Automatic Nonlinear Subspace Identification Using Clustering Judgment Based on Similarity Filtering

Accurately determining system order plays a vital role in system identification directly related to the accuracy of identification results, especially for nonlinear system identification. Due to the need for human subjective judgment, the traditional sequence determination method easily causes uncertainty in the results; and the phenomenon of the virtual mode or omission occurs. An automatic nonlinear subspace identification method is proposed to address the aforementioned problems. When the eigenvalue decomposition of the constructed Hankel matrix is performed, the calculation range of the modal order of the system is estimated. The similarity coefficient and distance function are introduced to cluster the identified modal results, the poles of the false modes are removed to obtain the cluster stabilization diagram, and the best order of the system is received. Then, the modal parameters and nonlinear coefficients are obtained. Simulation examples are carried out to verify the effectiveness and robustness of the proposed method. An experimental study is carried out on a multilayer building with nonlinear characteristics. Compared with the traditional stabilization graph, the accuracy of the automatic order determination proposed in this paper is proven.

Automated summary

To address the uncertainty and false mode or omission phenomena caused by traditional sequence determination methods, an automatic nonlinear subspace identification method is proposed. This method estimates the calculation range of system modal order through eigenvalue decomposition of constructed Hankel matrix, and introduces similarity coefficient and distance function for clustering the modal results to remove the poles of false modes and obtain the cluster stabilization diagram to determine the best system order. Then, the modal parameters and nonlinear coefficients are obtained, and the effectiveness and robustness of the proposed method are verified through simulation and experimental studies.