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A neural network-based approach for dynamic quality prediction in a plastic injection molding process
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Expert Systems with Applications Expert Systems with Applications 35 (2008) 843–849 www.elsevier.com/locate/eswa
A neural network-based approach for dynamic quality prediction in a plastic injection molding process Wen-Chin Chen a, Pei-Hao Tai a, Min-Wen Wang b, Wei-Jaw Deng c, Chen-Tai Chen
d,*
a
d
Graduate Institute of Industrial Engineering and System Management, Chung Hua University, 707 Wufu Road, Section 2, Hsinchu 300, Taiwan b Department of Mechanical Engineering, National Kaohsiung University of Applied Sciences, 415 Chien Kung Road, Kaohsiung 807, Taiwan c Graduate School of Business Administration, Chung Hua University, 707 Wufu Road, Section 2, Hsinchu 300, Taiwan Department of Computer Science and Information Engineering, Ta Hwa Institute of Technology, 1 Tahwa Road, Chiunglin, Hsinchu 307, Taiwan
Abstract This paper presents an innovative neural network-based quality prediction system for a plastic injection molding process. A self-organizing map plus a back-propagation neural network (SOM-BPNN) model is proposed for creating a dynamic quality predictor. Three SOM-based dynamic extraction parameters with six manufacturing process parameters and one level of product quality were dedicated to training and testing the proposed system. In addition, Taguchi’s parameter design method was also applied to enhance the neural network performance. For comparison, an additional back-propagation neural network (BPNN) model was constructed for which six process parameters were used for training and testing. The training and testing data for the two models respectively consisted of 120 and 40 samples. Experimental results showed that such a SOM-BPNN-based model can accurately predict the product quality (weight) and can likely be used for various practical applications. 2007 Elsevier Ltd. All rights reserved. Keywords: Neural network-based prediction system; Injection molding process; Self-organizing map; Back-propagation neural network; Dynamic quality predictor; Taguchi’s parameter design method
1. Introduction Plastic injection molding (PIM) is one of the most complex manufacturing processes due to the strong nonlinearities, even though numerous people regard it as a simple and common manufacturing process. This process includes four phases: plasticization, injection, packing, and cooling (Seaman, 1994). In previous injection molding research, many process parameters, such as the melting temperature, mold temperature, injection pressure, injection velocity, injection time, packing pressure, packing time, cooling temperature, and cooling time, were found to possibly influence the quality of injection-molded plastic products (Kurtaran & Erzurumlu, 2006; Zhao & Gao, 1999). Several *
Corresponding author. Tel.: +886 3 592 7700x2929; fax: +886 3 592 5679. E-mail address: [email protected] (C.-T. Chen). 0957-4174/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2007.07.037
PIM control process parameters have been used (Chiang & Chang, 2006; Huang & Tai, 2001; Wu & Liang, 2005). Huang and Tai (2001) presented six process parameters (mold temperature, melt temperature, gate dimension, packing pressure, packing time, and injection time) to determine the optimal initial process parameter settings for injection-molded plastic parts with a thin shell feature and under a single quality characteristic (warpage) consideration. Wu and Liang (2005) employed six process parameters (mold temperature, packing pressure, melt temperature, injection velocity, injection acceleration, and packing time) to discuss the effects of process parameters on the weld-line width of an injection-molded plastic product. Chiang and Chang (2006) proposed four control process parameters (mold temperature, melt temperature, injection pressure, and injection time) to determine the optimal initial process parameter settings for an injectionmolded plastic part with a thin shell feature in a model with
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multiple quality characteristics. Previously, engineers used trial-and-error processes which depend on the engineers’ experience and intuition to determine initial process parameter settings and adjust the process parameters of the injection molding process. However, trial-and-error processes are costly and time consuming, thus they are not optimal for complex manufacturing processes (Lam, Zhai, Tai, & Fok, 2004). In research by Hsu (2004), it was also argued that with a trial-and-error process, it is impossible to verify actual optimal parameter settings. Subsequently, Taguchi’s parameter design method was employed to complete the determination of the initial process parameter settings in industrial applications. However, Taguchi’s parameter design method can only find the best set of specified process parameter level combinations which include the discrete setting values of the process parameters. The application of a conventional Taguchi’s parameter design method is unreasonable when the variable of a process parameter is continuous and cannot help engineers obtain optimal initial process parameter setting results (Su & Chang, 2000). An unsuitable process parameter setting can cause many product defects (e.g., a long lead time, a large amount of scrap material, etc.) and unstable product quality during the injection molding process. Therefore, efficient analytical methodologies and tools are necessary to efficiently and rapidly analyze process parameters and control the product quality. To cope with these challenges, many researchers of injection molding processes have investigated the application of artificial neural networks (ANNs) to quality prediction (Lau, Ning, Pun, & Chin, 2001; Li, Jia, & Yu, 2002; Sadeghi, 2000; Yarlagadda, 2002). The main reason for using ANNs is that neural networks have the ability to ‘‘learn’’ arbitrary nonlinear mappings between noisy sets of input and output data. In finding the optimal parameter settings of an injection molding process, ANNs are also frequently combined with genetic algorithms and fuzzy logic as the quality predictor (Mok & Kwong, 2002; Ozcelik & Erzurumlu, 2006; Shi, Lou, Lu, & Zhang, 2003). In addition, the feedback control model often employs ANNs as a quality predictor (Huang, Tan, & Lee, 2004; Kenig, Ben-David, Omer, & Sadeh, 2001; Liang & Wang, 2002; Wang & Liang, 1999). Therefore, adequate process control and optimal parameter settings of product properties in injection processes require very accurate predictions. When the quality predictor is precise, the quality controller can adjust the controllable parameters closer to the target values of the injection molding process and an efficient optimization model can be obtained. Plastic housing components are widely used in many assembling manufacturing processes to produce final products. Since plastic housing components are usually housed in manufactured products or parts, the dimensional quality characteristics such as weight, length, and thickness are the major quality characteristic for their production. Previously, researchers showed that product weight is a critical quality attribute and a good indicator of manufacturing
process stability during injection molding (Kamal, Varela, & Patterson, 1999; Yang & Gao, 2006). Yang and Gao (2006) revealed that the product weight is an importance quality attribute for injection-molded products because the product weight has a close relation to other quality properties (e.g., surface properties and mechanical properties), particularly those other dimensional properties (e.g., dimensions and thickness). They also claimed that the performance of a manufacturing process and its quality control can be monitored through the product weight. Kamal et al. (1999) showed that the control of product weight is of great commercial interest and can produce great value for production management. Since injection molding is commonly used in the production of plastic housing components, product weight is a feasible single quality characteristic which can be used for product quality control of plastic housing component production via injection molding. In this research, we developed a precise and robust neural network-based prediction model for a plastic injection molding process. A self-organizing map plus back-propagation neural network (SOM-BPNN) model is proposed herein to generate a dynamic quality predictor. Three SOM-based dynamic extraction parameters with six manufacturing process parameters were dedicated to network training and testing. In addition, Taguchi’s design-of-experiment (DOE) method was also applied to enhance neural network performance. The remainder of this paper is organized as follows. Section 2 describes self-organizing maps and the back-propagation neural network. Section 3 specifies the Taguchi parameter design method. Section 4 illustrates the structure of the quality predictor. Section 5 describes the experimental sample and data. Section 6 implements the optimization of neural network parameters using Taguchi’s parameter design method. Section 7 presents experimental results and discussion. Conclusions are drawn in the last section. 2. Self-organizing maps and the back-propagation neural network 2.1. Self-organizing maps Self-organizing maps (SOMs) were developed by Kohonen (1982) and are a peculiar class of artificial neural networks based on unsupervised competitive learning which consists of iteratively modifying the synaptic weights. In self-organizing systems, the output neurons of the network compete among themselves to be activated, and an output neuron winning the competition is called a winner-takes-all neuron or a winning neuron. The neurons, selectively tuned to discrete input patterns, are located on a one- or twodimensional lattice in a topographic map, and they have intrinsic statistical features (nodes). There are three crucial processes, i.e., competition, cooperation and synaptic adaptation, and four principles of self-organization involved in the SOM algorithm (Haykin, 1999). Numerous
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researchers have proposed special SOM models such as the self-organizing Kohonen feature map (SOFM) to achieve high image quality and high compression, and kernel-based self-organizing maps (KSOMs) to cluster non-Euclidean structures in the data (Dai & Chen, 2006; Lee, You, & Park, 2001; Pei, Chuang, & Chuang, 2006). The present study employs a SOM to extract the dynamic process parameter characteristics as the network input. 2.2. Back-propagation neural network In much of the literature, back-propagation neural networks (BPNNs) have been adopted because they have the advantages of a fast response and high learning accuracy (Chen & Hsu, 2006; Lee et al., 2001; Maier & Dandy, 1998; Yao, Yan, Chen, & Zeng, 2005). The superiority of a network’s functional approach depends on the network architecture and parameters, as well as the problem complexity. If an inappropriate network architecture or parameters are selected, undesirable results may be obtained. Conversely, the results will be much more significant if a good network architecture and parameters are selected. The BPNN consists of an input layer, hidden layer, and output layer. The parameters for the BPNN include the number of hidden layers, number of hidden neurons, learning rate, momentum, etc. All of these parameters can significantly impact the performance of the neural network. Fogel (1991) proposed a final information statistical (FIS) process based on Akaike’s information criterion (AIC) to determine the number of hidden layers and neurons. The limitation of Fogel’s research is that the process can only perform simple binary classifications. Murata and Yoshizawa (1994) and Onoda (1995), respectively proposed methods to improve AIC. These methods, called the network information criterion (NIC) and neural network information criterion (NNIC), use statistical probabilities together with an error energy function to determine the number of hidden neurons. In this research, the steepest-descent method was used to find the weight change and to minimize the error energy function. The activation function is a hyperbolic sigmoid function. According to past studies (Cheng & Tseng, 1995; Hush & Horne, 1993), there are a few conditions for network learning termination: (1) when the root mean square error (RMSE) between the expected value and network output value is reduced to a preset value; (2) when the preset number of learning cycles has been reached; and (3) when cross-validation takes place between the training samples and test data. The first two methods are related to the preset values. This research adopts the first and second approaches by gradually increasing the network training time to gradually decrease the RMSE until it is stable and acceptable. The RMSE is defined as follows: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X 2 RMSE ¼ t ð1Þ ðd i y i Þ ; N i¼1
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where N, di, and yi are the number of training samples, the actual value for training sample i, and the predicted value of the neural network for training sample i, respectively. In network learning, input information and output results are used to adjust the weighting values of the network. The more detailed the input training classification and the greater the amount of learning information which are provided, the better the output will conform to the expected result. Since the learning and verification data for the BPNN are limited by the functional values, the data must be normalized by the following equation: PN ¼
P P min ðDmax Dmin Þ þ Dmin ; P max P min
ð2Þ
where PN is the normalized data, P is the original data, Pmax is the maximum value of the original data, Pmin is the minimum value of the original data, Dmax is the expected maximum value of the normalized data, and Dmin is the expected minimum value of the normalized data. When applying the neural network to the system, the input and output values of the neural network fall in the range of [0.1, 0.9]. 3. Taguchi’s parameter design method Taguchi’s parameter design method normally selects an appropriate formulation of the S/N ratio and calculates the S/N ratio for each treatment. There are three types of S/N ratios: nominal the best, the larger the better, and the smaller the better. Most engineers choose the highest S/N ratio treatment as the preliminary optimal initial process parameter setting. Taguchi’s method has also been used to design the parameters for neural networks in previous research (Khaw, Lim, & Lim, 1995; Santos & Ludermir, 1999). Khaw et al. (1995) applied Taguchi’s method to design the parameters and verified that the method could rapidly and robustly design the optimal parameters. Santos and Ludermir (1999) applied a factorial design to assist the design and implementation of a neural network. The formulae of the three types of S/N ratios are given as follows: nominal the best : 2 y S=N ¼ 10 log 2 ; S
ð3Þ
the larger the better :
! n 1X 1 ; and S=N ¼ 10 log n i¼1 y 2i the smaller the better : n 1X y2 S=N ¼ 10 log n i¼1 i
ð4Þ
! ¼ 10 log½y 2 þ S2 ;
ð5Þ
where yi is the response value of a specific treatment under i replications, n is the number of replications, y is the average
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of all yi values, and S is the standard deviation of all yi values. 4. Proposed approach Injection molding is a continuous manufacturing process for product cycles for which the manufacturing parameters are fixed. Process control and optimal parameter settings of product properties in injection molding processes require very accurate quality predictions. When the quality predictor is precise, the quality controller can more closely adjust the controllable parameters to the goals of the injection molding process, and an efficient optimization model can be obtained. Therefore, it is essential to extract the dynamic data of the process parameters in order to enhance the prediction precision of the product quality. This research presents a SOM-BPNN model for a dynamic quality predictor. Three SOM-based extraction parameters with six manufacturing process parameters are dedicated to training and testing the BPNN. The structure of the dynamic quality predictor is shown in Fig. 1. The three SOM-based input parameters are the injection stroke curve, injection velocity curve, and pressure curve, while the six BPNN input parameters are injection time, VP switch position, packing pressure, injection velocity, packing time and injection stroke; one BPNN output variable is weight (quality characteristic). 5. Experimental data Experimental data were collected from a Nissei ES-400 electric injection molding machine, the specifications of which are shown in Table 1. The experimental sample represented in Fig. 2 was measured using a Mettler AE-100
Table 1 Specifications of the Nissei ES-400 injection molding machine Maximum shot weight Maximum pressure Maximum velocity Maximum ram position Screw diameter Clamping force Clearance between tiebars Clamping stroke Minimum mold thickness Maximum daylight (opening)
35 g 255 MPa 210 mm/s 92 mm 22 mm 44 US tons (40 ton) 12.2 · 12.2 in (310 · 310 mm) 9.4 in (240 mm) 6.7 in (170 mm) 21.3 in (540 mm)
Fig. 2. The injection portion of the Nissei ES-400 system.
electric balance which has a precision of 0.05 mg. Three SOM-based parameters (injection stroke curve, injection velocity curve, and pressure curve) and six process parameters (injection time, VP switch position, packing pressure, packing time, injection velocity, and injection stroke) were the input parameters of the model, with one output variable of sample weight. Schematic plots based on the process parameters in the PIM process are shown in Fig. 3. During the injection molding process, these process data
Fig. 1. Structure of the dynamic quality predictor.
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replications, and the predicted weight of injection part (Y) is the evaluation value for different combinations of factor levels. Y is the average of five Y’s in each replication. The optimal combination of factor levels is the experiment with the largest S/N ratio. From the experimental results of Taguchi’s parameter design method, the optimal combination of factor levels is represented by the following: an architecture for BPNN of 9-8-1, the number of calculation generations of 30,000, a learning rate of 0.7, and a momentum of 0.8. 7. Results and discussion
Fig. 3. Schematic plots based on the process parameters of the PIM process.
were collected and stored in the computer database. The collected data can be regenerated into characteristic curves as shown in Fig. 3, where the horizontal axis is time and the vertical axis represents the injection stroke, injection velocity, and pressure. 6. Optimization of the neural network parameters using Taguchi’s parameter design method In this research, we applied the SOM and BPNN to create a dynamic quality predictor, and Taguchi’s parameter design method was used to solve the optimal parameter design problem of the BPNN. Since the number of hidden layers did not have a significant effect on convergence, the number of hidden layer was set to 1. The controlling factors of Taguchi’s method are the number of hidden neurons (P), learning rate (Q), momentum (R), and number of epochs (S). The numbers of neurons in the hidden layer under different levels were obtained by the method proposed by Khaw et al. (1995) and Haykin (1999). Information on the factors’ assumptive settings at different levels is listed in Table 2. The numbers of calculation generations and learning rate were determined by first finding the range in which these factors have better converging results, and second by determining the equal-distance value for the five levels. Under the condition of four factors, five levels, and no correlation among the four factors, the total degrees of freedom were 25 (i.e., 5 · (6 1)). An L25 (56) orthogonal array was selected for arranging the factors and carrying out the experiment. In this experiment, there were five
This research presents a SOM-BPNN-based approach to create a dynamic quality predictor. Three SOM-based dynamic extraction parameters with six BPNN manufacturing process parameters were dedicated to training and testing the network. In addition, Taguchi’s parameter design method was also applied to enhance the neural network performance. The values of the process parameter setting were an injection time of 1.5 s, a VP switch position of 8 mm, a packing pressure of 34 MPa, an injection pressure of 150 MPa, and an injection velocity of 50 mm/s. The neural networks were first trained using 120 samples of training data, then 40 samples of verifying data were used to make predictions, and the network performance was obtained by calculating the RMSE. The network performance between SOM+BPNN and BPNN is shown in Table 3. A comparison between the experimental and predicted values via SOM+BPNN and BPNN quality predictors is represented in Figs. 4 and 5. Based on these results, the training precision of the SOM+BPNN quality Table 3 Comparison of the network performance between the SOM+BPNN and BPNN quality predictors Item
SOM+BPNN
BPNN
Training RMSE Testing RMSE
0.015 0.0017
0.019 0.0029
Table 2 Information on the factors’ assumed settings at different levels Item
Control factor
Level 1
Level 2
Level 3
Level 4
Level 5
P
Number of neurons in the hidden layer Learning rate Momentum Epoch
4
6
8
10
12
0.5 0.5 15,000
0.6 0.6 20,000
0.7 0.7 25,000
0.8 0.8 30,000
0.9 0.9 35,000
Q R S
Fig. 4. Comparison between the predicted and actual values via SOM+BPNN quality predictor.
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References
Fig. 5. Comparison between the predicted and actual values via BPNN quality predictor.
predictor had an RMSE of up to 0.015 and its test precision amount was an RMSE of 0.0017, whereas the training precision of the BPNN quality predictor had an RMSE of up to 0.019 and its testing precision amount was an RMSE of 0.0029. Apparently, the performance of the SOM+BPNN quality predictor was better than that of the BPNN quality predictor. 8. Conclusions Plastic injection molding process control and optimal parameter settings for the product properties require very accurate quality prediction. When the quality predictor is precise, the quality controller can adjust the controllable parameters closer to the targets of the process control, and an efficient optimization model can be obtained for the initial parameter settings. Therefore, it is essential to extract the dynamic data of the process parameters in order to enhance the prediction precision of the product quality in the dynamic system. This research presents a self-organizing map plus a back-propagation neural network (SOM-BPNN) model for the dynamic quality predictor. Three SOM-based extraction parameters with six manufacturing process parameters were dedicated to training and testing the networks. In addition, another back-propagation neural network (BPNN) model was employed for comparison. The numerical results revealed that the proposed dynamic model not only effectively increased the prediction performance of product quality but also obtained more-reliable product quality in advance. In future extensions, the proposed dynamic approach will be employed to the process control for improving the prediction precision of the product quality in the dynamic PIM system. Acknowledgements This research has been conducted as part of a project sponsored by CoreTech System Co., Ltd.
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Expert Systems with Applications Expert Systems with Applications 35 (2008) 843–849 www.elsevier.com/locate/eswa
A neural network-based approach for dynamic quality prediction in a plastic injection molding process Wen-Chin Chen a, Pei-Hao Tai a, Min-Wen Wang b, Wei-Jaw Deng c, Chen-Tai Chen
d,*
a
d
Graduate Institute of Industrial Engineering and System Management, Chung Hua University, 707 Wufu Road, Section 2, Hsinchu 300, Taiwan b Department of Mechanical Engineering, National Kaohsiung University of Applied Sciences, 415 Chien Kung Road, Kaohsiung 807, Taiwan c Graduate School of Business Administration, Chung Hua University, 707 Wufu Road, Section 2, Hsinchu 300, Taiwan Department of Computer Science and Information Engineering, Ta Hwa Institute of Technology, 1 Tahwa Road, Chiunglin, Hsinchu 307, Taiwan
Abstract This paper presents an innovative neural network-based quality prediction system for a plastic injection molding process. A self-organizing map plus a back-propagation neural network (SOM-BPNN) model is proposed for creating a dynamic quality predictor. Three SOM-based dynamic extraction parameters with six manufacturing process parameters and one level of product quality were dedicated to training and testing the proposed system. In addition, Taguchi’s parameter design method was also applied to enhance the neural network performance. For comparison, an additional back-propagation neural network (BPNN) model was constructed for which six process parameters were used for training and testing. The training and testing data for the two models respectively consisted of 120 and 40 samples. Experimental results showed that such a SOM-BPNN-based model can accurately predict the product quality (weight) and can likely be used for various practical applications. 2007 Elsevier Ltd. All rights reserved. Keywords: Neural network-based prediction system; Injection molding process; Self-organizing map; Back-propagation neural network; Dynamic quality predictor; Taguchi’s parameter design method
1. Introduction Plastic injection molding (PIM) is one of the most complex manufacturing processes due to the strong nonlinearities, even though numerous people regard it as a simple and common manufacturing process. This process includes four phases: plasticization, injection, packing, and cooling (Seaman, 1994). In previous injection molding research, many process parameters, such as the melting temperature, mold temperature, injection pressure, injection velocity, injection time, packing pressure, packing time, cooling temperature, and cooling time, were found to possibly influence the quality of injection-molded plastic products (Kurtaran & Erzurumlu, 2006; Zhao & Gao, 1999). Several *
Corresponding author. Tel.: +886 3 592 7700x2929; fax: +886 3 592 5679. E-mail address: [email protected] (C.-T. Chen). 0957-4174/$ - see front matter 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2007.07.037
PIM control process parameters have been used (Chiang & Chang, 2006; Huang & Tai, 2001; Wu & Liang, 2005). Huang and Tai (2001) presented six process parameters (mold temperature, melt temperature, gate dimension, packing pressure, packing time, and injection time) to determine the optimal initial process parameter settings for injection-molded plastic parts with a thin shell feature and under a single quality characteristic (warpage) consideration. Wu and Liang (2005) employed six process parameters (mold temperature, packing pressure, melt temperature, injection velocity, injection acceleration, and packing time) to discuss the effects of process parameters on the weld-line width of an injection-molded plastic product. Chiang and Chang (2006) proposed four control process parameters (mold temperature, melt temperature, injection pressure, and injection time) to determine the optimal initial process parameter settings for an injectionmolded plastic part with a thin shell feature in a model with
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multiple quality characteristics. Previously, engineers used trial-and-error processes which depend on the engineers’ experience and intuition to determine initial process parameter settings and adjust the process parameters of the injection molding process. However, trial-and-error processes are costly and time consuming, thus they are not optimal for complex manufacturing processes (Lam, Zhai, Tai, & Fok, 2004). In research by Hsu (2004), it was also argued that with a trial-and-error process, it is impossible to verify actual optimal parameter settings. Subsequently, Taguchi’s parameter design method was employed to complete the determination of the initial process parameter settings in industrial applications. However, Taguchi’s parameter design method can only find the best set of specified process parameter level combinations which include the discrete setting values of the process parameters. The application of a conventional Taguchi’s parameter design method is unreasonable when the variable of a process parameter is continuous and cannot help engineers obtain optimal initial process parameter setting results (Su & Chang, 2000). An unsuitable process parameter setting can cause many product defects (e.g., a long lead time, a large amount of scrap material, etc.) and unstable product quality during the injection molding process. Therefore, efficient analytical methodologies and tools are necessary to efficiently and rapidly analyze process parameters and control the product quality. To cope with these challenges, many researchers of injection molding processes have investigated the application of artificial neural networks (ANNs) to quality prediction (Lau, Ning, Pun, & Chin, 2001; Li, Jia, & Yu, 2002; Sadeghi, 2000; Yarlagadda, 2002). The main reason for using ANNs is that neural networks have the ability to ‘‘learn’’ arbitrary nonlinear mappings between noisy sets of input and output data. In finding the optimal parameter settings of an injection molding process, ANNs are also frequently combined with genetic algorithms and fuzzy logic as the quality predictor (Mok & Kwong, 2002; Ozcelik & Erzurumlu, 2006; Shi, Lou, Lu, & Zhang, 2003). In addition, the feedback control model often employs ANNs as a quality predictor (Huang, Tan, & Lee, 2004; Kenig, Ben-David, Omer, & Sadeh, 2001; Liang & Wang, 2002; Wang & Liang, 1999). Therefore, adequate process control and optimal parameter settings of product properties in injection processes require very accurate predictions. When the quality predictor is precise, the quality controller can adjust the controllable parameters closer to the target values of the injection molding process and an efficient optimization model can be obtained. Plastic housing components are widely used in many assembling manufacturing processes to produce final products. Since plastic housing components are usually housed in manufactured products or parts, the dimensional quality characteristics such as weight, length, and thickness are the major quality characteristic for their production. Previously, researchers showed that product weight is a critical quality attribute and a good indicator of manufacturing
process stability during injection molding (Kamal, Varela, & Patterson, 1999; Yang & Gao, 2006). Yang and Gao (2006) revealed that the product weight is an importance quality attribute for injection-molded products because the product weight has a close relation to other quality properties (e.g., surface properties and mechanical properties), particularly those other dimensional properties (e.g., dimensions and thickness). They also claimed that the performance of a manufacturing process and its quality control can be monitored through the product weight. Kamal et al. (1999) showed that the control of product weight is of great commercial interest and can produce great value for production management. Since injection molding is commonly used in the production of plastic housing components, product weight is a feasible single quality characteristic which can be used for product quality control of plastic housing component production via injection molding. In this research, we developed a precise and robust neural network-based prediction model for a plastic injection molding process. A self-organizing map plus back-propagation neural network (SOM-BPNN) model is proposed herein to generate a dynamic quality predictor. Three SOM-based dynamic extraction parameters with six manufacturing process parameters were dedicated to network training and testing. In addition, Taguchi’s design-of-experiment (DOE) method was also applied to enhance neural network performance. The remainder of this paper is organized as follows. Section 2 describes self-organizing maps and the back-propagation neural network. Section 3 specifies the Taguchi parameter design method. Section 4 illustrates the structure of the quality predictor. Section 5 describes the experimental sample and data. Section 6 implements the optimization of neural network parameters using Taguchi’s parameter design method. Section 7 presents experimental results and discussion. Conclusions are drawn in the last section. 2. Self-organizing maps and the back-propagation neural network 2.1. Self-organizing maps Self-organizing maps (SOMs) were developed by Kohonen (1982) and are a peculiar class of artificial neural networks based on unsupervised competitive learning which consists of iteratively modifying the synaptic weights. In self-organizing systems, the output neurons of the network compete among themselves to be activated, and an output neuron winning the competition is called a winner-takes-all neuron or a winning neuron. The neurons, selectively tuned to discrete input patterns, are located on a one- or twodimensional lattice in a topographic map, and they have intrinsic statistical features (nodes). There are three crucial processes, i.e., competition, cooperation and synaptic adaptation, and four principles of self-organization involved in the SOM algorithm (Haykin, 1999). Numerous
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researchers have proposed special SOM models such as the self-organizing Kohonen feature map (SOFM) to achieve high image quality and high compression, and kernel-based self-organizing maps (KSOMs) to cluster non-Euclidean structures in the data (Dai & Chen, 2006; Lee, You, & Park, 2001; Pei, Chuang, & Chuang, 2006). The present study employs a SOM to extract the dynamic process parameter characteristics as the network input. 2.2. Back-propagation neural network In much of the literature, back-propagation neural networks (BPNNs) have been adopted because they have the advantages of a fast response and high learning accuracy (Chen & Hsu, 2006; Lee et al., 2001; Maier & Dandy, 1998; Yao, Yan, Chen, & Zeng, 2005). The superiority of a network’s functional approach depends on the network architecture and parameters, as well as the problem complexity. If an inappropriate network architecture or parameters are selected, undesirable results may be obtained. Conversely, the results will be much more significant if a good network architecture and parameters are selected. The BPNN consists of an input layer, hidden layer, and output layer. The parameters for the BPNN include the number of hidden layers, number of hidden neurons, learning rate, momentum, etc. All of these parameters can significantly impact the performance of the neural network. Fogel (1991) proposed a final information statistical (FIS) process based on Akaike’s information criterion (AIC) to determine the number of hidden layers and neurons. The limitation of Fogel’s research is that the process can only perform simple binary classifications. Murata and Yoshizawa (1994) and Onoda (1995), respectively proposed methods to improve AIC. These methods, called the network information criterion (NIC) and neural network information criterion (NNIC), use statistical probabilities together with an error energy function to determine the number of hidden neurons. In this research, the steepest-descent method was used to find the weight change and to minimize the error energy function. The activation function is a hyperbolic sigmoid function. According to past studies (Cheng & Tseng, 1995; Hush & Horne, 1993), there are a few conditions for network learning termination: (1) when the root mean square error (RMSE) between the expected value and network output value is reduced to a preset value; (2) when the preset number of learning cycles has been reached; and (3) when cross-validation takes place between the training samples and test data. The first two methods are related to the preset values. This research adopts the first and second approaches by gradually increasing the network training time to gradually decrease the RMSE until it is stable and acceptable. The RMSE is defined as follows: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X 2 RMSE ¼ t ð1Þ ðd i y i Þ ; N i¼1
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where N, di, and yi are the number of training samples, the actual value for training sample i, and the predicted value of the neural network for training sample i, respectively. In network learning, input information and output results are used to adjust the weighting values of the network. The more detailed the input training classification and the greater the amount of learning information which are provided, the better the output will conform to the expected result. Since the learning and verification data for the BPNN are limited by the functional values, the data must be normalized by the following equation: PN ¼
P P min ðDmax Dmin Þ þ Dmin ; P max P min
ð2Þ
where PN is the normalized data, P is the original data, Pmax is the maximum value of the original data, Pmin is the minimum value of the original data, Dmax is the expected maximum value of the normalized data, and Dmin is the expected minimum value of the normalized data. When applying the neural network to the system, the input and output values of the neural network fall in the range of [0.1, 0.9]. 3. Taguchi’s parameter design method Taguchi’s parameter design method normally selects an appropriate formulation of the S/N ratio and calculates the S/N ratio for each treatment. There are three types of S/N ratios: nominal the best, the larger the better, and the smaller the better. Most engineers choose the highest S/N ratio treatment as the preliminary optimal initial process parameter setting. Taguchi’s method has also been used to design the parameters for neural networks in previous research (Khaw, Lim, & Lim, 1995; Santos & Ludermir, 1999). Khaw et al. (1995) applied Taguchi’s method to design the parameters and verified that the method could rapidly and robustly design the optimal parameters. Santos and Ludermir (1999) applied a factorial design to assist the design and implementation of a neural network. The formulae of the three types of S/N ratios are given as follows: nominal the best : 2 y S=N ¼ 10 log 2 ; S
ð3Þ
the larger the better :
! n 1X 1 ; and S=N ¼ 10 log n i¼1 y 2i the smaller the better : n 1X y2 S=N ¼ 10 log n i¼1 i
ð4Þ
! ¼ 10 log½y 2 þ S2 ;
ð5Þ
where yi is the response value of a specific treatment under i replications, n is the number of replications, y is the average
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of all yi values, and S is the standard deviation of all yi values. 4. Proposed approach Injection molding is a continuous manufacturing process for product cycles for which the manufacturing parameters are fixed. Process control and optimal parameter settings of product properties in injection molding processes require very accurate quality predictions. When the quality predictor is precise, the quality controller can more closely adjust the controllable parameters to the goals of the injection molding process, and an efficient optimization model can be obtained. Therefore, it is essential to extract the dynamic data of the process parameters in order to enhance the prediction precision of the product quality. This research presents a SOM-BPNN model for a dynamic quality predictor. Three SOM-based extraction parameters with six manufacturing process parameters are dedicated to training and testing the BPNN. The structure of the dynamic quality predictor is shown in Fig. 1. The three SOM-based input parameters are the injection stroke curve, injection velocity curve, and pressure curve, while the six BPNN input parameters are injection time, VP switch position, packing pressure, injection velocity, packing time and injection stroke; one BPNN output variable is weight (quality characteristic). 5. Experimental data Experimental data were collected from a Nissei ES-400 electric injection molding machine, the specifications of which are shown in Table 1. The experimental sample represented in Fig. 2 was measured using a Mettler AE-100
Table 1 Specifications of the Nissei ES-400 injection molding machine Maximum shot weight Maximum pressure Maximum velocity Maximum ram position Screw diameter Clamping force Clearance between tiebars Clamping stroke Minimum mold thickness Maximum daylight (opening)
35 g 255 MPa 210 mm/s 92 mm 22 mm 44 US tons (40 ton) 12.2 · 12.2 in (310 · 310 mm) 9.4 in (240 mm) 6.7 in (170 mm) 21.3 in (540 mm)
Fig. 2. The injection portion of the Nissei ES-400 system.
electric balance which has a precision of 0.05 mg. Three SOM-based parameters (injection stroke curve, injection velocity curve, and pressure curve) and six process parameters (injection time, VP switch position, packing pressure, packing time, injection velocity, and injection stroke) were the input parameters of the model, with one output variable of sample weight. Schematic plots based on the process parameters in the PIM process are shown in Fig. 3. During the injection molding process, these process data
Fig. 1. Structure of the dynamic quality predictor.
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replications, and the predicted weight of injection part (Y) is the evaluation value for different combinations of factor levels. Y is the average of five Y’s in each replication. The optimal combination of factor levels is the experiment with the largest S/N ratio. From the experimental results of Taguchi’s parameter design method, the optimal combination of factor levels is represented by the following: an architecture for BPNN of 9-8-1, the number of calculation generations of 30,000, a learning rate of 0.7, and a momentum of 0.8. 7. Results and discussion
Fig. 3. Schematic plots based on the process parameters of the PIM process.
were collected and stored in the computer database. The collected data can be regenerated into characteristic curves as shown in Fig. 3, where the horizontal axis is time and the vertical axis represents the injection stroke, injection velocity, and pressure. 6. Optimization of the neural network parameters using Taguchi’s parameter design method In this research, we applied the SOM and BPNN to create a dynamic quality predictor, and Taguchi’s parameter design method was used to solve the optimal parameter design problem of the BPNN. Since the number of hidden layers did not have a significant effect on convergence, the number of hidden layer was set to 1. The controlling factors of Taguchi’s method are the number of hidden neurons (P), learning rate (Q), momentum (R), and number of epochs (S). The numbers of neurons in the hidden layer under different levels were obtained by the method proposed by Khaw et al. (1995) and Haykin (1999). Information on the factors’ assumptive settings at different levels is listed in Table 2. The numbers of calculation generations and learning rate were determined by first finding the range in which these factors have better converging results, and second by determining the equal-distance value for the five levels. Under the condition of four factors, five levels, and no correlation among the four factors, the total degrees of freedom were 25 (i.e., 5 · (6 1)). An L25 (56) orthogonal array was selected for arranging the factors and carrying out the experiment. In this experiment, there were five
This research presents a SOM-BPNN-based approach to create a dynamic quality predictor. Three SOM-based dynamic extraction parameters with six BPNN manufacturing process parameters were dedicated to training and testing the network. In addition, Taguchi’s parameter design method was also applied to enhance the neural network performance. The values of the process parameter setting were an injection time of 1.5 s, a VP switch position of 8 mm, a packing pressure of 34 MPa, an injection pressure of 150 MPa, and an injection velocity of 50 mm/s. The neural networks were first trained using 120 samples of training data, then 40 samples of verifying data were used to make predictions, and the network performance was obtained by calculating the RMSE. The network performance between SOM+BPNN and BPNN is shown in Table 3. A comparison between the experimental and predicted values via SOM+BPNN and BPNN quality predictors is represented in Figs. 4 and 5. Based on these results, the training precision of the SOM+BPNN quality Table 3 Comparison of the network performance between the SOM+BPNN and BPNN quality predictors Item
SOM+BPNN
BPNN
Training RMSE Testing RMSE
0.015 0.0017
0.019 0.0029
Table 2 Information on the factors’ assumed settings at different levels Item
Control factor
Level 1
Level 2
Level 3
Level 4
Level 5
P
Number of neurons in the hidden layer Learning rate Momentum Epoch
4
6
8
10
12
0.5 0.5 15,000
0.6 0.6 20,000
0.7 0.7 25,000
0.8 0.8 30,000
0.9 0.9 35,000
Q R S
Fig. 4. Comparison between the predicted and actual values via SOM+BPNN quality predictor.
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References
Fig. 5. Comparison between the predicted and actual values via BPNN quality predictor.
predictor had an RMSE of up to 0.015 and its test precision amount was an RMSE of 0.0017, whereas the training precision of the BPNN quality predictor had an RMSE of up to 0.019 and its testing precision amount was an RMSE of 0.0029. Apparently, the performance of the SOM+BPNN quality predictor was better than that of the BPNN quality predictor. 8. Conclusions Plastic injection molding process control and optimal parameter settings for the product properties require very accurate quality prediction. When the quality predictor is precise, the quality controller can adjust the controllable parameters closer to the targets of the process control, and an efficient optimization model can be obtained for the initial parameter settings. Therefore, it is essential to extract the dynamic data of the process parameters in order to enhance the prediction precision of the product quality in the dynamic system. This research presents a self-organizing map plus a back-propagation neural network (SOM-BPNN) model for the dynamic quality predictor. Three SOM-based extraction parameters with six manufacturing process parameters were dedicated to training and testing the networks. In addition, another back-propagation neural network (BPNN) model was employed for comparison. The numerical results revealed that the proposed dynamic model not only effectively increased the prediction performance of product quality but also obtained more-reliable product quality in advance. In future extensions, the proposed dynamic approach will be employed to the process control for improving the prediction precision of the product quality in the dynamic PIM system. Acknowledgements This research has been conducted as part of a project sponsored by CoreTech System Co., Ltd.
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