Subinterval Decomposition-Based Interval Importance Analysis Method

The importance analysis method represents a powerful tool for quantifying the impact of input uncertainty on the output uncertainty. When an input variable is described by a specific interval rather than a certain probability distribution, the interval importance measure of input interval variable can be calculated by the traditional non-probabilistic importance analysis methods. Generally, the non-probabilistic importance analysis methods involve the Monte Carlo simulation (MCS) and the optimization-based methods, which both have high computational cost. In order to overcome this problem, this study proposes an interval important analytical method avoids the time-consuming optimization process. First, the original performance function is decomposed into a combination of a series of one-dimensional subsystems. Next, the interval of each variable is divided into several subintervals, and the response value of each one-dimensional subsystem at a specific input point is calculated. Then, the obtained responses are taken as specific values of the new input variable, and the interval importance is calculated by the approximated performance function. Compared with the traditional non-probabilistic importance analysis method, the proposed method significantly reduces the computational cost caused by the MCS and optimization process. In the proposed method, the number of function evaluations is equal to one plus the sum of the subintervals of all of the variables. The efficiency and accuracy of the proposed method are verified by five examples. The results show that the proposed method is not only efficient but also accurate.