Differential Correction Method Research Articles

Correct block artifacts by differential projection for a dynamic computed tomography system

In the aero-engine industry, it is important to carry out regular and effective tests on engines in service. However, current detection methods often have problems such as a limitation on materials characteristics or geometry structures. Recently, a novel dynamic computed tomography (CT) system was proposed to provide highly efficient CT inspection for rotating parts, in particular the blades of aero-engines in operation. However, one problem exists in the proposed system in that some components remain static when the engine is in operation. These static parts will appear as strip artifacts in projection and ultimately as ring artifacts in the reconstructed image, which are called block artifacts. In this paper, we put forward a differential projection correction method to correct block artifacts and reconstruct the blades of the aero-engine. The method makes use of the distribution of the blades and the static parts to remove the artifacts. The experiment results show that the proposed method can effectively remove the block artifacts while maintaining the grayscale and geometry structure of the blades, furthermore, we also verify its ability to detect defects using numerical experiments. The differential projection correction method makes the system more practicable for in situ inspection of aero-engines.

Preliminary Clinical Validation of a Differential Correction Method for Improving Measurement Accuracy in Noninvasive Measurement of Blood Glucose Using Near-Infrared Spectroscopy.

One of the main challenges in the noninvasive sensing of blood glucose by near-infrared (NIR) spectroscopy is the background variations from light source drift, sweating, and temperature change at the human-machine interface. In this paper, a differential correction method based on the spectra from the floating-reference position and measuring position is proposed to eliminate these spectral variations from background interferences. Its effectiveness was validated by invitro and invivo experiments in which the diffuse reflectance of intralipid solutions and human skin was collected at the source distances of 0.6 mm and 2 mm by the custom-built system with six super-luminescent emitting diodes (SLEDs) light source. The results showed that, for the invitro experiments of intralipid solutions, the coefficients of variations of diffuse reflectance decreased by 20.5% under all the six wavelengths after differential correction. For the invivo experiments of oral glucose tolerance tests (OGTTs), partial least squares (PLS) regression models between glucose concentrations and the diffuse reflectance from palm skin were built, and the root mean square error of cross validation (RMSECV) decreased by 38.0% on average after the differential correction. Further, the spectra of the oral water tolerance tests (OWTTs) were collected for correlation with glucose concentration in OGTTs, and their correlation coefficients (R) decreased by 35.0% on average after the differential correction. Therefore, this differential correction method based on the spectra from the floating-reference position and measuring position can weaken the influence of background variations on the NIR spectroscopy and has promising potential in invivo detection, especially for noninvasive blood glucose measurement.

Differential correction method applied to measurement of the FAST reflector

The Five-hundred-meter Aperture Spherical radio Telescope (FAST) adopts an active deformable main reflector which is composed of 4450 triangular panels. During an observation, the illuminated area of the reflector is deformed into a 300-m diameter paraboloid and directed toward a source. To achieve accurate control of the reflector shape, positions of 2226 nodes distributed around the entire reflector must be measured with sufficient precision within a limited time, which is a challenging task because of the large scale. Measurement of the FAST reflector makes use of stations and node targets. However, in this case the effect of the atmosphere on measurement accuracy is a significant issue. This paper investigates a differential correction method for total stations measurement of the FAST reflector. A multi-benchmark differential correction method, including a scheme for benchmark selection and weight assignment, is proposed. On-site evaluation experiments show there is an improvement of 70%–80% in measurement accuracy compared with the uncorrected measurement, verifying the effectiveness of the proposed method.

A UKF based design method for lunar free-return trajectories

A method based on unscented Kalman filter parameter estimation is proposed for the design of lunar free-return trajectories. The method avoids calculating the Jacobian matrix and obtains large convergence ability compared with the common differential-correction method. Given that the initial estimate of the free-return trajectory is only required to be generated under the two-body Earth–spacecraft model, the difficulty of guessing a good initial estimate is greatly reduced. Through converting the original problem to a parameter estimation representation, the method is used to find the converged final solution that satisfies the constraints at injection, perilune, and Earth-entry interface under a high-fidelity gravitational model. In addition to its deceptively simplicity, the method proves to be quite effective through numerical examples in finding the solution to lunar free-return trajectories within a few iterations with great numerical accuracy.

Precise halo orbit design and optimal transfer to halo orbits from earth using differential evolution

The mission design to a halo orbit around the libration points from Earth involves two important steps. In the first step, we design a halo orbit for a specified size and in the second step, we obtain an optimal transfer trajectory design to the halo orbit from an Earth parking orbit. Conventionally, the preliminary design for these steps is obtained using higher order analytical solution and the dynamical systems theory respectively. Refinements of the design are carried out using gradient based methods such as differential correction and pseudo arc length continuation method under the of circular restricted three body model. In this paper, alternative single level schemes are developed for both of these steps based on differential evolution, an evolutionary optimization technique. The differential evolution based scheme for halo orbit design produces precise halo orbit design avoiding the refinement steps. Further, in this approach, prior knowledge of higher order analytical solutions for the halo orbit design is not needed. The differential evolution based scheme for the transfer trajectory, identifies the precise location on the halo orbit that needs minimum energy for insertion and avoids exploration of multiple points. The need of a close guess is removed because the present scheme operates on a set of bounds for the unknowns. The constraint on the closest approach altitude from Earth is handled through objective function. The use of these schemes as the design and analysis tools within the of circular restricted three body model is demonstrated through case studies for missions to the first libration point of Sun–Earth system.

A Distribution Method of High Precise Differential Corrections for a Network Beidou/RTK System Based on Vehicular Networks

Abstract In recent years urban traffic safety has become a widely concerned issue due to the increasing traffic accidents caused by the growth of private car ownership. A very promising method is to provide high precision navigation service to prevent accidents. Therefore, a Network BDS/RTK System Based on Vehicular Networks (NBRSBVNs) is proposed for high precision positioning in an urban complex traffic environment in this paper. This system considers comprehensively the characteristics of the vehicular network and network RTK techniques, and also provides a new distribution method of high precision differential correction information. According to the massive field tests, this system scheme can support real-time and online high precision navigation service of multiple users at the same time. It has important practical significance in applications for vehicles active safety in a complex urban environment.

基于近红外波长组合快速检测油页岩含油率

To detect rapidly the oil yield of an oil shale on a single point measurement,a detection method was proposed based on combination of wavelengths by aportable near infrared spectroscopy.By taking the kaolin mixed with oil simulating samples as the research object,how to select the combination of wavelengths by near infrared spectroscopy was performed.With proposed method,the full spectral reflectivity data were firstly acquired by the developed portable spectrometer.Then the preliminary selection for the combination of wavelengths was implemented by differential multiplicative scatter correction method and correlation coefficient method,and the optimum combination of wavelengths was determined by combination generation method and leave one cross validation Multiple Linear Regression(MLR).Finally,the data for the optimum combination of wavelengths were verified by MLR modeling.The results show that the optimum combination of wavelengths is 1 644,1 720,2 210 and 2 260 nm,and the determination coefficients for calibration set(R2c),prediction set(R2p)of30modeling samples and validation(R2p)of 11 validation samples are 0.995 4,0.997 7and 0.990 1,respectively.The method provides a basis for design of a rapid detecting spectrometer in oil yields of oil shapes.

Improving CMD Areal Density Analysis: Algorithms and Strategies

Essential ideas, successes, and difficulties of Areal Density Analysis (ADA) for color-magnitude diagrams (CMD's) of resolved stellar populations are examined, with explanation of various algorithms and strategies for optimal performance. A CMD-generation program computes theoretical datasets with simulated observational error and a solution program inverts the problem by the method of Differential Corrections (DC) so as to compute parameter values from observed magnitudes and colors, with standard error estimates and correlation coefficients. ADA promises not only impersonal results, but also significant saving of labor, especially where a given dataset is analyzed with several evolution models. Observational errors and multiple star systems, along with various single star characteristics and phenomena, are modeled directly via the Functional Statistics Algorithm (FSA). Unlike Monte Carlo, FSA is not dependent on a random number generator. Discussions include difficulties and overall requirements, such as need for fast evolutionary computation and realization of goals within machine memory limits. Degradation of results due to influence of pixelization on derivatives, Initial Mass Function (IMF) quantization, IMF steepness, low Areal Densities (<TEX>$\mathcal{A}$</TEX>), and large variation in <TEX>$\mathcal{A}$</TEX> are reduced or eliminated through a variety of schemes that are explained sufficiently for general application. The Levenberg-Marquardt and MMS algorithms for improvement of solution convergence are contained within the DC program. An example of convergence, which typically is very good, is shown in tabular form. A number of theoretical and practical solution issues are discussed, as are prospects for further development.

Outline design and performance analysis of navigation constellation near earth-moon libration point

The outline design problem of navigation constellation near libration point is studied for deep space exploration. Firstly, the model of circular restricted three body problem near libration point is given, and the differential correction method is provided to calculate periodic orbits, of which the stability factor is also introduced. Secondly, the concept of effective coverage is defined, and the elements and the steps to design the constellation are proposed. Then, the outline design, performance analysis and evaluation of the navigation constellation are carried out concretely from aspects of orbits selection, space coverage, geometric dilution of precision factor, signal transmission and navigation precision. Compared with the case of global position system, the feasibility of the navigation constellation in libration point orbit is proved, and the performance index is provided. By analysis, the designed navigation constellation in L3-Vertical orbit with 5 satellites is able to provide navigation service for most of the spacecrafts in the space of between the earth and the moon, and the navigation precision is better than 10 m if the orbit determination errors of the constellation are not considered.

Detecting the Storm Movement by Sub Pixel Registration Approach of Newton Raphson Method

The change detection, storm detection and forecasting the weather condition consist of in the field of natural disaster management as the essential role. The detecting of the storm direction is provided to manage and to prevent the possible attacked region of the land. The sub pixel registration approach is applied for computing the movement of the interested cloud region. The direction of the storm can be tracked from these computations. Especially, the attacked region of Myanmar Land is forecasted from multi-date satellite image by using the digital image correlation based on the sub-pixel accuracy with Newton Raphson method. The proposed method is very effective because of its experiment and its result. Human can't be terminated the natural disaster. The weather prediction is very important for human daily life to prevent and reduce the attack of natural disaster. The storm direction detecting system is developed based on the sub-pixel accuracy with Newton Raphson method. The pixel correlation among the images is computed accurately by the Digital Image Correlation (DIC) for motion detection. The main application of DIC is in experimental mechanics. During the last two decades, various applications had been reported for two-dimensional measurement of displacement and strain field using the method of DIC. The most fundamental applications of two-dimensional DIC are found in fracture mechanics studies (1), (2), including measurement of strain field near crack-tips at high temperatures (3), strain measurement near stationary and growing crack-tips (4) and measurement of crack-tip opening displacement during crack growth (5), (6). H. A. Bruck et al. (1) proves that the computation of the digital image correlation using Newton Raphson method of partial differential correction. The integer pixel registration algorithm is used in their correlation computation. Moreover, DIC should serve as a valuable tool for biomedical research and the two-dimensional in-plane displacement and strain calculation problem and strain deformation (7)-(9). et al. (10) describes the performance of three different types of sub-pixel displacement registration algorithms in terms of the registration accuracy and the computational efficiency.

Design and analysis of an extended mission of CE-2: From lunar orbit to Sun–Earth L2 region

Chang’E-2 (CE-2) has firstly successfully achieved the exploring mission from lunar orbit to Sun–Earth L2 region. In this paper, we discuss the design problem of transfer trajectory and at the same time analyze the visible segment of Tracking, Telemetry & Control (TT&C) system for this mission. Firstly, the four-body problem of Sun–Earth–Moon and Spacecraft can be decoupled in two different three-body problems (Sun–Earth+Moon Restricted Three-Body Problems (RTBPs) and Earth–Moon ephemeris model). Then, the transfer trajectory segments in different model are computed, respectively, and patched by Poincaré sections. The full-flight trajectory including transfer trajectory from lunar orbit to Sun–Earth L2 region and target Lissajous orbit is obtained by the differential correction method. Finally, the visibility of TT&C system at the key time is analyzed. Actual execution of CE-2 extended mission shows that the trajectory design of CE-2 mission is feasible.

The equilibria and periodic orbits around a dumbbell-shaped body

This paper investigates the equilibria, their stability, and the periodic orbits in the vicinity of a rotating dumbbell-shaped body. First, the geometrical model of dumbbell-shaped body is established. The gravitational potential fields are obtained by the polyhedral method for several dumbbell-shaped bodies with various length–diameter ratios. Subsequently, the equilibrium points of these dumbbell-shaped bodies are computed and their stabilities are analyzed. Periodic orbits around equilibrium points are determined by the differential correction method. Finally, in order to understand further motion characteristic of dumbbell-shaped body, the effect of the rotating angular velocity of the dumbbell-shaped bodies is investigated. This study extends the research work of the orbital dynamics from simple shaped bodies to complex shaped bodies and the results can be applied to the dynamics of orbits around some asteroids.

A scheme for weak GPS signal acquisition aided by SINS information

In order to enhance the acquisition performance of global positioning system (GPS) receivers in weak signal conditions, a high-sensitivity acquisition scheme aided by strapdown inertial navigation system (SINS) information is proposed. The carrier Doppler shift and Doppler rate are pre-estimated with SINS aiding and GPS ephemeris, so that the frequency search space is reduced, and the dynamic effect on the acquisition sensitivity is mitigated effectively. Meanwhile, to eliminate the signal-to-noise ratio gain attenuation caused by data bit transitions, an optimal estimation of the unknown data bits is implemented with the Viterbi algorithm. A differential correction method is then utilized to improve the acquisition accuracy of Doppler shift and therefore to meet the requirement of carrier-tracking loop initialization. Finally, the reacquisition experiments of weak GPS signals are implemented in short signal blockage situations. The simulation results show that the proposed scheme can significantly improve the acquisition accuracy and sensitivity and shorten the reacquisition time.

Transfer Trajectory Design for Mars Exploration

With regard to the human exploration of Mars, low energy transfer trajectory is designed for Mars exploration based on the combination of invariant manifolds, differential correction and aerobraking methods. The whole transfer trajectory is composed of four stages: 1) from the Earth parking orbit to the Lyapunov orbit around Lagrange point L2 in the Sun-Earth system; 2) from the Lyapunov orbit around L2 to the Lyapunov orbit around L1 in the Sun-Mars system; 3) from the Lyapunov orbit around L1 in the Sun-Mars system to the large elliptical orbit around Mars; and 4) from the large elliptical orbit around Mars to the near-Mars parking orbit. In the first three stages, the circular restricted three-body problem is considered, and the trajectory is designed by using invariant manifolds and the differential correction method. The simulation results show that the transfer trajectory designed by means of the invariant manifolds of the Lyapunov orbit costs lower energy and shorter time of flight than that designed by means of the invariant manifold of the Halo orbit. In the fourth stage, the two-body problem is considered, and the aerobraking method is applied. A comparative performance analysis of static and rotating atmospheric models is carried out by using the details of duration, aerodynamic loading of the Mars vehicle, and other orbital parameters. It is shown that, on the low periareon where the influence of the atmospheric density increases, the changes of orbit parameters between rotating and static atmospheric environments are in large difference, such as orbital semimajor axis, orbital eccentricity, and so on. The influence of Martian rotating atmospheric environment should be considered.

Design of Earth—Moon Free-Return Trajectories

A new algorithm for designing free-return lunar flyby trajectories between the Earth and the moon is developed. The pseudostate theory is adopted to get the initial solution of the free-return trajectory. Using this initial solution, an improved differential-correction method is employed to find the final solution with a more complicated dynamic model. Compared with the original differential-correction method, the improved one can extend the convergence domain and have a fast convergence speed. A large number of numerical examples are carried out to test the reliability and efficiency of the algorithm, and also study the global features of free-return lunar flyby trajectories. The features are mainly affected by the geometric relationship between the Earth and the moon, the altitude of perilune, and the transfer time from perigee to perilune.

Orbits of the visual binaries ADS 8814 and ADS 8065 from observations along a short arc

The orbits of the visual binaries ADS 8814 and ADS 8065 are determined for the first time. The orbits were calculated using the parameters of the apparent motion, based on position observations along short arcs obtained on the 26-inch refrector of the Pulkovo Observatory, supplemented with radial-velocity observations for the stellar components in both pairs obtained on the 1-m telescope of the Simeiz Section of the Crimean Astrophysical Observatory. All previous visual and photographic observations of these stars after 1832 were also taken into account. The orbit of ADS 8814 was refined using the differential-correction method. The orbital periods of these two stars are about 800 and 6000 years, respectively. The mass estimates derived for the known parallaxes from the Hipparcos catalog correspond to the spectral types of these stars. The polar vectors of the obtained orbits in Galactic coordinates are also given.

Comparison Between Fast Steady-State Analysis Methods for Time-Periodic Nonlinear Magnetic Field Problems

This paper investigates the effectiveness of various methods to accelerate the convergence to a steady state in time-periodic electromagnetic field problems. We first introduce the time-periodic explicit error correction (TP-EEC) method taking account of both the dc and linearly-varying error components and propose the harmonics TP-EEC method which enables us to achieve the increase in error correction frequency. Then, we discuss the convergence property of the TP-EEC methods based on the error analysis. The advantages and disadvantages of the TP-EEC method and the time differential correction (TDC) method are investigated from the viewpoints of computational costs and application scope.

Lunar Soft-landing Trajectory Design Based on Evolutionary Strategy

应用进化策略和微分修正法建立了一套多约束、多目标条件下的月球软着陆轨道设计方法. 根据中国发射场和火箭运载的实际情况, 给出了软着陆轨道需要满足的过程约束及终端条件, 提出了利用进化策略进行轨道初步设计,通过微分修正法对初步设计结果进行修正的软着陆轨道设计思路, 并采用STK进行了仿真和结果验算. 分析表明, 基于进化策略的初步设计能够为微分修正提供良好的初值, 保证了其收敛性. STK仿真结果验证了设计思路的有效性及结果的正确性. 本文提出的方法能够为月球软着陆轨道设计提供参考.

Consistent multi-time-point brain atrophy estimation from the boundary shift integral

Brain atrophy measurement is increasingly important in studies of neurodegenerative diseases such as Alzheimer's disease (AD), with particular relevance to trials of potential disease-modifying drugs. Automated registration-based methods such as the boundary shift integral (BSI) have been developed to provide more precise measures of change from a pair of serial MR scans. However, when a method treats one image of the pair (typically the baseline) as the reference to which the other is compared, this systematic asymmetry risks introducing bias into the measurement. Recent concern about potential biases in longitudinal studies has led to several suggestions to use symmetric image registration, though some of these methods are limited to two time-points per subject. Therapeutic trials and natural history studies increasingly involve several serial scans, it would therefore be useful to have a method that can consistently estimate brain atrophy over multiple time-points. Here, we use the log-Euclidean concept of a within-subject average to develop affine registration and differential bias correction methods suitable for any number of time-points, yielding a longitudinally consistent multi-time-point BSI technique. Baseline, 12-month and 24-month MR scans of healthy controls, subjects with mild cognitive impairment and AD patients from the Alzheimer's Disease Neuroimaging Initiative are used for testing the bias in processing scans with different amounts of atrophy. Four tests are used to assess bias in brain volume loss from BSI: (a) inverse consistency with respect to ordering of pairs of scans 12 months apart; (b) transitivity consistency over three time-points; (c) randomly ordered back-to-back scans, expected to show no consistent change over subjects; and (d) linear regression of the atrophy rates calculated from the baseline and 12-month scans and the baseline and 24-month scans, where any additive bias should be indicated by a non-zero intercept. Results indicate that the traditional BSI processing pipeline does not exhibit significant bias due to its use of windowed sinc interpolation, but with linear interpolation and asymmetric registration, bias can be pronounced. Either improved interpolation or symmetric registration alone can greatly reduce this bias, and our proposed method combining both aspects shows no significant bias in any of the four experiments.

Equilibria, periodic orbits around equilibria, and heteroclinic connections in the gravity field of a rotating homogeneous cube

This paper investigates the dynamics of a particle orbiting around a rotating homogeneous cube, and shows fruitful results that have implications for examining the dynamics of orbits around non-spherical celestial bodies. This study can be considered as an extension of previous research work on the dynamics of orbits around simple shaped bodies, including a straight segment, a circular ring, an annulus disk, and simple planar plates with backgrounds in celestial mechanics. In the synodic reference frame, the model of a rotating cube is established, the equilibria are calculated, and their linear stabilities are determined. Periodic orbits around the equilibria are computed using the traditional differential correction method, and their stabilities are determined by the eigenvalues of the monodromy matrix. The existence of homoclinic and heteroclinic orbits connecting periodic orbits around the equilibria is examined and proved numerically in order to understand the global orbit structure of the system. This study contributes to the investigation of irregular shaped celestial bodies that can be divided into a set of cubes.