Hybrid Reliability Analysis Method Research For Structure With Uncertainty

Inevitably,various uncertainties exist in the design of actual engineering structures,such as material properties,load conditions and use environments,the usage of reasonable methods for effective analysis and control of uncertainties is of great significance for ensuring the usability and structural reliability of products.The first order second moment method is the most classic and commonly used method in structural reliability analysis,but this method has limitations in dealing with uncertainties,so based on this,we introduce interval variables to characterize the uncertainties and then converting reliability index solving optimization problems into reliability index boundary search problems under interval variables.Aiming at this search problem,we propose a method for solving reliability index based on SQP algorithm and trying to improve convergence and stability in situations where the limit state surfaces are highly nonlinear.The main research contents of this paper are as follows:Firstly,we introduced interval parameters and then proposed a hybrid reliability analysis method with uncertainty on the basis of the advanced first-order second moment method.This method transforms the single reliability index optimization problem into a boundary parameter search problem of reliability index.In the process of model construction we found that the cumulative probability function has a different monotonicity for different distribution parameters,a certain correspondence between boundary of reliability index and boundary of interval is obtained based on the monotonicity analysis results and it efficiently simplifies the iterative search process.Secondly,a method for solving structural reliability index based on SQP algorithm is proposed.According to the definition of reliability index,the reliability index optimization model was deduced and the equation-constrained SQP algorithm was used to solve the reliability index optimization problem.This method has good performance in both efficiency and accuracy of the reliability index solution based on the great advantage of SQP algorithm in solving nonlinear constrained optimization.Finally,the sensitivity explicit expressions of the failure probability to the mean and standard deviation of the variables are further deduced based on the advanced first-order second moment method because of reliability sensitivity analysis helps to identify variables that have a large impact on the reliability of the structure.We can identify the change rules of positive or negative correlation of the failure probability to the mean and standard deviation and accurately identify the variables that have a great influence on the reliability of the structure according to its numerical value.The sensitivity index can be obtained based on the reliability analysis solutions of the advanced first-order second moment method without any additional calculations.Practical examples demonstrate the efficiency and accuracy of the algorithm.