Nonlinear Fault Detection of Batch Processes Using Functional Local Kernel Principal Component Analysis

In order to guarantee and improve the product quality, the data-driven fault detection technique has been widely used in industry. For three-way datasets of batch process in industry process (i.e., batch × variable × time), a novel method named functional local kernel principal component analysis (FLKPCA) is proposed. Since the variables' trajectories often show functional nature and can be considered as smooth functions rather than just vectors. Firstly, the variables' trajectory is expressed as the combination of smooth basis functions using functional data analysis (FDA), which means that the datasets of batches process would be transformed from the three-ways array into two-ways function matrix. Then, kernel locality preserving projections (LKPCA) is used to perform dimensionality reduction on two-way function matrix directly. Different from kernel principal component analysis (KPCA). LKPCA aims at preserving the both local and global structure of the data in a new optimization objective. Consequently, FLKPCA could more effectively seek the potential information that hidden in the three-ways datasets. Lastly, the effectiveness of the proposed approach is illustrated by the benchmark of fed-batch penicillin fermentation process and the hot strip rolling process.