Structural reliability analysis based on probability and probability box hybrid model

In many structural reliability analysis problems, probability approach is often used to quantify the uncertainty, while it needs a great amount of information to construct precise distributions of the uncertain parameters. However, in many practical engineering applications, distributions of some uncertain variables may not be precisely known due to lack of sufficient sample data. Hence, a complex hybrid reliability problem will be caused when the random and non-precise probability variables both exist in a same structure. In this paper, a new hybrid reliability analysis method is developed based on probability and probability box (p-box) models. Random distributions are used to deal with the uncertain parameters with sufficient information, while the probability box models are employed to deal with the non-precise probability variables. Due to the existence of the p-box parameters, a limit-state band will be resulted and the corresponding reliability index will belong to an interval instead of a fixed value. According to the interval analysis, the hybrid reliability model based on random and probability box variables is constructed and the complex nesting optimization problem will be involved in this hybrid reliability analysis. In order to obtain the minimal and maximal reliability index, the corresponding solution strategy is developed, in which the intergeneration projection genetic algorithm (IP-GA) with fine global convergence performance is employed as inner and outer optimization solver. Four numerical examples are investigated to demonstrate the effectiveness of the present method.