Non-Probabilistic Robust Equilibrium Optimization of Complex Uncertain Structures

Robust optimization of complex uncertain structures usually involves multiple conflicting and competing structural performance indices. Present approaches for achieving the final design of such an optimization problem always involve a decision-making process, which is a demanding task that requires the rich experience and expert skills of designers. To overcome the difficulty, an interval robust equilibrium optimization approach is proposed to find the optimal design of complex uncertain structure based on the robust equilibrium strategy for multiple conflicting and competing structural performance indices. Specifically, a new concept of closeness and crossing coefficient between interval boundaries (CCCIBs) is proposed at first, based on which the tri-dimensional violation vectors of all interval constraints can be calculated and the feasibility of a design vector can be assessed. Then, the robust equilibrium assessment of multiple objective and constraint performance indices is investigated, based on the results of which the feasible design vectors can be directly ranked according to the robust equilibrium strategy for all structural performance indices. Subsequently, the algorithm for the robust equilibrium optimization of complex uncertain structures is developed by integrating the Kriging technique and nested genetic algorithm. The validity, effectiveness, and practicability of the proposed approach are demonstrated by two illustrative examples.