Batch process fault detection and identification based on discriminant global preserving kernel slow feature analysis

The DGKSFA based batch process fault detection and identification procedure includes two stages: fault detection stage and fault identification stage, as illustrated in Fig. 5, and the fault detection stage can be further divided into an offline modeling stage and an online detection stage. In the offline modeling stage, the fault pattern dataset F are first constructed using C kinds of historical fault data, then, the three-way normal dataset X(I×J×K) and the fault pattern dataset F are utilized to build DGKSFA model. Lastly, the confidence limit of monitoring statistic is determined bases on the normal dataset. During the online detection stage, the collected test data is first normalized, then, the mean centered test kernel vector kˆt is calculated. Lastly, the monitoring statistic Ddist is built using test kernel vector kˆt and average kernel matrix K¯(K×IK) of normal dataset to determine whether the process is normal. In the fault identification stage, a new DGKSFA model is first rebuilt only using the normal dataset X and the fault snapshot dataset S. Then, the contribution of each original variable in the fault snapshot dataset is computed based on DGKSFA nonlinear biplot to determine which variable is responsible for the fault.188