Probabilistic Analysis for Structures with Hybrid Uncertain Parameters

In practical engineering problems, the distribution parameters of random variables cannot be determined precisely due to limited experimental data. The hybrid uncertain model of interval and probability can deal with the problem, but it will produce extensive computation and it is difficult to meet the requirement of the complex engineering problem analysis. In this scenario, this paper presents a vertex method for the uncertainty analysis of the hybrid model. By combining the traditional finite element method, it can be applied to the structural uncertainty analysis. The key of this method is to demonstrate the monotonicity between expectation and variance of the function and distribution parameters of random variables. Based on the monotonicity analysis, interval bounds of the expectation and variance are directly calculated by means of vertex of distribution parameter intervals. Two numerical examples are used to evaluate the effectiveness and accuracy of the proposed method. The results show the vertex method is computationally more efficient than the common interval Monte Carlo method under the same accuracy. Two practical engineering examples are to show that the vertex method makes the engineering application of the hybrid uncertain model easy.