Nonlinear fault detection of batch processes based on functional kernel locality preserving projections

Data-driven fault detection technique has exhibited its wide applications in industrial process monitoring. The batch dataset is often organized as a special three-way array (i.e., batch x variable x time), and the research of data-based batch process monitoring has attracted considerable attention in the literature. A novel method named functional kernel locality preserving projections (FKLPP) is proposed for batch process monitoring. Since the variables' trajectories often show functional nature and can be considered as smooth functions rather than just vectors, then the three-way data can be transformed into a two-way function matrix. Firstly, the variables' trajectories are expressed by using the functional data analysis (FDA). By doing so, the original batch process data can be transformed into a two-way manner (batches x functions of the variable trajectories) by describing each variable trajectory as a function of time. Then, kernel locality preserving projections is used to perform dimensionality reduction on two-way function matrix directly. Different from principal component analysis (PCA) which aims at preserving the global Euclidean structure of the data, the FKLPP aims to preserve the local neighborhood information and to detect the intrinsic manifold structure of the data. The kernel trick is applied to the construction of nonlinear kernel model. Consequently, FKLPP may be useful to seek more meaningful intrinsic information hidden in the observations. Lastly, the effectiveness and potentials of the FKLPP-based monitoring approach are illustrated by a benchmark fed-batch penicillin fermentation process and the hot strip rolling process.