using artificial neural networks to model extrusion processes

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N Mekras and I Artemakis
ANTER Ltd., Feidippidou 22 Str., 11527, Athens, Greece
Email: [email protected]; [email protected]
Abstract. In this paper a methodology and an application example are presented aiming to show how Artificial Neural Networks (ANNs) can be used to model manufacturing processes when mathematical models are missing or are not applicable e.g. due to the micro- & nano- scaling, due to non-conventional processes, etc. Besides the ANNs methodology, the results of a Software System developed will be presented, which was used to create ANNs models for micro & nano manufacturing processes. More specifically results of a specific application example will be presented, concerning the modeling of extrusion processes for polymeric micro-tubes. ANNs models are capable for modeling manufacturing processes as far as adequate experimental and/or historical data of processes’ inputs & outputs are available for their training. The POLYTUBES ANNs models have been trained and tested with experimental data records of process’ inputs and outputs concerning a micro-extrusion process of polymeric micro-tubes for several materials such as: COC, PC, PET, PETG, PP and PVDF. The main ANN model of the extrusion application example has 3 inputs and 9 outputs. The inputs are: tube’s inner & outer diameters, and the material density. The model outputs are 9 process parameters, which correspond to the specific inputs e.g. process temperature, die inner & outer diameters, extrusion pressure, draw speed etc. The training of the ANN model was completed, when the errors for the model’s outputs, which expressed the difference between the training target values and the ANNs outputs, were minimized to acceptable levels. After the training, the micro-extrusion ANN is capable to simulate the process and can be used to calculate model’s outputs, which are the process parameters for any new set of inputs. By this way a satisfactory functional approximation of the whole process is achieved. This research work has been supported by the EU FP7 NMP project POLYTUBES.
1. Introduction In this paper a proposed methodology will be presented concerning the modeling of processes for the manufacturing of polymeric micro-tubes using Artificial Neural Networks (ANNs). Also the results of an ANNs processes modeling software application will be presented, which has been developed by the authors of this paper for the implementation of the proposed methodology. An existing micro- extrusion process for manufacturing polymeric micro-tubes will be used as case example. The physical process data were used by the authors of this paper at ANTER Ltd to create, train and test the micro- extrusion Neural Network. Artificial Neural Networks (ANNs) are considered a research area of Artificial Intelligence (AI) with significant applications in several domains, including the manufacturing processes domain [7-11]. ANNs are useful on several applications like for example on applications of systems modeling, materials modeling [1, 5, 12, 15], function approximation, forecasting & prediction [2, 4, 14], classification problems, pattern recognition, etc. Generally, ANNs
International Conference on Structural Nano Composites (NANOSTRUC 2012) IOP Publishing IOP Conf. Series: Materials Science and Engineering 40 (2012) 012041 doi:10.1088/1757-899X/40/1/012041
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can be used in cases that mathematical models are completely missing or are not adequate and accurate enough to represent a real world model of a physical process or system. In most cases ANNs are capable to learn and approximate real world models when adequate historical and/or experimental data sets of model’s inputs & outputs are available for the training of the ANN.
In the following Figureure 1 the ANNs structure that was used for creating the POLYTUBES micro-manufacturing processes models is given. This structure represents the MLP (Multilayer Perceptron) feed-forward Neural Network model with 1 input layer, 2 hidden layers and 1 output layer, which uses the back-propagation training algorithm [3, 6]. In the cases of the POLYTUBES processes, the number of inputs and the number of neurons of the output layer correspond to the inputs and outputs of the physical process as these are defined by the relevant manufacturing theory and the needs of the process engineers. After the ANNs training is completed the ANNs model can be used to simulate the processes behavior and provide output results for any set of inputs provided by the user.
Figure 1. MLP Feed forward ANN (R–S1–S2–S3) with 2 hidden layers.
2. Application case: Extrusion of polymer micro-tubes The first step for modeling the micro-extrusion process concerned the selection of the Neural Network architecture and the selection of the number of the hidden neurons. The numbers of neurons of the 1st
and 2nd hidden layers for the micro-extrusion process were estimated during the ANNs training and were adjusted through a test & trial procedure in an effort to minimize the training error for all process’ outputs [13]. For the specific micro-extrusion ANN a 3-20-20-9 architecture was applied, with 20 neurons in the 1st hidden layer and 20 neurons in the 2nd hidden layer respectively. The Hyperbolic Tangent Sigmoid [3] was chosen as transfer function for both the 1st and the 2nd hidden layers and the linear function was chosen for the output layer. More specifically:
f1() =
, f2() =
, f3() = (1)
The extrusion process ANN model that was created had 3 inputs and 9 outputs. The 3 model inputs are: the micro-tube inner & outer diameters (mm), and also the material type, which is expressed by the material density (Kg/cm3). The 9 model outputs are: the process die temperature (C), the melt density (Kg/m3), the melt flow (rpm), the extrusion die inner diameter (mm), the extrusion die outer
Output Layer2nd Layer1st Layer
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diameter (mm), the extrusion die pressure (bar), the die Nitrogen inside pressure (bar), the distance to the cooling media (water) (cm) and the draw speed (m/min). 30000 iterations were applied for the training of the ANN, with a learning rate of 0.005, and the training was stopped when the errors for all model’s outputs, which was expressed by the absolute value of the difference between the training target values and the ANNs calculations results, were minimized to satisfactory levels for all the process outputs. The Mean Absolute Errors (MAE) achieved for the 9 process output parameters are:
Table 1. MAE achieved for the 9 process outputs of the 3-20-20-9 ANN model.
Output No Process Parameters (Outputs) Units MAE MAE (%) 1 Process die temperature °C 1.12651 0.50182 2 Melt density Kg/m3 6.37156 0.63903 3 Melt flow rpm 1.43085 5.93685 4 Extrusion die inner diameter mm 0.00571 0.69026 5 Extrusion die outer diameter mm 0.00596 0.35029 6 Extrusion die pressure bar 0.78528 5.66754 7 Die Nitrogen inside pressure bar 0.00325 0.31442 8 Distance to the cooling media cm 0.03320 3.13089 9 The draw speed m/min 1.90809 9.15724
In Figureure 2, we show 9 comparison charts, which were created after the training of the ANN that correspond to all the 9 process parameters (models’ outputs). Each chart includes two curve lines. The first line represents the training target values (red dashed line) and the second line represents the Neural Network calculation results (blue line) for each of the corresponding outputs. For testing the behavior of the trained model and for creating the 9 comparison charts, the 100 records of the training inputs data set were used as inputs to the trained ANN, which provided the 9 corresponding calculation outputs (process parameters) for each triad of input values. The convergence of the micro- extrusion ANN training was satisfactory, considering the fact that our model was a complicated model that had only 3 inputs concerning tube features (outer and inner diameter and polymer material density) and is providing 9 outputs, which are the 9 process parameters. After the training and the testing of the micro-extrusion ANN, the model was capable to provide as outputs the required 9 process parameters for any set of inputs, which correspond to the 3 product features (outer & inner diameter, and material density).
Additionally and besides the above 3-20-20-9 model, the proposed methodology and the software tool was used and tested also for the inverse process model. In the inverse model, we used as inputs the above 9 process parameters and as outputs the above 3 product features. For this model a 9-15-15- 3 feed-forward Neural Network was created and trained using the back-propagation algorithm. After training and testing this ANN, the Mean absolute Errors (MAE) achieved for all the 3 outputs are:
Table 2. MAE achieved for the 3 process outputs of the 9 Inputs - 3 Outputs ANN model.
Output No Product features Units MAE MAE (%) 1 Outer Diameter mm 0.02371 2.16339 2 Inner Diameter mm 0.02428 3.35821 3 Material Density Kg/m3 1.22700 0.10206
In Figureure 3, we show also the 3 comparison charts, which were created after the training of the second ANN model and which correspond to the above 3 product features (models’ outputs). For testing the behavior of the 9-15-15-3 trained ANN model and for creating the 3 comparison charts, the training data set, consisting of the 100 records, was used with the 9 process parameters being used as inputs.
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Figure 2.2. Output2 - Melt density (Kg/m3).
Figure 2.3. Output3 - Melt flow (rpm).
Figure 2.4. Output4 - Extrusion die inner diameter (mm).
Figure 2.5. Output5 - Extrusion die outer diameter (mm).
Figure 2.6. Output6 - Extrusion die pressure (bar).
Figure 2.7. Output7 - Die Nitrogen inside pressure (bar).
Figure 2.8. Output8 - Distance to cooling media (water) (cm).
Figure 2.9. Output9 - Draw speed (m/min).
ANNs Results Training Output Target Values
Figure 2. Process outputs comparison charts between ANN’s results and Target Outputs of the 3- 20-20-9 micro-extrusion ANN model.
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3. Conclusions The proposed Neural Network methodology was implemented as a Web application using the .NET programming environment of Visual Studio 2010. More specifically the programming languages C#, ASP.NET were used and also the MS-SQL Server as Database Management system. The whole research work was supported by the EU FP7 NMP project POLYTUBES (2009-2012) and the implementation case example, which was presented, concerned a functional approximation of the POLYTUBES extrusion process for the production of polymeric micro-tubes based on COC, PC, PET, PETG, PP and PVDF materials. Especially for the extrusion process, the main ANN model created included 3 inputs and 9 outputs, in an effort to support process engineers to calculate the required 9 process parameters when the 3 product features (tube’s outer/inner diameter and material density) are provided as inputs. Even though the 3 Inputs / 9 Outputs ANN model is considered a complicated model and the achieved Mean Absolute training Error (MAE) varies among the 9 model’s outputs, it is considered useful for process engineers since it gives the possibility to estimate with a satisfactory approximation of less than one 1% most of the process parameters, which are required for specific micro-tube’s dimensions and material type. Additionally, the inverse 9 inputs / 3 outputs ANN model was created giving the possibility to the process engineers to cross check the output calculation results of both models.
4. Acknowledgments The authors would like to thank the Swedish Research Center SWEREA IVF AB and more specifically Dipl. Eng. Daniel Wendels and Dr. Erik Perzon of SWEREA, who provided the experimental data concerning the micro-extrusion physical process of the polymer micro-tubes. Without their contribution, the training and the testing of the micro-extrusion ANNs models would not be feasible. Also the authors would like to acknowledge the support of the European Commission, which funded this research work through the EU FP7 NMP project POLYTUBES (http://www.polytubes.net).
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Figure 3.1. Output1- Outer Diameter (mm)
MAE1 = 2.16339 %.
MAE2 = 3.35821 %.
MAE3 = 0.10206 %.
ANNs Results Training Output Target Values
Figure 3. Process outputs comparison charts between ANN’s results and Target Outputs of the inverse 9-15-15-3 micro-extrusion ANN model.
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using artificial neural networks to model extrusion processes

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