·Table of Contents ·Computer Processing and Simulation | Flow Pattern Identification based on Fuzzy Neural Network Using Multi-Electrode Capacitance SensorXia Jingbo, Yang XiatieAirforce university of engineering, Xi'an 710077, P.R.China Wang Shi PO Box 321, School of Information , Northeastern University, Shenyang 110006, P.R.China E-mail: MCGMZWZC @pub.ln.cninfo.net Tel&Fax: 86-24-23891977 Contact |
Key words : neural network, fuzzy logic,identification,two phase flow, capacitance sensor
Fig 1: Schematic diagram of an 8-electrode sensor array |
(1) |
and the associate boundary conditions (the Direchlet boundary conditions) are the potentials applied to the electrodes and the screens. Ñ is Hamilton's operator, e _{0} is the free-space permittivity, and f are, respectively, the relative dielectric constant and potential distributions in the field, r is distributions of free charge density, is the spatial position vector.
(2) |
The potential distribution is dependent on the dielectric distribution once the boundary conditions are fixed. In an N-electrode capacitance transducer, when electrode i is source electrode (potential f ¹ 0 is applied) the charges sensed by detecting electrode j is C_{ij} by Gauss's law:
(3) |
It is obviously that C_{ij} is a function of the dielectric distribution . A capacitance value is related with shape, size, relative position of electrodes and the dielectric materials in between. The capacitance value in fact indicates the properties of dielectric distribution within the electrodes. Since dielectric distribution is in general, very irregular, there is no analytical solution Therefore, a numerical method base on three-dimensional (3D) finite element method model (FEM) is used for optimum design of capacitance sensors in this study.
Fig 2: Schematic diagram of flow pattern identification ANN |
(4) |
c_{i} (i=1,2,..,28),each dimension of C, to be fuzzified by membership function, The purpose of making input data fuzzy is to strengthen the pattern features. In general, a fuzzy membership function divides the c_{i}(i=1,2,..,28) into "VS--very small", "NS--negative small", "S--small", "PS--positive small", "NM--negative middle", "M--middle", "PM--positive middle", "NB--negative big", "B--big", "PB--positive big", "VB--very big". Membership function of each dimension c_{i} (i=1,2,..,28) is shown in Figure 3.
Fig 3: Membership function of c_{i}(i=1,2,..,28) |
(5) |
The fuzzified data is inputted into Kohonen network shown in Figure 4. the node number of the input layer is 308.
Fig 4: Neuron's connection between input layer and competitive layer |
Kohonen's rule starts with a choosing a 'winner' from the layer of processing elements and the weight of the processing element is strengthened by the following rule[6]:
(6) |
Where a is a learning rate constant, W is the weight connecting input-output nodes X is the input pattern, over a period of training step t. The winning node and its neighbouring neurons will modify its weight vector to align with the input vector.
Flow pattern | Recognition rate |
Empty flow | 93.6 % |
Full flow | 94.1 % |
Stratified flow(1/2) | 87.5 % |
Stratified flow(1/3) | 86.2 % |
Stratified flow(2/3) | 90 % |
Annular flow | 84.6 % |
Core flow | 85.3 % |
Others flow | 81.3 % |
Table 1 : Results of flow pattern identification |
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