Subspace Method For System Identification And Its Application To Complicated Structures

This thesis focuses on the performances, extensions of subspace identification methods and their applications to complicated structures, based on the basic theory of subspace-based state-space system identifica- tion (4SID). 1 .The theory of subspaee identification algorithms is summarized systematically. Based on the realization theory, the stochastic properties and subspace structures of linear system are described. And three main steps of all subspace algorithms are explored. First, using an LQ-decomposition, the projection of the row space of specific data Hankel matrices is calculated. Next, the SV-decomposition of the projection is calculated to directly lead to the observability matrices and a Kalman filter estimation of the state sequences. Last, the system matrices are extracted from the observability matrices and/or the estimated state sequences. 2.A unified framework of subspace algorithm is structured through analyzing and comparing of the similarities among various subspace algorithms. It is shown that all these are special cases of one unified theorem. The results reveal that existing 4SID methods use exactly the same subspace to determine the order and the extended observability matrix, but that the weighting matrix, to calculate a basis for the column space of observability matrix is different among them. 3.The closed-loop subspace identification methods are studied in order to apply the 4SID to engineering practices. In terms of the theories of the projection and identification for closed-loop system, as the open-loop does, two identification algorithms are presented using the observability matrices and/or the estimated state sequences directly from closed-loop input-output data. A simulation is carried out to compare the differences between the closed-loop algorithms and open-loop one. 4.A subspace identification method with multiple-data sets is proposed to adapt 4SID to practical problems. Via the theoretical and mathematical derivation, the 4SID methods of single input-output data set are readily ii 2 .2 ABSTRACT modified to handle the cases of multiple data sets. It is very useful for most of practices where the multiple data sets related the same dynamic system are collected, but with possibly different initial conditions. By means of two examples, the algorithm is shown good efficiency and feasibility. 5.The given subspace identification methods are applied to two complicated structures: to model an aero-engine and to estimate the modal parameters of a Mini-Mast, and the satisfied results are obtained. Which show that the subspace methods have the advantages of simple operation and good numerical stability, and prove that it is an excellent method for the identification of high order, multi-variable complicated system.