Stochastic dynamic responses and reliability analysis of nonlinear system based on K-L decomposition and TVD finite difference method

Aiming at the problems of long computation time and complex probability density evolution rate of dynamic stochastic reliability solving methods for nonlinear dynamic systems, a finite difference method based on Karhunen-Loève (K-L) decomposition and total variation diminishing (TVD), combined with equivalent linearization, is proposed to solve the probability density evolution process, and then the entropy weight method is used to solve the dynamic stochastic reliability of nonlinear systems. The K-L decomposition method is used to determine the rate of probability density evolution of the system and reveal the statistical characteristics of random variables in the dynamic process. The probability density evolution equation of the system is solved by TVD finite difference method combined with a new initial value scheme, and the probability distribution is accurately described in the process of time evolution. The nonlinear system is linearized by the equivalent linearization method, which provides a simplified model for the analysis of complex system. In addition, the entropy weight method is used to calculate the reliability weights of each random parameter to further solve the overall reliability of the system, which provides a theoretical basis for reliability evaluation. The nonlinear gear system is taken as the research object, and the correctness of the proposed method is verified by comparing with Monte Carlo method. Furthermore, compared with the existing path integral method, the calculation time of the proposed method is reduced by more than 95%, and the calculation efficiency is significantly improved.