Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “ERROR FUNCTION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

A table of integrals of the error function. II - Additions and corrections.

Integrals of products of error functions with other functions are presented, taking into account a combination of the error function with powers, a combination of the error function with exponentials and powers, a combination of the error function with exponentials of more complicated arguments, definite integrals from Laplace transforms, and a combination of the error function with trigonometric functions. Other integrals considered include a combination of the error function with logarithms and powers, a combination of two error functions, and a combination of the error function with other special functions.

Geller, M.↗
DOE OSTI2015

SU-E-T-385: Evaluation of DVH Change for PTV Due to Patient Weight Loss in Prostate VMAT Using Gaussian Error Function

Purpose: We proposed a method to predict the change of dose-volume histogram (DVH) for PTV due to patient weight loss in prostate volumetric modulated arc therapy (VMAT). This method is based on a pre-calculated patient dataset and DVH curve fitting using the Gaussian error function (GEF). Methods: Pre-calculated dose-volume data from patients having weight loss in prostate VMAT was employed to predict the change of PTV coverage due to reduced depth in external contour. The effect of patient weight loss in treatment was described by a prostate dose-volume factor (PDVF), which was evaluated by the prostate PTV. Along with the PDVF, the GEF was used to fit into the DVH curve for the PTV. To predict a new DVH due to weight loss, parameters from the GEF describing the shape of DVH curve were determined. Since the parameters were related to the PDVF as per the specific reduced depth, we could first predict the PDVF at a reduced depth based on the prostate size from the pre-calculated dataset. Then parameters of the GEF could be determined from the PDVF to plot the new DVH for the PTV corresponding to the reduced depth. Results: A MATLAB program was built basing on the patient dataset with different prostate sizes. We input data of the prostate size and reduced depth of the patient into the program. The program then calculated the PDVF and DVH for the PTV considering the patient weight loss. The program was verified by different patient cases with various reduced depths. Conclusion: Our method can estimate the change of DVH for the PTV due to patient weight loss quickly without CT rescan and replan. This would help the radiation staff to predict the change of PTV coverage, when patient’s external contour reduced in prostate VMAT.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

SU-E-J-164: Estimation of DVH Variation for PTV Due to Interfraction Organ Motion in Prostate VMAT Using Gaussian Error Function

Purpose: We developed a method to predict the change of DVH for PTV due to interfraction organ motion in prostate VMAT without repeating the CT scan and treatment planning. The method is based on a pre-calculated patient database with DVH curves of PTV modelled by the Gaussian error function (GEF). Methods: For a group of 30 patients with different prostate sizes, their VMAT plans were recalculated by shifting their PTVs 1 cm with 10 increments in the anterior-posterior, left-right and superior-inferior directions. The DVH curve of PTV in each replan was then fitted by the GEF to determine parameters describing the shape of curve. Information of parameters, varying with the DVH change due to prostate motion for different prostate sizes, was analyzed and stored in a database of a program written by MATLAB. Results: To predict a new DVH for PTV due to prostate interfraction motion, prostate size and shift distance with direction were input to the program. Parameters modelling the DVH for PTV were determined based on the pre-calculated patient dataset. From the new parameters, DVH curves of PTVs with and without considering the prostate motion were plotted for comparison. The program was verified with different prostate cases involving interfraction prostate shifts and replans. Conclusion: Variation of DVH for PTV in prostate VMAT can be predicted using a pre-calculated patient database with DVH curve fitting. The computing time is fast because CT rescan and replan are not required. This quick DVH estimation can help radiation staff to determine if the changed PTV coverage due to prostate shift is tolerable in the treatment. However, it should be noted that the program can only consider prostate interfraction motions along three axes, and is restricted to prostate VMAT plan using the same plan script in the treatment planning system.

60 APPLIED LIFE SCIENCES↗
NASA NTRS2019

A comprehensive line spread function error for the Off-plane Grating Rocket Experiment

The Off-plane Grating Rocket Experiment (OGRE) is a soft X-ray grating spectrometer to be flown on a suborbital rocket. The payload is designed to obtain the highest-resolution soft X-ray spectrum of Capella to date with a resolution goal of R(lambda/delta lambda) > 2000 at select wavelengths in its 10 - 55 A bandpass of interest. The optical design of the spectrometer realizes a maximum resolution of R 5000 with all components performing optimally, in perfect alignment, and not considering in-flight pointing errors; however, performance errors, misalignments, and in-flight pointing errors work to degrade this performance. A comprehensive line spread function (LSF) error budget has been constructed for the spectrometer to identify errors contributing to the LSF, to determine how each affects the LSF, and to inform performance requirements and alignment tolerances for the spectrometer. In this document, the comprehensive LSF error budget for the OGRE spectrometer is presented and its implications are discussed.

Benjamin D Donovan↗
DOE OSTI2015

Density-functional errors in ionization potential with increasing system size

This work investigates the effects of molecular size on the accuracy of density-functional ionization potentials for a set of 28 hydrocarbons, including series of alkanes, alkenes, and oligoacenes. As the system size increases, delocalization error introduces a systematic underestimation of the ionization potential, which is rationalized by considering the fractional-charge behavior of the electronic energies. The computation of the ionization potential with many density-functional approximations is not size-extensive due to excessive delocalization of the incipient positive charge. While inclusion of exact exchange reduces the observed errors, system-specific tuning of long-range corrected functionals does not generally improve accuracy. These results emphasize that good performance of a functional for small molecules is not necessarily transferable to larger systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1988

Threshold computations for detection of failures in SISO systems with transfer function errors

The author considers the problem of detecting failures in SISO systems using analytic redundancy concepts. Since the models used are subject to error, a method of determining the detection thresholds that account for these errors is sought. The methodology presented utilizes a straightforward application of Parseval's relation to develop a threshold computation that is performed online as a function of the input signal. The threshold is set at a quiescent value to account for sensor noise and is adjusted (upward) according to the activity of the input signal. An application to detection of actuator failures is presented.

Weiss, Jerold L.↗
NASA NTRS1992

The effects of weighting function errors on spatial filters for structural control

Distributed-effect sensors, which respond to spatially distributed inputs over a significant gauge length, encompass piezoelectric laminate films, modal-domain optical fiber sensors, and holographic sensors; they can be fabricated with spatially varying sensitivity to a distributed measurand for spatial filtering. Such spatial filters are configurable to extract various structural parameters from distributed measurements that cannot be directly measured by sensors. A modeling is presently conducted for distributed-effect sensors' integration into state-space structural models, noting the effects of fabrication errors on sensor operation.

Lindner, Douglas K.↗
NASA NTRS2000

A Posteriori Error Estimation for Finite Volume and Finite Element Approximations Using Broken Space Approximation

We consider a posteriori error estimates for finite volume and finite element methods on arbitrary meshes subject to prescribed error functionals. Error estimates of this type are useful in a number of computational settings: (1) quantitative prediction of the numerical solution error, (2) adaptive meshing, and (3) load balancing of work on parallel computing architectures. Our analysis recasts the class of Godunov finite volumes schemes as a particular form of discontinuous Galerkin method utilizing broken space approximation obtained via reconstruction of cell-averaged data. In this general framework, weighted residual error bounds are readily obtained using duality arguments and Galerkin orthogonality. Additional consideration is given to issues such as nonlinearity, efficiency, and the relationship to other existing methods. Numerical examples are given throughout the talk to demonstrate the sharpness of the estimates and efficiency of the techniques. Additional information is contained in the original.

Barth, Timothy J.↗
NASA NTRS2004

Single Event Effects in Highly Scaled Devices for Space Applications

This paper discusses single-event upset (SEU) in memories and microprocessors that are the "drivers" of highly scaled commercial integrated circuits. Despite the decrease in critical charge that occurs for highly scaled CMOS devices, recent test data has shown that SEU rates are actually somewhat lower for scaled devices compared to older devices with larger feature size. Hard errors, which are increasingly important for memories, are discussed along with conventional soft errors. Functional errors in memories and microprocessors are particularly significant, and tend to dominate the response of highly scaled devices from an application standpoint. Predictions for future devices are made using the Semiconductor Industry Roadmap along with recent modeling and radiation test results.

microelectronics↗