Markov Chain Neighborhood Sparse Preserving Graph Embedding Based on Tensor Factorization for Batch Process Monitoring

Abstract

If the three-dimension data of batch process are unfolded the two-dimension data, some important information would lose, and outliers such as noise would lead to poor monitoring results. Therefore, a Markov chain neighborhood sparse preserving graph embedding algorithm based on tensor factorization (TMNSPGE) is proposed. Firstly, tensor factorization is used to directly process the three-dimension data in batch process, which can avoid the information loss. Secondly, by using the neighborhood preserving embedding algorithm and sparse manifold coding, the local linear relationship and local sparse manifold structure of data are preserved. On this basis, Markov chain analysis is introduced to construct a similar graph to make the data after dimensionality reduction have a certain probability interpretation. Finally, the statistics and control limits are determined to realize process monitoring. Numerical example and penicillin fermentation simulation process prove the effectiveness of TMNSPGE algorithm in batch process monitoring.

Keywords

• Batch process monitoring
• finite Markov chain
• graph embedding
• neighborhood preserving embedding
• sparse representation
• tensor factorization