J. Cent. South Univ. (2013) 20: 1332−1340 DOI: 10.1007/s11771-013-1620-x
Multidisciplinary design optimization on production scale of underground metal mine ZUO Hong-yan(左红艳), LUO Zhou-quan(罗周全), GUAN Jia-lin(管佳林), WANG Yi-wei(王益伟) School of Resource and Safety Engineering, Central South University, Changsha 410083, China © Central South University Press and Springer-Verlag Berlin Heidelberg 2013 Abstract: In order to ensure overall optimization of the underground metal mine production scale, multidisciplinary design optimization model of production scale which covers the subsystem objective function of income of production, safety and environmental impact in the underground metal mine was established by using multidisciplinary design optimization method. The coupling effects from various disciplines were fully considered, and adaptive mutative scale chaos immunization optimization algorithm was adopted to solve multidisciplinary design optimization model of underground metal mine production scale. Practical results show that multidisciplinary design optimization on production scale of an underground lead and zinc mine reflect the actual operating conditions more realistically, the production scale is about 1.25 Mt/a (Lead and zinc metal content of 160 000 t/a), the economic life is approximately 14 a, corresponding coefficient of production profits can be increased to 15.13%, safety factor can be increased to 5.4% and environmental impact coefficient can be reduced by 9.52%. Key words: underground metal mines; production scale; multidisciplinary design optimization; adaptive mutative scale chaos optimization algorithm immunization
1 Introduction Production scale of underground metal mine is a very important decision factor in the metal mining development process [1], and production capacity configuration involves technical, economic, resource and ecological environment factors [2−4]. The regional heterogeneity distribution of metal mine resources is a key factor in restricting the flow of metal and mineral resources, while rational mineral resources transportation system can promote to a greater extent and optimize the production scale layout of the underground metal mine, and optimally configure metal mine production capacity [5−7] by using artificial intelligence technology [8]. Currently, the discrete, uncertain, dynamic and complex natures of metal mining production process are often overlooked when mine production scale is designed, the production scale of mineral resource was directly issued in the design and planning of mine construction engineering instead, inevitably leading to blindness in mine construction and engineering design practices, and the production scale of mine can not meet the actual situation of the mine and the community. Therefore, the phenomenon of renovation and expansion often occurs during the metal mine production process. It not only
delays the recovery of mineral resources production, but also wastes a lot of money. Therefore, with comprehensive consideration of the impact of the discrete, uncertain, dynamic and complex natures of metal mining production process on the underground metal mine production optimization, effective study on the rational allocation of underground metal mine production scale, achieving the overall optimization of the underground metal mine production scale, is an important issue to be solved in the research areas of domestic and foreign resource extraction recovery. Nearly for ten years in the field of nonlinear complex engineering booms the multi-disciplinary design optimization (multidisciplinary design optimization, MDO) [9−12], a new technology idea which can solve the system and overall design of underground metal mine production scale optimization. With regards to this, a multidisciplinary design optimization model of underground metal mine production scale was built by using multidisciplinary design optimization method, which can provide decision support for the metal mine development, and its findings will provide important theoretical and academic value for the timely development and take full advantage of the metal mine resources, improvement of metal mining economic benefits and the sustainable development of
Foundation item: Project(2012BAK09B02-05) supported by the National “Twelfth Five-year” Science & Technology Support Plan of China Received date: 2012−02−22; Accepted date: 2012−06−13 Corresponding author: ZUO Hong-yan, PhD, Tel: +86−15084931748; E-mail:
[email protected]
J. Cent. South Univ. (2013) 20: 1332−1340
metal mining areas.
2 Underground metal mine production scale multidisciplinary design optimization 2.1 Ideas of underground metal mine production scale multidisciplinary design optimization The rational allocation of underground metal mine production scale will directly affect the economic, social and ecological environment of the metal mining enterprises and the surrounding area. Taking into account the particularity of metal mining, underground metal mine production scale configuration optimization should maximize economic benefits, and should also consider the impact on safety and environment. To this end, the idea of underground metal mine production scale multidisciplinary design optimization is to integrate the various disciplines knowledge in the underground metal mine production scale configuration process, to apply effective optimization strategy and distributed computer network system on the design optimization of the underground metal mine production scale, by full collaboration interaction among various disciplines (subsystems), getting the overall optimal design results of underground metal mine production scale. Grading structure of underground metal mine production scale multidisciplinary optimization design is shown in Fig. 1.
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Multidisciplinary design optimization on production scale in the underground metal mine was done by system level and subsystem level (Safety, environmental impact and incomes of production) and the bound variable level (Geological structure conditions, seam conditions, the levels of mechanization, mining levels, ventilation conditions, transport level, filling level, the amount of waste rock, the volumes of waste water, the volumes of waste gas, the economic life, the numbers of employees, product prices, the original ore grades, fine ore grades and tailings grades). The function of overall optimization design of underground metal mine production scale was to achieve the maximum production profits, safety and the smallest environmental impact of metal mine production process, in the case of ensuring the maximize production scale of underground metal mines. At the same time, the indicators of the subsystem were allocated, and consistent indicators of systems and subsystems were taken as the constraints. Minimum difference between subsystem-level optimization design and system-level allocation index was the objective function. Under the conditions of meeting the constraints of the subsystem level, each bound variable was allocated target. The objective function of the bound variable level optimization design was the minimum difference with subsystem level distribution index. To meet the constraints of various disciplines bound variable level, by adjusting the parameters of the bound variable, design of the constraint variable and subsystem as well as system will achieve consistent coordination, and the optimal design production scale of underground metal mine will be got by the three-level optimization. 2.2 Multidisciplinary design optimization theory model of underground metal mine production scale Multidisciplinary design optimization problem of underground metal mine production scale is a mathematical programming optimization problem in mathematics, which can be described as Max G(X, Y) s.t.
Fig. 1 Grading structure of multidisciplinary optimization design
(1)
fi(X, Y)≤0, i=1, 2, …, n
where G(X, Y) is the objective function of underground metal mine production scale ratio, and G(X, Y)=F(X, Y)/F0=W1F1(X, Y)/F10+W2F2(X, Y)/F20+W3F30/F3(X, Y); F(X, Y) is the objective function of underground metal mine production scale; F0 is the initial value of underground metal mine production scale without multidisciplinary optimization; F1(X, Y) represents the objective function of production profits, F2(X, Y) represents the objective function of safety, F3(X, Y) represents the objective function of environment impact; F10 is the initial value of production profits without
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multidisciplinary optimization, F20 is the initial value of safety without multidisciplinary optimization, and F30 is the initial value of the environmental impact without multidisciplinary optimization; W1, W2 and W3 respectively represent the weighting coefficients of the objective function of production profits, the objective function of safety and the objective function of environmental impact on the overall objective planning. Further, W1+W2+W3=1; X is the design variable, X=(X1, X2, …, Xi, …, XI)T, Y is the state variable, Y=(Y1, Y2, …, Yj, …, YJ)T; fi(X, Y) which are constraint conditions. Taking the profits of production, safety and environmental impact of underground metal mine production scale as the objective functions, multiple working conditions of the metal mine production process as constraint conditions, multidisciplinary optimization of the integration physical parameters of the different subsystems was carried out. The main process is shown in Fig. 2.
J. Cent. South Univ. (2013) 20: 1332−1340
3；i≠j) is the coupling variable between the subsystems, that is, both are the output variables of subsystem i, and are the input variables of subsystem j. The three disciplines (contributing analysis, CA) exchange information by the connecting variable y2. The optimized performance of underground metal mine production scale configuration (performance function) fb2i is the function of the input parameter x2 and the connection variable y2. The multidisciplinary optimization design of underground metal mine production scale can be expressed by the non-linear simultaneous equations as shown in Eq. (2): y21 [ y212 , y213 ] CA1 ( x2 , z2 , y221 , y231 ) y22 [ y221 , y223 ] CA2 ( x2 , z2 , y212 , y232 ) y [ y , y ] CA ( x , z , y , y ) 231 232 3 2 2 213 223 23
(2)
Fig. 3 Chart of MDO solving process about production scale of resource recycling in metallic miner
2.3 Adaptive mutative scale chaos immune optimization algorithm 2.3.1 Selection of chaotic model E et al [13−14] showed that the number of one-dimensional self-mappings fold is infinite as shown in Eq. (3), and there are an infinite number of fixed points and zero in the interval [−1, 1], which has a more obvious chaotic characteristics than logistic model:
Fig. 2 Chart of MDO process about production scale of metal mine
Analysis process of underground metal mine production scale multidisciplinary design optimization problem is shown in Fig. 3. In Fig. 3, the design variable x2 represents characteristics of metal mine production process, which can be controlled and is independent of each other in the configuration process of the underground metal mine production scale; z2 is constant parameter in the configuration process of the underground metal mine production scale; the state variable y2 is the parameter to describe the performance and characteristics of the metal mine production process, which also can be expressed as y2=[y212, y213, y221, y223, y231, y232], y2 is the vector composed of all connection variables, and y2ij (i, j=1, 2,
xn 1 sin(2 / xn ), 0,1, 2, , n 1 xn 1, xn 0
(3)
2.3.2 Parallel chaos immune clustering algorithm Matching algorithms or evolutionary algorithms are used to implement the training data and immunological memory in the artificial immune algorithm, and evolutionary algorithm shows better performance than the matching algorithm. Therefore, the immune clustering algorithm can be expressed as follows. Step 1: Input antigen {gA}, and do normalization. Select Eq. (3) as chaotic random model of chaotic variable, which generate N initialized antibody {bA} in (0, 1). Step 2: Operation of each antigen gAi as follows: 1) Calculate affinity aij of each antibody bA between antigen gAi: aij
n
(bAik gAjk )2 k 1
(4)
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2) Select m antibodies with the highest affinity as the network cells; 3) The m network cells were chosen to do the cloning operation. The higher the affinity network cells, the more the number of clones Nc; 4) Do mutation operation with cloned cells by application of C=C−α(C−X), where C is the clone of antibody cells, X is the clone of antigen cells, and α is the mutation rate; 5) Recalculate the affinity of C after the mutation operation; 6) Select ζ with the best affinity as part of the memory cell data sets Mp; 7) Calculate the similarity sij of each antibody bAi between antibody bAj, eliminate individual where similarity sij is greater than the threshold σs in Mp: sij
n
(bAik bAjk )2
(5)
k 1
Step 3: Merge Mp to data set M which has been the memory. Step 4: Do chaotic fine search with optimum individual. Select 10% of the individual in memory set to do chaotic fine search, of which fitness value is comparatively large. Set the optimum individual as X=(X1, X2, …, Xk), and narrowing of the search range of chaotic variable can be expressed as ai X i (bi ai ) bi X i (bi ai )
(6)
where ξ is the constriction factor, ξ∈(0, 0.5). To ensure that the new range will not be cross-border, handle as follows: if ai bi, bi =bi. Therefore, Yi is determined by Eq. (7) after Xi reduction treatment in the new interval [ ai , bi ]: X ai Yi i bi ai
(7)
Taking linear combination of Yi and Xi, n+1 as a new chaotic variables, then search by this chaotic variable. X i, n 1 (1 i )Yi i X i ,n 1
(8)
where βi is the adaptive adjustment coefficient, 0
