Simultaneous reliability and reliability-sensitivity analyses based on the information-reuse of sparse grid numerical integration

In this paper, a new method is put forward for simultaneous reliability and reliability-sensitivity analyses based on the information-reuse of sparse grid numerical integration (SGNI). First, the reliability analysis is conducted on the basis of fractional exponential moments-based maximum entropy method (FEM-MEM), where the SGNI is employed for FEM assessments. The reliability index can be evaluated by integrating over the distribution derived by FEM-MEM. Then, the reliability-sensitivity analysis is carried out by reusing the output samples in previous reliability analysis and updating the corresponding weights, where no additional model evaluations are required. Then, the FEM-MEM is applied again to derive the conditional distribution and reliability index. By comparing the conditional and original reliability indexes, one can define the reliability-sensitivity index to identify the importance of each random variable to reliability. Since only one-round of model evaluations are necessary in the proposed method, the computational efficiency is highly desirable. Four numerical examples are investigated to check the effectiveness of the proposed method, where pertinent results obtained from Monte Carlo simulations (MCS) and Sobol's index are compared. The results demonstrate the proposed method is accurate and efficient for simultaneous reliability and reliability-sensitivity analyses.