A Study Of The Bayesian Statistics Inference Based Method For Structural Damage Identification

More and more long span structures and high buildings are constructed with science and technique development; it is a hot topic in civil engineering field for structural damage identification in construction and employment. It is an effective approach to solve structural damage identification problem based on the structural dynamic parameters.The state of arts of researches about structural damage identification is depicted in this dissertation, and the different structural damage identification methods are introduced; the characters of different methods are analyzed. Then the rationale of Bayesian statistics reasoning algorithm is depicted, and the feasibility using Bayesian theory for structural damage identification is expatiated. Compared with traditional damage identification methods, Bayesian statistics reasoning can realize structural parameters identification and structural damage pattern identification by different approachs.The essence of Kalman filtering (KF) is to gain the most optimal solution using recursion algorithm; therefore, KF is the most intuitionistic expression of Bayesian statistics reasoning method. Traditional KF is utilized to identify structural parameters by transformation from dynamic system differential equation to state space, and combining structural parameters and responses in system state vectors in this dissertation.The state equations and measurement equations of traditional KF are linear. Many engineering systems are not linear systems in reality. The extended Kalman filtering (EKF) method adopts the method to linearize the non-linear system approximately, and the problem of non-linear system filtering is solved. But the EKF method has the disadvantages that the linearization of system is only approximative, and it should have Gaussian noise hypothesis in system. Therefore, the EKF method has low identification precision. KF method and EKF method are adopted to identify structural parameters of liner/non-liner structural system in this paper, and the result of non-liner structural system identification is not converged in experiment. The facts have proved that KF method and EKF method have intrinsic limitation.The KF can get the optimal estimate in the Linear-Gaussian model, but it can not be applied in the nonlinear and non-Gaussian model. In this case, Particle filtering (PF) method is studied abroad for its wide application. The PF is a filter method based on Monte-Carlo simulation and recursive Beyesian estimation. As other predictive filters, state space is recursively got from measure space with system model by using the PF. It uses particles to describe the state space. The discretely random measure composed by particles and associated weights approximates to the true posterior state distribution, and is updated by recursion of the algorithm. The PF can resolve the problem of nonlinear model equations and non-Gaussian noise distribution, and is suitable for the structural damage identification fields. The traditional PF method has the disadvantages that the particle numbers is fixed, and the PF can not adjust the particle number in system identification.Since the particle numbers are fixed in particle filtering process, in order to guarantee the precision of system identification, the large particle numbers must be used which is not beneficial to the parameter identification of non-stationary system. An adaptive particle filtering (APF) method is proposed to identify non-stationary structural system parameters damage identification. In the APF, the sampling particle numbers are updated by the K-L distance rule between the system posterior probability density and current probability density of sampling particles set; it reduces the computations greatly in system identification by adaptive adjusting particle numbers by the state of non-stationary system (It adopts large particle numbers in non-stationary system state, vice versa.), hence it has a good time tracking ability, and it is more suitable for tracking the non-stationary system than the conventional PF. The numerical simulations confirm the effectiveness of the proposed method for the online structural damage identification.The Bayesian probabilistic neural network (PNN) describes measurement data in Bayesian statistics theory; it shows great ability of structural damage pattern recognition with noisy conditions. By combining wavelet analysis with PNN, a wavelet probabilistic neural network (WPNN) is proposed for structural damage identification in the dissertation; and the effect factors to damage identification result of wavelet function, wavelet scales and noise level etc. were analyzed. The identification result shows that the WPNN has high identification accuracy and noise-resistant and, huge structural damage pattern identification future.This dissertation focuses on structural system parameters identification and damage pattern identification problems based on Bayesian statistics reasoning theory, and at last, the main contributions and conclusions of this dissertation are summarized and some problems which need further research are put forward.