Research Jurnal f Applied Sciences, Engineering and Technlgy 5(2): 465-469, 2013 ISSN: 2040-7459; E-ISSN: 2040-7467 Maxwell Scientific Organizatin, 2013 Submitted: May 08, 2012 Accepted: May 29, 2012 Published: January 11, 2013 Analysis n the Stability f Reservir Sil Based n Fuzzy Artificial Neural Netwrk Lianguang M and Zheng Xie Hunan City University Yiyang, Hunan, 413000, China Abstract: Owing t the fact that the relatin between the reservir sil slpe stability and its influencing factrs is cmplicated and fuzzy, a methd-fuzzy neural netwrk t analyze the reservir sil slpe stability is prpsed. The methd infuses fuzzy reasning prcess int the structure f neural netwrk, makes the physical meaning f neurn and weight f neural netwrk clear, reduces the prcess f regulatin match, raises the speed f reasning and imprves greatly the self-adaptin capacity f the system. In the end, the fuzzy neural netwrk mdel is trained and tested by the cllected 21 cases f sil slpe data samples. The result prves that the fuzzy neural netwrk is a valid methd, which has significant advantages ver general BP neural netwrk mdel in analyzing effectiveness and quality. Keywrds: Fuzzy thery, neural netwrk, sil slpe, stability INTRODUCTION Up t nw, mre than 80,000 reservirs f all kinds have been established in China, ranked the first in amunt all arund the wrld. Hwever, ver 37,000 f them are dangerus reservirs that can t functin effectively but have the danger f cllapse instead, which des great harm t scial public security and ecnmic sustainable develpment. And the instability f reservir slpe is ne f the main reasns causing cllapsing. There are varied factrs influencing reservir slpe stability, whse influence n the reservir slpe stability is a nnlinear cmplicated prcess. Mst f the influence has undetermined features like being stchastic and fuzzy. Therefre, it s rather difficult t exactly evaluate the stability f reservir slpe. At present, the mar methds t study slpe stability are limit equilibrium methd, numerical analysis methd, grey system methd1, fuzzy cmprehensive evaluatin (Wei and Li, 1996; Li et al., 1998; Wei, 1994; Zha et al., 2004) and neural-net algrithms etc. Hwever, the evaluatin results are always nt s satisfactry because f the limitatin f all methds themselves (Xia and Li, 2002). Under this circumstance, this study prpses a fuzzy artificial neural netwrk methd that can prcess determined and undetermined infrmatin simultaneusly. By the preprcess f input knwledge and the after-treatment f utput knwledge, the mdel invlves fuzzy lgical reasning int the nnlinear algrithm f neural netwrk and fuzzy evaluatin is achieved by neural netwrk. STRUCTURE OF FUZZY NEURAL NETWORK This study makes general BP neural netwrk fuzzy. T be specific, n the basis f reserving riginal structure f neural netwrk, neurn is fuzzily prcessed directly. In ther wrds, input value r weight value are changed t fuzzy quantity expressed by membership grade; by netwrk study, the utput fuzzy subcllectin is diverted t nn-fuzzy digital quantity. The specific mdel f fuzzy neurn is a multi-input but single-utput five-layer fuzzy neural netwrk, with its tplgical structure as Fig. 1. The first layer is the input layer: In the layer, every neurn refers t ne input variable, that is, ne factr influencing the stability f reservir slpe. The neurn in this layer sends the input value t the neurn in the next layer directly as fllws: I (1) h = X h, O (1) h = I (1) h (1) In which: h = 1, 2, m, m refers t m input variables. The secnd layer is the fuzzy layer: Clear input variables in the previus layer will becme fuzzy here. The cnnectin weight between neurn in this layer and that f the previus layer is 1, using trapezium distributin fr the membership functin f every neurn. The relatinship between the input and utput is as fllws: I (2) i = O (1) h, O (2) i = U (u) (2) Crrespnding Authr: Lianguang M, Hunan City University Yiyang, Hunan, 413000, China 465
Fig. 1: The structure design f fuzzy neural netwrk where, U (u) refers t the trapezium membership functin, with the frmula as: 1, b x ( x), b a 0, 0, x a ( x), b a 1, 0 x a a x b x b x a a x b x b (3) (4) The value f a and b in frmula (3) and (4) is determined by the value range f the case index. As fr the input sample data, if it belngs t quantitative data, it will be fuzzily prcessed by the abve membership functin; if it belngs t qualitative data (discrete type), it will be fuzzily prcessed by the applicatin f experience assignment methd. The third layer is the regulatin layer: The cnnectin strength between the neurn in this layer and that f the secnd layer is 1, regular neurn accmplishing the fuzzy lgical YU peratin, namely: (3) (2) min( ) i ii (5) In frmula (5), I refers t the subscript cllectin f the neurn in the secnd layer which is cnnected t the number neurn in the third layer. O (2) I refers t the utput f the number i neurn in the secnd layer. The furth layer is the utput layer f neural netwrk: In this layer, the membership functin f 466 every neurn has trapezium distributin and the initial cnnectin weight t the neurn in the third layer is stchastically selected in the range f [-1, 1]. The activatin degree f every regulatin is determined by the square f the weight. The functin in this layer is like the fllwing: ( 4 ) k max( I k (3 ) w 2 ) k (6) In frmula (6) I k refers t the subscript cllectin f all the neurn in the third layer cnnected t the number k neurn in this layer. The fifth layer is the layer f deblurring: The functin f this layer is deblurring, the deblurring f utput knwledge is analyzed by the applicatin f single fuzzy cllectin methd and the principle f largest membership grade II 8. In which: A 1, A 2,, A n refers t n bservatin pints; C 1, C 2,, C m refers t m attributes; x i refers t the value f attribute number i frm bservatin pint number ; refers t weight vectr, k refers t the weight f bservatin number k. CASE STUDY OF RESERVOIR SOIL SLOPE STABILITY Analysis f the factrs influencing reservir sil slpe stability: The analysis and statistic f the factrs influencing reservir sil slpe stability prve that the stability is the result f multi-factrs nnlinear cmprehensive functin. Therefre, accrding t the result f the cmprehensive influence f multi-factrs n reservir sil slpe stability, they can be classified int 8 indices:
Table 1: Simulatin result f engineering cases and netwrk mdels f the reservir slpe Serial number f cases X1 (m) X2 KN/m 3 X3 (KPa) X4 ( ) X5 X6 ( ) K (cm/s) v Safety Mdel Calculati n result 1 150 22.44 0.00 35.00 0.25 23.75 0.084 6.8 0.912 Unstable Training 0.912 2 150 22.44 0.00 35.00 0.25 23.75 0.200 6.8 0.798 Unstable Training 0.798 3 150 22.44 0.00 35.00 0.25 23.75 0.137 6.8 1.235 Stable Training 1.235 4 150 22.44 0.00 35.00 0.25 23.75 0.200 6.8 1.189 Stable Training 1.189 5 78 23.00 0.00 40.00 0.22 26.50 0.060 1.0 1.465 Stable Training 1.465 6 46 19.80 0.00 32.00 0.25 26.50 0.060 3.0 1.011 Stable Training 1.011 7 46 19.80 0.00 32.00 0.25 21.80 0.060 3.0 1.028 Stable Training 1.028 8 39 20.19 9.80 21.00 0.25 19.29 0.047 0.3 0.981 Unstable Training 0.981 9 73 22.44 0.00 35.00 0.25 18.43 0.141 2.9 1.125 Stable Training 1.125 38 18.13.0 24.25 0.40 17.07 0.002 1.0 1.122 Stable Training 1.122 11 54 20.90 11.9 20.40 0.75 21.04 0.020 0.7 1.080 Stable Training 1.080 12 53 19.60 5.00 26.50 0.40 15.52 0.007 2.7 0.841 Unstable Training 0.841 13 53 19.60 5.00 22.00 0.40 15.52 0.007 2.7 0.754 Unstable Training 0.754 14 51 17.35 20.0 24.00 0.40 18.43 0.4 3.1 0.961 Unstable Training 0.961 15 51 17.88 21.2 13.92 0.40 18.43 0.4 3.1 1.056 Stable Training 1.056 16 40 18.66 8.00 26.00 0.40 21.80 0.007 0.5 0.909 Unstable Training 0.909 17 40 18.66 8.00 26.00 0.40 21.80 0.007 0.6 0.934 Unstable Testing 0.929 18 40 18.00 21.0 21.33 0.40 21.80 0.007 0.2 0.938 Unstable Testing 0.935 19 9 19.60.0 16.00 0.40 21.80 0.002 12.0 1.346 Stable Testing 1.345 20 9 19.60.0 8.000 0.40 21.80 0.002 12.0 1.049 Stable Testing 1.046 21 15 18.42 14.95 21.20 0.40 45.00 0.4 21.0 1.051 Stable Testing 1.054 Case 1 t 4: Cmes frm Huang He Xia Lang Di Reservir; Case 5: Cmes frm Xin Jiang Xia Ban Reservir; Case 6 and 7: Cmes frm Tng Cheng Jing Zhu Mia Reservir; Case 8 and 9: Cmes frm Yue Cheng Reservir; Case : Cmes frm Qing Hai Gu Shan Reservir; Case 11: Cmes frm Jiangxi La Bu Reservir; Case 12 and 13: Cmes frm Shanxi Yu He Reservir; Case 14 and 15: Cmes frm Fuian Hng Wu Yi Reservir; Case 16 t 18: Cmes frm Fuian Ling Li Reservir; Case 19 and 20: Cmes frm Zheiang seawall; Case 21: Cmes frm Hunan An Xiang Reservir The height f the reservir slpe X1 The weight f the reservir slpe X2 The chesiveness f the reservir slpe X3 The internal frictinal angel f the reservir slpe X4 The pre pressure rati f the reservir slpe X5 The slpe angle f the reservir slpe X6 The permeability f the reservir slpe K The drp speed f water level V Mdel sample data:the study cllects 21 cases f reservir slpe frm reference 9, amng which 12 are stable slpes and the ther 9 are unstable nes, as shwn in Table 1. Determinatin f the membership grade f input variables: Given the height f the reservir slpe [a, b] = [9,150] and its membership functin frmula (3); the weight f the reservir slpe [a, b] = [17.35, 22.14] and its membership functin frmula (3); the chesiveness f the reservir slpe [a, b] = [0.21, 2] and its membership functin frmula (4); the internal frictinal angle [a, b] = [8, 40] and its membership functin frmula (4); the pre pressure rati f the reservir slpe [a, b] = [0.25, 0.75] and its membership functin frmula (3); the slpe angle f the reservir slpe [a, b] = [15.52, 45] and its membership functin frmula (3); the permeability f the reservir slpe k [a, b] = [0.002, 0.200] and its membership functin frmula; the drp 467 Training-blue Gal-black 0-1 -2 0 500 00 1500 2000 Stp training 2266 epchs Train in g-black 0-1 -2-3 -4-5 -6-7 (a) BP algrithm (2266 times) learning curve 0 50 0 150 200 306 epchs (b) Fuzzy BP algrithm learning curve Fig. 2: Result f simulatin 250 300 speed f water level V [a, b] = [0.2, 21.0] and its membership functin frmula (3).
Table 2: The cmparisn f the testing results f reservir sil slpe stability based n BP neural netwrk mdel and fuzzy neural netwrk mdel Serial Actual situatin ---------------------------------- BP neural netwrk mdel -------------------------------------------------------- Fuzzy neural netwrk mdel ----------------------------------------------------- number f the testing sample Actual Actual f the slpe Estimated Cmparative errr (%) Estimated Cmparative errr (%) 17 0.934 Unstable 0.945 1.18 Unstable 0.929 0.54 Unstable 18 0.938 Unstable 0.972 3.62 Unstable 0.935 0.32 Unstable 19 1.346 Stable 1.306 2.97 Stable 1.345 0.07 Stable 20 1.049 Stable 0.987 5.91 Unstable 1.046 0.29 Stable 21 1.051 Stable 1.021 2.85 Stable 1.054 0.29 Stable 5.000E+01 4.500E+01 4.000E+01 3.500E+01 3.000E+01 2.500E+01 2.000E+01 1.500E+01 1.000E+01 5.000E+02 0.000E+00 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 3.000E+03 2.500E+03 2.000E+03 1.500E+03 1.000E+03 5.000E+04 (a) Training-errr curve f BP neural netwrk 0.000E+00 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 (b) Training-errr curve f fuzzy neural netwrk Fig. 3: Training-errr curve The training and testing f netwrk mdel: The study takes the abve 8 influencing factrs as the input variable f neural netwrk and the stability f the reservir slpe as the utput variable. Studying and training are prcessed by the applicatin f the 16 practical engineering cases in sample Table 1 until the utput errr reaches the standard. By the applicatin f the 5 engineering cases in sample Table 1, testing is prcessed t crss validate the fuzzy reasning mdel. The result f the training and testing can be seen in Table 1. If the sample is trained by traditinal BP neural netwrk mdel, the accuracy f the errr can reach 0.1 after 2266 times f training. Hwever, the accuracy f 468 the errr can reach -6 nly after 300 times f training by the current fuzzy neural netwrk. The specific training prcess f the netwrk mdel can be seen in Fig. 2 and Table 2. Evaluatin f the mdel: The errr curve f netwrk mdel after 300 times f training is shwn in Fig. 3. CONCLUSION On the basis f the previus evaluating theries and methds f slpe stability, the study analyzes the reservir sil slpe stability by the applicatin f thecmbined methd f fuzzy thery and neural netwrk. The result f the study prves: Fuzzy neural netwrk methd can adequately apprximate cmplicated nnlinear relatin and simulate dynamic characteristics cnfrming t undetermined system. Fuzzy neural netwrk can slve the cmplicated prblem f being undetermined and nnlinear. The sil slpe stability f sme reservirs are estimated by fuzzy neural netwrk. And the result f the estimatin cnfrms t that f the actual result, which shws that fuzzy neural netwrk can be applied t qualitatively estimate the reservir sil slpe stability, being cnvenient, practical and valid as well. Owing t the cmplicated nnlinear relatin amng factrs influencing the reservir slpe stability and the many decisive gelgic factrs they include, the analysis f the reservir sil slpe stability by fuzzy neural netwrk is significantly better in speed and accuracy that that f general BP neural netwrk mdel when cmpared. REFERENCES Li, Z.Z., J.P. He and G.Y. Xue, 1998. Analysis n the recgnitin methd f practical dam estimatin fuzzy mdel. J. Wuhan Univ. Hydraulic Electr. Eng., 31: 1-4.
Wei, W.B., 1994. Study n the Cmprehensive Evaluatin Methd f Dam Safety. Wuhan University, Wuhan. Wei, W.B. and Z.Z., Li, 1996. Analysis n the fuzzy cmprehensive evaluatin methd f dam. Design Hydrpwer Statin, 12: 1-8. Xia, Y.Y. and M. Li, 2002. stability and its develping trend. Rck Sil Mech., 32(5): 1437-1452. Zha, J.J., R.Q., Huang and J.X., Xiang, 2004. Secnd fuzzy cmprehensive evaluatin f the near dam reservir bank slpe stability f a certain hydrpwer statin. Hydrgel. Eng. Gel., 2: 45-49. 469