Quality Management Using Electrical Capacitance Tomography and Genetic Programming: A new Framework Alaa F. Sheta, Peter Rausch and Alaa Al–Afeef Abstract Currently, many automotive companies struggle with expensive product recalls. To overcome these issues the need for quality management increases. Hence, we propose a monitoring and control framework for Lost Foam Casting (LFC) manufacturing processes using Electrical Capacitance Tomography (ECT) and an evolutionary Genetic Programming (GP) based system. The multi-tier framework simulates the process output, helps simulating a metal filling modeling part of the process and supports product quality control. The results are very promising.
1 Introduction Currently, many automotive companies struggle with quality issues. To reinforce quality management and to reduce defects of parts or products, tomography can be deployed. Tomography is a method of producing a sectional image of the internal structures of an object using waves of energy [1, 2]. Technically, tomography involves taking direct sectional images (e.g. X-ray, infrared or ultrasound tomogram) or reconstructing indirect sectional images using boundary measurements based on the internal characteristics of the monitored object (e.g. electrical tomogram) [3]. It is one of the few feedback tools that gives information about what is actually happening inside an industrial process. This information is extremely important to support quality management, to develop processes efficiently and to reduce production costs. In this paper, we propose a general framework for monitoring and control of industrial manufacturing processes which supports quality management. Despite the fact, that the ideas discussed in this paper are focused on LFC processes in the automotive industry, it is important to notice, that the results of our research can be transferred to many fields of application as well. LFC is a casting process that uses foam patterns as molds in which the molten metal decomposes the foam pattern and creates a casting in its shape [2, 4]. It is very simple and cheap to cast complex patterns. In order to ensure quality, imaging techniques can be used. ECT based approaches have become very popular. They have been applied successfully to study various industrial processes using capacitance measurements to generate images [1]. LFC uses the ECT technique to express Alaa F. Sheta, Computer Science Department, The World Islamic Science and Education (WISE) University, Amman, Jordan, e-mail:
[email protected] Peter Rausch, Computer Science Department, Georg Simon Ohm University of Applied Sciences, Nuremberg, Germany, e-mail:
[email protected] Alaa Al–Afeef, Image Technologies Inc. (ITEC), Amman, Jordan, e-mail:
[email protected]
M. Bramer et al. (eds.), Research and Development in Intelligent Systems XXVIII, DOI 10.1007/978-1-4471-2318-7_15, © Springer-Verlag London Limited 2011
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the metal fill profile and to simulate the properties of molten metal inside the foam patterns during the casting process [4]. ECT is a method for the determination of the dielectric permittivity distribution in the interior of an object from external capacitance measurements and has a lot of advantages [5]. Compared to hard field tomography, it is fast and relatively inexpensive. However, the quality and accuracy of the reconstructed images of ECT measurement systems is often insufficient [6]. Especially in terms of the mentioned challenges concerning car parts’ quality, this is an important issue. It can be managed with evolutionary software which is a component of the presented monitoring and control framework.
2 A Monitoring and Control Framework for Manufacturing Figure 1 shows a block diagram of the proposed framework.
Fig. 1 Remote monitoring and control framework
A Matlab server is deployed to run the GP based evolutionary software which is used to simulate the metal filling modeling part of the process. Its models use sensor inputs and will be explained later. The software is used to simulate the process output. The underlying ECT system contains capacitance sensors which provide the necessary input (i.e. capacitance readings). Other components allow remote mobile access to communicate directly between the stationary server and mobile devices. So, users can keep track of the processes and have full capabilities to configure and (re)start execution remotely. Deploying the ECT approach in combination with the GP-based image representation, data from the manufacturing process execution layer can be monitored and analyzed using a controlling system on a regular base. The results produced by the Production Activity Control (PAC) component can be evaluated by quality and production managers. Like Figure 1 shows, it is also possible to establish an ERP interface and to supply a Business Intelligence (BI)-system with data. So, analysis on the strategic level can be supported. The following sections will provide more details of framework’s components.
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3 Image Reconstruction There are two major computational problems in the ECT image reconstruction [7]: The first is the forward problem in which the capacitance measurement C i j between electrodes i and j is determined from the permittivity distribution ε (x, y): C i j = F(ε (x, y)). Additionally, the inverse problem has to be solved which is the process of finding the inverse relationship such that the permittivity distribution is estimated using capacitance measurements and (as a result) constructing a visual image using a reconstructing algorithm. This process is also called image reconstruction process. The inverse relationship can be expressed as in Equation 1.
ε (x, y) = F −1 (C12 ,C13 ,C14 , . . . ,Ci j , . . . ,CN−1,N )
(1)
There are a couple of issues making the implementation of ECT systems a challenge [5, 8]: Soft fields affect the sensors in which the electric field lines are dependent on the permittivity distribution in the imaging domain. Additionally, the ill-condition problem occurs. This means ill-posed response of the sensor due to a different location in the imaging domain. Also, the limited number of independent measurements affects the process. This is why usually very low resolution tomograms are produced [8]. Another issue is the ill-posed ECT problem. Getting worse, non-linearity of the relationship between the measured capacitance and permittivity distribution exits [8]. Furthermore, it is hard to establish an analytical and explicit expression which describes this relationship. In order to master these challenges and to improve the imaging accuracy, more accurate reconstruction algorithms must be developed. So, in the following sections the idea of applying GP to the image reconstruction problem will be discussed. Our objective is to find a GP Inverse Solver that mathematically describes the nonlinear relationship F between the capacitance input variables C and the image pixel P of image vector G which represents the distribution of metal in the imaging area. G p = F(C1 ,C2 , . . . ,C N(N−1) )
(2)
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In our case, the inverse solver consists of 64 GP models. Each model is responsible for deriving a relationship between capacitance measurements [C 1 − C66 ] and a specific pixel in an ECT image of 64 pixels. In another word, P in Equation 2 is ranging from 1 to 64 pixels, N is 12 electrodes. In Figure 2 the structure of the proposed system is shown. The number of measurements is 66 representing all the unique combinations of measurements between the 12 electrodes distributed around the measuring area. These measurements are represented by the symbols C 1 , ...,C66 . One at a time, all the measurements are presented to each of the 64 GP systems. To deploy the GP model, the MatLab toolbox was used. It was extended by a socalled ECTGP module which provides a Graphical User Interface (GUI) for solving the nonlinear inverse problems of ECT. By using another module of the ECTGP toolbox, the user is able to view capacitance measurements and ECT images, provided that he supplies the associated input. Supported by a GUI, the toolbox helps
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Fig. 2 Proposed GP Inverse Solver Model
setting up experiments (for instance to prepare training and testing data), executing a training session and loading resulted ECT images and the performance data. As a final step, the user can analyze and plot the GP performance over all runs using the MatLab extension. He can view the results, for instance estimated images, and analyze errors between original and estimated data according to many criteria. The GP was trained using lilgp with ANSYS generated examples (see Figure 3).1 A training set of 268 ECT images with the corresponding capacitance measurements was provided to the GP system. To test the performance of the GP models, a testing set of size 67 was used. A subset of these patterns and their corresponding GP estimated patterns are shown in Figure 3. One of the major problems in GP is over-fitting in which the algorithm tends to follow a pattern based on the learning samples. To resolve this problem we used different data sets for testing and training in which the selected testing data set was different enough for testing the performance of the GP Inverse Solver. The Best-so-far curve of the run is shown in Figure 4. It visualizes errors (y-axis) of the generations (x-axis) for all models (z-axis). The overall error percentage for the developed GP simulation in the training case was 2.53% and 2.63% in the testing case as given in Equation 3.
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The data was provided by Drs. Mohamed Abdelrahman and Wael Deabes, Tennessee Technological University. It was produced in conjunction with research project GO14228 supported by US Department of Energy (DOE), USA.
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Fig. 4 Best-so-far curve of the GP Models accessible by mobile devices
α β Gset − OAE Actual Estimated , where OAE = − G (3) G ∑∑ Gset set is either the training or testing set of the experiment. EPset represents the error percentage of a given set. G set denotes the total number of pixels of all images in that set. The Overall Absolute Error (OAE) is the summation of the absolute difference between the actual and the GP estimated image pixels of the complete image set. GActual and GEstimated are the actual and estimated pixel, respectively. α represents total number of images in the set. β denotes the image-size (i.e. the total number of a single image’s pixels). In Equation 4, G 64 is the estimated pixel number 64 of image G and Cne represents the corresponding capacitance measurement of the input variables n. e denotes an exponent. EPset =
3 38 4 18 2 (C46 ∗ C52 ∗ C54 − C24 ∗ C46 ∗ C52 − C54 ) G64 = C54 ∗ C46
(4)
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In this model, it was found that G 64 is mostly affected by the measurements C 46 , C52 , C24 and C54 . The values of the input variables, for instance C n , are in the range: 0 ≤ Cn ≤ 1. This prevents the values of G from exceeding a range of −1 ≤ G ≤ 1 which is mapped using threshold levels into {0, 1}.
4 Conclusions and Future Work In this paper, a new technique for solving the non-linear inverse problem of ECT has been introduced. The technique is based on GP to identify the models relating the sensors’ capacitance measurements to the permittivity distributions. The presented technique showed promising results in terms of accuracy, the quality of reconstruction results and convergence rates. Furthermore, it could be shown that: companies can benefit a lot from the proposed framework. It can be an important contribution to quality management. Expensive product recalls and the related image damages can be avoided or at least reduced. The main limitation of the presented GP approach is the training time needed. Sufficient training data has to be provided, and data has to be expressive of the problem in order to have a successful prediction. As a future work, it is intended to investigate other metal distributions and to apply GP to the forward problem of ECT. Additionally, the development of a process in order to improve the reconstructed images using look-up tables with all possibilities of grid formation to reduce the training time is needed. It would be also very interesting to extend the analysis and reporting components.
References 1. A. Al-Afeef. Image reconstructing in electrical capacitance tomography of manufacturing processes using genetic programming. Master’s thesis, Al-Balqa Applied University, July 2010. 2. A. Al-Afeef, A. F. Sheta, and A. Al-Rabea. Image reconstruction of a metal fill industrial process using genetic programming. In ISDA, pages 12–17. IEEE, 2010. 3. M.S. Beck and R.A. Williams. Process tomography: a european innovation and its applications. Measurement Science and Technology, 7(3):215–224, 1996. 4. M. Abdelrahman, A. Sheta, and W. Deabes. Fuzzy mathematical modeling for reconstructing images in ect of manufacturing processes. In Proc. Fuzzy Mathematical Modeling for Reconstructing Images in ECT of Manufacturing Processes, December 2009. 5. J. Lei, S. Liu, Z. Li, and M. Sun. Image reconstruction algorithm based on the extended regularised total least squares method for electrical capacitance tomography. IET Science, Measurement and Technology, 2(5):326–336, September 2008. 6. S.M. Hoyle, B.S. Thorn, C. Lenn, C.G. Xie, S.M Huang, and M.S. Beck. Electrical capacitance tomography for flow imaging system model for development of image reconstruction algorithms and design of primary sensor. In IEEE Proceedings G 139, pages 89–98, 1992. 7. K. Alme and S. Mylvaganam. Electrical capacitance tomographysensor models, design, simulations, and experimental verification. IEEE SENSORS, 6(5), OCTOBER 2006. 8. O. Isaksen. A review of reconstruction techniques for capacitance tomography. Sensors Journal, IEEE, 7(3):325–337, March 1996.
