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This memorandum builds upon Section 3.8 of SRNL (2016) and Flach (2017) by defining key error analysis, uncertainty quantification, and sensitivity analysis concepts and terms, in preparation for the next E-Area Performance Assessment (WSRC 2008) revision.
A polychromatic microwave quadrature interferometer has been characterized using several laboratory plasmas. Reflections between the transmitter and the receiver have been observed, and the effects of including reflection terms in the data reduction equation have been examined. An error analysis which includes the reflections, modulation of the scene beam amplitude by the plasma, and simultaneous measurements at two frequencies has been applied to the empirical database, and the results are summarized. For reflection amplitudes around 1096, the reflection terms were found to reduce the calculated error bars for electron density measurements by about a factor of 2. The impact of amplitude modulation is also quantified. In the complete analysis, the mean error bar for high- density measurements is 7.596, and the mean phase shift error for low-density measurements is 1.2". .
As thermal errors are reduced instrumental and troposphere correlated errors will increasingly become more important. Work in progress shows that troposphere covariance error models improve data analysis results. We expect to see stronger effects with higher data rates. Temperature modeling of delay errors may further reduce temporal correlations in the data.
The structural analysis methods research has several goals. One goal is to develop analysis methods that are general. This goal of generality leads naturally to finite-element methods, but the research will also include other structural analysis methods. Another goal is that the methods be amenable to error analysis; that is, given a physical problem and a mathematical model of that problem, an analyst would like to know the probable error in predicting a given response quantity. The ultimate objective is to specify the error tolerances and to use automated logic to adjust the mathematical model or solution strategy to obtain that accuracy. A third goal is to develop structural analysis methods that can exploit parallel processing computers. The structural analysis methods research will focus initially on three types of problems: local/global nonlinear stress analysis, nonlinear transient dynamics, and tire modeling.
The Jimsonde, a high-resolution lightweight temperature sensor developed for use with the FPS-16 Radar/Jimsphere wind system, and its related systems are discussed; and an error analysis that shows the sonde to have an rms error of 0.41 C at sea level and 0.56 C at 18 km is presented. Five flight tests, a sequence of four tests and one individual test, of the Jimsonde were made. For comparative purposes, radiosonde temperature data are presented along with the Jimsonde data.
A first-order theory of satellite orbit determination using time-difference data is developed for the case of a synchronous, equatorial spacecraft. Also, a first order error analysis is presented that permits one to estimate how errors in assumed or measured quantities affect the values of the derived orbital parameters. The theory is applied to observational data obtained during a series of VLBI (Very-Long-Baseline Interferometry) experiments conducted between stations at Rosman, North Carolina, and Mojave, California, using the ATS-3 satellite as a radio source. Orbit parameters derived from the VLBI data show good agreement with those determined by the ATS project office using more conventional tracking techniques.
Satellite geodesy techniques previously applied to artificial earth satellites have been extended to obtain a high-resolution gravity field for Mars. Two-way Doppler data collected by 10 Deep Space Network (DSN) stations during Mariner 9 and Viking 1 and 2 missions have been processed to obtain a twelfth degree and order spherical harmonic model for the martian gravitational potential. The quality of this model was evaluated by examining the rms residuals within the fit and the ability of the model to predict the spacecraft state beyond the fit. Both indicators show that more data and higher degree and order harmonics will be required to further refine our knowledge of the martian gravity field. The model presented shows much promise, since it resolves local gravity features which correlate highly with the martian topography. An isostatic analysis based on this model, as well as an error analysis, shows rather complete compensation on a global (long wavelength) scale. Though further model refinements are necessary to be certain, local (short wavelength) features such as the shield volcanos in Tharsis appear to be uncompensated. These are interpreted to place some bounds on the internal structure of Mars.
Two suites of geomagnetic field models were generated at the request of Los Alamos National Lab. concerning Strategic Defense Initiative (SDI) research. The first is a progression of five models incorporating MAGSAT data and data from a sequence of batches as a priori information. The batch sequence is: post 1979.5 observatory data, post 1980 land survey and selected aeromagnetic and marine survey data, a special White Sands (NM) area survey by Project Magnet with some additional post 1980 marine survey data, and finally DE-2 satellite data. These models are of 13th deg and order in their main field terms, and deg and order 10 in their first derivative temporal terms. The second suite consists of four models based solely upon post 1983.5 observatory and survey data. They are of deg and order 10 in main field and 8 in a first deg Taylor series. A comprehensive error analysis was applied to both series, which accounted for error sources such as the truncated core and crustal fields, and the neglected Sq and low deg crustal fields. Comparison of the power spectrum of the MGST (10/81) model with those of this series show good agreement.
Error analysis on moment distribution functions of magnetohydrodynamic plasma equations
This paper presents a feasibility analysis, tradeoffs, and implementation for a one-way Doppler extractor system. A Doppler error analysis is discussed which shows that quantization error is a primary source of Doppler measurement error. Several competing extraction techniques are compared, and a 'Vernier' technique is presented which obtains high Doppler resolution with low-speed logic. Parameter tradeoffs and sensitivities for this Vernier technique are discussed, leading to a hardware design configuration. Also presented is a performance evaluation of the resulting breadboard model that verifies the theoretical performance predictions. The breadboard model contains the circuitry to interface with an S-band transponder, to extract the Doppler and time-interval counts, to compute navigational parameters by means of a microprocessor, and to display the results. Performance tests have verified that the breadboard is capable of extracting Doppler, on an S-band signal, to an accuracy of better than 0.02 hertz for a one-second averaging period. This corresponds to a range rate error of no more than 3 millimeters per second.
In order to establish realistic deviation limits for the ASTP (SA-210) Launch Vehicle Operational Flight Trajectory, a dispersion analysis was conducted. The nominal trajectory prescribed for this analysis is the ASTP (SA-210) Launch Vehicle 500 Pound Launch Window Opening OT. The error sources considered are those associated with predictions of vehicle characteristics, vehicle systems performance, and flight environment. The nominal vehicle, the boost trajectory simulations, the error sources, the analytic procedures utilized, and the results are discussed. Launch vehicle guidance system inaccuracies were determined from the guidance error analysis. These data are composed of individual error source trajectory parameter dispersion envelopes.
Social media plays a valuable role in rapid news dissemination, but it also serves as a vehicle to propagate unverified information. For example, news shared on Facebook or Twitter may actually contain disinformation, propaganda, hoaxes, conspiracies, clickbait or satire. This paper presents an in-depth analysis of the behavior of suspicious news classification models including error analysis and prediction confidence. We consider five deep learning architectures that leverage combinations of text, linguistic and image input signals from tweets. The behavior of these models is analyzed across four suspicious news prediction tasks. Our findings include that models leveraging only the text of tweets outperform those leveraging only the image (by 3-13% absolute in F-measure), and that models that combine image and text signals with linguistic cues e.g., biased and subjective language markers can, but do not always, perform even better. Finally, our main contribution is a series of analyses, in which we characterize text and image traits of our classes of suspicious news and analyze patterns of errors made by the various models to inform the design of future deceptive news prediction models.
Here in this work, we investigate the applicability of the harmonic balance method (HBM) to predict periodic solutions of a single degree-of-freedom forced Duffing oscillator with freeplay nonlinearity. By studying the route to impact, which refers to a parametric study as the contact stiffness increases from soft to hard, the convergence behavior of the HBM can be understood in terms of the strength of the non-smooth forcing term. HBM results are compared to time-integration results to facilitate an evaluation of the accuracy of nonlinear periodic responses. An additional contribution of this study is to perform convergence and stability analysis specifically for isolas generated by the non-smooth nonlinearity. Residual error analysis is used to determine the approximate number of harmonics required to get results accurate to a given error tolerance. Hill’s method and Floquet theory are employed to compute the stability of periodic solutions and identify the types of bifurcations in the system.
In this communication, a novel optical technique has been proposed for the reconstruction of the shape of a Taylor bubble using measurements from multiple arrays of optical sensors. The deviation of an optical beam passing through the bubble depends on the contour of bubble surface. A theoretical model of the deviation of a beam during the traverse of a Taylor bubble through it has been developed. Using this model and the time history of the deviation captured by the sensor array, the bubble shape has been reconstructed. The reconstruction has been performed using an inverse algorithm based on Bayesian inference technique and Markov chain Monte Carlo sampling algorithm. The reconstructed nose shape has been compared with the true shape, extracted through image processing of high speed images. Finally, an error analysis has been performed to pinpoint the sources of the errors.
We present the largest search to date for Y-band dropout galaxies (z ∼ 8 Lyman break galaxies, LBGs) based on 350 arcmin{sup 2} of Hubble Space Telescope observations in the V, Y, J, and H bands from the Brightest of Reionizing Galaxies (BoRG) survey. In addition to previously published data, the BoRG13 data set presented here includes approximately 50 arcmin{sup 2} of new data and deeper observations of two previous BoRG pointings, from which we present 9 new z ∼ 8 LBG candidates, bringing the total number of BoRG Y-band dropouts to 38 with 25.5 ≤ m{sub J} ≤ 27.6 (AB system). We introduce a new Bayesian formalism for estimating the galaxy luminosity function, which does not require binning (and thus smearing) of the data and includes a likelihood based on the formally correct binomial distribution as opposed to the often-used approximate Poisson distribution. We demonstrate the utility of the new method on a sample of 97 Y-band dropouts that combines the bright BoRG galaxies with the fainter sources published in Bouwens et al. from the Hubble Ultra Deep Field and Early Release Science programs. We show that the z ∼ 8 luminosity function is well described by a Schechter function over its full dynamic range with a characteristic magnitude M{sup ⋆}=−20.15{sub −0.38}{sup +0.29}, a faint-end slope of α=−1.87{sub −0.26}{sup +0.26}, and a number density of log{sub 10} ϕ{sup ⋆}[Mpc{sup −3}]=−3.24{sub −0.24}{sup +0.25}. Integrated down to M = –17.7, this luminosity function yields a luminosity density log{sub 10} ϵ[erg s{sup −1} Hz{sup −1} Mpc{sup −3}]=25.52{sub −0.05}{sup +0.05}. Our luminosity function analysis is consistent with previously published determinations within 1σ. The error analysis suggests that uncertainties on the faint-end slope are still too large to draw a firm conclusion about its evolution with redshift. We use our statistical framework to discuss the implication of our study for the physics of reionization. By assuming theoretically motivated priors on the clumping factor and the photon escape fraction we show that the UV luminosity density from galaxy samples down to M = –17.7 can ionize only 10%-50% of the neutral hydrogen at z ∼ 8. Full reionization would require extending the luminosity function down to M = –15. The data are consistent with a substantial fraction of neutral hydrogen at z > 7, in agreement with recent suggestions based on deep spectroscopy of z ∼ 8 LBGs.
A classical reduced order model (ROM) for dynamical problems typically involves only the spatial reduction of a given problem. Recently, a novel space–time ROM for linear dynamical problems has been developed [Choi et al., Space–tume reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems, Journal of Computational Physics, 2020], which further reduces the problem size by introducing a temporal reduction in addition to a spatial reduction without much loss in accuracy. The authors show an order of a thousand speed-up with a relative error of less than 10−5 for a large-scale Boltzmann transport problem. In this work, we present for the first time the derivation of the space–time least-squares Petrov–Galerkin (LSPG) projection for linear dynamical systems and its corresponding block structures. Utilizing these block structures, we demonstrate the ease of construction of the space–time ROM method with two model problems: 2D diffusion and 2D convection diffusion, with and without a linear source term. For each problem, we demonstrate the entire process of generating the full order model (FOM) data, constructing the space–time ROM, and predicting the reduced-order solutions, all in less than 120 lines of Python code. We compare our LSPG method with the traditional Galerkin method and show that the space–time ROMs can achieve O(10−3) to O(10−4) relative errors for these problems. Depending on parameter–separability, online speed-ups may or may not be achieved. For the FOMs with parameter–separability, the space–time ROMs can achieve O(10) online speed-ups. Finally, we present an error analysis for the space–time LSPG projection and derive an error bound, which shows an improvement compared to traditional spatial Galerkin ROM methods.
The results of an intensive literature review in the general topics of human error analysis, stress and job performance, and accident and safety analysis revealed no usable techniques or approaches for analyzing human error in ground or space operations tasks. A task review model is described and proposed to be developed in order to reduce the degree of labor intensiveness in ground and space operations tasks. An extensive number of annotated references are provided.
A mathematical theory for development of "higher order" software to catch computer mistakes resulted from a Johnson Space Center contract for Apollo spacecraft navigation. Two women who were involved in the project formed Higher Order Software, Inc. to develop and market the system of error analysis and correction. They designed software which is logically error-free, which, in one instance, was found to increase productivity by 600%. USE.IT defines its objectives using AXES -- a user can write in English and the system converts to computer languages. It is employed by several large corporations.