Probability Of Bridge Structure Damage Identification Method Based On The Riccati Transfer Matrix Method

Bridges play a significant part in transportation. Their health conditions are vital to ensure the fluency on roads. Recently frequent severe accidents with tremendous casualties amid collapse of bridges make the health monitoring and damage identification of bridges one of the hot research focuses. In this realm, because of complexity of the problem, there are no satisfactory solutions so far in the world.In this thesis, after reviewing present researches on the health monitoring and damage identification, and further basing on the perturbation Riccati transfer matrix, the probability damage identification is proposed to tackle this problem. The contents can be divided into three parts:The first part: According to bridge's characteristic of having one dimension, the element matrix formulas of the zero-order (no perturbation), the first-order and the second-order perturbation of the common transfer matrix in different conditions are given by using the common element transfer matrix. After recombining according to the essential idea of Riccati transfer matrix, every order of perturbation Riccati transfer matrix in different conditions are obtained. At the same time, the first-order and the second order recurrence relations of transfer matrix and the vectors of every section are derived. Based on the boundary conditions, the frequency equations of the zero-order, the first-order and the second-order perturbation of the bridges with random parameters are given as follows:The frequency equations are solved by numerical value method. And the results of eigenvalues of the zero-order, the first-order and the second-order perturbation are subsequently produced. Moreover using singular value decomposition to decompose the transfer matrix of the final section, the equations to solve the zero-order, the first-order and the second-order of the state-space vector of the final section are given as follows:According to the calculated result of the final section state-space vectors, the values of every section state-space vector can be calculated by the recurrence relations of the section state-space vector. The zero-order, the first-order and the second-order perturbation of the eigenvector are also obtained.On the basis of the above formulas, the calculating program is worked out. A simple supported beam, as an example, is calculated when the anti-bending and the mass of every element are taken as random parameters separately. The values of the program are compared with the theoretical values to verify the program and the formulas which are used in the calculation of the statistics of the eigenvalues and the eigenvectors of a structure withrandom parameters.The second part: On the basis of Taylor's expansion of the eigenvalues of structures with random parameters, the formulas calculating the statistics (the mean value and the variance) of the eigenvalues and the mode shapes with random parameters are obtained. Using the perturbation Riccati transfer matrix method, the calculating program is produced. Again, a simple supported beam with stochastic mass density is used as an example. Its statistics (the mean value and the variance) are calculated and compared with the theoretical values to verify the correctness of the used formulas. Eventually this becomes the theoretical basis of the probability damage identification of the bridges.The third part: According to the verified structural damage identification method and supposing the to-be identified parameters to be independent and have normal distribution, the scheme of identifying bridge structure damage is proposed by using the probability damage identification method. Assume the zero-order, the first-order and the second-order perturbation statistics of the frequencies and the mode shapes of the bridge structures are known, and substitute them into the statistics property formulas of the frequencies and the mode shapes, as a result an objective function including the mean values and the variance of all the identified parameters is established. Set...