证据理论和区间分析相结合的可靠性优化设计方法

Method of Reliability Design Optimization Using Evidence Theory and Interval Analysis

提出一种基于证据理论和区间分析方法的可靠性优化设计方法。对于给定的失效概率许用值f_0,通过证据理论求出可靠性约束条件的似真度P1(F),以P1(F)≤f_0作为可靠性约束条件的替代模型,进而提出基于证据理论的广义可靠性优化设计建模方法。当仅考虑随机不确定性时,所建立的模型退化为传统的随机可靠性优化设计模型。给出似真度P1(F)的数值计算方法,并引入区间分析理论计算约束函数的值域,提高似真度的计算效率和可靠性优化的求解速度。开发基于证据理论和区间分析的可靠性优化设计遗传算法程序。给出了内压容器的可靠性优化设计实例。设计实例表明,所提出的方法正确、有效。

An evidence theory and interval analysis-based method of reliability design optimization is proposed. For the preconcerted failure probability f0, the plausibility measure of reliability constraint, PI（F）, is calculated by using evidence theory. With PI（F）≤f0 used as a surrogate model of reliability constraint, an evidence theory-based model of generalized reliability design optimization is formulated. If there is only random uncertainty in the formulated model, this model degenerates to a conventional model of reliability design optimization. A numerical method for calculating PI（F） is presented. The theory of interval analysis is used for approximately calculating the value range of constraint function, then the computational efficiency of PI（F） is significantly improved and the computational cost for solving the reliability optimization model is reduced. A genetic algorithm program for the evidence theory and interval analysis-based reliability design optimization is developed. The proposed method is demonstrated with a pressure vessel example. The example shows that the proposed method is effective and practical.