Application of Improved BP Neural Network in Controlling the Constant-Force Grinding Feed

Transcription

1 Appication of Iproved BP Neura Networ in Controing the Constant-Force Grinding Feed Zhaoxia Chen, Baiin He, and Xianfeng Xu Key Laboratory of Ministry of Education for Conveyance and Equipent, East China Jiaotong University, Nanchang, P.R. China Abstract. BP neura networ is appied to contro the aount of feed, which is the ey probe during the constant-force grinding. Firsty, BP neura networ is constructed. Because its convergence is sow and oca inius often occur, the adaptive earning rate is used and certain oentus are added to iprove BP neura networ. Then the feature paraeters in tie and frequency doain are piced up in grinding vibration signas. With these feature paraeters BP neura networ is trained. As the resut it aes the aount of grinding feed recognized precisey. Coparing the practica aount of feed with the set one, the syste sends coands to increase or decrease the feed.so the aount of feed regains the set one. This ethod reaizes the autocontro of the grinding feed, and puts forward a new ethod for constant-force grinding. It cobines the features in tie doain with those in frequency doain, and overcoes the iitation of the ethod which pics up feature paraeters ony in tie doain or in frequency doain. At the sae tie this ethod provides a new cue of integrating other feature paraeters in the grinding. Practice proves its good effect. Keywords: BP neura networ, Feature paraeter, Constant-force grinding, Feed. Introduction The grinding is a ethod of achining with high precision. As a ind of grinding, the constant-force grinding is advanced to for curve shapes, which contros the force in the grinding and aes the whee contact the worpiece unifory. The preise of reaizing the constant-force grinding is to recognize the feed of the whee. Great attention has been paid by the researchers to the ways of onitoring the grinding on ine [] [2]. Generay, severa feature paraeters which can refect the state pattern of grinding are the ain basis for this wor. Thus whether the on-ine onitoring can be done depends on the effectiveness of the feature paraeters. In soe references the feature paraeters are piced up ony in tie doain or in frequency doain [3] [4], and by this ethod the grinding feed cannot be recognized precisey inevitaby. As BP neura networ has the distinctive advantage in erging various feature paraeters, this paper presents the appication of iproved BP neura networ on the basis of picing up the feature paraeters of the vibration signas in the grinding. The D. Li, Y. Liu, and Y. Chen (Eds.): CCTA 200, Part IV, IFIP AICT 347, pp , 20. IFIP Internationa Federation for Inforation Processing 20

2 64 Z. Chen, B. He, and X. Xu ai is to recognize the grinding feed, contro the aount of feed autoaticay and reaize the constant-force grinding. 2 Principe of BP Neura Networ BP neura networ defines the earning process consists of the forward propagation of the signa and bacward propagation of error. In the forward propagation, the input sape is transitted fro the input ayer, after processed by every hidden ayer in sequence, then to the output ayer. If the actua output cannot atch the expected one (i.e. teaching signa), the bacward propagation of error begins. This propagation eans passing the output error through the hidden ayers to the input ayer reversey in soe way. At the sae tie, the error is aocated to a units of each ayer to obtain the error signa of each ayer, which is the basis of correcting every unit weight. This adustent of the weight for each ayer is cyced, which is ust the training process of the networ. The process ends off when the output error is diinished to what is accepted or when the earning ties is up to what is set in advance. The ain structure of BP neura networ is that, the networ is coposed of nodes at different eves and the outputs fro the nodes at a certain eve are passed to those at next eve. These outputs are apified, attenuated or inhibited for different connection weight. Except the input ayer, the input to each node is the weighted su of the output fro the forer node. The stiuation output of each node is deterined by the input, the activation function and the threshod. Figure shows the ain structure of BP neura networ. y y 2 y v v L L w w Ln x x 2 x n Fig.. The ain structure of BP neura networ

3 Appication of Iproved BP Neura Networ 65 The earning agorith of BP neura networ is the gradient search rue to ae the ean square deviation between the actua and expected outputs of the networ east. As the error is propagated bacward, it is corrected siutaneousy. This is the earning process of the networ, which contains two steps: forward cacuation and bacward adustent. The activation function is S-typed: f ( x ). + e x The input to node in the hidden ayer is expressed by n net ( x) w x + θ. (2) The output fro node in the hidden ayer is deterined according to () h s( net ( x)). (3) The input to node in the output ayer is expressed by L net ( h) v h + θ. (4) The output fro node in the output ayer is deterined according to y s( net ( h)). (5) y L s( vs( w n,2,, x + θ ) + θ ). (6) For a continuous apping n F : R R, a sape is the data representing the ( x, x2, xn; o, o2,, o and is fit for the input and output, which is ) reationship: F( x, x2, xn ) ( o, o2,, o ). (7) The error of networ can be cacuated by foowing equation: E 2 ( y o ) 2 2 e 2. (8) ( here, e y o that is the difference between networ output and apping output.)

4 66 Z. Chen, B. He, and X. Xu To ae the networ aster this sape, the error ust be as itte as possibe. This can be reaized by adusting the weights v and w, the sipest ethod of which is gradient descent agorith. E ν st e s s e e y ( nets ( h) ) h δ sh y net net ν st. (9) E w i e s ( net ( h) ) ν s ( net ( x) ) i e δ ν s e y y net i ( neti( x) ) x δix net w i i x. (0) The correction vaue reationship can be expressed δ i ( δ v ) s i ( neti ( x)). Δ v and w () Δ is is proportiona to error function and the Δ v ηδ h. (2) s t Δ w ηδ i x. (3) The threshod θ is variabe and aso need correcting, the principe of which is the sae as the correction of weights. Because oca inius often occur in BP neura networ, certain oentus shoud be added to avoid it. Meanwhie, the adaptive earning rate ust be used to speed the training [5] [6]. 3 Anaysis of Grinding Experient The grinding experient is ade on the CNC externa cyindrica grinding to obtain constant-force grinding. In the experient, the acceeration sensor is fixed on the side of grinding carriage and the sapes are piced up with the high-speed A/D saper, the frequency (fs) of which is MHz. The worpiece is cyindrica and ade fro GCY5.The whee is ade fro red corundu the granuarity of which is 80.First, the vibration signas are recorded when the feed is μâ2μâ3μ respectivey.

5 Appication of Iproved BP Neura Networ 67 Then the feature paraeters about different feed are piced up to train the networ. Finay, the trained networ is used to recognize the feed, ensuring it is 2μ. 3. Features Pic-Up of Signas Soe wor ust be done to fufi rea-tie onitoring. That is to anayze appropriate data, udge the current feed, and give coands the grinding too shoud go ahead or bac. For instance, if the current feed is cacuated to be 3μ and the expected is 2μ, the whee is controed to retreat for μ. If the quantity of data anayzed each tie is too big, the processing tie is ong and the operation is not ive. If the quantity of data anayzed each tie is too itte, the features piced up are representative. After a ot of tests, the quantity of data anayzed each tie is 500. Fro the 500 data anayzed each tie, soe features shoud be piced up in tie and frequency doains, to study the features of signas coprehensivey. In tie doain, they are ean and standard deviation. In frequency doain, they are axiu vaue of apitude spectru and frequency there. A part of feature paraeters are showed in Tabe, 2 and 3.Tests show any one in the four inds of features cannot recognize the feed individuay, because they are overapped in every feed. So it is necessary to integrate the four inds of features to recognize the feed precisey. Tabe. Feature paraeters for the μ feed ean standard deviation axiu vaue of apitude spectru frequency (KHz) Tabe 2. Feature paraeters for the 2μ feed ean standard deviation axiu vaue of apitude spectru frequency (KHz) Tabe 3. Feature paraeters for the 3μ feed ean standard deviation axiu vaue of apitude spectru frequency (KHz)

6 68 Z. Chen, B. He, and X. Xu 3.2 Construction and Training of Iproved BP Neura Networ The first thing is to deterine the structure of the networ. According to Koogov theore [7], an N (2N+) M three-ayered networ is designed as recognizer, whose structure is shown in Figure 2. Here, N is the nuber of coponents of input vectors and M is the nuber of output categories. In this paper, N is 4 and M is 3.So in the networ there are 4 input nodes, 9 hidden-ayer nodes and 3 output nodes. When the output node is expressed as (,0,0), the feed is μ. Siiary, (0,,0)eans 2μ and (0,0,)eans 3μ. In BP networ ode, the activation function of hidden ayers is tansig and the one of output ayers is ogsig. Because in the three eeents of output vectors one is and the other are 0, the outputs ust be processed by copetitive transferring function [8] [9]. Fig. 2. The structure of the actua BP Neura networ 0 0 Perforance is , Goa is 0.05 Training-Bue Goa-Bac Epochs Fig. 3. The training error curve of the networ In order to train the networ ore fuy, 40,000 saping data are chosen, and fro every 500 saping data the features are piced up. The adaptive earning rate is used and certain oentus are added to iprove BP neura networ, because the veocity of its converge is very sow, and the networ fas into the situation of oca extrea easiy. Figure 3 shows the training error curve of the networ. Fro Figure 3, it can be seen that the networ converges is very we.

7 Appication of Iproved BP Neura Networ 69 The progra is copied in MATLAB. The ain code incuding interpretation is as foowing. %Read the training data fro fie which is ade fro saping data. poad('tezheng.txt'); %According to the feature of networ, p ust be transposed. pp'; %Construct the networ netnewff(inax(p),[9 3], {'tansig','ogsig'}, 'traingdx'); %Set the starting vaue of networ net.lw{2,}net.lw{2,}*0.0; net.b{2}net.b{2}*0.0; %Set the paraeter of the networ net.perforfcn'sse'; net.trainpara.goa0.05; net.trainpara.show00; net.trainpara.epochs5000; net.trainpara.c0.97; %Read the target vaue of the networ. toad('target.txt'); %According to the feature of networ, t ust be transposed. tt'; %Training the networ. [net, tr]train(net, p, t); 3.3 Verification of the Networ To verify the recognition abiity of the iproved BP networ, the author coects corresponding data respectivey when the feed is μ, 2μ and 3μ. After piced up, the feature paraeters are inputted into the networ. The networ can recognize the feed quicy and precisey. The verification code in MATLAB is as foowing. %Read the data used to test the networ fro fie which is ade fro saping data. ppoad('test.txt'); %According to the feature of networ, pp ust be transposed. pppp'; %Test the networ ttsi(net, pp) %The output shoud handed by copetitive transferring function, so that the outcoe can be 0 or ttcopet(tt);

8 70 Z. Chen, B. He, and X. Xu 4 Ending The feature paraeters in tie and frequency doain of grinding vibration signas are fused into the iproved BP neura networ successfuy. The feed of grinding too can be recognized precisey. This ethod provides a new cue of integrating feature paraeters fro different doains in the grinding.aso, this ethod aes it possibe that constant-force grinding transfors fro experience-contro to autocontro. Practice proves its good effect. References. Zhang, X., Kuhenotter, B., Knueuper, K.: An Efficient Method for Soving the Signorini Probe in the Siuation of Free-for Surfaces Produced by Bet Grinding. Internationa Journa of Machine Toos & Manufacture, (2005) 2. Li, H.: Deterination of Frequency Cacuation Range of Feature Paraeters in Grinding State Monitoring. Too Engineering, (2006) 3. Leea, D.E., Hwanga, I., Vaenteb, C.M.O.: Precision Manufacturing Process Monitoring with Acoustic Eission. Internationa Journa of Machine Toos &Manufacture, (2006) 4. Karpuschewsi, B., Weheier, M., Inasai, I.: Grinding Monitoring Syste Based on Power and Acoustic Eission Sensors. Annas CIRP, (2000) 5. Ferrari, S., Stenge, R.F.: Sooth function: Approxiation Using Neura Networs. IEEE Trans. on Neura Networs, (2005) 6. Horni, K., Stinchcobe, M., White, H.: Universa Approxiation of An Unnown Mapping and Its Derivatives Using Mutiayer Feedforward Networs. Neura Networs, (990) 7. Yang, Y., Xie, G.-S.: Handwritten Digit Recognition Based on BP Neura Networ. Journa of East China Geoogica Institute, (2003) 8. Tang, D., Sun, H., Wang, H.: Miing Deforation Forecast with BP Neura Networ. Manufacturing Technoogy & Machine Too, (2007) 9. Wu, J., Li, Y.: Intrusion detection ode based on BP neura networ and feature seection. Coputer Engineering and Appications, 4 8 (2008)