Study On Vectorial Cooperative Response Surface Method And Its Optimal Probabilistic Collocation Points For Structural Reliability Analysis

There are two key problems needed to be solved for structural reliability analysis with the cooperative stochastic response surface method (CRSM):one is how to develop cooperative base vector in a preconditioner Krylov subspace; the other is how to select the optimal probabilistic collocation point in the basic random variable subspace. One of the most important problems is how to deal with non-Gaussian correlated rondom variables properly in order to improve applicability, accuracy and efficiency. Aiming at solving these problems, this paper analyzed the structural reliability analysis involving various rondom variables such as Gaussion, non-Gaussion, uncorrelated or correlated variables. An improved CRSM for structural reliability analysis involving Gaussian correlated random variables was proposed, while the optimal probabilistic collocation points were slelected according to the full row rank criterion of collocation point matrix. Then the problem of probabilistic collocation point selection was solved and the cooperative base vector was proposed based on approximately equivalent probability transformation and Nataf transformation.The main contents of this thesis are as follow:1. A new method of CRSM which was optimal probabilistic collocation point based on the orthogonal and standardized was proposed. the stochastic row vector was constructed by the combination of basic random variables in accord with cooperative base vectors. The collocation point matrix was constructed by the stochastic row vector with particular collocation points and the optimal probabilistic collocation points were slelected according to the full row rank criterion of collocation point matrix. The criterion provided a scientific evidence for the probabilistic collocation point selection of CRSM. Results show that the proposed method is of high accuracy and efficiency.2. An improved vector CRSM for structural reliability analysis involving non-Gaussian correlated random variables was proposed based on approximately equivalent probability transformations. The non-Gaussian cooperative base vector was proposed according to the orthogonal transformation firstly.Then the location of collocation points in the random variable space was determined according to approximately equivalent probability transformation. It provied a approximate method for structural reliability analysis involving non-Gaussian correlated random variables. Results show that the proposed method is of high accuracy and efficiency.3. Based on the CRSM of approximately equivalent probability transformations,an improved vector CRSM for structural reliability analysis involving non-Gaussian correlated random variables was proposed according to the Nataf transformation. The non-Gaussian cooperative base vector was proposed according to the orthogonal transformation firstly and the location of the optimal probabilistic collocation points in the random variable space was determined according to the Nataf transformation. And the adaptability of CRSM for structural reliability analysis involving non-Gaussian correlated random variables was improved. Results show that the proposed method is of high accuracy and efficiency.4. It showed too much error for structural reliability analysis under random variables with large variability. In this paper, the variability and distribution pattern of elasticity modulus for the influence of structural reliability analysis was maily discussed with CRSM and monte carlo method (MCS).No matter the variable and distribution pattern of the load for the influence of structural reliability analysis, results calculated by CRSM and MCS show that the accuracy is high. And the results of MCS and CRSM are incorrect when the elasticity modulus is normal distribution and large variable. The accuracy is improved according to different treatments including probabilistic collocation points recombination, elimination of the larger deviation probabilistic collocation points and symmetrization of probabilistic collocation points recombination. However the error is still large. So further studies have to be made.