Estimation of uncertainty of mean velocity of flue gas in a conduit as determined by the traverse method within the gravimetric measurement of particulate concentration

In gravimetric measurements of dust emissions from industrial technological plants, the required mean gas velocity in a conduit is often determined by Pitot traverse method. It is commonly seen as a method giving good approximate values of mean gas velocity, although the actual rate of this approximation is not considered in the analysis of measurement results. It was seen that there was a need to establish what magnitude of error might occur in practice due to the small number of measurement points and typical non-uniformity of the gas velocity profiles in conduits of rectangular cross-section. The calculations were based on the concept of treating a measurement plane as one consisting of a set of elementary planes. The elementary gas velocity profiles in these elementary planes were simulated, the mean velocity for these profiles were calculated based on point velocity values, and the measurement uncertainty of this mean velocity determined. This uncertainty results in the uncertainty of the mean velocity across the entire measurement plane. It appears that, depending on the number of measurement points and gas velocity profile non-uniformity, the value is not small and is of the order of several percent, and hence needs to be taken into account in the budget of the combined uncertainty of mean velocity, which in turn contributes to the uncertainty of gas volumetric flow rate and dust pollutant mass flow rate.     

Uncertainty assessment of a prototype of multilateration coordinate measurement system

Large Volume Metrology is essential to many high value industries to go towards the factory of the future, but also to many science facilities for fine alignment of large structures. In this context, we have developed a multilateration coordinate measurement system, traceable to SI metre, and suitable for outdoor measurements or industrial environments. It is based on a high accuracy absolute distance meter developed in-house and shared between several measurement heads by fibre-optic links. Thus, from these measurement stations, multiple distance measurements of several positions of a target can be performed. At the end, coordinates of the heads and of the different target locations are determined using a multilateration algorithm with self-calibration.In this paper, the uncertainty of this multilateration coordinate measurement system is determined with a consistent metrological approach. First, 13 different sources of errors are listed and quantified. Then, thanks to Monte Carlo simulations, the standard uncertainty on a single absolute distance measurement is assessed to 4.7 μm. This includes the uncertainty contribution of the telemetric system itself, but also the contributions of the mechanical designs of the measurement heads and the target. Lastly, measurements of three-dimensional coordinates of target positions are performed in a control environment, then in a large workshop without temperature control: these measurements validate the uncertainty assessment of the system.     

Simultaneous interferometric measurement of the absolute thickness and surface shape of a transparent plate using wavelength tuning Fourier analysis and phase shifting

The absolute optical thickness and surface shape of optical devices are considered as the fundamental characteristics when designing optical equipment. The thickness and surface shape should be measured simultaneously to reduce cost. In this research, the absolute optical thickness and surface shape of a 6–mm-thick fused silica transparent plate of diameter 100 mm was measured simultaneously by a three-surface Fizeau interferometer. A measurement method combining the wavelength tuning Fourier and phase shifting technique was proposed. The absolute optical thickness that corresponds to the group refractive index was determined by wavelength tuning Fourier analysis. At the beginning and end of the wavelength tuning, the fractional phases of the interference fringes were measured by the phase shifting technique and optical thickness deviations with respect to the ordinary refractive index and surface shape were determined. These two kinds of optical thicknesses were synthesized using the Sellmeier equation for the refractive index of fused silica glass, and the least square fitting method was used to determine the final absolute optical thickness distribution. The experimental results indicate that the all the measurement uncertainties for the absolute optical thickness and surface shape were approximately 3 nm and 35 nm, respectively.     

How to measure actual tire shape in the rolling condition using Scanning LDV

This work presents the development of a new method which makes use of Scanning Laser Doppler Vibrometry (LDV) for the indirect measurement of the shape of the tire sidewall in the rolling condition.Scanning LDV is widely adopted for the measurement of vibrational Operational Deflection Shape (ODS) in rolling tires using either the Eulerian or the Lagrangian approach. Residual effects of geometry are usually removed by an AC coupling.This paper presents a new approach in LDV velocity data processing that allows the processing of the velocity data obtained with a Scanning LDV in the Eulerian approach on a rolling tire in order to obtain not only ODS but also static shape.This technique does not require additional sensors or systems since it is based only on signal processing.The uncertainty of the obtained result is also evaluated and a comparison with a state-of-the-art solution in shape measurement is presented.     

Machine tool calibration: Geometric test uncertainty depends on machine tool performance

In order to show a sufficient geometric performance, every machine tool has to be calibrated geometrically before it may come into operation. The geometric machine errors have to be identified. They can afterwards be compensated either mechanically or numerically in the machine control.Machine tools are usually calibrated geometrically by performing a sequence of different measurements to identify single errors such as squareness errors between linear axes, straightness errors, positioning errors etc.The uncertainty of such measurements is of course affected by the uncertainty of the measuring device under the given environmental conditions. Methods to describe such influences are widely known and applied.Other effects having an impact on the error parameters to be determined (e.g. squareness errors) are dependent on the performance of the machine tool under test. Neglected geometric errors, hysteresis and thermal drift affect the measurement result. Such effects may be much more important contributors to the overall test uncertainty than the measurement uncertainty of the measuring device.In this paper the problem of error interdependencies leading to a worse test uncertainty is explained. The occurrence of such effects is shown with exemplary measuring results. A method for estimating the overall test uncertainty even for complex measurements is introduced. The dependence of the test uncertainty on the geometric machine performance is explained.     

Integration of a laser interferometer and a CMM into a measurement system for measuring internal dimensions

In order to improve the existing comparative procedure for calibrating internal dimensions, we have developed a new measurement set-up for traceable absolute measurements. It consists of a co-ordinate measuring machine (CMM) and a laser interferometer (LI). The LI serves as a traceable measurement system, while the CMM is only used as a guiding system for the measuring probe. Extended research focused on defining probe parameters such as diameter, bending and indentation, as well as probing head repeatability and other error sources. The final goal of the research was to determine uncertainty of measurement under existing laboratory conditions. The main outcomes of the research and final uncertainty of measurement are presented in this article.     

Prototype cantilevers for quantitative lateral force microscopy

Prototype cantilevers are presented that enable quantitative surface force measurements using contact-mode atomic force microscopy (AFM). The "hammerhead" cantilevers facilitate precise optical lever system calibrations for cantilever flexure and torsion, enabling quantifiable adhesion measurements and friction measurements by lateral force microscopy (LFM). Critically, a single hammerhead cantilever of known flexural stiffness and probe length dimension can be used to perform both a system calibration as well as surface force measurements in situ, which greatly increases force measurement precision and accuracy. During LFM calibration mode, a hammerhead cantilever allows an optical lever "torque sensitivity" to be generated for the quantification of LFM friction forces. Precise calibrations were performed on two different AFM instruments, in which torque sensitivity values were specified with sub-percent relative uncertainty. To examine the potential for accurate lateral force measurements using the prototype cantilevers, finite element analysis predicted measurement errors of a few percent or less, which could be reduced via refinement of calibration methodology or cantilever design. The cantilevers are compatible with commercial AFM instrumentation and can be used for other AFM techniques such as contact imaging and dynamic mode measurements.     

System for measuring the coordinates of tire surfaces in transient conditions when rolling over obstacles: description of the system and performance analysis

This paper describes the development of a system for measuring surface coordinates (commonly known as "shape measurements") which is able to give the temporal evolution of the position of the tire sidewall in transient conditions (such as during braking, when there are potholes or when the road surface is uneven) which may or may not be reproducible. The system is based on the well-known technique of projecting and observing structured light using a digital camera with an optical axis which is slanted with respect to the axis of the projector. The transient nature of the phenomenon has led to the development of specific innovative solutions as regards image processing algorithms. This paper briefly describes the components which make up the measuring system and presents the results of the measurements carried out on the drum bench. It then analyses the performance of the measuring system and the sources of uncertainty which led to the development of the system for a specific dynamic application: impact with an obstacle (cleat test). The measuring system guaranteed a measurement uncertainty of 0.28 mm along the Z axis (the axial direction of the tire) with a measurement range of 250(X) x 80(Y) x 25(Z) mm(3), with the tire rolling at a speed of up to 30 km/h.     

Fundamental uncertainty analysis of flowrate measurement using the ultrasonic Doppler velocity profile method

The present paper describes a fundamental uncertainty analysis for a flowrate measurement in a pipe using an ultrasonic Doppler velocity profile method and an evaluation of the estimated uncertainty by an actual flow calibration. The uncertainties are estimated for internal factors originating from the measurement equipment; UVP provided by Met-Flow sa. and external factors depending on on-site measurements, such as the inclination angle of the ultrasonic transducer. The relative expanded uncertainty due to internal factors is estimated to be 0.34% with a coverage factor of 2. The relative external uncertainty including external factors is estimated to be from 0.42% to 2.13% depends on the inclination angle of the transducer. The results of the actual flow calibration under the same condition as the uncertainty analysis are within the range of uncertainty considering the internal factors.     

Interferometric,absolute sensor of angular micro-displacement

A design of a new, absolute sensor for measurement of an angular micro-displacement is presented. In this sensor deflections of incident laser beam generate changes of the constant of the interference fringes that are created by the double arm special interferometer. Fringe constant is determined using a CCD camera and proposed analysis algorithms. Sensor's operating principle and metrological properties are presented. Sensor was tested using reference interferometer. Obtained measurement uncertainty is equal to ±10 μrad in the multi-milliradian range. The concept of a two-sensor system for increasing twice the measuring range is presented.     

Alignment uncertainties in ideal indentation styli

In this work, the first and second order uncertainty contributors in depth-sensing hardness measurements are investigated. Each term in the hardness expanded uncertainty is examined to determine the typical sources and the magnitude errors contributed to the measurement. In particular, using simulations based on ideal indenter geometries the depth uncertainty with area function uncertainty due to rotational misalignments between the stylus and the specimen is evaluated. Three typical styli are simulated; standard Berkovich, modified Berkovich, and Vickers geometries. Considering the maximum allowable tip and tilt from ISO 14577, the area function uncertainty was less than 1%. Also considered is the effect of the twist about the central axis which shows that, because of the asymmetric shape, the Berkovich geometries have larger errors as a function of rotational deviations than the Vickers geometry from a perfect alignment.     

Metrological evaluation of skin conductance measurements

Electrodermal activity is a frequently measured physiological response in various applications. It is also being increasingly used in clinical applications. Numerous published papers report results of skin conductance measurements in absolute values, but few are concerned with the quality of results. This paper describes a procedure for metrological evaluation of skin conductance measurement. Three commercial devices for measuring skin conductance were calibrated by comparison with a precision digital ohmmeter used as a reference. Combined measurement uncertainty of skin conductance meters was calculated by means of uncertainty of reference instrument and uncertainties due to measurement repeatability, reproducibility, resolution and environmental condition. Additionally, a procedure for evaluation of the effect of electrode displacement and electrode gel was shown. A model of finger skin conductance profile was build. Measurement uncertainty analysis showed that contributions due to resolution and sensitivity of the measuring device, usually obtained from specifications, are negligible when compared to uncertainty of measuring method. Our results indicate that measurement uncertainty does not meet target uncertainty requirements for certain applications.     

A new method for defining the measurement-uncertainty model of CNC laser-triangulation scanner

This article examines the measurement uncertainty in terms of the incident angle, the object colour and the measurement distance for a Computer Numerical Control (CNC) laser-scanning process. It describes a new method for predicting the measurement uncertainty that simultaneously considers all three parameters. A set of measurements with different values for these parameters was made in order to describe the measurement uncertainty for the whole measuring range of the laser-scanning device. The final result of this research is an equation model that allows an accurate prediction of the measurement uncertainty within the investigated measurement field while the results of the extrapolated measurement field give an accuracy of the prediction that is better than 15%. In general, the model can also be useful as a measuring guideline for any other laser-triangulation measuring device, although the values would need to be adapted to each particular device. The, thus, obtained equation model could then be implemented into automatic inspection/control lines or used for self-adaptive measuring CNC paths to perform measurements in the optimal measuring range for a particular surface.     

光学原子力显微镜中的蒙特卡罗方法

扫描探针显微镜(Scanning probe microscopy,SPM)是显微镜的一个分支,它利用物理探针扫描标本形成样本表面图像.而原子力显微镜(Atomic force microscopy,AFM)是SPM中一种多功能的表面成像和测量工具,对导电、不导电、真空中、空气中或流体中的各种样本均可测量.原子力显微镜最面临的最大挑战之一是评估其在表面测量过程中所伴随的不确定度.本研究通过XYZ Phase的标定,对一台光学原子力显微镜进行了校准.该方法旨在克服在评估一些无法实验确定的不确定部件时遇到的困难,如尖端表面相互作用力和尖端几何.运用蒙特卡罗方法来确定根据相关容差和概率密度函数(PDFs)随机绘制参数而引起的相关不确定度.整个过程遵循《测量不确定度表示指南》(GUM)补编2.经本方法验证,原子力显微镜的评估不确定度为10nm左右.     

Evaluation of shape measurements by using non-orthogonal sine functions

Problems and experience with the development of an improved evaluation algorithm for shape measurements are discussed. The model bases are deterministic as well as stochastic shares as parts of the measuring value sequences. The application of a new approximation method with non-orthogonal sine functions is shown for different evaluation tasks. The new method avoids in principle a series of disadvantages of the usual evaluation methods connected with the finite measuring length and the finite number of measuring values. Taking two examples from measurement practice, the experience gained is shown. The first example results in a substantial data reduction and a significant reduction of measuring uncertainty. The second example is an extensive analysis of a surface profile. It becomes apparent that the typical periodic profile of a milled surface is superimposed by a considerable stochastic share.     

Derivation and comparison of fundamental uncertainty limits for laser-two-focus velocimetry,laser Doppler anemometry and Doppler global velocimetry

Laser-2-focus velocimetry (L2F), laser Doppler anemometry (LDA) and Doppler global velocimetry (DGV) are common measurement techniques for flow analysis, but a fundamental comparison of their minimum achievable measurement uncertainties is still missing. In order to reveal the measurement principle with the lowest uncertainty, the Cramér-Rao lower bounds (CRLB) are derived analytically regarding two inevitable fundamental disturbances: photon shot noise and thermal detector noise. The CRLB results are compared with each other assuming equal temporal resolutions. For both noise sources, a relative uncertainty limit results for L2F and LDA, and an absolute uncertainty limit for DGV. Hence, DGV seems to be appropriate for investigating high-speed flows. However, the threshold velocities strongly depend on the possible viewing angles. The CRLBs are calculated and compared with each other for typical conditions in turbomachinery as an example.     

Analytical estimation of measurement uncertainty in surface plate calibration by the Moody method using differential levels

Surface plate quality influences the calibration of artifacts, instruments, working gauges and, by extension, the quality of manufactured parts. A statement of uncertainty for the surface plate calibration is needed for conformance testing and for estimating uncertainty in calibrations that rely on the surface plate. An analytical approach to the estimate of uncertainty for a common measurement method is given. The residual height at each position on the surface is expressed in terms of the measurement parameters and the measured angles. Uncertainty of each residual height value is then derived following the common methods for propagation of uncertainty. The maximum uncertainty is at the center of the surface and the calculated bounds on error compare well with values of closure from actual measurements. The uncertainty of height values is proportional to the spacing of the measurement positions and to the squareroot of the number of positions. Using data from many plates of various size and quality, a generalized uncertainty in flatness for the measurement method was estimated. The derivations also allow calculations for specific applications. Finally, a method is proposed for reporting uncertainty in surface slope which is required for estimating uncertainties of items calibrated on a surface plate.     

Measurement uncertainty of torque measurements with rotating torque transducers in power test stands

The objective of the presented study is to introduce a method for estimating the measurement uncertainty of torque measurements. Unlike the well-known approaches, the uncertainty shall take into account the effects acting during torque measurement in industrial applications like power test stands. These effects include the effects also known from laboratory calibration like hysteresis, linearity or interpolation deviation, repeatability, reproducibility. Special emphasis is put on an estimation of their impact under the conditions in the power test stand. Additionally, further effects are included in the consideration, like temperature effects, the influences of parasitic loads and of rotational speed. The mathematical method for an estimation of the uncertainty is presented, the input quantities are discussed and suggestions are made as to how the uncertainty can be reduced for given applications.     

Flow field investigation in a rectangular shallow reservoir using UVP, LSPIV and numerical modelling

Low velocity and shallow-depth flow fields often are a challenge to most velocity measuring instruments. In the framework of a research project on reservoir sedimentation, the influence of the reservoir geometry on sediment transport and deposition was studied. An inexpensive and accurate technique for Large-Scale Particle Image Velocimetry (LSPIV) was developed to measure the surface velocity field in 2D. An Ultrasonic Doppler Velocity Profiler (UVP) and LSPIV techniques were used for verification and validation of the numerical simulations. The velocities measured by means of UVP allowed an instantaneous measurement of the 1D velocity profile over the whole flow depth. The turbulence large-scale structures and jet expansion in the basin have been determined based on UVP, LSPIV and numerical simulations. Vertical velocity distributions were defined to study the vertical velocity effect. UVP measurements confirm 2D flow map in shallow reservoir. LSPIV has potential to measure low velocities. The comparison between LSPIV, UVP and numerical simulation gives good agreements.