Optimal localization of complex surfaces in CAD-based inspection

Complex surface inspection requires the optimal localization of the measured surface related to the design surface so that the two surfaces can be compared in a common coordinate frame. This paper presents a new technique for solving the localization problem. The basic approach consists of two steps: 1) rough localization of the measured points to the design surface based on curvature features, which can produce a good initial estimate for the optimal localization; 2) fine localization based on the least-square principle so that the deviation between the measured surface and the design surface is minimized. To efficiently compute the closest points on the design surface of the measured points, a novel method is proposed. Since this approach does not involve an iterative process of solving non-linear equations for the closest points, it is more convenient and robust. The typical complex surface is used to test the developed algorithm. Analysis and comparison of experimental results demonstrate the validity and applicability of the algorithm.     

Profile error evaluation of free-form surface using sequential quadratic programming algorithm

Profile error of free-form surface is evaluated in this paper based on sequential quadratic programming (SQP) algorithm. The optimal localization model is established with the minimum zone criterion firstly. Subsequently, the surface subdivision method or STL (STeror Lithography) model is used to compute the point-to-surface distance and the approximate linear differential movement model of signed distance is deduced to simplify the updating process of alignment parameters. Finally, the optimization model on profile error evaluation of free-form surface is solved with SQP algorithm. Simulation examples indicate that the results acquired by SQP method are closer to the ideal results than the other algorithms in the problem of solving transformation parameters. In addition, real part experiments show that the maximum distance between the measurement points and their corresponding closest points on the design model is shorter by using SQP-based algorithm. Lastly, the results obtained in the experiment of the workpiece with S form illustrate that the SQP-based profile error evaluation algorithm can dramatically reduce the iterations and keep the precision of result simultaneously. Furthermore, a simulation is conducted to test the robustness of the proposed method. In a word, this study purposes a new algorithm which is of high accuracy and less time-consuming.     

Accurate evaluation of free-form surface profile error based on quasi particle swarm optimization algorithm and surface subdivision

Although significant progress has been made in precision machining of free-form surfaces recently, inspection of such surfaces remains a difficult problem. In order to solve the problem that no specific standards for the verification of free-form surface profile are available, the profile parameters of free-form surface are proposed by referring to ISO standards regarding form tolerances and considering its complexity and non-rotational symmetry. Non-uniform rational basis spline(NURBS) for describing free-form surface is formulated. Crucial issues in surface inspection and profile error verification are localization between the design coordinate system(DCS) and measurement coordinate system(MCS) for searching the closest points on the design model corresponding to measured points. A quasi particle swarm optimization(QPSO) is proposed to search the transformation parameters to implement localization between DCS and MCS. Surface subdivide method which does the searching in a recursively reduced range of the parameters u and v of the NURBS design model is developed to find the closest points. In order to verify the effectiveness of the proposed methods, the design model is generated by NURBS and the measurement data of simulation example are generated by transforming the design model to arbitrary position and orientation, and the parts are machined based on the design model and are measured on CMM. The profile errors of simulation example and actual parts are calculated by the proposed method. The results verify that the evaluation precision of freeform surface profile error by the proposed method is higher 10%-22% than that by CMM software. The proposed method deals with the hard problem that it has a lower precision in profile error evaluation of free-form surface.     

New Approach for Measured Surface Localization Based on Umbilical Points

Measured surface localization (MSL) is one of the key essentials for the assessment of form error in precision manufacturing. Currently, the researches on MSL have focused on the corresponding relation search between two surfaces, the performance improvement of localization algorithms and the uncertainty analysis of localization. However, low efficiency, limitation of localization algorithms and mismatch of multiple similarities of feature points with no prior are the common disadvantages for MSL. In order to match feature points quickly and fulfill MSL efficiently, this paper presents a new localization approach for measured surfaces by extracting the generic umbilics and estimating their single complex variables, describing the match methods of ambiguous relation at umbilics, presenting the initial localization process of one pair matched points, refining MSL on the basis of obtained closet points for some measured points by the improvement directed projection method. In addition, the proposed algorithm is simulated in two different types of surfaces, two different localization types and multiple similar surfaces, also tested with the part of B-spline surface machined and bottle mould with no knowledge, finally the initial and accurate rigid body transformation matrix, localization errors between two surfaces and execution time are got. The experimental results show that the proposed method is feasible, more accurate in localization and high in efficiency. The proposed research can not only improve the accuracy and performance of form error assessment, but also provide an effective guideline for the integration of different types of measured surfaces.     

复杂曲面加工检测中的精确定位方法

测量数据的精确定位是实现复杂曲面加工检测的关键,针对其在初始变换估计和最近点计算等方面存在的问题,提出一种快速、精确的定位方法.该方法以曲面的曲率为联系特征,建立起满足角度、距离约束的对应关系,能够实现测量数据的初始定位,从而为后续迭代算法向全局最优收敛提供一个良好的初始变换.进而以Bernstein多项式算术运算为基础,给出一种新的最近点计算方法,能够克服传统方法需要给定初始迭代点的不足.最后利用基于最小二乘的迭代算法完成测量数据定位的精确调整,达到全局最优的目标.试验结果显示,所提出的方法快速、可靠,并且具有良好的定位精度.     

采用基于群智能的模拟退火算法优化起重机箱形梁

详细论述了传统模拟退火算法的基本原理及求解过程,针对算法中存在的缺陷,提出了一种基于群智能的改进方案,采用种群搜索方式进行基于模拟退火的优化设计,提高了算法搜索迭代计算效率;采用Matlab编程软件,在算法运行过程中添加一个数据存储器,用以记录当前最优计算结果,保证全局极值点的准确输出;采用经典的起重机箱形梁优化模型,对改进后的算法进行测试。优化结果表明,改进后的模拟退火算法不仅能克服传统算法效率低的缺点,还具有高效的优化计算能力,为机械结构的优化设计提供了一种高效可行的新方案。     

工程稳健优化设计

本文从工程设计观点讨论了设计解的稳健性、稳健设计和稳健优化设计的基本概念,提出了一种基于随机优化技术的稳健优化设计的建模原理和求解算法,这一方法将通过调整设计变量的名义值和控制它的容差来考虑可控变量和不可控参数的变差对产品质量的影响,以提高设计解的可行稳健性和质量函数的不灵敏性。     

离散萤火虫算法的复杂装备测试点优化选择

测试点优化选择是复杂装备测试性设计的重要环节,本文提出一种用于解决测试点优化选择问题的离散萤火虫算法(DFA)。首先建立了测试点优化选择问题的数学模型,接着对传统的萤火虫算法(FA)进行了离散化改进,给出了离散化萤火虫算法的实施步骤,并分析了不同的吸引度函数和二值化函数(sigmoid和tanh函数)对算法结果的影响。最后针对5个不同规模的实际系统验证了离散萤火虫算法的有效性,并与粒子群算法(PSO)和遗传算法(GA)等传统的元启发式搜索算法的计算性能进行了比较分析。结果显示:在满足系统要求的故障检测率和故障隔离率的前提下,利用本文提出的离散萤火虫算法得到的5个系统测试代价最优值分别比PSO算法和GA算法平均降低了10.1%和14.6%。实验结果表明:离散萤火虫算法能快速收敛到更高质量的全局最优解,避免过早收敛而陷入局部最优值,对于解决大型复杂装备的测试点优化选择问题具有很好的应用前景。     

A new multi-objective ant colony algorithm for solving the disassembly line balancing problem

The disassembly line is the best choice for automated disassembly of disposal products. Therefore, disassembly line should be designed and balanced so that it can work as efficiently as possible. In this paper, a mathematical model for the multi-objective disassembly line balancing problem is formalized firstly. Then, a novel multi-objective ant colony optimization (MOACO) algorithm is proposed for solving this multi-objective optimization problem. Taking into account the problem constraints, a solution construction mechanism based on the method of tasks assignment is utilized in the algorithm. Additionally, niche technology is used to embed in the updating operation to search the Pareto optimal solutions. Moreover, in order to find the Pareto optimal set, the MOACO algorithm uses the concept of Pareto dominance to dynamically filter the obtained non-dominated solution set. To validate the performance of algorithm, the proposed algorithm is measured over published results obtained from single-objective optimization approaches and compared with multi-objective ACO algorithm based on uniform design. The experimental results show that the proposed MOACO is well suited to multi-objective optimization in disassembly line balancing.     

A unified localization approach for machining allowance optimization of complex curved surfaces

The goal of workpiece localization is of interest to find the optimal Euclidean transformation that aligns the sampled points to the nominal CAD model to ensure sufficient stock allowance during the machining process. In this paper, a unified localization technique is developed for sculptured surface machining. This technique concerns an alignment process to satisfy a user-defined set of constraints for some specific surfaces where the machining allowance is preferentially guaranteed. The mathematical model of the constrained optimization alignment is firstly established, and is efficiently solved by a combination of the multipliers method and the BFGS algorithm to handle the large number of constraints in allowance optimization. To efficiently calculate the Euclidean oriented distance, a novel approach, which combines the robust arithmetic for multivariate Bernstein-form polynomials and Bezier surface segmentation algorithm, is presented based on recursive quadtree decomposition. Two typical sculptured surfaces are used to test the developed algorithm and comparisons between the proposed algorithm and the existing algorithms are given. Experiment results show that the proposed method is appropriate and feasible to distribute the stock allowance for proper sculptured surface machining.     

A framework for non-contact measurement and analysis of NURBS surfaces

The paper presents an implementation of a methodology for reliable and feasible dimensional measurement of engineering components containing free-form surfaces. Two main requirements had to be satisfied. First, a large number of points had to be accurately measured. Secondly, the set of corresponding points on the nominal model had to be computed within a reasonable time. The first aspect was satisfied by adopting a non-contact measurement technique based on laser triangulation. High accuracy was achieved through software prealignment for precise component localisation and through appropriate measurement planning, both based on the CAD model. Determination of the corresponding nominal points was solved by best-fitting. Significant speed improvements were achieved through an implementation of the iterative closest point algorithm, based on a dual representation of the surface. The nominal surface is defined using NURBS entities and its approximation is determined as a polyhedral mesh. A sampling criterion for complex surfaces was derived and implemented, producing encouraging results. Validity of the proposed approach is supported by experiments and by simulation studies involving real engineering components.     

Concept optimization for mechanical product by using ant colony system

The aim of conceptual design is to generate the best design candidate. Concept solving in conceptual design can be viewed as a problem of combinatorial optimization, in which there exists a “combinational explosion” phenomenon when using the traditional morphological matrix method to tackle it. In this research, a concept optimization problem is studied based on an Ant Colony System (ACS). By analyzing the similarity between concept solving and Traveling Salesman Problem (TSP), concept solving is transformed into a problem of optimal path in combinatorial optimization, where the dynamic programming based solution space model and the longest path based optimization model are developed. Then, the ant algorithm to resolve TSP is adopted to implement concept optimization according to the positive feedback searching mechanism of ACS, and some improvements are made incorporating crossover and mutation operators of a genetic algorithm (GA), to obtain the optimal scheme rapidly and effectively. Finally, a conceptual design case of press is given to demonstrate the feasibility and rationality of this proposed approach. The employment of ACS enables concept solving to be implemented with an algorithm and thus possesses better operability, which offers a promising way to solve the “combinatorial explosion” problem in conceptual design.     

基于三坐标测量机的螺旋曲面重建

介绍了一种螺旋曲面的重建方法,详细阐述了设计流程。由三坐标测量机获取螺旋曲面数据,实现了测量数据中噪声点的剔除,利用Delaunay三角化重建了曲面。通过滚刀实例的初步验证,说明方法正确可行。     

Repeated surface registration for on-line use

We consider the problem of matching sets of 3D points from a measured surface to the surface of a corresponding computer-aided design (CAD) object. The problem arises in the production line where the shape of the produced items is to be compared on-line with its pre-described shape. The involved registration problem is solved using the iterative closest point (ICP) method. In order to make it suitable for on-line use, i.e., make it fast, we pre-process the surface representation of the CAD object. A data structure for this purpose is proposed and named Distance Varying Grid tree. It is based on a regular grid that encloses points sampled from the CAD surfaces. Additional finer grids are added to the vertices in the grid that are close to the sampled points. The structure is efficient since it utilizes that the sampled points are distributed on surfaces, and it provides fast identification of the sampled point that is closest to a measured point. A local linear approximation of the surface is used for improving the accuracy. Experiments are done on items produced for the body of a car. The experiments show that it is possible to reach good accuracy in the registration and decreasing the computational time by a factor 700 compared with using the common kd-tree structure.     

DISCRETIZATION APPROACH USING RAY-TESTING MODEL IN PARTING LINE AND PARTING SURFACE GENERATION

Surface classification, 3D parting line, parting surface generation and demoldability analysis which is helpful to select optimal parting direction and optimal parting line are involved in automatic cavity design based on the ray-testing model. A new ray-testing approach is presented to classify the part surfaces to core/cavity surfaces and undercut surfaces by automatic identifying the visibility of surfaces. A simple, direct and efficient algorithm to identify surface visibility is developed. The algorithm is robust and adapted to rather complicated geometry, so it is valuable in computer-aided mold design systems. To validate the efficiency of the approach, an experimental program is implemented. Case studies show that the approach is practical and valuable in automatic parting line and parting surface generation.     

一种基于几何分析的协同优化方法

从几何角度分析协同优化方法,并据此提出一种新的系统级优化模型,相对于代数分析,几何分析更简洁直观。分析学科级优化的几何意义,指出在学科级优化中最优设计点是距系统级提供的目标点最近的点,同时根据几何分析还能在该最优点处方便地获得主动约束边界的梯度,基于该最优点及此点处的梯度信息,可以构造出主动约束边界的一个线性近似并提供给系统级。随着迭代的进行,更多的线性约束将加入到系统级优化中,这一系列线性近似的组合构成的设计空间逐步逼近了原问题的设计空间。采用基于几何分析的协同优化方法对一齿轮减速箱进行优化设计,并将设计结果与传统协同优化方法的设计结果进行对比,研究结果表明,本方法在保持计算精度的前提下提高了计算效率。     

基于分位数型设计准则的模糊健壮设计新方法

在模糊目标和模糊设计约束的条件下,同时考虑了质量特性的健壮性和设计约束的可行健壮性,提出望目特性、望大特性和望小特性模糊健壮设计的分位数型设计准则。在该设计准则的基础上,建立不同类型质量特性的模糊健壮设计优化模型,并将常规优化算法和基于最大可能点的分位数求解算法相结合构成该模型的求解框架。最后通过实例验证了该方法的有效性。     

Storage location assignment and order picking optimization in the automotive industry

The objective of this study is to design storage assignment and order picking system using a developed mathematical model and stochastic evolutionary optimization approach in the automotive industry. It is performed in two stages. At the first stage, storage location assignment problem is solved with a class-based storage policy with the aim of minimizing warehouse transmissions by using integer programming. At the second stage, batching and routing problems are considered together to minimize travel cost in warehouse operations. A warehouse in the automotive industry is analyzed, and an optimum solution is obtained from an integer programming model. Due to the computational time required for solving the integer programming problem, a faster genetic algorithm is also developed to form optimal batches and optimal routes for the order picker. The main advantage of the algorithm is the quick response to production orders in real-time applications. The solutions showed that the proposed approach based on genetic algorithms can be applied and integrated to any kind of warehouse layout in automotive industry.     

基于离群算法组合曲面特征点提取的研究

为了克服目前组合曲面提取特征点算法中阈值选取困难导致边界特征点误判的缺点，在对组合曲面特性进行分析的基础上，提出了一种基于离群算法的组合曲面特征点提取算法。该算法根据曲面特性定义了曲面域和曲面域深度，在空间统计学基础上引入正态分布的标准单位数和置信系数，采用空间数据挖掘中的离群算法提取组合曲面特征点。通过在某型摩托车零件中的应用，表明了该方法可以有效地避免阈值选取问题，且证明了该算法的有效性和实用性。     

基于分层块状全局搜索的三维点云自动配准

提出了一种分层块状全局搜索到临近点局部搜索的改进迭代最近点(ICP)算法,用于进一步提高ICP算法的配准速度并消除点云缺失对点云配准的影响。该配准方法在粗略配准之后,以点云块为分层单元对模型点集进行选取,并对选取的少量模型点进行全局搜索获取其对应最近点;然后,以这些模型点对应的最近点作为搜索中心,在场景点集中进行局部搜索,获取这些模型点的大量临近点的对应最近点;最后,剔除错误对应最近点对,并求取坐标变换。与基于KD-Tree的ICP算法和基于LS+HS(Logarithmic Search Combined with Hierarchical Model Point Selection )的ICP算法相比,该配准算法对Happy bunny扫描数据的配准速度分别提高了78%和24%;对Dragon扫描数据的配准速度分别提高了73%和30%。这些结果表明该算法可以快速、精确地实现三维点云间的配准。