Sensitivity importance-based robust optimization of structures with incomplete probabilistic information

Robust design optimization (RDO) is usually performed by minimizing the nominal value of a performance function and its dispersion considering equal importance to each individual gradient of the performance function. However, it is well known that all gradients are not equally important. An efficient sensitivity importance-based RDO technique is proposed in the present study for optimum design of structures characterized by bounded uncertain input parameters. The basic idea of the proposed RDO formulation is to improve the robustness of a performance function by using a new gradient index that utilizes the importance factors proportional to the importance of the gradients of the performance function. The same concept is also extended to the constraints. To enhance the robustness of the constraints, the constraint functions are also modified by using the importance factor proportional to the importance of the associated gradient of the constraint. Because all the variables are not equally important to capture the presence of uncertainty, an improved robust solution is obtained by the proposed approach compared with the conventional RDO approach. The present formulation is illustrated with the help of three informative examples. The results are compared with the conventional RDO results to study the effectiveness of the proposed RDO approach.