Direct optimization of uncertain structures based on degree of interval constraint violation

A constrained interval optimization model is proposed for the optimization of uncertain structures with their mechanical performance indices described as the objective and constraint functions of the design vector and interval uncertain parameters. Present indirect approaches for solving such interval optimization models by converting them into deterministic ones will result in the loss of uncertainty information and deviate from the original intention of realistically modeling engineering optimization problems. To overcome these shortcomings, a novel optimization algorithm is proposed for directly solving the nonlinear constrained interval optimization models based on a novel concept of the degree of interval constraint violation (DICV) and the DICV-based preferential guidelines. A nested genetic algorithm (GA) is developed to realize the direct interval ranking of various design vectors. The outer layer GA locates the optimal solution based on direct interval ranking. The inner layer GAs integrated with Kriging technique compute the intervals of the mechanical performance indices of every design vector in the current population of the outer layer GA. The validity and superiority of the proposed direct interval optimization algorithm was verified by three numerical examples. Finally, the proposed direct interval optimization method was applied to the optimization of the cone ring fixture with uncertain material properties in a large turbo generator aimed at moving its natural frequencies away from the exciting one. The results demonstrated its feasibility and effectiveness in optimizing practical engineering structures under uncertainties.