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At least 1,009 records · Page 56

Sensitivity to Error Fields in NSTX High β Plasmas

It was found that error field threshold decreases for high β in NSTX, although the density correlation in conventional threshold scaling implies the threshold would increase since higher β plasmas in our study have higher plasma density. This greater sensitivity to error field in higher β plasmas is due to error field amplification by plasmas. When the effect of amplification is included with ideal plasma response calculations, the conventional density correlation can be restored and threshold scaling becomes more consistent with low β plasmas. However, it was also found that the threshold can be significantly changed depending on plasma rotation. When plasma rotation was reduced by non-resonant magnetic braking, the further increase of sensitivity to error field was observed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Enabling Predictive Simulation and UQ of Complex Multiphysics PDE Systems by the Development of Goal-Oriented Variational Sensitivity Analysis and A Posteriori Error Estimation Methods

It was demonstrated that a posteriori analyses in general and in particular one that uses adjoint methods can accurately and efficiently compute numerical error estimates and sensitivity for critical Quantities of Interest (QoIs) that depend on a large number of parameters. Activities include: analysis and implementation of several time integration techniques for solving system of ODEs as typically obtained from spatial discretization of PDE systems; multirate integration methods for ordinary differential equations; formulation and analysis of an iterative multi-discretization Galerkin finite element method for multi-scale reaction-diffusion equations; investigation of an inexpensive postprocessing technique to estimate the error of finite element solution of the second-order quasi-linear elliptic problems measured in some global metrics; investigation of an application of the residual-based a posteriori error estimates to symmetric interior penalty discontinuous Galerkin method for solving a class of second order quasi-linear elliptic problems; a posteriori analysis of explicit time integrations for system of linear ordinary differential equations; derivation of accurate a posteriori goal oriented error estimates for a user-defined quantity of interest for two classes of first and second order IMEX schemes for advection-diffusion-reaction problems; Postprocessing finite element solution; and A Bayesian Framework for Uncertain Quantification of Porous Media Flows.

97 MATHEMATICS AND COMPUTING↗

Systematic Error Study for ALICE charged-jet v2 Measurement

We study the treatment of systematic errors in the determination of v 2 for charged jets in √ sNN = 2:76 TeV Pb-Pb collisions by the ALICE Collaboration. Working with the reported values and errors for the 0-5% centrality data we evaluate the Χ 2 according to the formulas given for the statistical and systematic errors, where the latter are separated into correlated and shape contributions. We reproduce both the Χ 2 and p-values relative to a null (zero) result. We then re-cast the systematic errors into an equivalent co-variance matrix and obtain identical results, demonstrating that the two methods are equivalent.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Error studies of Halbach Magnets

These error studies were done on the Halbach magnets for the CBETA “First Girder” as described in note [CBETA001]. The CBETA magnets have since changed slightly to the lattice in [CBETA009]. However, this is not a large enough change to significantly affect the results here. The QF and BD arc FFAG magnets are considered. For each assumed set of error distributions and each ideal magnet, 100 random magnets with errors are generated. These are then run through an automated version of the iron wire multipole cancellation algorithm. The maximum wire diameter allowed is 0.063” as in the proof-of-principle magnets. Initially, 32 wires (2 per Halbach wedge) are tried, then if this does not achieve 1e-­4 level accuracy in the simulation, 48 and then 64 wires. By “1e-4 accuracy”, it is meant the FOM defined by √(Σ n≥sextupole a n 2 +b n 2 ) is less than 1 unit, where the multipoles are taken at the maximum nominal beam radius, R=23mm for these magnets. The algorithm initially uses 20 convergence interations. If 64 wires does not achieve 1e-­4 accuracy, this is increased to 50 iterations to check for slow converging cases. There are also classifications for magnets that do not achieve 1e-4 but do achieve 1e-3 (FOM ≤ 10 units). This is technically within the spec discussed in the Jan 30, 2017 review; however, there will be errors in practical shimming not dealt with in the simulation, so it is preferable to do much better than the spec in the simulation.

43 PARTICLE ACCELERATORS↗

AEDAM: Whole Program Adaptive Error Detection and Mitigation (Final Report)

The overall goals of the AEDAM project were to fundamentally transform software transient-error detection through the design of configurable specialized detectors, quantitative characterization of hardware resilience and software vulnerabilities, and composition of the specialized detectors to most efficiently protect the whole program. Within this scope, UT Austin's research contribution related to enabling and studying the composition of detectors and possible different hardware errors, specifically: (1) developed the Hamartia open-source error injection framework that is designed to make composition studies simple, and (2) develop the methodology and demonstrate the potential benefits of error detector composition.

97 MATHEMATICS AND COMPUTING↗

Applying Multi-Frequency AC LOCO for Finding Sextupole Errors

A fast and precise technique of multi-frequency AC LOCO has been developed and tested for finding the sextupole alignment and field-offset errors at NSLS-II. This technique is based on sine-wave beam excitation simultaneously at multiple frequencies via different fast correctors. The unique combination of the fast speed and high measurement accuracy opens the door for two different types of potential applications: finding the sextupole alignment and field-offset errors. Beam excitation via fast correctors results in the elimination of the systematic error caused by the hysteresis effect. Systematic errors of the sextupole alignment caused by orbit drift and power supply calibration are also eliminated because the measurement takes only two minutes and does not depend on the current-to-field conversion of sextupole magnets. Furthermore, the simulation studies indicate that multi-frequency AC LOCO together with an orbit bump bigger than 0.5 mm can be applied to measure the relative field offset of a sextupole magnet with a precision better than 10%. The measurement technique is described and the results of two proof-of-principle experiments carried out at NSLS-II are presented.

43 PARTICLE ACCELERATORS↗

A Logarithmic Bayesian Approach to Quantum Error Detection

We consider the problem of continuous quantum error correction from a Bayesian perspective, proposing a pair of digital filters using logarithmic probabilities that are able to achieve near-optimal performance on a three-qubit bit-flip code, while still being reasonable to implement on low-latency hardware. These practical filters are approximations of an optimal filter that we derive explicitly for finite time steps, in contrast with previous work that has relied on stochastic differential equations such as the Wonham filter. By utilizing logarithmic probabilities, we are able to eliminate the need for explicit normalization and can reduce the Gaussian noise distribution to a simple quadratic expression. The state transitions induced by the bit-flip errors are modeled using a Markov chain, which for log-probabilities must be evaluated using a LogSumExp function. We develop the two versions of our filter by constraining this LogSumExp to have either one or two inputs, which favors either simplicity or accuracy, respectively. Using simulated data, we demonstrate that the single-term and two-term filters are able to significantly outperform both a double threshold scheme and a linearized version of the Wonham filter in tests of error detection under a wide variety of error rates and time steps.

97 MATHEMATICS AND COMPUTING↗

Errors in radial velocity variance from Doppler wind lidar

A high-fidelity lidar turbulence measurement technique relies on accurate estimates of radial velocity variance that are subject to both systematic and random errors determined by the autocorrelation function of radial velocity, the sampling rate, and the sampling duration. Our paper quantifies the effect of the volumetric averaging in lidar radial velocity measurements on the autocorrelation function and the dependence of the systematic and random errors on the sampling duration, using both statistically simulated and observed data. For current-generation scanning lidars and sampling durations of about 30 min and longer, during which the stationarity assumption is valid for atmospheric flows, the systematic error is negligible but the random error exceeds about 10%.

54 ENVIRONMENTAL SCIENCES↗

The effect of timing errors in optical digital systems

The effects of imperfect timing in direct detection (non-coherent) optical binary systems using both PPM and on-off keying for bit transmission are investigated. Particular emphasis is placed on specification of timing accuracy, and an examination of system degradation when this accuracy is not attained. Bit error probabilities are shown as a function of timing errors, from which average error probabilities can be computed for specific synchronization methods. Of significant importance is the presence of a residual, or irreducible error probability in both systems, due entirely to the timing system, that cannot be overcome by the data channel.

Gagliardi, R.↗

Multipath error in range rate measurement by PLL-transponder/GRARR/TDRS

Range rate errors due to specular and diffuse multipath are calculated for a tracking and data relay satellite (TDRS) using an S band Goddard range and range rate (GRARR) system modified with a phase-locked loop transponder. Carrier signal processing in the coherent turn-around transponder and the GRARR reciever is taken into account. The root-mean-square (rms) range rate error was computed for the GRARR Doppler extractor and N-cycle count range rate measurement. Curves of worst-case range rate error are presented as a function of grazing angle at the reflection point. At very low grazing angles specular scattering predominates over diffuse scattering as expected, whereas for grazing angles greater than approximately 15 deg, the diffuse multipath predominates. The range rate errors at different low orbit altutudes peaked between 5 and 10 deg grazing angles.

Sohn, S. J.↗

The effect of timing errors in optical digital systems.

The use of digital transmission with narrow light pulses appears attractive for data communications, but carries with it a stringent requirement on system bit timing. The effects of imperfect timing in direct-detection (noncoherent) optical binary systems are investigated using both pulse-position modulation and on-off keying for bit transmission. Particular emphasis is placed on specification of timing accuracy and an examination of system degradation when this accuracy is not attained. Bit error probabilities are shown as a function of timing errors from which average error probabilities can be computed for specific synchronization methods. Of significance is the presence of a residual or irreducible error probability in both systems, due entirely to the timing system, which cannot be overcome by the data channel.

Gagliardi, R. M.↗

Some effects of experimental error in fracture testing

Effects of experimental imprecision on the stress intensity factors calculated for various practical specimen types are shown. A general form equation for the stress intensity factor is presented and a general error equation is derived. The expected error in the stress intensity factor is given in terms of the precision levels of the basic experimental measurements and derivatives of the stress intensity calibration factor. Nine common fracture specimen types are considered, and the sensitivity of the various types to experimental error is illustrated. Some implications for fracture toughness testing and crack growth rate testing are discussed and methods of analysis are proposed to compensate for the effects of experimental error.

Orange, T. W.↗

Floating-point system quantization errors in digital control systems

The results are reported of research into the effects on system operation of signal quantization in a digital control system. The investigation considered digital controllers (filters) operating in floating-point arithmetic in either open-loop or closed-loop systems. An error analysis technique is developed, and is implemented by a digital computer program that is based on a digital simulation of the system. As an output the program gives the programing form required for minimum system quantization errors (either maximum of rms errors), and the maximum and rms errors that appear in the system output for a given bit configuration. The program can be integrated into existing digital simulations of a system.

Phillips, C. L.↗

Some effects of experimental error in fracture testing.

The purpose of this paper is to show the effects of experimental imprecision on the stress intensity factors calculated for various practical specimen types. A general form equation for the stress intensity factor is presented, and a general error equation is derived. The expected error in the stress intensity factor is given in terms of the precision levels of the basic experimental measurements and derivatives of the stress intensity calibration factor. Nine common fracture specimen types are considered, and the sensitivity of the various types to experimental error is illustrated. Some implications for fracture toughness testing and crack growth rate testing are discussed, and methods of analysis are proposed to compensate for the effects of experimental error.

Orange, T. W.↗

Analytical expressions for position error in triangulation solution of point in space for several station configurations

Analytical expressions are derived to first order for the rms position error in the triangulation solution of a point object in space for several ideal observation-station configurations. These expressions provide insights into the nature of the dependence of the rms position error on certain of the experimental parameters involved. The station geometries examined are: (1) the configuration of two arbitrarily located stations; (2) the symmetrical circular configuration of two or more stations with equal elevation angles; and (3) the circular configuration of more than two stations with equal elevation angles, when one of the stations is permitted to drift around the circle from its position of symmetry. The expressions for the rms position error are expressed as functions of the rms line-of-sight errors, the total number of stations of interest, and the elevation angles.

Long, S. A. T.↗

An error criterion for determining sampling rates in closed-loop control systems

The determination of an error criterion which will give a sampling rate for adequate performance of linear, time-invariant closed-loop, discrete-data control systems was studied. The proper modelling of the closed-loop control system for characterization of the error behavior, and the determination of an absolute error definition for performance of the two commonly used holding devices are discussed. The definition of an adequate relative error criterion as a function of the sampling rate and the parameters characterizing the system is established along with the determination of sampling rates. The validity of the expressions for the sampling interval was confirmed by computer simulations. Their application solves the problem of making a first choice in the selection of sampling rates.

Brecher, S. M.↗

Design, performance, and calculated error of a Faraday cup for absolute beam current measurements of 600-MeV protons

A mobile self-contained Faraday cup system for beam current measurments of nominal 600 MeV protons was designed, constructed, and used at the NASA Space Radiation Effects Laboratory. The cup is of reentrant design with a length of 106.7 cm and an outside diameter of 20.32 cm. The inner diameter is 15.24 cm and the base thickness is 30.48 cm. The primary absorber is commercially available lead hermetically sealed in a 0.32-cm-thick copper jacket. Several possible systematic errors in using the cup are evaluated. The largest source of error arises from high-energy electrons which are ejected from the entrance window and enter the cup. A total systematic error of -0.83 percent is calculated to be the decrease from the true current value. From data obtained in calibrating helium-filled ion chambers with the Faraday cup, the mean energy required to produce one ion pair in helium is found to be 30.76 + or - 0.95 eV for nominal 600 MeV protons. This value agrees well, within experimental error, with reported values of 29.9 eV and 30.2 eV.

Beck, S. M.↗

The effect of measurement errors and computational approximations on a perspective ILM radar image

The effect was examined of aircraft position and attitude, of measurement errors, and of computational approximations on the size, shape, and position of a perspective radar image of an airport runway as might be displayed by an independent landing monitor in transport aircraft. The effect on runway image geometry was examined for different aircraft attitudes and different aircraft positions relative to a standard three degree glide slope. Measurement errors investigated were errors in radar azimuth angle and range, and errors in those aircraft parameters supplied to the radar for use in converting the radar image into a perspective format (namely pitch, roll, and altitude). Also investigated were the effects of using certain mathematical approximations, such as small angle, in the coordinate transformation which converts the image to a perspective format.

Bundick, W. T.↗