A feature based solution to the forward problem in electrical capacitance tomography.

摘要

Lost Foam Casting (LFC) process is a widely accepted casting process in industries due to its energy efficiency and environmental advantages. In LFC process, it is advantageous to monitor the metal fill profile to avoid and minimize the fill-related defects. Electrical Capacitance Tomography (ECT) provides a simple, cheaper, and nondestructive way of monitoring such process. There are two major computational problems in ECT: the forward problem and the inverse problem. The forward problem is to determine mutual capacitance between sensor electrodes for a given grounded metal distribution. Reconstructing the metal distribution image from capacitance measurements is known as inverse problem. The inverse problem is inherently nonlinear in nature. The accurate solution to inverse problem requires several iteration of both forward and inverse problem solution (iterative algorithms). Accuracy of the inverse problem solution critically depends on the accuracy of the forward problem solution. Accurate solution to forward problem through present methods is very time-consuming. Consequently iterative algorithms cannot be used for online monitoring of the process. To produce accurate distribution images online, a fast solution to the forward problem is necessary.;This thesis investigated a faster and accurate solution to the forward problem based on key features extracted from the given metal distribution and an Artificial Neural Network (ANN). The linear sensitivity matrix produced a linear solution (i.e. solution without considering any nonlinearity) to the forward problem. Simulations based on ANSYS finite element analysis and MATLAB showed that linear solution can be adjusted for nonlinear effects by a correction factor. This factor depends on both the sensor electrode pair and the given metal distribution itself. With sufficient amount of training examples and proper learning algorithm, an ANN can map nonlinear and complex function between the given metal distribution and corresponding correction factor for the subject electrode pair. Instead of providing the whole distribution itself as input to the ANN, the distribution and electrode pair information was provided in the form of the key features extracted from the metal distribution. The use of features significantly reduced the size of the ANN, number of training examples required, and other computer resources (such as training time and computer memory) requirements. The training data are generated through finite element analysis carried out using ANSYS. The ANN was implemented and trained using MATLAB Neural Network Toolbox. After the training with about 2000 example metal distributions and over 90,000 capacitive readings and corresponding correction factors, the ANN was able to map the complex relationship between key features and correction factor with 2.21% RMS error with the training distributions and 2.19% RMS error for the previously unseen arbitrary test metal distributions.