Nonlocal and local structure preserving projection and its application to fault detection

• A novel nonlocal and local structure preserving projection (NLLSPP) algorithm is proposed.
• NLLSPP is able to extract more useful data characteristics than PCA and LPP.
• A process monitoring method is developed based on the NLLSPP algorithm.
• The NLLSPP-based method has much better monitoring performance than traditional methods.

A novel dimensionality reduction method named nonlocal and local structure preserving projection (NLLSPP) is proposed and used for process monitoring. NLLSPP can simultaneously preserve the nonlocal structure (i.e., data variance) and the local structure (i.e., neighborhood relationships between data points) of the data set. According to nonadjacent or neighboring relationships of different pairs of data points, NLLSPP defines nonlocal or local similarity weight coefficients for pairwise data points on the basis of their distances. The nonlocal similarity weight coefficients force two nonadjacent data points to be projected far apart from each other. The local similarity weight coefficients force two neighboring data points to be projected near each other. In this way, nonlocal and local structures of the data set are naturally preserved and highlighted in a lower-dimensional space. Because of this advantage, NLLSPP is more powerful than principal component analysis (PCA) and locality preserving projections (LPP) in extracting important data characteristics. A process monitoring method is developed based on the NLLSPP algorithm. Its advantages are illustrated by a case study on the Tennessee Eastman process. The results indicate that the NLLSPP-based method has better monitoring performance that the PCA-based and LPP-based methods.