形位误差包容评定的理论与实践—线性鞍点规划方法的应用

本文探讨应用线性鞍点规划方法来研究形位误差的包容评定问题，按照维数及类别的不同，将各种评定问题归结为统一的规划模型，文中还应用这一方法，讨论了最小条件（判别准则），并给出了几何解释。     

线性鞍点规划与形位误差的包容评定

本文将线性鞍点规划用于形位误差的包容评定。该方法有明确的停机条件(判别准则),并具有求解方便、覆盖面宽等优点。     

最小外接圆法和最大内切圆法圆度评估的快速算法

本文介绍了采用计算机进行简单几何计算求解最小外接圆，最大内切圆度误差的快速算法，该方法也可以推广适用于直线度，平面度等具有明确几何判别准则的形位误差评估。     

按最小条件评定空间直线度误差的理论研究

本文首先按最小条件建立了评定空间直线度误差的非线性数学模型。通过误差分析，从理论上证明了该数学模型不能进行线性化处理，并提出了最小条件判别准则。文中给出了计算机评定空间直线度误差的实例。最后用几何方法验证了其判别的正确性。     

孔组复合位置度误差的评定和判别

本文探讨孔组复合位置度误差最小条件的判别准则和评定方法。一、判别准则实现孔组复合位置度误差最小条件的两个关键问题是:(1)如何判别误差达到了最小(判别准则);(2)如何求得这一最小值(评定方法)。我们首先讨论第一个问题。孔组的理论位置和测量偏差可以用直角坐标,也可用极坐标表示。     

球度误差的判别准则和评定方法

本文建立了评定球度误差的数学模型,阐明线性模型的合理性和优越性,给出了球度误差的判别准则和评定方法,实现了代数判别和计算机判别。根据极点的数目和分布,建立了实际球度误差型谱。     

六项形状误差的判别方法

本文根据线性极差极小化理论,运用集合论观点和多维画法几何图解法,具体地提出了六项形状误差的代数判别法和几何判别法。这些方法既可实现计算机仲裁,又便于人工图算判别,有利于形位误差判别的统一和完善。     

基于鞍点规划法的形位误差计算机评定

建立起了形位误差评定的统一鞍点规划模型 ,给出了“最小条件”判据 ,提出了直接求解鞍点规划模型的遗传算法。最后以空间直线度误差为例 ,进行了误差评定。     

发动机凸轮升程误差的评定方法

通过对发动机凸轮升程误差曲线的分析，提出了按“最小条件”评定凸轮升程误差的判别准则，从而避免了因测量基准不同而引起误判。     

球度误差包容评定的高精度实现方法

依据数学规划理论,构造一种以线性包容评定模型的迭代运算去逼近非线性的精确包容评定模型优化解的球度误差评定算法,并建立了适用于计算判别的球度误差包容评定最优条件判别准则。算法具有评定精度高,收敛速度快、计算稳定等优点。     

基于改进遗传算法评定圆柱度误差

针对圆柱度误差评定的特点,提出了一种基于实数编码的改进遗传算法同时实现圆柱度误差的最小区域法、最小外接圆柱法和最大内接圆柱法评定。同时建立了用遗传算法实现圆柱度误差最小区域法、最小外接圆柱法和最大内接圆柱法评定时目标函数数学模型的计算方法。通过不同评价方法对圆柱度误差在不同初始值下进行多次评定,证明该方法都能收敛到全局最优解,而且计算结果稳定。该算法可以推广应用到其它形状误差评定中。     

基于FFT的舍入不确定度评估

舍入不确定度是快速傅里叶算法不确定度评估中的一个重要来源。将表示成向量矩阵的FFT算法分解为稀疏矩阵,以此确定信号传递流图,从而得出舍入不确定度在每一级的传递形式。再利用GUM中的B类方法对其进行评定,评定时假设舍入测量不确定度为均匀分布,通过对FFT算法中基-2算法的舍入不确定度进行评定,最终经过算法传递后得到其舍入不确定度的结果,在此基础上建立了FFT舍入测量不确定度的通用评估方法。     

Least-squares estimation of imaging parameters for an ultrasonic array using known geometric image features

Ultrasonic array images are adversely affected by errors in the assumed or measured imaging parameters. For non-destructive testing and evaluation, this can result in reduced defect detection and characterization performance. In this paper, an autofocus algorithm is presented for estimating and correcting imaging parameter errors using the collected echo data and a priori knowledge of the image geometry. Focusing is achieved by isolating a known geometric feature in the collected data and then performing a weighted leastsquares minimization of the errors between the data and a feature model, with respect to the unknown parameters. The autofocus algorithm is described for the estimation of element positions in a flexible array coupled to a specimen with an unknown surface profile. Experimental results are shown using a prototype flexible array and it is demonstrated that (for an isolated feature and a well-prescribed feature model) the algorithm is capable of generating autofocused images that are comparable in quality to benchmark images generated using accurately known imaging parameters.     

The Correction Capability of the Berlekamp–Massey–Sakata Algorithm with Majority Voting

Sakata’s generalization of the Berlekamp–Massey algorithm applies to a broad class of codes defined by an evaluation map on an order domain. In order to decode up to the minimum distance bound, Sakata’s algorithm must be combined with the majority voting algorithm of Feng, Rao and Duursma. This combined algorithm can often decode far more than (d _min −1)/2 errors, provided the errors are in general position. We give a precise characterization of the error correction capability of the combined algorithm. We also extend the concept behind Feng and Rao’s improved codes to decoding of errors in general position. The analysis leads to a new characterization of Arf numerical semigroups.     

Some questions relating to the construction of a digital instrument for the complex monitoring of gear wheels and transmissions

Conclusions The method of interpreting the discrete values of the kinematic error here developed has enabled us to realize a digital system based on unified functional elements for measuring and recording the kinematic, local kinematic, and cyclic errors for complete automation of the measuring process.The proposed error-calculation algorithm and accumulated experience in the complex testing of gear wheels and transmission provides genuine prerequisites for the development of improved complex-testing digital instruments based on the block-module principle of construction involving the use of integrated circuits.Translated from Izmeritel'naya Tekhnika, No. 2, pp. 61–63, February, 1976.     

基于模糊综合评价法和着重加权法的水尺计重误差算法研究

水尺计重易受多种因素影响而产生误差。结合水尺计重的特点,采用模糊综合评价法与加权着重法设计出误差算法,实现输入风险指标值,就能获取该条件下水尺计重的误差。模糊综合评价法体现出水尺计重误差风险指标多因素、多层次以及部分指标难以量化的特点,而加权着重法则弥补了模糊综合评价法风险衰减的不足。基于模糊综合评价法与加权着重法的水尺计重误差算法可以计算出不同情况下水尺计重工作的误差风险,确保水尺计重误差低于0.5%的技术要求。     

姿态稳定的深水多波束测深系统归位模型的误差分析

为了获得高质量的深水多波束测深数据,必须考虑归位计算过程中的误差影响。因此,提出了一种基于姿态稳定的深水多波束测深系统归位模型的误差分析方法。首先,建立发射全姿态稳定、接收横滚姿态稳定的波束归位模型,在此基础上,分析归位过程中的误差分量并推导误差传播公式,最终得到了深水多波束测深系统不确定度的计算模型。实验利用系统的传感器和设备相关指标进行计算,给出了典型波束角下的测深不确定度,对深水多波束测深系统的测深数据精度评估具有较好的参考价值。     

An implicit unitless error and step‐size control method in integrating unified viscoplastic/creep ODE‐type constitutive equations

A series of numerical analyses are carried out to investigate the difficulties in numerical integration of unified viscoplastic/creep constitutive equations, which are normally represented as a system of ordinary differential equations (ODEs). The problems of numerically integrating the constitutive equations are identified and analysed. To overcome the stiffness problems, implicit methods are used for the numerical integration and a generic technique is introduced to calculate the Jacobian matrix. A normalization technique is introduced in the paper to convert the integration errors for each time increment to unitless errors. Thus, a single tolerance can be used to control the accuracy and step size in integrating a set of unified viscoplastic/creep constitutive equations. In addition, an implicit step‐size control method is proposed and used in the integrations. This method reduces the possibility of rejection of an integration increment due to poor accuracy. Copyright © 2007 John Wiley & Sons, Ltd.     

微分进化算法在圆度误差评定中的应用

为了精确快速计算圆度误差,提出了基于微分进化智能优化算法的最小区域圆度误差评定方法。介绍了微分进化算法的基本原理及种群初始化、变异、交叉、选择实现步骤,建立了该算法求解最小区域圆度误差的数学模型。为验证算法的有效性,进行了大量实验并与多种算法进行对比,证实了方法的评定结果不仅小于最小二乘法及标准遗传算法评定结果,精度高,而且计算结果稳定,运算速度快。实验表明:微分进化算法用于最小区域圆度误差评定有较强的自适应能力、快速全局收敛性和高稳定性,适于对高精度圆度误差的快速评定。     

二维精密工作台离散点测量结果误差分离的新方法研究

针对测量结果中包含的误差,提出一种能够分离精密工作台系统误差的方法。首先利用辅助测量栅格板和二维精密工作台的不同位置进行测量,然后根据栅格板上标记点的测量数据和标称值建立误差分离的数学模型,最终实现对测量结果的误差分离。通过仿真验证了算法的有效性。仿真结果表明:当不存在测量噪声时,能够实现误差的完全分离;当存在测量噪声时,计算值与给定值标准差的相对误差在X轴和Y轴上分别为1.95%和1.52%。对于不同幅度的噪声,工作台系统误差计算值稳定。该算法对噪声不敏感,表现出很好的鲁棒性,可用于测量结果和仪器性能的评价。