優(yōu)化巷道布置系統(tǒng)模型的理論依據(jù)及其應(yīng)用外文文獻翻譯

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英文原文Optimization model of Coal Mine roadway layout system Based on Evidence Theory and Its ApplicationJinfeng Wang1, Mingzhong Zhao 1, Lijie Feng1,2, Xia Chen11 Institute of Management Engineering, Zhengzhou University, Zhengzhou, 4500012 Henan Rescuing Center for Mineral Disaster, Henan Zhengzhou, P.R.China, 450014(E-mail: jinfengwangzzu.edu.cn)Abstract - Chinas coal mine roadway layout systems are complicated, multi-production and poor matching. And thus affect the overall effectiveness of the coal production logistics system. Although the research content on coal mine logistics system at home and abroad are many, however, research on the optimization method of coal mine roadway layout system are very few. In this paper, we did an in-depth analysis on coal mine roadway layout system, established an optimization factors system of coal mine roadway layout system, and determined the relative weight of the influencing factors at each levels using analytic hierarchy process to according to experts advices. At the same time, by introducing D-S evidence theory in this article, we established optimization model of coal mine roadway layout system and described its application process through empirical analysis. Finally, the results of the discussion can provide the optimization and transform of coal mine roadway layout systems in practice with a theoretical basis. Key words - Coal mine roadway layout system, influencing factors Evidence theory, Optimization modelI INTRODUCTIONCoal mine roadway not only can transport, ventilation, drainage, access to walk for both people and equipment, but also provide a space for all kinds of activities of underground. It not only contains the roadway subsystem, also includes associated coal mine production systems and equipment systems. Therefore, to study the coal mine roadway layout systems engineering, we must focus on analysis of the overall coal mine and its associated state and process, so as to enable the roadway system coordinate the various components of each other, and thus to reach the aim that technically advanced, reliable operation, economic on cost-effective, and ultimately get the best cost-effectiveness of integrated1,2.In this paper, on the basis of giving full consideration to the economy, efficiency, safety three factors, we did an in-depth analysis on coal mine roadway layout system, established a optimization factors system of coal mine roadway layout system, and determined the relative weight of the influencing factors at each levels using analytic hierarchy process3,4 (AHP) according to experts advices. And then, by introducing D-S evidence theory 5,6 in this article, we established optimization model of coal mine roadway layout system. Through empirical analysis explained its process and application. The results show that the optimization model is reasonable and feasible. THE ESTABLISHMENT OF INFLUENCING FACTORS OF OPTIMIZATION OF COAL MINE ROADWAY LAYOUT SYSTEMCoal mine roadway is not only can transport, ventilation, drainage, access to walk for both people and equipment, but also provide a space for all kinds of activities of underground. It is a large and complex system which consisting by multi-level sub-system. And it will result in the entire coal production logistics system inefficient while the resources will be serious waste if one sub-system have problem 1,2. For such a complex system, how to choose a reasonable optimization program and parameters of the mine roadway layout system, so that roadway layout systems get optimized and transformed, has been the research focus of many scholars. For optimizing and transforming the coal mine roadway layout systems, it involves the analysis of a large number of qualitative indicators. If the optimization is still mainly qualitative optimization, it is easy to lack uniform quantify standards and selection procedures. By introducing evidence theory, it can make up for its lack to some extent, and eliminate uncertainties existence in the systems.Through referring to coal mine roadway layout system literature 1,2, combining with systems engineering7, and considering the economy, efficiency, safety factors, we established four secondary factors as following: economy of engineering equipment, production efficiency, and the use of space and equipment efficiency, safety and reliability. And 12 three-tier influencing factors as following: the reasonableness of roadway project costs, costs of construction equipment maintenance, energy consumption of production and auxiliary equipment, depreciation rate of production and maintenance equipment, convenience of production and construction equipment, and the reasonableness of transport and enhance routes, the efficiency of auxiliary systems, and production efficiency of unit personnel and equipment, the ratio of shared roadway space, efficiency of the use of production and maintenance equipment, improvement of engineering and maintenance systems, and stability of auxiliary equipment and materials transport system 1,2. The specific is shown in Fig.l(In order to facilitate the definition of the four indicators of the second layer as attributes, we call the third-tier factor as indicators.)The factors of the system mostly arc qualitative factors, so it is necessary to determine the rating level of each factor. To enable the grade of various factors criteria clear and easy to operate, this article will set four grades: excellent, good, medium and poor. We build identify frameworks based on evaluation of evidence, get subjective judgments from a number of experts in related fields, and in accordance with the evaluation of evidence identification of the element of uncertainty given the subjective judgments, combined with the theory of evidence synthesis we draw a comprehensive evaluation of coal roadway layout roadway system. And combined with the results of the optimization, we gave some recommendations to optimize and improve the program. And so that it can provide the optimization and transform of coal mine roadway layout systems in practice with a theoretical basis.Fig.1 Influencing factors of optimization of coal mine roadway layout systemIII.EVIDENCE THEORY AND EVIDENCE SYNTHESIS METHODSA.Evidence TheoryDempster-Shafer evidence theory is theorized by Shafer in his monograph The Mathematical of Evidence Theory published in 1976 on the basis of Dempsters upper and lower probability and its synthesis rules5,9.D-S evidence theory has attracted widely attention in its advantages of expression of uncertainty, measurement and synthesis and so on. It improves its own defects, at the same time, combined the strengths of other methods. Its application has extended to probability and fuzzy sets. And it not only can synthesize prior information like Bayesian, and can deal with evidence of vague concepts such as language10.B. Evidence synthesis methodsDempster synthesis rule is a rule that reflects of the combination effects of evidence, and the specific content is as follows:Set that Bel1 and Bel2 are the two confidence function of the same framework to identify, and q1,q2 are the corresponding public functions. If there is Bel1 Bel2 and their publics function is q, then Among them, Clearly k is not dependent on A.Popularize to the n-dimensional: Among them, Symbol q(A) reflects the degree of the joint support to proposition A of evidence corresponding to m1,m2 .The rules will synthesize independent information of evidence that comes from different sources, resulting in more reliable evidence-information.IV OPTIMIZATION MODEL OF COAL MINE ROADWAY LAYOUT SYSTEM BASED ON EVIDENCE THEORYA.The relative weight between factorsWeight of factor reflects the relative importance of the quantitative distribution. Therefore, the coal mine tunnel system optimization factors layout system should be established after the establishment of factors of relative weight. Assumption that the object will be decomposed into r factors were: El,，Er， factors as the evidence of sources of information theory, evidence is not necessarily as important as between them there are also divided into primary and secondary, so can use the Analytic Hierarchy Process (AHP)3,4 approach to determine the factors for the relative weight of Ei is wi（i=1，r）, to meet: i=1rwi=1，w1，wn0. The weight of different factors, optimizing the outcome of the various factors to optimize the ultimate goal of support is different.B.Discount rate of and support FunctionsIncluded in the evidences uncertainty is usually to commitment by identify the framework of the assumptions, or through the support function s: 2 0,1, to explain, but the following situation is occur, that is not a support function that reflects the entire evidence of a some specific uncertainties, and therefore a support function s: 2 0,1 it seems that it is not clear. In fact, we have the evidence as a whole, only degrees of plausibility“a”0a1,which is reflected in the meaning of the parameters of the factors that decision-makers evaluate he results given the discount rate. Following giving an optimization model for multi-factor in the level of structure, how to combine the factors of the relative weight of factors to optimize the results will be translated into evidence of the credibility of the theory of the basic method of distribution.If wk= max(w1 , , wn ) , said a key factor for this indicator. The key factors Ek based on the state of j (to identify the framework of elements) of the probability iskj,j=1, n, is determined by the policy makers,based on kj in the value of the extent of how much he can believe that the statej, will happen, given the corresponding discount rate, charged with m jk=kj(j=1, n), m jk means that the key factors on the decision-makers the degree of support or confidence.Non-critical factors Ei, based on the state probability givenj forij . Similarly, we can also discount throughij to generate the corresponding level of support. The importance of the degree of Ei with Ek is wi/wk, and thereforeij an appropriate discount rate check (wi /wk ) ,note:mjk= (wi /wk )ij, (j=1, n) (4)Use m ij to denote non-critical indicatorsj proposition to provide the degree of support. For any Ei,so thatMi(j)=mij, (j=1, n) (5)Mi()=1-mij (6)mi is the indicators (factors) arising from the evaluation of the results of function m, (i = 1, ., r).So that we can use the results of the multi-factor model of the optimization problem corresponding to the establishment of a model of evidential reasoning, and apply appropriate methods of evidence synthesis of the basic credibility of the integrated m function. The model that is, coal mine roadway layout optimization model system.V.EMPIRICAL ANALYSIS OF THE OPTIMIZATION OF COAL MINE COAL MINE ROADWAY LAYOUT SYSTEMA.Determination of the example(1)Determine the reviews set:=1 , 2 , 3 , 4 said that the reviews set and the identification framework representing excellent, good, in, poor in four reviews.(2)In accordance with the evaluation index system as shown in Fig.1, we set that X as the second tier set of attributes. And that is, X=( x1 , x2 , x3 , x4 ), in which the attributes set of x1 isEi, i=1, 2, 3, 4 . There are four attributes in the set x1 ,that is E1 =e11 , e12 , e13 , e14 . Similarly, E2=e21 , e22 , e23 , e24 ，E3=e31 , e32 ,E4=e41 , e42 .(3)Determine the relative weight of the indicators at all levels: In this paper, we use analytic hierarchy process to identify the relative weight of indicators at all levels, and the weight set W=( w1 , w2 , w3 , w4 ) = (0.518, 0.292,0.090, 0.100). The weight vector of attribute set ( E1 , E2 , E3 , E4 ) respectively recorded as:V1=(v11 , v12 , v13 , v14 )=(0.35, 0.25, 0.25, 0.15, )V2=(v21 , v22 , v23 , v24 )=(0.4, 0.2, 0.1, 0.3)V3=(v31 , v32 )=(0.65, 0.35)V4=(v41 , v42 )=(0.4, 0.6)Assume that 10 experts in coal mine logistics give evaluation to the sample of the roadway layout system, and the basic reliability allocation are as shown in Table 1:TABLE 1 THE TABLE OF THE BASIC RELIABILITY ALLOCATIONB.Evidence synthesis of the influencing factorsThe attribute x1 on the economics of engineering equipment were analyzed, and its weight are as following: V1=(v11 , v12 , v13 , v14 )=(0.35, 0.25, 0.25, 0.15, ) And their evaluation information is as shown in Table 2: TABLE 2 THE BASIC RELIABILITY ALLOCATION OF THE ECONOMY OF ENGINEERING EQUIPMENTAccording to the size of the weight, we select e11 as the key factor, and the remaining factors are the non-key factors. And we set1 = 0.8 as the discount rate of the key factor, while the discount rate of non-key factors are follows: (v12 v11) =0.5714, (v13 v11) =0.5714， (v14 v11) =0.3429。Then use the formula of D-S Synthesis to synthesize the four function m of the factors x1, to the following function m, so the total reliability allocation is as shown in Table 3: TABLE3 THE TOTAL RELIABILITY ALLOCATION OF THE ECONOMY OF ENGINEERING EQUIPMENT Similarly, the total reliability allocations of other attributes are as shown in Table 4 to 6.TABLE 4 THE TOTAL RELIABILITY ALLOCATION OF PRODUCTION EFFICIENCY(Note: The key factor is E21, the discount rate2= 0.9) TABLE 5 THE TOTAL RELIABILITY ALLOCATION OF THE USE OF SPACE AND EQUIPMENT EFFICIENCY(Note: The key factor is E31, the discount rate3= 0.9) TABLE 6 THE TOTAL RELIABILITY ALLOCATION OF SAFETY AND RELIABILITY(Note: The key factor is E41, the discount rate4 = 0.9) C. The total reliability allocations of the systemWe set all the above attributes (E1, E2, E3, E4) as the evidences of a coal mine roadway layout system, and then synthesized four the total reliability allocations function m of the attributes (E1， E2，E3，E4) into one function m using D-S formula, and thus got the total reliability allocation. The final results of the total reliability allocations are as shown in Table 7:TABLE 7 THE TOTAL RELIABILITY ALLOCATION OF COAL MINE ROADWAY LAYOUT SYSTEMVI. CONCLUSIONS In this paper, we did an in-depth analysis on coal mine roadway layout system, established a optimization factors system of coal mine roadway layout system, and determined the relative weight of the influencing factors at each levels using analytic hierarchy process according to experts advices; We used D-S synthesis formulas to synthesize the views of experts, focused on the uncertainty exited in experts advices. Except the completely conflicting views, D-S synthesis formulas can get good synthesize effect; domestic the research on optimization methods and optimization model of coal mine roadway layout system is still very weak, applying evidence theory applied to the coal mine roadway layout system has a good reference to optimization and transformation of coal mine roadway layout system; empirical analysis shows that the optimization model is reasonable and feasible.ACKNOWLEDGMENT This paper is sponsored by Program for Science Technology Innovation Talents in Universities of Henan Province (NO. 2008HASTIT010), and sponsored by Natural Science Foundation of China (NO. 70740002). REFERENCES 1 Wang Jinfeng, management of coal mine logistics system M, Henan Peoples Publishing House, 2004 2 Wang Jinfeng, coal mine production logistics system D, Tianjin University, 2005 3 Yang Ping, Liu Weidong. The level evaluation method of group decision-making based on evidence theoryJ. 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Upper and lower probabilities induced by a multi-valued mapping J.Annual Math statist,1997, 38(4)9 Shafer G,A Mathematical Theory of EvidenceM.Princeton Uni-versity Press, Princeton, New Jersey,1976,1-610 Tong Jianjun, Research of the evidence theory and its application in decision-making and evaluationD, Hefei University of Technology, 2005中文譯文優(yōu)化巷道布置系統(tǒng)模型的理論依據(jù)及其應(yīng)用王金鳳1，趙明中 1，馮立杰1,2，陳夏11鄭州大學(xué)工程管理學(xué)院，鄭州，4500012河南省礦產(chǎn)災(zāi)害搶救中心，河南鄭州， 450014（電子郵箱：jinfengwangzzu.edu.cn）摘要一中國煤礦巷道布置系統(tǒng)復(fù)雜，多個工作面同時生產(chǎn)以及機械裝備落后，從而影響煤炭生產(chǎn)物流系統(tǒng)的整體成效。雖然國內(nèi)外關(guān)于煤礦物流系統(tǒng)的研究內(nèi)容很多，但是研究煤礦巷道布局系統(tǒng)優(yōu)化方法的卻很少。本文中，我們對煤礦巷道布置系統(tǒng)進行深入地分析，設(shè)定了影響煤礦巷道布置方法的系統(tǒng)優(yōu)化因素，并根據(jù)專家建議，使用層次分析法確定了每個層次影響因素的相對權(quán)重；同時，通過引入D-S證據(jù)理論，我們建立了優(yōu)化煤礦巷道布置系統(tǒng)的模型并通過實證分析闡述了其應(yīng)用過程。最后，討論的結(jié)果可以為優(yōu)化和改造煤礦巷道布置系統(tǒng)的實踐提供理論依據(jù)。關(guān)鍵字煤礦巷道布置系統(tǒng)，影響因素，證據(jù)理論，優(yōu)化模型。1簡介煤礦巷道不僅可以用于運煤，通風，排水以及運送人員和設(shè)備，而且還為井下各種生產(chǎn)作業(yè)提供了工作空間。它不僅包含巷道子系統(tǒng)，還包括與其相關(guān)的煤礦生產(chǎn)和設(shè)備系統(tǒng)。因此，為了研究煤礦巷道布置系統(tǒng)的工程，我們必須著眼于礦井的整體分析及其相關(guān)現(xiàn)狀和發(fā)展過程，從而使巷道系統(tǒng)組成的各個部分相互協(xié)調(diào)，這樣就能達到“技術(shù)先進，運行可靠，經(jīng)濟節(jié)約”的目地，并最終獲得最佳的總體效益 1，2。本文，在充分考慮經(jīng)濟，效率，安全三個因素的基礎(chǔ)上，我們對煤礦巷道布置系統(tǒng)進行了深入地分析，設(shè)定了煤礦巷道布置系統(tǒng)的優(yōu)化因素，并根據(jù)專家建議，使用層次分析法 3，4確定了每個層次影響因素的相對權(quán)重。然后在這篇文章中通過引入D-S證據(jù)理論 5，6，我們建立了煤礦巷道布置系統(tǒng)的優(yōu)化模型。通過實證分析解釋其應(yīng)用過程，結(jié)果表明，該優(yōu)化模型是合理和可行的。2影響煤礦礦井巷道布置系統(tǒng)的優(yōu)化因素的建立煤礦巷道不僅可以用于運煤，通風，排水以及運送人員和設(shè)備，而且還為井下各種生產(chǎn)作業(yè)提供了工作空間。這是一個龐大復(fù)雜的系統(tǒng)，由許多層次的子系統(tǒng)組成。如果一個子系統(tǒng)有問題，它會導(dǎo)致整個煤炭生產(chǎn)物流系統(tǒng)效率低下，使資源嚴重浪費1，2。對于這樣一個復(fù)雜的系統(tǒng)，如何選擇一個合理的優(yōu)化方案和礦井巷道布置系統(tǒng)參數(shù)，使巷道布置系統(tǒng)得到優(yōu)化和改造，一直是眾多學(xué)者研究的重點。為了優(yōu)化和改造煤礦巷道布置系統(tǒng)，它涉及大量定性指標的分析。盡管優(yōu)化主要還是質(zhì)的優(yōu)化，很容易缺乏統(tǒng)一的量化標準和篩選程序，但通過引入D-S證據(jù)理論，可以在一定程度上彌補其不足，消除了巷道布置系統(tǒng)中存在不確定性。通過查詢煤礦巷道布置系統(tǒng)的文獻1，2，與系統(tǒng)工程結(jié)合7，并考慮到經(jīng)濟，效率，安全三個因素，我們確定了工程設(shè)備節(jié)約量，生產(chǎn)效率，工作空間和設(shè)備利用率以及安全性和可靠性四個次要因素；和巷道項目成本的合理性，施工設(shè)備維護費，生產(chǎn)和輔助設(shè)備的能源消耗，生產(chǎn)和維修設(shè)備的折舊率，生產(chǎn)和工程設(shè)備的便利程度，以及運輸及加強路線的合理性，輔助系統(tǒng)的效率，人員和設(shè)備生產(chǎn)工效，共用巷道的比例，生產(chǎn)和維修設(shè)備使用效率，工程和維護系統(tǒng)的改善，以及輔助設(shè)備和材料運輸系統(tǒng)的穩(wěn)定性12個三級影響因素1，2。具體如圖1所示（為了便于定義第二層的四個指標為屬性，我們呼吁以第三層的影響因素作為指標）。圖1 煤礦巷道布局優(yōu)化的影響因素該系統(tǒng)的因素主要是定性因素，因此有必要確定每個因素的評級水平。為使各方面的因素分級標準明確，且易于操作，本文設(shè)置四個等級：“優(yōu)，良，中，差”。我們根據(jù)證據(jù)評估建立鑒別框架，從相關(guān)領(lǐng)域的一些專家的獲得主觀判斷標準，并依照主觀判斷的不確定性因素識別證據(jù)評估，結(jié)合證據(jù)合成理論，我們得出煤巷道布置巷道系統(tǒng)的全面評估。并與最優(yōu)化的結(jié)果相結(jié)合，我們提出了一些建議，以優(yōu)化和改善方案。因此，它可以為優(yōu)化和改造煤礦巷道布置系統(tǒng)的實踐提供理論基礎(chǔ)。3依據(jù)理論與依據(jù)合成方法（1）證據(jù)理論謝弗基于登普斯特的“上限和下限的可能性”及其合成規(guī)則5，9，在1976年發(fā)表的著作“證據(jù)理論數(shù)學(xué)”上將Dempster Shafer證據(jù)理論理論化。 D-S依據(jù)理論由于其在不確定性、度量以及合成等方面的論述的優(yōu)點，引起廣泛的關(guān)注。它在自我完善的同時，也融入了其他方法的優(yōu)點，它的應(yīng)用已經(jīng)擴展到概率和模糊集，不僅能合成像貝葉斯的先驗信息，也能處理模糊概念證據(jù)，如語言10。（2）證據(jù)合成方法登普斯特合成規(guī)則是一種證據(jù)組合效果反映的規(guī)則，具體內(nèi)容如下：設(shè)Bel1和Bel2是同一鑒別框架的兩個可信的函數(shù)，q1，q2是對應(yīng)的公眾函數(shù)。如果有Bel1 Bel2和他們的公眾函數(shù)q，則 其中，顯然，k是不依賴于A。推廣到n維： 其中： 符號q（A）反映了與證據(jù)命題A相應(yīng)的m1，mn的聯(lián)合支持程度。規(guī)則將綜合各自獨立的不同來源的證據(jù)信息，結(jié)果將產(chǎn)生更可靠的證據(jù)信息。4基于依據(jù)理論的煤礦巷道布置系統(tǒng)的優(yōu)化模型（1）各因素之間的相對權(quán)重因素的權(quán)重反映了定量分配的相對重要性，因此，影響煤礦巷道布置系統(tǒng)的優(yōu)化因素應(yīng)建立在因素的相對權(quán)重確定以后。假設(shè)該對象將被分解成r個因素，分別是：El，Er，作為信息理論來源的證據(jù)因素，他們被分為首要的和次要的，證據(jù)并不一定像他們之間那么重要，所以可以使用層級程序法（AHP）3，4，近似確定各因素Ei的相對權(quán)重是wi（i=1，r）滿足：i=1rwi=1，w1，wn0。對不同因素的權(quán)重，各種因素支撐優(yōu)化的最終結(jié)果是不同的。（2）折扣率和支撐函數(shù)依據(jù)的不確定性通常是被約束在假設(shè)的一致性框架內(nèi)，或通過支撐函數(shù)S：2 0，1來解釋，但是會出現(xiàn)以下的情形，即一個支撐函數(shù)并不能完全反映一些特定的不確定的證據(jù)。因此，一個支持函數(shù)S：2 0，1似乎并不明確。事實上，我們把證據(jù)作為一個整體，只是用反映決策因素參數(shù)意義的可信度“”（01）評估得到折扣率的結(jié)果。接下來在同一結(jié)構(gòu)層次中對多因素建立優(yōu)化模型，如何結(jié)合因素的相對權(quán)重因子來優(yōu)化結(jié)果將落實到基本分配方法理論的可信性的證據(jù)上。如果用wk= max(w1 ， ，wn )反映這項指標的關(guān)鍵因素，基于j（用于鑒定元素框架）狀態(tài)的關(guān)鍵因素Ek的概率是kj，j=1， n，它取決于決策者相信j狀態(tài)在多大范圍內(nèi)將發(fā)生，扣除mik=kj（j = 1，. n），從而得到相應(yīng)的折扣率， mik的意味著決策者對關(guān)鍵因素支持或信任程度。基于j狀態(tài)的非關(guān)鍵因素Ei的概率為ij為基礎(chǔ)。類似地，我們也可以近似地通過ij產(chǎn)生相應(yīng)級別的支持度。Ei和 Ek受關(guān)注程度的重要性是wi/wk，因此ij用適當?shù)恼劭勐市?wi /wk ) ，記為：mij= (wi /wk )ij， (j=1， n) (4)用m ij來表示決策者對非關(guān)鍵指標j命題提供的支持程度。對于任意Ei，故mi(j) = mij，(j=1，n) (5)mi()=1-mij (6)mi（i = 1，.，r）是指標（因素）從函數(shù)m的結(jié)果評估中所產(chǎn)生的。因此，我們可以使用優(yōu)化問題的多因素模型的結(jié)果并運用全部m函數(shù)基本可靠性的證據(jù)合成的恰當方法建立相對應(yīng)的證據(jù)推理模型，該模型是煤礦巷道布置優(yōu)化系統(tǒng)模型。5 煤礦巷道布置優(yōu)化系統(tǒng)的