Statistical And Fuzzy Modelling Of Grain Material

STATISTICAL AND FUZZY MODELLING OF GRAIN MATERIAL SAMPING AND OPERATIONS

SELECTED APPROACHES

MODELOWANIE STATYSTYCZNE I ROZMYTE PRÓBKOWANIA I OPERACJI TECHNOLOGICZNYCH MATERIAŁÓW UZIARNIONYCH

MONOGRAFIA

Anna Walaszek - Babiszewska

Stan książki: NOWA

Wydawnictwo Politechniki Śląskiej

Stron: 118

Okładka: miękka

Format: B5

Nakład: 150 egz.

Wydział: Informatyka

Spis treści:

1.    Introduction..9

2.    Multivariate distributions dcscribing properties of grain materials. 11

2.1.  Introduction11

2.2.  Empirical probability distribution of a two-dimcnsional random variable -grain diameter and grain density. 12

2.2.1.  Empirical  marginal distributions of a grain diameter and a grain density...14

2.2.2.  Empirical conditional distributions of a grain diameter and a grain density... 17

2.3.  Mcan values ofthe quality parameters of grain materials18

3.    Sample charactcristics and probability cstimators of grain materiał parameters...20

3.1.  Mass balance in a sampic of grain materiał...20

3.2.  Yields of grain sizc grades and density fractions in a sample...23

3.3.  Ash conlcnt in a coal sample26

3.4. General form of a content of sclccted components in a sampic..28

4.   Sampling errors32

4.1.  Sampling errors of a single fraction...32

4.2.  Sampling errors whilc estimaling the grain size or densimetrie charactcristics.33

4.3.  Examplcs of calculations...37

4.4.  Excmplary results of measurements and simulation tests.44

5.   Quality parameters of grain materials as functions of a probability p...48

5.1. Basic assumptions.48

5.2.  Thcorclical analysis when thc populalion consists of two lypcs of grains

of thc same class 49

5.3. Theorctical analysis when thc population consists of two lypcs of grains

of thc same mean density51

6.   Basic operations and sampling of grain matcrials55

6.1.  Mixing of two lypcs of grain matcrials; charactcristics and sampling errors 55

6.1.1.  Mixing of matcrials with different densimelric charactcristics.55

6.1.2.  Mixing of matcrials with different grain sizc characlcrislics58

6.1.3.  Sampling error of matcrials mixture..61

6.2.  Static probability charactcristics and sampling errors of separalion produets... 62

6.3.  Probability dynamics charactcristics and sampling tests..63

6.3.1.  Sampling tests in thc course oftransporting granular malcrial mass ..63

6.3.2.  Probability charactcristics of batch separalion process64

6.3.3.  Dynamics of separation processes explains by Markovłs processes...66

6.3.4.  Sampling tests on process dynamics.68

6.4.  Principlcs of decision making on sampling...70

6.4.1.  On sampling optimi/ation problcms.71

6.4.2.  Application of Baycs's rules to determine thc typc of grain materiał..73

7.   Fuzzy modclling for sampling research of grain matcrials..75

7.1.  Sampling obscrvation as a fuz/y variablc..75

7.1.1.  Fuzzy scls and fuzzy numbers .75

7.1.2.  Fuzzy veclors84

7.1.3.  Functions which valucs arc fuzzy sets..84

7.2.  Fuzzy probability for modclling of minerał preparalion processes...85

7.2.1.  Definitions of fuzzy evcnts hirudina and fuzzy probabilities.86

7.2.2.  Fuzzy probability of a two-dimensional random variablc as input materiał characlcrislics 88

7.2.3. Quality parameters as fuzzy mean valucsc>2

7.2.4.  Fuzzy probability as a characteristic of preparalion processes...93

7.2.4.1.  Mixing matcrials; fuzzy characteristic of hctcrogcneily...93

7.2.4.2.  Fuzzy static characlcrislics of separation processes 94

7.2.4.3.  Process dynamics in laboralory separators...95

7.3.  Application of fuzzy systems theory.96

7.3.1. Fuzzy regression analysis..97

7.3.2.  Rulc-bascd fuzzy models.101

7.3.2.1.  Linguistic models..101

7.3.2.2.  Modcis of the Takagi-Sugcno type..103

7.3.3.  Fuzzy linear programming.. 105

References 109

Summary..115