Robust optimization of engineering structures involving hybrid probabilistic and interval uncertainties

A novel, yet practically feasible, robust optimization approach is proposed in this study for engineering structures involving hybrid uncertainties. Both stochastic and interval uncertain system parameters are incorporated within a single analysis-design computational scheme. The generalized beta distribution is adopted to model the bounded stochastic system uncertainties, which offers the benefit of evaluating the performance of objective function and constraints of the robust optimization. A multi-layered refining Latin hypercube sampling-based Monte Carlo simulation approach is proposed to assess the robustness of the objective function. Furthermore, a new concept, namely, the interval angular vector, is presented to evaluate the robust feasibility of the constraints of the optimization problem. In order to systematically solve the robust optimization problem, a new genetic algorithm is presented in this study which utilizes the order preference by similarity to ideal solution technique so the feasible design vectors can be sorted according to their distances to the negative ideal solution. The effectiveness and applicability of the proposed computational approach are demonstrated by one numeral example and two realistic complex engineering structures including the bucket linkage mechanism of an excavator and the upper beam of a high-speed punching machine.

Automated summary

A novel robust optimization approach is proposed in this study for engineering structures with hybrid uncertainties, incorporating both stochastic and interval uncertain system parameters. The method utilizes generalized beta distribution to model stochastic system uncertainties and introduces the concept of interval angular vector to evaluate the robust feasibility of constraints. A genetic algorithm is presented to systematically solve the robust optimization problem and demonstrate its effectiveness through numerical and realistic engineering examples.