Hybrid Control Strategy of Vehicle Semi-active Suspension Based on the Genetic Algorithm Optimization

Transcription

1 Hybrid Control Stratgy of Vhicl Smi-activ Suspnsion Basd on th Gntic Algorithm Optimization Quanmin Guo 1, 2 1 School of Mchanical and Prcision Instrumnt Enginring, Xi an Univrsity of chnology, Xi an , Shaanxi, China 2 School of Elctronics Information Enginring, Xi'an chnological Univrsity, Xi'an , Shaanxi, China Dngxin Hua School of Mchanical and Prcision Instrumnt Enginring, Xi an Univrsity of chnology, Xi an , Shaanxi, China Lingfi Kong School of Mchanical and Prcision Instrumnt Enginring, Xi an Univrsity of chnology, Xi an , Shaanxi, China Abstract For unfavorabl control ffct du to difficult prcis modling of systm and complx road conditions in th vhicl smi-activ suspnsion control, this papr proposs a fuzzy PID hybrid control stratgy basd on gnric algorithm optimization. his mthod cods th fuzzy control rul by using th floating numbr coding, uss th rciprocal of suspnsion prformanc valuation function as th fitnss function of gntic algorithm, and optimizs th fuzzy control ruls by using th gntic oprations such as probability slction, multipoint crossovr and singl-point mutation. h numrical computing and analysis indicats that th proposd control stratgy can ffctivly improv prformanc indxs of body vrtical acclration, suspnsion dynamic dflction and tyr dynamic load. Compard to th passiv suspnsion, PID-controlld and fuzzy PID-controlld smi-activ suspnsion, th fuzzy PID controlld optimizd by th gnric algorithm can ffctivly improv vhicl rid comfort, handling stability and scurity. Ky words: VEHICLE SUSPENSION, SEMI-ACIVE CONROL, DYNAMIC FEAURE, FUZZY RULE 70 Mtallurgical and Mining Industry, 2015, No. 4

2 1. Introduction h vhicl suspnsion is th gnral nam of th forc transmission dvic btwn th chassis and whl axl, includs multipl forcs, and dtrmins th rid comfort, road handling stability and scurity of a vhicl [1]. h rigidity and dampnss of a traditional passiv suspnsion is not adjustabl, so it can only nsur that th systm control ffct can b optimal undr a spcific opration condition. It is difficult to mt rquirmnts of rid comfort and handling stability undr diffrnt opration conditions. h activ suspnsion faturs xcllnt prformanc, but its application in vhicls is rstrictd du to high nrgy consumption, complx structur and high cost. h smi-activ suspnsion systm faturs an actuator with lowr powr consumption, simpl structur and low pric, and can rach control ffct lik it of th activ suspnsion [2], so it is xtnsivly focusd by th scholars. Many control stratgis ar proposd for it,.g. sky-hook control, ground-hook control, optimal control, adaptiv control, sliding mod control, PID control, fuzzy control and nural ntworks control [3-9]. For th complx nonlinar vibration systm such as vhicl suspnsion, gnrally xpctd control ffct cannot b rachd by using singl control mthod du to difficult prcis systm modling and complx road conditions, so th adaptiv hybrid control stratgy indpndnt of prcis modling will b mainly studid in futur. h traditional PID control dos not rquir undrstanding on th mathmatic modl of th controlld objcts. h rgulator paramtrs can b adjustd according to th xprincs to gt satisfactory rsults. his mthod faturs simpl algorithm, bttr practicability and highr rliability. h waknss is that th st control paramtrs cannot b adjustd, so this is snsitiv to paramtr chang of th controlld objct and th systm is not vry robust. h fuzzy control dos not dpnd on prcis mathmatic modl, faturs fuzzy and uncrtain procssing, and is not snsitiv to chang of systm paramtrs and nvironmnt, so th fuzzy PID hybrid control stratgy of both control mthods faturs flxibl control, high prcis and strongr slf-adaptation, ovrcoms waknss of th PID control mthods, and has bttr control ffct [10], but th fuzzy logic control rul dpnds on knowldg and xprincs of xprts and is not asy to st. For th waknsss of th abov control mthods, this papr proposs a fuzzy PID hybrid control stratgy basd on th gnric algorithm (GA). his papr dsigns a fuzzy PID controllr for 1/4 vhicl of a sdan with 2 dgrs of frdom, optimizs this fuzzy PID control rul by using th gnric algorithm, and compars its control ffct with it of a passiv suspnsion, PID control and fuzzy PID-controlld smi-activ suspnsion systm, and validats control ffct of th fuzzy PID hybrid control stratgy optimizd by th gnric algorithm. 2. Modling of vhicl smi-activ suspnsion o simplify dynamic modling of vhicl smi-activ suspnsion systm, th following rasonabl assumptions ar providd [11]. 1) body and fram ar rigid and ar connctd via rigid connctor; 2) h vhicl structur is symmtric for th vrtical plan and only vrtical vibration is considrd; 3) h vhicl suspnsion rigidity and tyr rigidity ar th linar function of th shift and th suspnsion dampnss is th linar function of th rlativ spd; 4) h tyr kps contact with th road surfac and dos not jump. h simplifid modl of 1/4 vhicl smi-activ suspnsion with 2 dgrs of frdom is shown as th figur 1, m 1 is th mass of th vhicl body, m 2 is th mass of th tyr, k 1 is th rigidity of th suspnsion spring, C is th dampnss cofficint of th suspnsion dampr (including rfrnc dampnss C 0 and adjustabl dampnss C r ), k 2 is th tyr rigidity, x 1 is th body displacmnt, x 2 is th whl displacmnt, and x 3 is th road disturbanc. k 1 k 2 m 1 m 2 Figur 1. 1/4 vhicl smi-activ Suspnsion modl with 2 dgrs of frdom Basd on Nwton's scond law of motion, th motion diffrntial quation of 1/4 vhicl smi-activ quation with 2 dgrs of frdom can b xprssd as follows: m1x& 1+ k1( x1 x2) + C0( x& 1 x& 2) + f = 0 m2x& 2 + k2( x2 x3) k1( x1 x2) C0( x& 1 x& 2) f = 0 (1) whr f is th adjustabl damping forc and its valu is: f = Cr ( x& 1 x& 2). c x 1 x 2 x 3 Mtallurgical and Mining Industry, 2015, No. 4 71

3 For asy computing, th stat variant whr A is th systm matrix, B is th control X = [ x&& 1, x2, x1, x2, x3] is slctd. h kintic input matrix, E is th disturbanc output matrix, U quation (1) can b convrtd to th stat is th adjustabl damping forc and U=f, and w(t) quation: is band-limitd whit nois. X & = AX () t + BU + Ew() t (2) C C k k m m m m C C k ( k + k ) k A= m m m m m B= E= ( ) m m α v o assss control ffct of th smi-activ suspnsion, th body acclration x& 1, suspnsion dynamic dflction x 1 -x 2 and tyr dynamic load x 2 - x 3, which can indicat vhicl rid comfort, handling stability and scurity, ar slctd as th systm output and th output variant Y is dscribd as follows: Y = x& 1,( x1 x2), ( x2 x3). h output quation is: Y = CX () t + DU (3) whr C is th output matrix and D is th fdforward matrix. C0 C0 K1 K1 0 m1 m1 m1 m 1 1 C = D= m Control stratgy of smi-activ suspnsion h fuzzy PID control stratgy can kp th strngths of PID control such as simpl and ral-tim paramtr adjustmnt, fatur strong adaptiv fuzzy logic, raliz automatic adjustmnt of thr paramtrs of th PID controllr, and improv th systm robustnss, but th fuzzy logic control rul for dciding th systm control ffct dpnds on knowldg and xprincs of xprts. o ovrcom waknsss of this mthod and gt optimal fuzzy control rul, this papr optimizs th fuzzy PID control rul by using th gnric algorithm. h figur 2 shows th fuzzy PID control systm optimizd by th gnric algorithm. v(t) - Fuzzy control ruls c d/dt yr dynamic load Suspnsion Dynamic dflction Body acclration GA Fuzzy controllr Kp Ki Kd f PID controllr Vhical Suspnsion Road input Figur 2. Fuzzy PID control systm basd on GA optimization 3.1 Dsign of fuzzy PID controllr his papr uss th diffrnc btwn th vrtical spd of th body and rfrnc (st as 0) and th vrtical spd chang of body (namly vrtical acclration c of body) as th input variants of th fuzzy controllr. h paramtr K p, K i and K d of th PID controllr ar th output of th fuzzy controllr. h output of th fuzzy PID controllr is th adjustabl damping forc f of th smi-activ suspnsion systm. h structural diagram of th fuzzy PID control algorithm is shown as th figur 3. v(t) - d/dt c Fuzzy controllr Kp Ki Kd PID controllr Figur 3. Fuzzy PID control thory Controlld objct In practic, th vrtical spd of th vhicl smi-activ suspnsion systm varis within [-0.15,0.15], so th basic domain of th input rror can b st as [-0.15,0.15]. h quantification factor of th diffrnc is 72 Mtallurgical and Mining Industry, 2015, No. 4

4 k =3/0.15=20. h basic domain of th body s vrtical acclration is [-3,3]. If th fuzzy domain is st as Ec=[-3,3], th quantification factor of diffrnc chang rat c is k c =3/3=1. In dsign of th fuzzy controllr, th input variant and c and output variant K p, K i and K d ar slctd from 7 fuzzy substs [NB, NM, NS, ZO, PS, PM, PB], namly ngativ big (NB), ngativ middl (NM), ngativ small (NS), zro (ZO), positiv small (PS), positiv middl (PM) and positiv big (PB). h corrsponding fuzzy domain of th input variants and output variants ar [-3, -2, -1, 0, 1, 2, 3] and th mmbrship function of, c, K p, K i and K d is th triangl mmbrship function. h fuzzy domain of th input variants and output variants ar [-3, -2, -1, 0, 1, 2, 3] and th fuzzy control rul of K p is shown as th tabl 1. h fuzzy control rul of K i and K d is similar to it of K p. abl1. Control ruls of K p K p c N N NS ZO PS PM PB NB PB PB P PM PS PS ZO N PB PB P PM PS ZO ZO NS P PM P PS ZO NS N ZO PS PS PS ZO NS N N PS PS PS ZO NS NS N N PM ZO ZO NS N N N NB PB ZO NS NS NS N NB NB 3.2 Fuzzy control rul optimizd by gnric algorithm h gnric algorithm is usd to optimiz th fuzzy PID controllr. Its fitnss function nd not b diffrntiabl and its dpndnc on problms is small, so this gnric algorithm is a global optimization mthod and can valuat algorithm s ffct according to th fitnss function to avoid local optimization. By analyzing th fuzzy PID controllr and vhicl smi-activ suspnsion systm, this papr optimizs th control rul of th fuzzy PID controllr by using th gnric algorithm. First th mmbrship function of th input and output variant is spcific. h rul numbr is idntifid according to th mmbrship function and possibl control rul tabls listd. h fuzzy control ruls ar codd by using th floating numbr coding rul. Finally th fuzzy control ruls ar optimizd via th gnric algorithm. h stps for optimizing th control ruls of th fuzzy PID controllr by using th gnric algorithm ar dscribd as follows: 1) h dtrmination of objctiv function h suspnsion systm prformanc is masurd by body acclration x 1,suspnsion dynamic dflction (x 1 -x 2 ) and tyr dynamic load (x 2 -x 3 ). h valus of thr paramtrs should b rducd as much as possibl, so th prformanc valuation indicator function of th smi-activ suspnsion systm can b dscribd as follows: H = qh 1 1+ qh 2 2+ qh 3 3 (4) whr h 1, h 2 and h 3 indicat th root man squar (RMS) of th body vrtical acclration, suspnsion dynamic dflction and tyr dynamic load, rspctivly. q 1, q 2 and q 3 ar th wight cofficint. Suspnsion prformanc optimization in this papr aims to improv vhicl rid comfort, and considr vhicl handling stability and scurity, so th wight cofficint q 1 =0.5, q 2 =0.3 and q 3 =0.2. 2) Coding of fuzzy control rul h input variants of th fuzzy controllr ar and c and th output variants ar K p, K i and K d in th fuzzy PID-controlld vhicl smi-activ suspnsion systm. h fuzzy languag st is slctd from fuzzy substs [NB, NM, NS, ZO, PS, PM, PB]. h fuzzy PID controllr includs 3 control rul tabls and 147 lmnts pr tabl, which can b connctd to a string of numbrs in turn. A string of numbrs indicats individuals. Whn th fuzzy control rul is codd, if th traditional binary coding mthod is usd, too long individual cod will lad to too larg sarch spac of th algorithm and too long sarch tim. o improv fficincy, this papr uss th floating numbr coding and th numbr 1,2,3,4,5,6 and 7 ar usd to rplac th languag variant NB, NM, NS, ZO, PS, PM and PB in th fuzzy control rul tabl in th gnric algorithm.g. h K p control ruls in th tabl 1 can b codd as follows: { } 3) Gnration of initial population his papr gnrats th initial population randomly in an offlin mannr. h siz of th population N is 20. Each population includs 147 individuals. h maximum volutionary gnration numbr of th population is rgulatd as populations ar randomly gnratd. h first population group includs: { } Mtallurgical and Mining Industry, 2015, No. 4 73

5 4) Idntify fitnss function h fitnss function F is th rciprocal of th prformanc valuation function, namly F=1/H. Biggr fitnss indicats bttr prformanc of th idntifid control rul. Aftr optimization nds, th cod of th control rul with top fitnss is obtaind. 5) Slction, crossovr and mutation opration Slction opration indicats to slct th individuals with th strongst vitality and gnrat nw population. Individuals with biggr fitnss will b inhritd into th nxt population at a highr possibility. h slction probability is computd by th quation P i =F i /ΣF i in this papr. h slction probabilitis of th initial population gnratd in this papr ar dscribd as follows: P 1 = P 2 = P 3 = P 4 = P 5 = P 6 = P 7 = P 8 = P 9 = P 10 = P 11 = P 12 = P 13 = P 14 = P 15 = P 16 = P 17 = P 18 = P 19 = P 20 = Aftr th slction probability of ach individual is idntifid, th uniform random numbrs within [0,1] will b gnratd to dcid th mating individuals. h individuals with highr slction probability may b slctd and thir gntic gn will b xpandd in th population. h individuals with smallr slction probability may b liminatd. Crossovr opration is also calld as rcombination, which will slct two individuals with biggr probability from th population and xchang on or som bits of individuals to gnrat nw individuals. Multi-point crossovr mthod will b usd in this papr. h crossovr point 30, 60, 90 and 120 ar slctd in th first crossovr and th crossovr probability Pc is 0.6. Assuming that 1 st group corrsponds to 11 th group, 2 nd group corrsponds to 12 th group and 10 th group corrsponds to 20 th group in th population. Whn crossovr opration is implmntd, th random numbrs will b compard with th crossovr probability. If th crossovr conditions ar mt, th crossovr opration is prformd and th cods of th corrsponding bits will b xchangd. Othrwis, crossovr calculation is not prformd. Finally th crossovr points will rduc with growth of gntic gnration numbr. Mutation indicats to chang on or som bits of corrsponding individual cod strings at a smallr probability and gnrat nw individuals. Som gns in individual cod strings ar rplacd by othr alllic gns in th gntic algorithm in ordr to gnrat nw individuals. Singl-point mutation is slctd and th mutation probability P m is 0.02 in this papr. 6) Optimization rul Whn th fitnss rror f max -f min 0.01, optimization will stop, optimal individuals ar obtaind, and computing stops. Othrwis, gntic opration 5) is rpatd till maximal gntic gnration numbr is rachd. Finally chck whthr th prformanc rquirmnts of th suspnsion systm ar mt. If th rquirmnts ar mt, th fuzzy control rul tabl can b idntifid and optimization is trminatd. Othrwis, th corrsponding gntic oprations will continu. 3.3 Optimization rsults Aftr th paramtrs of th gntic algorithms ar idntifid, simulation is prformd by using MALAB according to th initial valus of th randomly gnratd fuzzy control rul tabl. Aftr multipl itrations, th optimizd K p, K i and K d fuzzy control rul can b obtaind finally. h fuzzy control ruls of K p ar shown as th tabl 2. h fuzzy control ruls of K i and K d ar similar to thos of K p. abl2. Optimizd Control ruls of K p K p c N N NS ZO PS P PB NB ZO PB P PB PS NS PB N ZO N NS PS Z P PB NS PB ZO PB NB N NS PS ZO ZO PB ZO ZO Z PS NB PS P NB ZO N Z PS N PM PS NS PB NB N PB N PB ZO PB P PB PS NS PB 4. Numrical xampls and analysis his papr mainly studis vhicls of crtain typ and th usd suspnsion paramtrs ar shown as th tabl 3. o ffctivly validat th dsignd fuzzy PID control stratgy optimizd by th gntic algorithm, simulation is prformd for random road surfac input and diffrnt vhicl spds on diffrnt road surfac lvls and th rsults ar compard with thm of passiv suspnsion, PID control and non-optimizd fuzzy PID-controlld smi-activ suspnsion for analysis. 74 Mtallurgical and Mining Industry, 2015, No. 4

6 abl3. Vhicl suspnsion paramtrs Suspnsion m 1 /kg m 2 /kg k 1 /(N m -1 ) k 2 /(N m -1 ) C 0 /(N s m -1 ) Valus Random road surfac input h unvn road surfac is th main factor to affct th dynamic faturs of th suspnsion systm and vhicl vibration [12]. o nsur that th proposd mthod is xtnsivly applicabl, this papr introducs th filtrd whit nois random road surfac input modl, which tim domain is xprssd as th following mathmatical quation: qt &() = αν qt () + ω() t (5) whr q(t) is th road surfac random xcitation on th whl, v is th driving spd of vhicls, ω(t)is th band-limitd whit noiss (h man is 0 and th strngth is 1), and α is a constant cofficint. Whn th road surfac grads ar diffrnt, α is diffrnt. α is for grad B road surfac and 0.12 for grad C road surfac. h figur 4 shows random road surfac input wav in th tim domain whn a vhicl is driving at 50km/h spd on th grad B road surfac. h figur 5 shows simulation rsults of body s vrtical acclration, suspnsion dynamic dflction and tyr dynamic load whn random road surfac input. h tabl 4 shows th comparison rsults of passiv suspnsion, PIDcontrolld, non-optimizd and optimizd fuzzy PID-controlld smi-activ suspnsion. Figur 4. Random road input wav in tim domain (a) Body vrtical acclration (b) Suspnsion dynamic dflction (c) yr dynamic load Figur 5. Simulation rsults whn random road input abl 4. Comparison of simulation rsults whn random load input Suspnsion Prformanc (RMS) Passiv suspnsi on PIDcontrolld suspnsio n Fuzzy PID-controlld suspnsion Bfor Aftr optimizati optimizati prformanc improvmnt/% PID Bfor optimizati Aftr optimizati Mtallurgical and Mining Industry, 2015, No. 4 75

7 Body acclration/(m/s 2 ) Suspnsion Dynamic dflction/mm yr dynamic load/n From figur 5 and tabl 4, whn th vhicls driv through th grad B road surfac at 50km/h spd, compard to a passiv suspnsion, th RMS of th body s vrtical acclrations of PID-controlld smi-activ suspnsion systm and fuzzy PID-controlld smi-activ suspnsion bfor and aftr optimization dcrass by 10.11%, 15.86% and 19.97% rspctivly. h suspnsion dynamic dflction dcrass by 11.80%, 20.76% and 22.07% rspctivly. h tyr dynamic load dcrass by 9.34%, 21.62% and 20.12% rspctivly. h numrical analysis rsults indicat that th rid comfort, handling stability and scurity of th fuzzy PID-controlld smi-activ suspnsion vhicl optimizd by GA is improvd much, which validats ffctivnss and xcllnc of th dsignd fuzzy PID controllr improvd by GA. For fuzzy PIDcontrolld smi-activ suspnsion, th improvd prformanc of th tyr dynamic load rducs from 21.62% bfor optimization to 20.12% aftr optimization, but th improvd prformanc of th body s vrtical acclration incrass from 15.86% to 19.97%. his is bcaus th wight valu of th body s vrtical acclration in th targt function is far biggr than it of th tyr s dynamic load by using th gntic algorithm optimization. Lss dcras of tyr s dynamic load can improv th body s vrtical acclration much. 4.2 Simulation analysis on road surfacs of diffrnt grads undr diffrnt vhicl spds Simulation is prformd for th optimizd fuzzy PID-controlld smi-activ suspnsion systm at low spd, mdium spd and high spd (20km/h, 50km/h and 100km/h) on two road surfacs (grad B and C). h simulation rsults of th body s vrtical acclration, suspnsion dynamic dflction and tyr dynamic load ar shown as th figur 6 and 7. h tabl 5 lists th RMS of th suspnsion systm prformanc. (a) Body vrtical acclration (b) Suspnsion dynamic dflction (c) yr dynamic load Figur 6. Simulation rsults of diffrnt spds on th class B road (a) Body vrtical acclration (b) Suspnsion dynamic dflction (c) yr dynamic load Figur 7. Simulation rsults of diffrnt spds on th class C road abl 5. Comparison of simulation rsults whn diffrnt spds on th diffrnt class road 76 Mtallurgical and Mining Industry, 2015, No. 4

8 Suspnsion Prformanc (RMS) Body acclration /(m/s 2 ) Suspnsion dynamic dflction /mm Grad B road surfac Grad C road surfac 20km/h 50km/h 100kn/h 20km/h 50km/h 100kn/h yr dynamic load /N From th figur 6 and 7 and tabl 5, whn th vhicl drivs at th constant spd on th grad B road surfac, if th spd incrass from 20km/h to 50km/h and 100km/h, th RMS of th body s vrtical acclration of th suspnsion systm will incras by 56.43% and126.07% rspctivly, th RMS of th suspnsion dynamic dflction will incras by 60.46% and % rspctivly, and th corrsponding tyr dynamic load will incras by 54.21% and % rspctivly. whn th vhicl drivs at th constant spd on th grad C road surfac, if th spd incrass from 20km/h to 50km/h and 100km/h, th body s vrtical acclration of th suspnsion systm will incras by 55.61% and % rspctivly, th suspnsion dynamic dflction will incras by 55.78% and % rspctivly, and th corrsponding tyr dynamic load will incras by 53.71% and % rspctivly, so th body s vrtical acclration, suspnsion dynamic dflction and tyr dynamic load of th suspnsion systm will incras with growth of th vhicl spd on th grad B and C road surfac, namly th suspnsion prformanc will dtriorat with growth of th vhicl spd on th sam grad road surfac. It indicats that th vhicl spd has rmarkably influncs on th prformanc of th suspnsion systm. From th tabl 5, whn a vhicl is driving at th constant 20km/h on th grad B and C road surfac, th RMS of th body s vrtical acclration, suspnsion dynamic dflction and tyr dynamic load of th suspnsion systm will incras by 0.86%, 4.22% and 0.40%. Whn a vhicl is driving at constant 50km/h spd on th grad B and C road surfac, th RMS of thr prformanc indicators will incras by 0.33%, 1.18% and 0.08% rspctivly. Whn a vhicl is driving at constant 100km/h spd on th grad B and C road surfac, th valu of thr prformanc indicators will incras by 0.33%, 1.18% and 0.08% rspctivly, so whn a vhicl is driving at sam spd on th road surfac of diffrnt grads, th body s vrtical acclration, suspnsion dynamic dflction and tyr dynamic load of th suspnsion systm will chang littl, namly th chang of th road surfac grad will hav smallr influnc on vhicl rid comfort, handling stability and scurity. 5. Conclusions his papr improvs th dynamic prformanc of th suspnsion systm via th dsignd fuzzy PID controllr. o ovrcom th dpndncy of th traditional fuzzy PID controllr on xprt xprincs, th gntic algorithm is usd to optimiz th control ruls of th fuzzy PID controllr. For th road surfac random input, th comparison rsults of th passiv suspnsion, PID-controlld smi-activ suspnsion and fuzzy PID-controlld smi-activ suspnsion bfor and aftr optimization validat xcllnc of th fuzzy PID controllr optimizd by th gntic algorithm. Simulation rsults for diffrnt road surfacs and vhicl spds validat that th suspnsion systm prformanc is influncd by th vhicl spd much and is affctd by th road surfac grad littl. Acknowldgmnts his rsarch is supportd by th National Natural Scinc Foundation of China (No ), Shaanxi provinc natural scinc foundation rsarch projct (No. 2014JM2-6112) and Natural Scinc Foundation of Shaanxi Provincial Dpartmnt of Education (No.14JK1342). Rfrncs 1. Pan GJ, Liu XD (2005) Optimal Control Mthod for Optimization of Vhicl Suspnsion Paramtrs. ransactions of th Chins Socity for Agricultural Machinry, 36(11), p.p Yoon Y.S. (1995) Smi-activ suspnsion with prviw using a frquncy-shapd Mtallurgical and Mining Industry, 2015, No. 4 77

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