The information analysis and the research on entropy for measurement data ; Matavimo duomenų informacinė analizė ir entropijos tyrimas

Vytautas Giniotis

Sujets

• Informatics engineering
• Entropy (information theory)
• Measurement
• Uncertainty

Informations

• Publié par: vilnius_gediminas_technical_university
• Publié le: 01 janvier 2006
• Nombre de lectures: 12
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

VILNIUS GEDIMINAS TECHNICAL UNIVERSITY





Mindaugas Rybokas





THE INFORMATION ANALYSIS AND THE RESEARCH ON
ENTROPY FOR MEASUREMENT DATA

Doctoral Dissertation








Technological Sciences, Informatics Engineering (07T)





















VILNIUS, 2006 VILNIUS GEDIMINO TECHNIKOS UNIVERSITETAS





Mindaugas Rybokas





MATAVIMO DUOMEN Ų INFORMACIN Ė ANALIZĖ IR
ENTROPIJOS TYRIMAS

Daktaro disertacija








Technologijos mokslai, informatikos inžinerija (07T)





















VILNIUS, 2006

Doctoral dissertation was prepared at Vilnius Gediminas Technical University in
2002–2006.

Scientific Supervisor

Assoc Prof Dr Regina Kulvietien ė (Vilnius Gediminas Technical University,
Technological Sciences, Informatics Engineering – 07T).



CONTENTS

INTRODUCTION......................................................................................................................... 6

CHAPTER 1. REVIEW AND ANALYSIS OF THE RESEARCH
CONCERNING DATA PROCESSING ................................................................................... 10

1.1. Overview of information presentation and its evaluation...................................................... 10
1.2 Variety of information about the object status........................................................................ 11
1.3. Sampling strategy as a constituent of data validity................................................................ 14
1.4. Data uncertainty evaluation ................................................................................................... 17
1.5. Research on technical information-measuring systems......................................................... 20
1.6. Sampling and evaluation in sociological surveys .................................................................. 30
1.7. Conclusions............................................................................................................................ 35

CHAPTER 2. APPLICATION OF INFORMATION ENTROPY FOR DATA
ASSESSMENT ............................................................................................................................ 36
2.1. Research on information evaluation ...................................................................................... 36
2.2. Application of information entropy. Uncertainty and indeterminacy.................................... 39
2.3. Technical implementation...................................................................................................... 45
2.4. Conclusions............................................................................................................................ 55

CHAPTER 3. MUTUAL INFORMATION ANALYSIS ........................................................ 57
3.1. The application of bivariate distributions and mutual information in measurement............. 57
3.2. The application of the trivariate conditional distribution ...................................................... 63
3.3. Conclusions............. 67

CHAPTER 4. COMPUTERISED DATA ACQUISITION AND PROCESSING
IN A TECHNICAL APPLICATION........................................................................................ 68
4.1. Process control and data processing by computer ................................................................. 68
4.2. Technical specifications of scale measurement and basic approach to the PC
simulation...................................................................................................................................... 69
4.3. System realization.................................................................................................................. 71
4.4. Research on the accuracy of angle calibration....................................................................... 72
4.5. Measurement simulation of circular scales............................................................................ 77

4.6. The program for simulating angular scale measurement....................................................... 83
4.7. Conclusions............................................................................................................................ 90
GENERAL CONCLUSIONS .................................................................................................... 91
References..................................................................................................................................... 92
Appendix. The Full Code for the Angular Scale Simulation Program....................................... 101



Chapter 1. Review and analysis of the research works

INTRODUCTION

The Topicality of the Research

Modern information technologies enable to evaluate information data in a substantially new
fashion decreasing the duration and cost of the evaluation processes. Results of evaluation are
usually presented as an estimate of the systematic (mean) value within the range, often called
uncertainty, that depends on the standard deviation given the appropriate level of confidence.
This is a commonly accepted form of presenting the results of data evaluation. It covers all kinds
of information data including social and demographic investigations, research in chemistry,
biology and various types of technical systems, information measuring systems among them.
Information theory is taken here as the basis for assessing of information data during an analysis
and the result presentation of different objects and as an example of this approach selecting
technical information-measuring systems.
Information entropy parameter helps to expand an understanding of the object’s informational
status significantly. An entropy parameter shows a reduced uncertainty of the information about
the object after receiving a message on its status (for example, before measuring the object and
after the measurement on random points on the object). The evaluated data on the object usually
are very restricted due to technical capabilities applied to this process. It is impossible for
modern information systems to determine (or to perform a calibration operation as it is applied in
technical systems) at every digit of the output information from the object. The same applies to
chemical, biological, demographic, atmospheric, etc. measurement and monitoring objects.
The results of theoretical research, data evaluation model presented and practical results
achieved show a possibility to select, assess and evaluate information on the object completely
covering the data (for a chosen example, measurement data on the raster scale) received from the
object.

The Objectives of the Research

The aim of this work is the evaluation of data informativeness taking into account the full set of
information on the object. The goals of this research can be formulated as follows:
• to perform an analysis data assessment and presentation as well as an analysis of their
advantages and disadvantages;
• to develop a new approach for data presentation based on the characteristics of information
entropy;

6Chapter 1. Review and analysis of the research works

• to develop theoretical assessment formulas for multidimensional information systems;
• to present computer simulation means for the complete evaluation of the object presenting an
investigation of the raster scales’ parameters as an example.

The Object of the Research

The object of the research is the informative content of data assessment focusing on technical
measurement data.

The Scientific Novelty

• A new model for data processing has been proposed, supplementing it by the information
entropy parameter that shows what portion of information on the object has been used out of
the total available data.
• A method for evaluating mutual information for two- and three-dimensional objects has been
proposed.
• A computerized modelling system enabling to model an investigation of the parameters of
the raster scale and calculate the results of measurement using variable substitution has been
developed. It permits to calculate the results with tens or rather hundreds of thousands
variables in the information system.

Methodology of the Research

Analytical research has been performed examining scientific and technical literature on
information evaluation and assessment in mechanical and chemical engineering, information
measuring systems, data acquisition and assessment systems and to a limited extent in social
sciences. Statistical methods of data evaluation have been reviewed. Methods of information
theory and mathematical statistics have been used in deriving expressions for data evaluation.
Software packages Mathematica 5 and Visual