Modal Parameters Identification Of Bridge By Stochastic Subspace Identification Method

The dissertation focuses on the performances, extensions of subspace identification methods and their applications in modal parameters identification of bridge structures, based on the basic theory of numerical algorithms for subspace-based state-space system identification.The basic theory of subspace 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 subspace algorithms are explored. First, using a QR-decomposition, the projection of the row space of specific data Hankel matrices is calculated. Then, the singular value decomposition of the projection is calculated, and the observability matrices and a Kalman filter estimation of the state sequences are gained. Finally, the system matrices are extracted from the observability matrices and/or the estimated Kalman state sequences. The key issue in stochastic subspace identification is to gain the order of the system. In above setups, the order equals to the number of singular values in the singular value decomposition of projection. In practice, it is difficult to operate. In many practical cases, stabilization diagram can decide the order of system. The stabilization diagram can improve the identification results and operability of identification process.A program for modal parameters identification by using the stochastic subspace method is coded. A numerical simulation on a three-span continuous beam is carried out. From the analysis of the identification results, stochastic subspace identification has the follow advantage: 1) the user-specified parameters less than the classis methods, the only user-specified parameter is the order of the system. 2)Because the method does not involve iterative, there are no convergence problems. On the other hand, the stochastic subspace identification has some drawbacks: such as false modes, modes missing, and the long computing time etc. The false modes and modes missing affect the identification results. Therefore, the reasons causing the false modes and modes missing are investigated. The author concluded that there are two reasons: the first reason is because of the theory of SSI, the other is because the inputs of the system do not satisfy the assumptions that the input must be white noise and/or the output is disturbed by noise.To overcome the long computing time of the method, an improvement of computing efficiency for stochastic subspace identification method is proposed. Signals from parts of test points are taken part in the signals from all points as the past output data. A linear relation is established between the Kalman filter sequence and the parts signals. The improved method can reduce the calculation time and workload. In this study, the improved method is validated by a numerical simulation example. Comparing to an unconverted disarray stabilization diagram, the improved stabilization diagram is clearer.The stochastic subspace identification is improved in order to distinguish the false modes and to avoid modes missing. There are two improved methods distinguishing false modes: one is to improve stabilization diagram and the other one is to use two-stage stabilization diagram. The improvement to stabilization diagram is to distinguish the false modes by using modal assurance criteria. Furthermore, due to the structural damping in practice is quite scuttered so it is eliminated as judgment criteria for stabilization diagram, so more precision results are obtained. The two-stage stabilization diagram is a method dividing the output signals of structure into several segment, the stochastic subspace identification is used to each segment of output signal. Then the stabilization diagram is used to all the identified parameters of each segment. Then the false modes are distinguished. The two-stage stabilization diagram based stochastic subspace identification can avoid modes missing.In order to validate the availability of the improved methods, the same numerical simulation of a three-span continuous beam is identified by the two improved methods. And two real world bridges are analyzed. The identification results indicate that the two improve methods are successful methods.