Advanced modeling and computer technologies for fluvial water quality research and control / Karlos J. Kachiashvili and D. Y. Melikdzhanian.

Format:

Book

Author/Creator:

Kachiashvili, Karlos J.

Contributor:

Melikdzhanian, D. Y.

Series:

Water resource planning, development and management series.

Computer science, technology and applications

Water Resource Planning, Development and Management

Language:

English

Subjects (All):

Water quality--Measurement--Mathematics.

Water quality.

Water--Pollution--Simulation methods.

Water.

Physical Description:

1 online resource (360 p.)

Edition:

1st ed.

Place of Publication:

New York : Nova, c2012.

Language Note:

English

Summary:

The results discussed in this book are interesting and useful for a wide range of specialists and scientists working in the field of applied mathematics, and in the modelling and monitoring of pollution of natural waters, ecology, hydrology, power engineering and building of different structures of water objects. Their importance and practical value are submitted in the friendly form for comprehension and are ready for direct application for the solution of practical tasks. Advantages of the elaborated methods and algorithms are shown not only through theoretical judgements and calculations, but also through the demonstration of results of particular calculus and modelling.

Contents:

Intro

ADVANCED MODELING AND COMPUTER TECHNOLOGIES FOR FLUVIAL WATER QUALITY RESEARCH AND CONTROL

Library of Congress Cataloging-in-Publication Data

CONTENTS

INTRODUCTION

Chapter 1 DETERMINISTIC MATHEMATICAL MODELS OF POLLUTANTS TRANSFER IN RIVERS

1.1. MATHEMATICAL MODELING OF POLLUTANTS TRANSFER IN RIVERS

1.2. MATHEMATICAL MODELS OF TRANSFER AND TURBULENT DIFFUSION

1.3. SOME ANALYTICAL METHODS USING AT SOLVING MULTIDIMENSIONAL PROBLEMS

1.4. DESCRIPTION OF RIVER BANKS BY SPLINES

1.4.1. The Contour of the River

1.4.2. Using Spline-Interpolation for Giving a Curve

1.4.3. Trigonometrical Spline-Interpolation

1.4.4. Spline-Interpolation by Integrals of Fractional-Rational Functions

1.4.5. Final Remarks

1.5. ABOUT APPROXIMATION OF RIVER CURRENT SPEED

Chapter 2 CALCULATION SCHEMATA OF MATHEMATICAL MODELS

2.1. NUMERICAL METHODS OF SOLVING DIFFUSION EQUATIONS

2.1.1. Boundary Problem

2.1.2. Diffusion Equation

2.2. FINITE-DIFFERENCE AND ANALYTICAL METHODS OF SOLUTION OF ONE-DIMENSIONAL IN SPACE MODELS OF POLLUTANTS TRANSFER

2.3. ALGORITHMIC PRESENTATION OF THE FINITE-DIFFERENCE METHOD

2.4. ALGORITHMS FOR SOLVING TWO-DIMENSIONAL MATHEMATICAL MODELS

2.5. ALGORITHMS FOR REALIZATION OF THREE-DIMENSIONAL DIFFUSION MODELS

2.6. OPTIMIZATION PROBLEMS OF THE ALGORITHMS CONNECTED WITH DIFFERENCE SCHEMES

2.6.1. Optimization, Used in Boundary Problem

2.6.2. Optimization, Used at Solving Diffusion Equation

2.6.3. Estimation of Unknown Function Derivatives

2.6.4. Examples of Using of the Offered Optimization

2.7. THE EFFECT OF SMOOTHNESS OF THE INHOMOGENEOUS PART OF THE DIFFUSION EQUATION ON THE ACCURACY OF THE RESULTS.

Chapter 3 STOCHASTIC MATHEMATICAL MODELS DESCRIBING POLLUTION OF THE RIVERS

3.1. STATISTICAL MODELS OF POLLUTANTS TRANSPORT IN THE RIVERS

3.1.1. Statistical Models of Propagation of Pollutants in the Rivers

3.2. METHODS OF IDENTIFICATION OF NON-LINEAR REGRETIONS BY MODIFIED LEAST SQUARES CRITERION

3.3. RESTORATION OF POLYNOMIAL REGRESSION ON THE BASIS OF ACTIVE EXPERIMENT

3.4. INTERPOLATION OF NONLINEAR FUNCTIONS OF CERTAIN CLASS

3.4.1. One-parametrical Families of Functions of Polynomials

3.4.2. Nonlinear Functions of the Certain Class of Limited Quantity of Parameters

1. Function eba cx

2. Function ebxa )( cx0

3. Function

4. Function

5. Function ebea Let be

6. Function ebeah

7. Function sin()cos((xBxAe sxy

8. Function ))sin()cos((BxAeh

3.4.3. Solution of Transcendental Equations of Special Types

1. Equation containing sum two exponents.

2. Equation containing sum of several exponents.

3.5. CONSTRUCTION OF CONFIDENCE INTERVALS FOR MATHEMATICAL EXPECTATIONS OF RANDOM VARIABLES

3.6. IMITATIVE MODELING OF FORMATION OF THE QUALITY OF SEWAGES

3.7. SIMULATION OF REAL MULTIDIMENSIONAL STATIONARY GAUSS-MARKOV SERIES WITH GIVEN DEPTH OF CONNECTIVITY

Chapter 4 METHODS OF MAKING DECISIONS IN MONITORING OF RIVER POLLUTION

4.1. GENERALIZATION OF BAYESIAN RULE OF MANY HYPOTHESES TESTING

4.2. GENERAL SOLUTIONS OF UNCONDITIONAL AND CONDITIONAL BAYESIAN TASKS

4.2.1. Restrictions on Conditional Probabilities of Omitting True Parameters

4.2.2. Restrictions on Averaged Probability of Omitted True Parameters

4.2.3. Restrictions on Conditional Probabilities of Omitting Each True Parameter

4.2.4. Restrictions on Unconditional Probabilities of Omitting Each True Parameter.

4.3. ALGORITHMS OF SOLVING UNCONDITIONAL BAYESIAN PROBLEMS OF MANY SIMPLE HYPOTHESES TESTING

4.3.1. Step Loss Function j

4.3.2. Non-Step Loss Function

4.4. ALGORITHMS OF SOLVING CONDITIONAL BAYESIAN PROBLEM OF MANY SIMPLE HYPOTHESES TESTING

4.5. SOLUTION OF UNCONDITIONAL BAYESIAN PROBLEM AT NUMBER OF HYPOTHESES EQUAL TO TWO

4.6. Solution of Conditional Bayesian Problem at Number of Hypotheses Equal to Two

4.7. QUASI-OPTIMAL METHOD OF MANY-HYPOTHESES TESTING

4.8. RATIO OF VALUES OF THE RISK-FUNCTIONS IN PUT PROBLEMS AND THEIR NUMERICAL RESEARCHES

4.9. CONCLUSIVE REMARKS

Chapter 5 MATHEMATICAL BASES FOR SOLVING PROBLEM OF IDENTIFICATION OF THE SOURCES OF EXCESSIVE RIVER POLLUTION

5.1. ESSENCE OF IDENTIFICATION PROBLEM

5.2. FORMALIZATION OF THE PROBLEM

5.3. GENERALIZED BLOCK-DIAGRAM FOR SOLVING IDENTIFICATION PROBLEM

5.4. ALGORITHM OF HYPOTHESES FORMATION

5.5. CALCULATION OF A PRIOR PROBABILITIES

5.6. DECORRELATION OF THE MEASURED VALUES VECTOR

5.7. ALGORITHMS OF CLUSTER-ANALYSIS FOR IDENTIFICATION OF EMERGENCY RELEASE SOURCES

Chapter 6 SOFTWARE OF MATHEMATICAL MODELS OF POLLUTANTS TRANSPORT IN RIVERS

6.1. ASSIGNMENT AND POSSIBILITY OF THE PACKAGE

6.2. INPUT AND EDITING OF THE INITIAL DATA

6.3. MANAGEMENT OF WORK OF THE SOFTWARE

6.3.1. Description of the Files used in the Software

6.3.2. Working Language

6.3.3. Help Service and Notes

6.3.4. Parameters of the Package

6.3.5. Data Input and Editing

6.4. REALIZATION OF COMPUTATION AND REPRESENTATION OF THE RESULTS

Chapter 7 SOFTWARE OF IDENTIFICATION OF THE SOURCES OF EXCESSIVE RIVER POLLUTION

7.1. APPOINTMENT OF THE PACKAGE

7.2. POSSIBILITY OF THE PACKAGE AND ITS APPLICATION

Chapter 8 INVESTIGATION OF DEVELOPED ALGORITHMS AND PROGRAMS.

8.1. STUDY OF ALGORITHMS FOR CALCULATION OF POLLUTANT CONCENTRATIONS IN RIVERS BY MEANS OF DIFFUSION EQUATIONS

Designations

Bounds

One-dimensional Model. Function I

Considered Function

Function

One-dimensional Model. Function II

Considered Equation

Two-dimensional model. Function I

Two-dimensional Model. Function II

Three-Dimensional Model ~

8.2. COMPLEX TESTING OF THE DEVELOPED PACKAGE

8.2.1. Sensitivity of the Models of Different Dimensionality to Geometric Sizes of the River Cross-Section

8.2.2. Dependence of the Identification Quality on the Noise Level

8.3. MODELING OF POLLUTANTS TRANSPORT IN RIVERS

8.3.1. The Initial Data for Modeling

8.3.1.1. The River Chogha

8.3.1.2. The River Khobistskali

8.3.2. Calculation Results

8.3.2.1. The River Choga

One- and Two-Dimensional Models

Basic initial data

Accuracy of calculations

Geometry and dynamics of the section

Water parameters

Calculation results: at 1 m

Calculation results: at 2 m.

8.3.22. The River Khobistskali

Calculation results: at 1 m.

8.3.3. Results of Modeling and Discussion 7

8.4. RIVER POLLUTION COMPONENTS MEAN ANNUAL VALUES ESTIMATION BY COMPUTER MODELING

CONCLUSION

APPENDIX 1. GENERATOR OF RANDOM VARIABLES OBEYING THE GIVEN PROBABILITY DISTRIBUTION LAWS

APPENDIX 2. GENERATOR OF NORMALLY DISTRIBUTED RANDOM VECTORS [212]

APPENDIX 3. GENERATOR OF MULTIDIMENSIONAL NORMAL MARKOVIAN SERIES WITH A GIVEN CONNECTIVITY DEPTH [1, 213].

APPENDIX 4. THE RESULTS OF REALIZATION OF DESCRIBED IN SECTION 3.2 GENERAL METHODOLOGY FOR IDENTIFICATION OF NONLINEAR REGRESSIONS FOR CERTAIN CLASS OF FUNCTIONAL DEPENDENCES AND PROPERTIES OF RESTORED DEPENDENCES

1. GEOMETRICAL REGRESSION

2. EXPONENTIAL REGRESSION

3. LOGARITHMIC REGRESSION

4. GEOMETRIC- EXPONENTIAL REGRESSION

5. EXPONENTIAL REGRESSION WITH THE FREE MEMBER

6. GEOMETRICAL REGRESSION WITH THE FREE MEMBER

7. INVERSE EXPONENTIAL REGRESSION

8. LINEAR - EXPONENTIAL REGRESSION

9. LINEAR - EXPONENTIAL DEPENDENCE WITH THE FREE MEMBER

10. PRODUCT OF GEOMETRICAL DEPENDENCES

11. SUM OF EXPONENTIAL DEPENDENCES

12. SUM OF GEOMETRICAL DEPENDENCES

13. SUM OF EXPONENTIAL DEPENDENCES WITH THE FREE MEMBER

14. SUM OF GEOMETRICAL DEPENDENCES WITH THE FREE MEMBER

15. EXPONENTIAL - SINE WAVE REGRESSION

16. EXPONENTIAL - SINE WAVE REGRESSION WITH THE FREE MEMBER

17. POLYNOMIAL REGRESSION

18. GEOMETRICAL - POLYNOMIAL REGRESSION

19. EXPONENTIAL - POLYNOMIAL REGRESSION

20. LOGARITHMIC - POLYNOMIAL REGRESSION

21. PERIODIC REGRESSION

22. REGRESSION ANALYSIS

23. MULTIPLE LINEAR REGRESSION

24. THE BASIC PROPERTIES OF RESTORED DEPENDENCES

Geometrical Dependence

Exponential Dependence

Logarithmic Dependence

Geometric-exponential Dependence

Inverse-exponential Dependence

Geometrical Dependence with the Free Member

Exponential Dependence with the Free Member

Linear-Exponential Dependence

Linear-exponential Dependence with the Free Member

Product of Geometrical Dependences

The Sum of Exponential Dependences

The Sum of Geometrical Dependences

The Sum of Exponential Dependences with the Free Member

The Sum of Geometrical Dependences with the Free Member

Exponential-sine Wave Dependence

Exponential-sine Wave Dependence with the Free Member.

Polynominal Dependence.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from title page (ebrary, July 18, 2013).

ISBN:

1-61470-170-9

OCLC:

854569193