Physically driven GE-GDEE and absorbing boundary processes for the first-passage reliability assessment of high-dimensional systems under stochastic excitations - Chen, Jianbing; ICASP14; Sun, Tingting (My University, 2023)
Accurate reliability assessment of high-dimensional systems excited by stochastic loads is demanding and challenging. The recently developed Globally-Evolving-Based Generalized Probability Density Evolution Equation (GE-GDEE) combined with the absorbing boundary processes (ABPs) has been successfully applied to the first-passage dynamic reliability assessment of high dimensional systems with fair efficiency and accuracy in capturing small failure probabilities. In this GE-GDEE-based method, the ABPs are constructed first, and then the GE-GDEE that governs the evolution of the PDFs of the ABPs, usually a one- or two-dimensional partial differential equation, is established. However, reversing the procedure, that is, first deriving the GE-GDEE for the underlying original process and then imposing the absorbing boundary conditions, will lead to errors in dynamic reliability evaluation. This work aims to explain why directly imposing absorbing boundaries on the GE-GDEE for original processes cause such errors in reliability assessment and the necessity of constructing ABPs. First, this paper illustrates that the critical factor causing the errors is the effective drift coefficients in the GE-GDEE of the ABPs are different from that of the original processes. Since the effective drift coefficients in the GE-GDEE serve as the physical driving forces that control the remaining probability densities to evolve, it is essential to involve in the effective drift coefficients the information of finite-dimensional distributions and the influence of the threshold. Then, several typical multi-degree-of-freedom systems subjected to Gaussian white noise are taken as examples to demonstrate the idea, where the analytical or semi-analytical effective drift coefficients for the original processes are available. The effective drift coefficients in the GE-GDEE of ABPs and original processes and the resulting reliability are compared. The comparison shows that differences between the effective drift coefficients of the APBs and the original process are confined within the vicinity of the boundaries of the safety domain. This work also finds that directly imposing absorbing boundaries on the GE-GDEE of original processes lead to systematical discrepancies in the obtained failure probabilities but still holds the same order of magnitude as the real solution, whether the threshold is low or high. Through the lens of the physically driving force, the local deviations in the effective drift coefficients explain the phenomenon well.
14th International Conference on Applications of Statistics and Probability in Civil Engineering(ICASP14)
PUBLISHED