scholarly journals Measurement of Continuous Quantities and their Statistical Evaluation

2014 ◽  
Vol 44 (1) ◽  
pp. 25-32
Author(s):  
Reinhard Karl Viertl
Keyword(s):  
Mathematical Model ◽  
Statistical Analysis ◽  
Statistical Evaluation ◽  
Measurement Data ◽  
Real Numbers ◽  
Measurement Results ◽  
Continuous Quantities ◽  
Fuzzy Subsets

Measurement results of continuous quantities are always more or less imprecise. This imprecision is different from errors. The most suitable mathematical model to describe imprecision is by special fuzzy subsets of the set of real numbers R, called characterizing functions. The statistical analysis of fuzzy measurement data is subject of this paper. 

Statistical Analysis of the Roundness Error Data

2012 ◽  
Vol 472-475 ◽  
pp. 869-874 ◽  
Author(s):  
Zhao Peng Dong ◽  
Li Ling Huang ◽  
Hai Ting Xie ◽  
Fu Gui Huang
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Statistical Analysis ◽  
Normal Distribution ◽  
Mathematical Knowledge ◽  
Measurement Data ◽  
Roundness Error ◽  
Main Emphasis ◽  
The Mathematical Model ◽  
Roundness Measurement

In order to simulate the actual roundness measurement accurately, must find the mathematical model of the actual roundness data, the paper’s main emphasis is doing statistical analysis by plenty of measurement data of roundness, using mathematical knowledge to prove that the actual characteristics of roundness parameters obey the normal distribution, and providing the basis for subsequent computer simulation in the future

scholarly journals A Statistical Evaluation and Modeling on the Social Transitivity Behavior

2017 ◽  
Vol 5 (2) ◽  
Author(s):  
Chiao Yi Yang ◽  
Frederick Kin Hing Phoa ◽  
Yen-Sheng Chiang
Keyword(s):  
Mathematical Model ◽  
Social Network ◽  
Statistical Analysis ◽  
Social Environment ◽  
Statistical Evaluation ◽  
Experimental Results ◽  
Human Society ◽  
Key Factors ◽  
The Social ◽  
Sharing Behavior

Transitivity is one of the most important mechanisms to form a social network in a human society, but it remains unclear how such behavior is quantified and affected by some key factors, including the social environment and the participants' characters. This study investigates the sharing behavior based on the notion of transitivity and an experiment is conducted on a variety of populations from kindergarteners to teenagers. The key effects that have high impacts to the sharing behavior are identified from the statistical analysis of the experimental results. A mathematical model is built for the experimental results and its performance compared with other models is also illustrated.

A study on the key techniques of application of REVO five-axis system in non-orthogonal coordinate measuring machine

2016 ◽  
Vol 231 (4) ◽  
pp. 730-736 ◽  
Author(s):  
Haitao Zhang ◽  
Shugui Liu ◽  
Xinghua Li
Keyword(s):  
Mathematical Model ◽  
Measurement Data ◽  
Coordinate Measuring Machine ◽  
Coordinate Measuring Machines ◽  
Measurement Results ◽  
Measuring Machine ◽  
Key Techniques ◽  
Five Axis ◽  
The Mathematical Model ◽  
Body Theory

REVO five-axis system, designed for the orthogonal coordinate measuring machines, must be reconfigured for the application in the non-orthogonal coordinate measuring machines. First, in this article, error sources of the system and components of measurement data are analyzed; then, scale values of coordinate measuring machine axes, which are essential to derive the coordinates of measured points in non-orthogonal coordinate measuring machine, are separated out. Besides, the mathematical model of REVO is established based on the quasi-rigid body theory, from which the measurement results can be evaluated by data derived instead of that returned by the system. The effectiveness of both separation of scale values and mathematical model of REVO is proved by experiments and practice. The research of this article is of great significance to the application of REVO five-axis system in the non-orthogonal coordinate measuring machine.

scholarly journals Characterization and Correction of the Geometric Errors using a Confocal Microscope for Extended Topography Measurement, Part II: Experimental Study and Uncertainty Evaluation

Electronics ◽  
2019 ◽  
Vol 8 (11) ◽  
pp. 1217 ◽  
Author(s):  
Wang ◽  
Gómez ◽  
Yu
Keyword(s):  
Mathematical Model ◽  
Measurement Data ◽  
Confocal Microscope ◽  
Geometric Errors ◽  
Data Partition ◽  
The Monte Carlo Method ◽  
Measurement Results ◽  
The Mean ◽  
The Mathematical Model ◽  
Certified Values

This paper presents the experimental implementations of the mathematical models and algorithms developed in Part I. Two experiments are carried out. The first experiment determines the correction coefficients of the mathematical model. The dot grid target is measured, and the measurement data are processed by our developed and validated algorithms introduced in Part I. The values of the coefficients are indicated and analyzed. Uncertainties are evaluated using the Monte Carlo method. The second experiment measures a different area of the dot grid target. The measurement results are corrected according to the coefficients determined in the first experiment. The mean residual between the measured points and their corresponding certified values reduced 29.6% after the correction. The sum of squared errors reduced 47.7%. The methods and the algorithms for raw data processing, such as data partition, fittings of dots’ centers, K-means clustering, etc., are the same for the two experiments. The experimental results demonstrate that our method for the correction of the errors produced by the movement of the lateral stage of a confocal microscope is meaningful and practicable.

Profile Voltage on One Phase Cable Channel at Every Distance 17 Meters in All 102 Meter That was 1000 Watt with Least Square Method

2019 ◽  
Vol 16 (12) ◽  
pp. 5175-5179
Author(s):  
Sofiah ◽  
Abdul Majid ◽  
Cekmas Cekdin
Keyword(s):  
Mathematical Model ◽  
Measurement Data ◽  
Least Square Method ◽  
Equation Model ◽  
Least Square ◽  
Cable Channel ◽  
Percentage Difference ◽  
Measurement Results ◽  
The Mathematical Model

In this paper, it is discussed to determine a voltage modeling on a 102 meter one-phase cable channel which is loaded with a 1000 Watt lamp with the least square method. To obtain this method is by measuring the voltage at the points specified in the cable. After the measurement data is obtained then it is calculated to determine the mathematical model with the least square method. The least square method is a method for predicting a certain price. This method is also called the smallest quadratic method with the equation V = a + bX. With V is the measurement voltage (Volt) at distance X from the source, X distance from the source (meter), n ila a and b are calculated based on the measurement data. After the equation model is obtained, then we compare it with the measurement results. This comparison is useful to know what percentage difference between the results of the measurement and calculation.

scholarly journals Characterization and Correction of the Geometric Errors in Using Confocal Microscope for Extended Topography Measurement. Part II: Experimental Study and Uncertainty Evaluation

2019 ◽  
Author(s):  
Chen Wang ◽  
Emilio Gomez ◽  
Yingjie Yu
Keyword(s):  
Mathematical Model ◽  
Measurement Data ◽  
Confocal Microscope ◽  
Geometric Errors ◽  
Data Partition ◽  
The Monte Carlo Method ◽  
Measurement Results ◽  
The Mean ◽  
The Mathematical Model ◽  
Certified Values

This paper presents the experimental implementations of the mathematical models and algorithms developed in Part I. Two experiments are carried out. The first experiment aims at the determinations of the correction coefficients of the mathematical model. The dot grid target is measured and the measurement data are processed by our developed and validated algorithms introduced in Part I. The values of the coefficients are indicated and analysed. Uncertainties are evaluated with implementation of the Monte Carlo method. The second experiment measures a different area of the dot grid target. The measurement results are corrected according to the coefficients determined in the first experiment. The mean residual between the measured points and their corresponding certified values reduced 29.6% after the correction. The sum of squared errors reduced 47.7%. The methods and the algorithms for raw data processing, such as data partition, fittings of dots’ centres, K-means clustering, etc., are the same for both two experiments. The experimental results demonstrate that our method for the correction of the errors produced by the movement of lateral stage of confocal microscope is meaningful and practicable.

scholarly journals Modeling of German Low Voltage Cables with Ground Return Path

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1265 ◽  
Author(s):  
Johanna Geis-Schroer ◽  
Sebastian Hubschneider ◽  
Lukas Held ◽  
Frederik Gielnik ◽  
Michael Armbruster ◽  
...  
Keyword(s):  
Low Voltage ◽  
Measurement Data ◽  
Analytical Calculation ◽  
Laboratory Measurement ◽  
Model Parameters ◽  
Calculation Methods ◽  
Modeling Approach ◽  
Measurement Results ◽  
Simulation Results ◽  
Return Path

In this contribution, measurement data of phase, neutral, and ground currents from real low voltage (LV) feeders in Germany is presented and analyzed. The data obtained is used to review and evaluate common modeling approaches for LV systems. An alternative modeling approach for detailed cable and ground modeling, which allows for the consideration of typical German LV earthing conditions and asymmetrical cable design, is proposed. Further, analytical calculation methods for model parameters are described and compared to laboratory measurement results of real LV cables. The models are then evaluated in terms of parameter sensitivity and parameter relevance, focusing on the influence of conventionally performed simplifications, such as neglecting house junction cables, shunt admittances, or temperature dependencies. By comparing measurement data from a real LV feeder to simulation results, the proposed modeling approach is validated.

scholarly journals Inverse Infiltration Modeling of Dike Covers Made of Dredged Material Using PEST and AMALGAM

Geosciences ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 41
Author(s):  
Tim Jurisch ◽  
Stefan Cantré ◽  
Fokke Saathoff
Keyword(s):  
Large Scale ◽  
Measurement Data ◽  
Fine Grained ◽  
Dredged Materials ◽  
Measurement Results ◽  
Large Scale Field ◽  
Eigenvalue Ratio ◽  
Ill Posed ◽  
Materials Used ◽  
Installation Technology

A variety of studies recently proved the applicability of different dried, fine-grained dredged materials as replacement material for erosion-resistant sea dike covers. In Rostock, Germany, a large-scale field experiment was conducted, in which different dredged materials were tested with regard to installation technology, stability, turf development, infiltration, and erosion resistance. The infiltration experiments to study the development of a seepage line in the dike body showed unexpected measurement results. Due to the high complexity of the problem, standard geo-hydraulic models proved to be unable to analyze these results. Therefore, different methods of inverse infiltration modeling were applied, such as the parameter estimation tool (PEST) and the AMALGAM algorithm. In the paper, the two approaches are compared and discussed. A sensitivity analysis proved the presumption of a non-linear model behavior for the infiltration problem and the Eigenvalue ratio indicates that the dike infiltration is an ill-posed problem. Although this complicates the inverse modeling (e.g., termination in local minima), parameter sets close to an optimum were found with both the PEST and the AMALGAM algorithms. Together with the field measurement data, this information supports the rating of the effective material properties of the applied dredged materials used as dike cover material.

scholarly journals The Impact of Elongation on Change in Electrical Resistance of Electrically Conductive Yarns Woven into Fabric

Materials ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3390
Author(s):  
Željko Knezić ◽  
Željko Penava ◽  
Diana Šimić Penava ◽  
Dubravko Rogale
Keyword(s):  
Mathematical Model ◽  
Electrical Resistance ◽  
Electrically Conductive ◽  
Textile Materials ◽  
Measurement Results ◽  
Conductive Yarns ◽  
Yarn Count ◽  
As Relationship ◽  
The Impact ◽  
The Mathematical Model

Electrically conductive yarns (ECYs) are gaining increasing applications in woven textile materials, especially in woven sensors suitable for incorporation into clothing. In this paper, the effect of the yarn count of ECYs woven into fabric on values of electrical resistance is analyzed. We also observe how the direction of action of elongation force, considering the position of the woven ECY, effects the change in the electrical resistance of the electrically conductive fabric. The measurements were performed on nine different samples of fabric in a plain weave, into which were woven ECYs with three different yarn counts and three different directions. Relationship curves between values of elongation forces and elongation to break, as well as relationship curves between values of electrical resistance of fabrics with ECYs and elongation, were experimentally obtained. An analytical mathematical model was also established, and analysis was conducted, which determined the models of function of connection between force and elongation, and between electrical resistance and elongation. The connection between the measurement results and the mathematical model was confirmed. The connection between the mathematical model and the experimental results enables the design of ECY properties in woven materials, especially textile force and elongation sensors.

scholarly journals Measurement experiences with FluxSet digital D/I station

2017 ◽  
Vol 6 (2) ◽  
pp. 279-284 ◽  
Author(s):  
László Hegymegi ◽  
János Szöllősy ◽  
Csaba Hegymegi ◽  
Ádám Domján
Keyword(s):  
Measurement Method ◽  
Measurement Data ◽  
Digital Form ◽  
New Instrument ◽  
Measurement Results ◽  
Inclination Angles ◽  
Flux Gate

Abstract. Geomagnetic observatories use classical theodolites equipped with single-axis flux-gate magnetometers known as declination–inclination magnetometers (DIM) to determine absolute values of declination and inclination angles. This instrument and the measurement method are very reliable but need a lot of handwork and experience. The authors developed and built a non-magnetic theodolite which gives all measurement data in digital form. Use of this instrument significantly decreases the possibility of observation errors and minimises handwork. The new instrument is presented in this paper together with first measurement results in comparison to the classical DIM.

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