Robust error estimation in optical analysis software using subdivided and recombined ray traces

The influence of jitter on the interface between space camera and satellite platform may cause the camera structural distortion, which will change ideal assembly and adjustment relationship of optical system, and affect the imaging quality. An integrated model of a high resolution space camera comprising reaction wheel assemblies disturbance which induced the largest jitter of spacecraft, structures and optics systems was developed in order to predict the expected dynamic performance of the camera in terms of MTF descending and image motion. The process as currently implemented uses Pro/Engineer for design, PATRAN and Hypermesh for model building and results visualization, NASTRAN for structural analysis, and Code V for optical analysis. A translator was developed in MATLAB to transfer PATRAN results to Code V optical analysis software. This jitter analysis results are used to assess image quality, improve the structural design, and mitigate the disturbance impact.

Floating-point computation generates errors at the bit level through four processes, namely, overflow, underflow, truncation, and rounding. Overflow and underflow can be detected electronically, and represent systematic errors that are not of interest in this study. Truncation occurs during shifting toward the least-significant bit (herein called right-shifting), and rounding error occurs at the least significant bit. Such errors are not easy to track precisely using published means. Statistical error propagation theory typically yields conservative estimates that are grossly inadequate for deep computational cascades. Forward error analysis theory developed for image and signal processing or matrix operations can yield a more realistic typical case, but the error of the estimate tends to be high in relationship to the estimated error. In this paper, we discuss emerging technology for forward error analysis, which allows an algorithm designer to precisely estimate the output error of a given operation within a computational cascade, under a prespecified set of constraints on input error and computational precision. This technique, called bit accounting, precisely tracks the number of rounding and truncation errors in each bit position of interest to the algorithm designer. Because all errors associated with specific bit positions are tracked, and because integer addition only is involved in error estimation, the error of the estimate is zero. The technique of bit accounting is evaluated for its utility in image and signal processing. Complexity analysis emphasizes the relationship between the work and space estimates of the algorithm being analyzed, and its error estimation algorithm. Because of the significant overhead involved in error representation, it is shown that bit accounting is less useful for real-time error estimation, but is well suited to analysis in support of algorithm design.

In this paper we review the basic concepts to obtain a posteriori error estimates for the finite element solution of an elliptic linear model problem. We give the basic ideas to establish global error estimates for the energy norm as well as goal-oriented error estimates. While we show how these error estimation techniques are employed for our simple model problem, the emphasis of the paper is on assessing whether these procedures are ready for use in practical linear finite element analysis. We conclude that the actually practical error estimation techniques do not provide mathematically proven bounds on the error and need to be used with care. The more accurate estimation procedures also do not provide proven bounds that, in general, can be computed efficiently. We also briefly comment upon the state of error estimations in nonlinear and transient analyses and when mixed methods are used.

New a posteriori error estimator and adaptive mesh refinement strategy for 2-D crack problems

This investigation examines the influence of sample design on the sampling errors of several multivariate statistics which are frequently used in educational survey research. Student’s empirical sampling technique is used to generate sampling distributions for several complex sample designs which are often used to sample schools, classrooms and students. Some results are presented for two error estimation techniques: “Jackknifing” and “Balanced Repeated Replication”.

Many rate constant measurements, including some “direct” measurements, involve fitting a complex reaction mechanism to experimental data. Two techniques for estimating the error in such measurements were compared. In the first technique, local first‐order elementary sensitivities were used to rapidly estimate the sensitivity of the fitted rate constants to the remaining mechanism parameters. Our group and others have used this technique for error estimation and experimental design. However, the nonlinearity and strong coupling found in reaction mechanisms make verification against globally valid results desirable. Here, the local results were compared with analogous importance‐sampled Monte Carlo calculations in which the parameter values were distributed according to their uncertainties. Two of our published rate measurements were examined. The local uncertainty estimates were compared with Monte Carlo confidence intervals. The local sensitivity coefficients were compared with coefficients from first and second‐degree polynomial regressions over the whole parameter space. The first‐order uncertainty estimates were found to be sufficiently accurate for experimental design, but were subject to error in the presence of higher order sensitivities. In addition, global uncertainty estimates were found to narrow when the quality of the fit was used to weight the randomly distributed points. For final results, the global technique was found to provide efficient, accurate values without the assumptions inherent in the local analysis. The rigorous error estimates derived in this way were used to address literature criticism of one of the studies discussed here. Given its efficiency and the variety of problems it can detect, the global technique could also be used to check local results during the experimental design phase. The global routine, coded using SENKIN, can easily be extended to different types of data, and therefore can serve as a valuable tool for assessing error in rate constants determined using complex mechanisms. © 2001 John Wiley & Sons, Inc. Int J Chem Kinet 33: 784–802, 2001

LEDs have becoming the most suitable candidate replacing traditional fluorescent lamps because of its energy-efficient, the introduction of high brightness LEDs with white light and monochromatic colors have led to a movement towards general illumination. This revolutionizes the optoelectronics market, enabling engineers to use LEDs for general lighting applications as well as medical, indoor lighting and automotive solutions. So variable LED array modules were developed, they are making great strides in terms of lumen performance and reliability, however the barrier to widespread use in general illumination still remains the cost or luminous efficiency, special requirements concerning optical properties and optomechanical layout have to be met. In order to meet the requirements of indoor illumination, a LED daylight lamp model was designed, it can replace traditional fluorescent lamp without insteading additional power supply establishment. The optical properties of the model were simulated using optical analysis software, its luminous efficiency is about 41 lm/W, the illuminance is about 50 lux when the distance is 1.5 m between the center of the model and measured spot, With the theoretically-optimized design of the LED model, experiments based on the results of the optimal simulation in the laboratory were conducted to verify the performance of the proposed LED model, it reaches a power factor of about 0.8 at 11 W. Results of the simulation are very similar with the measured values, it was testified that simulative method is one of the effective tools for LED lighting optical design.

The study proposes an optical optimal design system of light guide plate (LGP). The optimization design is conducted in the longitudinal structure of the LGP incidence plane with 3-piece LED light source. Taguchi method is also used in carrying out the design of experiment through the TracePro, optical analysis software, and the experiment data were employedd as the back-propagation neural network (BPNN) training and testing samples, and then created an optical quality predictor of the longitudinal structure; BPNN can predict the impact of incidence plane luminance versus the different constructed parameters. Finally, the optical quality predictor can effectively generate the optimal parameters settings combined with genetic algorithm (GA). The simulation results show that the proposed system improves the non-uniformity problem of the incidence plane but also makes it easier to design the longitudinal structure of the incidence plane.

In 1983, Rocketdyne Division of Rockwell International constructed the OASIS code in support of the Air Force to meet increasing needs for diffractive optical system analysis. The OASIS code (Optical Analysis Software for Interactive Systems) was developed to meet these needs in the context of new supercomputer environments. From its inception, the code was anticipated to be a highly interactive analysis tool featuring the basic required physics, plus generality and flexibility. A valuable teaching tool, the code is command line driven and offers complete documentation.

Up-regulation of KHK activation on a high fructose diet is positively associated with the subsequent development of several metabolic diseases, including high fructose diet-induced heart disease. Hypoxic exercise is considered an effective means of treating and preventing metabolic diseases and improving cardiac function. However, it is unclear whether the link between hypoxic exercise and high fructose-induced heart disease exists. Therefore, the aim of this study was to investigate the link between the modulation of KHK by hypoxic exercise and high fructose diet heart disease. Method: Three hundred virgin flies of the wild-type W1118 strain were collected and randomly assigned to control (NC), high fructose diet (HF), and high fructose diet (HE) groups, with 100 flies’ group. Drosophila on a high fructose diet were fed continuously with high fructose from birth to 12 days old, and Drosophila on hypoxic exercise were fed with a self-developed hypoxic exercise device for 5 consecutive days of 1 hour per day from 7 days old, and each group was sampled at 13 days old. Changes in KHK expression levels in the heart were detected by RT-qPCR, and various kinds of Drosophila cardiac function were quantified using an EM-CCD digital camera and semi-automatic optical heartbeat analysis software. Compared with the NC group, KHK mRNA expression was increased (P < 0.05), arrhythmia index was increased (P < 0.05), systolic intervals (P < 0.01), diastolic intervals were bradycardic, systolic diameter and diastolic diameter were decreased (P < 0.01), and ejection fraction was decreased (P < 0.001) in Drosophila hearts after the high fructose diet; compared with the HF group, in Drosophila hearts of the HE group KHK mRNA expression decreased (P < 0.05), arrhythmia index decreased (P < 0.05), cardiac inter-systolic interval decreased (P < 0.001), diastolic bradycardia improved, systolic diameter increased, diastolic diameter increased (P < 0.05), and ejection fraction increased (P < 0.01) in Drosophila hearts from the HE group. Hypoxic exercise improved cardiac rhythmic function and pumping dysfunction on a high-fructose diet by inhibiting KHK expression in the heart.

The Free-space Optical Communications Analysis Software (FOCAS) was developed at the Jet Propulsion Laboratory (JPL) to provide mission planners, systems engineers and communications engineers with an easy to use tool to analyze optical communications link.

Aiming to solve the track refined correlation problem of the group targets with systematic errors, based on the characteristics of the group tracks, an algorithm of track refined correlation with in group targets based on systematic error compensation is proposed with the error estimation technique and the track correlation technique. In this algorithm, the groups are identified with the tracks of the sensors based on the circulatory threshold model firstly. Secondly, the preparatory correlation groups with the nearest resolving state are searched or established based on group track state identification model. Thirdly, the final systematic errors are estimated with group track systematic error estimation model and error validation model. What is more, the error compensation is completed. Finally, group track refined correlation is done with the traditional track correlation algorithms. The analysis results of the simulation data show that the general performance of this algorithm, which can meet the engineering requirement of the track refined correlation of the group targets with systematic errors very well, is better than that of fuzzy track alignment-correlation algorithm based on target topological information, track alignment-correlation algorithm based on iterative closest track and modified weighted track correlation algorithm.

This is the first of two articles concerning error estimation and adaptive refinement techniques applied to convective heat transfer problems. This study presents the detailed development of the proposed error estimator. The error estimator takes into account the coupling effects of the dependent variables (e.g., velocity and temperature) on the discretization error and, consequently, on the adaptive meshes. An averaging procedure is also proposed as a substitute for the smoothing/recovery procedure used to evaluate the gradients. The implementation of the averaging technique is simple and cost effective. Numerical experiments demonstrate that the proposed methodology results in a dramatic reduction in computational costs.

In the study of the atmospheric boundary layer, Large Eddy Simulation (LES) results are nearly considered to be experimental data. However, where experimental results on turbulent quantities are occasionally accompanied by an estimation of the statistical error in the result, this is not the case for LES results. From the statistical literature methods are available to estimate the statistical error in central moments of arbitrary order of one and two variables based on higher moments of those variables. For statistics other than central moments (e.g. terms in a flux budget) resampling algorithms are available such as the jackknife method and bootstrap method. All these methods rely on the assumption that samples are independent. Statistics are derived from atmospheric LES results by averaging in all homogeneous dimensions (usually time and both horizontal directions) and the total number of samples equals the product of the number of samples in each direction. The number of independent samples, however, depends on the spatial and temporal correlation. For discretely sampled data the effect of the correlation between samples can either be determined using the integral scale or using the number of zero-crossings of the variable under consideration (after subtraction of the mean). An LES of a convective boundary layer will be used to demonstrate the use and results of the estimation of statistical errors in central moments and flux budgets

Extensions to the CART algorithm