Abstract:

As an alternative or complementary approach to the classical probability theory, the ability of the evidence theory in uncertainty quantification (UQ) analyses is subject of intense
research in recent years. Two state-of-the-art numerical methods, the vertex method and the sampling method, are commonly used to calculate the resulting uncertainty based on the evidence theory. The vertex method is very effective for the monotonous system, but not for the non-monotonous one due to its high computational errors. The sampling method is applicable for both systems. But it always requires a high computational cost in UQ analyses, which makes it inefficient in most complex engineering systems. In this work, a computational intelligence approach is developed to reduce the computational cost and improve the practical utility of the evidence theory in UQ analyses. The method is demonstrated on two challenging problems proposed by Sandia National Laboratory. Simulation results show that the computational efficiency of the proposed method outperforms both the vertex method and the sampling method without decreasing the degree of accuracy. Especially, when the numbers of uncertain parameters and focal elements are large, and the system model is non-monotonic, the computational cost is five times less than that of the sampling method.