Kernel Fisher Envelope Surface for Pattern Recognition

It is found that the batch process is more difficultly monitored compared with the continuous process, due to its complex features, such as nonlinearity, non-stable operation, unequal production cycles, and most variables only measured at the end of batch. Traditional methods for batch process, such as multiway FDA (Chen 2004) and multi-model FDA (He et al. 2005), cannot solve these issues well. They require complete batch data only available at the end of a batch. Therefore, the complete batch trajectory must be estimated real time, or alternatively only the measured values at the current moment are used for online diagnosis. Moreover, the above approaches do not consider the problem of inconsistent production cycles.