THE CALCULATION PRECISION OF PROBABILITY DENSITY EVOLUTION EQUATION DIFFERENCE SCHEME AND THE IMPROVEMENT OF INITIAL CONDITION

Since the first time derivative of engineering structure response under random load was often larger than the structure response itself, if the time step which only meets the precision requirements of deterministic structural response analysis was used to solve the probability density evolution equation (PDEE), the standard deviation of structural response calculated by total variation diminishing (TVD) property difference method cannot meet the precision requirements. The computational precision of three probability density evolution equation numerical solution methods, such as one-sided difference method, Lax-Wendroff (L-W) two-sided difference method and TVD property difference method are compared under different difference time steps. In order to improve the solving precision of TVD property difference method, a reasonable difference time step selection method and initial value condition of normal distribution type are proposed, and the precision and universality of the time step selection method and initial value condition of normal distribution type are verified by numerical examples. The results of numerical examples show that the sample discreteness of the two-sided difference method is the smallest, and the time difference step size is the largest within the allowable error range. When only the mean value and standard difference are concerned, the two-sided difference method is suggested. The numerical error caused by TVD property difference method can be effectively reduced by using this method. The minimum mean error can be obtained when the standard deviation of the initial condition of normal distribution is equal to the space step.