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

Xiaoqiang Zhao,Miao Mou

doi:10.1109/access.2021.3052197

Xiaoqiang Zhao, Miao Mou

Open Access

https://doi.org/10.1109/access.2021.3052197

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Journal: IEEE Access	Publication Date: Jan 1, 2021
Citations: 27	License type: CC BY 4.0

Affiliation: Lanzhou University of Technology

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.

Highlights

Batch process has become an important industrial production mode due to its high production efficiency and high added value [1]–[3]
In order to solve the above problems, we propose a Markov chain neighborhood sparse preserving graph embedding algorithm based on tensor factorization (TMNSPGE) for batch process monitoring
When traditional graph embedding methods are used for batch process monitoring, they are often sensitive to the selection of neighbors and ignore the impacts of noise in the monitoring process and information loss by unfolding data

Summary

INTRODUCTION

Batch process has become an important industrial production mode due to its high production efficiency and high added value [1]–[3]. In order to solve the above problems, we propose a Markov chain neighborhood sparse preserving graph embedding algorithm based on tensor factorization (TMNSPGE) for batch process monitoring. GRAPH EMBEDDING (GE) In order to better explain the meaning of the dimensionality reduction algorithm in the fault feature extraction process, scholars proposed graph embedding learning to describe the structural relationship between data. The proposed algorithm extracts local structure information and sparse information from the augmented matrix, and constructs the similarity matrix through finite Markov chain analysis, so that the points after dimensionality reduction has a clear probability interpretation. Traditional algorithms need to unfold the data into a two-dimension form before modeling, no matter along which direction of the data unfold, the internal structure of the data would be destroyed For this reason, TMNSPGE can extract spatial information and timing information from tensor space.

SIMILARITY GRAPH DESIGN BASED ON FINITE MARKOV CHAIN

DERIVATION OF TMNSPGE

PROCESS MONITORING BASED ON TMNSPGE

CONCLUSION