A New Method for Achieving Flexibility in Hierarchical Multilevel System Design

Analytical target cascading (ATC) method has been widely applied to solve multilevel decomposed system design optimization problems. In the ATC method, concurrent design is achieved by target cascading. However, due to the complexity and the presence of uncertainty, it is a challenging task to set proper targets. In this article, instead of using point value targets, interval targets are analyzed and propagated through the multilevel system with the goal of reducing the effects of uncertainty while providing more flexibility to a design process. In the proposed method, the design of a hierarchical system at each level is taken as a single-objective optimization problem, by minimizing the degree of deviation between the target response interval and the achievable response interval. Not only the optimal design performance is considered in this method, but also the acceptable variation range of the performance is analyzed. When the present target for a lower level system and the achievable response from a lower level system are not point values, but rather intervals, their probability distributions are not available. Therefore, these variables are treated as interval variables. When the random and interval variables are present, the most probable point-based first-order reliability and the interval analysis methods are used to calculate the reliability bounds. The proposed method for flexibility under uncertainty provides more degree of freedom to the design of lower level systems, while also keeping the performance of the upper systems stable within a tolerable range. The accuracy of the proposed method is demonstrated via comparing results from both the proposed and traditional methods.