Study On Response Surface Method Of Structural Reliability And Its Engineering Application

With the research and development of reliability theory, there are many reliability calculation methods and achievements currently and most of them are trying to reduce performance function evaluations and improve accuracy of reliability index. First order reliability method is commonly used for reliability analysis. However, in practical engineering structures, performance function is generally difficult to expressed as an explicit function of the random variables, then Monte Carlo Method (MCM) and Response Surface Method (RSM) are often used to calculate structural reliability. The result of MCM based on finite element analysis is often used as the exact answer, but its main disadvantage is large computational cost and high time consumption. The basic idea of RSM is to use a fitted approximate explicit function to replace the implicit performance function, and then use common reliability methods for the approximate explicit performance function. Currently, the main research interests of RSM are:selecting performance function model, determining the location of the sampling center and selecting the sample points.The main content of this paper can be summarized as the following:1. Introduction to the conventional calculation methods of reliability index is given, including mean first order second moment method, advanced first order second moment method, HL method, JC method, RSM and MCM. Then a reliability index calculation method based on logarithmic transformation is proposed. For special polynomial performance functions with only logarithmic normal distributed random variables, the logarithm transformation is adopted to linearize the performance function and the formula is derived to calculate the reliability index. Three examples demonstrated that this method is simple and effective and provides precise solution with no need of iterative computation.2. Traditional RSM and experimental design methods of selecting sample points are briefly introduced. Then a new response surface methodology using second-order Taylor expansion (SOTE-RSM) of performance functions is proposed. Three examples were analyzed including a ten-bar truss and a multilayer frame. The results showed that SOTE-RSM is a reliable and stable method with high accuracy, and has better convergence rate than the traditional RSM. 3. A 18.5m transmission tower is finite element modelled and analyzed on its local stability reliability. Besides the structure gravity load, wind load in four directions is considered. The structure is made of equal angle steel. The equal angle steel cross-sectional dimensions of the structural member groups and the basic wind pressure are taken as random variables. The proposed SOTE-RSM, traditional RSM and MCM are used to calculate the structural reliability.-The results show that the proposed method is practical and efficient in reliability calculation of engineering structures.