Joural of Cotrol Sciece ad Egieerig, Article ID 686130, 4 pages http://dx.doi.org/10.1155/2014/686130 Research Article Research o Applicatio of Regressio Least Squares Support Vector Machie o Performace Predictio of Hydraulic Excavator Zha-bo Che 1,2 1 Zhoga Uiversity of Ecoomics ad Law, Wuha 430074, Chia 2 HubeiUiversityofEcoomics,Wuha430205,Chia Correspodece should be addressed to Zha-bo Che; chezhabo2014@163.com Received 15 July 2014; Revised 11 October 2014; Accepted 22 October 2014; Published 11 November 2014 Academic Editor: Our Toker Copyright 2014 Zha-bo Che. This is a ope access article distributed uder the Creative Commos Attributio Licese, which permits urestricted use, distributio, ad reproductio i ay medium, provided the origial work is properly cited. I order to improve the performace predictio accuracy of hydraulic excavator, the regressio least squares support vector machie is applied. First, the mathematical model of the regressio least squares support vector machie is studied, ad the the algorithm of the regressio least squares support vector machie is desiged. Fially, the performace predictio simulatio of hydraulic excavator based o regressio least squares support vector machie is carried out, ad simulatio results show that this method ca predict the performace chagig rules of hydraulic excavator correctly. 1. Itroductio The hydraulic excavator belogs to the costructio machiery, which has bee applied i may fields successfully, such as trasportatio idustry, miig idustry, costructio idustry, ad hydraulic egieerig. The hydraulic excavator is made up of three parts, which are workig equipmet, upper turtable, ad travelig gear. Normally workig coditios of the hydraulic excavator are bad, ad the loads beig applied to the hydraulic excavator are big; therefore, the egie will deviate from operatig mode with low fuel cosumptio, ad the hydraulic excavator will exhibit poor performace. I additio, the eergy cosumptio of the hydraulic pressure system is big, which ca lead to the big eergy wastig. Therefore, it is ecessary to predict the performace of the hydraulic excavator correctly, ad the the workig efficiecy of the hydraulic excavator ca be improved [1]. The performace predictig processio is oliear, which is affected by may ucertai factors; therefore, a effective predictig techology should be chose. At preset, there are may performaces predictio methods, such as artificial eural etwork techology, grey predictio techology, ad extesio techology [2]. However, the curret predictio techologies have some disadvatages: the predictig precisio is low, the predictig efficiecy is low, ad the operatio is difficult [2]. Geerally, the support vector machie has the oliear ad ucertai characteristics. I recet years, the support vector machie was established by Vapik, which has bee cocered by may scietists, ad the support vector has strog learig ability. Some scietists have improved the support vector machie. The least squares support vector machieisputforwardbysukkes.theleastsquaressupport machie itroduces the least squares system ito the support vector, while the traditioal support machie applies the two plaig methods to deal with fuctio estimatio problem; therefore, this method has higher predictig ability tha the traditioal support machie, which ca be applied i the performacepredictioofthehydraulicexcavator. 2. Mathematical Model of Least Squares Support Vector Machie The support vector machie is a machie learig techology, which is better tha artificial eural etwork techology, grey predictio techology, ad extesio techology i predictig ability. The support vector machie applies
2 Joural of Cotrol Sciece ad Egieerig to the performace predictio of small samples, ad the predictig reliability is good; at the same time, it has good superior ability, ad the the high predictig precisio ca be obtaied. Therefore, the good predictig effect ca be obtaiedbasedoleastsquaressupportvectormachiefor the hydraulic excavator [3]. The traiig samples {(x i,y i )} (x i,y i R; i,j = 1,2,..., ) are kow, ad the least squares support vector machie maily applies a oliear mappig fuctio to make the data trasfer to a high dimesioal space ad the be mapped back to the origial space to achieve the liear regressio of iput space; the liear regressio model is show as follows: f (x) =[ ω, φ (x)]+b, (1) where ω deotes the weighted vector, φ(x) deotes the mappig fuctio, ad b deotes the threshold value. The regressio least squares support vector machie applies two-time pealty fuctio to trasfer the regressio problem ito two-time optimizatio problem, ad the correspodig objective fuctio is expressed as follows: R ref [f] =R emp [f] +η ψ 2 = l=1 C (e l ) +η ψ 2, (2) where R ref [f] deotes the structural risk, R emp [f] deotes the empiric risk, ψ 2 deotes the cofidece risk, C( ) deotes the loss fuctio, η deotes regularizatio factor, e l =f(x l ) y l,ad deotes the sample size. The ε isesitive loss fuctio is put forward by Vapik, which has a isesitive zoe that offers ay loss value, ε zoe. The iformatio of sample poits i ε zoe caot appear i regressio fuctio, ad the the regressio fuctio is sparse ad simple. The optimal fuctio is costructed based o the idea of ε isesitive loss fuctio, which is expressed as follows [4]: mi ω,b,τ,τ s.t. J= 1 2 ωt ω+c (τ i +τ i ) (3) { y i ω T φ(x i ) b μ+τ i, { ω T φ(x i )+b y i μ+τ i, { τ i,τ i 0, where τ i ad τ i deote the relaxatio factors, C deotes the pealtyfuctio, C > 0,adμ deotes the precisio. The core fuctio is itroduced, ad the dual fuctio of expressio (4) cabeexpressedasfollows[5]: max β,β J= 1 2 s.t. μ i,j (β i β i )(β j β j ) K(x i,x j ) (β i +β i )+ i (β i β i ), β i,β i (0, C], y i (β i β i ) (5) where β i ad β i arealsolagrageoperatorsadk(x i,x j ) deotes the core fuctio. (4) The estimatig fuctio of the least squares support vector machie ca be expressed as follows [6, 7]: f (x) = (β i β i )K(x,x k)+b. (6) The parameters optimizatio of the least squares support vector machie is very importat. The core fuctio geerally applies the radial fuctio. There is a ukow factor γ, ad improvig the value of γ ca improve the covergece rate of the algorithm. I additio, there is aother parameter, which is the parameter of the least squares support vector machie η; the parameters Gamma ad η cadecidethe learig ability of the least squares support vector machie together. 3. Algorithm of the Least Squares Support Vector Machie The algorithm procedure of the least squares support vector machieislistedasfollows. Step 1.Therageofthetwoparametersγ ad η is cofirmed based o basic priciples of the least squares support vector machie, ad the empirical rage of the two parameters is listed as follows: γ [0.01, 0.1], η [0.02, 10000]. Step 2. The values of the two parameters γ ad η are cofirmed i rage; the the two-dimesioal plae (γ i,η i ), i = 1,2,...,m;1,2,..., ca be costructed. The value of Gamma ca be chose accordig to the real situatio of traiig samples ad relatig experieces. Step 3. The pairs of parameters (γ i,η i ) i differet plae grid odesareiputitotheleastsquaressupportvectormachie, the correspodig traiig is carried out based o traiig samples, ad the the traiig error is output. (γ i,η i ) with least error is used as the most optimal results [8]. Step 4. Whe the traiig precisio of algorithm caot satisfy the real requiremet, the optimal parameter is used as ceter to costruct the ew plae grids ad cofirm the ear parameter; the the ew traiig is carried out agai; the the precisio of the algorithm ca be improved, ad the procedures metioed above ca be carried out repeatedly; the the multilayers parameter optimizatio plae etwork ca be formed; fially, the optimal parameters of the least squares support vector machie ca be obtaied; the the ideal traiig precisio ca be obtaied [9]. 4. Predictio Simulatio of Hydraulic Excavator Based o Least Squares Support Vector Machie The predictio model of the hydraulic excavator performace is costructed based o the followig basic steps. (1) The characteristics ad performace idexes of the hydraulic excavator are cofirmed. Ad the learig samples of the regressio least squares support vector machie are obtaied.
Joural of Cotrol Sciece ad Egieerig 3 Table 1: Data sample of performace predictio for the hydraulic excavator. ICE r/mi EM r/mi P r/mi T ICE T EM T P N ICE kw P MPa 800 800 800 20 15 35 20 0.3 850 850 850 25 20 45 25 0.5 1000 1000 1000 30 25 55 28 0.6 1100 1100 1100 40 30 70 32 0.7 1200 1200 1200 45 40 85 36 0.8 1250 1250 1250 50 45 95 43 0.9 1300 1300 1300 55 50 105 47 1.0 1400 1400 1400 60 55 115 53 1.2 1500 1500 1500 70 65 135 58 1.4 1600 1600 1600 75 70 145 63 1.5 1650 1650 1650 80 85 165 69 1.7 1750 1750 1750 90 95 185 75 1.9 Output power of egie (kw) 75 60 45 30 15 0 0 10 20 30 40 Measured value Predictio value Time (s) Figure 1: Performace predictig curve ad measured curve of output power for egie. (2) The core fuctio is chose; the mappig relatio betwee the iput ad output parameters is obtaied through sample learig. (3) The ew parameters are iput ito the regressio least squares support vector machie to carry out predictio of the hydraulic excavator performace. (4) The ew learig samples of the hydraulic excavator system are added to the regressio least squares support vector machie; the the predictio ability of model ca be improved. The predictio effect of the least squares support vector machie ca be judged by the root-mea-square error, which is expressed as follows [10]: E= 1 ( y 2 i y i ) 100%. (7) y i Through field test for the hydraulic excavator 100 group samples are obtaied, ad the former 60 groups of samples are used as performace predictig samples of the hydraulic excavator, ad the other 40 groups of samples are used as verificatio samples of predictio model; the performace predictio simulatio programmer of the hydraulic excavator is compiled by MATLAB software. The iput parameters of performace predictio model for the hydraulic excavator are listed as follows: rotatig speed of egie ICE, the rotatig speed of motor EM,rotatig speed of the hydraulic pump P,thetorqueoftheegieT ICE, the torque of the motor T EM,adthetorqueofthehydraulic pump T P ; the output parameters of the model are output power of the egie N ICE ad the pilot cotrollig pressure of hydraulic cotrol valve P, respectively; the part samples are show i Table 1. The performace predictig curve ad actual measuremetcurveofoutputpowerfortheegieareshowi Figure 1. AsseefromFigure 1, the output power of the egie chages i the momet with time, ad output power Table 2: Output power predictio results of the hydraulic excavator based o differet predictio model. Time/s Measured output power/kw Predictio output power/kw LS-SVM Traditioal SVM BP eutral etwork 5 46 49 53 57 10 64 66 69 73 15 63 65 70 74 20 49 52 58 61 25 36 38 41 45 30 38 40 45 52 35 35 38 43 49 chages irregularly; the predictig results agree with the actual measuremets, ad these results show that the least squares support vector machie based o regressio has better predictio ability. Durig the workig process of the hydraulic excavator, the iput parameter ca be regulated based o the predictio results of the least squares support vector machie based o regressio; the the hydraulic excavator ca work steadily, ad it ca be i the optimal performace poit; the workig efficiecy of the hydraulic excavator ca be improved accordigly. The output power predictio results of the hydraulic excavator from the regressio least square support vector machie, traditioal support vector machie, ad BP eutral etwork are compared, which are show i Table 2. As see from Table 2, the predictio results from the regressio least support vector machie are closer to the measured value tha those from traditio support vector machie ad BP eutral etwork. The regressio least support vector machie ca obtai best performace predictio results of the hydraulic excavator.
4 Joural of Cotrol Sciece ad Egieerig 5. Coclusios The least squares support vector machie based o regressio isapplieditheperformacepredictioofthehydraulic excavator, the model of the least squares support vector machie based o regressio is established, the correspodig algorithm procedure is desiged, ad the performace predictio model of the hydraulic excavator is established. The performace predictio simulatio is carried out, ad resultsshowthattheregressioleastsquaressupportvector machie has higher predictio precisio, which ca predict the chagig rules of the performace for the hydraulic excavator ad improve the workig efficiecy, which has wide applicatio space. Coflict of Iterests The author declares that there is o coflict of iterests regardig the publicatio of this paper. Refereces [1] M. Haga, W. Hiroshi, ad K. Fujishima, Diggig cotrol system for hydraulic excavator, Mechatroics, vol. 11, o. 6, pp. 665 676, 2001. [2] Z.-Y.Jia,J.-W.Ma,F.-J.Wag,adW.Liu, Hybridofsimulated aealig ad SVM for hydraulic valve characteristics predictio, Expert Systems with Applicatios,vol.38,o.7,pp.8030 8036, 2011. [3] Q. P. Ha, Q. H. Nguye, D. C. Rye, ad H. F. Durrat- Whyte, Impedace cotrol of a hydraulically actuated robotic excavator, Automatio i costructio,vol.9,o.5,pp.421 435, 2000. [4] Y. Hog ad C. W. W. Ng, Base stability of multi-propped excavatios i soft clay subjected to hydraulic uplift, Caadia Geotechical Joural,vol.50,o.2,pp.153 164,2013. [5] J.Jiag,C.Sog,adL.Bao, ForwardGeeselectioalgorithm based o least squares support vector machie, Joural of Bioaosciece,vol.7,o.3,pp.307 312,2013. [6] M.-Y. Ye ad X.-D. Wag, Chaotic time series predictio usig least squares support vector machies, Chiese Physics, vol. 13, o. 4, pp. 454 458, 2004. [7] S.Swaddiwudhipog,K.K.Tho,Z.S.Liu,J.Hua,adN.S.B. Ooi, Material characterizatio via least squares support vector machies, Modellig ad Simulatio i Materials Sciece ad Egieerig,vol.13,o.6,pp.993 1004,2005. [8] Y. Wa, Pump performace aalysis based o least squares support vector machie, Trasactios of the Chiese Society of Agricultural Egieerig,vol.25,o.8,pp.115 118,2009. [9] X. Wag, X. Tia, ad Y. Cheg, Value approximatio with least squares support vector machie i reiforcemet learig system, Joural of Computatioal ad Theoretical Naosciece, vol. 4, o. 7-8, pp. 1290 1294, 2007. [10] K.Huag,H.J.Wag,H.R.Xu,J.P.Wag,adY.B.Yig, NIR spectroscopy based o least square support vector machies for quality predictio of tomato juice, Spectroscopy ad Spectral Aalysis,vol.29,o.4,pp.931 934,2009.
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