting in early 2007, the Goddard DAAC will use this algorithm to analyze near real time AIRS/AMSU observations. These products are then made available to the scientific community for research purposes. The products include twice daily measurements of the Earth's three dimensional global temperature, water vapor, and ozone distribution as well as cloud cover. In addition, accurate twice daily measurements of the earth's land and ocean temperatures are derived and reported. Scientists use this important set of observations for two major uses. They provide important information for climate studies of global and regional variability and trends of different aspects of the earth's atmosphere. They also provide information for researchers to improve the skill of weather forecasting. A very important new product of the AIRS Version 5 algorithm is accurate case-by-case error estimates of the retrieved products. This heightens their utility for use in both weather and climate applications. These error estimates are also used directly for quality control of the retrieved products.

Susskind, Dr. Joel↗

A Systematic Approach to Sensor Selection for Aircraft Engine Health Estimation

A systematic approach for selecting an optimal suite of sensors for on-board aircraft gas turbine engine health estimation is presented. The methodology optimally chooses the engine sensor suite and the model tuning parameter vector to minimize the Kalman filter mean squared estimation error in the engine s health parameters or other unmeasured engine outputs. This technique specifically addresses the underdetermined estimation problem where there are more unknown system health parameters representing degradation than available sensor measurements. This paper presents the theoretical estimation error equations, and describes the optimization approach that is applied to select the sensors and model tuning parameters to minimize these errors. Two different model tuning parameter vector selection approaches are evaluated: the conventional approach of selecting a subset of health parameters to serve as the tuning parameters, and an alternative approach that selects tuning parameters as a linear combination of all health parameters. Results from the application of the technique to an aircraft engine simulation are presented, and compared to those from an alternative sensor selection strategy.

Simon, Donald L.↗

Maximum likelihood techniques applied to quasi-elastic light scattering

There is a necessity of having an automatic procedure for reliable estimation of the quality of the measurement of particle size from QELS (Quasi-Elastic Light Scattering). Getting the measurement itself, before any error estimates can be made, is a problem because it is obtained by a very indirect measurement of a signal derived from the motion of particles in the system and requires the solution of an inverse problem. The eigenvalue structure of the transform that generates the signal is such that an arbitrarily small amount of noise can obliterate parts of any practical inversion spectrum. This project uses the Maximum Likelihood Estimation (MLE) as a framework to generate a theory and a functioning set of software to oversee the measurement process and extract the particle size information, while at the same time providing error estimates for those measurements. The theory involved verifying a correct form of the covariance matrix for the noise on the measurement and then estimating particle size parameters using a modified histogram approach.

Edwards, Robert V.↗

Adaptive Finite Element Technology in Integrated Design and Analysis

An assessment of the potential impact of adaptive finite element technology on the analysis part of the aircraft structural synthesis process is presented. The main conclusion is that adaptive application of the p-version of the finite element method based on indirect error estimation procedures results in substantial cost reduction and increased reliability of the computed data. Adaptivity based on direct a posteriori error estimation has the potential for additional savings.

Szabo, B. A.↗

On state estimation for an orbiting single tether system

The effects of instrumentation accuracy and configuration on estimation error are studied for the small expendable-tether deployment system (SEDS) using a continuous-discrete extended Kalman filter (CDEKF) state estimator. A twelfth order model that incorporates the rigid body modes of the tether as well as the satellite attitude dynamics is developed. Simulation results using the model and the estimator indicate that the originally planned instrumentation package could not estimate the state vector adequately. Recommendations are made and results presented that reduce the estimation error by adding instruments and increasing selected measurement accuracies.

Greene, Michael E.↗

Dynamic Modeling using Output-Error Parameter Estimation based on Frequency Responses Estimated with Multisine Inputs

A method is developed for estimating model parameters, such as nondimensional stability and control derivatives, by fitting transfer function or state-space models to empirical frequency response data using the output-error approach. The frequency response data were computed using Fourier transforms of measured input and output data. The control surfaces were excited with periodic multisine inputs which facilitated time-ecient estimation of multiple-input multiple-output frequency responses. The method was applied to lateral data from a nonlinear flight dynamics simulation of the F-16 aircraft, and to longitudinal data from multiple repeated flight test maneuvers of the NASA T-2 subscale aircraft. Results using simulation data showed the frequency response method compared well to other standard methods for parameter estimation. In addition to including all the available inputs, outputs, and harmonic frequencies in the estimation, relatively small subsets of the measured data could also be used to focus on identifying specific parts of the model. Results from flight test data showed that parameter estimates and uncertainties determined from repeated maneuvers were accurate and in statistical agreement with each other.

Grauer, Jared A.↗

Geopositional Statistical Methods

RMSE based methods distort circular error estimates (up to 50% overestimation). The empirical approach is the only statistically unbiased estimator offered. Ager modification to Shultz approach is nearly unbiased, but cumbersome. All methods hover around 20% uncertainty (@ 95% confidence) for low geopositional bias error estimates. This requires careful consideration in assessment of higher accuracy products.

Ross, Kenton↗

Shape Optimization by Bayesian-Validated Computer-Simulation Surrogates

A nonparametric-validated, surrogate approach to optimization has been applied to the computational optimization of eddy-promoter heat exchangers and to the experimental optimization of a multielement airfoil. In addition to the baseline surrogate framework, a surrogate-Pareto framework has been applied to the two-criteria, eddy-promoter design problem. The Pareto analysis improves the predictability of the surrogate results, preserves generality, and provides a means to rapidly determine design trade-offs. Significant contributions have been made in the geometric description used for the eddy-promoter inclusions as well as to the surrogate framework itself. A level-set based, geometric description has been developed to define the shape of the eddy-promoter inclusions. The level-set technique allows for topology changes (from single-body,eddy-promoter configurations to two-body configurations) without requiring any additional logic. The continuity of the output responses for input variations that cross the boundary between topologies has been demonstrated. Input-output continuity is required for the straightforward application of surrogate techniques in which simplified, interpolative models are fitted through a construction set of data. The surrogate framework developed previously has been extended in a number of ways. First, the formulation for a general, two-output, two-performance metric problem is presented. Surrogates are constructed and validated for the outputs. The performance metrics can be functions of both outputs, as well as explicitly of the inputs, and serve to characterize the design preferences. By segregating the outputs and the performance metrics, an additional level of flexibility is provided to the designer. The validated outputs can be used in future design studies and the error estimates provided by the output validation step still apply, and require no additional appeals to the expensive analysis. Second, a candidate-based a posteriori error analysis capability has been developed which provides probabilistic error estimates on the true performance for a design randomly selected near the surrogate-predicted optimal design.

Patera, Anthony T.↗

Consistent Evaluation of ACOS-GOSAT, BESD-SCIAMACHY, CarbonTracker, and MACC Through Comparisons to TCCON

Consistent validation of satellite CO2 estimates is a prerequisite for using multiple satellite CO2 measurements for joint flux inversion, and for establishing an accurate long-term atmospheric CO2 data record. Harmonizing satellite CO2 measurements is particularly important since the differences in instruments, observing geometries, sampling strategies, etc. imbue different measurement characteristics in the various satellite CO2 data products. We focus on validating model and satellite observation attributes that impact flux estimates and CO2 assimilation, including accurate error estimates, correlated and random errors, overall biases, biases by season and latitude, the impact of coincidence criteria, validation of seasonal cycle phase and amplitude, yearly growth, and daily variability. We evaluate dry-air mole fraction (X(sub CO2)) for Greenhouse gases Observing SATellite (GOSAT) (Atmospheric CO2 Observations from Space, ACOS b3.5) and SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY) (Bremen Optimal Estimation DOAS, BESD v2.00.08) as well as the CarbonTracker (CT2013b) simulated CO2 mole fraction fields and the Monitoring Atmospheric Composition and Climate (MACC) CO2 inversion system (v13.1) and compare these to Total Carbon Column Observing Network (TCCON) observations (GGG2012/2014). We find standard deviations of 0.9, 0.9, 1.7, and 2.1 parts per million vs. TCCON for CT2013b, MACC, GOSAT, and SCIAMACHY, respectively, with the single observation errors 1.9 and 0.9 times the predicted errors for GOSAT and SCIAMACHY, respectively. We quantify how satellite error drops with data averaging by interpreting according to (error(sup 2) equals a(sup 2) plus b(sup 2) divided by n (with n being the number of observations averaged, a the systematic (correlated) errors, and b the random (uncorrelated) errors). a and b are estimated by satellites, coincidence criteria, and hemisphere. Biases at individual stations have year-to-year variability of 0.3 parts per million, with biases larger than the TCCON predicted bias uncertainty of 0.4 parts per million at many stations. We find that GOSAT and CT2013b under-predict the seasonal cycle amplitude in the Northern Hemisphere (NH) between 46 and 53 degrees North latitude, MACC over-predicts between 26 and 37 degrees North latitude, and CT2013b under-predicts the seasonal cycle amplitude in the Southern Hemisphere (SH). The seasonal cycle phase indicates whether a data set or model lags another data set in time. We find that the GOSAT measurements improve the seasonal cycle phase substantially over the prior while SCIAMACHY measurements improve the phase significantly for just two of seven sites. The models reproduce the measured seasonal cycle phase well except for at Lauder_125HR (CT2013b) and Darwin (MACC). We compare the variability within 1 day between TCCON and models in June-July-August; there is correlation between 0.2 and 0.8 in the NH, with models showing 10-50 percent the variability of TCCON at different stations and CT2013b showing more variability than MACC. This paper highlights findings that provide inputs to estimate flux errors in model assimilations, and places where models and satellites need further investigation, e.g., the SH for models and 45-67 degrees North latitude for GOSAT and CT2013b.

ACOS-GOSAT↗

Optical range and range rate estimation for teleoperator systems

Range and range rate are crucial parameters which must be available to the operator during remote controlled orbital docking operations. A method was developed for the estimation of both these parameters using an aided television system. An experiment was performed to determine the human operator's capability to measure displayed image size using a fixed reticle or movable cursor as the television aid. The movable cursor was found to yield mean image size estimation errors on the order of 2.3 per cent of the correct value. This error rate was significantly lower than that for the fixed reticle. Performance using the movable cursor was found to be less sensitive to signal-to-noise ratio variation than was that for the fixed reticle. The mean image size estimation errors for the movable cursor correspond to an error of approximately 2.25 per cent in range suggesting that the system has some merit. Determining the accuracy of range rate estimation using a rate controlled cursor will require further experimentation.

Shields, N. L., Jr.↗

Multiscale modeling high-order methods and data-driven modeling

Projection-based reduced-order models (ROMs) comprise a promising set of data-driven approaches for accelerating the simulation of high-fidelity numerical simulations. Standard projection-based ROM approaches, however, suffer from several drawbacks when applied to the complex nonlinear dynamical systems commonly encountered in science and engineering. These limitations include a lack of stability, accuracy, and sharp a posteriori error estimators. This work addresses these limitations by leveraging multiscale modeling, least-squares principles, and machine learning to develop novel reduced-order modeling approaches, along with data-driven a posteriori error estimators, for dynamical systems. Theoretical and numerical results demonstrate that the two ROM approaches developed in this work - namely the windowed least-squares method and the Adjoint Petrov - Galerkin method - yield substantial improvements over state-of-the-art approaches. Additionally, numerical results demonstrate the capability of the a posteriori error models developed in this work.

97 MATHEMATICS AND COMPUTING↗

Observing System Simulations for Small Satellite Formations Estimating Bidirectional Reflectance

The bidirectional reflectance distribution function (BRDF) gives the reflectance of a target as a function of illumination geometry and viewing geometry, hence carries information about the anisotropy of the surface. BRDF is needed in remote sensing for the correction of view and illumination angle effects (for example in image standardization and mosaicing), for deriving albedo, for land cover classification, for cloud detection, for atmospheric correction, and other applications. However, current spaceborne instruments provide sparse angular sampling of BRDF and airborne instruments are limited in the spatial and temporal coverage. To fill the gaps in angular coverage within spatial, spectral and temporal requirements, we propose a new measurement technique: Use of small satellites in formation flight, each satellite with a VNIR (visible and near infrared) imaging spectrometer, to make multi-spectral, near-simultaneous measurements of every ground spot in the swath at multiple angles. This paper describes an observing system simulation experiment (OSSE) to evaluate the proposed concept and select the optimal formation architecture that minimizes BRDF uncertainties. The variables of the OSSE are identified; number of satellites, measurement spread in the view zenith and relative azimuth with respect to solar plane, solar zenith angle, BRDF models and wavelength of reflection. Analyzing the sensitivity of BRDF estimation errors to the variables allow simplification of the OSSE, to enable its use to rapidly evaluate formation architectures. A 6-satellite formation is shown to produce lower BRDF estimation errors, purely in terms of angular sampling as evaluated by the OSSE, than a single spacecraft with 9 forward-aft sensors. We demonstrate the ability to use OSSEs to design small satellite formations as complements to flagship mission data. The formations can fill angular sampling gaps and enable better BRDF products than currently possible.

small satellite↗

Flood basalt volcanism during the past 250 million years

A chronology of the initiation dates of major continental flood basalt volcanism is established from published potassium-argon (K-Ar) and argon-argon (Ar-Ar) ages of basaltic rocks and related basic intrusions. The dating is therefore independent of the biostratigraphic and paleomagnetic time scales. Estimated errors of the initiation dates of the volcanic episodes determined from the distributions of the radiometric ages are, approximately, + or - 4 percent. There were 11 distinct episodes during the past 250 million years. Sometimes appearing in pairs, the episodes have occurred quasi-periodically with a mean cycle time of 32 + or - 1 (estimated error of the mean) million years. The initiation dates of the episodes are close to the estimated dates of mass extinctions of marine organisms. Showers of impacting comets may be the cause.

Rampino, Michael R.↗