Non-probabilistic optimization model of engineering structures with dependent interval variables

To solve the design problems of engineering structures with multiple conflicting performance indices under uncertainties, a non-probabilistic optimization model which takes into consideration the correlation of uncertainties was proposed in this paper. The multidimensional parallelepiped model was utilized to describe the uncertainties and deal with their correlation. Further, a novel concept of feasible discriminant of interval constraints was proposed to identify the feasible solutions, and a competitive strategy for design vectors was proposed to achieve equilibrium design of structures. To improve the efficiency of optimization and promote its applications in engineering, a direct solution framework was constructed in this paper. This framework was based on response surface model and integrated the interval analysis with the genetic algorithm. The effectiveness and superiority of the proposed approach were illustrated by two numerical examples. Finally, the proposed method was applied to structural design of the upper and lower beams of forming machine, and the design of lightweight and equilibrium were achieved. This structural design example demonstrated the applicability and effectiveness of the proposed method in engineering.