A wavelet-based methodology for grinding wheel condition monitoring

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International Journal of Machine Tools & Manufacture 47 (2007) 580–592 www.elsevier.com/locate/ijmactool

A wavelet-based methodology for grinding wheel condition monitoring T. Warren Liaoa,, Chi-Fen Tingb, J. Quc, P.J. Blauc a

Industrial Engineering Department, Louisiana State University, 3128 CEBA, Baton Rouge, LA 70803, USA b Computer Science Department, Louisiana State University, LA, USA c Metals and Ceramics Division, Oak Ridge National Laboratory, USA Received 20 December 2005; received in revised form 21 April 2006; accepted 10 May 2006 Available online 18 July 2006

Abstract Grinding wheel surface condition changes as more material is removed. This paper presents a wavelet-based methodology for grinding wheel condition monitoring based on acoustic emission (AE) signals. Grinding experiments in creep feed mode were conducted to grind alumina specimens with a resinoid-bonded diamond wheel using two different conditions. During the experiments, AE signals were collected when the wheel was ‘sharp’ and when the wheel was ‘dull’. Discriminant features were then extracted from each raw AE signal segment using the discrete wavelet decomposition procedure. An adaptive genetic clustering algorithm was finally applied to the extracted features in order to distinguish different states of grinding wheel condition. The test results indicate that the proposed methodology can achieve 97% clustering accuracy for the high material removal rate condition, 86.7% for the low material removal rate condition, and 76.7% for the combined grinding conditions if the base wavelet, the decomposition level, and the GA parameters are properly selected. r 2006 Elsevier Ltd. All rights reserved. Keywords: Grinding wheel wear; Condition monitoring; Discrete wavelet decomposition; Acoustic emission; Adaptive genetic algorithm; Clustering

1. Introduction Machining is a major manufacturing process involved with material removal. Major machining operations include turning, milling, drilling, and grinding. Among them, grinding is known to be most complicated. All machining operations require a tool. The tool is normally made of some material with a specially designed form. As more materials are removed, the form and properties of the tool are changed. As a result of this change, the machining operation often becomes inefficient and the quality of the machined workpiece is affected negatively most of the time. Tool condition monitoring is thus necessary, especially during critical and/or finishing operations. Traditionally, the tool condition monitoring task is usually carried out by the operator. To realize full automation of machining operations, there has been an earnest interest in developing automated tool condition monitoring technologies. Two major methods can be Corresponding author. Tel.: +1 225 578 5365; fax: +1 225 578 5109.

E-mail address: [email protected] (T. Warren Liao). 0890-6955/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2006.05.008

distinguished: direct and indirect. The direct methods directly evaluate the tool condition using some optical sensor. Kurada and Bradley [1] performed a review of machine vision sensors for tool condition monitoring. Two recent studies that focused on the use of direct method for grinding wheel condition monitoring are Fan et al. [2] and LaChance et al. [3]. The direct methods, however, require stopping the machining operations. On the other hand, the indirect methods rely on some sensory signals such as forces, power, vibration, and acoustic emission (AE) that correlate with the tool condition. They are more popular because no interruption of machining operations is needed. Numerous tool condition monitoring studies that adopt the indirect methods have been published. It is not our intention to review them here. The interested readers shall refer to survey papers such as Dimla [4], Li [5], and Rehorn et al. [6]. This study focuses on using the indirect method to monitor the condition of grinding wheels. A brief review of past research on the specific topic is given below. Mokbel and Maksoud [7] analyzed raw AE signals using a fast Fourier transform (FFT) and compared the AE spectral

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amplitudes of different diamond wheel bond types, grit sizes, and their conditions generated by using different grinding wheel/truing speed ratios with the surface roughness (Ra) of the ground mild steel specimens. Hwang et al. [8] reported that the amplitude of the AE signal, collected in high-speed grinding of silicon nitride using an electroplated single-layered diamond wheel, monotonically increases with wheel wear. To monitor an alumina wheel surface condition in cylindrical grinding of carbon steel, Lezanski [9] extracted statistical and spectral features from multiple signals (forces, vibration, and AE) and applied a feed-forward backpropagation neural network to select eight features, which are grinding depth of cut, coolant volume rate, standard deviation of vibration, means value of vibration power spectrum, range of vibration power spectrum, mean value of AE RMS, range of AE RMS, and range of RMS power spectrum. The eight selected features were used to train a neuro-fuzzy model for classification. A best performance of 83.3% classification accuracy was reported. In their keynote paper on grinding process monitoring, Tnshoff et al. [10] reviewed the sensors used to monitor both the micro- and macro-topography of the active abrasive layer of the grinding wheel, which were recognized as the dominant features of the grinding process. Furutani et al. [11] introduced an in-process method for measuring the topography change of an alumina grinding wheel in cylindrical grinding. A pressure sensor is set beside a

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grinding wheel with a small gap. When grinding fluid is dragged into the gap, hydrodynamic pressure, which corresponds to the gap length and the wheel topography, can be measured. The pressure signals were analyzed by FFT. Higher frequency components of the pressure spectra were found to increase with the wheel loading and dulling. Warkentin and Bauer [12] investigated the relationships between wheel wear and grinding forces for different depths of cut when surface grinding mild steel with an aluminum oxide wheel. For depths of 10, 20, and 30 mm, respectively, the average normal and tangential forces show a trend with a slight positive slope. For depths of 40 and 50 mm, the data show a negative slope and piecewise negative slope, respectively. Hosokawa et al. [13] developed a practical wheel surface condition monitoring system, in which the characteristics of the wheel surface are discriminated on the basis of the dynamic frequency spectrum signals of grinding sound using a neural network technique. The system was successfully tested in the plunge grinding of carbon steel with a vitrified-bonded alumina wheel and in the plunge grinding of hardened die steel with a resinoid-bonded CBN wheel. Kwak and Ha [14] showed that the grinding force signal in surface plunge grinding of STD11 with an alumina wheel could be better processed by wavelet denoising than by FFT filtering. To detect the wheel dressing time clearly, the approximation coefficients A4 of Daubechies wavelet transform were used because they were

Table 1 Summary of grinding wheel condition monitoring studies Reference

Tool state(s)

Grinding conditions

Signal(s) used

Signal analysis

Features

Prediction/ detection algorithm

Test results

Furutani et al. [11]

Fixed

Hydrodynamic pressure Sound

FFT

Not available

Neural network

80–100%

Hwang et al. [8]

Wheel wear

Fixed

AE

Power spectral density

None used

Not available

Kwak and Ha [14]

Wheel loading

Fixed

Force

None used

Not available

Lezanski [9]

Wheel wear

Three depths of cut

Forces, vibration, and AE

Daubechies wavelet transform Statistical and spectral

Spectral amplitude Sound pressure level values within the frequency range at 20 Hz intervals RMS of AE signals, magnitude of peak frequency of AE power spectral density Approximation coefficients A4

None used

Hosokawa et al. [13]

Wheel loading and dulling Wheel wear

Neuro-fuzzy model

83.3% classification accuracy

Mokbel and Maksound [7]

Generated by using different grinding/truing speed ratios

Fixed

AE

8 statistical and spectral features selected by a feed-forward BP neural network Spectral amplitude

None used

Not available

Varied dressing feed

Frequency spectrum

Fast Fourier transform

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suitable for the detection of a sudden signal change at the time or frequency domain. Table 1 summarizes the previous studies in using the indirect method for grinding wheel condition monitoring. Our study differs from those above-reviewed studies in the following aspects: (1) the grinding operation experimented is creep feed surface grinding of alumina materials with a resinoid-bonded diamond wheel; (2) the AE signals are analyzed by wavelet transform rather than by FFT (note that wavelet transform was used by Kwak and Ha to analyze force signals, not AE signals as done here); (3) the decision algorithm is a unsupervised genetic clustering rather than supervised classification algorithms such as neural networks used by Hosokawa et al. and neural fuzzy models used by Lezanski. In the next section, grinding experiments carried out for this study and sample AE signals collected for analysis are shown. Section 3 describes the discrete wavelet decomposition algorithm used to analyze and extract features from raw AE signals. Section 4 presents the adaptive genetic clustering method developed for unsupervised classification of two wheel states: ‘‘sharp’’ and ‘‘dull’’ based on the extracted features. The test results are given in Section 5, followed by the discussion. The last section concludes the paper and identifies possible topics for future research. 2. Grinding experiments and AE signals The grinding experiments were performed on the 10horsepower K.O. Lee Vigor Creep Feed Grinder using a resin-bonded diamond wheel (Norton SD220 R75 B56 1/8 of 229 mm diameter) to grind alumina materials (Coors AD995 CAP3). The experimental setup is shown in Fig. 1. The grinding procedure has the following steps: (1) True the wheel using the procedure detailed in Subsection 2.1. (2) Dress the wheel using the procedure detailed in Subsection 2.2. (3) Grind a block of alumina to stabilize the wheel. (4) Grind an alumina specimen to check the steady-state performance of the wheel using selected grinding conditions with the monitoring system on. (5) Grind the alumina block more to reach the worn-out state of the wheel. (6) Grind another alumina specimen to check the worn-out state performance of the wheel using selected grinding conditions with the monitoring system on. During grinding, the workpiece was flooded with copious amount of coolant (water diluted CIMTECH 500 with 20:1 ratio according to the manufacturer’s instruction) with flow rate measured at about 10 gallons per minute (gpm). The grinding process was monitored with multiple signals including 3-component forces, spindle power, vibration, and AE (raw as well as root mean square).

Accelerometer & Power transducer

Data acquisition & display

Diamond wheel

Ceramic Magnetic chuck Dynamometer Work table

AE sensor

CNC Surface Grinder Fig. 1. Experimental setup.

The raw AE signals were collected at 1 MHz and the other signals were sampled at 4096 Hz. The dynamometer is Kistler 9255B, which was mounted on the magnetic table and the fixture for holding the specimen was placed on top of the dynamometer. The maximum load allowed along y which measures the normal force on the KO Lee grinder is 1000 N, which turns out to be a major limitation. The accelerometer was placed behind the wheel spindle casing. The AE sensor (Physical Acoustics) was mounted on the side of dynamometer. The fixed grinding parameters include wheel speed which was set at 3232 m/min (4500 rpm), and grinding width which was set at 11.43 mm. Two combinations of work speed and depth of cut were used to grind the alumina specimens: one with 8.47 mm/s work speed and 1.27 mm depth of cut (the high material removal rate condition) and another with 1.67 mm/s work speed and 1.02 mm depth of cut (the low material removal rate condition). Fig. 2 shows samples of segmented AE raw signals acquired at wheel steady state (the ‘sharp’ wheel condition) and wheel worn out (the ‘dull’ wheel condition) state for each one of the two grinding conditions experimented. The corresponding wheel surface in ‘sharp’ condition captured by the indium imprint technique is shown in Fig. 3. Unfortunately we failed to capture a good image for the ‘dull’ condition of the same wheel. Nevertheless, we expect that the grits in ‘dull’ condition are quite flat compared with those in ‘sharp’ condition. Each AE signal segment has 4000 data points, which equal to approximately a duration of 0.3 grinding wheel revolution. The segment size is chosen based on two competing considerations: to shorten the processing time and to retain sufficient amount of information. Based on our preliminary analysis, segment size of 4000 data points is found to work well. Note that for

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Fig. 2. Segmented AE raw signals for (a) high MRR and (b) low MRR.

better visualization in each figure 3 V was added to every point of the top series; 2 V was added to every point of the second top series; and 1 V was added to every point of the second bottom series. Original data values were processed in the subsequent analyses.

2.1. Truing procedure A hydraulic powered truing device, namely Norton AX-1416, with a diamond truing wheel (Norton SD40N90MSA-0.5) mounted on it was used to true the

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Fig. 3. A local area of wheel surface in ‘sharp’ condition.

diamond grinding wheel selected for this study. The truing device was magnetically held on the table with its truing wheel spindle aligned parallel to the grinding wheel spindle. The truing parameters were 2.963 mm/s (700 /min) cross feed, 0.0254 mm (0.000100 ) down feed, and grinding wheel spindle speed of 4500 rpm. The wheel surface was marked with red crayon before truing. Based on the condition of the wheel, a total down feed amount was chosen to run the truing operation. To prevent overheating the truing device, a maximum total down feed of 0.127 mm (0.00500 ) was set in each run. The wheel was visually checked after each program run. The truing procedure was repeated until all red marks were cleanly removed and the wheel surface was smooth when felt with finger. 2.2. Dressing procedure Once trued, the wheel was dressed to open up the diamond grains using alumina dressing sticks made of various grain sizes, going from rough to fine. The question of when the wheel is properly dressed was determined primarily based on the operator’s feel of resistance in the dressing operation. 3. Signal processing and feature extraction Sensory signals are time series data. For continuous online monitoring, signal data can accumulate quickly like stream data. Ideally, only signals during grinding operation shall be collected to save space and to prevent the need for preprocessing to separate the grinding signals from nongrinding signals. To ease subsequent processing, the grinding signals are typically segmented and undergo dimensionality reduction. The process of dimensionality reduction is to transform the raw signal segments into a transformed space using a specific transformation function. To achieve dimensionality reduction some subset of the transformed coefficients are selected as features or go

through another step of reduction. These features form a feature space which is simply a projection of the transformed space and serve as the basis of subsequent operations such as clustering and classification. Various transformation functions have been used. These functions either work in the time domain or in the frequency domain. This paper focuses only on the latter, particularly the wavelet transform method. It is well known that Fourier transform is a useful tool for transforming a signal (time series) from the time domain to the frequency domain. The Fourier transform is based on the simple observation that every signal can be represented by a supposition of sine and cosine waves. The Discrete Fourier Transform (DFT) and Discrete Cosine Transform (DCT) are efficient forms of the Fourier transform often used in various applications including tool condition monitoring. However, they are not capable of identifying non-stationary transient information. Wavelet transforms are more powerful and versatile than the Fourier transform due to the following properties:



  

Some wavelet transforms have compact support, thus are able to capture local time-dependent properties of data, whereas Fourier transforms can only capture global properties. Wavelet transforms are more efficient even when compared with the FFT. The wavelet transform is hierarchical and allows much fine tuning for a variety of applications. Unlike the Fourier transform, wavelet transforms have an infinite set of possible basis functions.

In Subsection 3.1, the basics of wavelet transforms commonly used in tool condition monitoring are presented. Our use of discrete wavelet transform (DWT) to extract features for this study is described in Subsection 3.2. 3.1. Basics of wavelet transforms The continuous wavelet transform of a function or signal f corresponds to the decomposition of f on the family of wavelets, cs,t(x), generated from one single function c (the mother wavelet) by dilatations and translations, Z 1 f ðxÞcs;t ðxÞ dx; (1) CWTf ðs; tÞ ¼ 1

 x  t cs;t ðxÞ ¼ s1=2 c . s In Eq. (1), the variables x, scale s, and translation t are all continuous and there is a redundancy in the CWT representation of f(x). For most practical applications, we would like to remove this redundancy. To this end discrete wavelets were introduced. Discrete wavelets are not continuously scalable and translatable, but can only be scaled and translated in discrete steps. A special case occurs when (s, t) are samples of a dyadic grid as s ¼ s0 j and

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t ¼ kt0 s0 j. These choices of s and t enable certain c to produce orthonormal cs,t(x). For computational efficiency, s0 ¼ 2 and t0 ¼ 1 are commonly used. Accordingly discrete wavelets are created as   x  k2j cj;k ðxÞ ¼ 2j=2 c . (2) 2j The variables j and k are integers that scale and translate the mother wavelet function to generate a family of discrete wavelets. The numbers of translations are limited by the duration of the signal under investigation. The number of scales is usually chosen as a power of 2. To cover the remaining spectrum not covered by dilations, the scaling function was introduced. There are many different ‘‘mother wavelets’’ that have been developed for wavelet transforms. The most simple one is the Haar wavelet. It is a step function taking values 1 and 1 on [0, 1/2] and [1/2,1], respectively. Being not continuous is an obvious disadvantage of the Haar wavelet. Ingrid Daubechies constructed a set of wavelet orthonormal basis functions that are perhaps the most elegant, and have become the cornerstone of wavelet applications today. Within each family of wavelets (such as the Daubechies family) are wavelet subclasses distinguished by the number of coefficients and by the level of iteration. In many practical applications the signal of interest is sampled. In this case, the DWT is needed. The DWT represents a one-dimensional (1D) signal of length N in terms of shifted versions of a low-pass scaling function f(x) and shifted and dilated versions of a prototype band-pass wavelet function c(x) as follows: f ðxÞ ¼

X

aj 0 ;k fj 0 ;k ðxÞ þ

1 X X j¼j 0

k

d j;k cj;k ðxÞ,

(3)

k

where j0 is an arbitrary starting scale and the aj 0 ;k and dj,k are real-valued ‘approximation’ and ‘detail’ expansion coefficients. In discrete multiresolution wavelet analysis, the approximation and detail coefficients at all resolutions are obtained by convolving the signal with a pair of quadrature mirror filters at different scales. The filters are composed of a high-pass filter, H(k), and a low-pass filter, L(k), that are used to obtain, respectively, the detail and approximation components of the signal. The relationship between high-pass and low-pass filters and the corresponding wavelet and scaling functions can be expressed as fðxÞ ¼

L1 pffiffiffi X

2

L½kfð2x  kÞ;

k¼0

cðxÞ ¼

1 pffiffiffi X 2 H½kfð2x  kÞ;

ð4Þ

k¼2L

where L½k ¼ 1=2hfðx=2Þ; fðx  kÞi, and H½k ¼ ð1Þk L½1  k. Accordingly, the filters for commonly used wavelets have been derived. The wavelet packet transform is a generalization of the procedure described above. The wavelet transform applies

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the transform step only to the low-pass result whereas the wavelet packet transform applies the transform to both the low-pass and the high-pass results. This provides the possibility to zoom into any desired frequency range for further decomposition. 3.2. Wavelet-based feature extraction The multilevel 1D wavelet decomposition function, wavedec, available in Matlab is chosen with the Daubechies wavelets (db1 which is the same as Haar wavelets) specified. It returns the wavelet decomposition of the signal X at level N. The decomposition process is iterated, with successive approximations being decomposed in turn, so that one signal is broken down into many lower resolution components. The result is called the wavelet decomposition tree. Twelve levels are initially chosen to decompose our AE signal data. Fig. 4 shows the 11-level wavelet decompositions of two segmented AE signals given in Fig. 2. The effect of using other decomposition levels is discussed in Section 6. The energy of each decomposed component at the node of the tree is computed. The energy of a signal is the sum of the squares of its values. For an N level decomposition, the number of extracted feature is N+1. For each AE signal segment shown in Fig. 3 and 12 features are thus extracted. Table 2 gives 16 samples of 12-feature values extracted from the decomposed signals according to the procedure described in this section. Note that for both conditions (samples 1–8 from the high MRR condition and samples 9–16 from the low MRR condition), a ‘dull’ wheel (with ‘e’ at the end of the file name) generally has higher energy values at the high-frequency bands (from d1 to d8) than a ‘sharp’ wheel. All of these features form a high-dimensional feature vector and the clustering algorithm presented in the next section basically put a feature vector being considered into the cluster that its medoid has a lower dissimilarity (measured by Euclidean distance) with the feature vector. Our approach thus differs from a thresholding approach, which usually chooses a dominant feature and set a threshold value; the wheel state is declared changed if the corresponding feature value crosses the set threshold. 4. An adaptive genetic clustering algorithm According to Mitchell [15], genetic algorithms are known to have the following elements: population of chromosomes, selection according to fitness, crossover to produce new offspring, and random mutation of new offspring. Essentially, our adaptive genetic clustering algorithm implements the k-medoid algorithm. Each chromosome is binary coded denoting the data records chosen as the cluster medoids. The pre-specified number of cluster medoids and the number of digits used to represent each medoid together determine the chromosome length. Each chromosome in the population is evaluated in two steps: first distributing each data point to the closest medoid

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according to the distance measure and then computing the fitness value. The cluster of each datum is determined to be the one medoid most close to it based on the nearestneighbor concept. The fitness function employed in our genetic clustering algorithm is modified from a validity index originally developed for determining the optimal number of clusters. The fitness function is 104/VSV, where VSV stands for the VSV index proposed by Kim et al. [16]. VSV is defined as follows: c X 1X n VSV ¼ ð j¼1 d E ðxj ; vi ÞÞ c i¼1

, ni þ

c , min d E ðvi ; vj Þ

(5)

iaj

where xj denotes each feature vector, n is the number of data records, vi denotes a cluster medoid, c is the number of clusters, and dE is the Euclidean distance. Note that the fitness value is set to zero whenever there is a cluster with no members in it. Based on our tests, this simple strategy

has been proved effective to discourage the formation of empty clusters. Standard roulette wheel selection is used to reproduce offspring for the next generation. Each current chromosome in the population has a roulette wheel slot sized in proportion to its fitness. Chromosomes with a higher fitness value thus have a higher probability of contributing more offsprings. Pairs of chromosomes are randomly chosen to perform the one-point crossover operation according to a specified probability. The mutation is then performed to flip some of the bits in a chromosome from ‘‘0’’ to ‘‘1’’ or ‘‘1’’ to ‘‘0’’ according to the specified probability of mutation. If the resultant chromosome contains an invalid cluster medoid, its fitness is then set to zero to prevent it surviving to the next generation. Our adaptive genetic clustering algorithm has the ability to adapt its mutation rate and crossover rate. The adaptive scheme follows that of Srinivas and Patnaik [17] proposed for multimodal function optimization to realize the dual goals of maintaining diversity in the population and

Fig. 4. Wavelet decomposition of (a) hh2 and (b) hh2e AE signals shown in Fig. 2(a).

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Fig. 4. (Continued)

Table 2 Sample 12-feature values extracted by discrete wavelet decomposition Sample

Raw

a11

d11

d10

d9

d8

d7

d6

d5

d4

d3

d2

d1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

hh1 hh1 hh2 hh2 hh1e hh1e hh2e hh2e llh1 llh1 llh2 llh2 llh1e llh1e llh2e llh2e

0.04 0.03 0.07 0.01 0.02 0.02 0.02 0.02 0.20 0.20 0.41 0.41 0.03 0.03 0.02 0.05

0.03 0.00 0.07 0.13 0.02 0.04 0.03 0.05 0.38 0.40 0.21 0.01 0.07 0.03 0.00 0.04

0.09 0.06 0.03 0.02 0.00 0.02 0.04 0.02 0.18 0.14 0.07 0.17 0.06 0.00 0.07 0.07

0.15 0.10 0.18 0.34 0.16 0.13 0.15 0.35 0.06 0.24 0.13 0.10 0.08 0.03 0.06 0.05

0.20 0.09 0.19 0.43 0.49 0.26 0.88 0.88 0.10 0.06 0.22 0.09 0.32 0.16 0.30 0.22

0.45 0.63 0.37 0.47 1.00 1.07 1.83 1.82 0.16 0.19 0.38 0.38 0.53 0.29 0.42 0.30

0.78 0.87 0.93 1.08 1.74 2.01 2.29 4.58 0.37 0.38 0.52 0.80 1.01 0.36 1.41 1.13

3.25 3.13 3.16 2.90 4.40 4.05 5.86 7.51 0.98 0.84 2.35 1.73 2.07 2.04 3.32 2.44

5.12 5.81 5.25 6.31 8.71 8.37 12.48 12.24 2.29 2.35 3.99 3.78 5.17 4.60 5.57 4.86

31.82 35.23 36.06 34.98 41.33 39.34 51.77 48.90 15.29 14.92 22.79 24.73 29.42 27.31 40.54 36.28

84.63 86.33 73.03 79.00 81.28 79.83 84.37 92.07 34.63 36.64 57.70 61.39 60.54 60.79 78.05 73.48

37.39 38.50 33.44 35.65 39.20 38.52 40.28 41.58 15.76 16.26 26.73 27.70 31.27 29.43 35.54 33.27

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8

Fitness Value

7 6 5 4 3 2

Avg fitness Max fitness

1 0 0

5

10

15 Generation No.

20

25

30

Fig. 5. Evolution of average fitness and maximum fitness of a GA run.

sustaining the convergence capacity of the GA. The adaptive GA varies the probabilities of crossover and mutation depending upon the fitness values of the solutions. Let fmax and favg be the maximum fitness and the average fitness of the entire population, and f0 be the larger of the fitness values of the two solutions to be crossed. The expressions for pc and pm are given as ( k1 ðf max  f 0 Þ=ðf max  f avg Þ; f 0 Xf avg pc ¼ (6) k3 ; f 0 of avg and pm ¼

(

k2 ðf max  f Þ=ðf max  f avg Þ; k4 ;

f Xf avg f of avg

(7)

where k1, k2, k3, k4p1.0. The k2 and k4 values are set at 0.5 to ensure the disruption of those solutions with average/ sub-average fitness. To force all solutions with a fitness value less than or equal to the average fitness to undergo crossover, k1 and k3 values are set equaling to 1. All GA runs in this study initially use a constant population size of 50 and stop at 25 generations of evolution. To evaluate the sensitivity of the adaptive genetic clustering algorithm to the initial population, each genetic clustering task is repeated five times and the mean and the standard deviation of the clustering accuracy are computed. Fig. 5 shows the evolution of the average and maximal fitness value of a GA run. The disruptive trend was caused by the adaptive scheme in changing the rate of crossover and the rate of mutation in order to explore other areas of the search space. The effects of three GA parameters are discussed in Section 6. 5. Test results The adaptive genetic clustering algorithm was applied to four sets of feature values with each set extracted using the procedure described in the previous sections from AE signals sampled during the grinding experiments. The first set has 30 records covering two different wheel states: ‘sharp’ and ‘dull’ for the high material removal rate condition. The average and standard deviation of cluster-

ing accuracies out of five runs are 97.3% and 3.7%, respectively. The second and third set also has 30 records covering the same two different wheel states for the low material removal rate condition. The third set differs from the second set only in including different AE signal segments from the same raw signal. The average and standard deviation of clustering accuracies out of five runs for the second data set are 76.7% and 7.5%, respectively. The same for the third data set are 84.7% and 1.8%, respectively. This indicates that sampling from different sections of the raw signals could affect the clustering accuracy as much as 8%. Compared with the first data set, the accuracy of the second and third set is 20% and 13% lower, respectively. The lower accuracy is caused primarily by the closeness between the dull wheel state in down grind (file with label ‘llh1e’) and the sharp wheel state in up grind (file with label ‘llh2’). The fourth set combines the first set and the third set. The average and standard deviation of clustering accuracies out of five runs for the fourth data set are 66.3% and 8.8%, respectively. The clustering accuracy is further reduced because the high-frequency energy for the sharp wheel state at high material removal rate condition (files with label ‘hh1’ and ‘hh2’) is higher than the dull wheel state at low material removal rate condition (files with label ‘llh1e’ and ‘llh2e’) and closer to the dull wheel state at high material removal rate condition (files with label ‘hh1e’ and ‘hh2e’). Fig. 6 shows the multisensor signals acquired in grinding the alumina specimens using the low material removal rate condition when the wheel is sharp (files labeled ‘llh1’ and ‘llh2’) and dull (files labeled ‘llh1e’ and ‘llh2e’), respectively. It can be visually observed that the average magnitude of nearly all sensory signals is higher for a dull wheel than for a sharp wheel. Signal magnitudes, however, are easily affected by cutting condition as well. Both time domain analysis, i.e., autoregressive (AR) modeling, and frequency domain analysis, i.e., discrete wavelet decomposition, were carried out to analyze these signals and to extract features. The results indicate that the extracted features from these signals are not discriminant for distinguishing different grinding wheel conditions. The most likely reason is that there is insufficient amount of

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Fig. 6. Multisignals sampled at 4096 Hz in grinding an alumina specimen at low material removal rate condition when the wheel is (a) sharp, (b) dull.

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information in the signals acquired at low sampling rate of 4906 Hz. If the sampling rate is high enough, it is expected that the proposed methodology will work on them as well as reported above.

6. Discussion There are several parameters in the proposed unsupervised grinding wheel condition monitoring methodology that could affect the performance. Related to the wavelet decomposition procedure are the decomposition level and the base wavelet. The results presented above are based on 11-level decomposition and the Haar wavelet. As far as the adaptive genetic clustering algorithm is concerned, relevant parameters include the fitness function, population size, 2nd Data Set Mean Clustering Accuracy

1.0000

0.8000 db1 db2 db3

0.6000

0.4000 2

4

6

10

8

12

14

Number of Features (Decomposition Level +1) Fig. 7. Average clustering accuracy as a function of decomposition level for the second data set.

and maximum number of generations set to stop the evolution process. The results presented above were obtained by using a modified VSV as the fitness function, population of 50, and maximum number of 25 generations. In this section, we first discuss how the results change when the decomposition level is varied and other base wavelets are used. Fig. 7 plots three curves for three base wavelets used, i.e., db1, db2, and db3, in clustering the second set of AE signal segments. For each curve, the decomposition level is varied from 2 to 12. The results indicate that: (1) the maximum average clustering accuracy is 86.7%, which can be achieved by using db1 with 7 levels of decomposition and using db2 with 4 levels of decomposition; (2) the highest average clustering accuracy that can be attained by db3 is 85.3% with 2 levels of composition; and (3) the optimal level of decomposition clearly changes with the base wavelet used. The lesson learnt is that effort must be made to find the best base wavelet and the optimal level of decomposition in order to devise a better condition monitoring methodology. By doing so, an improvement of 10% clustering accuracy on average can be achieved over arbitrarily selecting a base wavelet and a decomposition level, as done in the previous section. Fig. 8 plots the feature values obtained by using 7-level db1. Similar to that shown in Table 2, a ‘dull’ wheel again has higher energy levels at the higher frequency bands (d1–d3) than a ‘sharp’ wheel. The above results motivate us to repeat the test on the combined data (the fourth data set) to see whether similar

7-level db1

Energy

80 sharp 1 sharp 2 sharp 3 sharp 4 sharp 5

60 40 20

dull 1 dull 2 dull 3 dull 4 dull 5

0 1

2

3

4 5 Feature No.

6

7

8

Fig. 8. Feature values obtained by 7-level db1.

4th Data Set Mean Clustering Accuracy

0.8 0.7 0.6 0.5

db1

db2

db3

0.4 2

4 6 8 10 12 Number of Features (Decomposition Level +1)

14

Fig. 9. Average clustering accuracy as a function of decomposition level for the fourth data set.

ARTICLE IN PRESS T. Warren Liao et al. / International Journal of Machine Tools & Manufacture 47 (2007) 580–592

improvement can be made. Fig. 9 plots three curves for three base wavelets used, i.e., db1, db2, and db3, in clustering the fourth set of AE signal segments. The results indicate that (1) the maximum average clustering accuracy is 76.7%, which can be achieved by using db3 with 3 levels of decomposition; (2) the highest average clustering accuracy that can be attained by db1 is 71% with 8, 9, 10, or 11 levels of composition; and (3) db2 does not work well on this data set. Our effort pays off because it results in an approximately 10% improvement in the average clustering accuracy compared with our initial selection. To determine the effect of GA parameters, one of the two feature sets that produce the best average clustering accuracy for the second data set, i.e. db1 with 7 levels, was chosen for further study. Three GA parameters including the population size, maximum number of generations, and fitness function are varied at three levels. For each combination five replicated runs are executed. The other two fitness functions tested are: (1) 104/DB, where DB is short for the Davies–Bouldin index, which was used by Bandyopadhyay and Maulik [18] in their comparative study of validity indices using a variable string length genetic algorithm and by Bandyopadhyay and Maulik [19] in their genetic clustering of satellite images. Let ni denote the number of data in cluster I, Ci. The DB index is computed as   c WCVi =ni þ WCVj =nj 1X DB ¼ max , (8) c i¼1 j;jai d E ðvi ; vj Þ

WCVi ¼

n X

wij d E ðvi ; xj Þ.

c X

WCVi ¼

i¼1 n X

c X n X

wij d E ðvi ; xj Þ,

i¼1 j¼1 _

d E ðxk  xÞ;

k¼1

Population

25 25 25 25 25 25 25 25 25 50 50 50 50 50 50 50 50 50 100 100 100 100 100 100 100 100 100

Max. generation

15 15 15 25 25 25 50 50 50 15 15 15 25 25 25 50 50 50 15 15 15 25 25 25 50 50 50

Fitness function

DB PBM VSV DB PBM VSV DB PBM VSV DB PBM VSV DB PBM VSV DB PBM VSV DB PBM VSV DB PBM VSV DB PBM VSV

Classification accuracy Average

Std. dev.

0.6667 0.7000 0.8400 0.6667 0.7000 0.8400 0.6667 0.7000 0.8400 0.6667 0.7000 0.8467 0.6667 0.7000 0.8667 0.6667 0.7000 0.8667 0.6667 0.7000 0.8667 0.6667 0.7000 0.8667 0.6667 0.7000 0.8667

0.0000 0.0000 0.0596 0.0000 0.0000 0.0596 0.0000 0.0000 0.0596 0.0000 0.0000 0.0447 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

7. Conclusions

If xj 2 C i , then wij ¼ 1; else, wij ¼ 0. (2) PBM, which is short for the PBM index [20] is as given below:  2 1 E1   Dc , (9) PBM ¼ c TWCV

E1 ¼

Table 3 Effect of GA parameters on clustering results

population size and/or the maximum number of generations do not further improve the result.

j¼1

TWCV ¼

591

c

Dc ¼ max d E ðvi ; vj Þ. i;j¼1

_

In Eq. (9), x stands for the cluster center (or medoid) of forming all objects into only one cluster. Table 3 summarizes the average and standard deviation of clustering accuracy. The results indicate that: (i) the two added fitness functions do not produce as good as the one chosen initially; (ii) the best result cannot be obtained when the population size is reduced and/or the maximum number of generations is shorten; (iii) increasing the

This paper has presented a wavelet-based unsupervised grinding wheel condition monitoring methodology. The presented methodology involves collecting acoustic emission (AE) signals in grinding at different wheel states, taking segments from the AE raw signals, extracting wavelet-based energy features from each signal segment, and applying an adaptive genetic clustering algorithm to put each signal segment into one of two wheel states: ‘sharp’ and ‘dull’. Four data sets collected in creep feed grinding of alumina were used for testing. The test results indicate that the proposed methodology can achieve on average 97% clustering accuracy for the high material removal rate condition, 86.7% for the low material removal rate condition, and 76.7% for combined grinding conditions if the base wavelet, the decomposition level, and the GA parameters are properly selected. The above results are quite encouraging but further improvement might be possible if more discriminating features can be found. Continuous searching for better features thus will be part of our future effort. Combining data from different grinding conditions makes the clustering task more

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T. Warren Liao et al. / International Journal of Machine Tools & Manufacture 47 (2007) 580–592

difficult; it, however, is the only way to develop a more realistic monitoring system, i.e., one system for all conditions. No one has really carried out a study to understand how far we can go with this. Studying what is the minimum acceptable accuracy and how many conditions can be combined to still achieve that is a possible topic for future study as well. Acknowledgment This research was made possible with the support provided by two programs: (i) the High Temperature Materials Laboratory User Program, Oak Ridge National Laboratory sponsored by the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Transportation Technologies, and (ii) the Louisiana Board’s NSF ESPCoR Links Program with Contract no. NSF(2005)-LINK-06. References [1] S. Kurada, C. Bradley, A review of machine vision sensors for tool condition monitoring, Computers & Industry 34 (1) (1997) 55–72. [2] K.-C. Fan, M.-Z. Lee, J.-I. Mou, On-line non-contact system for grinding wheel wear measurement, International Journal of Advanced Manufacturing Technology 19 (2002) 14–22. [3] S. LaChance, A. Warkentin, R. Bauer, Development of an automated system for measuring grinding wheel wear flats, Journal of Manufacturing Systems 22 (2) (2003) 130–135. [4] D.E. Dimla, Sensor signals for tool wear monitoring in metal cutting operations—a review of methods, International Journal of Machine Tools & Manufacture 40 (8) (2000) 1073–1098. [5] X. Li, A brief review: acoustic emission method for tool wear monitoring during turning, International Journal of Machine Tools & Manufacture 42 (2002) 157–165. [6] A.G. Rehorn, J. Jiang, P.E. Orban, State-of-the-art methods and results in tool condition monitoring—a review, International Journal of Advanced Manufacturing Technology 26 (7-8) (2005) 693–710.

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