Estimation of void boundaries in flow field using expectation–maximization algorithm

Phase distribution in the flow field provides an insight into the hydrodynamics and heat transfer between the fluids. Void fraction, which is one of the key flow parameters, can be determined by estimating the phase boundaries. Electrical impedance tomography (EIT), which has high temporal characteristics, has been used as an imaging modality to estimate the void boundaries, using the prior knowledge of conductivities. The voids formed within the process vessel are not stable and their movement is random in nature, thus dynamic estimation schemes are necessary to track the fast changes. Kalman-type estimators like extended Kalman filter (EKF) assume the knowledge of model parameters, such as the initial states, state transition matrix and the covariance of process and measurement noise. In real situations, we do not have the prior information of the model parameters; therefore, in such circumstances the estimation performance of the Kalman-type filters is affected. In this paper, the expectation–maximization (EM) algorithm is used as an inverse algorithm to estimate the model parameters as well as non-stationary void boundary. The uncertainties caused in Kalman-type filters, due to the inaccurate selection of model parameters are overcome using an EM algorithm. The performance of the method is tested with numerical and experimental data. The results show that an EM has better estimation of the void boundary as compared to the conventional EKF.