The aim of this work is to propose a methodology to optimize the performance of a flexible rotor-bearing system taking into account parameter uncertainties. The idea of the optimization problem is to find the values of a set of parameters (e.g. stiffness of the bearing, diameter, etc.) for which the natural frequencies of the system are as far away as possible from the rotational speeds of the machine. For this purpose, the Campbell diagram is used and penalty functions are introduced to penalize natural frequencies close to the rotational speeds of the machine. Parameter uncertainties are taken into account (e.g. in the stiffness of the bearing, in the elasticity modulus of the material, etc.) and several probabilistic models are considered in the analysis (Gamma, Normal, Uniform, etc.). The global and bounded Nelder–Mead optimization algorithm is employed to minimize the proposed multi-objective function. The methodology proposed in this work is directly extended to complex rotor-bearing systems.

This article aims at optimizing laminated composite plates taking into account uncertainties in the structural dimensions. As laminated composites require a global optimization tool, the Particle Swarm Optimization (PSO) method is employed. A new Reliability Based Design Optimization (RBDO) methodology based on safety factors is presented and coupled with PSO. Such safety factors are derived from the Karush–Kuhn–Tucker optimality conditions of the reliability index approach and eliminate the need for reliability analysis in RBDO. The plate weight minimization is the objective function of the optimization process. The results show that the coupling of the evolutionary algorithm with the safety-factor method proposed in this article successfully performs the RBDO of laminated composite structures.