Measurement uncertainty evaluation for a non-negative measurand: an alternative to limit of detection

The interpretation and reporting the results of measurements on materials where the concentration of the analyte is close to or may even be zero has been the subject of much discussion with the use of such concepts as limit of detection (LOD) and limit of quantification (LOQ). While these concepts have taken into account the measurement uncertainty, they have not utilised the fact that the value of the measurand, i.e., the concentration, is constrained to be zero or greater. Taking this into account the distribution of values attributable to the measurand can be derived from the probability density function (PDF) that determines the distribution of the observed values. When this PDF is normal the distribution of the values attributable to the measurand is a truncated t distribution with a lower limit of re-normalised so that the total probability is one, where x _m is the mean of the n observed values and s their standard deviation. When x _m much greater than then the distribution reverts to the unmodified t distribution. The probability that the value of the measurand is above or below a limit can be calculated directly from this truncated t distribution and the interpretation of the result does not require the use of concepts such as LOD and LOQ. Also it deals with the problem of negative observations. This Report was written by Alex Williams (e-mail: aw@camberley.demon.co.uk) for the Statistical Subcommittee and approved by the Analytical Methods Committee.     

A comparison of location estimators for interlaboratory data contaminated with value and uncertainty outliers

While estimation of measurement uncertainty (MU) is increasingly acknowledged as an essential component of the chemical measurement process, there is little agreement on how best to use even nominally well-estimated MU. There are philosophical and practical issues involved in defining what is “best” for a given data set; however, there is remarkably little guidance on how well different MU-using estimators perform with imperfect data. This report characterizes the bias, efficiency, and robustness properties for several commonly used or recently proposed estimators of true location, μ, using “Monte Carlo” (MC) evaluation of “measurement” data sets drawn from well-defined distributions. These synthetic models address a number of issues pertinent to interlaboratory comparisons studies. While the MC results do not provide specific guidance on “which estimator is best” for any given set of real data, they do provide broad insight into the expected relative performance within broadly defined scenarios. Perhaps the broadest and most emphatic guidance from the present study is that (1) well-estimated measurement uncertainties can be used to improve the reliability of location determination and (2) some approaches to using measurement uncertainties are better than others. The traditional inverse squared uncertainty-weighted estimators perform well only in the absence of unrepresentative values (value outliers) or underestimated uncertainties (uncertainty outliers); even modest contamination by such outliers may result in relatively inaccurate estimates. In contrast, some inverse total variance-weighted-estimators and probability density function area-based estimators perform well for all scenarios evaluated, including underestimated uncertainties, extreme value outliers, and asymmetric contamination.     

Copenhagen quantum mechanics

In our quantum mechanics courses, measurement is usually taught in passing, as an ad-hoc procedure involving the ugly collapse of the wave function. No wonder we search for more satisfying alternatives to the Copenhagen interpretation. But this overlooks the fact that the approach fits very well with modern measurement theory with its notions of the conditioned state and quantum trajectory. In addition, what we know of as the Copenhagen interpretation is a later 1950s development and some of the earlier pioneers like Bohr did not talk of wave function collapse. In fact, if one takes these earlier ideas and mixes them with later insights of decoherence, a much more satisfying version of Copenhagen quantum mechanics emerges, one for which the collapse of the wave function is seen to be a harmless book keeping device. Along the way, we explain why chaotic systems lead to wave functions that spread out quickly on macroscopic scales implying that Schrödinger cat states are the norm rather than curiosities generated in physicists’ laboratories. We then describe how the conditioned state of a quantum system depends crucially on how the system is monitored illustrating this with the example of a decaying atom monitored with a time of arrival photon detector, leading to Bohr’s quantum jumps. On the other hand, other kinds of detection lead to much smoother behaviour, providing yet another example of complementarity. Finally we explain how classical behaviour emerges, including classical mechanics but also thermodynamics.     

Concentration on minimal submanifolds for a Yamabe-type problem

We construct solutions to a Yamabe-type problem on a Riemannian manifold M without boundary and of dimension greater than 2, with nonlinearity close to higher critical Sobolev exponents. These solutions concentrate their mass around a nondegenerate minimal submanifold of M, provided a certain geometric condition involving the sectional curvatures is satisfied. A connection with the solution of a class of PDE's on the submanifold with a singular term of attractive or repulsive type is established.     

Stationary focusing mean-field games

We consider stationary viscous mean-field games (MFG) systems in the case of local, decreasing and unbounded coupling. These systems arise in ergodic MFG theory and describe Nash equilibria of games with a large number of agents aiming at aggregation. We show how the dimension of the state space, the behavior of the coupling, and the Hamiltonian at infinity affect the existence and nonexistence of regular solutions. Our approach relies on the study of Sobolev regularity of the invariant measure and a blow-up procedure that is calibrated on the scaling properties of the system. In very special cases, we observe uniqueness of solutions. Finally, we apply our methods to obtain new existence results for MFG systems with competition, namely, when the coupling is local and increasing.     

基于单帧变形条纹的物体三维位移和速度测量

用隔行扫描摄像机采集到的运动物体单帧变形条纹测量三维位移和速度.该方法将一帧变形条纹分成两个单场,利用傅里叶变换轮廓术重建三维面形,从单场条纹的调制度中提取二值化模板,计算质心获得亚像素匹配定位点,通过双三次插值和标定,实现了一个场周期时间内三个维度上的位移和平均速度的测量.匀速运动物体实验结果表明:被测速度的最大绝对误差为0.6 mm/s,相对误差为0.57%.该方法仅用一帧变形条纹即可测量运动物体的三维位移和速度,提高了时间分辨率和测量准确度.     

基于VPX架构的测控通信综合测试系统设计

针对传统测控通信系统测试设备种类多、数量大、设备间连接关系复杂,难以满足当前型号任务快速、通用、集成的测试需求,提出了一种基于VPX总线架构的测控通信综合测试系统。系统将以往型号测试采用的前端设备、变频设备、基带设备综合集成,以VPX板卡形式集成到一台机箱,利用背板高速串行总线替代传统设备间电缆,显著简化了系统组成,提高测试设备通用性。     

基于C++Builder的换热器性能试验平台测控软件的开发

换热器性能测试是换热器设计过程中的重要环节,对其结构优化及性能评估具有重要作用。针对传统的换热器性能测试系统存在试验周期长、组合方案少,自动化水平不高、可重用应用性较差等不足,文章基于工业控制计算机和C++ Builder软件平台开发了换热器性能试验测控与仿真系统。该系统实现了试验工况参数的控制与过程仿真、试验数据的采集记录与分析处理等各项操作的自动化。文章在简要介绍换热器性能测试系统硬件设计的基础上,具体结合系统硬件介绍了利用C++ Builder制作的换热器仿真实验测控系统的方法及过程,最后给出换热器性能测试仿真实验用户界面及仿真实验运行结果。试验结果表明,测控系统具有交互界面良好、使用方便,可靠性高等特点,能够较好地满足换热器性能测试的要求。     

精密离心机动态半径的定位测量技术研究

精密离心机动态半径是影响精密离心机输出加速度精度的主要参数。对于高精度精密离心机的研制,必须对动态半径进行精密测量,并将测量结果作为补偿分量加入到精密离心机输出加速度修正数学模型中,以获得精确的加速度信号,同时为精密离心机输出加速度的精确评定奠定基础。本文介绍了精密离心机动态半径的外基准定位测试技术,包括多个定位平台的定位测试技术论证、测试系统配置等。该方法已应用于某高精度精密离心机动态半径测量中,实测结果表明,采用这种测量方法,动态半径的测量标准差为σ=0.21μm,其测量精度满足高精度精密离心机研制的技术指标要求。     

测定固体催化剂表面酸碱分布新方法的研究

酸碱催化是一类很重要的催化反应,酸碱强度分布和酸碱反应类型之间有着对应关系,因此,对表面酸碱的测定具有重要的意义。 固体表面酸碱的测定方法很多,常用的是Hammett指示剂酸碱滴定法,但这种方法不能用于测定有色催化剂,神保等研究的Al_2O_3和硅铝上苯酚的升温脱附曲线表明,Al_2O_3上有较强的碱性吸附点。Webb用HF-Al_2O_3吸附NH_3后再脱附并计算表面吸附的NH_3量,认为表面吸附的NH_3多,则表面酸也强,Shirasaki在SiO_2-Al_2O_3上吸附吡啶等气体后,以吸附量x对da/dx(s为吸附热)作图,得到酸碱分布图,Zetllemoyey用吸附热对吸附量的倒数作