On the geometry of a modern imaging diffractometer

1999 ◽  
Vol 55 (3) ◽  
pp. 543-557 ◽  
Author(s):  
W. A. Paciorek ◽  
M. Meyer ◽  
G. Chapuis
Keyword(s):  
Single Crystal ◽  
Least Squares ◽  
Least Squares Method ◽  
Measurement Data ◽  
Modern Imaging

The geometry of a modern imaging diffractometer is discussed in detail. A method to find all relevant instrument parameters from the control single-crystal measurement data is proposed and the limitations of such a procedure are indicated. Optimization of the instrument parameters by the least-squares method is presented.

A least-squares method for the determination of the orientation matrix in single-crystal diffractometry

1970 ◽  
Vol 26 (2) ◽  
pp. 295-296 ◽  
Author(s):  
K. Tichý
Keyword(s):  
Single Crystal ◽  
Least Squares ◽  
Least Squares Method ◽  
Reciprocal Vector ◽  
Orientation Matrix ◽  
The Matrix

An appropriate choice of the function minimized permits linearization of the least-squares determination of the matrix which transforms the diffraction indices into the components of the reciprocal vector in the diffractometer φ-axis system of coordinates. The coefficients of the least-squares equations are based on diffraction indices and measured diffractometer angles of three or more non-coplanar setting reflexions.

scholarly journals TREATMENT OF GEODETIC SURVEY DATA AS FUZZY VECTORS

2015 ◽  
Vol XL-3/W3 ◽  
pp. 29-33
Author(s):  
G. Navratil ◽  
E. Heer ◽  
J. Hahn
Keyword(s):  
Normal Distribution ◽  
Least Squares ◽  
Survey Data ◽  
Measurement Errors ◽  
Least Squares Method ◽  
Measurement Data ◽  
Geodetic Survey ◽  
Present Measurement ◽  
A Value ◽  
Light Signals

Geodetic survey data are typically analysed using the assumption that measurement errors can be modelled as noise. The least squares method models noise with the normal distribution and is based on the assumption that it selects measurements with the highest probability value (Ghilani, 2010, p. 179f). There are environment situations where no clear maximum for a measurement can be detected. This can happen, for example, if surveys take place in foggy conditions causing diffusion of light signals. This presents a problem for automated systems because the standard assumption of the least squares method does not hold. A measurement system trying to return a crisp value will produce an arbitrary value that lies within the area of maximum value. However repeating the measurement is unlikely to create a value following a normal distribution, which happens if measurement errors can be modelled as noise. In this article we describe a laboratory experiment that reproduces conditions similar to a foggy situation and present measurement data gathered from this setup. Furthermore we propose methods based on fuzzy set theory to evaluate the data from our measurement.

Crystal Structure of ζ2' Martensite in Au-49.5at%Cd Alloy

1991 ◽  
Vol 246 ◽  
Author(s):  
Yutaka Emura ◽  
Takuya Ohba ◽  
Kazuhiro Otsuka
Keyword(s):  
Crystal Structure ◽  
Single Crystal ◽  
Crystal Lattice ◽  
Least Squares ◽  
Least Squares Method ◽  
Diffraction Method ◽  
X Ray Diffraction ◽  
Full Matrix ◽  
X Ray ◽  
Lattice Constants

AbstractCrystal structure of the ζ2' martensite in a Au-49.5at%Cd ally has been analyzed by the single crystal x-ray diffraction method. The crystal lattice was trigonal and the lattice constants were a:0.8095(3) and c=o.57940(6) nm. There were 18 atoms in a unit cell. The space group was P3, which was different from that previously determined by Vatanayon and Hehemann. The structure was refined by the full matrix least squares method to a final R factor of 7.8% and a weighted R factor of 4.1%.

Total Least-Squares Methods for Active View Registration of Three-Dimensional Line Laser Scanning Data

2004 ◽  
Vol 127 (1) ◽  
pp. 50-56 ◽  
Author(s):  
F. Xi ◽  
D. Nancoo ◽  
G. Knopf
Keyword(s):  
Least Squares ◽  
Laser Scanning ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Measurement Data ◽  
Ordinary Least Squares ◽  
Total Least Squares ◽  
Position Measurement ◽  
Point Position ◽  
Ordinary Least Squares Method

In this paper a method is proposed to register three-dimensional line laser scanning data acquired in two different viewpoints. The proposed method is based on three-point position measurement by scanning three reference balls to determine the transformation between two views. Since there are errors in laser scanning data and sphere fitting, the two sets of three-point position measurement data at two different views are both subject to errors. For this reason, total least-squares methods are applied to determine the transformation, because they take into consideration the errors both at inputs and outputs. Simulations and experiment are carried to compare three methods, namely, ordinary least-squares method, unconstrained total least-squares method, and constrained total least-squares method. It is found that the last method gives the most accurate results.

scholarly journals Uncertainty Analysis and Experimental Validation of Identifying the Governing Equation of an Oscillator Using Sparse Regression

2022 ◽  
Vol 12 (2) ◽  
pp. 747
Author(s):  
Yaxiong Ren ◽  
Christian Adams ◽  
Tobias Melz
Keyword(s):  
Least Squares ◽  
Domain Knowledge ◽  
Least Squares Method ◽  
Nonlinear Dynamical Systems ◽  
Measurement Data ◽  
Estimation Method ◽  
Excitation Amplitude ◽  
Coefficient Of Determination ◽  
Sparse Regression ◽  
Single Mass

In recent years, the rapid growth of computing technology has enabled identifying mathematical models for vibration systems using measurement data instead of domain knowledge. Within this category, the method Sparse Identification of Nonlinear Dynamical Systems (SINDy) shows potential for interpretable identification. Therefore, in this work, a procedure of system identification based on the SINDy framework is developed and validated on a single-mass oscillator. To estimate the parameters in the SINDy model, two sparse regression methods are discussed. Compared with the Least Squares method with Sequential Threshold (LSST), which is the original estimation method from SINDy, the Least Squares method Post-LASSO (LSPL) shows better performance in numerical Monte Carlo Simulations (MCSs) of a single-mass oscillator in terms of sparseness, convergence, identified eigenfrequency, and coefficient of determination. Furthermore, the developed method SINDy-LSPL was successfully implemented with real measurement data of a single-mass oscillator with known theoretical parameters. The identified parameters using a sweep signal as excitation are more consistent and accurate than those identified using impulse excitation. In both cases, there exists a dependency of the identified parameter on the excitation amplitude that should be investigated in further research.

scholarly journals The Positioning of the Aircraft Using GPS/GLONASS Data

2019 ◽  
Vol 49 (3) ◽  
pp. 65-96
Author(s):  
Kamil Krasuski ◽  
Ewelina Kobiałka ◽  
Janusz Ćwiklak ◽  
Marek Grzegorzewski
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Measurement Data ◽  
Reference Trajectory ◽  
Flight Trajectory ◽  
Differential Technique ◽  
Stochastic Processing ◽  
Test Flight ◽  
Research Experiment

Abstract The article presents the results of aircraft positioning using GPS/GLONASS data in air navigation. In the work, the flight trajectory of the Cessna 172 aircraft was determined on the basis of GPS, GLONASS and GPS/GLONASS data. The coordinates of the Cessna 172 were determined using the least squares method in a stochastic processing compliant with the ICAO recommendations. In the air test, the Cessna 172 made a test flight over EPDE military airfield in Dęblin. The GPS, GLONASS and GPS/GLONASS measurement data from the Topcon HiperPro on-board aircraft installed on the Cessna 172 aircraft were used in the research experiment. The coordinates of the Cessna 172 in the geocentric XYZ and ellipsoidal BLh were compared with the precise flight reference trajectory determined from the differential technique RTK-OTF.

scholarly journals Quantitative Measurement of Path Loss Model Adaptation Using the Least Squares Method in an Urban DVB-T2 System

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Pitak Keawbunsong ◽  
Sarun Duangsuwan ◽  
Pichaya Supanakoon ◽  
Sathaporn Promwong
Keyword(s):  
Least Squares ◽  
Quantitative Measurement ◽  
Least Squares Method ◽  
Measurement Data ◽  
Path Loss ◽  
Model Adaptation ◽  
Loss Model ◽  
Path Loss Model ◽  
Proposed Model ◽  
Using Data

The aim of this paper was to propose quantitative measurement of path loss model adaptation in urban radio propagation for a second-generation, terrestrial digital video broadcasting standard (DVB-T2) system. The measurement data was analyzed using data processing based on the least squares (LS) method to verify the probabilistic quantitation of realistic data measurement such as mean error (ME), root mean square error (RMSE), and standard deviation of error (SD), as well as relative error (RE). To distinguish the experimental evaluation, the researchers compared between the conventional Hata path loss model and the proposed model. The result showed that path loss based on the proposed model was more accurate in predicting the quantitative measurement of propagation data properly.

X-ray powder diffraction analysis of adducts triglycine fluoroberyllic acid and triglycine selenic acid for pyroelectric application

2001 ◽  
Vol 16 (3) ◽  
pp. 167-169 ◽  
Author(s):  
Yunxia Che ◽  
Jimin Zheng ◽  
Jianmin Hao ◽  
Lianqing Chu
Keyword(s):  
Crystal Structure ◽  
Single Crystal ◽  
Diffraction Analysis ◽  
Least Squares ◽  
Powder Diffraction ◽  
Structure Data ◽  
Crystal Structure Data ◽  
Least Squares Method ◽  
Lattice Parameters ◽  
X Ray

Two adducts (NH2CH2COOH)3⋅H2BeF4(TGFb) and (NH2CH2COOH)3⋅H2SeO4(TGSe) were obtained and characterized by X-ray powder diffraction. The samples were indexed using the TREOR program [Werner, Z. Kristallogr. Kristallogeom. Kristallphys. Kristallchem. 120, 375–387 (1964)] on a monoclinic unit cell. The lattice parameters of adducts TGFb and TGSe were refined by a least-squares method using the Lattice Constant Refinement Program of the Rikagu software. The refined lattice parameters are a=9.1589(9) Å, b=12.6204(13) Å, c=5.6966(8) Å, β=105.451(9)° for TGFb. The Smith and Snyder figure [Smith and Snyder, J. Appl. Crystallogr. 12, 60–65 (1979)] is F30=39.4(0.0141,54). The refined lattice parameters a=9.5063(11) Å, b=12.8281(10) Å, c=5.8682(7) Å, β=110.353(77)° for TGSe. The Smith and Snyder figure is F30=39(0.0106,73). The powder diffraction results are in agreement with those obtained from single crystal structure data.

Statistical Analysis of Residual Stress Profiles Using a Heuristic Method

2008 ◽  
Author(s):  
H. Teng ◽  
S. K. Bate ◽  
D. W. Beardsmore
Keyword(s):  
Residual Stress ◽  
Statistical Analysis ◽  
Least Squares ◽  
Least Squares Method ◽  
Expert Knowledge ◽  
Heuristic Method ◽  
Measurement Data ◽  
Expert Judgement ◽  
Stress Profile ◽  
Residual Stress Profile

In this paper we present a recently developed heuristic method for statistical analysis of residual stress that is based on a combination of the weighted least-squares method and the application of expert judgement. The least-squares method allows a model of the best residual stress profile to be determined as a linear combination of basis functions; the expert knowledge gives the flexibility of applying expert judgement to determine the weights from the observed scatter in the residual stress data. The heuristic method has been applied to a set of measurement data of a Welded Bead-on-Plate specimen. The results show that with the heuristic method, it is possible to obtain less conservative residual stress profile to a known confidence level.

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