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Surface wavelength content based clustering using neural networks for manufacturing process mapping
International Journal of Machine Tools & Manufacture 43 (2003) 369–377
Surface wavelength content based clustering using neural networks for manufacturing process mapping B. Muralikrishnan a, J. Raja a,∗, K. Najarian b a b
Center for Precision Metrology, The University of North Carolina at Charlotte, Charlotte, NC 28223, USA Computer Science Department, The University of North Carolina at Charlotte, Charlotte, NC 28223, USA Received 31 October 2001; received in revised form 15 September 2002; accepted 11 November 2002
Abstract Manufacturing processes produce a unique texture on the surface that serves as a fingerprint of the process. It is possible to provide feedback to the process by studying the surfaces carefully. Analytical techniques such as Fourier analysis and digital filters are commonly used to characterize surface profiles. Parameters extracted from filtered profiles are monitored to detect variations in the process. This requires the development of an inference engine to map metrology parameters to manufacturing process parameters. This paper presents an artificial neural network (ANN) based inference engine for providing process feedback with surface finish input. Parameters such as Ra and Wa as well as advanced wavelet based features are extracted from surface finish data collected from a crankshaft manufacturing line and fed as input to the neural network. This input is then clustered using a competitive neural network trained in unsupervised mode. The resulting clusters are analyzed and discussed. The network is then tested with new data to evaluate the quality of the clusters previously generated and to demonstrate the applicability of this technique for detecting process variations. 2002 Elsevier Science Ltd. All rights reserved. Keywords: Neural networks; Surface metrology; Process diagnostics; Wavelet
1. Introduction Manufacturing processes produce a characteristic finish on the surface. The finish is unique to the process and it depends on a number of process and machine parameters such as feed, speed, tool material, machinetool stiffness etc. Because every process leaves behind a ‘fingerprint’ on the surface, it is only natural to use surface finish as a tool for detecting process variations. The use of surface profiles to control the process has been reported by Whitehouse in several articles [1][2] and also in the Handbook of Surface Metrology [3]. Raja [4][5] and Whitehouse [4] have shown how surface profiles can also be used to monitor the state of a machine tool. Traditionally, analytical tools have been used to characterize surface finish data. Parameters extracted
∗
Corresponding author. E-mail address: [email protected] (J. Raja).
from filtered profiles are used to quantify surface texture. These parameters are then monitored for any variations in the process. In a typical manufacturing facility with several shifts, surface finish is recorded at regular intervals. The profiles themselves are rarely stored for later reference. A large amount of data that could potentially be used for diagnostic purposes is thus discarded every day. In fact, process monitoring is almost non-existent in most cases; surface finish is typically used only for tolerance compliance and never for diagnostics. In order use surface finish for diagnostics, it is not only necessary to capture surface profile information over a long period of time, but also to develop an inference engine that maps surface finish to the process. There has been reported work in this area. Rao and Raja [6] have developed a knowledge-based system for predicting manufacturing process variations using surface finish. Rule based systems are however subjective and fixed boundaries always perform poorly on borderline cases. This paper presents a neural network approach to
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classifying surface texture data for manufacturing process mapping. Surface finish data were collected from ground and polished crankshafts over a period of three months. The data from these crankshafts are used to cluster the parts into different groups based on the wavelength content in the signal. A crankshaft contains complicated geometry and inspection of such geometries is very difficult. The surface finish of a crankshaft is important as it directly influences the function of the crank and can be used indirectly to provide valuable feedback on the grinding and polishing process. The resulting clusters from the neural network are examined and the results are discussed. The network is then tested on new data sets to evaluate the quality of the clusters and also to demonstrate the applicability of this technique for process mapping. Feature extraction is important for the performance of the neural network. This paper presents two approaches for feature extraction. In the first case, traditional parameters for numerical quantization of surface profiles such as Ra and Wa [7] are used as input to the network. In the second case, wavelets [8] are used to decompose the signal into multiple levels. The information from the coefficients is then used as input to the network. The application of wavelets for surface texture characterization has been reported by several researchers [9–11]. Neural networks have been commonly used in modeling manufacturing processes [12], for detecting tool condition [13–14] and for predicting surface roughness [15– [21]. However, manufacturing processes mapping using surface finish input with a neural network engine is a new area of application. Recent trends in outsourcing and distributed manufacturing make it necessary to control the process more closely. Because the syntax for surface finish is not exhaustive, the key to ensure desired functionality and reduced liability costs is to monitor the process. Thus, the motivation to develop tools for process monitoring and diagnostics comes from economics, a legal standpoint and the desire to build a knowledgebase of the process. This paper presents a neural network based tool for this purpose. Such toolboxes can be easily implemented in surface finish instruments, thus providing a mechanism for monitoring the process in the background while routine inspection of parts is being carried out on the floor. An overview of competitive neural networks is presented in the next section. Subsequent sections present the results from clustering using simple inputs and wavelets based inputs. This is followed by a discussion of the results and conclusions.
architecture and working of a neural network are referred to Fausett [22]. Unsupervised competitive networks are considered for this application because of the large number of data sets being dealt with and the lack of any information regarding the process itself. The architecture of a competitive network is shown in Fig. 1. Each neuron computes the distance between the weights to itself and the input vector. The distances of the input vector to each neuron are d1 ⫽ 冑(Ra⫺w11)2 ⫹ (Wa⫺w21)2 d2 ⫽ 冑(Ra⫺w12)2 ⫹ (Wa⫺w22)2 d3 ⫽ 冑(Ra⫺w13)2 ⫹ (Wa⫺w23)2
(1)
d4 ⫽ 冑(Ra⫺w14)2 ⫹ (Wa⫺w24)2 where Ra and Wa are the inputs, wij is the weight from the ith input to the jth neuron and di is the distance of the input vector to the ith neuron. The competitive layer identifies the winning neuron as the one that is closest to the input and assigns it a value of 1. The other neurons are assigned a value of zero. The weights of the winning neuron are updated according to the training rule below wij ⫽ wij ⫹ a(xi⫺wij)
(2)
where a is the training rate. Each input is presented to the network sequentially to cover one epoch. This process is iterated over several epochs till there is insignificant change in the error function between two epochs. The error function is computed as the sum of the squares of the distances of the training vectors to the nearest centre. In some cases, a subset of the nodes does all of the learning. A modification of the training rule called frequency-sensitive learning [23] addresses this problem. In this case, the distance functions are modified by defining
2. Competitive neural networks in unsupervised mode This paper presents unsupervised training of competitive neural networks for process mapping. The definition,
Fig. 1. Competitive neural network architecture for process clustering with simple inputs.
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a new distance function that is computed as the distance function in Eq. (1) multiplied by the number of times that neuron won in the previous learning competitions.
3. Manufacturing process overview and data collection Surface finish data is collected in a crankshaft manufacturing facility over a period of three months. A crankshaft undergoes numerous operations such as rough turning, milling, grinding, heat treatment, quenching, bearing grinding and polishing before entering the inspection room for final surface finish analysis. All surface texture measurements are made in the inspection room using the Rapid Stylus Profilometer [24]. Surface texture is recorded for both ground and polished crankshafts. One hundred and sixteen profiles are collected from ground crankshafts. Of these, one hundred profiles are used to train the neural network and the remaining sixteen are used to test the network. Eighty-nine profiles are collected from finished polished crankshafts. Eighty of these are used to train another neural network and the remaining nine are used in testing. The final finish on the crankshaft is the result of a number of manufacturing operations and serves to meet many different functional needs. A study by Malburg [25] illustrates the relationship between surface finish, manufacturing process and functional requirements of a crankshaft surface effectively.
4. Competitive neural networks for clustering with simple inputs In this section, training and testing results obtained by using competitive neural networks with very simple inputs are presented. The architecture of the network with two inputs and four neurons is shown in Fig. 1. The network was built with one layer of neurons for simplicity. The number of neurons was set to four because it was perceived that there would be approximately four output clusters (low and high roughness, low and high waviness). It was found that 20 epochs was sufficient to learn the training set, at which point, the error function begins to plateau. The learning rate was set to 0.1 to ensure reasonably fast learning. All surface profiles are filtered using a Gaussian filter with 0.8 mm cut-off according to ISO 11562 [26]. Ra and Wa values are calculated for each profile. These values are used as input to the neural network and the network is trained for clustering. The network is then tested with a different data set to evaluate the robustness of the clustering scheme.
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Table 1 Weight matrix table for ground profiles with simple inputs Neuron1 Weights before training 0.6946 Ra 0.6213 Wa Weights after training 0.5371 Ra 0.2081 Wa
Neuron2
Neuron3
Neuron4
0.7948 0.9568
0.5226 0.8801
0.173 0.9797
1.0589 0.1854
0.6463 0.3
0.3986 0.1764
4.1. Training and testing data from ground profiles An unsupervised competitive network with frequency sensitive implementation with four neurons is trained with the data from ground profiles over 20 epochs at a learning rate of 0.1. The initial and final weights for the training data from ground profiles are given in Table 1. The final weights after training the network on ground profiles indicates four clusters whose centres are given by the pair (Ra,Wa) in Table 1. Table 1 suggests a clustering scheme that depends more on Ra than on Wa. This is visually illustrated in Fig. 2. It can be seen from Fig. 2 that the parts produced from the grinding process fall into four broad clusters that range from low Ra to high Ra. Parts with low Ra are desirable products from the process. Parts with medium Ra are tolerable while parts with large Ra (could be due to chatter), may not have suitable performance. It is of interest to note that the clustering scheme using simple inputs such as Ra and Wa does not show any dependence on the waviness parameter Wa. While training the network can provide information about parts already produced, the motivation for building
Fig. 2.
Clustering ground profiles with simple inputs.
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Table 2 Weight matrix table for polished profiles with simple inputs Neuron1 Weights before training 0.7271 Ra 0.3093 Wa Weights after training 0.0649 Ra 0.0746 Wa
Neuron2
Neuron3
Neuron4
0.8385 0.5681
0.3704 0.7027
0.5466 0.4449
0.0724 0.2381
0.0620 0.1469
0.0633 0.1084
4.2. Training and testing data from polished profiles
Fig. 3. Testing ground profile clusters with simple inputs.
a neural network is to use it real-time for detecting any variations in the process as parts are continuously being produced in a plant. The network is tested with a different data set to emphasize the value of building a neural inference engine. The testing results indicate that some of the parts coming out of the line have high Ra values that could be because of chatter. The inference engine is able to deduct process variations as well as part functionality from the cluster information. The testing results are plotted in Fig. 3. Fig. 4 shows a representative profile from each cluster. One of the key advantages of developing such an inference engine is its use in both offline and online applications. While this paper has demonstrated an offline example, online situations where surface texture parameters are collected and dynamically fed to ANN inference engines are feasible, although not available yet.
Another competitive neural network with frequency sensitive implementation with four neurons is trained with the data from eighty polished profiles over 20 epochs at 0.1 learning rate. The initial and final weights are given in Table 2. From Table 2, it can noted that the centres of the cluster after training are more dependent on Wa than on Ra. Fig. 5 illustrates this visually. These clusters are in direct contrast to those obtained from ground profiles. The engineer at the line can infer that the tape polishers are introducing significant waviness while removing the high frequency signal in the crankshafts. It is thought that the removal of a high frequency signal is the result of the nature of material removal during the polishing process. Because the width of the polishing tape is smaller than the width of the bearing, the tape slides back and forth over the bearing surface during the polishing operation. This could potentially result in uneven material removal that could lead to large waviness in the surface. The network is then tested with the remaining nine data sets and the results are plotted in
Fig. 4. Representative profile of ground crankshafts from each cluster. Fig. 5.
Clustering of polished profiles with simple inputs.
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Fig. 6.
Testing polished profile clusters with simple inputs.
Fig. 6. The testing data clearly falls in appropriate zones indicating good clustering during training. Fig. 7 shows a representative profile from each cluster.
5. Competitive networks with wavelets feature extraction As an improvement over the clustering scheme developed in the previous section, an advanced clustering scheme with wavelet feature extraction is performed. All surface profiles are analyzed using a ‘coif4’ wavelet at eight levels. The power of the coefficients at each level are evaluated and sent as input to the neural network. Thus, there are nine inputs to the neural network for each profile (eight inputs from the details at each level and the approximation from the 8th level). The power at each level is computed as the root sum square of the coefficients divided by the number of coefficients at each level. Coif4 wavelet is chosen based on a study by Liu [27].
Fig. 7. Representative profile of polished crankshafts from each cluster.
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The schematic of the neural network with nine inputs and four neurons is shown in Fig. 8 (A8, D8, D7 etc represent the power of the coefficients at each level). Each level of the decomposition corresponds to a certain wavelength band as indicated in Fig. 8. As before, the weights before training are randomly selected from the input data set. The weights after training represent the coordinates of the centre of each cluster. Because the objective of clustering is to group profiles with similar wavelength contents together, the results are plotted with the approximation at level 8 in the vertical axis and details in the horizontal axis. It is important to note that the clustering scheme discussed in the previous section was based on partitioning a signal into two distinct wavelength bands: one signal contained all wavelengths below 0.8 mm and another signal contained all wavelengths above 0.8 mm. In this case, the input profile is sent through a wavelet transform that partitions the signal into multiple bands. The approximation layer contains all the long wavelength components in the signal while the details at each level contain a certain band of surface wavelengths depending on the scale. 5.1. Training and testing data from ground profiles An unsupervised network with four neurons is trained over eight epochs at 0.1 learning rate. A frequency selective implementation is used. The weights of the neurons from each input are tabulated in Table 3. The results are plotted for visual inspection in Figs. 9 and 10. From Fig. 9, it can be seen that the network has clustered ground profiles into four categories—(1) large A8 (waviness); (2) low D8 (roughness) and medium A8; (3) low D8 and low D8; and (4) large D8 with medium A8. This clustering scheme accounts for the effect of both the large wavelength and the small wavelength content in the signal.
Fig. 8. Competitive neural network architecture with wavelet inputs for process clustering.
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Table 3 Weight matrix for ground profiles with wavelet inputs Neuron1 Weights A8 D8 D7 D6 D5 D4 D3 D2 D1 Weights A8 D8 D5 D6 D5 D4 D3 D2 D1
Neuron2
before training 0.6408 0.3651 0.1909 0.3932 0.8439 0.5915 0.1739 0.1197 0.1708 0.0381 0.9943 0.4586 0.4398 0.8699 0.34 0.9342 0.3142 0.2644 after training 162.8799 439.8738 14.3205 193.3541 14.4 131.2064 13.1396 48.7622 6.9295 9.3105 2.2103 2.1302 0.5358 0.4372 0.0868 0.07 0.0084 0.0073
Neuron3
Neuron4
0.1603 0.8729 0.2379 0.6458 0.9669 0.6649 0.8704 0.0099 0.137
0.8188 0.4302 0.8903 0.7349 0.6873 0.3461 0.166 0.1556 0.1911
47.0482 15.3462 12.0853 7.2345 3.6757 1.4463 0.4081 0.0683 0.0067
135.3127 119.3393 85.4134 34.3099 8.4691 1.6444 0.3441 0.0583 0.0061
Fig. 10. Ground profiles clusters: Plot of long wavelength (A8) vs short wavelengths (D5).
Ra (low wavelengths), the scheme here shows the effect of both high and low frequency components depending on the level chosen. The network is then tested with the sixteen data sets as before. Fig. 11 plots the results from feeding the network with the testing data set. It can be seen that most of parts fall in acceptable zones while one of the parts has large D8 and large A8. If data sets are collected over a longer period of time, this network can then be used for real-time process mapping.
Fig. 9. Ground profile clusters: Plot of long wavelength (A8) vs short wavelengths (D8).
As there are multiple inputs, it is now possible to study the clustering results at more than one level. For example, the clustering plot in Fig. 9 shows clear demarcation between different zones. However, this clarity decreases in Fig. 10. In Fig. 10, the clusters are merged to form two broad clusters that depend on the long wavelengths alone. This is because of the dominant long wavelength components in the signal at that scale. While the clustering scheme in the previous section (Fig. 2) classified the ground parts predominantly on the basis of
Fig. 11. Testing ground profile clusters with wavelet inputs.
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Table 4 Weight matrix for polished profiles with wavelet inputs Neuron1
Neuron2
Weights before training 0.9316 0.8376 A8 0.3352 0.3716 D8 0.6555 0.4253 D7 0.3919 0.5947 D6 0.6273 0.5657 D5 0.6991 0.7165 D4 0.3972 0.5113 D3 0.4136 0.7764 D2 0.6552 0.4893 D1 Weights after training 5.9469 14.7205 A8 0.0892 0.0904 D8 0.0818 0.0804 D7 0.062 0.0645 D6 0.0517 0.0553 D5 0.0324 0.0342 D4 D3 0.0151 0.0161 0.0051 0.0055 D2 0.0013 0.0015 D1
Neuron3
Neuron4
0.1859 0.7006 0.9827 0.8066 0.7036 0.485 0.1146 0.6649 0.3654
0.14 0.5668 0.823 0.6739 0.9994 0.9616 0.0589 0.3603 0.5485
26.2496 0.0916 0.09 0.0777 0.0551 0.0318 0.0147 0.005 0.0013
62.5407 0.1016 0.0841 0.0617 0.0475 0.0284 0.0126 0.0043 0.0012
5.2. Training and testing data results from polished profiles An unsupervised network with four neurons is trained over 20 epochs at 0.1 learning rate. A frequency selective implementation is used. The weight matrices for the polished profiles are tabulated in Table 4. The results are plotted in Figs. 12 and 13. It is interesting to note that the finished products do not show any clustering that
Fig. 12. Polished profile clusters: Plot of long wavelength (A8) vs short wavelengths (D8).
Fig. 13. Polished profiles clusters: Plot of long wavelength (A8) vs short wavelengths (D5).
depends on the details (low wavelengths). The clustering is clearly demarcated at all levels and depends only on the waviness (approximation at level 8). This is of considerable interest to the quality engineer and the manufacturing engineer at the plant for establishing process stability and for predicting functional performance of components. The network is then tested with eight data sets and the results are plotted in Fig. 14.
Fig. 14.
Testing polished profile clusters with wavelet inputs.
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6. Discussion Sections 4 and 5 presented the results of clustering using a competitive neural network with different inputs. While it appears that the network performed reasonable clustering with simple inputs (Ra, Wa), it is observed that there is a qualitative improvement in clustering with features extracted with wavelets. The reason for this improvement lies in the strength of the signal at different scales. The approximation at level 8 corresponds to the long wavelength components (known as waviness) while the details correspond to short wavelength bands. While clustering ground profiles with features extracted from Gaussian filter, the different short wavelength bands are lumped to one signal that contains all wavelengths below 0.8 mm. The strength of this signal is considerably high and it dominates over the large wavelength effects. This has resulted in a clustering scheme that depends only on Ra. This shortcoming is overcome by the use of wavelets. Because the network now sees multiple inputs coming from different scales, it is able to detect subtle variations in the long wavelength components while also recognizing the patterns in the short wavelength components. It is interesting to note that finishing process has totally removed the short wavelength effects and introduced waviness into the profile that is evident at all scales. Current surface texture analysis systems do not have data storage and process monitoring tools. While they have a wide array of analysis tools to compute parameters on single profiles, they are not capable of analyzing multiple profiles or in establishing temporal relationships between profiles collected over a shift. Conventional power-frequency analysis is typically used in isolating single peaks in the frequency spectrum, as in detecting chatter. However, it is not possible to cluster data from multiple profiles collected over an entire shift. The toolbox described in this article utilizes traditional analysis techniques to isolate features from surface profiles to cluster data collected over several shifts to provide insight into the manufacturing process and eventually the function of the components. It is of value to note that all of the components fall within the specification for surface roughness (Ra). In light of this, it is particularly important to note the presence of multiple clusters in the data sets. An untrained operator merely looking at Ra value can easily pass all components during quality inspection. However, the presence of the neural network on the manufacturing line will aid the engineer in assessing the quality of the products produced. As conventional surface texture measurement instruments are geared towards verifying specification rather than performing process diagnostics, this tool will provide considerable value addition to traditional surface metrology. This neural network can be integrated with traditional surface finish measurement
equipment to provide the engineer with more process specific and functional information on the parts and not simply if the part meets or does not meet the specification. The key results can be summarized as 앫 Wavelet-based feature extraction provide scale based information for the network to cluster data effectively 앫 Characterizing the process at multiple stages, not just the final step, provides more data for advanced diagnostics 앫 The neural network toolbox with surface metrology input is useful for process mapping and also adds value to quality control.
7. Conclusions This paper has explored the use of a competitive neural network operating in unsupervised mode to cluster surface profiles of crankshafts produced in a manufacturing facility. Surface profiles collected over a long period of time are used to train a neural network and the resulting clusters are examined and analyzed. The results obtained from clustering ground profiles are significantly different from those obtained from the finished product. This result could be of considerable value to the engineers in the plant to evaluate process stability and assess component’s function. The neural network toolbox can be integrated with commercial instruments to provide real time process diagnostic capability. As current surface texture inspections are merely used for tolerance compliance, integration of advanced tools such as these will add value to surface finish measurements. This work is undertaken as part of a larger effort to develop a surface finish toolbox for manufacturing process diagnostics and functional correlation.
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Surface wavelength content based clustering using neural networks for manufacturing process mapping B. Muralikrishnan a, J. Raja a,∗, K. Najarian b a b
Center for Precision Metrology, The University of North Carolina at Charlotte, Charlotte, NC 28223, USA Computer Science Department, The University of North Carolina at Charlotte, Charlotte, NC 28223, USA Received 31 October 2001; received in revised form 15 September 2002; accepted 11 November 2002
Abstract Manufacturing processes produce a unique texture on the surface that serves as a fingerprint of the process. It is possible to provide feedback to the process by studying the surfaces carefully. Analytical techniques such as Fourier analysis and digital filters are commonly used to characterize surface profiles. Parameters extracted from filtered profiles are monitored to detect variations in the process. This requires the development of an inference engine to map metrology parameters to manufacturing process parameters. This paper presents an artificial neural network (ANN) based inference engine for providing process feedback with surface finish input. Parameters such as Ra and Wa as well as advanced wavelet based features are extracted from surface finish data collected from a crankshaft manufacturing line and fed as input to the neural network. This input is then clustered using a competitive neural network trained in unsupervised mode. The resulting clusters are analyzed and discussed. The network is then tested with new data to evaluate the quality of the clusters previously generated and to demonstrate the applicability of this technique for detecting process variations. 2002 Elsevier Science Ltd. All rights reserved. Keywords: Neural networks; Surface metrology; Process diagnostics; Wavelet
1. Introduction Manufacturing processes produce a characteristic finish on the surface. The finish is unique to the process and it depends on a number of process and machine parameters such as feed, speed, tool material, machinetool stiffness etc. Because every process leaves behind a ‘fingerprint’ on the surface, it is only natural to use surface finish as a tool for detecting process variations. The use of surface profiles to control the process has been reported by Whitehouse in several articles [1][2] and also in the Handbook of Surface Metrology [3]. Raja [4][5] and Whitehouse [4] have shown how surface profiles can also be used to monitor the state of a machine tool. Traditionally, analytical tools have been used to characterize surface finish data. Parameters extracted
∗
Corresponding author. E-mail address: [email protected] (J. Raja).
from filtered profiles are used to quantify surface texture. These parameters are then monitored for any variations in the process. In a typical manufacturing facility with several shifts, surface finish is recorded at regular intervals. The profiles themselves are rarely stored for later reference. A large amount of data that could potentially be used for diagnostic purposes is thus discarded every day. In fact, process monitoring is almost non-existent in most cases; surface finish is typically used only for tolerance compliance and never for diagnostics. In order use surface finish for diagnostics, it is not only necessary to capture surface profile information over a long period of time, but also to develop an inference engine that maps surface finish to the process. There has been reported work in this area. Rao and Raja [6] have developed a knowledge-based system for predicting manufacturing process variations using surface finish. Rule based systems are however subjective and fixed boundaries always perform poorly on borderline cases. This paper presents a neural network approach to
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classifying surface texture data for manufacturing process mapping. Surface finish data were collected from ground and polished crankshafts over a period of three months. The data from these crankshafts are used to cluster the parts into different groups based on the wavelength content in the signal. A crankshaft contains complicated geometry and inspection of such geometries is very difficult. The surface finish of a crankshaft is important as it directly influences the function of the crank and can be used indirectly to provide valuable feedback on the grinding and polishing process. The resulting clusters from the neural network are examined and the results are discussed. The network is then tested on new data sets to evaluate the quality of the clusters and also to demonstrate the applicability of this technique for process mapping. Feature extraction is important for the performance of the neural network. This paper presents two approaches for feature extraction. In the first case, traditional parameters for numerical quantization of surface profiles such as Ra and Wa [7] are used as input to the network. In the second case, wavelets [8] are used to decompose the signal into multiple levels. The information from the coefficients is then used as input to the network. The application of wavelets for surface texture characterization has been reported by several researchers [9–11]. Neural networks have been commonly used in modeling manufacturing processes [12], for detecting tool condition [13–14] and for predicting surface roughness [15– [21]. However, manufacturing processes mapping using surface finish input with a neural network engine is a new area of application. Recent trends in outsourcing and distributed manufacturing make it necessary to control the process more closely. Because the syntax for surface finish is not exhaustive, the key to ensure desired functionality and reduced liability costs is to monitor the process. Thus, the motivation to develop tools for process monitoring and diagnostics comes from economics, a legal standpoint and the desire to build a knowledgebase of the process. This paper presents a neural network based tool for this purpose. Such toolboxes can be easily implemented in surface finish instruments, thus providing a mechanism for monitoring the process in the background while routine inspection of parts is being carried out on the floor. An overview of competitive neural networks is presented in the next section. Subsequent sections present the results from clustering using simple inputs and wavelets based inputs. This is followed by a discussion of the results and conclusions.
architecture and working of a neural network are referred to Fausett [22]. Unsupervised competitive networks are considered for this application because of the large number of data sets being dealt with and the lack of any information regarding the process itself. The architecture of a competitive network is shown in Fig. 1. Each neuron computes the distance between the weights to itself and the input vector. The distances of the input vector to each neuron are d1 ⫽ 冑(Ra⫺w11)2 ⫹ (Wa⫺w21)2 d2 ⫽ 冑(Ra⫺w12)2 ⫹ (Wa⫺w22)2 d3 ⫽ 冑(Ra⫺w13)2 ⫹ (Wa⫺w23)2
(1)
d4 ⫽ 冑(Ra⫺w14)2 ⫹ (Wa⫺w24)2 where Ra and Wa are the inputs, wij is the weight from the ith input to the jth neuron and di is the distance of the input vector to the ith neuron. The competitive layer identifies the winning neuron as the one that is closest to the input and assigns it a value of 1. The other neurons are assigned a value of zero. The weights of the winning neuron are updated according to the training rule below wij ⫽ wij ⫹ a(xi⫺wij)
(2)
where a is the training rate. Each input is presented to the network sequentially to cover one epoch. This process is iterated over several epochs till there is insignificant change in the error function between two epochs. The error function is computed as the sum of the squares of the distances of the training vectors to the nearest centre. In some cases, a subset of the nodes does all of the learning. A modification of the training rule called frequency-sensitive learning [23] addresses this problem. In this case, the distance functions are modified by defining
2. Competitive neural networks in unsupervised mode This paper presents unsupervised training of competitive neural networks for process mapping. The definition,
Fig. 1. Competitive neural network architecture for process clustering with simple inputs.
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a new distance function that is computed as the distance function in Eq. (1) multiplied by the number of times that neuron won in the previous learning competitions.
3. Manufacturing process overview and data collection Surface finish data is collected in a crankshaft manufacturing facility over a period of three months. A crankshaft undergoes numerous operations such as rough turning, milling, grinding, heat treatment, quenching, bearing grinding and polishing before entering the inspection room for final surface finish analysis. All surface texture measurements are made in the inspection room using the Rapid Stylus Profilometer [24]. Surface texture is recorded for both ground and polished crankshafts. One hundred and sixteen profiles are collected from ground crankshafts. Of these, one hundred profiles are used to train the neural network and the remaining sixteen are used to test the network. Eighty-nine profiles are collected from finished polished crankshafts. Eighty of these are used to train another neural network and the remaining nine are used in testing. The final finish on the crankshaft is the result of a number of manufacturing operations and serves to meet many different functional needs. A study by Malburg [25] illustrates the relationship between surface finish, manufacturing process and functional requirements of a crankshaft surface effectively.
4. Competitive neural networks for clustering with simple inputs In this section, training and testing results obtained by using competitive neural networks with very simple inputs are presented. The architecture of the network with two inputs and four neurons is shown in Fig. 1. The network was built with one layer of neurons for simplicity. The number of neurons was set to four because it was perceived that there would be approximately four output clusters (low and high roughness, low and high waviness). It was found that 20 epochs was sufficient to learn the training set, at which point, the error function begins to plateau. The learning rate was set to 0.1 to ensure reasonably fast learning. All surface profiles are filtered using a Gaussian filter with 0.8 mm cut-off according to ISO 11562 [26]. Ra and Wa values are calculated for each profile. These values are used as input to the neural network and the network is trained for clustering. The network is then tested with a different data set to evaluate the robustness of the clustering scheme.
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Table 1 Weight matrix table for ground profiles with simple inputs Neuron1 Weights before training 0.6946 Ra 0.6213 Wa Weights after training 0.5371 Ra 0.2081 Wa
Neuron2
Neuron3
Neuron4
0.7948 0.9568
0.5226 0.8801
0.173 0.9797
1.0589 0.1854
0.6463 0.3
0.3986 0.1764
4.1. Training and testing data from ground profiles An unsupervised competitive network with frequency sensitive implementation with four neurons is trained with the data from ground profiles over 20 epochs at a learning rate of 0.1. The initial and final weights for the training data from ground profiles are given in Table 1. The final weights after training the network on ground profiles indicates four clusters whose centres are given by the pair (Ra,Wa) in Table 1. Table 1 suggests a clustering scheme that depends more on Ra than on Wa. This is visually illustrated in Fig. 2. It can be seen from Fig. 2 that the parts produced from the grinding process fall into four broad clusters that range from low Ra to high Ra. Parts with low Ra are desirable products from the process. Parts with medium Ra are tolerable while parts with large Ra (could be due to chatter), may not have suitable performance. It is of interest to note that the clustering scheme using simple inputs such as Ra and Wa does not show any dependence on the waviness parameter Wa. While training the network can provide information about parts already produced, the motivation for building
Fig. 2.
Clustering ground profiles with simple inputs.
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Table 2 Weight matrix table for polished profiles with simple inputs Neuron1 Weights before training 0.7271 Ra 0.3093 Wa Weights after training 0.0649 Ra 0.0746 Wa
Neuron2
Neuron3
Neuron4
0.8385 0.5681
0.3704 0.7027
0.5466 0.4449
0.0724 0.2381
0.0620 0.1469
0.0633 0.1084
4.2. Training and testing data from polished profiles
Fig. 3. Testing ground profile clusters with simple inputs.
a neural network is to use it real-time for detecting any variations in the process as parts are continuously being produced in a plant. The network is tested with a different data set to emphasize the value of building a neural inference engine. The testing results indicate that some of the parts coming out of the line have high Ra values that could be because of chatter. The inference engine is able to deduct process variations as well as part functionality from the cluster information. The testing results are plotted in Fig. 3. Fig. 4 shows a representative profile from each cluster. One of the key advantages of developing such an inference engine is its use in both offline and online applications. While this paper has demonstrated an offline example, online situations where surface texture parameters are collected and dynamically fed to ANN inference engines are feasible, although not available yet.
Another competitive neural network with frequency sensitive implementation with four neurons is trained with the data from eighty polished profiles over 20 epochs at 0.1 learning rate. The initial and final weights are given in Table 2. From Table 2, it can noted that the centres of the cluster after training are more dependent on Wa than on Ra. Fig. 5 illustrates this visually. These clusters are in direct contrast to those obtained from ground profiles. The engineer at the line can infer that the tape polishers are introducing significant waviness while removing the high frequency signal in the crankshafts. It is thought that the removal of a high frequency signal is the result of the nature of material removal during the polishing process. Because the width of the polishing tape is smaller than the width of the bearing, the tape slides back and forth over the bearing surface during the polishing operation. This could potentially result in uneven material removal that could lead to large waviness in the surface. The network is then tested with the remaining nine data sets and the results are plotted in
Fig. 4. Representative profile of ground crankshafts from each cluster. Fig. 5.
Clustering of polished profiles with simple inputs.
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Fig. 6.
Testing polished profile clusters with simple inputs.
Fig. 6. The testing data clearly falls in appropriate zones indicating good clustering during training. Fig. 7 shows a representative profile from each cluster.
5. Competitive networks with wavelets feature extraction As an improvement over the clustering scheme developed in the previous section, an advanced clustering scheme with wavelet feature extraction is performed. All surface profiles are analyzed using a ‘coif4’ wavelet at eight levels. The power of the coefficients at each level are evaluated and sent as input to the neural network. Thus, there are nine inputs to the neural network for each profile (eight inputs from the details at each level and the approximation from the 8th level). The power at each level is computed as the root sum square of the coefficients divided by the number of coefficients at each level. Coif4 wavelet is chosen based on a study by Liu [27].
Fig. 7. Representative profile of polished crankshafts from each cluster.
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The schematic of the neural network with nine inputs and four neurons is shown in Fig. 8 (A8, D8, D7 etc represent the power of the coefficients at each level). Each level of the decomposition corresponds to a certain wavelength band as indicated in Fig. 8. As before, the weights before training are randomly selected from the input data set. The weights after training represent the coordinates of the centre of each cluster. Because the objective of clustering is to group profiles with similar wavelength contents together, the results are plotted with the approximation at level 8 in the vertical axis and details in the horizontal axis. It is important to note that the clustering scheme discussed in the previous section was based on partitioning a signal into two distinct wavelength bands: one signal contained all wavelengths below 0.8 mm and another signal contained all wavelengths above 0.8 mm. In this case, the input profile is sent through a wavelet transform that partitions the signal into multiple bands. The approximation layer contains all the long wavelength components in the signal while the details at each level contain a certain band of surface wavelengths depending on the scale. 5.1. Training and testing data from ground profiles An unsupervised network with four neurons is trained over eight epochs at 0.1 learning rate. A frequency selective implementation is used. The weights of the neurons from each input are tabulated in Table 3. The results are plotted for visual inspection in Figs. 9 and 10. From Fig. 9, it can be seen that the network has clustered ground profiles into four categories—(1) large A8 (waviness); (2) low D8 (roughness) and medium A8; (3) low D8 and low D8; and (4) large D8 with medium A8. This clustering scheme accounts for the effect of both the large wavelength and the small wavelength content in the signal.
Fig. 8. Competitive neural network architecture with wavelet inputs for process clustering.
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Table 3 Weight matrix for ground profiles with wavelet inputs Neuron1 Weights A8 D8 D7 D6 D5 D4 D3 D2 D1 Weights A8 D8 D5 D6 D5 D4 D3 D2 D1
Neuron2
before training 0.6408 0.3651 0.1909 0.3932 0.8439 0.5915 0.1739 0.1197 0.1708 0.0381 0.9943 0.4586 0.4398 0.8699 0.34 0.9342 0.3142 0.2644 after training 162.8799 439.8738 14.3205 193.3541 14.4 131.2064 13.1396 48.7622 6.9295 9.3105 2.2103 2.1302 0.5358 0.4372 0.0868 0.07 0.0084 0.0073
Neuron3
Neuron4
0.1603 0.8729 0.2379 0.6458 0.9669 0.6649 0.8704 0.0099 0.137
0.8188 0.4302 0.8903 0.7349 0.6873 0.3461 0.166 0.1556 0.1911
47.0482 15.3462 12.0853 7.2345 3.6757 1.4463 0.4081 0.0683 0.0067
135.3127 119.3393 85.4134 34.3099 8.4691 1.6444 0.3441 0.0583 0.0061
Fig. 10. Ground profiles clusters: Plot of long wavelength (A8) vs short wavelengths (D5).
Ra (low wavelengths), the scheme here shows the effect of both high and low frequency components depending on the level chosen. The network is then tested with the sixteen data sets as before. Fig. 11 plots the results from feeding the network with the testing data set. It can be seen that most of parts fall in acceptable zones while one of the parts has large D8 and large A8. If data sets are collected over a longer period of time, this network can then be used for real-time process mapping.
Fig. 9. Ground profile clusters: Plot of long wavelength (A8) vs short wavelengths (D8).
As there are multiple inputs, it is now possible to study the clustering results at more than one level. For example, the clustering plot in Fig. 9 shows clear demarcation between different zones. However, this clarity decreases in Fig. 10. In Fig. 10, the clusters are merged to form two broad clusters that depend on the long wavelengths alone. This is because of the dominant long wavelength components in the signal at that scale. While the clustering scheme in the previous section (Fig. 2) classified the ground parts predominantly on the basis of
Fig. 11. Testing ground profile clusters with wavelet inputs.
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Table 4 Weight matrix for polished profiles with wavelet inputs Neuron1
Neuron2
Weights before training 0.9316 0.8376 A8 0.3352 0.3716 D8 0.6555 0.4253 D7 0.3919 0.5947 D6 0.6273 0.5657 D5 0.6991 0.7165 D4 0.3972 0.5113 D3 0.4136 0.7764 D2 0.6552 0.4893 D1 Weights after training 5.9469 14.7205 A8 0.0892 0.0904 D8 0.0818 0.0804 D7 0.062 0.0645 D6 0.0517 0.0553 D5 0.0324 0.0342 D4 D3 0.0151 0.0161 0.0051 0.0055 D2 0.0013 0.0015 D1
Neuron3
Neuron4
0.1859 0.7006 0.9827 0.8066 0.7036 0.485 0.1146 0.6649 0.3654
0.14 0.5668 0.823 0.6739 0.9994 0.9616 0.0589 0.3603 0.5485
26.2496 0.0916 0.09 0.0777 0.0551 0.0318 0.0147 0.005 0.0013
62.5407 0.1016 0.0841 0.0617 0.0475 0.0284 0.0126 0.0043 0.0012
5.2. Training and testing data results from polished profiles An unsupervised network with four neurons is trained over 20 epochs at 0.1 learning rate. A frequency selective implementation is used. The weight matrices for the polished profiles are tabulated in Table 4. The results are plotted in Figs. 12 and 13. It is interesting to note that the finished products do not show any clustering that
Fig. 12. Polished profile clusters: Plot of long wavelength (A8) vs short wavelengths (D8).
Fig. 13. Polished profiles clusters: Plot of long wavelength (A8) vs short wavelengths (D5).
depends on the details (low wavelengths). The clustering is clearly demarcated at all levels and depends only on the waviness (approximation at level 8). This is of considerable interest to the quality engineer and the manufacturing engineer at the plant for establishing process stability and for predicting functional performance of components. The network is then tested with eight data sets and the results are plotted in Fig. 14.
Fig. 14.
Testing polished profile clusters with wavelet inputs.
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6. Discussion Sections 4 and 5 presented the results of clustering using a competitive neural network with different inputs. While it appears that the network performed reasonable clustering with simple inputs (Ra, Wa), it is observed that there is a qualitative improvement in clustering with features extracted with wavelets. The reason for this improvement lies in the strength of the signal at different scales. The approximation at level 8 corresponds to the long wavelength components (known as waviness) while the details correspond to short wavelength bands. While clustering ground profiles with features extracted from Gaussian filter, the different short wavelength bands are lumped to one signal that contains all wavelengths below 0.8 mm. The strength of this signal is considerably high and it dominates over the large wavelength effects. This has resulted in a clustering scheme that depends only on Ra. This shortcoming is overcome by the use of wavelets. Because the network now sees multiple inputs coming from different scales, it is able to detect subtle variations in the long wavelength components while also recognizing the patterns in the short wavelength components. It is interesting to note that finishing process has totally removed the short wavelength effects and introduced waviness into the profile that is evident at all scales. Current surface texture analysis systems do not have data storage and process monitoring tools. While they have a wide array of analysis tools to compute parameters on single profiles, they are not capable of analyzing multiple profiles or in establishing temporal relationships between profiles collected over a shift. Conventional power-frequency analysis is typically used in isolating single peaks in the frequency spectrum, as in detecting chatter. However, it is not possible to cluster data from multiple profiles collected over an entire shift. The toolbox described in this article utilizes traditional analysis techniques to isolate features from surface profiles to cluster data collected over several shifts to provide insight into the manufacturing process and eventually the function of the components. It is of value to note that all of the components fall within the specification for surface roughness (Ra). In light of this, it is particularly important to note the presence of multiple clusters in the data sets. An untrained operator merely looking at Ra value can easily pass all components during quality inspection. However, the presence of the neural network on the manufacturing line will aid the engineer in assessing the quality of the products produced. As conventional surface texture measurement instruments are geared towards verifying specification rather than performing process diagnostics, this tool will provide considerable value addition to traditional surface metrology. This neural network can be integrated with traditional surface finish measurement
equipment to provide the engineer with more process specific and functional information on the parts and not simply if the part meets or does not meet the specification. The key results can be summarized as 앫 Wavelet-based feature extraction provide scale based information for the network to cluster data effectively 앫 Characterizing the process at multiple stages, not just the final step, provides more data for advanced diagnostics 앫 The neural network toolbox with surface metrology input is useful for process mapping and also adds value to quality control.
7. Conclusions This paper has explored the use of a competitive neural network operating in unsupervised mode to cluster surface profiles of crankshafts produced in a manufacturing facility. Surface profiles collected over a long period of time are used to train a neural network and the resulting clusters are examined and analyzed. The results obtained from clustering ground profiles are significantly different from those obtained from the finished product. This result could be of considerable value to the engineers in the plant to evaluate process stability and assess component’s function. The neural network toolbox can be integrated with commercial instruments to provide real time process diagnostic capability. As current surface texture inspections are merely used for tolerance compliance, integration of advanced tools such as these will add value to surface finish measurements. This work is undertaken as part of a larger effort to develop a surface finish toolbox for manufacturing process diagnostics and functional correlation.
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