Accurate calibration with highly distorted images

Camera calibration is a two-step process where first a linear algebraic approximation is followed by a nonlinear minimization. The nonlinear minimization adjusts the pin-hole and lens distortion models to the calibrating data. Since both models are coupled, nonlinear minimization can converge to a local solution easily. Moreover, nonlinear minimization is poorly conditioned since parameters with different effects in the minimization function are calculated simultaneously (some are in pixels, some in world coordinates, and some are lens distortion parameters). A local solution is adapted to parameters, which minimize the function easily, and the remaining parameters are just adapted to this solution. We propose a calibration method where traditional calibration steps are inverted. First, a nonlinear minimization is done, and after, camera parameters are computed in a linear step. Using projective geometry constraints in a nonlinear minimization process, detected point locations in the images are corrected. The pin-hole and lens distortion models are computed separately with corrected point locations. The proposed method avoids the coupling between both models. Also, the condition of nonlinear minimization increases since points coordinates are computed alone.     

Hierarchical subspace evolution method for super large parallel computing: A linear solver and an eigensolver as examples

Solving linear equations and finding eigenvalues are essential tasks in many simulations for engineering applications, but these tasks often cause performance bottlenecks. In this work, the hierarchical subspace evolution method (HiSEM), a hierarchical iteration framework for solving scientific computing problems with solution locality, is proposed. In HiSEM, the original problem is converted to a corresponding minimization function. The problem is decomposed into a series of subsystems. Subspaces and their weights are established for the subsystems and evolve in each iteration. The subspaces are calculated based on local equations and knowledge of physical problems. A small-scale minimization problem determines the weights of the subspaces. The solution system can be hierarchically established based on the subspaces. As the iterations continue, the degrees of freedom gradually converge to an accurate solution. Two parallel algorithms are derived from HiSEM. One algorithm is designed for symmetric positive definite linear equations, and the other is designed for generalized eigenvalue problems. The linear solver and eigensolver performance is evaluated using a series of benchmarks and a tower model with a complex topology. Algorithms derived from HiSEM can solve a super large-scale problem with high performance and good scalability.     

Implicit boundary method for analysis using uniform B‐spline basis and structured grid

Several analysis techniques such as extended finite element method (X‐FEM) have been developed recently, which use structured grid for the analysis. Implicit boundary method uses implicit equations of the boundary to apply boundary conditions in X‐FEM framework using structured grids. Solution structures for test and trial functions are constructed using implicit equations such that the boundary conditions are satisfied even if there are no nodes on the boundary. In this paper, this method is applied for analysis using uniform B‐spline basis defined over a structured grid. Solution structures that are C¹ or C² continuous throughout the analysis domain can be constructed using B‐spline basis functions. As a structured grid does not conform to the geometry of the analysis domain, the boundaries of the analysis domain are defined independently using equations of the boundary curves/surfaces. Compared with conforming mesh, it is easier to generate structured grids that overlap the geometry and the elements in the grid are regular shaped and undistorted. Numerical examples are presented to demonstrate the performance of these B‐spline elements. The results are compared with analytical solutions as well as with traditional finite element solutions. Convergence studies for several examples show that B‐spline elements provide accurate solutions with fewer elements and nodes compared with traditional FEM. They also provide continuous stress and strain in the analysis domain, thus eliminating the need for smoothing stress/strain results. Copyright © 2008 John Wiley & Sons, Ltd.     

基于C-B样条的三角形和四边形曲面生成

文章给出了基于C-B样条的由网格数据产生三角形和四边形曲面片的方法,C-B样条是由基底函数{sin t,cos t,t,1}导出的一种新型样条曲线,它可以克服现在正在使用的B样条和有理B样条为了满足数据网格的拓扑结构而增加多余的控制点,求导求积分复杂繁琐,阶数过高,从而讨论其连续拼接时增加了困难等缺点,如何将它推广成曲面就成为一个重要问题。作者利用边-顶点方法构造插值算子,再将这些算子进行凸性组合,将C-B样条曲线推广成三角形曲面片和四边形曲面片,它可以用于CAD的逆向工程中散乱数据的曲面重构。     

Illumination estimation via thin-plate spline interpolation

Thin-plate spline interpolation is used to interpolate the chromaticity of the color of the incident scene illumination across a training set of images. Given the image of a scene under unknown illumination, the chromaticity of the scene illumination can be found from the interpolated function. The resulting illumination-estimation method can be used to provide color constancy under changing illumination conditions and automatic white balancing for digital cameras. A thin-plate spline interpolates over a nonuniformly sampled input space, which in this case is a training set of image thumbnails and associated illumination chromaticities. To reduce the size of the training set, incremental k medians are applied. Tests on real images demonstrate that the thin-plate spline method can estimate the color of the incident illumination quite accurately, and the proposed training set pruning significantly decreases the computation.     

A Generalized Goal Programming Approach to the Minimal Interference, Multicriteria N × 1 Scheduling Problem

The conventional approach to the modeling and solution of most scheduling problems involves the development of a mathematical model which (1) employs discrete variables (e.g., linear integer programs), and (2) includes only a single objective to be maximized or minimized (e.g., minimization of makespan). Unfortunately, models involving discrete variables are inherently combinatorially explosive (i.e., methods such as branch-and-bound will exhibit computation times which grow exponentially with problem size). Further, scheduling problems encountered in the real world invariably involve multiple conflicting objectives, and thus using a single-objective representation can lead to gross oversimplification. In this paper we address a specific class of scheduling problem encountered in several real-world applications that may be efficiently addressed as a linear multiobjective model having only continuous variables. The model and its solution are compared with those of a highly acclaimed recent approach, and they appear to provide significant improvements.     

Transported snapshot model order reduction approach for parametric,steady-state fluid flows containing parameter-dependent shocks

A new model order reduction approach is proposed for parametric steady-state nonlinear fluid flows characterized by shocks and discontinuities whose spatial locations and orientations are strongly parameter dependent. In this method, solutions in the predictive regime are approximated using a linear superposition of parameter-dependent basis. The sought-after parametric reduced bases are obtained by transporting the snapshots in a spatially and parametrically dependent transport field. Key to the proposed approach is the observation that the transport fields are typically smooth and continuous, despite the solution themselves not being so. As a result, the transport fields can be accurately expressed using a low-order polynomial expansion. Similar to traditional projection-based model order reduction approaches, the proposed method is formulated mathematically as a residual minimization problem for the generalized coordinates. The proposed approach is also integrated with well-known hyper-reduction strategies to obtain significant computational speedups. The method is successfully applied to the reduction of a parametric one-dimensional flow in a converging-diverging nozzle, a parametric two-dimensional supersonic flow over a forward-facing step, and a parametric two-dimensional jet diffusion flame in a combustor.     

A genetic algorithm with memory for optimal design of laminated sandwich composite panels

This paper is concerned with augmenting genetic algorithms (GAs) to include memory for continuous variables, and applying this to stacking sequence design of laminated sandwich composite panels that involves both discrete variables and a continuous design variable. The term “memory” implies preserving data from previously analyzed designs. A balanced binary tree with nodes corresponding to discrete designs renders efficient access to the memory. For those discrete designs that occur frequently, an evolving database of continuous variable values is used to construct a spline approximation to the fitness as a function of the single continuous variable. The approximation is then used to decide when to retrieve the fitness function value from the spline and when to do an exact analysis to add a new data point for the spline. With the spline approximation in place, it is also possible to use the best solution of the approximation as a local improvement during the optimization process. The demonstration problem chosen is the stacking sequence optimization of a sandwich plate with composite face sheets for weight minimization subject to strength and buckling constraints. Comparisons are made between the cases with and without the binary tree and spline interpolation added to a standard GA. Reduced computational cost and increased performance index of a GA with these changes are demonstrated.     

Mechanically based models: Adaptive refinement for B‐spline finite element

This article presents two new methods for adaptive refinement of a B‐spline finite element solution within an integrated mechanically based computer aided engineering system. The proposed techniques for adaptively refining a B‐spline finite element solution are a local variant of np‐refinement and a local variant of h‐refinement. The key component in the np‐refinement is the linear co‐ordinate transformation introduced into the refined element. The transformation is constructed in such a way that the transformed nodal configuration of the refined element is identical to the nodal configuration of the neighbour elements. Therefore, the assembly proceeds as with classic finite elements, while the solution approximation conforms exactly along the inter‐element boundaries. For the h‐refinement, this transformation is introduced into a construction that merges the super element from the finite element world with the hierarchical B‐spline representation from the computational geometry. In the scope of developing sculptured surfaces, the proposed approach supports C⁰ as well as the Hermite B‐spline C¹ continuous shapes. For sculptured solids, C⁰ continuity only is considered in this article. The feasibility of the proposed methods in the scope of the geometric design is demonstrated by several examples of creating sculptured surfaces and volumetric solids. Numerical performance of the methods is demonstrated for a test case of the two‐dimensional Poisson equation. Copyright © 2003 John Wiley & Sons, Ltd.     

Explicit and implicit meshless methods for linear advection–diffusion‐type partial differential equations

Simple, mesh/grid free, explicit and implicit numerical schemes for the solution of linear advection–diffusion problems is developed and validated herein. Unlike the mesh or grid‐based methods, these schemes use well distributed quasi‐random points and approximate the solution using global radial basis functions. The schemes can be seen as generalized finite differences with random points instead of a regular grid system. This allows the computation of problems with complex‐shaped boundaries in higher dimensions with no need for complex mesh/grid structure and with no extra implementation difficulties. Copyright © 2000 John Wiley & Sons, Ltd.     

Linear and nonlinear solvers for variational phase‐field models of brittle fracture

The variational approach to fracture is effective for simulating the nucleation and propagation of complex crack patterns but is computationally demanding. The model is a strongly nonlinear non‐convex variational inequality that demands the resolution of small length scales. The current standard algorithm for its solution, alternate minimization, is robust but converges slowly and demands the solution of large, ill‐conditioned linear subproblems. In this paper, we propose several advances in the numerical solution of this model that improve its computational efficiency. We reformulate alternate minimization as a nonlinear Gauss–Seidel iteration and employ over‐relaxation to accelerate its convergence; we compose this accelerated alternate minimization with Newton's method, to further reduce the time to solution, and we formulate efficient preconditioners for the solution of the linear subproblems arising in both alternate minimization and in Newton's method. We investigate the improvements in efficiency on several examples from the literature; the new solver is five to six times faster on a majority of the test cases considered. © 2016 The Authors International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd.     

Heuristics for integrated job assignment and scheduling in the multi-plant remanufacturing system

We consider a multi-plant remanufacturing system where decisions have to be made on the choice of plant to perform the remanufacturing and the remanufacturing options. Each plant is in different geographical locations and differs in technological capability, labour cost, distance from customers, taxes and duties. There are three options of remanufacture: replacement, repair and recondition. Furthermore, the probability that each remanufacture job needs to be reworked depends on the remanufacturing option selected. We show the interdependencies among the plant selection, remanufacturing option and job scheduling when subject to resource constraints, which motivate the integrated solution proposed in this paper. The solution method is composed of the linear physical programming and the multi-level encoding genetic algorithm (GA). By performing a case study, we illustrate the use of the model and we present the resulting managerial insights. The results show that the proposed integrated approach performs better compared with the regular GA in terms of makespan.     

微平面模型取向与权重的改进计算方法

在介绍微平面模型中数值离散算法的基础上,指出了现有文献中对微平面取向及权重的确定方法的特点和不足。针对微平面取向不够均匀以及微平面形状和物理意义不明确的问题,提出了一种基于正多面体表面网格划分后向球面进行投影的方法计算微平面取向,再利用球面几何的知识计算微平面权重的方法。在比选基于不同微平面划分方案时,提出了拟合宏观弹性刚度矩阵的优化目标。计算结果表明,该文所提方法可以得到微平面形状、大小完全均匀的划分方案,计算精度比文献中的最优方案更精确。     

A Robust Asynchrophasor in PMU Using Second-Order Kalman Filter

Phasor Measurement Units (PMUs) provide Global Positioning System (GPS) time-stamped synchronized measurements of voltage and current with the phase angle of the system at certain points along with the grid system. Those synchronized data measurements are extracted in the form of amplitude and phase from various locations of the power grid to monitor and control the power system condition. A PMU device is a crucial part of the power equipment in terms of the cost and operative point of view. However, such ongoing development and improvement to PMUs’ principal work are essential to the network operators to enhance the grid quality and the operating expenses. This paper introduces a proposed method that led to low-cost and less complex techniques to optimize the performance of PMU using Second-Order Kalman Filter. It is based on the Asyncrhophasor technique resulting in a phase error minimization when receiving the signal from an access point or from the main access point. The MATLAB model has been created to implement the proposed method in the presence of Gaussian and non-Gaussian. The results have shown the proposed method which is Second-Order Kalman Filter outperforms the existing model. The results were tested using Mean Square Error (MSE). The proposed Second-Order Kalman Filter method has been replaced with a synchronization unit into the PMU structure to clarify the significance of the proposed new PMU.     

Self-consistent way to determine relative distortion of axial symmetric lens systems

We present a simple method to determine the relative distortion of axially symmetric lens systems. This method uses graphs to determine every parametric value instead of nonlinear minimization computation and is composed of an LCD screen to display a square grid pattern of pixel-wide spots and a set of analyzing processes for the spots in the image. The two Cartesian components of the spot locations are processed by a two-step linear least-square fitting to third-order polynomials. The graphs for the coefficients enable us to determine the amount of decentering of the camera lens axis with respect to the center of the image array and the tip/tilt of the screen, which in turn gives the relative distortion coefficient. We present experimental results to demonstrate the utility of the method by comparing our results with the corresponding values determined by open source software available online.     

Non‐convex dual forms based on exponential intervening variables,with application to weight minimization

We study the weight minimization problem in a dual setting. We propose new dual formulations for non‐linear multipoint approximations with diagonal approximate Hessian matrices, which derive from separable series expansions in terms of exponential intervening variables. These, generally, nonconvex approximations are formulated in terms of intervening variables with negative exponents, and are therefore applicable to the solution of the weight minimization problem in a sequential approximate optimization (SAO) framework. Problems in structural optimization are traditionally solved using SAO algorithms, like the method of moving asymptotes, which require the approximate subproblems to be strictly convex. Hence, during solution, the nonconvex problems are approximated using convex functions, and this process may in general be inefficient. We argue, based on Falk's definition of the dual, that it is possible to base the dual formulation on nonconvex approximations. To this end we reintroduce a nonconvex approach to the weight minimization problem originally due to Fleury, and we explore certain convex and nonconvex forms for subproblems derived from the exponential approximations by the application of various methods of mixed variables. We show in each case that the dual is well defined for the form concerned, which may consequently be of use to the future code developers. Copyright © 2009 John Wiley & Sons, Ltd.     

Contact algorithms for the material point method in impact and penetration simulation

The inherent no‐slip contact constraint in the standard material point method (MPM) creates a greater penetration resistance. Therefore, the standard MPM was not able to treat the problems involving impact and penetration very well. To overcome these deficiencies, two contact methods for MPM are presented and implemented in our 3D explicit MPM code, MPM3D. In MPM, the impenetrability condition may not satisfied on the redefined regular grid at the beginning of each time step, even if it has been imposed on the deformed grid at the end of last time step. The impenetrability condition between bodies is only imposed on the deformed grid in the first contact method, while it is imposed both on the deformed grid and redefined regular grid in the second contact method. Furthermore, three methods are proposed for impact and penetration simulation to determine the surface normal vectors that satisfy the collinearity conditions at the contact surface. The contact algorithms are verified by modeling the collision of two elastic rings and sphere rolling problems, and then applied to the simulation of penetration of steel ball and perforation of thick plate with a particle failure model. In the simulation of elastic ring collision, the first contact algorithm introduces significant disturbance into the total energy, but the second contact algorithm can obtain the stable solution by using much larger time step. It seems that both contact algorithms give good results for other problems, such as the sphere rolling and the projectile penetration. Copyright © 2010 John Wiley & Sons, Ltd.     

The optimal feedrate planning on five-axis parametric tool path with geometric and kinematic constraints for CNC machine tools

The optimal feedrate planning on five-axis parametric tool path with multi-constraints remains challenging due to the variable curvature of tool path curves and the nonlinear relationships between the Cartesian space and joint space. The methods for solving this problem are very limited at present. The optimal feedrate associated with a programmed tool path is crucial for high speed and high accuracy machining. This paper presents a novel feedrate optimisation method for feedrate planning on five-axis parametric tool paths with preset multi-constraints including chord error constraint, tangential kinematic constraints and axis kinematic constraints. The proposed method first derives a linear objective function for feedrate optimisation by using a discrete format of primitive continuous objective function. Then, the preset multi-constraints are converted to nonlinear constraint conditions on the decision variables in the linear objective function and are then linearised with an approximation strategy. A linear model for feedrate optimisation with preset multiple constraints is then constructed, which can be solved by well-developed linear programming algorithms. Finally, the optimal feedrate can be obtained from the optimal solution and fitted to the smooth spline curve as the ultimate feedrate profile. Experiments are conducted on two parametric tool paths to verify the feasibility and applicability of the proposed method that show both the planning results and computing efficiency are satisfactory when the number of sampling positions is appropriately determined.     

Concurrent Implementation of the Optimal Incremental Approximation Method for the Adaptive and Meshless Solution of Differential Equations

The optimal incremental function approximation method is implemented for the adaptive and meshless solution of differential equations. The basis functions and associated coefficients of a series expansion representing the solution are selected optimally at each step of the algorithm according to appropriate error minimization criteria. Thus, the solution is built incrementally. In this manner, the computational technique is adaptive in nature, although a grid is neither built nor adapted in the traditional sense using a posteriori error estimates. Since the basis functions are associated with the nodes only, the method can be viewed as a meshless method. Variational principles are utilized for the definition of the objective function to be extremized in the associated optimization problems. Complicated data structures, expensive remeshing algorithms, and systems solvers are avoided. Computational efficiency is increased by using low-order local basis functions and the parallel direct search (PDS) optimization algorithm. Numerical results are reported for both a linear and a nonlinear problem associated with fluid dynamics. Challenges and opportunities regarding the use of this method are discussed.     

Twenty-four–DOF four-node quadrilateral elements for gradient elasticity

Computational analysis of gradient elasticity often requires the trial solution to be C¹, yet constructing simple C¹ finite elements is not trivial. In this paper, three four-node 24-DOF quadrilateral elements for gradient elasticity analysis are devised by generalizing some of the advanced element formulations for thin-plate analysis. These include the discrete Kirchhoff method, a relaxed hybrid-stress method, and the hybrid-stress method with equilibrating internal force modes. The first two methods start with the derivation of a C⁰ displacement, which is quadratic complete in the Cartesian coordinates. In the first method, at the midside points are derived and interpolated together with those at the nodes. Strain is derived from the displacement interpolation yet the second-order displacement derivatives are derived from the displacement-gradient interpolation. In the second method, only the assumed constant double-stress modes are employed to enforce the continuity of the normal derivative of the displacement. In the third method, the equilibrating internal force modes require the C¹ displacement to be defined only along the element boundary and the domain interpolation can be avoided. Patch test involving linear stress and constant double stress as well as other tests are presented to validate the proposed elements.