Iterative Initial Value Research Articles

A Geometric Strategy Algorithm for Orthogonal Projection onto a Parametric Surface

In this paper, we investigate how to compute the minimum distance between a point and a parametric surface, and then to return the nearest point (foot point) on the surface as well as its corresponding parameter, which is also called the point projection problem of a parametric surface. The geometric strategy algorithm (hereafter GSA) presented consists of two parts as follows. The normal curvature to a given parametric surface is used to find the corresponding foot point firstly, and then the Taylor’s expansion of the parametric surface is employed to compute parameter increments and to get the iteration formula to calculate the orthogonal projection point of test point to the parametric surface. Our geometric strategy algorithm is essentially dependent on the geometric property of the normal curvature, and performs better than existing methods in two ways. Firstly, GSA converges faster than existing methods, such as the method to turn the problem into a root-finding of nonlinear system, subdividing methods, clipping methods, geometric methods (tangent vector and geometric curvature) and hybrid second-order method, etc. Specially, it converges faster than the classical Newton’s iterative method. Secondly, GSA is independent of the initial iterative value, which we prove in Theorem 1. Many numerical examples confirm GSA’s robustness and efficiency.

A Perturbation Method to Optimize the Parameters of Autoregressive Conditional Heteroscedasticity Model

As a linear regression parameter estimation method, the least square method plays an indispensable role in the parameter estimation of ARCH model. Although the least squares solution can minimize the sum of the squared errors, it will cause uneven distribution of errors, that is, some fitting errors are too large, and some fitting errors are too small, which will lead to overfitting. In response to this situation, we adopt a novel perturbation method to solve this problem. The specific theoretical derivation of the perturbation method is given in this paper. It takes parameters estimated by the least squares method as its initial iteration value. The maximum fitting error will decrease continuously from a series of iterations to final convergence. Furthermore, based on the perturbation method, this paper finds a condition that makes the ARCH model satisfy the non-negative limit of parameters. The experimental process uses real stock fund’s fluctuation data for fitting analysis and prediction. The experimental results show that the perturbation method can achieve the expected effect in the parameter estimation of the ARCH model, it can also effectively ensure that the fitting errors fluctuate within the controllable range when predicting the price fluctuation of stock funds in the future.

Forest Height Estimation Using PolInSAR Optimal Normal Matrix Constraint and Cross-Iteration Method

A novel method based on the optimal normal matrix constraint and cross-iteration algorithm is proposed in this letter to estimate the forest height using the polarimetric interferometry synthetic aperture radar (PolInSAR) data. First, to avoid the null ground-to-volume ratio assumption of the three-stage method, we use the PolInSAR optimal normal matrix constraint method to find out the pure volume coherence. This method can also provide a more accurate initial value for the least-squares iteration. Second, the cross-iteration is used for the forest height inversion, which provides better selection of the best polarization channel and solves the ill-conditioned matrix in the traditional least-squares iteration algorithm. This new method is validated using the BioSAR 2008 P-band data. The results show that the proposed method achieves an average accuracy of 2.6 m, which is better than that of the three-stage inversion method [root-mean-square error (RMSE) = 5.89 m] and the 6-D nonlinear iteration method (RMSE = 4.42 m).

Improved direct fitting algorithm for elliptic parameters

For the ellipse fitting problem often encounter in visual measurement, this paper proposes a method combining algebraic distance fitting method based on least squares and characteristic root method for ellipse fitting. Firstly, the improved hierarchical agglomerative clustering is used to denoise the data. Then the algebraic distance fitting method based on least squares is used to calculate the initial iteration value of the parameters in the characteristic root method. Finally, the Gauss-Newton iteration method is used to solve the elliptic parameters. This algorithm is used to detect the out-of-roundness of the optical fiber and compare the test results with the high-precision optical fiber tester FGM-502. The results prove the validity and accuracy of the ellipse fitting algorithm studied in this paper and show that the algorithm studied in this paper meets the requirements of actual ellipse fitting measurement.

The flow-difference feedback iteration method for aerostatic thrust bearings and its convergence characteristics

The flow-difference feedback iteration method for aerostatic thrust bearings is proposed to the flow balance-based iteration, and two modification methods are further provided to improve the adaptability. The bearing capability calculated by the proposed method is validated by the experimental data. Moreover, the influence of convergence rate factors, iterative initial values, and mesh grids on the iteration ratio is investigated. Compared with the conventional iteration methods, the proposed method with appropriate convergence rate factors provides a higher convergence efficiency. In addition, good convergence behavior under different iterative initial values and the mesh grid size is shown, and the convergence rate is insensitive to the finite difference method parameters. A series of calculations are conducted to investigate the generality of the proposed methods.

Multi station TDOA location method based on improved artificial bee colony algorithm

In modern battlefield, passive location technology based on multi-station TDOA of UAV platforms has important application value, but the traditional Newton iteration algorithm requires higher initial value of iteration, and the positioning accuracy needs to be improved. We have found a new algorithm in our research, which is based on ABC algorithm, and is also a method used in UAV positioning system. Comparing with the traditional algorithm, simulation results of this algorithm indicate that it can remarkably improve the precision of TDOA passive location.

Robust Time-Varying Parameter Identification for Composite Load Modeling

With the increasing integration of uncertain resources, e.g., renewables, electric vehicles, and demand responses, it is imperative to understand the characteristics of loads for power system analysis and control. Challenges of load modeling come from a variety of load components and time-varying compositions. In addition, the existence of outliers in measurements further complicates the problem. This paper proposes a robust time-varying parameter identification technique for composite ZIP and induction motor load models. A batch-model regression form, including time-varying parameters, is established based on state transition models and observation models with current observations and previous predictions to guarantee data redundancy. To deal with outliers, down-weighting coefficients of measurements are calculated with a projection statistics approach. Based on the batch-model regression and the down-weighting coefficients, parameter identification at each sample time is formulated as a weighted least squares optimization, which is solved by the Newton-Raphson approach with the previous estimated parameters as the initial iteration values. In addition, parameters’ sensitivities to different outliers in measurements are analyzed. Results on the IEEE 57-bus system and IEEE 118-bus system show that the proposed algorithm can robustly identify time-varying parameters for the composite load models.

A Real-Time Feedrate Planning Method and Efficient Interpolator With Minimal Feedrate Fluctuation for Parametric Toolpath

Different from linear and circular interpolation, feedrate fluctuation is inevitable for parametric toolpath, which is caused by the nonlinear relation between spline parameters and arc-length. In order to improve the accuracy and efficiency of real-time interpolation algorithm with minimal feedrate fluctuation, this thesis presents an iterative feedback interpolator to restrain the feedrate fluctuation. Estimator and corrector stage are two essential steps of our proposed method. The result of the first-order Taylor expansion is used for the iterative initial value in the estimator stage. Thereafter, based on Steffensen iterative accelerator method, the feedback of current feedrate and command feedrate will control to update parameters value repeatedly until feedrate fluctuation rate reaches the allowable value in the corrector stage. By means of the numerical method, it is proved that this iteration method can satisfy the high-order convergence and fast convergence theoretically. In the simulation, the third-degree B-spline curve is utilized to test the proposed method which is equipped with obvious effects on restraining the feedrate fluctuation and improving computation efficiency compared with four existing methods.

Fast algorithm based on TT-M FE system for space fractional Allen–Cahn equations with smooth and non-smooth solutions

In this article, a fast algorithm based on time two-mesh (TT-M) finite element (FE) scheme, which aims at solving nonlinear problems quickly, is considered to numerically solve the nonlinear space fractional Allen–Cahn equations with smooth and non-smooth solutions. The implicit second-order θ scheme containing both implicit Crank–Nicolson scheme and second-order backward difference method is applied to time direction, a fast TT-M method is used to increase the speed of calculation, and the FE method is developed to approximate the spacial direction. The TT-M FE algorithm includes the following main computing steps: firstly, a nonlinear implicit second-order θ FE scheme on the time coarse mesh τc is solved by a nonlinear iterative method; secondly, based on the chosen initial iterative value, a linearized FE system on time fine mesh τ<τc is solved, where some useful coarse numerical solutions are found by the Lagrange's interpolation formula. The analysis for both stability and a priori error estimates are made in detail. Finally, three numerical examples with smooth and non-smooth solutions are provided to illustrate the computational efficiency in solving nonlinear partial differential equations, from which it is easy to find that the computing time can be saved.

An improved fitting method for subgroup parameters based on the heterogeneous cells

ABSTRACT An accurate subgroup parameters fitting method, where background cross sections obtained based on heterogeneous cells are used to fit the subgroup level and subgroup weight, is proposed in this paper. Due to the dependence of background cross section on the subgroup level, the calculation of the subgroup parameters is a nonlinear problem, which causes the iteration between fitting subgroup parameters and updating background cross sections. The cubic spline interpolation method is used to update the background cross sections to avoid frequently solving fixed source equations. In the fitting process, the negative subgroup parameters are often obtained, and the accuracy of the subgroup parameters is very sensitive to the iterative initial values of subgroup levels. To avoid these problems, additional constraints ensuring positive subgroup parameters and guaranteeing numerical stability are added to the optimization function. Penalty function method is used to convert the optimization problem with constraints into the one without constraints, making the problem easy to be solved. The proposed method is tested against the problems of pin cell, pressurized water reactor assemblies and plate-type assembly. The numerical results show that the self-shielded cross sections calculated by the proposed method agree well with those by Monte Carlo code.

Shape reconstruction of large optical surface with high-order terms in fringe reflection technique

A fast and effective shape reconstruction method of large aspheric specular surfaces with high order terms is proposed in fringe reflection technique, which combines modal estimation with high-order finitedifference algorithm. The iterative equation with highorder truncation errors is derived for calculating the specular surface with large aperture based on high-order finite-difference algorithm. To achieve the wavefront estimation and improve convergence speed, the numerical orthogonal transformation method based on Zernike polynomials is implemented to obtain the initial iteration value. The reconstruction results of simulated surface identified the advantages of the proposed method. Furthermore, a freeform in illuminating system has been used to demonstrate the validity of the improved method in practical measurement. The results show that the proposed method has the advantages of making the reconstruction of different shape apertures accurate and rapid. In general, this method performs well in measuring large complex objects with high frequency information in practical measurement.

An orthogonal iteration pose estimation algorithm based on an incident ray tracking model

Although the pinhole imaging model prevails among current pose estimation algorithms, this idealized model gradually shows its limitation and inaccuracy, especially in harsh environments. In recent years, a few generic imaging models have been proposed to replace the dominant pinhole one. Among them, the camera model, named the incident ray tracking model, has proved to be superior. This model consists of mappings between pixels on the image and straight lines in 3D space. Based on the incident ray tracking camera model, a pose estimation algorithm, which can be called the perspective-ray-based orthogonal iteration (PROI), is proposed in this paper. The proposed algorithm introduces the popular orthogonal iteration algorithm into the incident ray tracking model. In this method, the object space collinearity error is expressed by a more accurate perspective ray instead of the traditional line of sight. The orthogonal rotation matrices are computed by an iterative algorithm and the iterative initial value is given in a weak perspective model. Experiment results on the pose estimation with better accuracy and efficiency by PROI have shown the superiority of the proposed method compared with the best currently employed optimization algorithms.

Forward Kinematics Analysis of a Novel 3-DOF Parallel Manipulator

A novel spatial parallel manipulator designed to assemble diagnostic instruments in SG-III is introduced in this paper. Firstly, resorting to screw theory, mobility analysis of this manipulator is investigated. Then the inverse kinematics problem is determined by the method of RPY transformation, with the singularity analyzed. As a key issue in parallel manipulators, it is more difficult to solve the forward kinematics problem, since it is highly nonlinear and coupled. In this work, three different approaches are presented to deal with this issue, which include the back propagation neural network, the simplified ant colony optimization and the proposed improved Newton iterative method. Simulation of each approach is conducted, and their merits and demerits are compared in detail. It is concluded that the improved Newton iterative method which can provide good initial iteration values possesses the best performance to estimate the nonlinear forward kinematic mapping of the considered parallel manipulator

A compensation method for the carrier interference of a three-component magnetic measurement system using a Cuckoo search algorithm

The magnetic interference field generated by ferromagnetic materials on the carrier decreases measurement precision, which has been a crucial factor limiting the application of three-component magnetic measurement. In this paper, a magnetic compensation method based on the Cuckoo search (CS) algorithm is proposed. The method can be separated into three steps. First, a measurement error model is established, based on which a formula of the absolute error sum will be derived. Then, compensation parameters are estimated using the CS algorithm by minimizing the absolute error sum. Finally, the geomagnetic intensity is calculated using estimates of the compensation parameters and measured data. As the CS algorithm possesses the advantages of insensitivity to iterative initial values and strong global search ability, optimal estimates of the compensation parameters can be obtained accurately using this method, which ensures high compensation precision. The experimental results show that, after compensation, the maximum error of the x-component can be reduced from 622 nT to 26 nT, the y-component from 329 nT to 19 nT, and the z-component from 669 nT to 15nT.

Prediction Techniques for Accelerating the Convergence of Alternating Solution Method during the Power System Dynamic Simulation Using SDC Integration Algorithm

The electric power of generator Pe and bus voltage of network V have a strong nonlinear coupling relationship with other variables, which results in bad effects on the convergence procedure for the alternating solution method during the power system dynamic simulation using the SDC integration algorithm. Deep research was conducted into this problem. The convergence procedure for Pe and V was illustrated during the simulation, and prediction techniques by applying the Lagrange interpolation to construct a better iterative initial value with smaller error for them was proposed. Based on the SDC simulation method, the proposed method was tested on an IEEE standard 3-generator 9-bus system on the platform of MATLAB, and results show that the prediction techniques performs quite well for the acceleration of convergence procedure Pe for V and and simulation efficiency of SDC integration algorithm.

Holographic near-eye display system based on double-convergence light Gerchberg-Saxton algorithm.

In this paper, a method is proposed to implement noises reduced three-dimensional (3D) holographic near-eye display by phase-only computer-generated hologram (CGH). The CGH is calculated from a double-convergence light Gerchberg-Saxton (GS) algorithm, in which the phases of two virtual convergence lights are introduced into GS algorithm simultaneously. The first phase of convergence light is a replacement of random phase as the iterative initial value and the second phase of convergence light will modulate the phase distribution calculated by GS algorithm. Both simulations and experiments are carried out to verify the feasibility of the proposed method. The results indicate that this method can effectively reduce the noises in the reconstruction. Field of view (FOV) of the reconstructed image reaches 40 degrees and experimental light path in the 4-f system is shortened. As for 3D experiments, the results demonstrate that the proposed algorithm can present 3D images with 180cm zooming range and continuous depth cues. This method may provide a promising solution in future 3D augmented reality (AR) realization.

A 2D phase zero algorithm for estimation of displacement in ultrasound elastography based on the optimization of initial value for iteration

ABSTRACTUltrasound elastography (UE) is an imaging technique based on tissues’ elasticity. UE based on gradient typically assumes that movement only occurs along the propagation direction of an ultrasound beam. However, when the target tissue is compressed by a transducer, lateral displacement of the scattering body occurs due to uniform hardness within the tissue. Before and after compression, the signal cross-correlations within a specific window along the scan lines may be very low. This is highly likely to result in large errors or even failed calculation of cross-correlated phase angles within this window. We proposed a modified 2D phase zero algorithm for the estimation of displacement. In this method, the initial value with threshold for iteration was optimized in order to decrease the errors result from lateral motion. Then, to verify the effectiveness of this algorithm, a contrast experiment on this new and conventional method was designed. The experiment indicated that this algorithm could effectively prevent failed calculation of elasticity due to lateral displacement of the scattering body. It could stably and efficiently reduce the errors in displacement estimation and enable a more accurate imaging of the target hard mass, like signal to noise of elastography () and contrast to noise of elastography ().

Time two-mesh algorithm combined with finite element method for time fractional water wave model

In this article, a new time two-mesh (TT-M) finite element (FE) method, which is constructed by a new TT-M algorithm and FE method in space, is proposed and analyzed. The numerical theories and algorithm are shown by solving the fractional water wave model including fractional derivative in time. The TT-M FE algorithm mainly covers three steps: firstly, a nonlinear FE system at some time points based on the time coarse mesh ΔtC is solved by an iterative method; further, based on the obtained numerical solution on time coarse mesh ΔtC in the first step, some useful numerical solutions between two time coarse mesh points are arrived at by the Lagrange’s interpolation formula; finally, the solutions on the first and second steps are chosen as the initial iteration value, then a linear FE system on time fine mesh ΔtF<ΔtC is solved. Some stable results and a priori error estimates are analyzed in detail. Furthermore, some numerical results are provided to verify the effectiveness of TT-M FE method. By the comparison with the standard FE method, it is easy to see that the CPU time can be saved by our TT-M FE method.

Iterative denoising of ghost imaging based on adaptive threshold method

Ghost imaging (GI) is an important technique in the fields of quantum imaging and classical optical imaging, and it can solve the problems which are difficult to solve by the traditional imaging techniques in the optically harsh environments. In this paper, we present the iterative denoising of GI based on an adaptive threshold method. This method is abbreviated as IDGI-AT, which takes the advantages of adaptive threshold, differential, binarization and iterative operation method, and can enhance image quality in GI. In addition, this method can reduce the number of measurements. As is well known, the enormous number of measurements and poor reconstruction quality are obstacles to the engineering application of GI. The correlation noise leads to low signal-to-noise ratio and low imaging efficiency in GI as well. Therefore, we establish a denoising model, which can reduce correlation noise and improve reconstruction quality. We first analyze the iterative denoising of ghost imaging (IDGI) theory, and use the adaptive threshold technique to calculate the ideal threshold associated with the correlation noise. It should be noted that the threshold can be obtained by this method under the condition without requiring prior knowledge of the object. Afterwards, we can construct the correlation noise in this denoising model. In the IDGI, the differential ghost imaging (DGI) image is taken as the initial iteration value. We use the adaptive threshold method, which is different from IDGI, to binarize the initial value of each iteration to make it closer to the original object's transmission coefficient. After three iterations, we can obtain a higher-quality reconstruction image. In order to demonstrate that the IDGI-AT is available, a GI experimental system with a pseudo-thermal light source is set up. The considerable simulation and experimental results show the advantage of our scheme in terms of removing reconstruction image background noise. Especially, the visual effects and peak signal-to-noise ratio values are improved in comparison with those from the traditional GI, DGI and IDGI. Besides, we demonstrate the role of binarization in our scheme. For a binary object, the iterative value binarization can achieve better image quality than that in the case without binarizing the iterative initial value. Therefore, this novel method is likely to provide an alternative mean for GI and further pave the way for the application fields of GI, such as lidar, biomedical engineering, etc.

New algorithms for motion error detection of numerical control machine tool by laser tracking measurement on the basis of GPS principle

As a three-dimensional measuring instrument, the laser tracker is widely used in industrial measurement. To avoid the influence of angle measurement error on the overall measurement accuracy, the multi-station and time-sharing measurement with a laser tracker is introduced on the basis of the global positioning system (GPS) principle in this paper. For the proposed method, how to accurately determine the coordinates of each measuring point by using a large amount of measured data is a critical issue. Taking detecting motion error of a numerical control machine tool, for example, the corresponding measurement algorithms are investigated thoroughly. By establishing the mathematical model of detecting motion error of a machine tool with this method, the analytical algorithm concerning on base station calibration and measuring point determination is deduced without selecting the initial iterative value in calculation. However, when the motion area of the machine tool is in a 2D plane, the coefficient matrix of base station calibration is singular, which generates a distortion result. In order to overcome the limitation of the original algorithm, an improved analytical algorithm is also derived. Meanwhile, the calibration accuracy of the base station with the improved algorithm is compared with that with the original analytical algorithm and some iterative algorithms, such as the Gauss-Newton algorithm and Levenberg-Marquardt algorithm. The experiment further verifies the feasibility and effectiveness of the improved algorithm. In addition, the different motion areas of the machine tool have certain influence on the calibration accuracy of the base station, and the corresponding influence of measurement error on the calibration result of the base station depending on the condition number of coefficient matrix are analyzed.