A novel subspace identification algorithm and its application in stochastic fault detection
Subspace identiﬁcation algorithms have drawn tremendous interests, not only because they are simple in parametrization, but also because of their numerical stability and moderate computational complexity. Started with the deterministic realization, subspace identiﬁcation went through the devel opment of stochastic realization theory and has become the solution to the combined deterministic-stochastic realization. Although subspace identiﬁca tion algorithms are quite successful in many applications, some drawbacks have been experienced. In this work, a novel subspace identiﬁcation algorithm (SIMPCA) is proposed to address two aspects: the errors-in-variables case and closed-loop identiﬁcation. In the proposed subspace identiﬁcation algorithm, principal component analysis is applied to extract the parity subspace, which naturally falls into the category of errors-in-variables formulation and resem bles total least squares. Because projecting out the future input is avoided, SIMPCA is applicable to closed-loop identiﬁcation provided that the input perturbation is autocorrelated. Consistency analysis is performed for the pro posed algorithm and the consistency conditions are given in several theorems. The eﬀect of the column weighting in the subspace identiﬁcation algorithms is discussed and the SIMPCA with column weighting is designed which shows improved eﬃciency. Two approaches for system order determination based on AIC index are proposed. A novel stochastic fault detection algorithm is pro posed based on SIMPCA. Through monitoring the second order statistics, the SIMPCA-based fault detection algorithm shows signiﬁcantly improved perfor mance compared to regular PCA and DPCA. PCA and DPCA using second order indices are also proposed. The performance of the proposed subspace identiﬁcation and fault detection algorithms is demonstrated through several simulation examples and compared with other benchmark methods.