Wear State Recognition of Drills Based on K-means Cluster and Radial Basis Function Neural Network

Transcription

1 International Journal of Automation and Computing 7(3), August 2010, DOI: /s z Wear State Recognition of Drills Based on K-means Cluster and Radial Basis Function Neural Network Xu Yang 1, 2 1 Department of Mechanical System Engineering, Faculty of Engineering, Gunma University, Kiryu , Japan 2 Department of Mechanical Engineering, School of Mechanical Engineering and Automation, Dalian Polytechnic University, Dalian , PRC Abstract: Drill wear not only affects the surface smoothness of the hole, but also influences the life of the drill. Drill wear state recognition is important in the manufacturing process, which consists of two steps: first, decomposing cutting torque components from the original signals by wavelet packet decomposition (WPD); second, extracting wavelet coefficients of different wear states (i.e., slight, normal, or severe wear) with signal features adapting to Welch spectrum. Finally, monitoring and recognition of the feature vectors of cutting torque signal are performed by using the K-means cluster and radial basis function neural network (RBFNN). The experiments on different tool wears of the multivariable features reveal that the results of monitoring and recognition are significant and effective. Keywords: Drill wear state recognition, cutting torque signals, wavelet packet decomposition (WPD), Welch spectrum energy, K-means cluster, radial basis function neural network. 1 Introduction In today s competitive manufacturing environment, the manufacturers are always striving to automate the manufacturing systems to improve product quality and reduce operating cost. Drilling represents over 30 % of all cutting operations performed in manufacturing engineering [1]. Drill wear directly determines the products quality, tool-life, and over-all cost [2]. Therefore, drill wear is a very important issue in manufacturing industries. Previous researchers have considered various kinds of signals as indicators of tool wear, such as cutting torque and thrust force [3], acoustic emission [4], and motor current [5]. The wavelet transform (WT) provides a time-frequency representation of the signal. It was developed to overcome the shortcoming of the short time Fourier transform (STFT). WT provides good solution in time and frequency domain, and it is capable of extracting more information in time domain in different frequency bands [6]. In the WT, only the previous approximation coefficients are decomposed. However, using wavelet packet decomposition (WPD), we can decompose both the approximation and detail coefficients [7]. WPD is widely used in image processing [8] and pattern recognition [9], fault diagnosis [10], etc. In this paper, the monitoring and recognition of tool wear states by using wavelet coefficients of torque signals are presented. Welch spectrum of the wavelet coefficients is used as features for identifying tool wear states. K-means is an automating learning algorithms that solves the clustering problem. The procedure follows an easy way to classify given observations through some number of clusters. Euclidean distance is used as a metric, and variance is used as a measure of cluster scatter [11]. A K- means cluster model is generally used for pattern recognition and classification of data [12, 13]. Artificial neural network (ANN) algorithms are regarded as multivariate non- linear analytical tools, i.e., they are capable of recognizing patterns from complex data and estimating their nonlinear relationships [14]. Thus, they have been used in monitoring and recognition applications. Li and Wu [15] introduced a fuzzy C-means clustering algorithm for monitoring of drill wear states. The thrust force and torque were selected as the features relevant to the drill wear states. Datta et al. [16] proposed tool condition monitoring strategies for face milling using tri-axes forces along with speed, feed, and depth of cut, using an ANN model. Govekar and Grabec [17] proposed an adaptive self-organizing neural network for identification and classification of the drill flank wear. Obikawa and Shinozuka [18] used unsupervised and self-organizing neural network adaptive resonance theory (ART2) for monitoring of flank wear in high-speed machining operation. Radial basis function neural network has been successfully used for sensor fault in time delay nonlinear systems [19]. Tsao [20] used the radial basis function network (RBFN) and adaptive radial basis function network (ARBFN) to predict the flank wear, and compared their results with experimental observation. Feature-based identification of drill wear states is essentially a pattern recognition problem in which there are two basic issues: feature selection and identification based on the selected features. The proposed method relies on features extraction of cutting torque signals in different wear states. WPD is used to decompose the original signal of cutting torque in different frequency regions. The extracted spectrum energy is further utilized to compose the feature vector. K-means cluster and RBFNN are applied to recognize the wear state. Experimental results show that the identification accuracy of RBFNN with spectrum energy features can provide a better result, i.e., the performance of RBFNN is higher than K-means cluster. In this paper, the rest of this paper is organized as follows. The research background is introduced in Manuscript received January 1, 2010; revised March 16, 2010

2 272 International Journal of Automation and Computing 7(3), August 2010 Section 1. The background of theoretical modeling techniques for wear states recognition is described in Section 2. The experimental setup is described in Section 3. The proposed method is verified and results are discussed in Section 4. Finally, conclusions and future work are given in Section 5. 2 Theoretical background 2.1 Wavelet packet decomposition Wavelet transform is a signal processing technique in the time-frequency domain. It uses dilations and translations of a mother wave function [7]. The mother wave function is defined as follows: ψ a,b = 1 ( ) a t ψ (1) a b where a and b are the dilation and translation parameters, respectively. Discrete wavelet transform (DWT) is a fast algorithm that computes digitally the transform coefficients on the dyadic scale by setting a = 2 j and b = k2 j. DWT is defined as follows: W ψ = 2 j 2 f(t)ψ (2 j t k)dt. (2) The wavelets ψ j,k (mother wavelet), orthonormal basis of L 2 is the space of square integrable functions, therefore, any function f(t) L 2 can be represented by the base functions ψ j,k and corresponding scaling functions φ n (father wavelet). f(t) = n= c(n)φ n(t) + j=0 k= d(j, k)ψ j,k (t) (3) where c(n) and d(j, k) are the approximation coefficients and details coefficients, respectively. At level l, we have a set of approximations and details. In order to get decomposition at level l, we decompose approximations A l 1 i proximations and details: and details D l 1 i into the following ap- A l 1 i {A l 2i, D l 2i}, l > 0 (4) D l 1 i {A l 2i+1, D l 2i+1}, l > 0 (5) where i = 0, 1,, 2 (l 1) 1. For three levels of decomposition, the WPD produces different coefficients. The decomposition tree is shown in Fig.1. The wavelet packet coefficients A 3 0 D3 3 (i.e., S130 S137) are obtained, respectively. Fig. 1 Binary tree of discrete wavelet packet decomposition 2.2 Welch spectrum The Welch spectrum method is an improvement of the standard periodogram method, and Bartlett s method in that it reduces noise in the estimated power spectra in exchange for reducing the frequency resolution [21]. The welch spectrum of signal x i(n) (M data) is defined as follows: P i(ω) = 1 N 1 MU x i(n)w(n)e jωn 2 (6) U = 1 M n=0 N w 2 (n) (7) n=0 where U is the normalized factor and w(n) is window function. 2.3 K-means cluster model The K-means method aims to partition n observations x = (x 1, x 2,, x n) into k clusters (k < n) centre C = (C 1, C 2,, C k ). K-means clustering is the minimization of the sum of squared distances between all observations and the cluster centre (within-cluster sum of squares). The within-cluster sum of squares (WCSS) E is defined as follows: k E = x j µ i 2 (8) i=1 x j C j where µ i is the mean of C i. This algorithm consists of the following steps: Step 1. Randomly assign k initial cluster centres m 1(1), m 1(2),, m 1(k). Step 2. Assign all observation x to the cluster with the closest mean C l i = {x j: x j m l i x j m l i for all i = 1, 2,, k}. (9) Step 3. Compute the new cluster centres m i(k + 1) such that the sum of the squared distances from all observations in m i(k) to the new cluster centre is minimized. The new cluster centre is given by m i = 1 x (10) N i x j C j where N i is the number of samples in C i(k). Step 4. If the algorithm has converged and the assignment no longer changes, i.e., m i(k) = m i(k + 1), then the algorithm procedure is terminated. Otherwise, repeat Steps Radial basis function neural network model The radial basis function neural network has a feed forward architecture with an input layer, a hidden layer, and an output layer as shown in Fig 2. Input element Ii P = 0, 1,, l enters the input layer and is subjected to direct transfer function and output from input layer is same as P input pattern. Between the inputs and outputs there are hidden units; each unit of them implements a radial basis function. The activation function

3 X. Yang / Wear State Recognition of Drills Based on K-means Cluster and Radial Basis Function Neural Network 273 of the hidden layer is Gaussian function, and is characterized by their centre vector and covariance matrices C i, i = 1, 2,, m, where m is the number of hidden units. It is assumed that the covariance matrices C i are of the form C i = σ 2 I P i. n is the number of output units. W is obtained from the standard least squares solution as given by W = (G T G) 1 G T Y. (15) So, W is an (m + 1) n matrix of weights. The elements of Y are specified as { 1, I Class j Y ij = (16) 0, otherwise. In the present case, centre selection algorithm has been considered for training of the RBFNN which consists of the following steps (it is shown in the flow chart of Fig. 3): Step 1. Initialize the samples to K-means (clusters) v ji. Step 2. Modify the corresponding centre vector closest to the sample as Fig. 2 Architecture of radial basis function neural network The hidden layer consists of the nodes which satisfy a unique property, i.e., being radially symmetric. Between the inputs and outputs there is a layer of hidden units, which uses radial basis function in the hidden units. Then, the activation function of the i-th hidden unit is given by ) g j(ii P ) = exp ( IP i v ji 2 (11) 2σ 2 where v ji and σ are calculated by using suitable clustering algorithm. Here, the K-means clustering algorithm is employed to determine the centres, where centre vector v ji in the input space, is made up of the cluster centre with element. The σ is the spread parameter determined from v n j = v n 1 j + η (I P i v n 1 j ) (17) where η is learning rate, i.e., 0 < η < 1. Step 3. Calculate spread parameter σ as (12). Step 4. Initialise the weights of output layer to small random values. Step 5. Calculate the output from the output layer as (13). Step 6. Calculate the mean square error (MSE) of the training sample. If the MSE training reaches the specified goal then the training is over, otherwise, the weight is updated based on gradient descent method by repeating Steps 2 6. σ = max( IP i v j ) (12) M and M is the number of centre vectors. These cluster means are used as the centres v j of the activation functions in the RBFNN. The output units are linear. Output from the output layer is given by Y k = m W jk g j(ii P ) (13) j=1 where g 0(Ii P ) = 1. The hidden layer units are connected to the n output layer units through weights W jk. The weights W jk are determined as follows: given that the Gaussian function centers and widths are computed from m training vectors, which may be written in matrix form as Y = GW (14) where Y is an l n matrix with elements Y ij = y j(i P i ), G is an l (m + 1) matrix with elements G ij = y j(i P i ), and Fig. 3 3 Experiment The training flow chart of RBFNN The schematic diagram of the experimental set-up is shown in Fig. 4. The experiments were performed on a

4 274 International Journal of Automation and Computing 7(3), August axis computer number control (CNC) machining center (MC1010-5XA). The torque signals were monitored using a piezoelectric dynamometer (YDZ-II02). The amplified torque signals were preprocessed by a charge amplifier (YE5850) and then sent to data acquisition system (NR- 2000) and computer (PC). Fig. 4 Schematic diagram of the experimental set-up In the experiments, Carbide K10 drills with 8 mm diameters were used for drilling in high silicon aluminum alloy work piece at different cutting conditions. The presented signals were collected at a spindle rotating speed of 4500 rpm/min and the feed rate was 0.2 mm/rev. The depth of these holes was 20 mm. The sampling frequency was set as 1 khz. The cutting torque signal in the drilling process in the slight wear (< 0.1 mm), normal wear (> 0.25 mm), severe wear (> 0.5 mm) are shown in Fig. 5 (a) (c). It can be seen that the amplitudes of torque signal with increasing drill wear will increase. 4 Results and discussion 4.1 Feature extraction of torque signals using WPD In this paper, we use the WPD to analyze the original torque signals. The decomposition level is 3, and approximation and detail coefficients are obtained in each level. Welch spectrum of the wavelet coefficients is employed to distinguish the tool wear states more distinctly here. It is shown in Fig. 6 in slight, normal, and severe wear states. From Fig. 6 (a) (c), P130 belongs to the frequency bandwidth (0 Hz, 62.5 Hz), and P130 P131 correspond to the frequency bandwidths (62.5 Hz, Hz), (125.0 Hz, Hz), (187.5 Hz, Hz), (250.0 Hz, Hz), (312.5 Hz, Hz), (375.0 Hz, Hz), (437.5 Hz, Hz), respectively. This means that wavelet coefficients spectrum is dominated by the drill thrust frequency f130, spindle rotating frequency f131 (75 Hz), and its harmonic. In the case of severe wear, we can see that the drill thrust frequency f130, spindle rotating frequency f131, and its harmonic f133, f134 increase as compared to the slight wear case and normal wear case. So, Welch spectrum of the wavelet coefficients can be called characteristic frequencies for tool state identification. Based on the energy in each spectrum, feature spectrums are selected by calculating the same as (18) given below: E i = ˆP (j) (18) where ˆP (j) is the spectrum peak value and i is coefficient number. The feature vectors of different wear states are made up of spectrum energy (E 0, E 1, E 3, and E 4). (a) Slight wear (b) Normal wear Fig. 5 (c) Severe wear Torque signals in different wear states. (a) Slight wear

5 X. Yang / Wear State Recognition of Drills Based on K-means Cluster and Radial Basis Function Neural Network 275 the weight matrix was calculated using the least squares algorithm for each of the feature vectors. Fig. 7 shows the variation of mean square error (MSE) in training with number of iterations. It can be observed that the network has been trained till 11 iterations in which the MSE for training is It can also be observed from Fig. 7 that the MSE of training sample rapidly reduces within 11 iterations until the network over fits. (b) Normal wear Fig. 7 Variation of training error with number of iterations for RBFNN. The identification performance (testing) of the system using RBFNN for recognition of drill wear states is given in Table 1, and it can be observed that the identification rate is within 92.31% (13 data sets, 12/13 recognizable). Table 1 The recognition result (testing) using RBFNN Wear states Vectors of input (E 0, E 1, E 3, E 4) Accredit logic Slight wear Normal wear Severe wear Fig. 6 (c) Severe wear Welch spectrum of the wavelet coefficients 4.2 Wear state recognition using RBFNN These features are given as input to the RBFNN model. Out of the 26 feature data sets, 13 data sets (training set) were selected at random and were used for training the network, whereas 13 data sets (testing set) were used to evaluate the testing error (accredit logic 0 or 1). The RBF centres were located using K-means algorithm. For training, 4.3 Wear state recognition using K-means cluster Using the K-means cluster arithmetic no the training data set (as described in Section 4.2) for automatic classification, the learning steps of the algorithm are set to 500. This approach will automatically classify test data into two clusters (cluster 1 and cluster 2), cluster centres are ( ) and ( ). Cluster results are shown in Table 2. It can be observed that the identification rate is within % (9 data sets,

6 276 International Journal of Automation and Computing 7(3), August /13 recognizable). By this result, K-means cluster arithmetic can effectively identify eigenvalue of serious wear out, but cannot discriminate slight wear and normal wear. Table 2 The cluster result using K-means cluster Wear states Vectors of input (E 0, E 1, E 3, E 4) Cluster result Slight wear Normal wear Severe wear 5 Conclusions Cluster 1 Cluster 2 This paper proposes the recognition method of drill wear states using K-means cluster and RBFNN. From the presented work, the following specific conclusions have been drawn: 1) The feature extraction of cutting torque is performed in different drill wear states using WPD and Welch spectrum. Cutting torque has low bandwidth with respect to its dynamic sensitivity and is very sensitive to the change of tool wear state. To separate useful torque signals from the original signals, wavelet packet decomposition is employed. The features of Welch spectrum are extracted as salient features from wavelet coefficients of cutting torque signals to indicate drill states. 2) We have proposed a drill wear states recognition method using K-means cluster and RBFNN. Experimental results show that the proposed identification rates of wear states are 69.23% and 92.31%, respectively. This proves that RBFNN can identify more precisely as compared with K-means. Therefore, the work indicates that the RBFNN method can be more effectively used for wear state recognition. References [1] Y. J. Choi, M. S. Park, C. N. Chu. Prediction of drill failure using features extraction in time and frequency domains of feed motor current. International Journal of Machine Tools and Manufacture, vol. 48, no. 1, pp , [2] B. Sick. On-line and indirect tool wear monitoring in turning with artificial networks: A review of more than a decade of research. Mechanical Systems and Signal Processing, vol. 16, no. 4, pp , [3] A. Noori-Khajavi, R. 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Sensor fault diagnosis for a class of time delay uncertain nonlinear systems using neural network. International Journal of Automation and Computing, vol. 5, no. 4, pp , [20] C. C. Tsao. Prediction of flank wear of different coated drills for JIS SUS 304 stainless steel using neural network. Journal of Materials Processing Technology, vol. 123, no. 3, pp , [21] P. Welch. The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms. IEEE Transactions on Audio and Electroacoustics, vol. 15, no. 2, pp , Xu Yang received M. Tech. degree in mechanical engineering from Dalian Polytechnic University, Dalian, PRC in He has been a lecturer of Dalian Polytechnic University. Currently, he is a Ph. D. candidate in the Department of Mechanical System Engineering at Faculty of Engineering of Gunma University, Kiryu, Japan. His research interests include mechanical automation, artificial intelligence, and virtual instrument. yangxv1994@163.com (Corresponding author)