| 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 development of stochastic realization theory and has become the solution to the combined deterministic-stochastic realization. Although subspace identification 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 resembles 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 proposed 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 proposed based on SIMPCA. Through monitoring the second order statistics, the SIMPCA-based fault detection algorithm shows significantly improved performance 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. |
