机械系统可靠性模糊多目标优化设计的综合协调法

Synthetic Coordination Methods for Fuzzy Multi-objective Optimization of the Reliability of Mechanical Systems

针对用常规优化方法难以处理具有相互矛盾属性的机械系统可靠性多目标优化设计问题,提出了一种基于模糊优化决策的综合协调函数法.该方法利用模糊集隶属函数的特性将各子目标函数模糊化处理为能够反映各子目标相对重要程度,具有加权指数的协调满意度函数形式;通过动态时变的协调校正加权函数再将各子目标的协调满意度函数综合成统一的单目标优化模型,然后用常规优化方法即可求出原多目标优化模型的满意解.最后给出一个实例以验证该方法的有效性.

In view of the fact that the problem of the multi-objective optimization of the reliability of mechanical systems with conflicting attributes is incapble of being solved by means of conven-tional mathematical programming techniques, a synthetic coordination method based on fuzzy optimization decision-making is presented to solve this problem. Using the property of membership function in fuzzy sets theory, each sub-objective function is transformed into coordination satisfac-tory function with weighted exponent, the weighted exponent shows the relative importance of each sub-objective function, and the coordination satisfactory function are synthesized into a sin-gle-objective optimization modei by correcting weighted function with dynamic real-time change. The satisfactory solution of the multi-objective optimization modei can be worked out by conven-tional multi-objective mathematical programming techniques. Finally, an example is given to illus-trative the method.