- Email: [email protected]
Monitoring manufacturing processes by utilizing empirical modeling
ELSEVIER
Ultrasonics 36 (1998) 2633271
Monitoring manufacturing
processes by utilizing empirical modeling
I. Grabec *, E. Govekar, Fuculty of’ Mrchunical Engineering.
E. SusiE, B. Antolovii:
Universit,v of‘Ljuh(jutw
PO Box 394, 1001 .Ljuh~junu. Slovmiu
Abstract Application of acoustic emission analysis to the characterization of manufacturing processes and produces is demonstrated. The relations between characteristics of AE signals and process parameters are modeled empirically. The model is built nonparametrically by a self-organized information processing system which resembles a neural network. The network structure is derived based on the statistical description of natural phenomena. During learning the modeler creates a set of representative data which comprise acoustic emission and process characteristics. These data are utilized at the process monitoring for an associative estimation of process characteristics from the input acoustic signals. The performance of the complete sensory-neural network is demonstrated using examples of turning, grinding and friction processes. It is shown how the cutting tool wear, the roughness of the ground surface and the quality of the surface which is generating friction can be estimated on-line. 0 1998 Elsevier Science B.V. Kepvord.s:
Acoustic
emission:
Empirical
modeling;
Process
monitoring
1. Introduction Automatic manufacturing systems require on-line supervision of process state and particularly of working tool conditions. Therefore new methods for characterization of processes and produces are intensively sought and developed. Various types of mechanical processing of materials include nonlinear deformations which are accompanied by excitation of chaotic vibrations and acoustic emission (AE). A possibility therefore exists to extract information about a process or a product from the detected AE signals. For this purpose an instrument is required by which the AE signals can be detected and transformed into process characteristics. Such a transformation generally represents a physical law. Because of the complexity of manufacturing processes and the stochastic properties of the majority of processed materials, modeling of the corresponding physical law in many cases cannot be performed analytically. So the only remaining option is empirical modeling which can either be carried out parametrically or nonparametrically. Parametrical modeling usually represents only an adaptation of analytical model and is consequently also of limited applicability. More generally applicable is a nonparametric modeling which can be based on a statis* Corresponding author. Fax: 386 61 1253 135: e-mail: [email protected] 0041-624><,‘98,1$19.00 0 1998 Elsevier Science B.V. All rights reserved. PII
SOO41-624X(97)00051-6
tical description of natural phenomena. The aim of this article is to demonstrate how the empirical modeling can be applied to the characterization of manufacturing processes using AE signals. For this purpose we first briefly represent some fundamentals of empirical modeling which has previously been thoroughly formulated elsewhere [4-61. The performance of the developed modeling system is then demonstrated using examples of estimation of tool sharpness in a turning process on a lathe, determination of the roughness of a surface generated by external grinding of cylindrical workpieces, and classification of the surface quality of paper.
2. Nonparametric
modeling of physical laws
In the nonparametric empirical modeling of natural laws we generally assume that there exists an experimental system with an array of sensors which provide data about M measured variables. A particular outcome of an experiment is described by a multi-dimensional vector variable X = (x1.. ..xM) which represents an empirical sample. We assume that experiment is repeated N times and that the acquired samples are stored in a data base {X,...X,). Most generally, the data are at least to a certain extent of stochastic nature, so that a probabilistic treatment is utilized for the description of the properties of the phenomenon under consideration. The basic item
I. Grabrr, et 01. J Uitrasonic:~ 36 ( 1998) 263-271
264
of this description is the probability density function of the variable X which can be empirically estimated by the expression
conditional average estimator. It is expressed in terms of stored prototype data by the equation
few=; $
fi=
&X-X,).
n
(1)
1
When the number of samples N is increasing without limit we introduce a fixed number of K prototype data vectors in order to prevent saturation of a memory device that contains the data base. The corresponding reference vectors are denoted Qk and form the representative data base {QI...QK}. The fundamental problem is then to adapt these prototype vectors to the empirical samples X, obtained by sequential repetition of the experiment. For NIK the prototypes can be initialized by the rule Q,=X,; n= 1. ..N. while for N>K the existing prototypes must be adapted to new samples by an appropriate changing process. By utilizing a concept of maximal preservation of empirical information, we have derived elsewhere an adaptation algorithm which resembles self-organized learning of neurons in a neural network [ 5,6]. The optimal adaptation is approximately described by the equation
AQ,=;
(Xn-Qdw(&-Qk) [
The window function w denotes a smooth approximation of the 6 function, as for example a Gaussian: w(X-Q)=
exp[ - “x~~“z],
(3)
Here o denotes a parameter which corresponds to a typical distance between prototype vectors. When the number of samples N is small the adaptation is not required because all the vectors X, can be used as prototypes. In our applications the sample vectors X comprise two types of components that represent AE and process characteristics. The model of their relation is represented by the set of prototype vectors. At the application of this model the problem is to extract the data about the process provided that AE characteristics are measured. In accordance with this problem the data vector is considered as a composition of two sub-vectors which represent the given AE characteristics and the hidden process descriptors: C=(x,.-.x,;#)
H=(#;x,+,...XM).
(4)
In this equation # denotes the set of missing data in the truncated vector. Based on the given truncated vector G the hidden truncated vector H is determined optimally with respect to the mean-square estimation error by the
2 Bk(G)Hk.
(5)
k=l
The estimator fi represents a nonparametric regression. The coefficients in the sum are called radial basis functions and are determined by the equation w(G -G,) &(G)=
cI”=i w(G-G,)’
(6)
They represent a nonlinear measure of similarity between the given data and the corresponding data stored in prototype* vectors. Based on this similarity the hidden vector H comprises truncated vectors H, that are associated to prototypes G,. The formation of the data vector X depends on a specific method of characterization of the phenomenon under observation. Most often the measured variables are not directly utilized as components, because a proper pre-processing can yield invariant representation of data with respect to time shift, displacement, etc. An invariant presentation usually simplifies modeling and reduces the volume of the data base. Quite often the variables that are detected on manufacturing systems represent stationary stochastic time signals. They are most easily characterized invariant with respect to time shift by the spectral density which can be determined by the fast Fourier transform. Similarly, the properties of the products can often be considered on limited regions as stationary stochastic processes. The spatially dependent properties are usually described by the correlation function of a characteristic variable which is equivalent to the spectral density. This is also the case in the exampIes that are explained in the following sections.
3. Tool wear classification in a turning process 3.1. The problem A turning process is based upon plastic deformations of materials by a cutting tool. This causes fluctuations of cutting forces which represent the lower frequency band of the generated acoustic emission. In the corresponding signals the noise generated in the cutting zone by the deformation of the cut material as well as the coupled vibrations of the machine, workpiece and the tool are reflected. As they are influenced by the tool condition, and in particular wear, much effort has been devoted to find a signal pre-processing which could feasibly extract useful information from detected AE signals. With this aim, the time-dependent fluctuations must be characterized by a proper set of time-independent features. Most often the properties of the AE
265
I. Grubrc et al. / Ultrasonics 36 ( IWS) 263 271
Off-line measurement of wear L____________________
, I
Fig.
I Experimental
set-up for the investigation
of significance
signals are represented in the frequency space by a power density. The spectral distribution is generally described by many components which need not be equally significant for the characterization of the tool condition. Some of them can be redundant or even noisy. In the following we introduce a technique which is applicable for definition of an optimal set of representative spectral components. For this purpose the methods which were developed in the theory of pattern recognition and artificial neural networks are utilized. In order to arrange the spectral components based upon their significance with respect to the rate of tool wear the class-scatter [l] and Karhunen-Loeve criteria [2] were applied. These criteria maximize inter-class separation and minimize the variance of each class. The first criterion arranges the features in the basic space of spectral components while the second criterion defines the features in the new space defined by Karhunen--Loeve transformation. An optimal set of features of power spectra was then introduced by analyzing the average classification error versus the number of selected components d. For classification purposes an empirical modeler with a structure of a self-organized neural network was developed [4]. The data vector X comprised optimally selected components of AE power spectra and the corresponding tool wear descriptors. From an extensive set of N sample vectors X,, the modeler forms a smaller set of K
for
sensory
data
3.2. E.xprrimmts
and
tool
P-7
wear
I I I
characterization.
und results on the turning procrss
The aim of our research was to investigate the applicability of selected spectral components of cutting forces to classify cutting tool wear. For this purpose four tool wear classes {R,; i= 1...4} were introduced which represent the tool wear of l/b=O.O mm, Vb=O.l mm, Vh= 0.2 mm and I/b 20.4 mm. Here Vb =0.x mm denotes the flank wear in the interval from 0.x to 0.(x + 1) mm. The wear was measured off-line by a microscope. With the aim of measuring fluctuations of the main cutting force and the feed force at a particular tool wear an experimental-data acquisition system was assembled, as shown in Fig. 1. The system comprised a lathe, a steel specimen, a cutting tool, a dynamo-meter, a digital spectrum analyzer, a computer and a microscope. During cutting the fluctuations of the main cutting and the feed force were measured by a multi-component dynamo-meter. For the purpose of time-invariant presentation of measured fluctuations the power spectra in the frequency band from 0 to 2.5 kHz were calculated by FFT in the spectrum analyzer. The power spectra were represented by 128 frequency components. For each particular tool wear class a set of 58 records of the feed and the main cutting force spectra was stored in the computer memory. Some representative examples of cutting S, and feed Sf force spectra are shown in Fig. 2. The classification between just two classes VbOO and VbO4 or just three classes VbOO, VbO2 and VbO4 was performed with 100% accuracy. Therefore, the results of classification of all four tool wear classes is described more in detail. 0.03
M
b
M
R, -
SC
0
Fig. 2. Power spectra I28 components.
of cutting
(a) and feed force (b) for particular
0.5
1
1.5
tool wear class R, in the frequency
2
band
2.5
from 0 to 2.5 kHz represented
by
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36 (19%‘) 263-271
0 0
25
50
75
100
125
0
25
50
75
Fig. 3. The average
classification
error versus number
d of selected components
Components of measured power spectra were at first arranged by their importance for tool wear classification using the class-scatter criterion. Fig. 3(a) and (b) shows the average classification error versus d number of arranged spectral components of the cutting and the feed force, respectively. Here the sign x denotes the results of the average-classification error that was achieved based only on initialization of K prototypes by randomly selected vectors X while 0 denotes the results obtained using prototypes which were adapted by the self-organization. It is evident from Fig. 3 that the self-organized adaptation of the empirical modeler essentially improves classification results. It is also evident that the classification error does not converge to zero with increasing number of selected spectral components. In some cases the classification error even increases. This indicates that it is reasonable to introduce a characteristic number of components. For this purpose we utilize the number of selected spectral components at which the classification error exhibits a minimum. This optimal number can be extracted from the diagrams in Fig. 3 and the corresponding errors of classification are shown in Table 1. If the cutting force is utilized as the basis for the classification, the optimal number of features is 50 while in the case of feed force this number is 45. Using the class-scatter criterion a joint feature set made up of arranged cutting and the feed force spectral components was further performed. The average classification error versus the number of features cl is shown in Fig. 4. The first minimum of the classification error occurs at d= 15 while the next is at d=35. The best classification is obtained using 80 selected features. In the last case 30 features represent the selected components of the cutting force spectra while the remaining Table 1 Minimal classification Signal
&
SC
50
&
45
100
125
d
d
error on the basis of selected components
from cutting
of the cutting
0
force (a) and the feed
25
50
force (b) power spectra.
75
100
125
d
Fig. 4. The average classification of cutting and feed force spectra
error achieved
by joint components
50 are selected from the spectra of the feed force. The contribution of the spectral features of both forces as well as the classification error corresponding to a particular wear class before and after adaptation is evident from Table 2. The effect of Karhunen-Loeve transformation on the selected features is demonstrated in Table 3. The rows show the signal used for classification, the optimal number of features dOin the original space, the number of features d, in transformed space, the average classification error, and the classification error for a particular wear class obtained by means of features from the original and from the transformed space. It is evident from Table 3 that a smaller number of features is required in the transformed space in order to achieve the same classification error as in the previous case. 3.3. Discussion oj’tool wur clus$cation Our experiments show that in spite of the complexity of the chaotic cutting process the tool wear can be well characterized by a set of characteristic features which
S, and feed force S, spectra
Unadapted
Adapted
Cc)
61
30.5 8.5
16.6
0
e2
c3
cd
(6)
61
c2
c3
c4
50.0 16.6
50.0 0
22.2 11.1
6.9 5.5
0 0
22.2 16.6
0 0
5.5 5.5
I. Cruhec et ul. / Ultrasonics
Table 2 Minimal rl
I5 35 80
classification dC
errors
4 9 30
SC & SC, SC,
II 26 50
components Adapted
(6)
61
t2
63
64
(E)
El
62
62
64
19.4 19.4 13.8
0.0 0.0 0.0
38.8 33.3 II.1
38.8 44.4 44.4
0.0 0.0 0.0
5.5 2.1 I.3
0.0 0.0 0.0
_-._3 77 I I.1 5.5
0.0 0.0 0.0
0.0 0.0 0.0
of relevant
features
0.0 0.0 II.0 0.0
16.6 16.6 II.1 5.5
22.2 0.0 0.0 0.0
0.0 5.5 0.0 0.0
transformation
on the number
Original
&
50 4s 45 80
of integrated
Unadapted
&
Table 3 EtTect of Karhunen-~Loeve Signal
versus number
267
36 ( IYW) ,763 ,771
35 36 38 59
and classification
error
space
Et
6.9 5.5 2.1 I.4
0.0 0.0 0.0 0.0
E3 22.2 16.6 I I.1 0.0
0.0 0.0 0.0 5.5
5.5 5.5 0.0 0.0
9.1 5.5 2.1 I .J
from from the cutting force spectra (Table 2). This indicates a higher significance of feed force for the tool wear description. In addition to this. the application of the Karhunen-Loeve transformation method shows that the dimensionality of the feature vector can be reduced while the classification error is preserved in comparison to classification results on basis of features defined in the original space.
are extracted from the power spectra of the cutting and the feed force. The minimal classification error 1.3% was achieved by means of 80 components selected from the cutting and feed force spectra. On the basis of comparison of results of tool wear classification obtained by unadapted and by self-organization adapted prototypes, it is evident that the self-organization decreases classification error. Results also indicate that the feed force signals are more appropriate for the empirical description of the tool wear. This is graphically represented in Fig. 5 which shows tool wear classes in the plane of the most important power spectrum components of the cutting and the feed force, respectively. In Fig. 5(a) overlapping of all classes with practically no clustering is observed. Contrary to this in Fig. 5(b) clusters of tool wear VbOl, l/b02 and VbO4 can be recognized while the overlapping of classes VhOO, HO2 is still present. This is further reflected in lower classification error when using a lower number of selected components of feed-force spectra. The same two components as utilized in Fig. 5(b) are also the most important when joining spectral components of both forces. With increasing number of selected joint features the corresponding set involves more components from feed than
4. Characterization
of ground surface by AE analysis
Grinding is a very complex manufacturing process whose empirical and analytical description is related with great difficulties [3]. For instance, the problem of the on-line characterization of ground surface has still not been satisfactorily solved which represents a serious obstacle for the progress at the development of modern grinding machines. For the ground surface characterization the measurement of profile correlation function is most significant. Although there exists many instruments -i
, 0
-I
I
0.02 Amp.
0.04 1.66 kHz
0.06
M
Fig. 5. Tool wear classes in the plane of selected
features:
0
0.01
Amp.
0.02 0.35 kHz
0.03
M
(+) + VhOO; (*) + VhOl; x + VhO2:
( ) + b’h(M.
268
I. Grabec rt al. / Ultrasonics 36 (I 998) 263-271
for direct off-line profile measurements by sliding stylus method, they do not enable on-line measurements and estimation of surface correlation function. Therefore, an indirect method is sought which could substitute the standard off-line methods. For this purpose acoustic emission analysis appears very promising because it is generated by deformation and friction in all grinding processes and can be simply detected on-line. However, for the purpose of the surface characterization the detected AE signal must be transformed into the surface correlation function, which represents a problem due to the lack of any corresponding analytical relationship. We therefore utilize an empirical model [4] which enables us to extract information on the surface roughness from on-line measured AE signals.
dard stylus method at the same location of workpiece surface where AE spectral distribution was previously recorded. From the measured profile the surface autocorrelation function R,, was calculated. It was concatenated to the vector S as the surface descriptor portion R. A set of joint data vectors {X,; n= 1...N} was used to represents the complete grinding process. During the grinding wheel lifetime about N= 150 samples of the joint data vectors were measured. From them 24 prototype data vectors were created by the self-organized adaptation [5]. They were stored in the memory of the information processing system and were considered as an empirical model of the grinding process.
4.2. Experiments on the grinding process
After learning, the empirical model was applied for the on-line estimation of the surface roughness correlation function based on the detected AE signal. For this purpose the detected AE signal was first pre-processed to obtain the spectral distribution portion S. This was considered as the given truncated vector of the complete data vector. The corresponding hidden vector, which represents the partial information about the auto-correlation function R of the surface profile, was estimated by the conditional average estimator. Typical results of the estimation during one complete wheel lifetime period are shown in Fig. 7. Results show that the auto-correlation function of a ground surface profile can be predicted during a complete period of wheel lifetime. More detailed analysis has shown that the estimation error is low during grinding by a used but not worn-out grinding wheel. In contrast to this the estimation error is greater when the grinding wheel is newly dressed as well as when it is worn out.
The experimental system for an on-line characterization of ground surface correlation function is shown in Fig. 6. Experiments were performed on a standard machine designed for external grinding of cylindrical workpieces. A set of 10 steel workpieces of diameter 28 mm and length 260 mm was utilized in the experimentation. The grinding parameters were adapted to the given workpiece material. They are described by the values of the grinding wheel speed v, = 30 m SC*, the workpiece speed v,=O.3 m SC’ and feed rate vr=O.O2 mm s-i. The cutting depth was set to a= 0.03 mm. The AE was detected on the workpiece surface by a wide-band PZT sensor which was coupled to the surface by the jet of cooling fluid. The detected AE signal was fed from the sensor to the spectrum analyzer in which the power spectrum distribution was determined in the frequency range from 0 to 600 kHz. The digitized distribution was stored as a partial data vector S. Experiments were designed to measure the AE spectral distribution and to acquire the workpiece profile data off-line for the complete lifetime period of the wheel. An experiment on a particular sample started with a uniformly dressed grinding wheel and was finished when the wheel became worn out. After completion of grinding the surface profile was measured off-line by a stan-
GRINDING
4.3. Results of experiments on the grinding process
5. Characterization of paper quality by analysis of AE generated by friction 5.1.
The problem
An advanced paper manufacturing process control necessitates a simple on-line surface quality testing of
NEURALNETWORK
PROCESS
ANALYZING MODE
--I’
Fig. 6. A system for surface profile autocorrelation
,
_.....
.,
CONDITIONAL j
; AVERAGE
functions estimation on AE basis.
/
XIWl
~loqucncyWI AE
269
36 ( 1998) 263-271
I. Grahrc et al. J Ultrasonics
=Lml
EStimatednor
Measured rxx
spectra
Fig. 7. Estimated
Fig. 8. Experimental
Surface
and measured
autocorrelation
set-up for characterization
functions
of paper
related
surface
to AE spectra.
quality
by AE analysis.
profile
Spectral 1.4
amplitude
-
‘sp.ml.tst’
~~
1.2
ii 0
0.5
I
1.5
2
2.5 mm
Fig. 9. A record
3
3.5
4
of paper
4.5
surface
0
0.05
profile (left) and its spectral
produced paper instead of a complicated off-line smoothness measurement, destructive testing, etc. in a laboratory. The aim of our research is to develop a system capable of classifying the produced paper surface based on the AE analysis. We suppose that the information about the surface quality, as well as about the production process itself, could be extracted from an AE signal generated by friction of the sensor which is sliding on the surface running in the processing machine. Friction is an example of phenomena in which the properties of the materials in contact influence the properties of sonic and ultrasonic signals and could therefore be characterized by AE analysis. Similarly, as in the previous two examples the complexity of this stochastic phenomenon prevents an analytical determination of a relation between AE signal characteristics and the properties of the production process and the
0
I
0.15 kHz
0 2
0 25
03
distributation
paper surface. Consequently, we again apply empirical modeling of the relation between the AE power spectrum and the process and surface descriptors. 5.2. Experiments
on chamctrrizrrtion
qf‘prrper quality
The experimental system is shown in Fig. 8. It is composed of a mechanical unit, in which the friction between an AE sensor and the paper surface is generated on a rotating paper sample, and an information processing system that comprised a spectrum analyser and a computer in which the empirical modeling is performed. The prototype vectors that are formed during learning in this case contain two types of data: the dynamic ones that are provided on-line by sensors which are monitoring typical variables during the friction process, and the static ones that are obtained by standard off-line meas-
I. Grahrc et al. / Ultrasoniu 36 (I 998) 263-271
270
Sl . PZT sensor
Pinducer
VP 1093
S2
0.005
.
0.0045
gramophone
needle
‘sp2.I.e-
Stanton
‘1glZ.tst’ -
0.004 0.0035
3 0.0006 0.0004
1
1.5
2
2.5
4
kHz
S1
PZT sensor
6
8
Ml2
Pinducer VP 1093 ‘sp3.M
S2
gramophone
needle
-
Stanton ‘igl3.w’
z
-
0.0008
5 0.0006
0
0.5
1
1.S
2
2.5
kHz
Sl - PZT senxx
kHz
Pinducer
VP 1093
S2 - gramophone
needle
Stanton
0.005 ‘spS.tAt’
0 0045
0.0014
-
‘igl5 tst’
-
0.004 0.003s 0.003 F ;
0002s 0.002 0.0015 0.001 0.0005 0 0
0.5
1.5
1
2
0
2.5
kHz
Fig. 10. Spectral distributions
2
4
6
8
kHz
of AE signals from the PZT sensor (left)
urement of surface roughness, hardness, etc. During the on-line characterization of a paper surface only the dynamic data are provided by on-line measurement, while the complementary static data are estimated by the modeler from the stored prototypes. In the experiment an especially constructed PZT sensor was utilized. The size and the shape of the contact surface as well as the contact force were varied during experimentation. In addition to this sensor a ‘Stanton’ gramophone head was also used. Examinations have shown that better results of classification of tested paper samples into re-determined paper classes were achieved by using the gramophone head than by the PZT transducer. Fig. 9 shows a characteristic record of a sample profile measured off-line using a stylus method. The same figure also shows the power spectrum of the
and the gramophone
head (right).
that would be observed if the point of observation were moving along the recorded surface profile with a velocity of 0.3 m s-l. This velocity corresponds to the speed of the paper tape in the experimental production machine. The most powerful components of the spectral density are observed mainly in the lower audible frequency region. Such records were further used for an analytical estimation of the signals generated in the AE sensors during their sliding along the paper surface. The true spectral distributions of the AE signals which were measured by the PZT sensor and the gramophone head are presented on Fig. 10. for three typical classes of paper quality. The complete experiment included measurement of AE spectra and surface roughness on a statistical set of similar samples for each type of paper. Altogether five
fluctuations
paper classes were used in the experimental investigations. From each class 20 samples were randomly selected. On each sample AE spectrum was measured 64 times and the average value of all records were used to represent the sample. Two types of modeling were performed. In the first one five representative samples were selected from all 20 samples based on visual observation of measured spectral distributions. These samples were then used as prototypes in the empirical model. In the second type of modeling the prototypes were determined automatically based upon self-organized adaptation. With respect to classification accuracy a better modeling result was obtained using the selforganization procedure. The information stored in the modeler was further applied for the on-line estimation of the paper class. In the examination of the modeler performance only the spectral distribution of the AE signal and the encoded descriptor of the paper class were considered. The task of the modeler was to estimate the paper class from the given AE spectrum. The performance was tested on an additional set of 50 randomly selected samples. The percentage of correct classification of test samples was 98% when using the gramophone head and 89% when using the PZT sensor. The better performance of the gramophone head is probably a consequence of its smaller sensor tip.
6. Conclusions Our experiments show that the acoustic emission phenomenon can be successfully utilized in a characterization of manufacturing and other industrial processes. For this purpose the nonparametric empirical modeling of natural phenomena can be considered as a basic tool. However, each particular process requires a specific design of AE sensors with properly adapted response characteristics. As shown above, for the purpose of
monitoring, not only ultrasonic but also audible region could be of importance. For successful monitoring attention must also be paid to the pre-processing of signals. In the cases presented here the spectral distributions and correlation functions have been utilized, but additional investigations have revealed that various methods which have already been developed during the research of chaotic dynamics also show promise for monitoring techniques [ 11. However. an on-line monitoring method is not the only final goal of application of acoustic emission in the industry. Recent explorations indicate that the nonparametric empirical modeling is also applicable for an optimal control of processes based on detected AE signals [6]. Therefore. intensive research in this direction is expected in the near future.
Acknowledgement The autors wish to acknowledge the support given to their projects by the Ministry for Science and Technology of Slovenia and the Volkswagen Foundation in Germany.
References [I] E. Govekar. Prediction of technical process parameters by means of neural networks. Ph.D. Thesis. No. D:l60. lYY4. [2] P.A. Devijver. J. Kittler. Pattern Recognition: A Statistical Approach. Prentice Hall. Englewood Clifis. YJ. 1982. [3] E. Susie. I. Grabec, Analysis of grinding process acoustic emission by a neural network. in: Ultrasonics International ‘93. Vienna. 1993, pp. 252-254. [4] I. Grdbec, W. Sachse, Automatic modeling ot physical phenomena: application to ultrasonic data. J. Appl. Phys. 69 (9) (1991) 6213-6244. [5] I. Grabec. Self-organization of neurons described by the mawimumentropy principle, Biolog. Cybernetics 63 ( lY90) 403 409. [6] I. Grabec. W. Sachse. Synergetics of Measurements. Prediction. and Control. Springer. Berlin. 1997.
Ultrasonics 36 (1998) 2633271
Monitoring manufacturing
processes by utilizing empirical modeling
I. Grabec *, E. Govekar, Fuculty of’ Mrchunical Engineering.
E. SusiE, B. Antolovii:
Universit,v of‘Ljuh(jutw
PO Box 394, 1001 .Ljuh~junu. Slovmiu
Abstract Application of acoustic emission analysis to the characterization of manufacturing processes and produces is demonstrated. The relations between characteristics of AE signals and process parameters are modeled empirically. The model is built nonparametrically by a self-organized information processing system which resembles a neural network. The network structure is derived based on the statistical description of natural phenomena. During learning the modeler creates a set of representative data which comprise acoustic emission and process characteristics. These data are utilized at the process monitoring for an associative estimation of process characteristics from the input acoustic signals. The performance of the complete sensory-neural network is demonstrated using examples of turning, grinding and friction processes. It is shown how the cutting tool wear, the roughness of the ground surface and the quality of the surface which is generating friction can be estimated on-line. 0 1998 Elsevier Science B.V. Kepvord.s:
Acoustic
emission:
Empirical
modeling;
Process
monitoring
1. Introduction Automatic manufacturing systems require on-line supervision of process state and particularly of working tool conditions. Therefore new methods for characterization of processes and produces are intensively sought and developed. Various types of mechanical processing of materials include nonlinear deformations which are accompanied by excitation of chaotic vibrations and acoustic emission (AE). A possibility therefore exists to extract information about a process or a product from the detected AE signals. For this purpose an instrument is required by which the AE signals can be detected and transformed into process characteristics. Such a transformation generally represents a physical law. Because of the complexity of manufacturing processes and the stochastic properties of the majority of processed materials, modeling of the corresponding physical law in many cases cannot be performed analytically. So the only remaining option is empirical modeling which can either be carried out parametrically or nonparametrically. Parametrical modeling usually represents only an adaptation of analytical model and is consequently also of limited applicability. More generally applicable is a nonparametric modeling which can be based on a statis* Corresponding author. Fax: 386 61 1253 135: e-mail: [email protected] 0041-624><,‘98,1$19.00 0 1998 Elsevier Science B.V. All rights reserved. PII
SOO41-624X(97)00051-6
tical description of natural phenomena. The aim of this article is to demonstrate how the empirical modeling can be applied to the characterization of manufacturing processes using AE signals. For this purpose we first briefly represent some fundamentals of empirical modeling which has previously been thoroughly formulated elsewhere [4-61. The performance of the developed modeling system is then demonstrated using examples of estimation of tool sharpness in a turning process on a lathe, determination of the roughness of a surface generated by external grinding of cylindrical workpieces, and classification of the surface quality of paper.
2. Nonparametric
modeling of physical laws
In the nonparametric empirical modeling of natural laws we generally assume that there exists an experimental system with an array of sensors which provide data about M measured variables. A particular outcome of an experiment is described by a multi-dimensional vector variable X = (x1.. ..xM) which represents an empirical sample. We assume that experiment is repeated N times and that the acquired samples are stored in a data base {X,...X,). Most generally, the data are at least to a certain extent of stochastic nature, so that a probabilistic treatment is utilized for the description of the properties of the phenomenon under consideration. The basic item
I. Grabrr, et 01. J Uitrasonic:~ 36 ( 1998) 263-271
264
of this description is the probability density function of the variable X which can be empirically estimated by the expression
conditional average estimator. It is expressed in terms of stored prototype data by the equation
few=; $
fi=
&X-X,).
n
(1)
1
When the number of samples N is increasing without limit we introduce a fixed number of K prototype data vectors in order to prevent saturation of a memory device that contains the data base. The corresponding reference vectors are denoted Qk and form the representative data base {QI...QK}. The fundamental problem is then to adapt these prototype vectors to the empirical samples X, obtained by sequential repetition of the experiment. For NIK the prototypes can be initialized by the rule Q,=X,; n= 1. ..N. while for N>K the existing prototypes must be adapted to new samples by an appropriate changing process. By utilizing a concept of maximal preservation of empirical information, we have derived elsewhere an adaptation algorithm which resembles self-organized learning of neurons in a neural network [ 5,6]. The optimal adaptation is approximately described by the equation
AQ,=;
(Xn-Qdw(&-Qk) [
The window function w denotes a smooth approximation of the 6 function, as for example a Gaussian: w(X-Q)=
exp[ - “x~~“z],
(3)
Here o denotes a parameter which corresponds to a typical distance between prototype vectors. When the number of samples N is small the adaptation is not required because all the vectors X, can be used as prototypes. In our applications the sample vectors X comprise two types of components that represent AE and process characteristics. The model of their relation is represented by the set of prototype vectors. At the application of this model the problem is to extract the data about the process provided that AE characteristics are measured. In accordance with this problem the data vector is considered as a composition of two sub-vectors which represent the given AE characteristics and the hidden process descriptors: C=(x,.-.x,;#)
H=(#;x,+,...XM).
(4)
In this equation # denotes the set of missing data in the truncated vector. Based on the given truncated vector G the hidden truncated vector H is determined optimally with respect to the mean-square estimation error by the
2 Bk(G)Hk.
(5)
k=l
The estimator fi represents a nonparametric regression. The coefficients in the sum are called radial basis functions and are determined by the equation w(G -G,) &(G)=
cI”=i w(G-G,)’
(6)
They represent a nonlinear measure of similarity between the given data and the corresponding data stored in prototype* vectors. Based on this similarity the hidden vector H comprises truncated vectors H, that are associated to prototypes G,. The formation of the data vector X depends on a specific method of characterization of the phenomenon under observation. Most often the measured variables are not directly utilized as components, because a proper pre-processing can yield invariant representation of data with respect to time shift, displacement, etc. An invariant presentation usually simplifies modeling and reduces the volume of the data base. Quite often the variables that are detected on manufacturing systems represent stationary stochastic time signals. They are most easily characterized invariant with respect to time shift by the spectral density which can be determined by the fast Fourier transform. Similarly, the properties of the products can often be considered on limited regions as stationary stochastic processes. The spatially dependent properties are usually described by the correlation function of a characteristic variable which is equivalent to the spectral density. This is also the case in the exampIes that are explained in the following sections.
3. Tool wear classification in a turning process 3.1. The problem A turning process is based upon plastic deformations of materials by a cutting tool. This causes fluctuations of cutting forces which represent the lower frequency band of the generated acoustic emission. In the corresponding signals the noise generated in the cutting zone by the deformation of the cut material as well as the coupled vibrations of the machine, workpiece and the tool are reflected. As they are influenced by the tool condition, and in particular wear, much effort has been devoted to find a signal pre-processing which could feasibly extract useful information from detected AE signals. With this aim, the time-dependent fluctuations must be characterized by a proper set of time-independent features. Most often the properties of the AE
265
I. Grubrc et al. / Ultrasonics 36 ( IWS) 263 271
Off-line measurement of wear L____________________
, I
Fig.
I Experimental
set-up for the investigation
of significance
signals are represented in the frequency space by a power density. The spectral distribution is generally described by many components which need not be equally significant for the characterization of the tool condition. Some of them can be redundant or even noisy. In the following we introduce a technique which is applicable for definition of an optimal set of representative spectral components. For this purpose the methods which were developed in the theory of pattern recognition and artificial neural networks are utilized. In order to arrange the spectral components based upon their significance with respect to the rate of tool wear the class-scatter [l] and Karhunen-Loeve criteria [2] were applied. These criteria maximize inter-class separation and minimize the variance of each class. The first criterion arranges the features in the basic space of spectral components while the second criterion defines the features in the new space defined by Karhunen--Loeve transformation. An optimal set of features of power spectra was then introduced by analyzing the average classification error versus the number of selected components d. For classification purposes an empirical modeler with a structure of a self-organized neural network was developed [4]. The data vector X comprised optimally selected components of AE power spectra and the corresponding tool wear descriptors. From an extensive set of N sample vectors X,, the modeler forms a smaller set of K
for
sensory
data
3.2. E.xprrimmts
and
tool
P-7
wear
I I I
characterization.
und results on the turning procrss
The aim of our research was to investigate the applicability of selected spectral components of cutting forces to classify cutting tool wear. For this purpose four tool wear classes {R,; i= 1...4} were introduced which represent the tool wear of l/b=O.O mm, Vb=O.l mm, Vh= 0.2 mm and I/b 20.4 mm. Here Vb =0.x mm denotes the flank wear in the interval from 0.x to 0.(x + 1) mm. The wear was measured off-line by a microscope. With the aim of measuring fluctuations of the main cutting force and the feed force at a particular tool wear an experimental-data acquisition system was assembled, as shown in Fig. 1. The system comprised a lathe, a steel specimen, a cutting tool, a dynamo-meter, a digital spectrum analyzer, a computer and a microscope. During cutting the fluctuations of the main cutting and the feed force were measured by a multi-component dynamo-meter. For the purpose of time-invariant presentation of measured fluctuations the power spectra in the frequency band from 0 to 2.5 kHz were calculated by FFT in the spectrum analyzer. The power spectra were represented by 128 frequency components. For each particular tool wear class a set of 58 records of the feed and the main cutting force spectra was stored in the computer memory. Some representative examples of cutting S, and feed Sf force spectra are shown in Fig. 2. The classification between just two classes VbOO and VbO4 or just three classes VbOO, VbO2 and VbO4 was performed with 100% accuracy. Therefore, the results of classification of all four tool wear classes is described more in detail. 0.03
M
b
M
R, -
SC
0
Fig. 2. Power spectra I28 components.
of cutting
(a) and feed force (b) for particular
0.5
1
1.5
tool wear class R, in the frequency
2
band
2.5
from 0 to 2.5 kHz represented
by
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36 (19%‘) 263-271
0 0
25
50
75
100
125
0
25
50
75
Fig. 3. The average
classification
error versus number
d of selected components
Components of measured power spectra were at first arranged by their importance for tool wear classification using the class-scatter criterion. Fig. 3(a) and (b) shows the average classification error versus d number of arranged spectral components of the cutting and the feed force, respectively. Here the sign x denotes the results of the average-classification error that was achieved based only on initialization of K prototypes by randomly selected vectors X while 0 denotes the results obtained using prototypes which were adapted by the self-organization. It is evident from Fig. 3 that the self-organized adaptation of the empirical modeler essentially improves classification results. It is also evident that the classification error does not converge to zero with increasing number of selected spectral components. In some cases the classification error even increases. This indicates that it is reasonable to introduce a characteristic number of components. For this purpose we utilize the number of selected spectral components at which the classification error exhibits a minimum. This optimal number can be extracted from the diagrams in Fig. 3 and the corresponding errors of classification are shown in Table 1. If the cutting force is utilized as the basis for the classification, the optimal number of features is 50 while in the case of feed force this number is 45. Using the class-scatter criterion a joint feature set made up of arranged cutting and the feed force spectral components was further performed. The average classification error versus the number of features cl is shown in Fig. 4. The first minimum of the classification error occurs at d= 15 while the next is at d=35. The best classification is obtained using 80 selected features. In the last case 30 features represent the selected components of the cutting force spectra while the remaining Table 1 Minimal classification Signal
&
SC
50
&
45
100
125
d
d
error on the basis of selected components
from cutting
of the cutting
0
force (a) and the feed
25
50
force (b) power spectra.
75
100
125
d
Fig. 4. The average classification of cutting and feed force spectra
error achieved
by joint components
50 are selected from the spectra of the feed force. The contribution of the spectral features of both forces as well as the classification error corresponding to a particular wear class before and after adaptation is evident from Table 2. The effect of Karhunen-Loeve transformation on the selected features is demonstrated in Table 3. The rows show the signal used for classification, the optimal number of features dOin the original space, the number of features d, in transformed space, the average classification error, and the classification error for a particular wear class obtained by means of features from the original and from the transformed space. It is evident from Table 3 that a smaller number of features is required in the transformed space in order to achieve the same classification error as in the previous case. 3.3. Discussion oj’tool wur clus$cation Our experiments show that in spite of the complexity of the chaotic cutting process the tool wear can be well characterized by a set of characteristic features which
S, and feed force S, spectra
Unadapted
Adapted
Cc)
61
30.5 8.5
16.6
0
e2
c3
cd
(6)
61
c2
c3
c4
50.0 16.6
50.0 0
22.2 11.1
6.9 5.5
0 0
22.2 16.6
0 0
5.5 5.5
I. Cruhec et ul. / Ultrasonics
Table 2 Minimal rl
I5 35 80
classification dC
errors
4 9 30
SC & SC, SC,
II 26 50
components Adapted
(6)
61
t2
63
64
(E)
El
62
62
64
19.4 19.4 13.8
0.0 0.0 0.0
38.8 33.3 II.1
38.8 44.4 44.4
0.0 0.0 0.0
5.5 2.1 I.3
0.0 0.0 0.0
_-._3 77 I I.1 5.5
0.0 0.0 0.0
0.0 0.0 0.0
of relevant
features
0.0 0.0 II.0 0.0
16.6 16.6 II.1 5.5
22.2 0.0 0.0 0.0
0.0 5.5 0.0 0.0
transformation
on the number
Original
&
50 4s 45 80
of integrated
Unadapted
&
Table 3 EtTect of Karhunen-~Loeve Signal
versus number
267
36 ( IYW) ,763 ,771
35 36 38 59
and classification
error
space
Et
6.9 5.5 2.1 I.4
0.0 0.0 0.0 0.0
E3 22.2 16.6 I I.1 0.0
0.0 0.0 0.0 5.5
5.5 5.5 0.0 0.0
9.1 5.5 2.1 I .J
from from the cutting force spectra (Table 2). This indicates a higher significance of feed force for the tool wear description. In addition to this. the application of the Karhunen-Loeve transformation method shows that the dimensionality of the feature vector can be reduced while the classification error is preserved in comparison to classification results on basis of features defined in the original space.
are extracted from the power spectra of the cutting and the feed force. The minimal classification error 1.3% was achieved by means of 80 components selected from the cutting and feed force spectra. On the basis of comparison of results of tool wear classification obtained by unadapted and by self-organization adapted prototypes, it is evident that the self-organization decreases classification error. Results also indicate that the feed force signals are more appropriate for the empirical description of the tool wear. This is graphically represented in Fig. 5 which shows tool wear classes in the plane of the most important power spectrum components of the cutting and the feed force, respectively. In Fig. 5(a) overlapping of all classes with practically no clustering is observed. Contrary to this in Fig. 5(b) clusters of tool wear VbOl, l/b02 and VbO4 can be recognized while the overlapping of classes VhOO, HO2 is still present. This is further reflected in lower classification error when using a lower number of selected components of feed-force spectra. The same two components as utilized in Fig. 5(b) are also the most important when joining spectral components of both forces. With increasing number of selected joint features the corresponding set involves more components from feed than
4. Characterization
of ground surface by AE analysis
Grinding is a very complex manufacturing process whose empirical and analytical description is related with great difficulties [3]. For instance, the problem of the on-line characterization of ground surface has still not been satisfactorily solved which represents a serious obstacle for the progress at the development of modern grinding machines. For the ground surface characterization the measurement of profile correlation function is most significant. Although there exists many instruments -i
, 0
-I
I
0.02 Amp.
0.04 1.66 kHz
0.06
M
Fig. 5. Tool wear classes in the plane of selected
features:
0
0.01
Amp.
0.02 0.35 kHz
0.03
M
(+) + VhOO; (*) + VhOl; x + VhO2:
( ) + b’h(M.
268
I. Grabec rt al. / Ultrasonics 36 (I 998) 263-271
for direct off-line profile measurements by sliding stylus method, they do not enable on-line measurements and estimation of surface correlation function. Therefore, an indirect method is sought which could substitute the standard off-line methods. For this purpose acoustic emission analysis appears very promising because it is generated by deformation and friction in all grinding processes and can be simply detected on-line. However, for the purpose of the surface characterization the detected AE signal must be transformed into the surface correlation function, which represents a problem due to the lack of any corresponding analytical relationship. We therefore utilize an empirical model [4] which enables us to extract information on the surface roughness from on-line measured AE signals.
dard stylus method at the same location of workpiece surface where AE spectral distribution was previously recorded. From the measured profile the surface autocorrelation function R,, was calculated. It was concatenated to the vector S as the surface descriptor portion R. A set of joint data vectors {X,; n= 1...N} was used to represents the complete grinding process. During the grinding wheel lifetime about N= 150 samples of the joint data vectors were measured. From them 24 prototype data vectors were created by the self-organized adaptation [5]. They were stored in the memory of the information processing system and were considered as an empirical model of the grinding process.
4.2. Experiments on the grinding process
After learning, the empirical model was applied for the on-line estimation of the surface roughness correlation function based on the detected AE signal. For this purpose the detected AE signal was first pre-processed to obtain the spectral distribution portion S. This was considered as the given truncated vector of the complete data vector. The corresponding hidden vector, which represents the partial information about the auto-correlation function R of the surface profile, was estimated by the conditional average estimator. Typical results of the estimation during one complete wheel lifetime period are shown in Fig. 7. Results show that the auto-correlation function of a ground surface profile can be predicted during a complete period of wheel lifetime. More detailed analysis has shown that the estimation error is low during grinding by a used but not worn-out grinding wheel. In contrast to this the estimation error is greater when the grinding wheel is newly dressed as well as when it is worn out.
The experimental system for an on-line characterization of ground surface correlation function is shown in Fig. 6. Experiments were performed on a standard machine designed for external grinding of cylindrical workpieces. A set of 10 steel workpieces of diameter 28 mm and length 260 mm was utilized in the experimentation. The grinding parameters were adapted to the given workpiece material. They are described by the values of the grinding wheel speed v, = 30 m SC*, the workpiece speed v,=O.3 m SC’ and feed rate vr=O.O2 mm s-i. The cutting depth was set to a= 0.03 mm. The AE was detected on the workpiece surface by a wide-band PZT sensor which was coupled to the surface by the jet of cooling fluid. The detected AE signal was fed from the sensor to the spectrum analyzer in which the power spectrum distribution was determined in the frequency range from 0 to 600 kHz. The digitized distribution was stored as a partial data vector S. Experiments were designed to measure the AE spectral distribution and to acquire the workpiece profile data off-line for the complete lifetime period of the wheel. An experiment on a particular sample started with a uniformly dressed grinding wheel and was finished when the wheel became worn out. After completion of grinding the surface profile was measured off-line by a stan-
GRINDING
4.3. Results of experiments on the grinding process
5. Characterization of paper quality by analysis of AE generated by friction 5.1.
The problem
An advanced paper manufacturing process control necessitates a simple on-line surface quality testing of
NEURALNETWORK
PROCESS
ANALYZING MODE
--I’
Fig. 6. A system for surface profile autocorrelation
,
_.....
.,
CONDITIONAL j
; AVERAGE
functions estimation on AE basis.
/
XIWl
~loqucncyWI AE
269
36 ( 1998) 263-271
I. Grahrc et al. J Ultrasonics
=Lml
EStimatednor
Measured rxx
spectra
Fig. 7. Estimated
Fig. 8. Experimental
Surface
and measured
autocorrelation
set-up for characterization
functions
of paper
related
surface
to AE spectra.
quality
by AE analysis.
profile
Spectral 1.4
amplitude
-
‘sp.ml.tst’
~~
1.2
ii 0
0.5
I
1.5
2
2.5 mm
Fig. 9. A record
3
3.5
4
of paper
4.5
surface
0
0.05
profile (left) and its spectral
produced paper instead of a complicated off-line smoothness measurement, destructive testing, etc. in a laboratory. The aim of our research is to develop a system capable of classifying the produced paper surface based on the AE analysis. We suppose that the information about the surface quality, as well as about the production process itself, could be extracted from an AE signal generated by friction of the sensor which is sliding on the surface running in the processing machine. Friction is an example of phenomena in which the properties of the materials in contact influence the properties of sonic and ultrasonic signals and could therefore be characterized by AE analysis. Similarly, as in the previous two examples the complexity of this stochastic phenomenon prevents an analytical determination of a relation between AE signal characteristics and the properties of the production process and the
0
I
0.15 kHz
0 2
0 25
03
distributation
paper surface. Consequently, we again apply empirical modeling of the relation between the AE power spectrum and the process and surface descriptors. 5.2. Experiments
on chamctrrizrrtion
qf‘prrper quality
The experimental system is shown in Fig. 8. It is composed of a mechanical unit, in which the friction between an AE sensor and the paper surface is generated on a rotating paper sample, and an information processing system that comprised a spectrum analyser and a computer in which the empirical modeling is performed. The prototype vectors that are formed during learning in this case contain two types of data: the dynamic ones that are provided on-line by sensors which are monitoring typical variables during the friction process, and the static ones that are obtained by standard off-line meas-
I. Grahrc et al. / Ultrasoniu 36 (I 998) 263-271
270
Sl . PZT sensor
Pinducer
VP 1093
S2
0.005
.
0.0045
gramophone
needle
‘sp2.I.e-
Stanton
‘1glZ.tst’ -
0.004 0.0035
3 0.0006 0.0004
1
1.5
2
2.5
4
kHz
S1
PZT sensor
6
8
Ml2
Pinducer VP 1093 ‘sp3.M
S2
gramophone
needle
-
Stanton ‘igl3.w’
z
-
0.0008
5 0.0006
0
0.5
1
1.S
2
2.5
kHz
Sl - PZT senxx
kHz
Pinducer
VP 1093
S2 - gramophone
needle
Stanton
0.005 ‘spS.tAt’
0 0045
0.0014
-
‘igl5 tst’
-
0.004 0.003s 0.003 F ;
0002s 0.002 0.0015 0.001 0.0005 0 0
0.5
1.5
1
2
0
2.5
kHz
Fig. 10. Spectral distributions
2
4
6
8
kHz
of AE signals from the PZT sensor (left)
urement of surface roughness, hardness, etc. During the on-line characterization of a paper surface only the dynamic data are provided by on-line measurement, while the complementary static data are estimated by the modeler from the stored prototypes. In the experiment an especially constructed PZT sensor was utilized. The size and the shape of the contact surface as well as the contact force were varied during experimentation. In addition to this sensor a ‘Stanton’ gramophone head was also used. Examinations have shown that better results of classification of tested paper samples into re-determined paper classes were achieved by using the gramophone head than by the PZT transducer. Fig. 9 shows a characteristic record of a sample profile measured off-line using a stylus method. The same figure also shows the power spectrum of the
and the gramophone
head (right).
that would be observed if the point of observation were moving along the recorded surface profile with a velocity of 0.3 m s-l. This velocity corresponds to the speed of the paper tape in the experimental production machine. The most powerful components of the spectral density are observed mainly in the lower audible frequency region. Such records were further used for an analytical estimation of the signals generated in the AE sensors during their sliding along the paper surface. The true spectral distributions of the AE signals which were measured by the PZT sensor and the gramophone head are presented on Fig. 10. for three typical classes of paper quality. The complete experiment included measurement of AE spectra and surface roughness on a statistical set of similar samples for each type of paper. Altogether five
fluctuations
paper classes were used in the experimental investigations. From each class 20 samples were randomly selected. On each sample AE spectrum was measured 64 times and the average value of all records were used to represent the sample. Two types of modeling were performed. In the first one five representative samples were selected from all 20 samples based on visual observation of measured spectral distributions. These samples were then used as prototypes in the empirical model. In the second type of modeling the prototypes were determined automatically based upon self-organized adaptation. With respect to classification accuracy a better modeling result was obtained using the selforganization procedure. The information stored in the modeler was further applied for the on-line estimation of the paper class. In the examination of the modeler performance only the spectral distribution of the AE signal and the encoded descriptor of the paper class were considered. The task of the modeler was to estimate the paper class from the given AE spectrum. The performance was tested on an additional set of 50 randomly selected samples. The percentage of correct classification of test samples was 98% when using the gramophone head and 89% when using the PZT sensor. The better performance of the gramophone head is probably a consequence of its smaller sensor tip.
6. Conclusions Our experiments show that the acoustic emission phenomenon can be successfully utilized in a characterization of manufacturing and other industrial processes. For this purpose the nonparametric empirical modeling of natural phenomena can be considered as a basic tool. However, each particular process requires a specific design of AE sensors with properly adapted response characteristics. As shown above, for the purpose of
monitoring, not only ultrasonic but also audible region could be of importance. For successful monitoring attention must also be paid to the pre-processing of signals. In the cases presented here the spectral distributions and correlation functions have been utilized, but additional investigations have revealed that various methods which have already been developed during the research of chaotic dynamics also show promise for monitoring techniques [ 11. However. an on-line monitoring method is not the only final goal of application of acoustic emission in the industry. Recent explorations indicate that the nonparametric empirical modeling is also applicable for an optimal control of processes based on detected AE signals [6]. Therefore. intensive research in this direction is expected in the near future.
Acknowledgement The autors wish to acknowledge the support given to their projects by the Ministry for Science and Technology of Slovenia and the Volkswagen Foundation in Germany.
References [I] E. Govekar. Prediction of technical process parameters by means of neural networks. Ph.D. Thesis. No. D:l60. lYY4. [2] P.A. Devijver. J. Kittler. Pattern Recognition: A Statistical Approach. Prentice Hall. Englewood Clifis. YJ. 1982. [3] E. Susie. I. Grabec, Analysis of grinding process acoustic emission by a neural network. in: Ultrasonics International ‘93. Vienna. 1993, pp. 252-254. [4] I. Grdbec, W. Sachse, Automatic modeling ot physical phenomena: application to ultrasonic data. J. Appl. Phys. 69 (9) (1991) 6213-6244. [5] I. Grabec. Self-organization of neurons described by the mawimumentropy principle, Biolog. Cybernetics 63 ( lY90) 403 409. [6] I. Grabec. W. Sachse. Synergetics of Measurements. Prediction. and Control. Springer. Berlin. 1997.