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Flow Pattern Identification based on Fuzzy Neural Network Using Multi-Electrode Capacitance Sensor Xia Jingbo, Yang Xiatie Airforce 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

Abstract

Investigation and control of flow phenomena in two-phase flow requires a detailed knowledge on the flow regimes and a number of phase flow properties. Electrical capacitance sensor is shown here to be a robust tool for this purpose, measured capacitance which reflect flow distribution are processed with fuzzy method. The inhomogeneity of sensors' sensitivity distribution and medium distribution are fully considered, a novel method for flow pattern identification based on fuzzy neural network is presented. By self-organizing learning of Kohonen network and supervision learning of BP neural network , The trained neural network has been applied to experimental data for flow pattern identification. Through the cases investigated, experimental results show that it is feasible for flow pattern identification of core, annular and stratified flow.

Key words : neural network, fuzzy logic,identification,two phase flow, capacitance sensor

1. INTRODUCTION

Electrical Capacitance Tomography (ECT) was developed in the late 1980's as a new kind of technique to measure the spatial distribution of a non-conductive two-phase flow [1][3]. The technique has been developed rapidly during the past 10 years. Some applications of this technique have been reported, such as liquid/gas pipe flow, oil/water/gas gravity separation, pneumatic conveying fluidized beds and flame combustion[11]. In an ECT system, image reconstruction is a key issue for its application. The most commonly used reconstruction algorithm for an ECT system is the Linear Back Projection (LBP)[1] originally developed for Medical Tomography systems. The LBP algorithm is very fast, but not very accurate due to the smoothening effects. This algorithm has subsequently been improved for use in a capacitance tomography system. Iterative methods, such as least square methods, have been investigated for image reconstruction. It was shown that the constrained least squares method gives the best result[10]. However, image reconstruction results using these methods are far from satisfactory. This is due to the limited number of independent measurements (typically less than 100) in an ECT system and also due to the soft field error. Artificial neural networks are introduced to recognize pipe flow patterns, such as core flow, annular flow and stratified flow. Based on this, a hybrid method of neural network and fuzzy logic has been studied for the ECT problem [1][8][9][11].

2. SENSOR STRUCTURES[1][3][11]

When artificial neural networks are used to recognize pipe flow patterns, the two-level electrode sensor structures can be chosen from. As one electrode level is acted as measurement electrodes, the guard electrodes are all at zero potentials, this kind of sensor structure is called earthed axial guard rings. Multiple measurement electrodes mounted equally around the cross-section of pipe , with an earthd screen outside the electrodes to reject external noise. For a sensor with N-measurement electrodes, there are N (N-1)/2 electrode pairs and thus N (N-1)/2 independent capacitance measurements. In a complete measurement cycle, measurement electrode 1 to electrode N-1 is selected as the excitation electrode in sequence while the others used as the detection electrodes are kept at ground potential. There are some specific requirements for the measuring circuit of capacitance: large dynamic range, high resolution, good linearity, and good stray capacitance immunity. For 8-electrode system(see Figure1), the total number of independent measurement is 28. After C/V conversion and certain signal process by sensor electronics, these data are fed into computer. The capacitance measurements are realized by measuring the induced charges on the detection electrodes and used to recognize pipe flow patterns (i.e. the permittivity distribution).

Fig 1: Schematic diagram of an 8-electrode sensor array


Usually, the capacitance electrode systems for the measurement of two-phase or multi-phase flow have inherently non-uniform sensitivity distribution over the pipe cross section and therefore have different responses to different flow regimes, modeling of the 8-electrode capacitance sensor can be treated as an electrostatic field problem., and can be characterized by Poisson's equation:

(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.


Because there may have inductive charges but no free charges within the field, Possion's equation can be simplified as Laplace's equation:

(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.

3. ANN MODEL FOR FLOW PATTERN IDENTIFICATION [2][4][5][7] [8][9][12]

Artificial neural networks (ANN) is commonly used to solve nonlinear problems. Neural networks techniques have bee been applied to many areas such as signal processing, pattern recognition, and so on. Among many neural networks, BP network is the one that has been widely used for its simplicity. It has been proved that this network with a hidden layer can solve most kinds of practical problems about nonlinear mapping. Kohonen [1987] formulated a self- organizing neural network architecture based on the close resemblance to the biological phenomenon of feature maps in the brain. In consideration of the stochastic and fuzzy characteristics of two phase flow, and sensitivity distribution being influenced by two-phase flow Inhomogeneity with capacitance measure. Fuzzy conception is combined with neural network, Based on this, a hybrid method of neural network and fuzzy logic has been studied . The structure of ANN is shown in Figure 2.

Fig 2: Schematic diagram of flow pattern identification ANN


For 8-electrode system, the vector C = [c₁,c₂,c₃, ... c₂₈] is constructed by 28 independent capacitance measurement values, the normalized independent measurements are denoted as follows:

(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 ci(i=1,2,..,28)


After fuzzifing of C, C = [c₁,c₂,c₃, ... c₂₈] are re-denoted as follows:

(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.


The output of Kohonen network is the input of BP network, a hide layer is added between the input layer and the output layer of BP network. In order to decrease training time, neuron of hidden layer is defined nonlinear, neuron transfer function of output layer is defined linear, the node number of the hide layer can be chosen through experiment. The node number of the output layer is the same as that of the flow pattern. According to the maximum likelihood criterion, the flow pattern whose relative node output is the biggest is the result of recognition. An accelerated algorithm is used to train the network in our research work in order to shorten the learning period[10]

4. RESULTS of FLOW PATTERN IDENTIFICATION

The experimental system is set up. Plastic pellets which have a diameter of 3mm are used to generate a wide range of flow patterns such as core flow, annular flow and stratified flow. At each position, one set of capacitance was measured. These real data are divided into two groups, one for training, one for testing. The node number of the output layer is 8, these nodes can classify whole flow pattern as full flow, stratified flow(1/2), stratified flow(1/3) ,stratified flow(2/3) , annular flow, core flow, Empty flow ,Others flow. Table 1 illustrates some results.

5. CONCLUSION

In this paper, a hybrid method of neural network and fuzzy logic has been studied .A neural network model was setup, First, projection information which reflect flow distribution are processed with fuzzy method. Through self-organizing learning of Kohonen network, the classified characteristic of input pattern examples can be picked up. By supervision learning of BP neural network, The experimental results show Fuzzy neural network based flow pattern identification algorithm have learning capability, high tolerance and classification performances. With the trained neural network, experimental data were used to verify the methods. The average recognition rate is 87.83%. An artificial neural network can be used for flow pattern identification, Training a neural network is heavily time-consuming. Some case studies were made to investigate the disadvantages and advantages of the method. It show that the method proposed here is feasible

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