A new subspace identification approach based on principal component analysis

Principal component analysis (PCA) has been widely used for monitoring complex industrial processes with multiple variables and diagnosing process and sensor faults. The objective of this paper is to develop a new subspace identification algorithm that gives consistent model estimates under the errors-in-variables (EIV) situation. In this paper, we propose a new subspace identification approach using principal component analysis. PCA naturally falls into the category of EIV formulation, which resembles total least squares and allows for errors in both process input and output. We propose to use PCA to determine the system observability subspace, the A, B, C, and D matrices and the system order for an EIV formulation. Standard PCA is modified with instrumental variables in order to achieve consistent estimates of the system matrices. The proposed subspace identification method is demonstrated using a simulated process and a real industrial process for model identification and order determination. For comparison the MOESP algorithm and N4SID algorithm are used as benchmarks to demonstrate the advantages of the proposed PCA based subspace model identification (SMI) algorithm.