The numerical method for the coverage interval determination in the conducted emission measurements

This paper presents a numerical method for the coverage interval determination of the output variable while knowing the probability density functions of two non-dependent input variables. The coverage interval is derived from distribution function. In order to obtain the probability density function of the output variable, which is of mixed distribution type, the numerical combined method is applied, consisted of the Monte Carlo method and the modified least-squares method. The proposed method is applied for the symmetric distributions in the conducted emission measurements. The validation of the combined method showed its satisfactory level of accuracy.     

Probability density function estimation of a temperature field obtained by pulsed radiometric defectoscopy

This paper presents testing of subsurface defects by Pulsed Radiometric Defectoscopy (PRD) techniques. Such techniques rely on transient infrared radiation from the sample heated by the short duration flux initiated by flesh. Response function is derivated by experimental measurement with infrared camera FLIR SC 620. Experimental results are considered for the samples with controlled designed defects. For illustration, PRD techniques analysis was applied to detect subsurface defects in the aluminum samples. The time history of the surface temperature after the absorption of a short light pulse is used to obtain information about the subsurface structure and the thermophysical properties of the material. For the obtained values of the temperature difference (measurand), which is the random quantity, it is necessary to determine the probability density function (PDF). Namely, PDF estimation of the temperature difference has been done using a Monte Carlo method and a modified least-squares method. Knowledge of the PDF for the output quantity is needed to determine a coverage interval.     

基于蒙特卡罗方法的圆度测量不确定度评定

利用蒙特卡罗方法对圆度测量的不确定度进行评定。首先,根据最小二乘法得到圆度的误差模型;然后采用蒙特卡罗仿真方法对测量值进行模拟仿真,从而得到圆度误差的不确定度;最后将评定结果与传统评定方法的结果进行比较。结果表明该方法是可行的,且计算更为简便。     

静态MC方法在公差分析中的三种用法

蒙特卡罗(Monte Carlo,MC)方法是一种用于仿真计算的随机模拟方法,静态蒙特卡罗方法简单易用,比较适合于用计算机模拟来解决公差分析这样的随机问题。论述计算机辅助公差分析中应用静态蒙特卡罗模拟的三种用法,即以样本矩的估计来计算闭环公差,以样本频率的估计来计算装配成功率,以样本次序统计量的估计来计算满足装配成功率要求的闭环公差,并给出具体的计算示例,说明用静态蒙特卡罗方法解决公差分析问题的可行性。     

基于蒙特卡罗法与GUM法的直线度测量不确定度评定

由于形位误差测量的复杂性和测量结果评定的多样性,导致在实际测量结果中形位误差的不确定度评定成了难题。通过GUM法和蒙特卡罗法对直线度的测量不确定度进行评定。首先,根据最小二乘法得到直线度的误差模型;然后采用GUM方法对测量结果进行不确定度评定,采用蒙特卡罗仿真方法对测量值进行模拟仿真,从而得到直线度误差的不确定度;设置实验对比,通过数据分析验证了蒙特卡罗方法评定的可行性,为形位误差测量结果不确定度评定提供了更加简便的方法。     

三坐标机测量齿轮齿廓的不确定度评价

介绍了坐标测量中几种常用的不确定度评价方法.指出传统的三坐标测量机的测量不确定度评价方法大都不适用于评价坐标测量中面向对象的测量不确定度,并对使用蒙特卡洛方法评价测量不确定度进行了研究.首先,根据三坐标测量机详细标定文件及补偿策略说明建立测量模型.然后,将测量中的采样点通过测量模型生成大量测量结果,并以此评价测量不确定度.在齿廓评价实验中,评定齿廓误差的测量不确定度为0.96 μm时,多次评价结果之间的最大差值不超过0.03 μm,具有可靠的理论依据和较稳定的评定结果.文章指出,目前商用三坐标测量机大都不能为特定的测量对象提供测量不确定度报告,使用蒙特卡洛方法有希望改变此现状.     

Modelling accelerometers for transient signals using calibration measurements upon sinusoidal excitation

A recently proposed accelerometer model is applied for determining the accelerometer’s output to transient accelerations. The model consists of a linear, second-order differential equation with unknown coefficients. It is proposed to estimate these model parameters from sinusoidal calibration measurements, and an estimation procedure based on linear least-squares is presented. In addition, the uncertainties associated with the estimated parameters are determined utilizing a Monte Carlo simulation technique.

The performance of the proposed modelling approach was tested by its application to calibration measurements of two back-to-back accelerometers (ENDEVCO type 2270 and Brüel & Kjær type 8305). For each of the two accelerometers, the model was first estimated from sinusoidal calibration measurements and then used to predict the accelerometer’s behaviour for two shock calibration measurements. Measured and predicted shock sensitivities were found consistent with differences below 1% in most cases which confirms the benefit of the proposed modelling approach.     

基于子集抽样的模糊失效概率分析新方法

针对结构失效和安全状态具有模糊性的失效概率分析问题,提出一种基于子集抽样的新方法.所提方法首先将模糊失效域离散为功能函数变化较小的若干子集,然后利用马尔可夫链Monte Carlo法求得各子集上不考虑状态模糊性的随机失效概率,最后利用各子集中功能函数对模糊失效域的隶属度与相应随机失效概率乘积的和,求得模糊失效概率.文中用简单算例和工程算例比较所提方法与Monte Carlo法的效率和精度,结果表明,文中方法在保证计算精度的条件下,具有更高的计算效率.     

Monte carlo method for the uncertainty evaluation of spatial straightness error based on new generation geometrical product specification

Straightness error is an important parameter in measuring high-precision shafts. New generation geometrical product specification(GPS) requires the measurement uncertainty characterizing the reliability of the results should be given together when the measurement result is given. Nowadays most researches on straightness focus on error calculation and only several research projects evaluate the measurement uncertainty based on "The Guide to the Expression of Uncertainty in Measurement(GUM)". In order to compute spatial straightness error(SSE) accurately and rapidly and overcome the limitations of GUM, a quasi particle swarm optimization(QPSO) is proposed to solve the minimum zone SSE and Monte Carlo Method(MCM) is developed to estimate the measurement uncertainty. The mathematical model of minimum zone SSE is formulated. In QPSO quasi-random sequences are applied to the generation of the initial position and velocity of particles and their velocities are modified by the constriction factor approach. The flow of measurement uncertainty evaluation based on MCM is proposed, where the heart is repeatedly sampling from the probability density function(PDF) for every input quantity and evaluating the model in each case. The minimum zone SSE of a shaft measured on a Coordinate Measuring Machine(CMM) is calculated by QPSO and the measurement uncertainty is evaluated by MCM on the basis of analyzing the uncertainty contributors. The results show that the uncertainty directly influences the product judgment result. Therefore it is scientific and reasonable to consider the influence of the uncertainty in judging whether the parts are accepted or rejected, especially for those located in the uncertainty zone. The proposed method is especially suitable when the PDF of the measurand cannot adequately be approximated by a Gaussian distribution or a scaled and shifted t-distribution and the measurement model is non-linear.     

一种计算随机变量函数均值和标准差的方法

在工程实践中常常需要对随机变量函数的均值和标准差进行计算。对于这种问题,通常采用的是Monte Carlo方法、Taylor级数展开法、Taguchi法及其改进方法、Rosenbluthe法及其改进方法等。其中最有效的是Monte Carlo方法,但其计算效率低。为此,提出利用数论方法产生分布均匀的数论网格点,以此伪随机数代表由Monte Carlo方法产生的随机数计算随机变量函数的均值及标准差。计算实例表明,这种利用伪随机数的方法不但克服了Rosenbluthe改进方法在处理高阶函数时计算结果偏离实际值的缺点,而且与Monte Carlo方法相比,提高了计算效率。     

Adaptive Monte Carlo and GUM methods for the evaluation of measurement uncertainty of cylindricity error

Measurement uncertainty is one of the most important concepts in geometrical product specification (GPS). The “Guide to the expression of uncertainty in measurement (GUM)” is the internationally accepted master document for the evaluation of uncertainty. The GUM method (GUMM) requires the use of a first-order Taylor series expansion for propagating uncertainties. However, when the mathematical model of measurand is strongly non-linear the use of this linear approximation may be inadequate. Supplement 1 to GUM (GUM S1) has recently been proposed based on the basis of probability density functions (PDFs) using the Monte Carlo method (MCM). In order to solve the problem that the number of Monte Carlo trials needs to be selected priori, adaptive Monte Carlo method (AMCM) described in GUM S1 is recommended to control over the quality of the numerical results provided by MCM.The measurement and evaluation of cylindricity errors are essential to ensure proper assembly and good performance. In this paper, the mathematical model of cylindricity error based on the minimum zone condition is established and a quasi particle swarm optimization algorithm (QPSO) is proposed for searching the cylindricity error. Because the model is non-linear, it is necessary to verify whether GUMM is valid for the evaluation of measurement uncertainty of cylindricity error. Then, AMCM and GUMM are developed to estimate the uncertainty. The procedure of AMCM scheme and the validation of GUMM using AMCM are given in detail. Practical example is illustrated and the result shows that GUMM is not completely valid for high-precision evaluation of the measurement uncertainty of cylindricity error if only the first-order terms in the Taylor series approximation are taken into account. Compared with conventional methods, not only the proposed QPSO method can search the minimum zone cylindricity error precisely and rapidly, but also the Monte Carlo simulation is adaptive and AMCM can provide control variables (i.e. expected value, standard uncertainty and lower and higher coverage interval endpoints) with an expected numerical tolerance. The methods can be extended to the evaluation of measurement uncertainty of other form errors such as roundness and sphericity errors.     

基于人工神经网络的结构零件可靠度仿真方法

提出结构零件可靠度计算的人工神经网络－蒙特卡罗仿真算法,针对结构零件可行度计算问题,利用有限元计算方法,得到一组结构输入基本变量及输出响应数据,采用人工神经网络后向传播ＢＰ模型,建立结构的输入－输出关系,在该模型上,用Ｍｏｎｔｅ Ｃａｒｌｏ方法进行结构零件可靠度仿真计算。算例表明,该方法正确可行。     

Uncertainty evaluation of multivariate quantities: A case study on electrical impedance

The paper discusses the evaluation of the uncertainty of a multivariate quantity using the Law of Propagation of Uncertainty defined in the Guide to the Expression of Uncertainty in Measurement (GUM) and a Monte Carlo method according to the GUM’s Supplement 2. The quantity analysed is the electrical impedance, which is not a scalar but a complex quantity. The used measuring method allows the evaluation of the impedance and of its uncertainty in different ways and the corresponding results are presented, compared and discussed. For comparison purposes, results of the impedance uncertainty obtained using the NIST Uncertainty Machine are also presented.     

Statistical analysis of the characteristics of some basic mass-produced passive electrical circuits used in measurements

Statistical properties of some basic mass-produced passive electrical circuits used in measurements are analyzed in this paper, using methods for expressing measurement uncertainty of indirectly measured quantities. The focus of this paper is on electrical circuits whose defining parameters are obtained as non-linear functions of component parameters. Variants of voltage divider and Wheatstone bridge circuits significant for measurement practice are investigated in detail. Even if distributions with symmetrical probability density functions (PDFs), such as uniform or normal, are adopted for the parameters of the components comprising a circuit, non-linearity of the circuit function gives rise to asymmetry in the PDF of the circuit’s parameter. The asymmetry of the PDF causes the mean and the nominal value of the circuit parameter to differ.     

疲劳短裂纹理论及寿命预测方法新进展

回顾短裂纹萌生和扩展机理、寿命预测以及短裂纹行为模拟方面的最新进展,侧重介绍疲劳短裂纹行为的统计模拟方法,马尔可夫链模型、威布尔分布函数、群体疲劳短裂纹的蒙特卡罗模拟和分形方法,以及应用蒙特卡罗方法及分形方法对低碳钢高温低周疲劳短裂纹行为所进行的模拟。对于基于BP(back propagation)神经网络的统计方法在疲劳短裂纹方面的应用也给予一定的介绍。     

Validation of the GUM using the Monte Carlo method when applied in the calculation of the measurement uncertainty of a compact prover calibration

This article presents the calibration of a compact prover using the weighing method. An evaluation of measurement uncertainty of the prover calibration has been developed using the GUM and Monte Carlo methodologies. A water draw kit was utilized to direct the liquid flow from the compact prover to a water container in order to weigh the transferred water mass on a balance. This amount of mass was used as reference for the calculation of the prover base volume. A modeling of the flow rate into the water draw kit as a function of time was conceived. This modeling was applied for calculating the error in the liquid volume of the water container due to the switching of two solenoid valves of the water draw kit. A mathematical model of the prover base volume has been developed. This model is non-linear and the two largest sources of uncertainty are related to the balance calibration certificate that together account for 31.84% of the uncertainty budget. This work showed that the GUM approach was validated by Monte Carlo method in the calculation of the measurement uncertainty of the calibration of a compact prover. The absolute differences of the respective endpoints of the coverage intervals of these two methods are less than 0.00023% of estimate of the prover base volume whose value is 151.427 dm³. This result was obtained for a coverage probability of 95% and ${10}^6$ Monte Carlo iterations. The density of the calibration water and its uncertainty have been calculated through an innovative approach.     

Influence of eccentricity on roughness distributions in side milling

In this paper, a numerical model was used based on the tool-piece geometric intersection, which enables the determination of a roughness profile as a function of feed, tool radii and tool eccentricity in side milling processes. Average roughness R_a and peak-to-valley roughness R_t were obtained for a group or family of tools, defined by an average radius value and a standard deviation value of all tool radii. The Monte Carlo method was used to generate N random combinations of radius values for each family, according to a normal distribution. The model was validated by means of experimental tests. For each family of tools, roughness distributions were obtained at different feed values and for different eccentricity values. It was found that the higher eccentricity, the more asymmetrical roughness distributions become.     

Monte Carlo simulation of grain growth of single-phase systems with anisotropic boundary energies

The grain growth in single-phase systems with various anisotropic boundary energies is simulated using a modified two-dimensional (2D) Monte Carlo algorithm. Structural self-similarity both in the grain shape distributions and the grain boundary configurations is found regardless of the degree and type of anisotropy. Parabolic evolution kinetics is observed in most cases. The growth rate represented by the time rate of average grain area change is found to be a function of the grain boundary properties. In some cases, the normalized grain size distributions are not time-invariant, and therefore, current grain growth theories cannot explain conclusively the occurrence of the parabolic kinetics in these cases. The effect of anisotropy on the grain growth kinetics is discussed.     

机器人工作空间求解的蒙特卡洛法改进和体积求取

针对传统的蒙特卡洛法求解机器人工作空间时精确度不够的问题,提出了一种改进的蒙特卡洛法。用传统的蒙特卡洛法生成一个种子工作空间,基于标准差动态可调的正态分布对种子工作空间进行扩展。在扩展过程中设定一个精度阈值,确保得到的工作空间中每个位置都能被准确的描述。基于得到的工作空间,提出了一种体元化算法求取工作空间的体积,寻找到工作空间的边界部分和非边界部分,通过对边界部分的不断细化,降低了体积求取误差。为了验证算法的有效性和实用性,以九自由度的超冗余串联机械臂为例,对本文改进的蒙特卡洛法和提出的体积求取算法进行仿真分析。结果表明:采样点数量相同时,改进的蒙特卡洛法生成的工作空间边界光滑,"噪声小";得到精确的工作空间时改进方法需要的采样点数仅是传统方法的4.67%;体积求取算法效率较高,相对误差小于1%;求得的工作空间体积可用于评估机械臂性能,为后续机械臂构型优化奠定了理论基础。