Abstract

Uncertainties are a daily issue to deal with in aerospace engineering and applications. Robust optimization methods commonly use a random generation of the inputs and take advantage of multi-point criteria to look for robust solutions accounting with uncertainty definition. From the computational point of view, the application to coupled problems, like fluid-dynamics (CFD) or fluid-structure interaction (FSI), can be extremely expensive. This work presents a coupling between stochastic analysis techniques and evolutionary optimization algorithms for the definition of a stochastic robust optimization procedure. At first, a stochastic procedure is proposed to be applied into optimization problems. The proposed method has been applied to both CFD and FSI problems for the reduction of drag and flutter, respectively.

Abstract

Conventional methods addressing the robust design optimization problem of structures usually require high computational requirements due to the nesting of uncertainty quantification within the optimization process. In order to address such a problem, this work proposes a methodology, based on Kriging models, to efficiently assess the uncertainty quantification in the optimization process. The Kriging model approximates the structural performance both in the design domain and in the stochastic domain, which allows to decouple the uncertainty quantification process and the optimization process. In addition, an infill criterion based on the variance of the Kriging prediction is included to update the Kriging model towards the global Pareto front. Three numerical examples show the applicability and the accuracy of the proposed methodology. The results show that the proposed method is appropriate to solve the robust design optimization problem with reasonable accuracy and a considerably lower number of function calls than required by conventional methods.

Abstract

The inherent uncertainty in the structural parameters directly affects the structural performance, and its variation may lead to improper designs and catastrophic consequences. When subjected to uncertainty, the structure design must be optimized to get an insensitive design using a Robust Design Optimization (RDO) technique. Such design aims to find a system design in which the structural performance is less sensitive (insensitive) to the uncertainty of the inherent structural parameter without eliminating them. This is usually achieved by simultaneously minimizing the mean and variance of the structural performance function. Various RDO approaches, such as those based on Taylor series expansion, simulation-based methods, dimension reduction, and metamodel, can effectively take into account these uncertainties. However, the computational efficiency and accuracy in evaluating the mean and variance of the performance function remain a challenging task. To obliviate this limitation, a novel stochastic simulation-based approach is proposed in the present work. The proposed approach is built on an `Augmented optimization problem,' in which design variables are artificially considered an uncertain parameters. An unconstraint Genetic algorithm (GA)based optimization approach is formulated to determine the optimal solution. As the mean and variance frequently conflict with each other, so to obtain the Pareto optimum, a linear scalarized objective function is adopted. To demonstrate the proposed approach, RDO of a four-bar structure is performed. The results obtained are compared with the conventional Monte Carlo simulation approach and confirm that the proposed approach yields accurate results. This paper allows the designers to design the insensitive structure systems by minimizing the variance of the performance function. Moreover, the proposed RDO approach is not only limited to the civil structures but can also be enforced in the design of any realistic linear/nonlinear structures and systems such as machine components (like clutches, gears, etc.), aerospace, etc., having uncertainties in their geometry or material, such as the residual strain, modulus, thickness, density, etc.