Analysis of structural reliability from time response using fully probabilistic

The probability density evolution of structural dynamic prediction models under several times random loads are proposed in this paper. Firstly, the probability density of several times stochastic loads can be obtained from the probability density of single time stochastic load. The prediction models of structural reliability from time responses under several times stochastic loads with and without strength degeneration over time are derived using the stress-strength interference theory and probability density evolution method. The differential equation in the models can be solved using the forward finite difference method. The probability density functions of the structural strength redundancy at any time can be obtained. In the end, structural dynamic reliability can be calculated using integral method. The efficiency of the proposed method is demonstrated numerically through a speed reducer. The results have shown that the proposed method is practicable, feasible and gives reasonable accurate prediction.