Real-time synchronization with expected distribution of synchronized index for on-line monitoring of uneven multiphase batch process

•Online synchronization without local constraint applied to uneven batch monitoring.•Relative proceeding rate is defined to measure the progress of ongoing batch.•Bayesian posterior probability applied to determine the online synchronization.•Selection of hyper-parameter using the auto-correlation of relative proceeding rate.•Accurate synchronization enhanced state estimation and fault detection accuracy. Because of the inconsistent batch duration, identifying the progress of an ongoing batch highly affects the performance of the on-line monitoring. In this paper, a real-time synchronization scheme is proposed based on relative proceeding rates, newly defined as the time difference between the trajectory of an ongoing batch and the nominal trajectory. As the relative proceeding rate indicates how early the point attains its desired value compared to the nominal trajectory, the synchronized index is obtained on-line by estimating the relative proceeding rate. Compared with the conventional methods that optimize the synchronized index with local constraints, the proposed method can estimate its distribution using the relative proceeding rate without applying local constraints. It can reduce synchronization errors and increase the accuracies of the state estimation and fault detection. The utility of the proposed method is verified via a case study of industrial penicillin production with a real-time unmeasurable variable.