Monitoring Grinding Wheel Redress-life Using Support Vector Machines

Transcription

1 International Journal of Automation and Computing 1 (2006) Monitoring Grinding Wheel Redress-life Using Support Vector Machines Xun Chen, Thitikorn Limchimchol School of Mechanical, Materials and Manufacturing Engineering, University of Nottingham, Nottingham NG7 2RD, UK Abstract: Condition monitoring is a very important aspect in automated manufacturing processes. Any malfunction of a machining process will deteriorate production quality and efficiency. This paper presents an application of support vector machines in grinding process monitoring. The paper starts with an overview of grinding behaviour. Grinding force is analysed through a Short Time Fourier Transform (STFT) to identify features for condition monitoring. The Support Vector Machine (SVM) methodology is introduced as a powerful tool for the classification of different wheel wear situations. After training with available signal data, the SVM is able to identify the state of a grinding process. The requirement and strategy for using SVM for grinding process monitoring is discussed, while the result of the example illustrates how effective SVMs can be in determining wheel redress-life. Keywords: Monitoring, grinding, support vector machine. 1 Introduction Condition monitoring is widely used in the manufacturing industry. In a machining process the variation of tool life due to different tool wear performance has a great impact on production quality, productivity, and cost. Reliable process monitoring tools are of fundamental importance to critical component machining processes, especially in the aerospace industry. Condition monitoring can be divided into two categories (1) direct and (2) indirect. The direct method generally involves determining tool wear directly from tool surface observation and measurement. Using metrological measurement, computer vision, and/or image processing, etc. Indirect methods monitor tool wear by sensing the physical behaviour of a machining process, which can include changes in force, vibration, and temperature, etc. In this paper, indirect monitoring is investigated for grinding wheel redress-life monitoring. Traditional machining monitoring, focuses on the average values of monitored signals as a time function. Signal features in the frequency domain are also commonly considered. To improve the accuracy of monitoring, artificial intelligence such as neural networks, fuzzy logic, or other pattern recognition techniques, have been applied [1 4]. However, the use of a neural network depends on the proper selection of the amount of training data, and the type of network structure, of Manuscript received March 1, 2005; revised September 28, Corresponding author. address: xun.chen@nottingham.ac.uk which the training process is a tedious job, and often relies on a trial and error approach. The recent developments of SVM [5 10], and Least Square Support Vector Machines (LS-SVM) [11], have been successfully applied to feature classifications in different fields. Using SVMs to judge the redress-life of a grinding wheel during grinding, would provide a rational test in developing a reliable tool for grinding process monitoring. This paper reports on an investigation of grinding process monitoring, using LS-SVM to analyse grinding force signals. Grinding force signals are analysed in both time, and frequency domains, using a Short Time Fourier Transform (STFT) analysis to create a power spectrum over time. These timefrequency domain methods offer a clear illustration of the features of grinding system performance. They demonstrate that the characteristics of grinding force extracted by a STFT can be used as input for a SVM. Good judgement of grinding wheel life using LS-SVM classification has been achieved. The paper is organized as follows. Grinding chatter and force characteristics are briefly described in section 2. In section 3, feature analysis by STFT is introduced, followed by the principles of SVMs in section 4, experimental results are discussed in section 5, while conclusions are given in section 6. 2 Grinding process characteristics Grinding performance characteristics can be related to the shape of grinding chips, which are influenced by a large number of parameters. Fundamentally, wheel speed, work speed, and the distribution of cutting edges

2 Xun Chen et al./ Monitoring Grinding Wheel Redress-life Using Support Vector Machines 57 on a wheel surface will determine the shape of grinding chips. A material removal rate can be expressed by an equivalent chip thickness. However, the distribution of a cutting edge on a wheel surface, varies continually, due to the effects of the dressing operation, and the nature of the wheel wear process. Wheel wear is a complex process, which includes cutting edge attritional wear, and the fracturing of grits and bonding materials. Because of the random distribution of grits in a wheel space, some of the most extrusive grits may wear quickly and form large plateaus on their surface. This causes large forces to act on them. Self-sharpening occurs due to the fracturing of grits or bonds. The influence of such wear behaviour can reflect on grinding forces, which consist of static and dynamic components. Static force relates to average material removal, while dynamic force refers to vibrations occurring in response to persistent disturbance, such as wheel, or workpiece imbalance, wheel run out, uneven grit wear distribution or other imbalanced rotating components of the grinding machine. Grinding chatter, also known as self-excited vibration, is a harmful phenomenon that can cause excessive dynamic forces leading to unacceptable wheel wear, and in extreme cases causes catastrophic disasters. Grinding chatter usually develops gradually, due to grinding wheel wear. Chatter makes a wheel surface uneven, resulting in poor surface quality, and low machining productivity. A dressing operation is often required to restore good wheel cutting ability. Therefore, judging wheel redress-life is an important issue in a grinding operation. a spectrogram is created when a window position is shifted by one or several measured values. The time characteristics of the process can be presented by repeating the Fourier transform for each window position. Although STFT has a fixed frequency resolution for all frequencies, once the size of a window is chosen, it enables an easier interpretation in terms of harmonics, and is faster in comparison to other methods [12]. The mathematical model of STFT is: STFT(t, ω) = s(τ)γ t,ω (τ t)e jωτ dτ. (1) Because the window function γ(t) has a short time duration, the Fourier transform of s(τ)γ(τ t) reflects the signal s local frequency properties. By moving γ(t) and repeating the same process, we can see how the signal s frequency contents evolve over time. However, there is a trade off in the selection of time and frequency resolution. If γ(t) is chosen to have a good time resolution, then its frequency resolution must be reduced, and vice versa. Equality only holds when γ(t) is a Gaussian function [13]. Fig.1 shows the results of a STFT analysis of grinding forces, where grinding depth of cut is 1 mm. The effect of grinding wear over a time-frequency domain, can easily be identified from the results to enable grinding wheel condition to be monitored in relation to force signal. It can be seen that some features in the force frequency spectrum increase during each grinding. 3 Process feature analysis Grinding force signals can be used to detect the development of chatter in grinding, because dynamic grinding forces represent the reaction of the grinding system to vibration. A Fourier transform is commonly used to analyse vibration behaviour in a frequency domain. However, for an unstable process, a Fourier transform cannot indicate how process features will change over time. In recent years, jointed timefrequency analysis has become popular as a method to overcome the drawback of a conventional Fourier transform. A STFT is a popular method for time-frequency analysis. The basic idea of a STFF, is to split a non stationary signal, into segments in a time domain by the proper selection of a window function; and then to carry out a Fourier transform on each of these segments separately. This process delivers an instantaneous spectrum. STFT decomposes time-varying signals into time-frequency domain components; hence Fig.1 Signals over a time-frequency domain for 4 grinding cuts after filtering with a band pass Chebchev II filter The objective of using STFT is to unify information from both a time and frequency domain, in order

3 58 International Journal of Automation and Computing 1 (2006) to provide more detailed information suitable for classification algorithms. 4 Support vector machines SVMs have been recognised as powerful machine learning tools, with good theoretical properties for convergence and generalisation. They were first introduced by Vapnik in the late 1960s [14] on the foundation of statistical learning theory; which is a general mathematical framework for estimating dependencies from empirical and finite data sets. The basic idea of a SVM is to determine a classifier machine that minimizes structural risk consisting of empirical error, and the complexity of a model leading to good generalization error. It can deal with both binary problems and multi-class problems. A classification problem, can be restricted to the consideration of a two-class problem without loss of generality. The aim is to separate two classes by a function induced from available examples, and produce a classifier that will work well on unseen examples. Assuming data to be classified is linearly separable, there will be many possible linear classifiers or functions that can be used to separate the data; but there is only one linear function that maximizes margin. A hyperplane can be defined using a number of support vectors, which can draw a boundary between the two classes. In non-linear cases, the use of support vectors allows complex boundaries to be created. Through the minimisation of a quadratic programming problem, the margin of separation between each class can be maximised. Nearest data points are used to define the margin, and are known as support vectors. Once support vectors contain all needed information, the SVM function then becomes a classifier. 4.1 Basic principle of support vector machines A SVM can be considered as simply creating a line, or a hyperplane, between two sets of data, as shown in Fig.2. It attempts to place a linear boundary between two different classes of data, and orientate it in such a way that margin is maximized. In other words, it is used to maximize the distance between the nearest data points, or boundary, of each class. A boundary is then placed in the middle of the margin between the two classes. Therefore the problem becomes: Minimize 1 2 w 2 (2) Subject to y i ((w x i ) + b 0, i = 1,,l (3) where the weighting vector w defines the direction of the separating hyperplane f(x), and b (bias), defines the distance of the hyperplane from the origin. The problem can be solved by using a Lagrange multiplier, as given in equation 4: L(w, b, α) = 1 m 2 (w w) α i [y i ((w i x i ) + b) 1]. (4) j=1 Therefore the optimal problem in (2) is equivalent to the maximization of the objective function shown in (5). Maximize: Fig.2 A hyperplane classifier towards a non-separable data set L(α) = Subject to: α i 1 2 y i y j α i α j (x i x j ) (5) i,j=1 y i α i = 0, α i 0, i = 1,,l. (6) The problem of classifying a new data point x, is solved simply by looking at the value of the following hyperplane decision function: f(x) = sign(w x + b ) (7) where the weight vector w, is calculated from function (8): w = y i α i x i (8)

4 Xun Chen et al./ Monitoring Grinding Wheel Redress-life Using Support Vector Machines 59 and b has to be calculated by making use of primal constraints, due to it s appearance in the dual problem in (9): b = max y i= 1( w x i ) + min y( w x i ). 2 (9) An unknown data example x is then classified as follows: { Class I, if f(x) > 0 x. (10) Class II, otherwise So far training data is assumed to be linearly separable. In cases where training data cannot be linearly separated, as in the example shown in Fig.2, non-negative slack variables ξ i are introduced to form equations 11 and 12, so as to produce a non-linear problem. In equation 11, the sum of slack variables is multiplied by a parameter C, which is chosen by a user. A larger C corresponds to a higher penalty for errors. This corresponds to the addition of an upper bound C to α i. In both cases, the decision function in (equation 7) is equivalent, and given by: Minimize: 1 2 w 2 + C ξi k (11) Subject to: y i ((w x i ) + b) 1 ξ i, ξ i 0, i = 1,,l. (12) Then an unknown data example x is classified as follows: { Class I, if f(x) > 0 x. (13) Class II, otherwise The above SVM classifier is an important concept for the analysis and construction of more complicated SVMs. 4.2 Nonlinear kernel mapping In the case where a linear boundary is inappropriate, the transformation of vector x into a higher dimensional feature space is required. The transformation into a higher-dimensional feature space requires relatively intensive computation. It is possible to calculate a kernel which is the inner products of a feature space, in an original data space i K(x i, x j ) = Φ(x i )Φ(x j ). (14) The idea of a kernel function, is to enable operations to be performed in an input space, rather than in a high dimension feature space. It is not necessary to know an actual mapping function Φ, hence there is no need to evaluate an inner product in the feature. Therefore in this case, a dot product (x i x j ) can be replaced with K(x i, x j ) in the algorithm. The SVM computes a value for α i that corresponds to the maximal margin hyperplane in the feature space, by replacing different kernel functions in (x i x j ). There are some common examples of kernel functions for mapping vectors in feature spaces. These include: Radial Basis Function kernel Polynomial Kernel Sigmoid function K(x i, x j ) = e xi xj 2 /2σ 2 (15) K(x i, x j ) = (x i x j + 1) d (16) K(x i, x j ) = tanh(x i x j θ). (17) In which the decision function will be: { } f(x) = sign α i y j K(x i, x j ) + b. (18) In this case, the unknown data example is classified in the following way: { Class I, if f(x) = 1 x Class II, if f(x) = 1. (19) 4.3 Least square support vector machines An original SVM, may not be suitable in practice, due to its time consumption during the computation of quadratic programming. A least square SVM, was developed by Suykens and Vandewalle for solving pattern recognition and non-linear function estimation problems [15]. The SVM equation modification developed by Suykens, is as follows: Minimize: 1 2 w 2 + C 1 ξi 2 (20) 2 Subject to: y i ((w x i ) + b) = 1 ξ i, ξ i 0, i = 1,,l. (21) The classifier in a dual space, is similar to the standard SVM case. { } f(x) = sign α i y j K(x i, x j ) + b i (22) Where α i are Lagrangian multipliers. The application of conditions for optimality yield the following linear KKT (Karush-Kuhn-Tucker) system: [ 0 y T y Ω + C 1 I ] [ ] b α [ 0 = 1 v ]. (23)

5 60 International Journal of Automation and Computing 1 (2006) Where: Ω = Z T Z, Z T = (y 1 Φ(x 1 ),, y n Φ(x n )), Y T = (y 1,, y n ), 1 v = (1,,1) and α = (α 1,, α n ). Then: Ω = ψ(x i, x l ) = Φ(x i ) T Φ(x l ), i, l = 1,,N. (24) By applying the kernel to the Ω matrix in equation 23, classifier function estimation becomes: { } f(x) = sign α i y j K(x i, x j ) + b. (25) The Vapnik formulation is modified here in two ways. First, instead of the inequality constraints (equation 21), one takes equality constraints, in which the value 1 on the right hand side is considered as a target, rather than a threshold value. Upon this target value, an error variable ξ i is applied, such that misclassifications can be tolerated in the case of overlapping distributions. These error variables play a similar role to the slack variable ξ i, in SVM formulations. Second, a squared loss function, as shown in equation 20 is taken for the error variable, as these modifications will greatly simplify the problem [11]. LS-SVM, offers most of the properties of the original SVM, such as great generalization capacity. Nonlinear problems can be solved by mapping data into a high dimension feature space using kernel methods. It is excellent for classifying a problem with an unseen data example. However, the greatest advantage of the LS-SVM is faster computational time, which is a key requirement for online condition monitoring. 5 Grinding process monitoring using SVM A set of grinding experiments were carried out on a Makino A55 CNC machine centre. A workpiece was ground using a VIPER wheel. Grinding depth of cut was 1 mm; grinding speed 35 m/s; and workpiece speed 1000 mm/min. Workpiece material was Inconel 718. Grinding forces were recorded using a LABVIEW program and data analysed using programs written within a MATLAB environment. Signal features extracted using a STFT program were sent to the SVM program to classify grinding conditions. A 3D view of the STFT spectrums of grinding force during 4 sequential grinding cuts, are illustrated in Fig.3. It can be seen that the feature frequency components of dynamic forces, increase with grinding time. The first classification test in the trials, was to identify air cutting, and actual grinding, grinding force signals. These were obtained by applying a moving average method to remove high frequency components of grinding forces. Analysis was carried out using a MATLAB LS-SVM toolbox [15]. A Radial Basis Function (RBF) kernel was selected for classification. This method can distinguish air cutting and actual grinding clearly, as shown in Fig.4, where the LS-SVM gives 1 for air cutting and 1 for actual grinding. The results from both training, and test sets, are completely satisfactory. Surprisingly, the method coped well with environmental noise, and the disturbance of coolant dynamic force did not affect its judgement. Fig.3 A 3D spectrogram of normal grinding force components during 4 sequential cuts Fig.4 Grinding detection using SVM Once actual grinding took place, another SVM classification program was employed to monitor the condition of the grinding wheel. The input signals of the SVM were, grinding forces, grinding power, and dynamic features extracted from grinding forces. The dynamic features of grinding forces were taken by using a STFT program. Force signals were pre-processed using a Chebychev II band-pass filter to reduce the influence

6 Xun Chen et al./ Monitoring Grinding Wheel Redress-life Using Support Vector Machines 61 of noise. The Radial Basis Function kernel was used in this SVM monitoring process. Fig.5 shows projections of the monitored force, power signals, and STFT spectrum, as grinding time functions during 4 grinding cuts. The output of the SVM, which is plotted on the lower part of the graph, clearly indicates the development of grinding chatter. The value 3 indicates good wheel condition, while a value 1 highlights the presence of grinding chatter. redress-life, as shown in Fig.6. In this experiment, grinding chatter developed intermittently. During the 4 th cut, chatter occurrence was greater than 50%. Therefore, the wheel should have been redressed after the 4 th cut, before continuous chatter occurred. The longer redress-life of the wheel was due to the lower grinding force generated at a higher grinding speed. Further experiments using different grinding conditions, (wheel speed: m/s, depth of cut: 1 2 mm and work speed: 1 2 m/min), also indicate that the SVM tool is a feasible method with which to monitor grinding wheel life. Fig.5 Grinding chatter monitoring using SVM It can be seen from Fig.5 that the development of grinding chatter is not an instantaneous event. A certain time period is required before continuous chatter is established. This is because the development of grinding chatter is the result of grinding wheel wear. As mentioned previously, grinding wheel wear involves two phenomena, attritious wear causing blunt cutting edges, and fracture wear creating sharp cutting edges. The sharpness of a grinding wheel depends on the equilibrant situation of different wear mechanisms. An occasional presence of grinding chatter does not require the redressing of a grinding wheel. However, continuous grinding chatter is dangerous to a grinding operation. It is rational to define that a greater than 50% level of chatter in one grinding cut, is an indicator of the end of a wheel s redress-life. Therefore, a SVM can be used for grinding wheel life monitoring. This is validated by the results illustrated in Fig.5. During a second grinding cut, chatter presence was 5%, which meant that grinding was normal for the remainder of the grinding operation. However, as chatter presence in the third cut was 55%, it indicates that the grinding wheel requires redressing. Without redressing, grinding chatter will occur continuously, as shown in Fig.5. If grinding wheel speed is increased to 55 m/s, a SVM can still provide a good indication of wheel Fig.6 Grinding chatter monitoring using SVM 6 Conclusions Condition monitoring using SVMs is feasible, and can ensure consistent production quality. In this paper, it has been successfully demonstrated that grinding process performance can be monitored, and identified, using a LS-SVM algorithm. Test results are satisfactory, since a LS-SVM can give good classification with a small quantity of training data and time. Using a decision support algorithm, the behaviour of a grinding process can be seen to relate to grinding wheel condition. In future work, more sensors will be applied to study chatter, and other defects which can occur during the grinding process, to provide more accurate process information. The development of a real-time remote diagnostic system, will provide manufacturers with precise and reliable information for managing and conducting manufacturing activities. References [1] H. Y. Kim, S. R. Kim, J. H. Ahn, S. H. Kim. Process monitoring of centerless grinding using acoustic emission. Journal of Materials Processing Technology, vol. 111, no. 1-3, pp , [2] Janez Gradisek, Andreas Baus, Edvard Govekar, Fritz Klocke, Igor Grabec. Automatic chatter detection in grinding. International Journal of Machine Tools and Manufac-

7 62 International Journal of Automation and Computing 1 (2006) ture, vol. 43, no. 14, pp , [3] Pawel Lezanski. An intelligent system for grinding wheel condition monitoring. Journal of Materials Processing Technology, vol. 109, no. 3, pp , [4] X. Chen, W. B. Rowe, Y. Li, B. Mills. Grinding Vibration Detection Using a Neural Network. the Journal of Engineering Manufacture, Proceedings of IMechE Part B, vol. 210, B4, , [5] B. Samanta. Gear fault detection using artificial neural networks and support vector machines with generic algorithms. Mechanical Systems and Signal Processing, vol. 18, no. 3, pp , [6] Lijuan Cao. Support Vector Machines experts for time series forecasting. Neurocomputing, vol. 51, pp , [7] M. A. Mohandes, T. O. Halawani, S. Rehman, Ahmed A. Hussain. Support vector machines for wind speed prediction. Renewable Energy, vol. 29, no. 6, pp , [8] Cosimo Distante, Nicola Ancona, Pietro Siciliano. Support vector machines for olfactory signals recognition. Sensors and Actuators, vol. B, no. 88, pp , [9] Yingjie Wang, Chin-Seng Chua, Yeong-Khing Ho. Facial feature detection and face recognition from 2D and 3D images. Pattern Recognition Letters, vol. 23, no. 10, pp , [10] Steve R. Gunn. Support Vector Machines for Classification and Regression. Technical Report, School of Electronics and Computer Science, Faculty of Engineering and Applied Science and Department of Electronics and Computer Science, [11] J. A. K. Suykens, T. V. Gestel, J. D. Brabanter, B. D. Moor, J. Vandewalle. Least squares support vector machines, World Sciencetific Publishing Co. Pte. Ltd, Singapore, [12] M. Kemal Kiymik, Inan Guler, Alper Dizibuyuk, Mehmet Akin. Comparison of STFT and wavelet transform methods in determining epileptic seizure activity in EEG signals for real-time application. Computers in Biology and Medicine, vol. 35, no. 7, pp , [13] S. Qian, D. Chen. Joint time-frequency analysis: methods and applications, Prentice Hall Inc, Upper Saddle River, NJ, [14] Vladimir N. Vapnik. The Nature of Statistical Learning Theory, Springer-Verlag New York, Inc., New York, USA [15] K. Pelckman, J. A. K. Suykens, T. V. Gestel, J. D Brabanter, L. Lukas, B. Hamers, B. D. Moor, J. Vandewalle. A Matlab/c toolbox for least square support vector machines. ESAT-SCD-SISTA Technical Report Xun Chen received his B. Eng. degress from Fuzhou University. He received his M. Sc. degree from Zhejiang University and his Ph. D. degree from Liverpool John Moores University. He has been a visiting professor to Fuzhou University since Dr. Chen has published more than 100 research papers. He is a founder member of the International Committee of Abrasive Technology. Before his employment at Nottingham, Dr. Chen was a lecturer of Mechanical Engineering at the University of Dundee. Prior to that, he was a research fellow, a Royal Society Royal Fellow at Liverpool John Moores University and a lecturer at Fuzhou University. His research interests include advanced manufacturing technology including application of computer science, mechatronics and artificial intelligence to manufacturing process monitoring and control, particularly to the high efficiency precision grinding. Application. Thitikorn Limchimchol received his B. Eng. (honour) degree in manufacturing engineering from University of Nottingham in United Kingdom in Currently he is undertaking his doctorial study on manufacturing engineering in the University of Nottingham. His main research interests include Grinding Technology, Artificial Intelligence, Support Vector Machines, Genetic Algorithm, and Java