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.

由于批次持续时间不一致，识别正在进行的批次的进度会极大地影响在线监控的性能。在本文中，提出了一种基于相对进行率的实时同步方案，新定义为正在进行的批次的轨迹与标称轨迹之间的时间差。由于相对前进速度表明该点与标称轨迹相比有多早达到其期望值，因此通过估计相对前进速度在线获得同步指数。与使用局部约束优化同步索引的传统方法相比，该方法可以在不应用局部约束的情况下使用相对进行率来估计其分布。它可以减少同步误差，提高状态估计和故障检测的准确性。通过具有实时不可测量变量的工业青霉素生产案例研究验证了所提出方法的实用性。