Prediction of the ledge thickness inside a high-temperature metallurgical reactor using a virtual sensor

A non-intrusive inverse heat transfer procedure for predicting the time-varying thickness of the phase-change ledge on the inner surface of the walls of a high-temperature metallurgical reactor is presented. An extended Kalman filter with augmented state is coupled with a nonlinear state-space model of the reactor in order to estimate on-line the position of the phase front. The data are collected by a heat flux sensor located inside or outside of the reactor wall. This non-intrusive method can be seen as a virtual sensor which is defined as the combination of an estimation algorithm with measurements for the estimation of 'hard to measure' on-line process variables. The inverse prediction of the ledge thickness with the virtual sensor is thoroughly tested for typical operating conditions that prevail inside an industrial facility. Due to the fact that the melting/solidification process inside the reactor is highly nonlinear, results show that the accuracy of the state-space identification and the virtual sensor estimation is far superior when a nonlinear state-space model and the extended Kalman filter are employed, as opposed to a linear state-space model and the classic Kalman filter. In the former, it is shown that the discrepancy between the exact and the estimated ledge thickness remains smaller than 10% at all times.