Multi-sensor integration for on-line tool wear estimation through radial basis function networks and fuzzy neural network

Neural Networks PERGAMON

Neural Networks 12 (1999) 355–370

Contributed article

Multi-sensor integration for on-line tool wear estimation through radial basis function networks and fuzzy neural network R.J. Kuo a,*, P.H. Cohen b a

b

Department of Industrial Engineering, National Taipei University of Technology, Taipei, Taiwan 10643, ROC Department of Industrial and Manufacturing Engineering, The Pennsylvania State University, University Park, PA 16804, USA Received 7 July 1997; accepted 13 October 1998

Abstract On-line tool wear estimation plays a very critical role in industry automation for higher productivity and product quality. In addition, appropriate and timely decision for tool change is significantly required in the machining systems. Thus, this paper is dedicated to develop an estimation system through integration of two promising technologies, artificial neural networks (ANN) and fuzzy logic. An on-line estimation system consisting of five components: (1) data collection; (2) feature extraction; (3) pattern recognition; (4) multi-sensor integration; and (5) tool/work distance compensation for tool flank wear, is proposed herein. For each sensor, a radial basis function (RBF) network is employed to recognize the extracted features. Thereafter, the decisions from multiple sensors are integrated through a proposed fuzzy neural network (FNN) model. Such a model is self-organizing and self-adjusting, and is able to learn from the experience. Physical experiments for the metal cutting process are implemented to evaluate the proposed system. The results show that the proposed system can significantly increase the accuracy of the product profile. 䉷 1999 Elsevier Science Ltd. All rights reserved. Keywords: Production and process control; Metal cutting; Multi-sensor integration; Radial basis function network; Fuzzy neural network

1. Introduction Wear of the cutting tool is an inevitable result of the metal cutting process (Dan, 1990). Since undesirable effects of tool wear include: (1) a loss in dimensional accuracy of the finished product; and (2) possible damage to the workpiece, the on-line prediction of cutting tool wear becomes crucial. There has been some research on tool wear estimation over the past several years, and models including analytical and empirical models have been proposed. However, most of them are lack practical application. Thus, some researchers have applied ANNs in this area recently. Tansel (1990) developed two ANN systems to represent cutting dynamics. The ANN systems are applicable to the cutting speed in the range of 50–105 m/min. Tansel and Laughlin (1991) also used Adaptive Resonance Theory (ART2) for detection of tool breakage in milling operations, with a 97.2% success rate. Guillot and Ouafi (1991) provided time domain inputs to a feedforward three-layer ANN which identified tool breakage at its output for milling. Similar applications are found in various reports (Malakooti and Zhou, 1992; Khanchustambham and Zhang, 1992; Elanayar and Shin, 1992; Das et al., 1996). However, all * Corresponding author; e-mail: [email protected]

the research only considers the case of a single sensor. Using a single sensor to monitor tool wear is generally not very reliable in practice. It is important to develop a multisensor integration method which can combine multiple sensor signals for reliable prediction, and also detect a defective sensor and compensate for it. Rangwala and Dornfeld (1987); Rangwala (1988); Rangwala and Dornfeld (1989); Rangwala and Dornfeld (1990) applied ANNs for monitoring tool wear states during a turning operation. A multiple sensor scheme utilizing cutting force and acoustic emission information was presented. In this work, using a Fast Fourier Transformation (FFT) yields the power spectrum representations of the time domain records. Combining the acoustic emission and cutting force spectra resulted in a vector of dimensions. Features were fed into an ANN for pattern recognition purposes. The results showed a 95% success rate for classifying binary tool wear states, fresh and worn. Chryssolouris and Domroese (1988, 1989) proposed an intelligent controller which uses a multi-sensor approach for process monitoring. Their paper focused on the module which integrates the sensor-based information in order to provide the controller with the best possible estimates for tool wear and wear rate. Three techniques, ANNs, leastsquares regression and the group method of data handling

0893-6080/99/$ - see front matter 䉷 1999 Elsevier Science Ltd. All rights reserved. PII: S0893-608 0(98)00137-3

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(GMDH) algorithm were employed for integration. Tests indicated that, when compared to the GMDH and leastsquares regression techniques, ANNs were more effective at learning a relationship for providing parameters and estimates, especially when the relationship between the sensorbased information and the actual parameter is non-linear. In addition, ANNs do not seem to be more sensitive, and in some cases may be less sensitive than the other sensor integration schemes considered, to deterministic errors in the sensor-based information. Later, a statistical approach (Chryssolouris et al., 1991, 1992), was used. The problem of this approach is that there is no information on the probability density function of tool wear. It is typically assumed to be Gaussian. Before applying the above-mentioned statistical approach for integration, the confidence distance measure for the support of sensor i by sensor j, defined as dij ˆ 2A where A is the area under the probability density curve Pi(u |xi) between xi and xj, is used to eliminate the non-consensus sensory values first. Masory (1991) has proposed a tool wear model based on the EBP learning algorithm of ANNs. Wherein, during training, the input vector to the network consists of the true RMS of the acoustic emission signal and the three components of the cutting force. Though this research tried to predict the continuous amount of tool wear, only a single cutting condition was performed. Similarly, ANNs were also applied by Kamarthi et al. (1991) as the pattern recognizer, where the input vector was the parameter of ARMA(8,8) and a Kohonen’s feature mapping network was used. Force and vibration sensors were used in this application. Kohonen’s feature map was also applied by Leem and Dreyfus (1992) for sensor fusion in turning, with 94% and 92% accuracy for classification into two and three levels of tool wear, respectively. Tansel (1992) used ART2 to combine the information from the dynamometer and laser vibrometer in drilling. The proposed system accurately detects the pre-failure phase, i.e. different cutting conditions, for all the cases. In addition, Kuo and Cohen (1998) employed three different sensors: force, vibration and acoustic emission; to estimate the amount of tool wear through feedforward neural network with EBP learning algorithm. Recently, fuzzy models have also been employed in tool wear monitoring where input is always divided into several groups with a vague boundary (Zadeh, 1965; Ko and Cho, 1994). This circumstance is very similar to tool wear where the status is fuzzy. It has been shown how to use fuzzy models to recognize the fuzziness of tool wear status. Similarly, the tool wear monitored is tool wear state instead of continuous value. However, most states can not be accurately applied in practice. Artificial neural networks (ANNs), fuzzy logic and genetic systems constitute three independent research fields regarding sixth generation systems (SGS) [Hertz et al., 1992; Freeman and Skapura, 1991; Kosko, 1992]. Motivated by the results in each of these areas and the potential

for mutual progress in computational modeling, integration of these concepts is very important (Kosko, 1992). ANNs and the fuzzy model have been used in many application areas (Lippmann, 1987; Lee, 1990a, 1990b), each pairing its own advantages and disadvantages. Thus, the integration of ANN and fuzzy logic has recently become a very promising research area (Jang, 1991, 1992; Jang and Sun, 1993; Takagi and Hayashi, 1991; Wang and Mendel, 1992; Shibata et al., 1992; Fukuda and Shibata, 1992; Nakayama et al., 1992; Lin and Lee, 1991, 1994; Kuo, 1999a, 1999b). Therefore, how to successfully combine these two approaches, ANNs and fuzzy modeling, in order to improve the performance of each and apply them in the tool wear estimation are two main objectives of this research. This research work applies the radial basis function (RBF) network to recognize the sensory signal pattern collected from the sensors. Moreover, a proposed fuzzy neural network (FNN) model, which is self-organizing and self-adjusting and is able to learn from experience, is employed to integrate the decisions from the different sensors. For the FNN model, the inputs and outputs are partitioned by Kohonen’s feature mapping, and the premise and consequence parameters are updated via an error backpropagation (EBP)-type learning algorithm. Physical experiments will be used in order to evaluate the proposed system. Three different kinds of sensors (force, vibration and acoustic emission) are used to detect sensory information about the cutting tool wear. The basic structure of the estimation system is to acquire the sensory signal pattern from each sensor first; then extract the features from the sensory signal pattern. RBFNs are employed to recognize the features from each sensor. Each RBFN provides a decision, the amount of tool wear, for each sensor. Then, the multi-sensor integration method (FNN) is applied to combine all the decisions from the different sensors. The proposed method is able to predict the continuous amount of tool wear better than multiple regression and RBFN both in speed and accuracy. In addition, the predicted amount of tool wear is used to adjust the distance between the working material and cutting tool in order to increase the precision of the finished product. The rest of this paper is organized as follows. Section 2 proposes the development of an on-line estimation system, while the methods for the experimental validation are described in Section 3. The data obtained from experiments described in Section 3 are used to evaluate the proposed system, and the results and discussion are detailed in Section 4. Sections 5 and 6 present the discussion and conclusions, respectively. Finally, future study is presented in Section 7.

2. Methodology An on-line estimation system for the amount of tool wear is proposed in this section. The system consists of five components: (1) data acquisition; (2) feature extraction;

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Fig. 1. Multi-sensor integration system.

(3) pattern recognition; (4) multi-sensor integration; and (5) tool/work distance compensation. Fig. 1 shows the general structure of the estimation system. 2.1. Data acquisition This system (Fig. 1) first collects a sensory signal pattern corresponding to particular characteristics of the process. Three sensors are assumed to be used, and from these three sensors, three sensory signal patterns can be collected through the acquisition system. 2.2. Feature extraction Different sensory signal patterns or signatures correspond to the wearing state of the tool. In order to analyze the relationship between the signal patterns and the amount of tool wear, it is critical to extract the features of the sensory

signal patterns in advance. Two different kinds of feature extraction methods, time series analyzer and frequency analyzer, were tested. Intuitively, time series consists of the sensory signal patterns obtained from sensors. By analyzing the time series data, a simple mathematical time series model can be constructed. This model concisely represents the time series data. The coefficients of the model can then be treated as the features. Three different kinds of models can be used. Thus, it is necessary to determine the suitability of the autoregressive model (AR), moving average model (MA), or ARMA, for the current data. For frequency analyzer, the Fourier Transformation (FT) is used to transform the time series data into the frequency domain. The algorithm used is the Fast FT (FFT). Five peak values of the frequency data points are selected as the features after examining the spectrum.

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2.3. Pattern recognition In this component, RBFNs (Moody and Darken, 1989) are employed to recognize the features corresponding to different amounts of tool wear. The inputs of the network are derived from the above feature extraction algorithms. Thus, if the number of features is n, then the number of network input nodes is also n. The number of outputs, which is the amount of tool wear, is one. Basically, the RBF network is a two-layer network whose output units form a linear combination of the basis (kernel) functions computed by the hidden units. The basis function in the hidden layer produces a localized response to the input. The most applied basis function is the Gaussian function, which is used for this study due to easy implementation. In the aspect of learning, the RBF network is much faster than the EBP network. The main reason is that the learning process of the RBF network consists of two stages. Thus, it is reasonable to call it a hybrid neural network, which combines the unsupervised and supervised learning algorithms. It should be reiterated that a single network is used for each sensor. Thus, if there are n sensors, then n total RBFNs should be implemented. Through these networks, n different predictions can be obtained. Next, a new approach for multisensor integration, FNN, will be employed in order to integrate these predicted amounts of tool wear. 2.4. Multi-sensor integration In multi-sensor integration, a new method (FNN) [Takagi and Sugeno, 1983] is employed. Basically, FNN consists of two stages as follows. 2.4.1. Self-organizing stage (SOS) SOS plays an important role in defining the membership function and in the consequence. The procedures of SOS are as follows: 1. Clustering: Kohonen’s feature mapping is used to divide the training data into a specified number of groups, and each group corresponds to an inference rule. 2. Shape and position determination: different membership functions can be chosen depending on the domain. As discussed by Wang and Mendel (1992), fuzzy modeling with membership functions of scaled Gaussian functions is actually a universal approximator that can approximate any non-linear input–output data arbitrarily well on a compact set. Thus, three parameters of a scaled Gaussian function should be determined. For each group or rule, the mean of the group is set as the center of the membership function. The width of the membership function is set as three times the standard deviation of each group. 3. Consequence determination: the consequence, which is the control action of each inference rule, is determined for each group, or rule, using the linear regression.

2.4.2. Self-adjusting stage (SAS) This stage basically employs the learning capability of the ANN to update the parameters, which have already been predetermined by the SOS, of fuzzy modeling. Consequently, fuzzy modeling should be represented as a form of an ANN. The proposed architecture of the used fuzzy model is based on Takagi’s fuzzy system (Takagi and Sugeno, 1983). The fuzzy model is then trained by using the EBPtype algorithm. 2.4.3. Learning algorithm for fuzzy model Based on the above fuzzy model, the corresponding ANN structure can be represented. The proposed fuzzy ANN consists of five layers. 1. Layer 1: the input layer which consists of the real-valued input variables. Intuitively, these variables are the sensory readings, or the single decision obtained from each ANN. In this research, they are the predicted amounts of tool wear from the sensors. 2. Layer 2: every node in this layer is the value of the membership function. 3. Layer 3: every node in this layer possesses the capability of multiplication. It is equivalent to the meaning of the firing strength in fuzzy modeling. 4. Layer 4: this layer calculates the i-th firing strength proportional to the sum of all the firing strengths. 5. Layer 5: this is the output layer which combines all the control action values from all the inference rules. In this research, the output is the amount of tool wear after multi-sensor integration. The weights connecting any two nodes are 1, except the weights between layers 4 and 5. They are the consequences for each rule. Since Takagi’s model is employed, these consequences are regression models. The proposed learning algorithm for the fuzzy model is trained by using the EBPtype algorithm so as to minimize the cost function E, which is defined as: Eˆ

1X e …z ⫺ Oe †2 2 e

where z and O are the desired and actual outputs, respectively, and e is the training example number. Each parameter of the control action function is updated by an amount proportional to the partial derivative of E with respect to that parameter. The updated learning rule is of the form …t⫹1† ˆ w…t† wi;j i;j ⫺ h

2E 2wi;j

where wij is the updated parameter and h is the training rate. All the above-mentioned equations are used to fine-tune the parameters which have been determined by SAS of the fuzzy inference system.

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Fig. 2. Modified FNN structure for testing.

2.4.4. Modified FNN structure for testing In the previous section, a new approach for multi-sensor integration was proposed. But that approach is only for training purposes. It needs to be modified for the condition of defective sensors. Fig. 2 shows the differences between the regular FNN and modified FNN. The main purpose of the change is to find the inconsistent sensor and change its prediction. The first step of the change is to find the most likely group for each sensory input. For instance, input i, the membership function of the linguistic term ‘small’ provides a larger value than the other linguistic terms. This implies that input i more properly belongs to the member ‘small’. On the basis of this linguistic variable, the membership function values for the others are calculated, and the absolute differences of membership function values between input i and the others are calculated as well. By definition, if these differences are all larger than the pre-defined threshold, then input i is not consistent with the other inputs. In

other words, input i is not in the same membership as the other inputs. In such a situation, input i is replaced by the largest input value and the membership function values are recalculated. Because it is better to overestimate the amount of tool wear instead of underestimating, the inconsistent input i is replaced by the largest input of the other input values. In the practical application, this will avoid breaking the cutting tool. 2.5. Tool/work distance compensation The final decision, the amount of tool wear, which is made by the multi-sensor integration technique, is used to decide whether the tool is fresh or worn out, and how to adjust the distance between the tool and working material. The approach used to keep the distance between the working material and tool constant is to adjust the depth of cut during the operation of CNC turning machines. For example, in the CNC turning machine program, the depth

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Fig. 3. Tool/work distance compensation.

of cut is adjusted according to the following equation: D…t ⫹ 1† ˆ D…t† ⫹ DD…t† where: W(t) ˆ the amount of tool wear at time t; D(t) ˆ the depth of cut at time t; DW(t) ˆ (W(t) ⫺ W(t ⫺ 1)); and DD(t) ˆ DW(t)tan(clearance angle) for each monitoring iteration. Fig. 3 shows that when the amount of flank wear is W(t), then the depth of cut should be increased by DD(t). If W(t) is larger than a predetermined constant, then a tool change is made.

3. Experimental setup In order to evaluate the proposed system, 20HP LeBlonde lathe was used. Three types of sensors: force, vibration and

acoustic emission; were employed (Fig. 4). For forces in the feed, radial and main cutting directions, a three-axis Kistler Z3392/b piezoelectric force dynamometer was used, while two PCB accelerometers were employed for vibrations in the feed and main cutting directions. A Physical Acoustics acoustic emission sensor, placed at the center of the tool holder, was used for monitoring acoustic emission signals. Force sensors, vibration sensors and acoustic emission sensor were connected to the Kistler 3-channel model 5804 charge amplifier, PCB charge amplifiers and DECI AE preamplifier, respectively. The force sensory outputs were connected to a National Instruments acquisition board connected to an IBM-compatible PC with the LabView software package, while vibration sensory outputs were connected to a Tektronix 2630 Fourier Analyzer connected to an IBM-compatible PC with a Fourier Analyzer package. The acoustic emission output was connected to an ANALOGIC acquisition board which was connected to an IBM-compatible PC with ANALOGIC FAST Series package. The sampling rates of forces, vibrations and acoustic emission were 3 KHz, 25.6 KHz and 1 MHz, respectively. In addition, in order to make sure that all three acquisition systems were triggered at the same time, an automatic trigger was connected to the three systems. Once the trigger was initiated, it started all three data acquisition systems simultaneously. This allowed sensor data to be taken at the end of a cut and the measured wear was found to correlate with the sensor data obtained. A chip breaker was mounted on top of the insert in order to avoid damage to the sensors by the chips. The flank wear was measured by Baush and Lomb toolmaker’s microscope, while surface roughness was measured

Fig. 4. The experimental setup.

R.J. Kuo, P.H. Cohen / Neural Networks 12 (1999) 355–370 Table 1 The cutting conditions and the corresponding tool numbers

Feed (inch)

Speed (fpm) 100

130

160

0.0064 0.0088 0.0112 0.0136 0.0156

T1 T2 T3 T4 T5

T6 T7 T8 T9 T10

T11 T12 T13 T14 T15

using a Federal Systems Pocket Surf. A Starrett micrometer caliper was used for measuring the diameter of the workpiece. All the sensory signals from three cutting forces in the feed, radial and main cutting directions, two vibrations in the feed and main cutting directions, and acoustic emission, were collected for each cut and saved as three files. Flank wear of the tool, diameter of workpiece and surface roughness were then measured off-line. All the sensor measurements were sequenced using a common trigger just prior to the end of the cut, as described. This experiment used SAE 6150 chromium–vanadium alloy steel as the test workpiece. The workpiece’s dimensions are 7.5 diameter by 36 length. The quench and tempered heat treatment procedures of the workpiece are as follows: 1. 2. 3. 4.

Heated to 1550F; Oil quenched; Tempered at 600F; Air cooled.

The resultant hardness ranges from 350 to 390 BHN. The Kennamental KSBR-164C tool holder was used for machining, while the cutting insert used was a Kennamental K68 grade carbide insert SPG 422 mounted on the tool holder. The cutting conditions were varied in order to obtain more reliable data sets. Feed rates were varied from 0.0064 ipr to 0.0156 ipr. Levels 0.0064, 0.0088, 0.0112, 0.0136 and 0.0156 ipr were selected. Three different cutting speeds, 100, 130 and 160 sfpm, were used. The depth of cut was kept constant at 0.05 inch. A full factorial experiment was performed. In total, 15 different cutting conditions, or treatments (three speeds × five feeds) were tried. The experimental procedures are described as follows: 1. Mounting the tool insert and chip breaker on the tool holder. 2. Setting up the cutting conditions and calibrating the ANALOGIC FAST Series package for the acoustic emission acquisition. 3. Cutting the workpiece for 1 min and initiation of the trigger at the end of the cut, for approximately 55 s, for collecting the sensory signals for forces in three directions, vibrations in two directions, and acoustic emission.

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4. Saving the sensory signals for force, vibration and acoustic emission in three different files. 5. Removing the tool insert from the tool holder and measuring the flank wear with the Baush and Lomb toolmaker’s microscope. 6. Measuring the diameter with the micrometer and surface roughness using the Federal Pocket Surf. 7. Remounting the tool insert and chip breaker, and repeating Steps (3)–(6) until severe wear, about 0.018 inch, is reached. Approximately 4096 data points were collected for each cutting experiment, but only 1024 data points were used in the next section, model validation. These sensory signal patterns were processed for feature extraction. 4. Model validation results and discussion An on-line estimation system and experimental setup have been discussed in the previous two sections. In this section, the evaluation of the proposed system using the data obtained from the physical experiments is discussed. 4.1. Data acquisition The data are obtained from three forces in the feed, radial and main cutting directions, two vibrations in the feed and main cutting directions, and acoustic emission. The cutting condition and the corresponding tool number are shown in Table 1. In total, 15 tools are employed in this experiment. Each tool has 10–13 samples. The total number of samples is 168. However, these 15 tools are divided into two groups for training and testing. Thus, the shadowed cells represent those data used for training RBFNs and multi-sensor integration methods. Otherwise, they are for the validation of multi-sensor integration methods. As a result of this division, the training samples can cover the range of cutting conditions. Therefore, the numbers of training and testing samples are 89 and 79, respectively. 4.2. Feature extraction Next, the data obtained from experiments are used to extract the features for the magnitudes of forces, vibrations and acoustic emission. 4.2.1. Time series analyzer The sensory signal pattern obtained from the sensor is a time series. In the following discussion, the sensory signal patterns mentioned are the magnitudes of the signals. The test developed by Dickey and Fuller (1976) is applied to test for non-stationarity first. For each sensor, 10 signal patterns are randomly selected. The results showed that most of them are stationary. Thus, it is not necessary to perform any transformation for the data. Then, by examining the autocorrelation function (ACF) and partial ACF (PACF) of the time series data, AR(5) is able to represent all the sensory

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Table 2 The RMS values (inch) after normalization of RBFN for three feature extraction methods

Sensors Force Feed Radial Main cutting Vibration Feed Main cutting Acoustic emission

Feature extraction algorithm Frequency Time domain

Combination

0.0824 0.0369 0.145

0.0693 0.0374 0.0642

0.0664 0.0361 0.0364

0.0994 0.0442 0.0389

0.0831 0.0365 0.238

0.0825 0.0363 0.211

signal patterns of force, vibration and acoustic emission. Since the constant term is also included in the model, there are six total features for all the sensory signal patterns. 4.2.2. Frequency analyzer The data patterns are transformed into frequency domain patterns through the FFT in order to observe the frequency spectrum. Next, the data are sorted, and the five largest values are selected for each pattern as the features of that pattern. 4.3. Pattern recognition In the previous section, the features were extracted through two different analyzers, time series and frequency. The time series analyzer employs AR(5) for all of the patterns, while five peak values are chosen as the features for the frequency analyzer after examining the spectrum. However, it is very important to find the better analyzer for this application. Thus, the features obtained from the above two feature extraction analyzers are used as the inputs to the RBFN, and the following three alternatives will be tested for each sensor: 1. Features extracted by the frequency analyzer; 2. Features extracted by the time series analyzer; and 3. Features extracted by both the frequency and time series analyzers. If an ANN can learn one set of features faster or more accurately than the others, then it is considered better than another. In addition, cutting conditions, feed and speed, and cutting time are also employed as features. For the features extracted from the time series analyzer, the RBFN architecture consists of nine input units, cutting time, speed, feed and six time series features, which are connected to 18 hidden units, which are connected to one output unit (predicted amount of flank wear). For the frequency analyzer, the RBFN architecture consists of eight input units, which are connected to 16 hidden units, which are connected to one output unit. If both of the different analyzers are combined in order to provide the inputs to the RBFN, the network architecture consists of 14 input

units, which are connected to 28 hidden units, which are connected to one output unit. Based on the above three different kinds of feature extraction algorithms, the computation is implemented by using C language. For all the different cases, the training is considered complete when the number of training epochs is 2,000,000, which is determined by examining the topology of the network structure and testing for different cases. Table 2 lists all the computational results, and the root mean square error (RMS) values. If the ANN can learn one training data set with a lower RMS value than the other data set, then it means that the former is more recognizable than the latter. Thus, e.g. the radial force with a combination feature extraction method of 0.0361 RMS value is the least when compared with the other two analyzers; but they are very close. Basically, it is not necessary to choose the combination feature extraction method, since its training time is much longer than the other two. Therefore, both the testing and training results indicate that radial force with frequency features will be the candidate for integration. A similar result exists for the feed and main cutting forces. However, in this research, only one will be selected among three different directions for force sensors. Thus, the radial force with frequency features will be used in the integration. Based on similar concepts, the main cutting vibration using the time series analyzers will be selected. For acoustic emission, features extracted from the frequency analyzer will only have the lowest RMS value, 0.0389. Figs. 5–7 list the testing results for the selected candidates. 4.4. Multi-sensor integration The amounts of tool wear obtained from three sensors, or RBFNs, are combined through three different multi-sensor integration methods: multiple regression, RBFN and FNN, for the purpose of comparison. The predicted and measured amounts of tool wear for training samples will train these three integration methods. In order to make a comparison of these three integration methods, the value of the RMS is calculated as the criterion. RMS was also used by Chryssolouris and Domroese (1989) for the purpose of comparison. By using RMS, the absolute distance between the predicted amount of tool wear and the measured, or actual, amount of tool wear can be observed. 4.4.1. Multiple regression For the regression model, there are three independent variables: predicted amounts of tool wear from the radial force, main cutting vibration and acoustic emission. Meanwhile, the dependent variable is the measured amount of tool wear. The multiple regression model will also include the constant term. The multiple regression model is determined by using the MINITAB statistical software. The fitted model is as follows: y^ ˆ 0:567024x1 ⫹ 0:434192x2 ⫹ 0:0046723x3 ⫹ 0:003911

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Fig. 5. Predicted (- A -) and measured (- V -) flank wear values for radial force with frequency domain features using RBFN.

where y^ is the predicted amount of tool wear after integration, and x1, x2 and x3 are the predicted values from the radial force, main cutting vibration and acoustic emission, respectively. RMS of the predicted amounts of tool wear is equal to 0.0314.

4.4.2. Artificial neural networks (RBFN) For the network, which integrates the results of the radial force, main cutting vibration and acoustic emission, the RBFN architecture consists of three input units which are connected to six hidden units which are connected to one

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Fig. 6. Predicted (- A -) and measured (- V -) flank wear values for main cutting vibration with time series features using RBFN.

output unit. The computational result shows that the value of RMS for the predicted amounts of tool wear is equal to 0.149 as the number of epochs is equal to 2,000,000. 4.4.3. FNN FNN consists of two stages, SOS and SAS. Kohonen’s

feature mapping divides the data into three groups in SOS representing small, medium and large amounts of tool wear, since the wear curve may be easily segmented in this manner for a physical reason. The physical reason means that the increase of tool wear with respect to time can be divided into three stages: fast, slow and

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Fig. 7. Predicted (- A -) and measured (- V -) flank wear values for acoustic emission with frequency domain features using RBFN.

then fast. For each group or rule, the mean and standard deviations are calculated. The center is set to be the mean. The width is set to be three times the standard deviation and the scale is set to be 1 for the initial state. Moreover, the regression model, which is the consequence of each rule or group, is also found. Through the above initial set-up, the self-adjusting stage

will fine-tune all of these parameters, scales, centers, widths and coefficients of the regression models for all of these three rules. Thus, by using the learning algorithm proposed in Section 2.4, these parameters are updated epoch by epoch. After epoch 1000, the RMS drops to 0.0274. If training is continued, RMS will decrease to 0.0263 when the number of epochs is 10,000. This implies that it is not

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Fig. 8. Predicted (- A -) and measured (- V -) amount of tool wear through FNN for cutting SAE6150(370BHN) with Kennamental K68/SPG422 insert.

necessary to train the FNN for a long time, since FNN is able to learn the training samples in a short time and its accuracy is not significantly improved if training is continued. So far, three different methods have been developed. In

the next section, these three methods will be evaluated by 79 test samples. 4.4.4. Testing/validation The testing results via FNN are shown in Fig. 8, and the

R.J. Kuo, P.H. Cohen / Neural Networks 12 (1999) 355–370 Table 3 RMS and percent increase of RMS for normal sensory signal patterns Method

RMS

Percent increase of RMS

FNN RBFN Multiple regression Radial force Main cutting vibration Acoustic emission

0.000732 0.001232 0.000921 0.001061 0.001647 0.001396

*** 68.31 25.82 44.95 125 90.71

RMS values for different integration approaches are shown in Table 3. 4.5. Testing for the defective sensory signal patterns In the above subsection, FNN has been shown to be better compared with multi-sensor integration methods (multiple regression and the RBFN) and the multi-sensor fusion method (RBFN). Defective sensory signal patterns will be used to test the validity of the multi-sensor integration methods (multiple regression, RBFN) and FNN, in this section. Based on the training results of the above three integration methods and one fusion method, the defective sensory signal patterns are artificially generated in order to verify the different methods, as some of the sensors are defective in this section. For the purposes of discussion, it is assumed that the sensor which monitors the radial force is defective and that the signals obtained do not correspond to the amount of tool wear. For the other two sensors, T1’s (100 sfpm speed and 0.0064 ipr feed) sensory signal patterns are used. For the purpose of simulation, the features of the radial force are copied from the main cutting vibration for cutting at 100 sfpm speed, 0.0088 ipr feed and 0.05 inch depth of cut. First, the integration methods are considered. As with the proposed estimation system, the features of each sensor are fed into a RBFN individually before integration. The

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predicted tool flank wear is shown in Table 4. The shadowed cells mean that these values are from the defective sensor, radial force. It is very clear that they are not consistent with the other two sensors predictions. Thereafter, these three amounts of tool wear are combined by multiple regression, RBFN and FNN, respectively. For multiple regression, RBFN and the fusion scheme, the testing structure is the same as the training structure, while there is only a small change for FNN. The main change is to compare the membership function value with the other two membership functions. If the absolute difference is within a predefined range, then the information of this sensor is consistent with the others. Otherwise, the value should be replaced by the largest of the other single sensor predictions. Refer to Section 4.4 for a more detailed explanation. Regarding the fusion method using a RBFN, all the features from three sensors are fed into a RBFN together. The RMS value and percent increase of RMS for each method are shown in Table 5. FNN has by far the smallest RMS value, 0.133, since it is capable of eliminating the inconsistent sensor.

5. Discussions For force sensors in the three directions, i.e. radial, feed and main cutting, a combination of time series and frequency analyzers can provide better convergence for an ANN. This is the same for the vibration sensors in the feed and main cutting directions. For acoustic emission, only features from the frequency domain can represent the sensory signal patterns better than the time domain. The combination of two analyzers provides better results for most of the cases because features extracted from two analyzers can improve each other’s performance. However, the acoustic emission result shows that only using the frequency domain features without combining with time series features can provide better results. This is because the features from the time series model can not be represented

Table 4 Testing amounts of tool wear for cutting SAE6150(370BHN) with Kennamental K68/SPG422 insert at 100 sfpm speed, 0.0088 ipr feed and 0.05 inch depth of cut when the radial force sensor is defective Predicted by sensors Data set Measured (inch)

Radial force (inch)

Main cutting vibration (inch)

Acoustic emission (inch)

T1-1 2 3 4 5 6 7 8 9 10 11 12

0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001

0.002841 0.004781 0.00749 0.008274 0.009979 0.011239 0.01266 0.014471 0.0152 0.016318 0.016904 0.017747

0.003395 0.005272 0.008101 0.010041 0.01047 0.011676 0.01334 0.013928 0.015712 0.017188 0.018712 0.019335

0.0021 0.0044 0.006 0.008 0.0095 0.0111 0.0124 0.0134 0.0142 0.0151 0.0164 0.0171

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Table 5 RMS and percent increase of RMS for defective sensory signal patterns Method

RMS

Percent increase of RMS

FNN RBFN Multiple regression Fusion

0.000796 0.003084 0.002204 0.003259

*** 287.45 176.93 309.41

by a time series. Furthermore, they have the opposite effect on the frequency domain features, since in the network, hidden layer nodes are fully connected to all of these features (i.e. input nodes). Among the forces in the feed, radial and main cutting directions, the radial force is able to converge fastest. For both force and vibration, the main cutting force is better than the feed force. The main reason is that the former is usually larger than the latter in practice. This research work employed RBFN for pattern recognition. For a single sensor, radial force is more closely related to the amount of tool wear based on the testing samples. It is also identical to the training results, since the network trained by radial force features can converge fastest. In multi-sensor integration, the results revealed that FNN can predict the amount of tool wear more accurately than the other two multi-sensor integration methods (multiple regression and RBFN) when no sensor is defective. FNN all outperformed multi-sensor fusion using RBFN. The principle reason is that FNN consists of two stages. The first stage SOS can accelerate the training speed. For the first stage of FNN, the training samples are divided into three groups via Kohonen’s feature mapping. Generally, the number of groups is based on the characteristic of the input and output variables. For this application, tool wear is always divided into three stages: initial, gradual and worn-out. Based on the physics of tool wear, training samples are divided into three groups. Although each group can be further sub-divided, this will not improve the results markedly but will increase training time. In the second stage of FNN, the EBP-type learning scheme can fine-tune the membership function parameters and regression model coefficients. The value of the cost function does not change much for 1000 epochs or 10,000 epochs. This implies that the first stage, SOS, has already organized the training samples very well. SAS only needs to fine-tune the parameters. Thus, the training speed of FNN is much faster than the RBFN. In addition, by comparison to the RBFN, the FNN will more easily find the global minimum instead of a local minimum, since there is the SOS first. The converge speed of FNN is also faster than the RBFN, though RBFN is able to converge faster than the feedforward network with the error backpropagation learning algorithm. Without doubt, the RMS value of FNN is less than the multiple regression’s RMS value. If the training samples are divided into several groups and use a multiple regression

model for each group, then the result will be better than the single multiple regression model. Similarly, FNN is very similar to this method which divides the training patterns into groups and uses a multiple regression model for each group. One difference is that FNN with its membership functions can more accurately model the relationship between the inputs and outputs. Also, the learning capability of FNN can fine-tune the parameters in order to improve accuracy. From the plotting of measured and predicted amounts of tool wear, it can be found that some amounts of tool wear can not be predicted very well because the hardness of the workpiece is not uniformly distributed. The sudden change of the hardness will significantly change the sensory signal patterns. Meanwhile, a crater is also found under conditions of high speed and/or feed. This will also affect the sensory signal patterns. For instance, flank wear will increase the force, while crater wear will decrease the force in some cases. Based on the above discussions, FNN, which is a kind of fuzzy model, is able to predict the amount of tool wear more accurately compared with the other methods. Though Ko and Cho (1994) have applied the fuzzy model for tool wear monitoring in diamond turning, the study only considers three wear states (i.e. initial, gradual and severe) instead of the continuous amount of tool wear. Chryssolouris et al. (1992) employ an ANN and statistical method for continuous amount of tool wear. However, the amount of experimental data is insufficient, since only seven tool inserts are used. For the current study, there is more sufficient experimental data, which is enough for both training and testing.

6. Conclusions In this paper, an on-line estimation system applied in the area of tool wear monitoring has been proposed. The proposed system is able to predict the amount of tool wear accurately. Utilization of RBFN can form a very good relationship between the tool wear value and the extracted features. The proposed multi-sensor integration method, FNN, is found to be more accurate than other methods, including multiple regression and a RBFN on the basis of RMS. It significantly reduces the training time compared with RBFN, since the first stage of FNN, SOS, has divided the training samples into several groups or rules, and the second stage, SAS, only needs to fine-tune the parameters.

7. Future study Future study may include: 1. Since the precision of the multi-sensor integration

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2.

3.

4.

5.

method depends on the precision of pattern recognition, it is necessary to improve the performance of an ANN. In this study, SOSAFM is based on Takagi’s fuzzy model. In Takagi’s fuzzy model, the consequence is a regression model instead of a fuzzy set. In the future, a fuzzy consequence or set may be considered instead of a regression model. An acoustic emission sensor does not provide the accurate prediction expected. In the future, a higher sampling rate should be tried since it may improve the characteristics of sensory signals collected. In this application, only flank wear is concerned. Crater wear should be included in a future study through the use of higher cutting speeds. SGS consists of ANNs, fuzzy logic and genetic algorithms. This study has demonstrated that the combined use of fuzzy logic and ANNs can improve system performance. Genetic algorithms, which have advantages for searching, can be combined with an ANN or fuzzy logic in order to improve its performance.

Acknowledgements This research work was financially supported in part by the National Science Council of Taiwan, ROC under Contract NSC 85-2213-E-214-014. Their support has been appreciated. In addition, the experimental data were collected in the Machining Research Lab., Department of Industrial and Manufacturing Engineering, The Pennsylvania State University, USA. Thus, the grants from the National Science Foundation, Ford and General Motors are also appreciated. The author would also like to thank the anonymous referees for reading the paper and offering many helpful comments.

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