Research On Structure Reliability Calculation Method And Sensitivity Analysis

Reliability theory plays a vital role in safety assessment and design by analysis. However, the traditional theory cannot take computational efficiency> accuracy and stability into consideration simultaneously or satisfy the practical demands when applied to complex engineering structures, thus the scope of application exits some limitations. This paper studies on a series of key theories of structural reliability, involving highly nonlinear problem, combined random vibration problem as well as reliability sensitivity analysis problem etc.,and provides some new theories and methods. Further research on these problems has important significance for perfecting structural reliability theory and guiding engineering practice. The main contributions of the dissertation are as follows:(1) A new method named rotation gradient algorithm (RGA) is proposed to overcome the divergence problem in reliability analysis when solving high nonlinear performance function by first order reliability method. The new iteration direction is determined by the linear combination of the negative gradient direction and former iteration direction. And the value of rotation angle is determined by the rotation coefficient and the relative rotaion rate is used to identify the different nonlinear degree of limited state function. So the algorithm can ensure convergence stability and convergence rates. No trial calculation and artificial parameters need preset, so it is suitable for reliability analysis of complex engineering structure.(2) Reliability calculation method suitable to complex structure based on the Kriging model is established systematically. Taking advantage of the characteristics of different weight of the test point with each experimental point according to different distance, an improved Kriging response surface method is proposed to reconstruct performance function by the strategy of increasing efficient points only. In order to further impove reliability calculation accuracy when dealing with high nonlinear performance function, Kriging importance sampling method is established by locating the sampling center at the design points.(3) Three methods are presented for the combined random reliability problem of linear structure. Firstly, derives the second order perturbation analytical expression for calculating the combined random reliability problem based on perturbation expansion method; Secondly, the calculation process of Kriging sampling method based on statistical conception are also given; and thirdly, the Kriging iteration method is constructed based on the first passage theory, where the structure random parameter is solved in the process of reliability index iteration. Meanwhile, this paper studies the structural random response, which affects the accuracy and efficiency of structural dynamic analysis and reliability calculation., and investigates the calculation method of non-stationary random response based on dynamic stiffness matrix method.(4) The correlation degree concept is introduced into sensitivity analysis of system with multiple failure modes and correlation coefficient formula is presented for multidimension conditional failure modes based on bi-normal conditional failure probabilities. Then the complex solving process of system sensitivity is carried out by computing the weight coefficient derivation process of failure probabilities that corresponding to all failure modes. Thus the analysis difficulty and workload is decreased but also the calculation process is more easily realized.(5) The paper constructs a new reliability sensitivity factor by the standard deviation sensitivities based on analysis and derivation of traditional reliability sensitivity factors. Different from the traditional sensitivity factor, the new one not only can reflect the importance difference of all variables to structural failure probability, but also represent the error caused by one or more variables considered as constant. According to the conclusion, the related influence information of each random variable to structural failure probability can be obtained by primary analysis of reliability sensitivity. Thus this method can improve the calculation efficiency and reduce the analysis difficulty greatly.