Output related fault detection and diagnosis based on multi block modified orthogonal Broyden-Fletcher-Goldfarb-Shanno algorithm

Abstract

In recent years, some progress has been made in fault diagnosis of multi-block regression model, but multi-block method uses the relationship between variables in Hilbert space to block, while the relationship between variables in complex industrial systems often exists in Banach space. In addition, Bayesian fusion method is used in fault monitoring, which can not accurately process the sub-block information and judge whether the fault information is related to the output. In this paper, a new multi-block method is proposed. Firstly, this method uses Ball Covariance (BCov) suitable for Banach space to describe the correlation between variables, and combines K-means clustering method to block variables to ensure that the blocking method is more reasonable. Secondly, an improved orthogonal decomposition Broyden-Fletcher -Goldfarb-Shanno (BFGS) algorithm is proposed. The MOBFGS algorithm performs orthogonal projection on potential structures, removing information orthogonal to the output from the input block. Furthermore, through complete orthogonal decomposition between the input block and the output block, information related to and unrelated to the output is completely separated, and used to detect output related and unrelated faults, respectively. Thirdly, at the block level, MOBFGS algorithm is used for fault detection and contribution graph method for fault diagnosis. Finally, numerical examples and Tennessee Eastman (TE) process simulation verify the effectiveness of this method.