Identification on rock and soil parameters for vibration drilling rock in metal mine based on fuzzy least square support vector machine

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1 J. Cent. South Unv. (4) : 85 9 DOI:.7/s Identfcaton on rock and sol parameters for vbraton drllng rock n metal mne based on fuzzy least square support vector machne ZUO Hong yan( 左红艳 ),, LUO Zhou quan( 罗周全 ), GUAN Ja ln( 管佳林 ), WANG Y we( 王益伟 ). School of Resource and Safety Engneerng, Central South Unversty, Changsha 483, Chna;. School of Busness, Hunan Internatonal Economcs Unversty, Changsha 45, Chna Central South Unversty Press and Sprnger Verlag Berln Hedelberg 4 Abstract: A sngle freedom degree model of drllng bt rock was establshed accordng to the vbraton mechansm and ts dynamc characterstcs. Moreover, a novel dentfcaton method of rock and sol parameters for vbraton drllng based on the fuzzy least squares (FLS) support vector machne (SVM) was developed, n whch the fuzzy membershp functon was set by usng lnear dstance, and ts parameters, such as penalty factor and kernel parameter, were optmzed by usng adaptve genetc algorthm. And FLS SVM dentfcaton on rock and sol parameters for vbraton drllng was made by changng the nput/output data from sngle freedom degree model of drllng bt rock. The results of dentfcaton smulaton and resonance column experment show that relatve error of natural frequency for some hard sand from dentfcaton smulaton and resonance column experment s.% and the dentfcaton precson based on the fuzzy least squares support vector machne s hgh. Key words: rock and sol; fuzzy theory; vbraton excavaton; least squares support vector machne; dentfcaton Introducton As an effcent energy savng advanced technology, vbraton cuttng has been successfully used n rock breakng and rock mnng and other felds. Some exploratory expermental researches have been done by usng of vbraton cuttng n coal mnng n 98s. The expermental research of the lgnte vbraton cuttng wth sngle tooth analog was developed by GOTTLIEB []. The cuttng process of the actual mnng was smulated by usng of relatve vbraton of the cuttng process between sngle pole teeth and the coal sample []. Frstly, the expermental model was bult accordng to the smlar theory, and then orthogonal expermental method was used to optmze the experment to fnd the combned parameters whch could sgnfcantly reduce the cuttng force and cuttng energy consumpton. The expermental results of vbraton cuttng n the rock crushng [3], such as vbraton cuttng of volcanc tuff, showed that there was a hyperbolc rapd declne for the rato of the horzontal cuttng resstance wth vbraton to the horzontal cuttng resstance wthout vbraton wth the ncrease of the vbraton frequency, and the cuttng effcency wth sne wave vbraton s hgher than that wth the trangle wave vbraton. Ultra hgh frequency vbraton test devce was developed to study the performance of the vbraton cuttng [4]. The results showed that the measured values for cuttng torque, man cuttng force, vertcal cuttng force n the vbraton state were smaller than those n non vbraton state when the vbraton frequency and the cuttng tool angle were changed and the phenomena such as hgh effcency and stable cuttng state appear when vbraton frequency was close to the natural frequency of the cuttng materal. The vbraton drllng and vbraton cuttng of rocks were completed due to vbraton generated by khz and kw ultrasonc [5]. And the applcaton results showed that the energy requred to cut rock was determned by the shape of the tool, statc pressure and tool rake angle. The above researches showed that the technology of adaptve vbraton drllng (namely automatcally adjustng the vbraton parameters, frequency, ampltude and nput waveform etc accordng to the rock and sol behavor of parameters) mght be of the quck dentfcaton functon on rock parameters (natural frequency and dampng rato) [6]. And fuzzy least square support vector machne (FLS SVM) [7 8] s of these unque advantages such as less modelng data, smple calculaton and quck dentfcaton capacty n Foundaton tem: Project(BAK9B 5) supported by the Natonal Key Technology R&D Program of Chna durng the Twelfth Fve year Perod; Project(5745) supported by the Natonal Natural Scence Foundaton of Chna Receved date: 9 ; Accepted date: 3 3 Correspondng author: ZUO Hong yan, PhD; E mal: zuohongyan8@6.com

2 86 resolvng above mentoned problems [9 3]. Therefore, rock and sol parameters for vbraton drllng were dentfed by usng fuzzy least square support vector machne based on the bult sngle freedom degree model about drllng rock and sol n ths work. It has a very mportant theoretcal sgnfcance and reference value for the realzaton of adaptve vbraton drllng of rock and sol. Sngle freedom degree model of vbraton drllng of rock and sol As shown n Fg., the process of vbraton drllng of rock and sol s actually manfested as nteracton between rock and drllng bt. The drllng bt drven by ultrasonc drlls rock and sol recprocatngly based on dynamc characterstcs and vbraton mechansm of vbraton drllng. The system of rock and drllng bt n the process of vbraton drllng s the sngle freedom degree system, as shown n Fg., where m r s the equvalent mass of the vbraton part n metal ore vbraton drllng machne, kg; m s s the mass of drllng bt, kg; k s the equvalent sprng stffness of the rock and sol, N/m; c s the equvalent dampng coeffcent of the rock and sol. Fg. Sngle freedom degree model of drllng bt rock Actually, the system consstng of rock and drllng bt n the process of vbraton drllng s the sngle freedom degree system n whch exctaton force F() s taken as nput and dsplacement y s taken as the output. Its dfferental equaton s d y d y m + c + ky = F ( ) () d d where s tme, s; m=m r +m s, kg. The sngle freedom degree system of rock and drllng bt n the process of vbraton drllng can be sampled by a very small samplng perod, and samplng equaton can be expressed as d y d n y( n ) y( n ) = () J. Cent. South Unv. (4) : 85 9 y y y n y n y n = ( ) = d d n d d d d ( ) ( ) + ( ) (3) After Eq. () and Eq. (3) are substtuted n Eq. (), the followng equaton can be gotten: m c m c ( k) y( n ) ( ) y( n ) T m y ( n ) = F ( n ) (4) Let + c + + m α =, m c k m β =, m + c + k ε =, and elmnate the n y(n ), m + c + k y(n ), y(n ) and F(n ) from Eq. (4), then the dfferental equatons of the sngle freedom degree system of rock and drllng bt n the process of vbraton drllng can be descrbed as y(n)+αy(n )+ βy(n )= εf(n) (5) where the values of the parameter such as α, β and ε are related wth the samplng perod. If the value of the parameters such as α, β and ε can be obtaned by recognton, the rock and sol parameters n the process of vbraton drllng can be expressed as m β, c α + β +, k α + = = = β (6) ε ε ε The natural frequency f y of the rock and sol n the resonance process of vbraton drllng rock can be expressed as f y + α + β = (7) β π In the dentfcaton of the rock and sol parameters n the process of vbraton drllng, a varety of random nterfere factors can be converted nto the output of the ultrasonc vbraton drllng bt sol system to concentrate as nose ψ(n), as shown n Fg.. Fg. Sngle freedom degree random model of drllng bt rock Therefore, the sngle degree of freedom random model of bt rock n the metal mne s expressed as y(n)+αy(n )+βy(n )=εf(n)+ψ(n) (8) After ψ(n) s denosed by usng wavelet analyss, Eq. (8) can be smplfed as Eq. (5).

3 J. Cent. South Unv. (4) : Identfcaton on rock and sol parameter based on FLS SVM 3. Fuzzy least squares support vector machne For the gven fuzzy samples, nonlnear mappng φ(x ) s led nto fuzzy least squares support vector machne to transform the nput varables nto a hgh dmensonal space. And then, lnear regresson s done n ths hgh dmensonal space. The objectve functon can be expressed as N c = R ( ω, ξ ) = ω + mn µ ( x ) ε ( x ) + b ε s. t. y = ω ϕ + (9) where ε s the slack varable, c s the penalty factor, and μ(x ) s the membershp degree of x. Thnkng of the Lagrange operator a (=,,, n), Lagrange equaton s establshed to solve the optmzaton problem. Fuzzy least squares support vector machne optmzaton problem s converted nto solvng lnear Eq. (): y L y y y y K ( x, x ) + c L y y K ( x, x ) N M M M M yn yn yk ( xn, x ) L yn yn K ( xn, xn ) + c b a = () M M a N Eventually, the fuzzy least squares support vector machne model can be expressed as N x () = ( ) (, ) f x = a K x + b where K(x, x ) s a kernel functon, K(x, x )=exp{ x x /σ }, and σ s the nuclear parameter. 3. Membershp functon defnton of fuzzy least squares support vector machne The membershp functon defnton of fuzzy least squares support vector machne s very mportant compared wth the tradtonal support vector machne (SVM). Therefore, how to effectvely construct fuzzy membershp functons s the key problem for dentfcaton on rock and sol parameters for vbraton drllng based on the FLS SVM. The membershp degree functon s constructed based on the lnear dstance n ths work. The man dea [4 7] s expressed as follows. Membershp degree s regarded as a dstance lnear functon of the sample pont to class center. The sze of ther membershp degrees s measured based on the dstance between the centers of the sample to the class. If the dstance s closer, the membershp degree wll be greater. For sample set {x, x,, x n }, let x be the center of the class, and r be the radus of the class, then x r = n n = x = x x () max x (3) The membershp functon of the sample can be expressed as µ ( x ) x x = (4) r + δ where δ s a small constant and s greater than, whch can avod the membershp functon beng. Therefore, the objectve functon as shown n Eq. (8) can be appled to solve after the membershp functon of the sample s gotten. 3.3 Identfcaton method on rock and sol parameters n process of vbraton drllng After the nose n the sgnal s denosed by usng of wavelet analyss, sngle freedom degree dscrete lnear system vbraton drllng can be expressed by the general dfferental equaton as y(n)= αy(n ) βy(n )+ εf(n) (5) As shown n Fg. 3, n order to acheve the dentfcaton on rock and sol parameters for vbraton drllng, FLS SVM method was used to dentfy the mathematcal model due to the changng data seres of the nputs and outputs from the vbraton drllng of bts rock sngle freedom degree system. That s to say, y(n ), y(n ), and F(n) were taken as nput tranng varables ({x, x, x 3 }) of FLS SVM, and y(n) was taken as the output tranng varable of FLS SVM. In order to make output y (n) of the dentfcaton model and output y(n) of the recognton system as close as possble, the dfference between y(n) and y(n) (e(n)=y(n) y (n)) must be kept as small as possble. Fg. 3 Identfcaton model of rock and sol parameter on vbraton drllng 3.3. Optmzaton of FLS SVM parameter based on adaptve genetc algorthm The optmzaton results of the penalty factor c and

4 88 the kernel parameter σ largely affect the dentfcaton accuracy of vbraton drllng parameters. Therefore, the adaptve genetc algorthm s used to optmze the FLS SVM parameters. The ftness functon of the adaptve genetc algorthm can be expressed as F( c, σ ) = n = [ y f ( x )] + e (6) where y s the expectaton output, f(x ) s the actual output, e s a small postve number whose role s to prevent appearng the case that the denomnator s zero. Here ts value s assgned to be 4. Error functon MSE (E) s defned as evaluaton ndex of generalzaton performance for fuzzy least squares support vector machne: m (7) M = E= [ f ( x ) y ] Intal crossover probablty and the ntal mutaton probablty can be represented by Eq. (8) and Eq. (9), respectvely: P P c m.9.3( f f ) /( f f ), f f =.9, else avg max avg avg..99( f f ) /( f f ), f f =., else max max avg avg (8) (9) where f s the larger ftness functon value for cross two body, f s ftness functon value of the correspondng ndvduals, f avg s the average ftness of the samples, and f max s the largest ftness of sample ndvduals. Crossover probablty and mutaton probablty change wth the evoluton of algebra. The change law can be expressed as t t.9 ( t / tmax ), P c <.6 P c =.6, else t m P ( λ t / t ) t m < max.e, P. =., else () () where t s the number of heredtary algebra, t max s the number of termnate algebra, and λ s a constant, assgned to be. Range of the penalty factor s [, ], range of nuclear parameters s [.5, ], populaton number N nd of adaptve genetc optmzaton process s 3, N var of optmzed parameters (namely the dmenson of the varable) s 3, and maxmum heredtary algebra M axgen s assgned to be 35. The number P rec of bts for each varable s assgned to be. Fnally, 3 3 bnary codes are assgned to an ntal value of or Identfcaton smulaton of rock and sol parameters n process of vbraton drllng Accordng to actual cases n the process of vbraton J. Cent. South Unv. (4) : 85 9 drllng of rock and sol, a group typcal data {α, β, ε, F(n)} about the hard sand are assgned as α=.747 7, β= , ε=.79 7 and F(n)= 6πcos(4 4 πn). y(n ), y(n ) and F(n) are taken as nput tranng varables of FLS SVM, and y(n) s taken as output tranng varable of FLS SVM. Two dfferent sample data sets are obtaned as follows: () Data set A ncludes 3 samples, 5 samples from the data set A are taken as tranng samples, and other 5 samples are taken as the test samples; () Data set B ncludes samples, samples from the data set B are taken as tranng samples, and other 5 samples are taken as the test samples. As shown n Fg. 4, the errors of speces correspondng to 3 ndvduals n a populaton are obtaned after teratve steps by usng the adaptve genetc algorthm. The average error s.3 for the dentfcaton smulaton on parameters n the process of vbraton drllng when tranng and test samples respectvely are. The average error s.8543 for the dentfcaton smulaton on rock and sol parameters n the process of vbraton drllng when tranng and test samples respectvely are 5. Fnally, the obtaned penalty factor c s 57.3, and the obtaned kernel parameter σ s.83. Fg. 4 Error of speces after steps: (a) tranng samples and test samples; (b) 5 tranng samples and 5 test samples

5 J. Cent. South Unv. (4) : As shown n Fg. 5, the errors of speces correspondng to 3 ndvduals n a populaton are obtaned after 35 teratve steps by usng the adaptve genetc algorthm. Fg. 6 Error of test sets: (a) 5 tranng samples and 5 test samples; (b) tranng samples and test samples Fg. 5 Error of speces after 35 steps: (a) 5 tranng samples and 5 test samples; (b) tranng samples and test samples The average error s.673 and the mnmum error s about.85 for the dentfcaton smulaton on rock and sol parameters n the process of vbraton drllng when tranng and test samples respectvely are. The average error s.683 and the mnmum error s about.733 for the dentfcaton smulaton on parameters n the process of vbraton drllng when tranng and test samples respectvely are 5. Fnally, the obtaned penalty factor c s 57.6, and the obtaned kernel parameter σ s.798. As shown n Fg. 6, the test errors of dentfcaton model for rock and sol parameters reveal that generalzaton capablty of FLS SVM s very strong n the process of vbraton drllng of rock and sol n the metal mne. The largest test error s.3 mm (relatve error s about.%) for the testng process ncludng 5 tranng samples and 5 test samples. The largest test error s.5 mm (relatve error s about.%) for the testng process ncludng tranng samples and test samples. It can be clearly seen that t s not obvous to dentfy rock and sol parameters based on FLS SVM by usng some excessve number data samples. Least squares support vector machnes (LS SVM), fuzzy least squares support vector machnes (FLS SVM) and fuzzy neural network (FNN) are respectvely used to dentfy parameters n the process of vbraton drllng n the metal mne. Identfcaton results of rock and sol parameters n the process of vbraton drllng n the metal mne are gven n Table. As shown n Table, there s qute dfference between dentfcaton results from LS SVM method or FNN method and the orgnal system parameters when the numbers of tranng samples and test samples are respectvely. When the numbers of tranng samples and test samples are 5 respectvely, the mprovement of dentfcaton accuracy from LS SVM method or FNN method s obvous. But there s not qute dfference between dentfcaton results from FLS SVM method and the orgnal system parameters whether the numbers of tranng samples and test samples are or 5. Compared wth the LS SVM method or FNN method, t s very obvous that FLS SVM method s of small dentfcaton errors and good dentfcaton ablty.

6 9 J. Cent. South Unv. (4) : 85 9 Table Identfcaton results of rock and sol parameters n process of vbraton drllng n metal mne Method tranng samples and test samples 5 tranng samples and 5 test samples α β ε α β ε Orgnal system LS SVM FLS SVM FNN Therefore, FLS SVM method s more ftful to dentfy the parameters of complex dynamc system than LS SVM method or FNN method. The dentfcaton results of rock and sol parameters for vbraton drllng of hard sand by usng FLS SVM method are α=.37, β=.85, ε=.76. After α=.37, β=.85, ε=.76 are substtuted n Eq. (6), then k = 998 kn/m, m=5.5 kg, and the natural frequency f of the hard sand s Hz. The measured natural frequency f of the hard sand s 4.84 Hz by usng resonant column experment. It s very obvous that the dentfcaton value of natural frequency f of the hard sand s very close to the measured natural frequency by usng resonant column experment. The relatve error between the dentfcaton value of natural frequency and ts measured natural frequency s only.%. Therefore, t s of hgh accuracy to dentfy rock and sol parameters for vbraton drllng n the metal mne based on FLS SVM. 4 Conclusons ) In order to dentfy rock and sol parameters of bt rock sngle freedom degree model for vbraton drllng n the metal mne, the penalty factor and kernel parameter of FLS SVM are optmzed based on adaptve genetc algorthm and the membershp functons are bult by usng lnear dstance. The dentfcaton on rock and sol parameters for vbraton drllng n the metal mne s acheved by FLS SVM method. The smulaton results show that the maxmum test error of rock and sol parameters dentfed by FLS SVM method s about.%. ) The relatve error between dentfcaton natural frequency of the hard sand by FLS SVM method and the measured natural frequency of the hard sand by resonant column experment s about.%, whch shows that t s of hgh accuracy to dentfy rock and sol parameters of bt rock sngle freedom degree model for vbraton drllng n the metal mne based on FLS SVM method. References [] GOTTLIEB L. Vbratory cuttng of brown coal [J]. Internatonal Journal of Rock Mechancs and Mnng Scences & Geomechancs, 98, 8(4): [] JING Yuan chang. Research of vbraton coal cuttng mechansm [D]. Bejng: Chna Unversty of Mnng & Technology,. (n Chnese) [3] MURO T, TRAN D T. Regresson analyss of the characterstcs of vbrocuttng blade for tuffaceous rock [J]. Journal of Terramechancs, 4, 4(3): 9 9. [4] ZHAO We mn, ZHOU Xan bao, LU Nan l, LI Y shen. Basc research of dggng rock and sol wth vbraton [J]. Constructon Machnery, (6): (n Chnese) [5] GRAFF K F. Applcaton of sonc power to rock cuttng [J]. Gas Engneerng and Management, 973, 4(6): [6] ZHU Jan xn. Study on vbratory excavaton mechansm, process optmzaton modelng and ntellgent control strategy of hydraulc excavator [D]. Changsha: Central South Unversty, 8. (n Chnese) [7] WANG Xao dan, WANG J qn. Research and applcaton of support vector machne [J]. Journal of Ar Force Engneerng Unversty: Natural Scence Edton, 4, 5(3): (n Chnese) [8] E Ja qang. Intellgent fault dagnoss and ts applcaton [M]. Changsha: Hunan Unversty Press, 6: 3. (n Chnese) [9] SANG Ha feng, WANG Fu l, HE Da kuo, ZHANG Da peng. Hybrd modelng of fermentaton process based on least square support vector machnes [J]. Chnese Journal of Scentfc Instrument, 6, 7(6): (n Chnese) [] LIN C F, WANG S D. Fuzzy support vector machnes [J]. IEEE Transactons on Neural Networks,, 3(): [] JIANG X F, YI Z, LV J C. Fuzzy SVM wth a new fuzzy membershp functon [J]. Neural Computng and Applcaton, 6, 5: [] LESKI J. M. An epsv margn nonlnear classfer based on fuzzy f then rules [J]. IEEE Transactons on Systems, Man, and Cybernetcs, Part B: Cybernetcs, 4, 34(): [3] ZHANG Yng, SU Hong ye, CHU Jan. Soft sensor modelng based on fuzzy least squares support vector machnes [J]. Control and Decson, 5, (6): (n Chnese) [4] WANG Y Q, WANG S Y, LAIK K. A new fuzzy support vector machne to evaluate credt rsk [J]. IEEE Transactons on Fuzzy Systems, 5, 3(6): [5] LIU Chang, SUN De shan. Determnaton method of membershp of fuzzy SVM [J]. Computer Engneerng and Applcatons, 8, 44(): 4 4, 46. (n Chnese) [6] ZHANG Xang, XIAO Xao lng, XU Guang you. Determnaton and analyss of fuzzy membershp for SVM [J]. Journal of Image and Graphcs, 6, (8): (n Chnese) [7] ZHANG Qu yu, JIE Yang, LI Ka. Method of membershp determnaton for fuzzy support vector machne [J]. Journal of Lanzhou Unversty of Technology, 9, 35(4): (n Chnese) (Edted by YANG Bng)