Structural Dynamic Response Reconstruction Based On The Bayesian Theory

Structural dynamic response reconstruction has drawn intensive attentions in the past decade, and it has the broad application prospect among many fileds about structural dynamics, such as structural vibration control, structural damage identification, inverse problems of structural dynamics, structural health monitoring, structural diagnostics and prognostics. Based on structural response reconstruction, the acceleration signal which is easy to be measured can be used to reconstruct the displacement and velocity signals which are difficult to be measured, and reconstructing more responses to reduce the ill-poseness of inverse problems, and much less sensors are needed to monitor the dynamic responses of the large scale mechanical engineering structure in real time, and also the measurable responses are used to reconstruct the responses which are in the inaccessibility of locations for measurement. This dissertation aims to contribute some useful studies and trials on the methods of structural response reconstruction, especially on the structure whose FE model is not correct. The features obtained in this dissertation are mainly as follows:1. The dissertation presents the improved versions of the response reconstruction method based on Empirical Mode Decomposition (EMD) for proportionally damped systems and non-proportionally damped systems in the presence of closely spaced modes, respectively. The key idea of the improved methods is to regard each set of closely spaced modes as an integral part and the two tools are EMD and Finite Element Method (FEM). The proposed methods are very efficient in terms of computational cosr due to the transformation equation and the mature EMD, and very suitable for various dynamic response reconstructions based on the different types of sensor measurements, and also very suitable for the situation of lacking sensors.2. The dissertation presents the response reconstruction method based on Kalman Filter for a linear structural system. Firstly, apply a simple but efficiently heuristic algorithm to optimize the sensor placement by taking the the minimum average reconstruction error variance as the objective function. Secondly, use the measured acceleraton signals to identify the structural state vectors by adopting the Kalman Filter algorithm. Finally, reconstruct the unmeasured responses based on the identified states and the observed matrices. Additionally, for the linear structures with unknown excitations, we introduce an algorithm from the filed of automatic control. The algorithm can get the unbiased minimum-variance input and state estimation for linear discrete-time systems. Then, a novel approach based on this algorithm is proposed for structural dynamic response reconstruction. The procedure is very similar as the procedure of the method based on the Kalman Filter. In general, the two proposed methods consider not only measurement errors but also model uncertainties.3. Structural model uncertainties are considered as the discrete errors of structural parameters. This dissertation presents a novel response reconstruction method based on the Extended Kalman Filter for the structural linear systems excitied by known forces. The uncertain parameters are arranged together with structural states into the augmented states, therefore, the state transition and observation equations are nonlinear. The Extended Kalman Filter is used to identify the augmented states from the two nonlinear equations. Based on the estimations of the states and the uncertain parameters, the desired responses are reconstructed. Additionally, the dissertation also presents a new method for structural linear systems with unknown excitations. The method is based on the linearization idea of the Extended Kalman Filter, and extending the second method in Point2with linearization. Then, the unknown excitations, the states and the uncertain parameters are identified together. Based on this extended algorithm, a new response reconstruction method is proposed to deal with the structural linear systems excited by unknown forces.4. The dissertation presents a novel response reconstruction method based on the improved Particle Filter for structural nonlinear systems with unknown forces. Exchange the locations of the time update step and the measurement step. Firstly, identify the excitations by the least-square method, and then, identify the states and the parameters with the identified forces, finally, reconstruct the desired responses with the above identified values. The method is extended into a parallel algorithm for two purposes. One is to assure the independent character among the partilces, and to alleviate the degradation problem. The other is to improve the real-time performance of the algorithm. Additionally, applying the MCMC technique into the resampling step is to prevent degradation at some extent.In summary, the dissertation is based on the Bayesian theory, and focusing on the response reconstruction of the structures with model uncertainties. Some new reconstruction method are proposed, especially the two improved methods which can identify the excitations, the states and the uncertain parameters, are not limited to structural response reconstruction but to be suitable for various fields of structural dynamics, such as force identification, parameter identification, damage identification and vibration control.