Theoretical analysis of fuzzy least squares support vector regression method for void fraction measurement of two-phase flow by multi-electrode capacitance sensor

Abstract

Abstract In order to improve the measurement accuracy of void fraction in cryogenic two-phase flow using the multi-electrode capacitance sensor, an algorithm based on the fuzzy least squares support vector regression (FLSSVR) is proposed to fit the void fraction and the capacitances. Liquid nitrogen-vapor nitrogen (LN2-VN2) are taken as the working pair for numerical experiments. Finite element calculations are firstly carried out to obtain the capacitance values of each pair of electrodes, then they are casted into a symmetric matrix, of which the eigenvalues are used as the inputs of the FLSSVR. Thus the dimensions of the sample space are evidently reduced, the computational load is accordingly reduced. In the sample selection process, a set of rules is established by using the centrosymmetric characteristics of this sensor, so that the number of independent variables is significantly reduced. Moreover, the fuzzy memberships are calculated based on the distances between the sample points and the regression hyperplane in the expanded feature space, which gives the regression function a better anti-noise ability. The feasibility of the algorithm applicable to void fraction measurement is verified by the numerical experiments. The results show that the regression functions obtained by FLSSVR have satisfying accuracy and anti-noise ability in calculating the void fraction of the involved two-phase flow in the pipe.