Modeling of Absolute Distance Meter Shift Inside a Laser Tracker

2017 ◽  
Author(s):  
He Li ◽  
Robert G. Landers ◽  
Douglas A. Bristow
Keyword(s):  
Measurement Errors ◽  
Radial Distance ◽  
Radial Component ◽  
Measurement Range ◽  
Error Modeling ◽  
Laser Tracker ◽  
Absolute Distance ◽  
Proposed Model ◽  
Temperature Constant ◽  
Shift Model

In the measurement of machine tool and robot geometric errors, one of the most extensively used instruments is the Laser Tracker (LT). Errors in the LT measurements will decrease the effectiveness of the error modeling and compensation methods that utilize these measurements. When the LT’s Absolute Distance Meter (ADM) is used without frequent referencing to a home position, large and long-term shifts occur. The ADM shift directly introduces errors in the radial component of every measurement in spherical coordinates, which will result in measurement errors in the Cartesian coordinates. Although the ADM shift is addressed in newer LT designs using internal referencing hardware, this paper presents a pragmatic and efficient software solution to ADM shift for LTs in which the internal referencing hardware is not embedded. The LT was measured for 22 hr in a temperature-constant room to examine the ADM shift effects on measurements. An ADM shift model was then proposed by assuming that the ADM shift equally affects radial components of all measurements wherever the target is, as long as it is within the measurement range. Another experiment was then performed to test the validity of the proposed model. After the model was identified and errors were corrected, the maximum temporal variation in the radial distance measurement is reduced by 80–86%.

scholarly journals LABORATORY TESTING OF LEICA AT401 LASER TRACKER

2016 ◽  
Vol 56 (2) ◽  
pp. 88 ◽  
Author(s):  
Filip Dvořáček
Keyword(s):  
Laboratory Testing ◽  
Laboratory Tests ◽  
Angle Measurement ◽  
Distance Measurement ◽  
Additive Constant ◽  
Laser Tracker ◽  
Simple Test ◽  
Absolute Distance ◽  
Warm Up ◽  
The Stability

<p>This paper describes laboratory tests on a Leica AT401laser tracker. As the newer Leica AT402 model also uses the same firmware package, most of the results should also be valid for this device. First, we present the instrument’s firmware errors and the software used for testing. The ASME B89.4.19-2006 standard for testing laser trackers is briefly presented. The warm-up effect of the instrument is inspected with respect to both angle measurement and distance measurement. The absolute distance meter (ADM) is compared with a laboratory interferometer on a 30-meter long rail and also on a bench with automated movement of the carriage of the reflector. A time series of measurements for determining the additive constant is evaluated. A simple test of the stability of the distance measurement in field conditions is introduced. Most of the tests were carried out at the Research Institute of Geodesy, Topography and Cartography (RIGTC) and at the Faculty of Civil Engineering (FCE) of the Czech Technical University in Prague (CTU).</p>

Error sources and models of the laser tracker without a beam steering mirror

2021 ◽  
Author(s):  
Radoslav Choleva ◽  
Alojz Kopáčik
Keyword(s):  
Measurement Accuracy ◽  
Beam Steering ◽  
Systematic Errors ◽  
Error Modeling ◽  
Laser Tracker ◽  
High Demand ◽  
Error Sources ◽  
Error Models ◽  
Measurement Results

AbstractThe laser tracker is a widely used instrument in many industrial and metrological applications with high demand measurement accuracy. Imperfections in construction and misalignment of individual parts deliver systematic errors in the measurement results. All error sources need to be identified and reduced to the minimum to achieve the best possible accuracy. The paper summarizes error sources of the laser tracker without beam steering mirror with emphasis on error modeling. Descriptions of error models are provided for the static and kinematic type of measurement.

scholarly journals Optical Setup for Error Compensation in a Laser Triangulation System

Sensors ◽  
2020 ◽  
Vol 20 (17) ◽  
pp. 4949
Author(s):  
Patrick Kienle ◽  
Lorena Batarilo ◽  
Markus Akgül ◽  
Michael H. Köhler ◽  
Kun Wang ◽  
...  
Keyword(s):  
Thermal Expansion ◽  
Measurement Errors ◽  
Beam Splitter ◽  
Reference Beam ◽  
Cost Effective ◽  
Laser Triangulation ◽  
Absolute Distance ◽  
Error Sources ◽  
Optical Setup ◽  
Achievable Accuracy

Absolute distance measurement is a field of research with a large variety of applications. Laser triangulation is a well-tested and developed technique using geometric relations to calculate the absolute distance to an object. The advantages of laser triangulation include its simple and cost-effective setup with yet a high achievable accuracy and resolution in short distances. A main problem of the technology is that even small changes of the optomechanical setup, e.g., due to thermal expansion, lead to significant measurement errors. Therefore, in this work, we introduce an optical setup containing only a beam splitter and a mirror, which splits the laser into a measurement beam and a reference beam. The reference beam can then be used to compensate for different error sources, such as laser beam dithering or shifts of the measurement setup due to the thermal expansion of the components. The effectiveness of this setup is proven by extensive simulations and measurements. The compensation setup improves the deviation in static measurements by up to 75%, whereas the measurement uncertainty at a distance of 1 m can be reduced to 85 μm. Consequently, this compensation setup can improve the accuracy of classical laser triangulation devices and make them more robust against changes in environmental conditions.

Better estimation of origin–destination matrix using automated intersection movement count data

2015 ◽  
Vol 42 (7) ◽  
pp. 490-502 ◽  
Author(s):  
Hediye Tuydes-Yaman ◽  
Oruc Altintasi ◽  
Nuri Sendil
Keyword(s):  
Measurement Errors ◽  
Programming Model ◽  
A Priori ◽  
Mathematical Formulation ◽  
A Priori Information ◽  
Matrix Estimation ◽  
Flow Estimation ◽  
Proposed Model ◽  
Priori Information ◽  
Link Count

Intersection movements carry more disaggregate information about origin–destination (O–D) flows than link counts in a traffic network. In this paper, a mathematical formulation is presented for O–D matrix estimation using intersection counts, which is based on an existing linear programming model employing link counts. The proposed model estimates static O–D flows for uncongested networks assuming no a priori information on the O–D matrix. Both models were tested in two hypothetical networks previously used in O–D matrix studies to monitor their performances assuming various numbers of count location and measurement errors. Two new measures were proposed to evaluate the model characteristics of O–D flow estimation using traffic counts. While both link count based and intersection count based models performed with the same success under complete data collection assumption, intersection count based formulation estimated the O–D flows more successfully under decreasing number of observation locations. Also, the results of the 30 measurement error scenarios revealed that it performs more robustly than the link count based one; thus, it better estimates the O–D flows.

scholarly journals The tilt of the velocity ellipsoid in the Milky Way with Gaia DR2

2019 ◽  
Vol 629 ◽  
pp. A70 ◽  
Author(s):  
J. H. J. Hagen ◽  
A. Helmi ◽  
P. T. de Zeeuw ◽  
L. Posti
Keyword(s):  
Velocity Distribution ◽  
Measurement Errors ◽  
Milky Way ◽  
Galactic Plane ◽  
Radial Distance ◽  
Zero Point ◽  
Dark Halo ◽  
The Galaxy ◽  
Dark Matter Distribution ◽  
Global Zero

The velocity distribution of stars is a sensitive probe of the gravitational potential of the Galaxy, and hence of its dark matter distribution. In particular, the shape of the dark halo (e.g. spherical, oblate, or prolate) determines velocity correlations, and different halo geometries are expected to result in measurable differences. Here we explore and interpret the correlations in the (vR, vz)-velocity distribution as a function of position in the Milky Way. We selected a high-quality sample of stars from the Gaia DR2 catalogue and characterised the orientation of the velocity distribution or tilt angle over a radial distance range of [4 − 13] kpc and up to 3.5 kpc away from the Galactic plane while taking into account the effects of the measurement errors. We find that the tilt angles change from spherical alignment in the inner Galaxy (R ∼ 4 kpc) towards more cylindrical alignments in the outer Galaxy (R ∼ 11 kpc) when using distances that take a global zero-point offset in the parallax of −29 μas. However, if the amplitude of this offset is underestimated, then the inferred tilt angles in the outer Galaxy only appear shallower and are intrinsically more consistent with spherical alignment for an offset as large as −54 μas. We further find that the tilt angles do not seem to strongly vary with Galactic azimuth and that different stellar populations depict similar tilt angles. Therefore we introduce a simple analytic function that describes the trends found over the full radial range. Since the systematic parallax errors in Gaia DR2 depend on celestial position, magnitude, and colour in complex ways, it is not possible to fully correct for them. Therefore it will be particularly important for dynamical modelling of the Milky Way to thoroughly characterise the systematics in astrometry in future Gaia data releases.

V̇o2, V̇co2, and RQ in a respiratory chamber: accurate estimation based on a new mathematical model using the Kalman-Bucy method

2004 ◽  
Vol 96 (3) ◽  
pp. 1045-1054 ◽  
Author(s):  
L. Granato ◽  
A. Brandes ◽  
C. Bruni ◽  
A. V. Greco ◽  
G. Mingrone
Keyword(s):  
Mathematical Model ◽  
Measurement Errors ◽  
Estimation Method ◽  
Accurate Estimation ◽  
Production Rates ◽  
Estimation Errors ◽  
Respiratory Chamber ◽  
Residual Noise ◽  
Proposed Model

A respiratory chamber is used for monitoring O2 consumption (V̇o2), CO2 production (V̇co2), and respiratory quotient (RQ) in humans, enabling long term (24-h) observation under free-living conditions. Computation of V̇o2 and V̇co2 is currently done by inversion of a mass balance equation, with no consideration of measurement errors and other uncertainties. To improve the accuracy of the results, a new mathematical model is suggested in the present study explicitly accounting for the presence of such uncertainties and error sources and enabling the use of optimal filtering methods. Experiments have been realized, injecting known gas quantities and estimating them using the proposed mathematical model and the Kalman-Bucy (KB) estimation method. The estimates obtained reproduce the known production rates much better than standard methods; in particular, the mean error when fitting the known production rates is 15.6 ± 0.9 vs. 186 ± 36 ml/min obtained using a conventional method. Experiments with 11 humans were carried out as well, where V̇o2 and V̇co2 were estimated. The variance of the estimation errors, produced by the KB method, appears relatively small and rapidly convergent. Spectral analysis is performed to assess the residual noise content in the estimates, revealing large improvement: 2.9 ± 0.8 vs. 3,440 ± 824 (ml/min)2 and 1.8 ± 0.5 vs. 2,057 ± 532 (ml/min)2, respectively, for V̇o2 and V̇co2 estimates. Consequently, the accuracy of the computed RQ is also highly improved (0.3 × 10-4 vs. 800 × 10-4). The presented study demonstrates the validity of the proposed model and the improvement in the results when using a KB estimation method to resolve it.

The structure of flat, counter-flow diffusion flames

1964 ◽  
Vol 279 (1379) ◽  
pp. 544-561 ◽  
Keyword(s):  
Heat Release ◽  
Diffusion Flames ◽  
Radial Distance ◽  
Radial Component ◽  
Gas Composition ◽  
Counter Flow ◽  
Stagnation Points ◽  
Kinetics Studies ◽  
Rate Of Heat Release ◽  
Maximum Temperatures

It is shown that the establishment of a large flat diffusion flame in the counter-flow régime of opposed jets of two gaseous reactants could very considerably extend the range of applicability of flame-kinetics studies by structure analysis. Suitable flames are stabilized and their characteristics and behaviour described. The flow patterns, spectrum , refractive index fields, temperature distributions and gas composition at a few selected points are studied for ethylene flames by methods including the use of thermocouples, sodium line reversal, illuminated particle tracks, interferometry and gas chromatography. The aerodynamic and thermal structures are analyzed to yield the distribution of the rate of heat release per unit volume. The following are among the conclusions: two stagnation points and two planes which particles cannot cross occur when the centres of the reaction and aerodynamic systems are made to coincide—this can be prevented by displacing the plane of stoichiometry from that of aerodynamic symmetry; the radial component of flow velocity is proportional to radial distance in the central parts. Isotherms are parallel to each other and to the flame, away from the edges, but maximum temperatures occur at the periphery, at least for some flames. The heat release profile shows regions where small amounts of heat are absorbed; C 2 H 6 and H 2 appear on the oxidant side of the flame. The most significant observation is that the zone of heat release is about ten times wider than would be expected of the equivalent pre-mixed flame and this makes the method applicable to the study of faster flame reactions.

scholarly journals A NONPARAMETRIC SYSTEM IDENTIFICATION BASED ON TRANSIENT ANALYSIS WITH PLANT PROCESS OF HEAT EXCHANGER AS STUDY CASE

2015 ◽  
Vol 1 (1) ◽  
pp. 19 ◽  
Author(s):  
T. Mulyana
Keyword(s):  
Heat Exchanger ◽  
Transient Analysis ◽  
Identification System ◽  
Calculation Error ◽  
First Order ◽  
Proposed Model ◽  
Study Case ◽  
Temperature Constant ◽  
Plant Process ◽  
Existing Data

<p class="TRANSAffiliation"><span>In this article, a nonparametric identification system based on transient analysis has been reviewed, by taking the case in some of the data plant process of heat exchanger. Results of the study found that the first-order transfer function without time-delay the proposed model to the data with a temperature constant value is 35.20 ºC and the time constant is 7200 seconds. This model has been fit to meet the existing data proving that the results of the calculation error do not exceed 2%.</span></p>

Bayesian cure fraction models with measurement error in the scale mixture of normal distribution

2020 ◽  
Vol 29 (9) ◽  
pp. 2411-2444
Author(s):  
Anna R S Marinho ◽  
Rosangela H Loschi
Keyword(s):  
Measurement Error ◽  
Normal Distribution ◽  
Measurement Errors ◽  
Error Variance ◽  
Scale Mixture ◽  
Time To Event Data ◽  
Proposed Model ◽  
Cure Fraction ◽  
Measurement Error Variance ◽  
Fraction Models

Cure fraction models have been widely used to model time-to-event data when part of the individuals survives long-term after disease and are considered cured. Most cure fraction models neglect the measurement error that some covariates may experience which leads to poor estimates for the cure fraction. We introduce a Bayesian promotion time cure model that accounts for both mismeasured covariates and atypical measurement errors. This is attained by assuming a scale mixture of the normal distribution to describe the uncertainty about the measurement error. Extending previous works, we also assume that the measurement error variance is unknown and should be estimated. Three classes of prior distributions are assumed to model the uncertainty about the measurement error variance. Simulation studies are performed evaluating the proposed model in different scenarios and comparing it to the standard promotion time cure fraction model. Results show that the proposed models are competitive ones. The proposed model is fitted to analyze a dataset from a melanoma clinical trial assuming that the Breslow depth is mismeasured.

scholarly journals A Compact Multifrequency Measurement System Based on an Integrated Frequency-Scanning Generator

2020 ◽  
Vol 10 (23) ◽  
pp. 8571
Author(s):  
Nuannuan Shi ◽  
Tengfei Hao ◽  
Wei Li ◽  
Ming Li
Keyword(s):  
Measurement System ◽  
Measurement Errors ◽  
Microwave Frequency ◽  
Frequency Measurement ◽  
Measurement Range ◽  
Single Frequency ◽  
Laser Array ◽  
Large Bandwidth ◽  
Frequency Scanning ◽  
Mapping Technology

A compact multifrequency measurement system based on frequency-to-time mapping technology is proposed and experimentally demonstrated using an integrated frequency scanning signal generator. The relationship between the input microwave frequency and the time difference of a pair of pulses is established to realize the frequency information mapping to the time information. As a main part in the proposed frequency measurement system, the frequency-scanning signal is generated by heterodyning of two lasers with the monolithic integrated laser array, of which one is modulated on a saw-tooth signal. In the proposed frequency measurement system, it can measure single/multiple frequency microwave signals with a large bandwidth for high resolution and flexible tunable measurement range for multifrequency band. In the experimental demonstration, the single frequency measurement errors are less than 90 MHz within the measurement range from 4 to 12 GHz. For two-tone signal, the measurement resolution reaches about 150 MHz.

Sign in / Sign up

Export Citation Format

Share Document