Applied Mechanics and Materials Vols. 368370 2013 pp 19791984 Online: 201308302013 Trans Tech Publications, Switzerland
doi:10.4028www.scientific.netAMM.368370.1979
Improvement of Analytic Hierarchy Process and Its Application for Coal Mine Safety Assessment
DONG Si Huia, ZHAO Yu Kub and LI Minc
School of Civil and Safety Engineering, Dalian Jiaotong University, Dalian 116028, China asunnytrip126.com, bcool1535251163.com, cJeweler163.com
Keywords: analytic hierarchy process; comprehensive evaluation; fuzzy math; rootmeansquare method; genetic algorithm
Abstract. The calculation of weigh value and consistency of the judgment matrix of analytic hierarchy process AHP were studied in this paper. And the study was applied for coal mine safety assessment. Due to the particularity and complexity of the coal mine environment, to make sure the comprehensive assessment for coal mine system safety, analytic hierarchy process was usually used. It is an important problem to solve the weight value and consistency of the judgment matrix when applying analytic hierarchy process. To obtain the weight value and ensure the consistence of the judgment matrix is the main research direction of AHP. The genetic algorithm was applied to calculate the weight value and the consistency of the judgment matrix. And fuzzy comprehensive evaluation method was applied to evaluate the safety condition of the coal mine system with the method of weight value solution in this paper. Case study shows that the calcuation resuts of applying genetic algorithm to calculate idnex weight value is better than additional methods.
0 Introduction
Since the reform and opening up policy, the energy demand of China coal increases year by year, coal mine becomes more important, and the price of coal has increased to a high place. More accidents have happened for the high strength labor in coal mine. Coal mining is a kind of highrisk industry. The work underground contains many unsafe factors: the gas, coal dust, roof collapse, fire, water inrush. The high temperature, high humidity, high wind speed can threat personnel health at any time. The cause of the accident is different because of the different production environment underground. These elements which can cause accidents are related, so how to deal with the coal mining safety assessment is particularly important.
There are numerous assessment indexes in coal mine safety assessment index system. It is difficult to give comprehensive evaluation for two or more indexes, which can consider all the indexes thoroughly. The importance degree among the indexes is difficult to be compared1. Analytical hierarchy process AHP is a comprehensive evaluation method, which can consider qualitative and quantitative factors. This method can acquire the importance degree of index through the index importance judgment matrix, which formed by expert through comparing the importance of each index. The importance of index by this method is relative objective relative to expert points approach.
AHP method always decomposes the assessment system into some levels include target level, standard level and scheme level2. And on this basis, AHP analyses the system qualitatively or quantitatively. The judgment matrix in AHP is based on expert points approach, so the data has some subjectivity, and sometimes the judgment matrix hasnt consistency3.
effectively.
1 Theoretical analysis
AHP is an effective new method to solve complex decision making problems. With the development of science and technology, some problems such factors, objects and concepts in economic, biological, psychological, organization management and other areas need to be researched
Genetic algorithm GA was applied to solve the consistency of judgment matrix and determine the
index weight values importance degree. The fuzzy comprehensive evaluation was applied to assess the safety condition of a coal mine. The case study and application results show that GA can be used
to solve the consistency of judgment matrix and to determine the weight values
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Frontiers of Green Building, Materials and Civil Engineering III
quantitatively urgently, which can only be studied qualitatively in the past. To some extent, AHP can meet this demand. According to the overall goal of the problem, AHP establish a hierarchical structure through decomposing the index of different level. The satisfying plan can be chosen according to the importance degree of different plans. The detail of how to analyze a problem with analytic hierarchy process is as follows.
1 Establish a hierarchical structure model. 2 Construct the judgment matrix such as A.
a11 a12 a1n a aa
Aa21 22 2n 1
ij nn
a31 a32ann
3 Calculation for the weight value of each index weight vector. There are some traditional
methods to calculate the weight vector, such as rootmeansquare method. The calculation formula of rootmeansquare method is as follows:
M m1,m2,,mn,mi n n aij 2 i1
W w1,w2,,wn 3
,i,j1,2,,n
m wi
i nj1 m
In which, mi is counted as the value of the element in row i of matrix A, wi is the value of mi after
being normalized with W.
4 The consistency check for the judgment matrix. The check can be executed according to the
following formula.
1 n Aw 4
max
j
i n j1 wi
So the maximum eigenvalue of matrix A can be got as max , and with the formula CRCI and RI
CImaxn , the value CI can be gotten. RI is meanstochasticconsistence index, which has been n1
acquired by some researcher with stochastic method. When CI0.1, the consistency of this judgment .
structure model of AHP has some levels usually, such as the target level A, first
decisionmaking level B, second decisionmaking C etc. In level B, it contains n decisions, named as
B , B ,, B ; the second decision level includes m decisions, named as C , C ,, C . So the 12n 12m
judgmentmatrix BBij,i,j1,2,,n canbegotten.Bk isoneelementofB,thenthereisa nn
ij
matrix can be accepted
The hierarchical
judgmentmatrix Cck,i,j1,2,,m;k1,2,,n inthehierarchicalstructuremodel.
mm
The final evaluation conclusion can be influenced by the accuracy of the weight. The traditional
methods for calculating weight value are not precise enough, such as rootmean square method. Genetic algorithm is introduced to solve the weight value calculation problem in AHP.
The consistency check of judgment matrix is the key step in the analytic hierarchy process. According to the definition of judgment matrix, if the matrix can satisfy the complete consistency, in theory, there are the following conditions:
0,n1,b i k,i,j1,2,,n,n bn ini1,2,,n
k
k ij
k1k1 k k1
n n bikkni 0 5 i1 i1
ik jk
kk
Applied Mechanics and Materials Vols. 368370
1981
the consistency problem of judgment matrix is transformed into a nonlinear function problem, the formula is as follows:
6
values. It is difficult to solve this function with conventional method. Therefore, genetic algorithm is introduced to deal with this function.
As above,
optimization
n n bikk ni
min CIF ni 1 k 1
s.t.k 0,nk1k 1,k1,2,,n
n
In formula 6, CIFn is the consistency function of judgment matrix,is the order weight
intelligent
Genetic algorithm is a kind of
function optimization method, it offers a general
framework on how to solve complex system problem4. In the process of GA method, the whole search strategy and optimization research method in computing is not dependent on gradient information or other auxiliary knowledge5. The basic operation process of GA is shown in figure one, it has three operators, they are select, cross and mutation. The operation of individual operator marches in the random selection, it will insure the migration rule of the optimal solution is random in
the group, and the directed research is more efficient
.
Initial population
End condition
Select
Output result
Random0,1Pc
Cross
Random0,1P
mutation
Fig. 1 Genetic algorithm operation process
In figure 1, Pc is the crossover probability of gene, Pm is the mutation probability of gene
2 Case study
135
.
There are two judgment matrixes as following. The calculation results of weight values for are
shown in table 1, which are solved by rootmeansquare method and GA respectively
17 15 16 1 13 14
152 1
153766 15 1 13 5 3 3
13 3 1 6 3 4
B113 1 12 ,B2
16 13 13 3 1 12
16131442 1
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Frontiers of Green Building, Materials and Civil Engineering III
From table 1, the conclusion can be gotten that the results of genetic algorithm are more accurate than the results of rootmeansquare method. For example, in the calculations of B1, when calculated with rootmeansquare method, the judgment matrix cannot pass the consistency check. The sort of weight value which calculated by genetic algorithm could make the consistency check of B1 satisfactorily. So the conclusion can be drawn that GA can get more accurate weight value and more accurate consistency check relative to rootmeansquare method.
Table 1 The comparison of the calculation results of two methods
3 Application for Coal Mine Safety Assessment
systematicness
3.1 Establishment of index system for coal mine safety assessment
There is the example about the coal mine production safety assessment6. The object of study is the whole coal mine production system7. The target layer is coal mine safety evaluation. The first decision layer of the index includes six indexes: geological conditions, technical equipment, personnel quality, safety education, environmental safety, management level. The second decision layer contains 26 factors. The index system is shown as figure 2.
Time
Judgment matrix
Sort of weight value
Consistency check
1
2
3
4
5
6
Rootmeansquare method
B1
0.6118
0.1789
0.2093
0.2821
GA
B1
0.6542
0.1403
0.2055
0.0499
Rootmeansquare method
B2
0.4549
0.1388
0.2331
0.0318
0.0618
0.0796
0.0833
GA
B2
0.4701
0.1381
0.2378
0.0291
0.0545
0.0698
0.0233
The fuzzy comprehensive evaluation method based on fuzzy mathematics is a comprehensive
evaluation methodology. It uses the membership degree theory to transform the qualitative evaluation into quantitative evaluation. It can use fuzzy mathematics to make a comprehensive evaluation for the objects or targets restricted by various factors. It can get a clearly result, and has strong
. So it can solve uncertainty problems, even the vague problems or the problems which
are hard to be quantized.
B1geological condition
B2 technical equipment
A The safety assessment index system of coal mine
B3 personnel quality
B4 safety education
B5 environment safety
B6 management level
C1
C2
C3
C4
C5
C6
C7
C8
C9
C10
C11
C12
C13
C14
C15
C16
C17
C18
C19
C20
C21
C22
C23
C24
C25
C26
Fig. 2 The safety assessment index system of coal mine
In figure 2, C1 represents coal seam occurrence condition; C2 represents coal seam hydrogeololgy condition; C3 represents the roof and floor structure of coal seam; C4 represents the gas condition; C5 represents mechanization level; C6 represents equipment deployment; C7 represents equipment maintainance; C8 represents research and innovation; C9 represents personnel makeup; C10 represents workmanship; C11 represents cultural level; C12 represents safety awareness; C13 represents implement of education plan; C14 represents prejob safety training; C15 represents daily safety education; C16 represents training for special type of worker; C17 represents noise control; C18 represents lighting; C19 represents dust prevention and control; C20 represents temperature and humidity; C21 represents air quality; C22 represents safety consciousness of leader; C23 represents safety investment; C24 represents safety culture; C25 represents safety alerting; C26 represents safety accident handling.
Applied Mechanics and Materials Vols. 368370
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3.2 Factor set and comment set
In figure 2, the factor set has three layers. The first layer is target A, the second layer is B, and B
contains B ,B ,B ,B ,B ,B . The last layer is C. 123456
BC,C,C,C, BC,C,C,C, BC,C,C,C, BC,C,C,C, 1 1 2 3 4 2 5 6 7 8 3 9 10 11 12 4 13 14 15 16
B5 C17,C18,C19,C20,C21,B6 C22,C23,C24,C25,C26
The comment set has five levels, Vworst, worse, general, better, best.
3.3 The determination of membership degree
The degree of membership describes the degree of an element subject to the fuzzy subset in the
fuzzy comprehensive evaluation method. The membership degree of first decision layer can be gotten
through expert decision and membership functions, which is RR , R , R , R , R , R . And there 123456
are 10 experts to grade for second decision layer. They confirm the membership degree matrixes, which are as follows:
0 0.1 0.4 0.3 0.2 0 0.2 0.3 0.3 0.3 0 0.2 0.4 0.2 0.2
0 0.2 0.3 0.5 0 0 0.1 0.4 0.4 0.1 0 0.3 0.3 0.4 0 R1 0 0.3 0.2 0.4 0.1,R2 0 0.2 0.3 0.3 0.2,R3 0 0.1 0.5 0.1 0.3,
0 0.2 0.5 0.2 0.1 0 0.1 0.5 0.2 0.3 0 0.2 0.4 0.3 0.1
0 0.1 0.5 0.2 0.2 0 0.2 0.3 0.2 0.3 0 0.2 0.3 0.2 0.3 0 0.2 0.4 0.3 0.1 0 0.1 0.4 0.4 0.1 0 0.1 0.3 0.3 0.3
R ,R0 0 0.5 0.2 0.3,R
4 0 0.1 0.3 0.4 0.2 0 0.3 0.4 0.3 0
0 0.3 0.5 0.1 0.1 0 0.1 0.4 0.5 0
D A C , and C c1;c2;c3;c4;c5;c6, ci i Ri, i 1,2,3,4,5,6. In which A is the element weight value of first decision layer. The evaluation result comment level is obtained with maximum
membership principle.
3.5 The judgment matrix
From the comparison of the importance degree, the judgment matrix of decision layer can be obtained as shown:
123534
3.4 The evaluation result
The evaluation result is calculated by following formula:
5
6 0 0.2 0.4 0.3 0.1
0 0.3 0.4 0.1 0.2
12 1 2 4 2 3 1 2 3 4 1 2 3 2
13 12 1 2 12 12 12 A ,B1
1 2 3 12 1 1 12 ,B2 15 14 12 1 14 12 13 12 1 2 13 1 1 3
13 12 2
14 13 2 3 12 1
4 1 2 14 13 12 1 12 2 13 1
1235 1342
1 2 5 3 4 12 1 2 1 3
12 1 1 2 13 1 2 12
B ,B ,B15 12 1 2 2
3 13 1 1 12 4 14 12 1 2 5
1311211
14 12 12 1 1
15 12 2 1 12 2 12 1
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Frontiers of Green Building, Materials and Civil Engineering III
3.6 The weight value and consistency check for judgment
The weight value and consistency check results with GA method are shown as table 2.
Judgment matrix
Table 2 The weight value and consistency check
Weight value
Consistency check 0.003 1 0.064 6 0.030 2 0.069 2 0.029 6 0.037 8 0.015 4
W1 W2 W3
W2 W5 0.092 6
0.175 6
0.148 3
0.204 6
0.122 4 0.070 3 0.106 3 0.166 8 0.044 6 0.157 2
W6
0.106 2
B1 0.469 2
B2 0.449 9
B3 0.512 2
B4 0.490 5
B5 0.449 8
B6 0.435 1
A 0.385 6
0.277 8 0.151 2 0.223 0 0.157 2 0.212 2 0.169 0 0.230 6
0.160 4 0.149 6 0.116 5 0.147 7 0.145 3 0.122 8 0.075 8
3.7 The final evaluation result
The final evaluation result is A0 0.1714 0.3511 0.3096 0.1780. According to the maximum membership, the safety level of the coal mine is general.
4 Conclusion
5 Acknowledgements
This work was supported by Science and Technology Planning Project of Liaoning Province 2012231004 and Educational Commission of Liaoning Province L2010088.
6 References
1 Z. Y. Du, S. Q. Yang and J. N. Li, The Application of Extension Superiority Evaluation Method in Coal Mine Safety Evaluation, ed. 10, vol. 43, pp. 221224, 2012.
2 T. L. Saaty, The Analytic Hierarchy Process, McGrawHill, New York.1980.
3 L. N. Hou, D. M. Chen and G. H. Peng, Improvement ofAHP and Its Application in Sichuan Agricu lturalD evelopm ent, Journal of Anhui Agricultural Sciences, ed. 16, vol. 37, pp. 77087711, 2009.
4 J. L. Jin, J. Ding, Genetic Algorithm and Its Applications to Water Science, Cheng Du: Sichuan University Press, 2000.
5 X. Q. Lv, Improvement of an Adaptive Genetic Algorithm Based on Discrete Variable, Journal of Changchun Normal University, ed. 12, vol. 31, pp. 2325, 2012.
6 Y. J. Liu, S. J. Mao, J. M. Yao, etc., Comprehensive Safety Evaluation of Coal Mine Based on Analytic Hierarchy Process, Mining Research and Development, ed. 2, vol. 27, pp. 8284, 2007.
7 C. L. Yang, M. J. Zhang, Fuzzy Comprehensive Evaluation of Mine Safety, Coal Technology, ed. 1, vol. 24., pp.3739, 2005.
AHP method is widely used in evaluation of safety and environment. The traditional method in
weight value calculation is not very precise. The genetic algorithm is introduced for weight value calculation. Case study shows that the calculation precision of GA is higher than the method traditional method obviously. Fuzzy comprehensive evaluation method is applied for coal mine safety evaluation. The calculation result proves the feasibility of AHP with GA in the field of security
engineering.
Frontiers of Green Building, Materials and Civil Engineering III
10.4028www.scientific.netAMM.368370
Improvement of Analytic Hierarchy Process and its Application for Coal Mine Safety Assessment
10.4028www.scientific.netAMM.368370.1979
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