Fuzzy comprehensive evaluation method of F statistics weighting in identifying mine water inrush source

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1 MultCraft Internatonal Journal of Engneerng, Scence and Technology Vol. 2, No. 7, 200, pp INTERNATIONAL JOURNAL OF ENGINEERING, SCIENCE AND TECHNOLOGY MultCraft Lmted. All rghts reserved Fuzzy comprehensve evaluaton method of F statstcs weghtng n dentfyng mne water nrush source L. Ma, Y. Lu 2*, X. P. Zhou School of Resources and Envronmental Engneerng, Hefe Unversty of Technology, Hefe , P.R. CHINA 2* School of Botechnology and Food Engneerng, Hefe Unversty of Technology, Hefe , P.R. CHINA *Correspondng Author: e-mal: Luy99999@63.com Abstract In order to rapdly dentfy the source of water nrush n coal mne, and provde the theoretcal bass for mne water damage preventon and control, fuzzy comprehensve evaluaton model was establshed. The F statstcs of water samples was normalzed as the weght of fuzzy comprehensve evaluaton for determnng the source of water nrush n coal mne. The determnaton result of F statstcs weghtng method to 47 water samples was compared wth that of over standard weghtng method, and the former accuracy rate s 93.6%, the later accuracy rate s 74.5%. The result shows that F statstcs reflects the dentfcaton ablty of varous ndcators wth hgher accuracy than the common over standard weghtng method. F statstcs weghtng method allocates weghts accordng to the dstngush abltes of the evaluaton factors, beng more sutable for seekng an objectve evaluaton and dscrmnaton from the dfferences of the statstcal samples themselves. Keywords: F statstcs, fuzzy comprehensve evaluaton, water nrush source, coal mne. Introducton Mne water hazard ssue has been n urgent need of study due to ts mpacts on safety of coal mne. It can cause the mne to stop producton and huge economc loss, even mneworker death. For example, a major water nrush accdent of Luotuoshan Coal Mne wth the maxmum water nflow 7200 m 3 /h happened n Match, 200, and 3 persons ded n ths accdent. Now, there are two man aspects to research mne water hazard ssue. One s the evaluaton and predcton of the possblty of water nrush n advance (Wu et al. 2008), and the other s the dscrmnaton of the water nrush source afterwards. Accurate and rapd dscrmnaton of water nrush source s the bass of control measure and a key technque for coal mne safe producton. In general, mne water hazard nvolves n fracture-karst aqufers. However, groundwater flow n these aqufers s always complex. And t s flowng n the hydro-geochemcal cycle and takes water-rock nteracton. It has the varaton characterstcs n space and tme. Therefore, many researchers have done a lot of basc research works on groundwater n dfferent aspects. For example, some studes nvolve n fracture-karst groundwater experments (Zmmerman et al. 2002; Brush and Thomson, 2003; Qan et al. 2005; Qan et al. 2006; Qan et al. 2007; Zheng et al. 2008; Luo et al. 2009), and others on groundwater numercal smulaton for assessment of groundwater resources (Qan et al. 2006; Qan et al. 2009). However, systemc survey on groundwater flow needed to conduct to assessment groundwater resource based on the above-mentoned studes. Now, an alternatve method by chemcal characterstc of groundwater to dscrmnate groundwater source obtans better applcaton effects n mne water damage flood preventon and control. There are some commonly used methods to dentfy the source of water burstng n coal mnes, such as fuzzy comprehensve evaluaton method (Ben et al. 2005), Bayesan dscrmnaton method (Chen et al. 2009; Song et al. 2005), gray correlaton analyss method (Gao et al. 2007), artfcal neural network (Wu et al. 2007), extenson dentfcaton (Zhang et al. 2009), and so on. Among them, fuzzy comprehensve evaluaton method due to good effect, smple calculaton, has a wde range of applcaton n dentfyng water nrush source. To fuzzy comprehensve evaluaton model, how to select an approprate weght calculaton method for your research felds for the model has been one of the dffcultes. Commonly used weghtng methods are over standard weghtng method (Ma et al.

2 24 Ma et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol. 2, No. 7, 200, pp ), basng weghtng method (Ben et al. 2006), analytc herarchy process (AHP)(Lu et al. 2009), and so on. Calculaton weghtng methods have a great mpact on dstngushng the results. F statstcs s the rato of mean square devaton between groups to mean square devaton n groups. It ndcates the dfferences between groups and the dfferences nner groups, and ts meanng s sut for the meanng of weght n the dscrmnaton of water nrush source. So, n ths paper, we tred to normalze F statstcs as the weght, establshed fuzzy comprehensve evaluaton model to determne the source of water burstng n coal mne. 2. Basc Theory 2. The basc theory and steps of fuzzy comprehensve evaluaton: Fuzzy comprehensve evaluaton method s a synthetcal assessment method that apples fuzzy mathematcal prncples to evaluate thngs and phenomenon affected by varety of factors (L et al. 200). It regards evaluaton objectves as a fuzzy set (named the Factor Set U) composed of varety of factors wth dfferent assessment levels selected. Another fuzzy set named the Evaluaton Set V s employed to calculate the membershp degree of each ndvdual factor n the Evaluaton Set to establsh a fuzzy matrx. The quanttatve evaluaton value of each factor s fnally determned by calculatng the weght dstrbuton of each factor n evaluaton goal. It apples the fuzzy transformaton theory and maxmum membershp degree law, and makes a comprehensve evaluaton to varous factors (Zhang et al. 992). Specfc steps are as follows: Determne the Factor Set of evaluaton object, that s U= {u, u 2,, u m }. It s a set composed of m knds of evaluaton factors. Determne the Evaluaton Set, that s V = {v, v 2,, v n }. It s a set composed of n knds of evaluaton standards. Construct sngle-factor evaluaton matrx. Evaluate sngle-factor and then get vector R. A sngle-factor evaluaton matrx R s consttuted by numbers of sngle-factor evaluaton vector put together. There are some commonly used membershp degree calculaton functon of sngle-factor, such as lnearty lower sem-ladder-shaped dstrbuton functon and so on. R r r2 L r n R 2 r2 r22 r 2n R= L = () M M M M Rm rm rm2 L rmn In (), R s a fuzzy relatonshp matrx composed of evaluaton Factor Set U and the Evaluaton Set V. Determne evaluaton factors weght vector E= {e, e 2,, e m }. There are many methods to calculate weght, such as over standard weghtng method, analytc herarchy process (AHP) and so on. Among them, over standard weghtng method s commonly used n artcles about all knds of fuzzy comprehensve evaluaton, whch s calculated as follows: e = x / a (2) In (2), x s the practce measure value of the factor n dstngushng samples, and a states the statstcal average value of the factor n dstngushng standard. As the weght of fuzzy comprehensve evaluaton method, t needs normalze, that s: m e = x / a / x / a (3) ( ) ( ) = Comprehensve evaluaton. The last results of comprehensve evaluaton can be got by dong complex operatons calculaton between sngle factor weght vector E and fuzzy relatonshp matrx R, whch s as follows. B= E R= { b, b2, K, bm} (4) In (4), b s the membershp degree value of evaluaton samples to each evaluaton standard. The determnaton results are usually defned accordng to the maxmum membershp degree law. 2.2 F statstcs: F statstcs states the rato of mean square devaton between groups to mean square devaton n groups, the rato s hgher, whch ndcates that the dfference between groups s greater, and the dfference nner groups s smaller. As the weght of fuzzy comprehensve evaluaton, the value of F statstcs s greater, whch shows that there s bgger dfference between varous evaluaton standards, and t s more concentrated dstrbuton n each evaluaton standards, the dstngushng ablty s stronger. Therefore, n some areas, t s more conforms to the functon and sgnfcance of weghtng. The specfc calculaton s as follows. 2 SA QA/( r ) F = = (5) S 2 E Q E /( n r ) In (5), the Q A s devaton square sum n group, that s: r n Q ( ) 2 A = Xj X (6) = j=

3 25 Ma et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol. 2, No. 7, 200, pp The Q E s devaton square sum between the groups, that s: r Q ( ) 2 E = n X X (7) = In (5), (6) and (7), r s the level number of dstngushng factor, X j s the jth sample value under the th level of dstngush factor. n s the sample number under the th level of dstngush factor. X s average value of the th dstngush gene, X s the total average value of dstngush factor, that s as follows. 3. Applcaton and Analyss X X n j n j = r n r = Xj n = j = = = X, =,2,..., r (8), n= n (9) 3. Fuzzy comprehensve evaluaton model of over standard weghtng method: For showng the feasble of F statstcs as weght and analyzng ts calculatons effects, water nrush source dscrmnaton of a coal mne was taken for example n ths paper. The major aqufers of the mne are the Ordovcan and Carbonferous lmestone karst fracture aqufer (lmestone water for short n the followed), coal measures sandstone fracture aqufer (coal measures water for short n the followed) and Cenozoc unconsoldated aqufer (Cenozoc water for short n the followed). There are 47 water samples of the three aqufers n Pany Coal Mne, whch are showed as Fg.. Sx common ons n groundwater are used as the evaluaton factors, that s U = (Ca 2+, Mg 2+, K + +Na +, HCO 3 -, Cl -, SO 4 2- ), and the apprasal set V = (Cenozoc water, coal water, lmestone water). Accordng to 47 water samples of the mne, the statstcal average values of aqufers sx on ndcators were calculated, whch are also the background valuea of the three aqufers, shown n Table. Fgure. Water samples dstrbuton of Pany Coal Mne, Chna

4 26 Ma et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol. 2, No. 7, 200, pp Table. The average value of aqufers water qualty ndcators (mg / L) Aqufers Ca 2+ Mg 2+ K + +Na + - HCO 3 Cl - 2- SO 4 Cenozoc water Coal measures water lmestone water The 47 water samples were calculated by usng fuzzy comprehensve evaluaton model of over standard weghtng method, and then every sample s aqufer was dscrmnated accordng the calculaton result. The dscrmnaton results (wrong dscrmnaton part) are shown n Table 3, of whch 2 samples are made a wrong dstngushed, and the dscrmnaton accuracy rate s 74.5%. 3.2 Fuzzy comprehensve evaluaton model of F statstcs weghtng method: ANOVA of these three groups 47 water samples was calculated n SPSS software. We obtaned F statstcs of the sx ons, and then dd normalzaton processng to F statstcs for servng as the weght. F statstcs and the normalzed results are shown n Table 2. From the table we can seen that F-value of Mg 2+ on ndcator s the largest, whch shows that the aqufers dentfcaton ablty s the strongest, so ts weght value 0.37 s the largest weght n fuzzy comprehensve evaluaton; SO 4 2- and Ca 2+ take second place, whose dentfcaton abltes are strong, and the weghts are 0.27 and 0.25; HCO 3 -, K + +Na + and Cl - the three ons F values are small, whch shows ther dentfcaton abltes are weak, and the weghts are respectvely 0.06,0.04 and Table 2. F statstcs and the normalzed results Indcators Ca 2+ Mg 2+ K + +Na + HCO 3 - Cl - SO 4 2- F statstcs Weghts Fuzzy comprehensve evaluaton model of F statstcs normalzed results as the weght was constructed. The 47 water samples were also calculated by the model, and every sample s aqufer was ndentfed accordng to the calculaton result. The result shows that there are three samples wrongly judged n total, and the accuracy rate s 93.6%, whch s hgher than the results of over standard weghtng method. The comparson of the two methods dscrmnaton results (wrong dscrmnaton part) are shown n Table 3. Aqufers Ca 2+ (mg/l) Table 3. Dscrmnaton results by F method vs over standard weghtng methods Mg 2+ K + +Na + - HCO 3 Cl - 2- SO 4 F statstcs weghtng Over standard weghtng (mg/l) (mg/l) (mg/l) (mg/l) (mg/l) 2 3 Results 2 3 Results Cenozoc water, 2 - coal measures water, 3 - lmestone water 3.3 Comparatve analyss of the two methods: From the above context, we can get that usng F statstcs normalzed results as the weght n fuzzy comprehensve evaluaton s feasble, and ts dscrmnaton effect s better than that of over standard weghtng method. The reason s that the over standard weghtng method s nclned to gve bgger weght to the excess parts of the evaluaton factors, and t s sutable for areas such as envronmental assessment, n whch the ndcator factors of beyond the

5 27 Ma et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol. 2, No. 7, 200, pp standard pollutants values gve greater weghts, thus emphaszng the serousness of too hgh polluton. The F statstcs s the rato of mean square devaton between groups to mean square devaton n groups, and ts value sze drectly reflects the dstrbuton of the samples from the statstcal samples themselves, and the weght values are allocated based on the dstngush abltes of the evaluaton factors. Therefore, the applcaton of F statstcs weghtng method more conforms to the realty sgnfcance of dscrmnatng water nrush source and dentfyng the aqufers of water samples. 4. Conclusons It s feasble that the normalzed results of F statstcs are ntroduced nto fuzzy comprehensve evaluaton as weght, and the result s better n water nrush source dstngush applcaton of a coal mne. The accuracy rate s as hgh as 93.6%, whch s hgher than the accuracy rate of over standard weghtng method. Compared wth AHP methods, F statstcs weghtng method overcomes the nterferences of artfcal subjectve factors, and s more n lne wth the objectve realty. Compared wth over standard weghtng method, F statstcs weghtng method express the rato of mean square devaton between groups to mean square devaton n groups, and the approprate weght values are allocated accordng to the dstngush abltes of the evaluaton factors, beng more sutable for seekng an objectve evaluaton and dscrmnaton from the dfferences of the statstcal samples themselves. Therefore, n some domans, usng F statstcs weghtng method may get better evaluate and dscrmnaton effects. Acknowledgement The research was supported by The Funds for Creatve Research Groups of Hefe Unversty of Technology(No. 2009HGCX0233), Natonal Natural Scence Foundaton of Chna (No ). We thank the revewer and the edtor for provdng rgorous and constructve comments whch help us mprove the manuscrpt substantally. References Ben, X.D., Guo, Y.H., Ren, Y.G., L, H.L., Dscusson on weghtng determnaton n comprehensve fuzzy water source judgment applcaton. Coal Geology of Chna, Vol. 7, pp ,70. (In Chnese) Ben, X.D., Guo, Y.H., Xe, Y.W., Shen, Y.L., Zhang, C.F., Png, L.H., Applcaton and dscusson of fuzzy comprehensve evaluaton n dentfyng mne nrush water source. Mnng Safety & Envronmental Protecton, Vol. 33, pp (In Chnese) Brush, D.J., Thomson, N.R., 2003, Flud flow n synthetc rough-walled fractures: Naver-Stokes, Stokes, and local cubc law smulatons. Water Resources Research, Vol. 39, No. 4, pp.085, do: 0.029/2002WR Chen, H.J., L, X.B., Lu, A.H., Studes of water source determnaton method of mne water nrush based on Bayes multgroup stepwse dscrmnant analyss theory. Rock and Sol Mechancs, Vol. 30, No. 2, pp Gao, W.D.,2007. Applcaton of grey stuaton decson method n dstngushng source of mne water nrush. Mnng Safety & Envronmental Protecton, Vol. 34, pp (In Chnese) L, M.S., Yu, Y.L., Lu, F.G., Hu, Y.B., Cheng, X.F., Zhao, Z.G., 200. A Fuzzy comprehenseve evaluaton model of mne shaft water resource outburst n Yaoqao coal mne. Ste Investgaton Scence and Technology, 200, pp (In Chnese) Lu, Y.P., Chen, Y.M., L, Y.C., He, T., Wang, T.M., Determnng the development potental of reservors at ultra-hgh water cut stage usng comprehensve fuzzy analytcal herarchy evaluaton method. Systems Engneerng-Theory &Practce, Vol. 29, pp (In Chnese) Luo, S., Qan, J., Zheng, J., Zhao, W., Expermental measurng and characterzng of the orgnal tensle-fracture and ts behavors n the crude bedrock. Geochmaca et Cosmochmca Acta, Vol. 73, No. 3, pp. A802. Ma, Y.J., Zheng, X.L., L, Y.X., Song, S., Improvement and Applcaton of Fuzzy Synthetc Evaluaton of Groundwater Qualty. Journal of Chna Unversty of Mnng & Technology, Vol. 38, pp (In Chnese) Qan, J.Z., Luo, S.H., Wu, J.F., Chen, Z., Qn, H., Expermental study of non-fckan transport n a sngle sands-flled fracture. Geochmca et Cosmochmca Acta, Vol. 70, No. 8, pp. A5-A5. Qan, J.Z., Zhan, H.B., Luo, S.H., Zhao, W.D., Expermental evdence of scale-dependent hydraulc conductvty for fully developed turbulent flow n a sngle fracture. Journal of Hydrology, Vol. 339, No. 3-4, pp Qan, J.Z., Zhan, H.B., Wu, J.F., Chen, Z., What can be learned from sequental mult-well pumpng tests n fracture-karst meda? A case study n Zhangj, Chna. Hydrogeology Journal, No. 7, No. 7, pp Qan, J.Z., Zhan, H.B., Wu, Y.F., L, F.L., Wang, J.Q., Fractured-karst sprng-flow Protectons: A Case Study n Jnan, Chna. Hydrogeology Journal, Vol.4, No. 7, pp Qan, J.Z., Zhan, H.B., Zhao, W.D., Sun, F.G., Expermental study of turbulent unconfned groundwater flow n a sngle fracture. Journal of Hydrology, Vol. 3, No.-4, pp Song, X.M., Gu, H.R., Chen, L.W., Bayesan multclass lnear dscrmnant analyss of underwater mcroelement n Huabe coal feld. Chna Coal, vol. 3, 2005, pp (In Chnese)

6 28 Ma et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol. 2, No. 7, 200, pp Wu, Q., Xe, S.H., Fe, Z.J., Ma, J.F., A new practcal methodology of the coal floor water burstng evaluatng Ⅲ: the applcaton of ANN vulnerable ndex method based on GIS. Journal of Chna Coal Socety, Vol. 32, pp (In Chnese) Wu. Q., Zhou. W.F., Predcton of groundwater nrush nto coal mnes from aqufers underlyng the coal seams n Chna: vulnerablty ndex method and ts constructon. Envron Geol, Vol.56, pp , do: 0.007/s Zhang, R.G., Qan, J.Z., Ma, L., Qn, H., Applcaton of extenson dentfcaton method n mne water-burstng source dscrmnaton. Journal of Chna Coal Socety, Vol. 34, pp (In Chnese) Zhang, Y., Zou, S.P., Su, F., 992. Fuzzy mathematcs method and applcaton. Bejng: Chna Coal Industry Press, pp (In Chnese) Zheng, Q., Dckson, S.E., Guo, Y., On the approprate equvalent aperture for the descrpton of solute transport n sngle fractures: Laboratory-scale experments. Water Resources Research, Vol. 44, W04502, do: 0.029/2007WR Zmmerman, M.D., Bennett, P.C., Sharp, J.M., Cho, W.J., Expermental determnaton of sorpton n fractured flow systems. Journal of Contamnant Hydrology, Vol. 58, No.-2, pp Bographcal notes L. Ma s a Doctoral student at the School of Resources and Envronmental Engneerng, Hefe Unversty of Technology, n Chna. Hs research nterests nclude groundwater resources assessment, GIS(Geographc Informaton System), groundwater hydrochemcal characterstcs, and dscrmnaton of water-nrush source of mne. He wrote around 0 academc papers on those topcs. Y. Lu s an Assocate Professor at the School of Botechnology and Food Engneerng, Hefe Unversty of Technology, n Chna. Hs research nterests nclude groundwater resources assessment, groundwater hydrochemcal characterstcs, and groundwater polluton remedaton. She wrote around 20 academc papers on those topcs. She also supervsed several students of masters. X.P. Zhou s a graduate student at the School of Resources and Envronmental Engneerng, Hefe Unversty of Technology, n Chna. Hs research nterests nclude groundwater resources assessment, GIS(Geographc Informaton System), groundwater hydrochemcal characterstcs, and dscrmnaton of water-nrush source of mne. He wrote around 5 academc papers on those topcs. Receved September 200 Accepted October 200 Fnal acceptance n revsed form October 200