J. Cent. South Univ. (2018) 25: 2462-2471

DOI: https://doi.org/10.1007/s11771-018-3929-y

A new approach for selecting best development face ventilation mode based on G1-coefficient of variation method

ZHOU Zhi-yong(周智勇)^{1, 2}, Mehmet KIZIL², CHEN Zhong-wei(陈中伟)^{2, 3}, CHEN Jian-hong(陈建宏)¹

1. School of Resources and Safety Engineering, Central South University, Changsha 410083, China;

2. School of Mechanical and Mining Engineering, the University of Queensland, QLD 4072, Australia;

3. State Key Laboratory for GeoMechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, China

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Abstract: The current popular methods for decision making and project optimisation in mine ventilation contain a number of deficiencies as they are solely based on either subjective knowledge or objective information. This paper presents a new approach to rank the alternatives by G1-coefficient of variation method. The focus of this approach is the use of the combination weighing, which is able to compensate for the deficiencies in the method of evaluation index single weighing. In the case study, an appropriate evaluation index system was established to determine the evaluation value of each ventilation mode. Then the proposed approach was used to select the best development face ventilation mode. The result shows that the proposed approach is able to rank the alternative development face ventilation mode reasonably, the combination weighing method had the advantages of both subjective and objective weighing methods in that it took into consideration of both the experience and wisdom of experts, and the new changes in objective conditions. This approach provides a more reasonable and reliable procedure to analyse and evaluate different ventilation modes.

Key words: development face ventilation; G1 method; coefficient of variation method; comprehensive evaluation; optimization

Cite this article as: ZHOU Zhi-yong, Mehmet KIZIL, CHEN Zhong-wei, CHEN Jian-hong. A new approach for selecting best development face ventilation mode based on G1-coefficient of variation method [J]. Journal of Central South University, 2018, 25(10): 2462–2471. DOI: https://doi.org/10.1007/s11771-018-3929-y.

1 Introduction

Underground mining is conducted in relatively small spaces, it is faced with many security threats in the mining process, among which dust contamination is a common issue for mine operators [1, 2]. Dust hazard seriously affects mine production safety and workers’ health [1–3]. Furthermore, with the exhaustion of shallow mineral resources, deep mining is the inevitable trend. One of the outstanding problems during deep mining is high temperature [4]. So, for an underground mine, good ventilation is the key for a safe production environment [5–8]. In development, ventilation for a single end drive is called the development face ventilation. It improves the operating environment by providing adequate fresh air for single end drive [2]. Development face ventilation is an imperative measure of the mine ventilation, which will continuously be the key difficulty for the mine production system [9]. This is significant for ensuring the health and safety of the development crew. Thus, it is essential to comprehensively evaluate the different development face ventilation modes for the optimal choice. In the past, the design of the mine ventilation system was done quite experimentally based on the experiences of the decision makers and through their comparison of the advantages, disadvantages, and limitations between the viable alternatives [10]. Thus, a method based on the multi-attribute decision making (MADM) theory is required. Many MADM methods or models were proposed to evaluate or assess the mine ventilation system [7]. MADM methods consist of numerous different techniques in selecting the best alternatives, which include fuzzy AHP, grey relational analysis, artificial neural network, genetic algorithms, etc.

2 State of art

A review of the literature reveals that the MADM techniques have been used for a variety of applications in decision making and project optimisation for mine ventilation systems. MIRHEDAYATIAN et al [10] used the fuzzy AHP for selecting the best tunnel ventilation system. CHENG et al [5] used the fuzzy AHP method to establish the reliability allocation model for the mine ventilation systems design. SA et al [11] used the grey system theory to optimize the ventilation system of a mine. WU [12] put forward an improved grey correlative method for risk assessment on mine ventilation system. CHENG et al [7] used the rough set theory to assist the selection of best ventilation indexes and the support vector machine to classify the risk ranks for the mine ventilation system. Based on a BP neural network approach, WANG [13] set up an evaluating model for mine ventilation system reliability. KARACAN [14] used reservoir models and artificial neural networks for optimising ventilation air requirements in development mining of coal seams. KOZYREV et al [15], DENG et al [16], SHRIWAS et al [17], ZHANG [18], LOWNDES et al [19] applied genetic algorithms for the optimisation of mine ventilation system. CHENG [20] presented a reliability assessment approach for evaluating the mine ventilation system based on a random simulation method, Monte-Carlo simulation. XU et al [21] proposed a simple and effective calibration method based on the non- linear optimization algorithm, to solve the problem that the simulated airflow distribution results do not match the measured data. The stated methods work to an extent in evaluating and optimum selection of mining ventilation systems, but all have some deficiencies. For example, the grey relational analysis method is mainly used for conditions where system information is incomplete or undefined, and cannot reflect the evaluated object’s absolute level. Artificial neural network does not have the unified metrics, which requires a normalization with the membership function, making a complicated calculation process. Also, with such method, the effect of the subjective factor is difficult to measure. In addition, the fuzzy comprehensive evaluation cannot solve the problem of repetition caused by the correlation of system index. The determination of the membership function is also rather subjective with the fuzzy comprehensive evaluation method.

According to Ref. [22], the combined weighting method has smaller misjudgment probability and error probability than the single weighting method. So, the purpose of this paper is to scientifically further improve the evaluation process, to remedy the deficiencies of evaluation index single weight determining method, and making use of both expert’s experience and wisdom and the new changes of objective conditions. By considering the advantages of the subjective and objective weight determining methods, this paper comprehensively uses both types of methods to achieve the combination weight determination. The paper uses a combination of the G1 [23] method (subjective), and the coefficient of variation method (objective). Taking this into consideration, the paper is able to construct the optimum evaluation model for development face ventilation systems based on the aspect of combination weight determining. The model was also used in a case study.

3 Methodology

3.1 Data standardization

Based on the mathematics piecewise function thought, indexes’ original data are made standardised with a dimensionless process [24]:

                          (1)

where D_i is the dimensionless value of A_i; maxA is the maximum value of index A, and minA is the minimum value of index A. When A is a positive index, m(A)=minA; when A is a negative index, m(A)=maxA; A_i is the ith specific value of index A.

Equation (1) is interpreted as: for index A, the dimensionless value presents the relative distance between the deviation between the ith value and the worst value, and the deviation between the maximum value and the minimum value. A bigger relative distance means a bigger D_i (the dimensionless value of A_i), which is in direct proportion to optimum.

3.2 Index combination weight determining

Subjective weight determining mainly makes use of the experience and wisdom of experts. Experience is the knowledge recognised from the past event after it happened. Once determined, it is rarely changed. Though such method is mature and commonly used, it lacks objectiveness. Similarly, objective weight determining is dynamic, reflecting in that index weight are related with index value, but also shows a lack of expert experience and knowledge [24]. By combining the G1 method and the coefficient of variation method, a combination weight determining method was created that has the advantages of both subjective weight determining and objective weight determining.

1) Subjective weight determining with G1 method

The G1 method [23] is a subjective weight determining method. In this method, the index weight is determined by first sequencing the index importance and then followed by estimating the relative degree of importance between the adjacent sequenced indexes. It is upgraded from the AHP method, and has resolved the disadvantages of the previous large and complex calculations and the required consistency checks.

(1) Index sequencing:

k=1, 2, …, m

where “” refers to that the index on the left has more importance than the index on the right.

, k=m, m–1, …, 3, 2

where r_k refers to the relative importance degree between adjacent indexes; ω_k is the kth index weight with G1 method.

(2) Index weight calculation:

                         (2)

                                (3)

2) Objective weight determining with coefficient of variation method

The coefficient of variation method [24] is an objective weight determining method that directly processes the index data with mathematics to calculate the index weight. It is able to achieve the index dynamic weight determining through a full consideration of the relative variation between each indexes and the reduction of the interferences from the subjective factors.

(1) Index coefficient of variation:

, k=1, 2, …, m                   (4)

where V_k is the coefficient of variation of the kth index; σ_k is the standard deviation of the kth index; X_k is the arithmetic mean value of the kth index.

(2) Index weight:

, k=1, 2, …, m                    (5)

where ω_k is the kth index weight with coefficient of variation method.

3) Index combination weight

Index combination weight is defined as the linear combination of the two weights mentioned from above, the expression [24] is

k=1, 2, …, m           (6)

where β is the percentage of subjective weight in combination weight and ω_k is the combination weight of the kth index.

Optimal value of β is calculated with the mathematical optimization problem inspirations, to achieve the optimal combination of the two weight. The objective function is built based on the rational of getting the minimum value of the quadratic sum with two deviations. In this case, one is the deviation between combination weight value and the weight value with G1 method, the other is the deviation between combination weight value and the weight value with coefficient of variation method. The expression is as follows:

           (7)

The process involves the substitute of Eq. (6) into Eq. (7), take derivative with respect to β, set its first-derivative value as 0, solve the equation, and get the optimal value of β(0.5). In the final, the optimal combination weight of the kth index is

                         (8)

The denotation of Eq. (8) is that the index combination weight has its optimal value when subjective weight and objective weight account for 50% and 50%, respectively. If the calculated combination weight is equal to the subjective weight and the objective weight, we can infer that both the subjective weight determining method and the objective weight determining method have the same cognition for index importance. Otherwise, the combination weight is the combined result of subjective weight and objective weight.

3.3 Optimum evaluation model of development face ventilation method based on combination weight

1) Definition of mathematical evaluation function

Based on the notion of mathematical function, evaluation value of the ventilation method can be defined as dependent variable, and the evaluation index can be defined as independent variable. With certain mathematical models, multi-index comprehensive evaluation issue is transferred to determine the indexes’ comprehensive evaluation values. In this case, values of indexes are fitted into matrix D=(d₁, d₂, d_m)^T, in which vector d_i=(d_i1, d_i2, …, d_ij) with 1≤i≤j represents the vector value of the ith index from the first project to the jth project. Index value matrix can be shown as

is the independent variable coefficient (index weight) vector.

The ith project has its comprehensive evaluation expression:

, 1≤i≤j                 (9)

2) Building optimum evaluation model

As the evaluation indexes are independent with each other, and the index weight value is consistent with this kind of index. The independent variable coefficient has apparent effect on the dependent variable in a linear function, and the dependent variables have a linear compensation effect. As a result, the optimum evaluation model [19] was constructed as

    (10)

where P_i is the comprehensive evaluation value of the ith method with a data range of [0, 1]. The value of P_i has direct proportion to optimum.

Equation (10) explains that the evaluation value of the ventilation method is equal to the sum of the product of each index values and their weight. Accordingly, Figure 1 illustrates the overall structure of the proposed approach in this paper for obtaining the final comprehensive evaluation values of alternatives. In the following section, this method will be used to design a ventilation system for a field case.

Figure 1 Overall structure of proposed approach for alternative prioritization in G1-coefficient of variation

4 Result analysis and discussion

There is a large copper polymetallic mine located at high altitude area. As the mine has severe dust pollution, an optimal design for the development face ventilation mode is planned to take in place to improve the working face environment and to ensure occupational health and safety of underground workers. The high altitude creates an extreme low oxygen and low pressured working environment, which evidently decreases both the worker’s and equipment’s working efficiency in comparison to a lower altitude area. Moreover, the single ventilation mode can easily form an anoxic area with the negative pressure, which threatens worker’s life. Thus, this mine’s unique character of the high altitude drives the requirement of a compound ventilation mode.

The inspected options for the ventilation mode are as follows: A₁—short-range pressing-long-range absorption (front pressing-back absorption)(Figure 2(c)), A₂—short-range pressing-long-range absorption (front absorption-back pressing)(Figure 2(d)), A₃—long-range pressing-short-range absorption (front pressing-back absorption)(Figure 2(a)), A₄—long-range pressing-short-range absorption (front absorption-back pressing)(Figure 2(b)), and A₅—long-range pressing-long- range absorption (front absorption-back pressing) (Figure 2(e)).

The evaluation index selection principle is to use as few indexes as possible to reflect the most important and comprehensive information. Decisions on adapting the appropriate ventilation mode can be made through an evaluation in the areas of technical feasibility, economic rationality, and safety reliability. The hierarchy of the decision-making problem is illustrated in Figure 3. The criteria and sub-criteria for this problem are listed in Table 1 [25]:

It should be noted that total ventilation resistance of development face, fan power, and exterior leakage are negative indexes, while the others are all positive indexes. Moreover, when exhaust ventilation is applied, the high altitude environment can easily lead to the appearance of negative pressure and an anoxic phenomenon.

Figure 2 Inspected options for ventilation mode:

Figure 3 Hierarchical structure of selecting best development face ventilation mode

Table 1 Criteria layer and sub-criteria layer for decisions on appropriate ventilation mode

Consequently, the oxygen level of the air is selected as a key factor for our safety indexes [25].

With all the criteria ready in place, the proposed method is now practiced for selecting the best development face ventilation mode. Evaluation index values for each ventilation mode are shown in Table 2. The values of S1 and S2 were obtained from expert’s advice.

4.1 Data dimensionless processing

With the use of Eq. (1), the original data of all indexes from Table 2 were transformed into their dimensionless values, as showed in Table 3.

Table 2 Evaluation index values of each ventilation mode

4.2 Index weight determining with G1 method

1) Criteria layer weight determining

According to the experts, the sequence of the three criteria layers (Technical indexes, Economic indexes and Safety indexes) and the rational assignment for the relative degree of importance between the three criteria layers are determined. These are respectively determined as

Table 3 Dimensionless values of evaluation index

Substituting r₂=1.8, r₃=1.8 into Eq. (2) and the weight (W_E) of criteria layer E can be derived, it is

Substituting ω₃=0.1656 into Eq. (3) and the weight (W_S) of criteria layer S can be derived, which is

ω₂=r₃ω₃=0.2981

Then, the weight (W_T) of criteria layer T can be derived, which is

ω₁=1–ω₂–ω₃=0.5363

And the weight vector is

(W_T, W_E, W_S )=(0.5363, 0.1656, 0.2981)

2) Sub-criteria layer weight determining

According to the experts, the sequence of the four sub-criteria layers of T (technical indexes) criteria layer and the rational assignments for relative degree of importance between the sequenced adjacent layers are determined. These are

Substituting the rational assignments into Eq. (2) and the weight (W_T2) of sub-criteria layer T₂ can be derived. Substituting the weight of T₂ into Eq. (3) and the weight (W_T4) of sub-criteria layer T₄ can be derived. Similarly, the weights of other sub-criteria layers T₃ and T₁ can be derived. Finally, the weight vector of the four sub-criteria layers under criteria layer T is determined as

(W_T1, W_T2, W_T3, W_T4)=(0.3526, 0.1092, 0.3526, 0.1856)

Correspondingly, the sequences of the sub- criteria layers under criteria layer E and layer S, and the rational assignments for relative degree of importance between the sequenced adjacent layers can be determined. These are

And the weight vector is

3) Index weight on overall objective

Using the results from Sections (1) and (2), the weights of T₁ on T, and the weight of T on overall objective can now be calculated. Finally, the weight of index T₁ on overall objective can be derived as

With this procedure, the weights of the other indexes on overall objective can be determined. The results are shown in Table 4.

Table 4 Combination weight of indexes

4.3 Index weight determining with coefficient of variation method

1) Index coefficient of variation

With the dimensionless values of the indexes shown in Table 3, the arithmetic mean value and the standard deviation of each index can be obtained. When substituting the results into Formula (4), the coefficient of variation of each index can be determined. The results are shown in Table 4.

2) Index weight determining

When substituting the coefficient of variation values from Table 4 into Eq. (5), the weight of each index can be obtained. The results are also shown in Table 4.

4.4 Index combination weight determining

The combination weight of each index can be determined by Eq. (8), with results shown in Table 4. It is important to understand the combination weight of each criteria layer is the sum of combination weight of each sub-criteria layer under the layer.

4.5 Final ranking of alternatives by comprehensive evaluation value

The comprehensive evaluation value is obtained through substituting the dimensionless values in Table 3 and the combination weight in Table 4 into Eq. (10). The results are shown in Table 5.

The evaluation values are shown in Figure 4. The following results are established: 1) A4 (long-range pressing-short-range absorption (front absorption-back pressing)) has the maximum evaluation score when ranking only by technical indexes; (2) A3 (long-range pressing-short-range absorption (front pressing-back absorption)) has the maximum evaluation score when ranking by both economic indexes and safety indexes; (3) The comprehensive evaluation score of A3 (long-range pressing-short-range absorption (front pressing- back absorption)) is evidently higher than others and can be chosen as the optimal ventilation mode, and A4 (long-range pressing-short-range absorption (front absorption-back pressing)) has the second- maximum comprehensive evaluation score and can be considered as an alternative ventilation mode.

The field experiments were conducted to verify the effectiveness of the preferred ventilation mode. The result showed that there was a significant reduction of the dust concentration in 0–300 s, and the dust in the development roadway can be almost completely discharged within 1200 s, at this time the dust mass concentration remained at 0.5 mg/m³ or less. Compared with other options, the ventilation mode of long-range pressing-short-range absorption (front pressing-back absorption) is more efficient, while it is more obvious for reducing the concentration of dust.

5 Conclusions

To comprehensively evaluate the different development face ventilation modes for the optimal choice, a novel method for calculating the comprehensive evaluation value of alternatives was introduced to select the best ventilation mode for development face. By considering the advantages of the subjective and objective weight determining methods, this study comprehensively used the above two methods to establish the optimum evaluation model of development face ventilation mode. The conclusions were obtained as follows.

1) According to the weight calculation results, the technical index was determined with the highest weight, the safety index weight was the second, and the economic index weight was the lowest. This shows that the effective and sufficient air supply is the most important at the development face, followed by the stability and quality of air supply, while the economic indexes are not the main factors of ventilation mode selection.

Table 5 Final evaluation value and ranking of alternatives

Figure 4 Bar graph of evaluation scores for alternatives

2) The comprehensive evaluation value of the optimal ventilation mode is the highest, but not every criteria layer index’s evaluation value of the final choice is the highest, the evaluation value of one criterion layer index is even in the medium level. Therefore, the optimal choice of ventilation mode is determined by the comprehensive evaluation of all the indexes, it does not compare each index of the inspected options respectively.

3) The case study considered in this work verified that the proposed approach is able to rank the alternative development face ventilation mode reasonably. It compensates for the disadvantages of the index single weight determining method, for it considers the experience and wisdom of experts and can reflect the new changes of objective conditions.

This study provides a more direct method for analysing and evaluating different ventilation modes, which can meet the demands for optimization of development face ventilation modes in mine. However, the evaluation indexes in this study apply to metal mine. Further study is needed to establish the evaluation indexes for other type mine.

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(Edited by HE Yun-bin)

中文导读

一种基于G1-变异系数法的井下掘进工作面通风方式优选方法

摘要：现有的矿山通风决策和优化方法往往是基于单一的主观经验或客观信息，不能将两者很好地结合起来进行考虑。论文提出了一种基于G1-变异系数法的优选方法，利用组合赋权，弥补评价指标单一赋权的缺陷。在实例研究中，建立了合理的评价指标体系，利用评价模型计算得出各备选通风模式的评估值，根据总的评估值来选择最优巷道掘进面通风方式。研究结果表明，该方法能够对掘进面通风方式备选方案进行合理排序，既具有主客观赋权方法的优点，又兼顾了专家的经验和智慧，以及客观条件的新变化。利用该方法进行掘进工作面通风方式分析、评价更为合理和可靠。

关键词：掘进工作面通风；G1方法；变异系数法；综合评价；优选

Foundation item: Projects(51504286, 51374242) supported by the National Natural Science Foundation of China; Project(2015M572270) supported by China Postdoctoral Science Foundation; Project(2015RS4004) supported by the Science and Technology Plan of Hunan Province, China

Received date: 2018-02-05; Accepted date: 2018-07-25

Corresponding author: ZHOU Zhi-yong, PhD, Lecturer; Tel: +86–13187011703; E-mail: csuzzy@126.com; ORCID: 0000-0002-8437- 5859