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The Use of Fuzzy Systems in the Designing of Mining Process in Hard Coal Mines

The Use of Fuzzy Systems in the Designing of Mining Process in Hard Coal Mines Arch. Min. Sci., Vol. 59 (2014), No 3, p. 741­760 Electronic version (in color) of this paper is available: http://mining.archives.pl DOI 10.2478/amsc-2014-0052 EDYTA BRZYCHCZY*, MAREK KSEK*, ANETA NAPIERAJ*, MARTA SUKIENNIK* WYKORZYSTANIE SYSTEMÓW ROZMYTYCH W PROJEKTOWANIU PROCESU WYDOBYWCZEGO W KOPALNIACH WGLA KAMIENNEGO This article presents examples of solutions supporting the design of certain elements of the mining process in coal mines. The focus is on two fuzzy systems: the first supports the selection of equipment longwall faces (FSES); and the second supports the estimation of production results (FSOE). System FSES generates proposals equipment in designed longwall faces. The module of fuzzing in this system enables a fuzzing operation the following quantitative variables: longwall length; longwall height; longitudinal and crosswise incline of the longwall, workability of the coal and thickness of rock vein in a given section of the longwall. The knowledge base includes over 100 fuzzy rules indicating possible options equipment under specified site conditions. After a proposal of equipment is generated, it is then possible to insert the values obtained into the second system FSOE, which estimates output a given shift time using the chosen parameters. The module of fuzzing in system FSOE includes 9 variables, which are crucial in determining shift output the given longwall face. The knowledge base in this system contains over 2000 rules. As a result of the operation of both systems, the designer receives both a proposal of equipment the designed longwall face and the size of shift output under the given conditions. Operation of the two systems has been presented using a case study. Keywords: coal mine, mining process, fuzzy logic, fuzzy systems, modelling Logika rozmyta pozwala na plynne i stosunkowo dokladne opisanie istotnych zalenoci pomidzy zmiennymi o charakterze nieprecyzyjnym lub malo dokladnym, które s danymi wejciowymi do procesu projektowania. Prowadzony przez system rozmyty proces wnioskowania na podstawie zapisanych w bazie wiedzy regul pozwala na uogólnienie posiadanej przez projektantów wiedzy, a take prowadzenie wnioskowania w sposób zbliony do rozumowania eksperta. W artykule zaprezentowano przyklady opracowanych rozwiza wspomagajcych projektowanie wybranych elementów procesu wydobywczego w kopalniach wgla kamiennego. Przedstawiono dwa systemy rozmyte, pierwszy wspomagajcy dobór wyposaenia do projektowanych wyrobisk cianowych (FSES) oraz drugi wspomagajcy szacowanie wyników produkcyjnych (FSOE). * AGH UNIVERSITY OF SCIENCE AND TECHNOLOGY, FACULTY OF MINING AND GEOENGINEERING, DEPARTMENT OF ECONOMICS AND MANAGEMENT IN INDUSTRY, AL. A. MICKIEWICZA 30, 30-059 KRAKOW, POLAND System FSES umoliwia wyznaczenie propozycji wyposaenia dla projektowanych wyrobisk cianowych. Modul rozmywania w tym systemie umoliwia przeprowadzenie operacji rozmycia nastpujcych zmiennych ilociowych: dlugo ciany, wysoko ciany, nachylenie podlune i poprzeczne ciany, urabialno wgla oraz grubo przerostów w przekroju ciany. Baza wiedzy obejmuje ponad 100 regul rozmytych wskazujcych w konkluzjach moliwe do zastosowania wyposaenie, w okrelonych warunkach wyrobiska. Po wyznaczeniu proponowanego wyposaenia, moliwe jest wprowadzenie otrzymanych wartoci do drugiego systemu FSOE, który umoliwia oszacowanie wydobycia zmianowego dla zadanych parametrów. Modul rozmywania systemu FSOE obejmuje 9 zmiennych, które konieczne s do wyznaczenia wydobycia zmianowego w projektowanym wyrobisku. Baza wiedzy tego systemu zawiera ponad 2000 regul. W efekcie dzialania obu systemów projektant otrzymuje propozycj wyposaenia dla projektowanego wyrobiska cianowego oraz oszacowan wielko wydobycia zmianowego dla podanych warunków. Wyniki te moe wykorzysta w procesie projektowania wybranych elementów procesu wydobywczego (wyrobisk cianowych) lub weryfikacji przyjtych planów produkcyjnych. Dzialanie opracowanych systemów zaprezentowano na wybranym przykladzie wyrobiska cianowego. Slowa kluczowe: kopalnia wgla kamiennego, proces wydobywczy, logika rozmyta, systemy rozmyte, modelowanie Introduction One of the basic tasks of a coal mine is to assure the required level of production and to protect the supply of raw materials within. This can be done through proper implementation of the mining process. The mining process is a specific kind of production process, which is based on the acquisition of non-renewable deposits (warehouse-transport process). The specificity of the mining process results from the fact that this process is carried out between nature and man, entailing specific consequences its operational course. The conditions conducting mining activities (uncertainty and risk related to the geology of deposits and other natural threats) compel designers to accumulate knowledge such as relevant inmation and past experience in an eft to improve the accuracy of design decisions. In the design of mining activities, knowledge plays a specific role in the cutting and selection order of the deposit, the selection of equipment suitable longwall face conditions, as well as the estimation of longwall face progress. example, the selection of equipment longwall face conditions can be done according to basic principles adapted to the producer's technical specifications; but an experienced designer knows that, in a given deposit, the geological and mining conditions can make it impossible to realize the planned amount of output. This knowledge comes from common experiences and specific rules that guide a given designer. Tacit knowledge can be obtained through the mulation with use of the expert methods (interviews, questionnaires, expert observations), or through advanced techniques of data exploration (with the use of algorithms designed to generate such knowledge). Obtained knowledge concerning the mining process can be stored in knowledge base systems (e.g. expert systems) (Brzychczy, 2011). In order to do this, knowledge must be appropriately represented e.g. as rules. Rules made by the experts are often characterized by a lack of precision, due to the inmal nature of human reasoning and the lack of reliable schemes of inference. In order to save these rules, it is possible to use fuzzy logic in the database, which enables a process of inference even when descriptions of the researched phenomenon are imprecise. Fuzzy logic also makes possible a general description of rules obtained in the process of knowledge discovery from data (Brzychczy, 2012). Making inferences in a way similar to the way an expert reasons (using the base of fuzzy rules) is made possible by fuzzy systems, the theoretical basis of which is described further in the article. 1. Logic and fuzzy systems Fuzzy systems are based on the theory of fuzzy logic. Fuzzy logic was developed by Lotfi A. Zadeh in the 1960s (Zadeh, 1965). It is an extension of classical reasoning closer to human reasoning. Fuzzy logic is used in process improvement and in various optimization tasks. One of the first examples of its application was controlling the Sendai metro in Japan. The control system was developed based on the experience of an engineer who, many years accumulated practical knowledge about controlling the metro system. His observations and proper use of fuzzy logic led to the creation of an automatic control system by Hitachi (Abel, 1991), (Piegat, 1999). The next achievements based on the principles of fuzzy sets or fuzzy numbers led to the fruition of increasingly newer and more developed fuzzy systems. The basic concept in fuzzy logic is fuzzy set A in X (mula 1). This is a set of pairs such that (Piegat, 1999); (Nowicki, 2009): A {( x, A ( x), ) x X } A : X [0,1] (1) where A is a function of membership, describing each x X the value of this element's membership A : X [0,1] to the fuzzy set A and A X The function of this membership thus assigns to each element x of a variable, a certain value from the range [0,1] and this value is called the degree of membership. In classic sets, the value is assigned as 1 when the element completely belongs to the set or 0 when it does not belong at all. In fuzzy logic theory, the element can belong to the set to a certain degree, meaning the function of membership can take the values from the whole unit bracket [0,1]. We can theree distinguish three cases: ­ A (x) = 1, which means full membership to set A, ­ A (x) = 0, which means total lack of membership to set A, ­ 0 < A (x) < 1, which means partial membership of element x to set A. The membership function can be expressed as a continuous or discreet diagram, a mula, table, sum, or a vector of membership. In practice, the creation of fuzzy systems, functions of membership are used, with different ms. Among the most common ms of the membership functions are: triangle, trapezoid, the letters "L", "S" and the Gaussian function. The selected membership functions are shown in Table 1. Functions of membership described using polygons or segments have many advantages, and a small number of parameters will suffice to define them. They are characterized by ease of parameter modification, on the basis of system input and output measurement values (Piegat, 1999). Describing the membership function using the Gaussian function entails many difficulties. Above all, the Gaussian function is symmetric, which means that the criteria of unifying fuzzy sets are not met. There is also the need to identify two parameters of the function. These factors hinder the acquisition of simple, locally linear surfaces of the fuzzy model. On the other hand, the function as such facilitates theoretical analysis of fuzzy systems, because its derivatives can be set to any level (Piegat, 1999). TABLE 1 Selected ms of the membership function and their graphic presentation Type of function Sets and membership functions Graphic representation of membership functions triangular xa 0, xa , a xb A x; a, b, c b a c x , b x c c b 0, xc xa 0, b x A x; a, b , a xb b a xc 1, xa 0, xa , a xb b a A x; a, b, c, d 1, bxc c x , cxd c b 0, xd "L" shape trapezoidal Gaussian function A x; x , e 1 x x 2 2 Fuzzy systems are models which process inmation using fuzzy rules. They are made up of 4 elements (Fig. 1): 1. A fuzzification module, which converts system input, i.e. acute numerical values into fuzzy ones. This is done via the membership function of defined fuzzy sets. 2. A knowledge base which stores the set of rules representing the knowledge about the problem. These rules can come from different sources: from experts appointed on the basis of qualitative modelling; and from algorithms which automatically generate knowledge. 3. A mechanism of inference, which simulates human reasoning through a fuzzy inference process according to the logic stored in the rules. 4. A module, which converts a fuzzy set indicated by the inference result into acute values. Fig. 1. Fuzzy system scheme based on (Nowicki, 2009) System works as follows: after inserting the input data, quantitative variables are converted into linguistic variables; then, inference is done according to the knowledge base, which contains fuzzy rules (representing knowledge about the problem being analysed); and finally, in the module, the resulting fuzzy set is converted into numerical values. The inference mechanism comprises a crucial element of the fuzzy system. It uses the knowledge base, and the rules contained within it. The "rule of inference" can be understood as a method of deriving conclusions from premises. This process can be carried out using the rules: modus ponendo ponens (inference through statement); modus tollendo tollens (inference through denial); conditional syllogism of the stoics; or the principles of distribution (Lski, 2008). "Ifthen" rules can be obtained in the following manner: ­ Specification of the premises, and then the conclusion. ­ Specification of the conclusions of a rule, and then the selection of its premises. ­ Independent determination of premises and conclusions. Among the basic methods of inference is the Mamdani model. Systems using this model rely on a base of rules and the use of linguistic operators, and inference is done through the aggregation of fuzzy sets resulting from all the rules. Thus, the fuzzy set is the resulting set. The second group is comprised of systems based on the Takagi-Sugeno-Kanga model. In this model ­ in contrast to the Mamdani model ­ the base of rules is fuzzy only in the first part; that is to say, the "if" part. In the second part ­ the "then" part ­ functional relationships occur. Obtaining a result from the fuzzy system is possible through the operation. This involves the determination of a qualitative or quantitative value the output variable, based on knowledge of the nature of the resulting fuzzy set. There are several methods of . The most common are (Lski, 2008; Nowicki, 2009): ­ Method of maximum (MD), in which the output value is the maximum value of the argument from the set of argument values of the membership function the resulting fuzzy set. ­ Method of height (HM), where the output value is affected by all the activated premises, and not just those that have the biggest impact on the given fuzzy set the output variable. In this method, fuzzy sets of the output variable are converted into single-element sets (Singletons). ­ Method of gravity centre (COG), in which the output variable is the centre of gravity the shape created by the output fuzzy set. Fuzzy systems enable effective modelling of complicated and advanced technological processes. Inference based on fuzzy rules, as well as the possibility of conducting analysis using quantitative and qualitative variables, can also be used in the designing of mining process. Examples of developed solutions in this field are presented later in this article. 2. Designing of mining process The designing of mining process can be divided into the following stages: 1. Work study. 2. Searching solutions. 3. Evaluation and selection of solutions. 4. Detailed design. 5. Implementation of design solutions. The basic mode of operations during work study is the accumulation of knowledge concerning the designed task (e.g. market analysis, diagnosis of the mal legal situation, familiarization with input data related to task data, or to geological documentation of the deposit in the case of a mine), specification of requirements and constraints the mulated design problem, and indication of evaluation criteria solutions with regard to uncertainty and risk. In the case of mining process, the main design tasks are: ­ Identification of longwall faces taking part in the mining process, as well as the essential surface infrastructure (elements of spatial structure). ­ Selection of equipment and the organization of work. ­ Specification of time intervals mining activities. Next in the modelling stage is the generation of potential design solutions, which are subjected to preliminary selection. The result of this stage is a set of descriptions of possible solutions. In the next stage is the evaluation of solutions and selection of the best, which detailed design is subsequently carried out. Then, design documentation is drawn up, which is essential implementing the chosen design solution. It should be highlighted that the quality of a design solution depends mainly on the stages of modelling and optimization. The designer can use different methods at different stages, which can significantly influence the design process and its results. Among these methods are algorithmic methods (i.e. systematic search methods, linear and nonlinear programming, dynamic programming, network programming, methods of mathematical statistics, the Monte Carlo method) and heuristic methods, including: greedy algorithms; simulated annealing; evolutionary algorithms; swarm algorithms; artificial immune systems; artificial neural networks and elements of fuzzy logic. More and more frequently, fuzzy logic finds use in the modelling of complex manufacturing systems. Its use in issues related to the process of mining, as well as in underground and surface mines, has been described inter alia in (Benovi et al., 2013; Vujic et al., 2011; Bazzazi et al., 2009; Grychowski, 2008; Bascetin & Kesimal, 1999; Nguyen, 1985; Hosseini et al., 2012; Dezyani et al., 2006; Li, 2009; Razani et al., 2013; Karadogan et al., 2008). This article focuses on the possibilities of using fuzzy logic in the design of mining process in an underground coal mine, with reference to selected elements of its spatial and technical structure. 3. Proposition of fuzzy systems supporting the design of selected elements in the mining process The selection of technical and technological equipment, as well as the organization of mining works to the geological and mining conditions, fundamentally affect the economic and production results of mines (Snopkowski & Sukiennik, 2012, 2013). Longwall faces are a main source of production (output) in an underground coal mine. Under Polish conditions, they are conducted using longwall systems (Snopkowski & Napieraj, 2012). Introduced later in this article solutions are developed equipment selection and the organization of mining activity in longwall faces. These solutions enable determination of production results in designed longwall faces ­ fuzzy systems FSES and FSOE. 3.1. Fuzzy system supporting equipment selection designed longwall faces ­ FSES (Fuzzy System Equipment Selection) The selection of equipment a designed longwall face involves specifying the machines and other equipment in longwall complex, which includes: a longwall coal-cutting machine (shearer); conveyor machinery; and sections of mechanized longwall support. The basic factors affecting the selection of shearer according to conducted surveys (Brzychczy & Ksek, 2007; Brzychczy & Napieraj, 2014) are: thickness of the deposit in the exploited area; thickness of rock vein in a given longwall section; crosswise inclination of the longwall; longitudinal inclination of the longwall; workability of the coal; category of methane hazard and longwall height. When choosing conveyor equipment, the following are taken into account: crosswise inclination of the longwall; longitudinal inclination of the longwall; length of the longwall and the type of shearing equipment being used. Selection of a mechanized longwall support is influenced by: thickness of the deposit; spoil in the roof; crosswise inclination of the longwall; floor class, ceiling class; level of rock burst hazard; longwall height and the method of roof protection. In the FSES system, a part of the abovementioned parameters affecting the selection of longwall face equipment (quantitative variables), was expressed using fuzzy sets. These sets, along with specific membership functions (included in the FSES fuzzy system model) are shown in table 2. In order to obtain a fuzzy rules knowledge base, data concerning the operating conditions of 250 longwall faces (and their equipment) from two multi-mine mining companies were used. Fuzzy rules were determined according to the algorithm described in (Wang & Mendel, 1992). In arranging machines and other equipment, an algorithm of association rules was used (Brzychczy, 2009). A fragment of the base of determined fuzzy rules the FSES system (consisting of over 100 rules) is shown in table 3. Due to the multitude of different types of mechanized longwall supports, the minimal limits of the operation range these devices were declared each fuzzy set describing the "longwall height" variable. Table 4 shows different combination rules shearing equipment and conveyor machinery. TABLE 2 Functions of membership select parameters in the FSES system Variable Sets and membership functions 1 175 l ( short ) (l ) 25 0 0 l 150 25 ( ) (l ) 1 275 l 25 0 l 150 150 l 175 l 175 l 150 150 l 175 175 l 250 250 l 275 l 275 Longwall length, l [m] l 275 0 l 250 (long ) (l ) 250 l 275 25 l 275 1 1 2 h (low) (h) 1 0 0 h 1 1 ( ) (h) 1 4 h 1 0 h 1 1 h 2 h2 h 1 1 h 2 2 h 3 3 h 4 h4 Longwall height, h [m] h3 0 h 3 ( high ) (h) 3 h 4 1 h4 1 1 10 c (low) (c) 2 0 c8 8 c 10 c 10 c8 8 c 10 Longitudinal inclination of the longwall, c [] 0 c 8 2 ( ) (c) 1 25 c 5 0 10 c 20 20 c 25 c 25 c 20 0 c 20 ( high ) (c) 20 c 25 5 c 25 1 TABLE 2. CONTINUED 1 5 p (low) ( p) 2 0 p3 3 p 5 p5 p3 3 p 5 5 p 10 Crosswise inclination of the longwall, p [] 0 p 3 2 ( ) ( p) 1 15 p 5 0 10 p 15 p 15 p 10 0 p 10 ( high ) ( p) 10 p 15 5 p 15 5 1 1, 2 f ( good ) ( f ) 1, 2 0 0 f 1, 2 0, 4 ( hard ) ( f ) 1, 6 f 0, 4 0 f 0 f 1, 2 f 1, 2 f 1, 2 Coal workability (coefficient f) 1, 2 f 1, 6 1, 6 f 2 f 2 f 2 0 f 2 (very hard ) ( f ) 2 f 2, 2 0, 2 1 f 2, 2 1 0,5 g (low) ( g ) 0, 2 0 0 g 0,3 0, 2 ( ) ( g ) 1 0,9 g 0, 2 0 0 g 0, 7 ( high ) ( g ) 0, 2 1 g 0,3 0,3 g 0,5 g 0,5 g 0,3 0,3 g 0,5 Thickness of rock vein in a given longwall section, g [m] 0,5 g 0, 7 0, 7 g 0,9 g 0,9 g 0, 7 0, 7 g 0,9 g 0,9 TABLE 3 Fragment of the fuzzy rule base the FSES system Premises IF ... and ... and ... Conclusions Ceiling class = I V III I III III III III III IV IV I I II III 0 IV IV 0 IV 0 III 0 I III 0 0 IV II Category of methane hazard.= THEN shearer type = KGE 750 Eickhoff SL300 KSW 2000E KGS 600 JOY 4L KSW 620EZ KSW 1140E Electra 1000 KSW 880EU KSW 460N Strug GH 1600 KGE 710FM KSW 475 JOY 7LS6 c= low low low low hard good very hard low low low I III II VI I III II hard good good good hard good very hard low I III hard low I good low II good low III very hard low II f= g= Floor class = Rule no. l= h= p= high high long high low high low low 5 low low high low high long 8 low low low low low short low low short 13 low low high low Category of THEN min/max rock bust support system range = hazard. = According to type / I above 3,5 m According to type / III above 3,5 m According to type / I above 3,5 m 1,5m 0 to 3,5m According to type / I above 3,5 m According to type / 0 above 3,5 m 1,5m III to 3,5m 1,5m I to 3,5m 1,5m 0 to 3,5m 1,5m 0 to 3,5m According to type / to 0 1,5 m 1,5m 0 to 3,5m 1,5m 0 to 3,5m According to type / I above 3,5 m TABLE 4 Rules of combination shearing equipment and conveyor machinery Rule no. Premise IF shearer = ==> Conclusion THEN conveyor = Confidence (%) Eickhoff SL300 Electra 1000 JOY 4L JOY 7LS6 KGE 710FM KGE 750 KGS 600 KSW 1140E KSW 2000E KSW 460N KSW 475 KSW 620EZ KSW 880EU Strug GH 1600 ==> ==> ==> ==> ==> ==> ==> ==> ==> ==> ==> ==> ==> ==> RYBNIK 850 RYBNIK 850 RYBNIK 850 RYBNIK 1100 RYBNIK 850 RYBNIK 850 RYBNIK 750 RYBNIK 850 RYBNIK 1100 RYBNIK 750 RYBNIK 850 RYBNIK 850 RYBNIK 850 PF 4/1032 36,3636 100,0000 56,2500 100,0000 60,0000 81,2500 43,7500 66,6667 100,0000 41,0256 64,7059 100,0000 46,6667 100,0000 each type of shearer, rules with the highest confidence coefficient were chosen (CC). This coefficient shows the relationship between the number of shearer combinations K with a given conveyor device P, and the number of occurring shearers K, which can be shown with the mula: CC P( K P) 100% K (2) where: P ­ is the number of occurrences of given elements of a longwall complex. A diagram of the developed system (FSES) is shown in figure 2. Inference in the system is done in two stages. After the insertion of data and the fuzzification, inference based on fuzzy rules stored in the system knowledge base is conducted. Then are shown the minimal intervals the operation range of the mechanized longwall support and active rules, the is conducted using the max method (MD). The result is a proposition of longwall shearer which is suitable use under the given conditions. The next stage of inference uses association rules the pairing of shearers and conveyors a given element of the longwall complex. After determining the proposition the given longwall complex, it is possible to specify the duration and output each production cycle according to fuzzy system FSOE, which is described later in this article. Insertion of data concerning the designed longwall face Fuzzification with use of fuzzy sets Start of inference procedure Checking premises of fuzzy rules Checking premises of associative rules Proposition of longwall shearer type Determination of minimal operational ranges mechanized longwall supports Proposition of longwall conveyor type Proposition of longwall complex FSOE Fig. 2. Operational scheme of FSES system 3.2. Fuzzy system FSOE (Fuzzy System Output Estimation) supporting estimation of production results The production process realized in longwall faces of coal mines is characterized by the fact that its operation is influenced by many factors. These factors are related to geological, technical, organizational and mining conditions. Fuzzy system FSOE is a continuation of system FSES and enable to estimate the duration of the production cycle and the level of shift output in coal mines. The results can be used when making decisions concerning the design and management of the mining process. System FSOE makes inferences according to the scheme shown in figure 3. First, based on inserted input data, a fuzzy set is determined the duration of the production cycle; which in turn, then becomes an input parameter the magnitude of shift output. FSES Insertion of input data into system FSOE Fuzzification with use of fuzzy sets Start of inference procedure Estimation of shift output Estimation of production cycle duration Checking premises of fuzzy rules Generation of shift output values designed longwall face Fig. 3. Operation scheme fuzzy system FSOE The duration of a production cycle is the sum of the individual elements realization times (Snopkowski & Napieraj 2012) e.g. cleaning with use of the shearer within a section (xp ­ dk), cutting with use of the shearer within a section (L ­ xp), slotting with use of the shearer within a section (xo + dk + p + s), cutting with use of shearer within a section equal to (xo + dk + p + s), turning station replacement, and driving unit replacement. It can be expressed by the mula: Tc where: Tc L Vr Vz Vm xp dk xo p s tz tn 1 1 1 1 ( x p d k ) ( L x p ) ( xo d k p s ) t z tn Vcz Vr Vz Vr (3) -- -- -- -- -- -- -- -- -- -- -- -- production cycle duration [min], longwall length [m], shearer operational advance rate [m/min], advance rate of the slotting shearer [m/min], shearer maneuver advance rate (shearer advance rate during cleaning the shearer route) [m/min], distance between shearer stoppage place and longwall-roadway crossing [m], shearer length [m], distance between shifted conveyor and support[m], minimal distance between shifted conveyor and shearer [m], distance between support and shearer [m], turning station replacement time [min], turning drive unit replacement time [min]. A part of these parameters is shown as fuzzy sets which, along with their functions of membership, are shown in table 5. TABLE 5 Fuzzy sets and functions of membership parameters inserted into the FSOE system Parameter Sets and membership functions 1 8 V m (low) (Vm ) 4 0 0 V 4 m 4 ( ) (Vm ) 1 22 V m 9 0 Vm 4 4 Vm 8 Vm 8 Vm 4 4 Vm 8 8 Vm 13 0,2 0 0 5 10 15 20 25 30 Vm ­ shearer maneuver advance rate, [m/min] 13 Vm 22 Vm 22 low high Vm 13 0 V 13 m 13 Vm 22 ( high ) (Vm ) 9 Vm 22 1 TABLE 5. CONTINUED xp ­ distance between shearer stoppage place and longwallroadway crossing, [m] x p 14 1 16 x p (low) ( x p ) 14 x p 16 2 x p 16 0 x p 14 0 x p 14 14 x p 16 2 16 x p 19 ( ) ( x p ) 1 21 x p 19 x p 21 2 0 x p 21 0 x p 19 ( high ) ( x p ) 2 1 x p 19 0,2 0 10 15 20 25 low high 19 x p 21 x p 21 1 3,8 Vr (low) (Vr ) 2,8 0 Vr 1 1 Vr 3,8 Vr 3,8 Vr 1 1 Vr 3,8 Vr ­ shearer operational advance rate [m/min] 0 V 1 r 2,8 ( ) (Vr ) 6, 7 Vr 2,9 0 3,8 Vr 6, 7 Vr 6, 7 0,2 0 0 2 4 6 8 Vr 3,8 0 Vr 3,8 ( high ) (Vr ) 3,8 Vr 6, 7 2,9 1 Vr 6, 7 1 5,9 Vz (low) (Vz ) 3,9 0 Vz 2 low high 2 Vz 5,9 Vz 5,9 Vz 2 2 Vz 5,9 Vz ­ advance rate of the slotting shearer [m/min] 0 V 2 z 3,9 ( ) (Vz ) 10 Vz 4,1 0 0 V 5,9 ( high ) (Vz ) z 4,1 1 5,9 Vz 10 Vz 10 Vz 5,9 0,2 0 0 2 4 6 8 10 12 low high 5,9 Vz 10 Vz 10 TABLE 5. CONTINUED 1 15 s (low) ( s ) 7 0 s8 8 s 15 s 15 s8 8 s 15 s ­ distance between support and shearer [m] 0 s 8 ( ) ( s ) 7 20 s 5 0 15 s 20 s 20 0,2 0 0 5 10 15 20 25 30 s 15 0 s 15 15 s 20 ( high ) ( s ) 5 s 20 1 1 8 t z (low) (t z ) 5 0 tz 3 low high 3 t z 8 tz 8 tz 3 3 tz 8 tz ­ turning station replacement time [min] 0 t 3 z 5 ( ) (t z ) 13 t z 5 0 8 t z 13 t z 13 0,2 0 0 5 10 15 tz 8 0 t 8 z 8 t z 13 ( high ) (t z ) 5 t z 13 1 1 13 t n (low) (tn ) 10 0 tn 3 low high 3 tn 13 tn 13 tn 3 3 tn 13 0,2 0 0 5 10 15 20 25 30 tn ­ turning drive unit replacement time [min] 0 t 3 n ( ) (tn ) 10 25 tn 12 0 13 tn 25 tn 25 tn 13 0 t 13 n 13 tn 25 ( high ) (tn ) 12 tn 25 1 low high Table 6 shows selected rules used in the system inference process at this stage of work. These rules were determined on the basis of timing research conducted in longwall faces of Polish coal mines. The knowledge base contains over 2000 rules. TABLE 6 Combinations of selected FSOE system rules estimation of production cycle duration Rule no. Premise IF ... and ... and ... Vz = s= ==> tz = tn = l= Conclusion THEN Tc = Vm = xp = Vr = low low high high low high low high low low high high high high low high low low low low low low short ==> high low low short ==> high low low low short ==> low high short ==> low ==> high high high high long ==> low high high long ==> low low low high long ==> low high high high long ==> low low low high high high The level of shift output from a longwall face depends not only on the duration of the production cycle, but also on: longwall height; shearer web; disposable shift time. The relationship is described by the following equation: Wzm where: Td Tc h z l Td h z l Tc (4) -- -- -- -- -- -- disposable shift time [min/zm], duration of the production cycle [min], longwall hight [m], shearer web [m], longwall length [m], coal specific weight [Mg/m3]. Table 7 summarizes the membership functions these parameters, which are also included in the fuzzing module of the FSOE system. Table 8 shows selected rules used in the second stage of FSOE system inference. TABLE 7 Fuzzy sets and membership functions of the abovementioned parameters the FSOE system ­ c.d. Parameter Sets and membership functions 1 0, 75 z (low) ( z ) 0, 05 0 0 z 0, 7 0, 05 ( ) ( z ) 0,8 z 0, 05 0 z 0, 6 0, 6 z 0, 7 z 0,8 z 0, 6 0, 6 z 0, 7 z ­ shearing web [m] 0, 75 z 0,8 z 0,8 0,2 0 0,6 0,65 low 0,7 0,75 0,8 high 0,85 z 0, 75 0 z 0, 75 0, 75 z 0,8 ( high ) ( z ) 0, 05 1 z 0,8 1 355 T d (low) (Td ) 15 0 0 T 340 d 15 ( ) (Td ) 370 Td 15 0 T ( high ) (Td ) d Td 340 340 Td 355 Td 355 Td 340 Td ­ disposable shift time [m/zm] 340 Td 355 355 Td 370 Td 370 0,2 0 320 340 low 360 380 high 0 Td 355 355 355 Td 370 15 1 Td 370 TABLE 8 Combination of selected FSOE inference rule used to determine shift output Rule no. Tc = Premise IF ... and ... and ... h= z= Td = ==> l= Conclusion THEN Wzm = high high low low low low low low low high low low low high high short short short long ==> ==> ==> ==> ==> low low low TABLE 8. CONTINUED high low low high high high high high high high high high high long long long long ==> ==> ==> > high high high Operation of fuzzy systems is presented with use of a case study in chapter 3.3. 3.3. Case study The designed longwall face is characterized by the parameters presented in Table 9. TABLE 9 Longwall face parameters Longwall length = 220 m Longwall height = 4,2 m · · · · Transverse inclination = 1,5° Floor class = II Coefficient f = 1,1 Category of methane hazard = lack · · · · Longitudinal inclination 3,2° Roof class = III Thickness of rock vein in coal seam = 0,2 m Level of rock burst threat = I The above data were inserted into fuzzy system FSES which, on the grounds of the rule base and the inference process conducted (table 3 rule 3), proposed shearer type KSW 2000E, as well as requirements regarding the range of longwall support system (according to type/above 3,5 m). In addition, on the basis of the rules combining machines with other equipment (table 4 rule 9), it proposed the last element of the longwall complex ­ conveyor Rybnik 1100. The obtained data were then inserted into FSOE system to estimate the shift output in the designed longwall face. The input parameters were supplemented by the following data: ­ dk ­ shearer length, dk = 10 [m], ­ xo ­ distance between shearer stoppage place and longwall-roadway crossing, xo = 3,2 [m], ­ p ­ minimal distance between shifted conveyor and shearer, p = 5,25 [m], ­ ­ coal specific weight, = 1,35 [g/m3]. As a result of the inference process, a fuzzy set was generated the duration of the production cycle (table 6 rule 5), which was then defuzzied by the geometric method of gravity center (COG), thus yielding the numerical value Tc = 91,22 [min]. This value was then used to estimate shift output (activating rule 5 table 8). Likewise, in this case the end results were determined using by the COG method. In the analysed case the given parameters of the designed longwall face and selected equipment, the shift output determined by system FSOE amounted to 3664 [Mg/zm]. 4. Summary The mining process is a process of production affecting the economic state of countries in possession of mineable natural resources. Its design includes distinguished structures; and in terms of space, technology and time, it should take into account the knowledge accumulated by mines and mining enterprises in order to improve the quality of design decisions. The storage and use of this knowledge is enabled by systems with a knowledge base, which also include elements of fuzzy logic (creating i.e. fuzzy systems). This work has introduced fuzzy systems, which can be applied when designing elements of the mining process. The first of them is system FSES, which facilitates the selection of equipment according to the conditions of longwall faces. The fuzzification module in this system makes possible a fuzzy operation the following quantitative variables: longwall length; longwall height; longitudinal and cross-wise incline of the longwall; workability of coal and the thickness of rock vein in a given longwall section. The knowledge base includes over 100 fuzzy rules determining equipment suitable use under the specified conditions of an longwall face. After determination of the proposed equipment, it is then possible to insert the values obtained into the second system FSOE, which enables estimation of shift output according to the selected parameters. The fuzzification module in system FSOE includes 9 linguistic variables, which are necessary determining shift output in the designed longwall face. The system knowledge base contains over 200 rules. As a result of the operation of both systems, the designer receives both a proposition longwall face equipment, and the estimated shift output under given conditions. These results can be used when designing certain elements of the mining process (longwall faces) or the verification of adopted plans. Fuzzy logic allows a smooth and relatively precise description of key relationships between variables of imprecise nature which serve as input data the design process. The fuzzy inference conducted by the system on the basis of rules saved in the knowledge base generalizes the knowledge possessed by the designer, as well as a method of inference is similar to that of the reasoning of an expert. Fuzzy systems can effectively support ­ among other things ­ the design of selected elements of the mining process, as presented in the above article. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archives of Mining Sciences de Gruyter

The Use of Fuzzy Systems in the Designing of Mining Process in Hard Coal Mines

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Arch. Min. Sci., Vol. 59 (2014), No 3, p. 741­760 Electronic version (in color) of this paper is available: http://mining.archives.pl DOI 10.2478/amsc-2014-0052 EDYTA BRZYCHCZY*, MAREK KSEK*, ANETA NAPIERAJ*, MARTA SUKIENNIK* WYKORZYSTANIE SYSTEMÓW ROZMYTYCH W PROJEKTOWANIU PROCESU WYDOBYWCZEGO W KOPALNIACH WGLA KAMIENNEGO This article presents examples of solutions supporting the design of certain elements of the mining process in coal mines. The focus is on two fuzzy systems: the first supports the selection of equipment longwall faces (FSES); and the second supports the estimation of production results (FSOE). System FSES generates proposals equipment in designed longwall faces. The module of fuzzing in this system enables a fuzzing operation the following quantitative variables: longwall length; longwall height; longitudinal and crosswise incline of the longwall, workability of the coal and thickness of rock vein in a given section of the longwall. The knowledge base includes over 100 fuzzy rules indicating possible options equipment under specified site conditions. After a proposal of equipment is generated, it is then possible to insert the values obtained into the second system FSOE, which estimates output a given shift time using the chosen parameters. The module of fuzzing in system FSOE includes 9 variables, which are crucial in determining shift output the given longwall face. The knowledge base in this system contains over 2000 rules. As a result of the operation of both systems, the designer receives both a proposal of equipment the designed longwall face and the size of shift output under the given conditions. Operation of the two systems has been presented using a case study. Keywords: coal mine, mining process, fuzzy logic, fuzzy systems, modelling Logika rozmyta pozwala na plynne i stosunkowo dokladne opisanie istotnych zalenoci pomidzy zmiennymi o charakterze nieprecyzyjnym lub malo dokladnym, które s danymi wejciowymi do procesu projektowania. Prowadzony przez system rozmyty proces wnioskowania na podstawie zapisanych w bazie wiedzy regul pozwala na uogólnienie posiadanej przez projektantów wiedzy, a take prowadzenie wnioskowania w sposób zbliony do rozumowania eksperta. W artykule zaprezentowano przyklady opracowanych rozwiza wspomagajcych projektowanie wybranych elementów procesu wydobywczego w kopalniach wgla kamiennego. Przedstawiono dwa systemy rozmyte, pierwszy wspomagajcy dobór wyposaenia do projektowanych wyrobisk cianowych (FSES) oraz drugi wspomagajcy szacowanie wyników produkcyjnych (FSOE). * AGH UNIVERSITY OF SCIENCE AND TECHNOLOGY, FACULTY OF MINING AND GEOENGINEERING, DEPARTMENT OF ECONOMICS AND MANAGEMENT IN INDUSTRY, AL. A. MICKIEWICZA 30, 30-059 KRAKOW, POLAND System FSES umoliwia wyznaczenie propozycji wyposaenia dla projektowanych wyrobisk cianowych. Modul rozmywania w tym systemie umoliwia przeprowadzenie operacji rozmycia nastpujcych zmiennych ilociowych: dlugo ciany, wysoko ciany, nachylenie podlune i poprzeczne ciany, urabialno wgla oraz grubo przerostów w przekroju ciany. Baza wiedzy obejmuje ponad 100 regul rozmytych wskazujcych w konkluzjach moliwe do zastosowania wyposaenie, w okrelonych warunkach wyrobiska. Po wyznaczeniu proponowanego wyposaenia, moliwe jest wprowadzenie otrzymanych wartoci do drugiego systemu FSOE, który umoliwia oszacowanie wydobycia zmianowego dla zadanych parametrów. Modul rozmywania systemu FSOE obejmuje 9 zmiennych, które konieczne s do wyznaczenia wydobycia zmianowego w projektowanym wyrobisku. Baza wiedzy tego systemu zawiera ponad 2000 regul. W efekcie dzialania obu systemów projektant otrzymuje propozycj wyposaenia dla projektowanego wyrobiska cianowego oraz oszacowan wielko wydobycia zmianowego dla podanych warunków. Wyniki te moe wykorzysta w procesie projektowania wybranych elementów procesu wydobywczego (wyrobisk cianowych) lub weryfikacji przyjtych planów produkcyjnych. Dzialanie opracowanych systemów zaprezentowano na wybranym przykladzie wyrobiska cianowego. Slowa kluczowe: kopalnia wgla kamiennego, proces wydobywczy, logika rozmyta, systemy rozmyte, modelowanie Introduction One of the basic tasks of a coal mine is to assure the required level of production and to protect the supply of raw materials within. This can be done through proper implementation of the mining process. The mining process is a specific kind of production process, which is based on the acquisition of non-renewable deposits (warehouse-transport process). The specificity of the mining process results from the fact that this process is carried out between nature and man, entailing specific consequences its operational course. The conditions conducting mining activities (uncertainty and risk related to the geology of deposits and other natural threats) compel designers to accumulate knowledge such as relevant inmation and past experience in an eft to improve the accuracy of design decisions. In the design of mining activities, knowledge plays a specific role in the cutting and selection order of the deposit, the selection of equipment suitable longwall face conditions, as well as the estimation of longwall face progress. example, the selection of equipment longwall face conditions can be done according to basic principles adapted to the producer's technical specifications; but an experienced designer knows that, in a given deposit, the geological and mining conditions can make it impossible to realize the planned amount of output. This knowledge comes from common experiences and specific rules that guide a given designer. Tacit knowledge can be obtained through the mulation with use of the expert methods (interviews, questionnaires, expert observations), or through advanced techniques of data exploration (with the use of algorithms designed to generate such knowledge). Obtained knowledge concerning the mining process can be stored in knowledge base systems (e.g. expert systems) (Brzychczy, 2011). In order to do this, knowledge must be appropriately represented e.g. as rules. Rules made by the experts are often characterized by a lack of precision, due to the inmal nature of human reasoning and the lack of reliable schemes of inference. In order to save these rules, it is possible to use fuzzy logic in the database, which enables a process of inference even when descriptions of the researched phenomenon are imprecise. Fuzzy logic also makes possible a general description of rules obtained in the process of knowledge discovery from data (Brzychczy, 2012). Making inferences in a way similar to the way an expert reasons (using the base of fuzzy rules) is made possible by fuzzy systems, the theoretical basis of which is described further in the article. 1. Logic and fuzzy systems Fuzzy systems are based on the theory of fuzzy logic. Fuzzy logic was developed by Lotfi A. Zadeh in the 1960s (Zadeh, 1965). It is an extension of classical reasoning closer to human reasoning. Fuzzy logic is used in process improvement and in various optimization tasks. One of the first examples of its application was controlling the Sendai metro in Japan. The control system was developed based on the experience of an engineer who, many years accumulated practical knowledge about controlling the metro system. His observations and proper use of fuzzy logic led to the creation of an automatic control system by Hitachi (Abel, 1991), (Piegat, 1999). The next achievements based on the principles of fuzzy sets or fuzzy numbers led to the fruition of increasingly newer and more developed fuzzy systems. The basic concept in fuzzy logic is fuzzy set A in X (mula 1). This is a set of pairs such that (Piegat, 1999); (Nowicki, 2009): A {( x, A ( x), ) x X } A : X [0,1] (1) where A is a function of membership, describing each x X the value of this element's membership A : X [0,1] to the fuzzy set A and A X The function of this membership thus assigns to each element x of a variable, a certain value from the range [0,1] and this value is called the degree of membership. In classic sets, the value is assigned as 1 when the element completely belongs to the set or 0 when it does not belong at all. In fuzzy logic theory, the element can belong to the set to a certain degree, meaning the function of membership can take the values from the whole unit bracket [0,1]. We can theree distinguish three cases: ­ A (x) = 1, which means full membership to set A, ­ A (x) = 0, which means total lack of membership to set A, ­ 0 < A (x) < 1, which means partial membership of element x to set A. The membership function can be expressed as a continuous or discreet diagram, a mula, table, sum, or a vector of membership. In practice, the creation of fuzzy systems, functions of membership are used, with different ms. Among the most common ms of the membership functions are: triangle, trapezoid, the letters "L", "S" and the Gaussian function. The selected membership functions are shown in Table 1. Functions of membership described using polygons or segments have many advantages, and a small number of parameters will suffice to define them. They are characterized by ease of parameter modification, on the basis of system input and output measurement values (Piegat, 1999). Describing the membership function using the Gaussian function entails many difficulties. Above all, the Gaussian function is symmetric, which means that the criteria of unifying fuzzy sets are not met. There is also the need to identify two parameters of the function. These factors hinder the acquisition of simple, locally linear surfaces of the fuzzy model. On the other hand, the function as such facilitates theoretical analysis of fuzzy systems, because its derivatives can be set to any level (Piegat, 1999). TABLE 1 Selected ms of the membership function and their graphic presentation Type of function Sets and membership functions Graphic representation of membership functions triangular xa 0, xa , a xb A x; a, b, c b a c x , b x c c b 0, xc xa 0, b x A x; a, b , a xb b a xc 1, xa 0, xa , a xb b a A x; a, b, c, d 1, bxc c x , cxd c b 0, xd "L" shape trapezoidal Gaussian function A x; x , e 1 x x 2 2 Fuzzy systems are models which process inmation using fuzzy rules. They are made up of 4 elements (Fig. 1): 1. A fuzzification module, which converts system input, i.e. acute numerical values into fuzzy ones. This is done via the membership function of defined fuzzy sets. 2. A knowledge base which stores the set of rules representing the knowledge about the problem. These rules can come from different sources: from experts appointed on the basis of qualitative modelling; and from algorithms which automatically generate knowledge. 3. A mechanism of inference, which simulates human reasoning through a fuzzy inference process according to the logic stored in the rules. 4. A module, which converts a fuzzy set indicated by the inference result into acute values. Fig. 1. Fuzzy system scheme based on (Nowicki, 2009) System works as follows: after inserting the input data, quantitative variables are converted into linguistic variables; then, inference is done according to the knowledge base, which contains fuzzy rules (representing knowledge about the problem being analysed); and finally, in the module, the resulting fuzzy set is converted into numerical values. The inference mechanism comprises a crucial element of the fuzzy system. It uses the knowledge base, and the rules contained within it. The "rule of inference" can be understood as a method of deriving conclusions from premises. This process can be carried out using the rules: modus ponendo ponens (inference through statement); modus tollendo tollens (inference through denial); conditional syllogism of the stoics; or the principles of distribution (Lski, 2008). "Ifthen" rules can be obtained in the following manner: ­ Specification of the premises, and then the conclusion. ­ Specification of the conclusions of a rule, and then the selection of its premises. ­ Independent determination of premises and conclusions. Among the basic methods of inference is the Mamdani model. Systems using this model rely on a base of rules and the use of linguistic operators, and inference is done through the aggregation of fuzzy sets resulting from all the rules. Thus, the fuzzy set is the resulting set. The second group is comprised of systems based on the Takagi-Sugeno-Kanga model. In this model ­ in contrast to the Mamdani model ­ the base of rules is fuzzy only in the first part; that is to say, the "if" part. In the second part ­ the "then" part ­ functional relationships occur. Obtaining a result from the fuzzy system is possible through the operation. This involves the determination of a qualitative or quantitative value the output variable, based on knowledge of the nature of the resulting fuzzy set. There are several methods of . The most common are (Lski, 2008; Nowicki, 2009): ­ Method of maximum (MD), in which the output value is the maximum value of the argument from the set of argument values of the membership function the resulting fuzzy set. ­ Method of height (HM), where the output value is affected by all the activated premises, and not just those that have the biggest impact on the given fuzzy set the output variable. In this method, fuzzy sets of the output variable are converted into single-element sets (Singletons). ­ Method of gravity centre (COG), in which the output variable is the centre of gravity the shape created by the output fuzzy set. Fuzzy systems enable effective modelling of complicated and advanced technological processes. Inference based on fuzzy rules, as well as the possibility of conducting analysis using quantitative and qualitative variables, can also be used in the designing of mining process. Examples of developed solutions in this field are presented later in this article. 2. Designing of mining process The designing of mining process can be divided into the following stages: 1. Work study. 2. Searching solutions. 3. Evaluation and selection of solutions. 4. Detailed design. 5. Implementation of design solutions. The basic mode of operations during work study is the accumulation of knowledge concerning the designed task (e.g. market analysis, diagnosis of the mal legal situation, familiarization with input data related to task data, or to geological documentation of the deposit in the case of a mine), specification of requirements and constraints the mulated design problem, and indication of evaluation criteria solutions with regard to uncertainty and risk. In the case of mining process, the main design tasks are: ­ Identification of longwall faces taking part in the mining process, as well as the essential surface infrastructure (elements of spatial structure). ­ Selection of equipment and the organization of work. ­ Specification of time intervals mining activities. Next in the modelling stage is the generation of potential design solutions, which are subjected to preliminary selection. The result of this stage is a set of descriptions of possible solutions. In the next stage is the evaluation of solutions and selection of the best, which detailed design is subsequently carried out. Then, design documentation is drawn up, which is essential implementing the chosen design solution. It should be highlighted that the quality of a design solution depends mainly on the stages of modelling and optimization. The designer can use different methods at different stages, which can significantly influence the design process and its results. Among these methods are algorithmic methods (i.e. systematic search methods, linear and nonlinear programming, dynamic programming, network programming, methods of mathematical statistics, the Monte Carlo method) and heuristic methods, including: greedy algorithms; simulated annealing; evolutionary algorithms; swarm algorithms; artificial immune systems; artificial neural networks and elements of fuzzy logic. More and more frequently, fuzzy logic finds use in the modelling of complex manufacturing systems. Its use in issues related to the process of mining, as well as in underground and surface mines, has been described inter alia in (Benovi et al., 2013; Vujic et al., 2011; Bazzazi et al., 2009; Grychowski, 2008; Bascetin & Kesimal, 1999; Nguyen, 1985; Hosseini et al., 2012; Dezyani et al., 2006; Li, 2009; Razani et al., 2013; Karadogan et al., 2008). This article focuses on the possibilities of using fuzzy logic in the design of mining process in an underground coal mine, with reference to selected elements of its spatial and technical structure. 3. Proposition of fuzzy systems supporting the design of selected elements in the mining process The selection of technical and technological equipment, as well as the organization of mining works to the geological and mining conditions, fundamentally affect the economic and production results of mines (Snopkowski & Sukiennik, 2012, 2013). Longwall faces are a main source of production (output) in an underground coal mine. Under Polish conditions, they are conducted using longwall systems (Snopkowski & Napieraj, 2012). Introduced later in this article solutions are developed equipment selection and the organization of mining activity in longwall faces. These solutions enable determination of production results in designed longwall faces ­ fuzzy systems FSES and FSOE. 3.1. Fuzzy system supporting equipment selection designed longwall faces ­ FSES (Fuzzy System Equipment Selection) The selection of equipment a designed longwall face involves specifying the machines and other equipment in longwall complex, which includes: a longwall coal-cutting machine (shearer); conveyor machinery; and sections of mechanized longwall support. The basic factors affecting the selection of shearer according to conducted surveys (Brzychczy & Ksek, 2007; Brzychczy & Napieraj, 2014) are: thickness of the deposit in the exploited area; thickness of rock vein in a given longwall section; crosswise inclination of the longwall; longitudinal inclination of the longwall; workability of the coal; category of methane hazard and longwall height. When choosing conveyor equipment, the following are taken into account: crosswise inclination of the longwall; longitudinal inclination of the longwall; length of the longwall and the type of shearing equipment being used. Selection of a mechanized longwall support is influenced by: thickness of the deposit; spoil in the roof; crosswise inclination of the longwall; floor class, ceiling class; level of rock burst hazard; longwall height and the method of roof protection. In the FSES system, a part of the abovementioned parameters affecting the selection of longwall face equipment (quantitative variables), was expressed using fuzzy sets. These sets, along with specific membership functions (included in the FSES fuzzy system model) are shown in table 2. In order to obtain a fuzzy rules knowledge base, data concerning the operating conditions of 250 longwall faces (and their equipment) from two multi-mine mining companies were used. Fuzzy rules were determined according to the algorithm described in (Wang & Mendel, 1992). In arranging machines and other equipment, an algorithm of association rules was used (Brzychczy, 2009). A fragment of the base of determined fuzzy rules the FSES system (consisting of over 100 rules) is shown in table 3. Due to the multitude of different types of mechanized longwall supports, the minimal limits of the operation range these devices were declared each fuzzy set describing the "longwall height" variable. Table 4 shows different combination rules shearing equipment and conveyor machinery. TABLE 2 Functions of membership select parameters in the FSES system Variable Sets and membership functions 1 175 l ( short ) (l ) 25 0 0 l 150 25 ( ) (l ) 1 275 l 25 0 l 150 150 l 175 l 175 l 150 150 l 175 175 l 250 250 l 275 l 275 Longwall length, l [m] l 275 0 l 250 (long ) (l ) 250 l 275 25 l 275 1 1 2 h (low) (h) 1 0 0 h 1 1 ( ) (h) 1 4 h 1 0 h 1 1 h 2 h2 h 1 1 h 2 2 h 3 3 h 4 h4 Longwall height, h [m] h3 0 h 3 ( high ) (h) 3 h 4 1 h4 1 1 10 c (low) (c) 2 0 c8 8 c 10 c 10 c8 8 c 10 Longitudinal inclination of the longwall, c [] 0 c 8 2 ( ) (c) 1 25 c 5 0 10 c 20 20 c 25 c 25 c 20 0 c 20 ( high ) (c) 20 c 25 5 c 25 1 TABLE 2. CONTINUED 1 5 p (low) ( p) 2 0 p3 3 p 5 p5 p3 3 p 5 5 p 10 Crosswise inclination of the longwall, p [] 0 p 3 2 ( ) ( p) 1 15 p 5 0 10 p 15 p 15 p 10 0 p 10 ( high ) ( p) 10 p 15 5 p 15 5 1 1, 2 f ( good ) ( f ) 1, 2 0 0 f 1, 2 0, 4 ( hard ) ( f ) 1, 6 f 0, 4 0 f 0 f 1, 2 f 1, 2 f 1, 2 Coal workability (coefficient f) 1, 2 f 1, 6 1, 6 f 2 f 2 f 2 0 f 2 (very hard ) ( f ) 2 f 2, 2 0, 2 1 f 2, 2 1 0,5 g (low) ( g ) 0, 2 0 0 g 0,3 0, 2 ( ) ( g ) 1 0,9 g 0, 2 0 0 g 0, 7 ( high ) ( g ) 0, 2 1 g 0,3 0,3 g 0,5 g 0,5 g 0,3 0,3 g 0,5 Thickness of rock vein in a given longwall section, g [m] 0,5 g 0, 7 0, 7 g 0,9 g 0,9 g 0, 7 0, 7 g 0,9 g 0,9 TABLE 3 Fragment of the fuzzy rule base the FSES system Premises IF ... and ... and ... Conclusions Ceiling class = I V III I III III III III III IV IV I I II III 0 IV IV 0 IV 0 III 0 I III 0 0 IV II Category of methane hazard.= THEN shearer type = KGE 750 Eickhoff SL300 KSW 2000E KGS 600 JOY 4L KSW 620EZ KSW 1140E Electra 1000 KSW 880EU KSW 460N Strug GH 1600 KGE 710FM KSW 475 JOY 7LS6 c= low low low low hard good very hard low low low I III II VI I III II hard good good good hard good very hard low I III hard low I good low II good low III very hard low II f= g= Floor class = Rule no. l= h= p= high high long high low high low low 5 low low high low high long 8 low low low low low short low low short 13 low low high low Category of THEN min/max rock bust support system range = hazard. = According to type / I above 3,5 m According to type / III above 3,5 m According to type / I above 3,5 m 1,5m 0 to 3,5m According to type / I above 3,5 m According to type / 0 above 3,5 m 1,5m III to 3,5m 1,5m I to 3,5m 1,5m 0 to 3,5m 1,5m 0 to 3,5m According to type / to 0 1,5 m 1,5m 0 to 3,5m 1,5m 0 to 3,5m According to type / I above 3,5 m TABLE 4 Rules of combination shearing equipment and conveyor machinery Rule no. Premise IF shearer = ==> Conclusion THEN conveyor = Confidence (%) Eickhoff SL300 Electra 1000 JOY 4L JOY 7LS6 KGE 710FM KGE 750 KGS 600 KSW 1140E KSW 2000E KSW 460N KSW 475 KSW 620EZ KSW 880EU Strug GH 1600 ==> ==> ==> ==> ==> ==> ==> ==> ==> ==> ==> ==> ==> ==> RYBNIK 850 RYBNIK 850 RYBNIK 850 RYBNIK 1100 RYBNIK 850 RYBNIK 850 RYBNIK 750 RYBNIK 850 RYBNIK 1100 RYBNIK 750 RYBNIK 850 RYBNIK 850 RYBNIK 850 PF 4/1032 36,3636 100,0000 56,2500 100,0000 60,0000 81,2500 43,7500 66,6667 100,0000 41,0256 64,7059 100,0000 46,6667 100,0000 each type of shearer, rules with the highest confidence coefficient were chosen (CC). This coefficient shows the relationship between the number of shearer combinations K with a given conveyor device P, and the number of occurring shearers K, which can be shown with the mula: CC P( K P) 100% K (2) where: P ­ is the number of occurrences of given elements of a longwall complex. A diagram of the developed system (FSES) is shown in figure 2. Inference in the system is done in two stages. After the insertion of data and the fuzzification, inference based on fuzzy rules stored in the system knowledge base is conducted. Then are shown the minimal intervals the operation range of the mechanized longwall support and active rules, the is conducted using the max method (MD). The result is a proposition of longwall shearer which is suitable use under the given conditions. The next stage of inference uses association rules the pairing of shearers and conveyors a given element of the longwall complex. After determining the proposition the given longwall complex, it is possible to specify the duration and output each production cycle according to fuzzy system FSOE, which is described later in this article. Insertion of data concerning the designed longwall face Fuzzification with use of fuzzy sets Start of inference procedure Checking premises of fuzzy rules Checking premises of associative rules Proposition of longwall shearer type Determination of minimal operational ranges mechanized longwall supports Proposition of longwall conveyor type Proposition of longwall complex FSOE Fig. 2. Operational scheme of FSES system 3.2. Fuzzy system FSOE (Fuzzy System Output Estimation) supporting estimation of production results The production process realized in longwall faces of coal mines is characterized by the fact that its operation is influenced by many factors. These factors are related to geological, technical, organizational and mining conditions. Fuzzy system FSOE is a continuation of system FSES and enable to estimate the duration of the production cycle and the level of shift output in coal mines. The results can be used when making decisions concerning the design and management of the mining process. System FSOE makes inferences according to the scheme shown in figure 3. First, based on inserted input data, a fuzzy set is determined the duration of the production cycle; which in turn, then becomes an input parameter the magnitude of shift output. FSES Insertion of input data into system FSOE Fuzzification with use of fuzzy sets Start of inference procedure Estimation of shift output Estimation of production cycle duration Checking premises of fuzzy rules Generation of shift output values designed longwall face Fig. 3. Operation scheme fuzzy system FSOE The duration of a production cycle is the sum of the individual elements realization times (Snopkowski & Napieraj 2012) e.g. cleaning with use of the shearer within a section (xp ­ dk), cutting with use of the shearer within a section (L ­ xp), slotting with use of the shearer within a section (xo + dk + p + s), cutting with use of shearer within a section equal to (xo + dk + p + s), turning station replacement, and driving unit replacement. It can be expressed by the mula: Tc where: Tc L Vr Vz Vm xp dk xo p s tz tn 1 1 1 1 ( x p d k ) ( L x p ) ( xo d k p s ) t z tn Vcz Vr Vz Vr (3) -- -- -- -- -- -- -- -- -- -- -- -- production cycle duration [min], longwall length [m], shearer operational advance rate [m/min], advance rate of the slotting shearer [m/min], shearer maneuver advance rate (shearer advance rate during cleaning the shearer route) [m/min], distance between shearer stoppage place and longwall-roadway crossing [m], shearer length [m], distance between shifted conveyor and support[m], minimal distance between shifted conveyor and shearer [m], distance between support and shearer [m], turning station replacement time [min], turning drive unit replacement time [min]. A part of these parameters is shown as fuzzy sets which, along with their functions of membership, are shown in table 5. TABLE 5 Fuzzy sets and functions of membership parameters inserted into the FSOE system Parameter Sets and membership functions 1 8 V m (low) (Vm ) 4 0 0 V 4 m 4 ( ) (Vm ) 1 22 V m 9 0 Vm 4 4 Vm 8 Vm 8 Vm 4 4 Vm 8 8 Vm 13 0,2 0 0 5 10 15 20 25 30 Vm ­ shearer maneuver advance rate, [m/min] 13 Vm 22 Vm 22 low high Vm 13 0 V 13 m 13 Vm 22 ( high ) (Vm ) 9 Vm 22 1 TABLE 5. CONTINUED xp ­ distance between shearer stoppage place and longwallroadway crossing, [m] x p 14 1 16 x p (low) ( x p ) 14 x p 16 2 x p 16 0 x p 14 0 x p 14 14 x p 16 2 16 x p 19 ( ) ( x p ) 1 21 x p 19 x p 21 2 0 x p 21 0 x p 19 ( high ) ( x p ) 2 1 x p 19 0,2 0 10 15 20 25 low high 19 x p 21 x p 21 1 3,8 Vr (low) (Vr ) 2,8 0 Vr 1 1 Vr 3,8 Vr 3,8 Vr 1 1 Vr 3,8 Vr ­ shearer operational advance rate [m/min] 0 V 1 r 2,8 ( ) (Vr ) 6, 7 Vr 2,9 0 3,8 Vr 6, 7 Vr 6, 7 0,2 0 0 2 4 6 8 Vr 3,8 0 Vr 3,8 ( high ) (Vr ) 3,8 Vr 6, 7 2,9 1 Vr 6, 7 1 5,9 Vz (low) (Vz ) 3,9 0 Vz 2 low high 2 Vz 5,9 Vz 5,9 Vz 2 2 Vz 5,9 Vz ­ advance rate of the slotting shearer [m/min] 0 V 2 z 3,9 ( ) (Vz ) 10 Vz 4,1 0 0 V 5,9 ( high ) (Vz ) z 4,1 1 5,9 Vz 10 Vz 10 Vz 5,9 0,2 0 0 2 4 6 8 10 12 low high 5,9 Vz 10 Vz 10 TABLE 5. CONTINUED 1 15 s (low) ( s ) 7 0 s8 8 s 15 s 15 s8 8 s 15 s ­ distance between support and shearer [m] 0 s 8 ( ) ( s ) 7 20 s 5 0 15 s 20 s 20 0,2 0 0 5 10 15 20 25 30 s 15 0 s 15 15 s 20 ( high ) ( s ) 5 s 20 1 1 8 t z (low) (t z ) 5 0 tz 3 low high 3 t z 8 tz 8 tz 3 3 tz 8 tz ­ turning station replacement time [min] 0 t 3 z 5 ( ) (t z ) 13 t z 5 0 8 t z 13 t z 13 0,2 0 0 5 10 15 tz 8 0 t 8 z 8 t z 13 ( high ) (t z ) 5 t z 13 1 1 13 t n (low) (tn ) 10 0 tn 3 low high 3 tn 13 tn 13 tn 3 3 tn 13 0,2 0 0 5 10 15 20 25 30 tn ­ turning drive unit replacement time [min] 0 t 3 n ( ) (tn ) 10 25 tn 12 0 13 tn 25 tn 25 tn 13 0 t 13 n 13 tn 25 ( high ) (tn ) 12 tn 25 1 low high Table 6 shows selected rules used in the system inference process at this stage of work. These rules were determined on the basis of timing research conducted in longwall faces of Polish coal mines. The knowledge base contains over 2000 rules. TABLE 6 Combinations of selected FSOE system rules estimation of production cycle duration Rule no. Premise IF ... and ... and ... Vz = s= ==> tz = tn = l= Conclusion THEN Tc = Vm = xp = Vr = low low high high low high low high low low high high high high low high low low low low low low short ==> high low low short ==> high low low low short ==> low high short ==> low ==> high high high high long ==> low high high long ==> low low low high long ==> low high high high long ==> low low low high high high The level of shift output from a longwall face depends not only on the duration of the production cycle, but also on: longwall height; shearer web; disposable shift time. The relationship is described by the following equation: Wzm where: Td Tc h z l Td h z l Tc (4) -- -- -- -- -- -- disposable shift time [min/zm], duration of the production cycle [min], longwall hight [m], shearer web [m], longwall length [m], coal specific weight [Mg/m3]. Table 7 summarizes the membership functions these parameters, which are also included in the fuzzing module of the FSOE system. Table 8 shows selected rules used in the second stage of FSOE system inference. TABLE 7 Fuzzy sets and membership functions of the abovementioned parameters the FSOE system ­ c.d. Parameter Sets and membership functions 1 0, 75 z (low) ( z ) 0, 05 0 0 z 0, 7 0, 05 ( ) ( z ) 0,8 z 0, 05 0 z 0, 6 0, 6 z 0, 7 z 0,8 z 0, 6 0, 6 z 0, 7 z ­ shearing web [m] 0, 75 z 0,8 z 0,8 0,2 0 0,6 0,65 low 0,7 0,75 0,8 high 0,85 z 0, 75 0 z 0, 75 0, 75 z 0,8 ( high ) ( z ) 0, 05 1 z 0,8 1 355 T d (low) (Td ) 15 0 0 T 340 d 15 ( ) (Td ) 370 Td 15 0 T ( high ) (Td ) d Td 340 340 Td 355 Td 355 Td 340 Td ­ disposable shift time [m/zm] 340 Td 355 355 Td 370 Td 370 0,2 0 320 340 low 360 380 high 0 Td 355 355 355 Td 370 15 1 Td 370 TABLE 8 Combination of selected FSOE inference rule used to determine shift output Rule no. Tc = Premise IF ... and ... and ... h= z= Td = ==> l= Conclusion THEN Wzm = high high low low low low low low low high low low low high high short short short long ==> ==> ==> ==> ==> low low low TABLE 8. CONTINUED high low low high high high high high high high high high high long long long long ==> ==> ==> > high high high Operation of fuzzy systems is presented with use of a case study in chapter 3.3. 3.3. Case study The designed longwall face is characterized by the parameters presented in Table 9. TABLE 9 Longwall face parameters Longwall length = 220 m Longwall height = 4,2 m · · · · Transverse inclination = 1,5° Floor class = II Coefficient f = 1,1 Category of methane hazard = lack · · · · Longitudinal inclination 3,2° Roof class = III Thickness of rock vein in coal seam = 0,2 m Level of rock burst threat = I The above data were inserted into fuzzy system FSES which, on the grounds of the rule base and the inference process conducted (table 3 rule 3), proposed shearer type KSW 2000E, as well as requirements regarding the range of longwall support system (according to type/above 3,5 m). In addition, on the basis of the rules combining machines with other equipment (table 4 rule 9), it proposed the last element of the longwall complex ­ conveyor Rybnik 1100. The obtained data were then inserted into FSOE system to estimate the shift output in the designed longwall face. The input parameters were supplemented by the following data: ­ dk ­ shearer length, dk = 10 [m], ­ xo ­ distance between shearer stoppage place and longwall-roadway crossing, xo = 3,2 [m], ­ p ­ minimal distance between shifted conveyor and shearer, p = 5,25 [m], ­ ­ coal specific weight, = 1,35 [g/m3]. As a result of the inference process, a fuzzy set was generated the duration of the production cycle (table 6 rule 5), which was then defuzzied by the geometric method of gravity center (COG), thus yielding the numerical value Tc = 91,22 [min]. This value was then used to estimate shift output (activating rule 5 table 8). Likewise, in this case the end results were determined using by the COG method. In the analysed case the given parameters of the designed longwall face and selected equipment, the shift output determined by system FSOE amounted to 3664 [Mg/zm]. 4. Summary The mining process is a process of production affecting the economic state of countries in possession of mineable natural resources. Its design includes distinguished structures; and in terms of space, technology and time, it should take into account the knowledge accumulated by mines and mining enterprises in order to improve the quality of design decisions. The storage and use of this knowledge is enabled by systems with a knowledge base, which also include elements of fuzzy logic (creating i.e. fuzzy systems). This work has introduced fuzzy systems, which can be applied when designing elements of the mining process. The first of them is system FSES, which facilitates the selection of equipment according to the conditions of longwall faces. The fuzzification module in this system makes possible a fuzzy operation the following quantitative variables: longwall length; longwall height; longitudinal and cross-wise incline of the longwall; workability of coal and the thickness of rock vein in a given longwall section. The knowledge base includes over 100 fuzzy rules determining equipment suitable use under the specified conditions of an longwall face. After determination of the proposed equipment, it is then possible to insert the values obtained into the second system FSOE, which enables estimation of shift output according to the selected parameters. The fuzzification module in system FSOE includes 9 linguistic variables, which are necessary determining shift output in the designed longwall face. The system knowledge base contains over 200 rules. As a result of the operation of both systems, the designer receives both a proposition longwall face equipment, and the estimated shift output under given conditions. These results can be used when designing certain elements of the mining process (longwall faces) or the verification of adopted plans. Fuzzy logic allows a smooth and relatively precise description of key relationships between variables of imprecise nature which serve as input data the design process. The fuzzy inference conducted by the system on the basis of rules saved in the knowledge base generalizes the knowledge possessed by the designer, as well as a method of inference is similar to that of the reasoning of an expert. Fuzzy systems can effectively support ­ among other things ­ the design of selected elements of the mining process, as presented in the above article.

Journal

Archives of Mining Sciencesde Gruyter

Published: Oct 20, 2014

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