Advanced Modeling and Computer Technologies for Fluvial Water Quality Research and Control

ADVANCED MODELING AND COMPUTER TECHNOLOGIES FOR FLUVIAL WATER QUALITY RESEARCH AND CONTROL......Page 2
ADVANCED MODELING AND COMPUTER TECHNOLOGIES FOR FLUVIAL WATER QUALITY RESEARCH AND CONTROL......Page 5
Library of Congress Cataloging-in-Publication Data......Page 6
CONTENTS......Page 7
INTRODUCTION......Page 9
1.1. MATHEMATICAL MODELING OF  POLLUTANTS TRANSFER IN RIVERS......Page 13
1.2. MATHEMATICAL MODELS OF TRANSFER  AND TURBULENT DIFFUSION......Page 24
1.3. SOME ANALYTICAL METHODS USING AT SOLVING MULTIDIMENSIONAL PROBLEMS......Page 28
1.4. DESCRIPTION OF RIVER  BANKS BY SPLINES......Page 34
1.4.1. The Contour of the River......Page 35
1.4.2. Using Spline-Interpolation for Giving a Curve......Page 37
1.4.3. Trigonometrical Spline-Interpolation......Page 38
1.4.4. Spline-Interpolation by Integrals of Fractional-Rational Functions......Page 41
1.4.5. Final Remarks......Page 43
1.5. ABOUT APPROXIMATION OF RIVER CURRENT SPEED......Page 44
2.1.1. Boundary Problem......Page 45
2.1.2. Diffusion Equation......Page 49
2.2. FINITE-DIFFERENCE AND ANALYTICAL METHODS OF SOLUTION OF ONE-DIMENSIONAL IN SPACE MODELS OF  POLLUTANTS TRANSFER......Page 52
2.3. ALGORITHMIC PRESENTATION OF THE  FINITE-DIFFERENCE METHOD......Page 53
2.4. ALGORITHMS FOR SOLVING TWO-DIMENSIONAL MATHEMATICAL MODELS......Page 55
2.5. ALGORITHMS FOR REALIZATION OF  THREE-DIMENSIONAL DIFFUSION MODELS......Page 58
2.6.1. Optimization, Used in Boundary Problem......Page 62
2.6.2. Optimization, Used at Solving Diffusion Equation......Page 65
2.6.3. Estimation of Unknown Function Derivatives......Page 68
2.6.4. Examples of Using of the Offered Optimization......Page 69
2.7. THE EFFECT OF SMOOTHNESS OF THE  INHOMOGENEOUS PART OF THE DIFFUSION  EQUATION ON THE ACCURACY OF THE RESULTS......Page 74
3.1.1. Statistical Models of Propagation of Pollutants in the Rivers......Page 85
3.2. METHODS OF IDENTIFICATION OF NON-LINEAR REGRETIONS BY MODIFIED LEAST SQUARES CRITERION......Page 91
3.3. RESTORATION OF POLYNOMIAL  REGRESSION ON THE BASIS OF ACTIVE EXPERIMENT......Page 103
3.4.1. One-parametrical Families of Functions of Polynomials......Page 110
1. Function ebacx......Page 114
2. Function ebxa)( cx0......Page 115
3. Function......Page 117
 4. Function......Page 118
6. Function ebeah......Page 121
7. Function sin()cos((xBxAesxy......Page 123
8. Function ))sin()cos((BxAeh......Page 124
1. Equation containing sum two exponents.......Page 126
2. Equation containing sum of several exponents.......Page 128
3.5. CONSTRUCTION OF CONFIDENCE INTERVALS FOR MATHEMATICAL EXPECTATIONS OF RANDOM VARIABLES......Page 130
3.6. IMITATIVE MODELING OF FORMATION  OF THE QUALITY OF SEWAGES......Page 143
3.7. SIMULATION OF REAL MULTIDIMENSIONAL STATIONARY GAUSS-MARKOV SERIES WITH GIVEN DEPTH OF CONNECTIVITY......Page 151
Chapter 4    METHODS OF MAKING DECISIONS IN MONITORING OF RIVER POLLUTION......Page 161
4.1. GENERALIZATION OF BAYESIAN RULE OF  MANY HYPOTHESES TESTING......Page 162
4.2. GENERAL SOLUTIONS OF UNCONDITIONAL  AND CONDITIONAL BAYESIAN TASKS......Page 164
4.2.1. Restrictions on Conditional Probabilities of  Omitting True Parameters......Page 166
4.2.2. Restrictions on Averaged Probability of  Omitted True Parameters......Page 167
4.2.4. Restrictions on Unconditional Probabilities of  Omitting Each True Parameter......Page 168
4.3.1. Step Loss Function j......Page 169
4.3.2. Non-Step Loss Function......Page 171
4.4. ALGORITHMS OF SOLVING CONDITIONAL BAYESIAN  PROBLEM OF MANY SIMPLE HYPOTHESES TESTING......Page 177
4.5. SOLUTION OF UNCONDITIONAL BAYESIAN PROBLEM AT NUMBER OF HYPOTHESES EQUAL TO TWO......Page 184
4.6. Solution of Conditional Bayesian Problem at Number of Hypotheses Equal to Two......Page 186
4.7. QUASI-OPTIMAL METHOD OF  MANY-HYPOTHESES TESTING......Page 187
4.8. RATIO OF VALUES OF THE RISK-FUNCTIONS  IN PUT PROBLEMS AND THEIR NUMERICAL RESEARCHES......Page 190
4.9. CONCLUSIVE REMARKS......Page 193
5.1. ESSENCE OF IDENTIFICATION PROBLEM......Page 195
5.2. FORMALIZATION OF THE PROBLEM......Page 196
5.3. GENERALIZED BLOCK-DIAGRAM FOR  SOLVING IDENTIFICATION PROBLEM......Page 198
5.4. ALGORITHM OF HYPOTHESES FORMATION......Page 199
5.5. CALCULATION OF A PRIOR PROBABILITIES......Page 201
5.6. DECORRELATION OF THE MEASURED VALUES VECTOR......Page 202
5.7. ALGORITHMS OF CLUSTER-ANALYSIS FOR IDENTIFICATION OF EMERGENCY RELEASE SOURCES......Page 203
6.1. ASSIGNMENT AND POSSIBILITY  OF THE PACKAGE......Page 205
6.2. INPUT AND EDITING OF THE INITIAL DATA......Page 206
6.3. MANAGEMENT OF WORK OF THE SOFTWARE......Page 213
6.3.1. Description of the Files used in the Software......Page 214
6.3.2. Working Language......Page 215
6.3.3. Help Service and Notes......Page 216
6.3.4. Parameters of the Package......Page 217
6.3.5. Data Input and Editing......Page 218
6.4. REALIZATION OF COMPUTATION AND  REPRESENTATION OF THE RESULTS......Page 220
7.1. APPOINTMENT OF THE PACKAGE......Page 223
7.2. POSSIBILITY OF THE PACKAGE AND ITS APPLICATION......Page 224
8.1. STUDY OF ALGORITHMS FOR CALCULATION OF POLLUTANT CONCENTRATIONS IN RIVERS BY MEANS  OF DIFFUSION EQUATIONS......Page 227
Function......Page 229
Function......Page 230
Considered Equation......Page 231
8.2.1. Sensitivity of the Models of Different Dimensionality to Geometric Sizes of the River Cross-Section......Page 232
8.2.2. Dependence of the Identification Quality on the Noise Level......Page 233
8.3.1.2. The River Khobistskali......Page 238
Geometry and dynamics of the section......Page 242
Calculation results: at 1m......Page 243
Calculation results: at 2m.......Page 245
Water parameters......Page 247
Calculation results: at 1m.......Page 248
Calculation results: at 2m.......Page 250
8.3.3. Results of Modeling and Discussion 7......Page 251
8.4. RIVER POLLUTION COMPONENTS MEAN ANNUAL VALUES ESTIMATION BY COMPUTER MODELING......Page 264
CONCLUSION......Page 270
APPENDIX 1.  GENERATOR OF RANDOM VARIABLES OBEYING THE GIVEN PROBABILITY DISTRIBUTION LAWS......Page 273
APPENDIX 2.  GENERATOR OF NORMALLY DISTRIBUTED RANDOM VECTORS [212]......Page 275
APPENDIX 3.  GENERATOR OF MULTIDIMENSIONAL NORMAL MARKOVIAN SERIES WITH A GIVEN CONNECTIVITY DEPTH [1, 213]......Page 277
1. GEOMETRICAL REGRESSION......Page 279
2. EXPONENTIAL REGRESSION......Page 280
4. GEOMETRIC- EXPONENTIAL REGRESSION......Page 281
5. EXPONENTIAL REGRESSION WITH THE FREE MEMBER......Page 282
7. INVERSE EXPONENTIAL REGRESSION......Page 283
8. LINEAR – EXPONENTIAL REGRESSION......Page 284
9. LINEAR – EXPONENTIAL DEPENDENCE WITH THE FREE MEMBER......Page 285
10. PRODUCT OF GEOMETRICAL DEPENDENCES......Page 286
11. SUM OF EXPONENTIAL DEPENDENCES......Page 287
13. SUM OF EXPONENTIAL DEPENDENCES WITH THE FREE MEMBER......Page 288
15. EXPONENTIAL – SINE WAVE REGRESSION......Page 289
16. EXPONENTIAL – SINE WAVE REGRESSION  WITH THE FREE MEMBER......Page 290
17. POLYNOMIAL REGRESSION......Page 291
18. GEOMETRICAL – POLYNOMIAL REGRESSION......Page 292
19. EXPONENTIAL – POLYNOMIAL REGRESSION......Page 293
20. LOGARITHMIC – POLYNOMIAL REGRESSION......Page 294
21. PERIODIC REGRESSION......Page 295
22. REGRESSION ANALYSIS......Page 297
23. MULTIPLE LINEAR REGRESSION......Page 298
Geometrical Dependence......Page 299
Exponential Dependence......Page 300
Geometric-exponential Dependence......Page 301
Inverse-exponential Dependence......Page 302
Linear-Exponential Dependence......Page 303
Linear-exponential Dependence with the Free Member......Page 304
Product of Geometrical Dependences......Page 305
The Sum of Exponential Dependences......Page 307
The Sum of Geometrical Dependences......Page 310
Exponential-sine Wave Dependence......Page 311
Exponential-sine Wave Dependence with the Free Member......Page 312
Periodic Dependence......Page 313
APPENDIX 5.  GRAPHS OF EXPERIMENTAL INVESTIGATION OF DETERMINISTIC MATHEMATICAL MODELS......Page 315
REFERENCES......Page 341
INDEX......Page 355