An approach to robust optimization of impact problems using random samples and meta-modelling

Abstract

Conventionally optimized structures may show a tendency to be sensitive to variations, for instance in geometry and loading conditions. To avoid this, research has been carried out in the field of robust optimization where variations are taken into account in the optimization process. The overall objective is to create solutions that are optimal both in the sense of mean performance and minimum variability. This work presents an alternative approach to robust optimization, where the robustness of each design is assessed through multiple sampling of the stochastic variables at each design point. Meta models for the robust optimization are created for both the mean value and the standard deviation of the response. Furthermore, the method is demonstrated on an analytical example and an example of an aluminium extrusion with quadratic cross section subjected to axial crushing.It works well for the chosen examples and it is concluded that the method is especially well suited for problems with a large number of random variables, * Corresponding author. Tel.:+46-13-282475; fax:+46-13-282717.Email address: david.lonn@liu.se (David Lönn)Preprint submitted to International Journal of Impact Engineering July 2, 2009 M A N U S C R I P T A C C E P T E D ARTICLE IN PRESSsince the computational cost is essentially independent of the number of random variables. In addition, the presented approach makes it possible to take into consideration variations that cannot be described with a variable. This is demonstrated in this work by random geometrical perturbations described with the use of Gaussian random fields.

Optimization of Vehicle Structures under Uncertainties

“…Metamodels have also been widely used in order to minimize the computational effort for RDO (Koch et al 2004;Zhang et al 2007;Lönn et al 2010;Sun et al 2011;Aspenberg et al 2013;Gu et al 2013;Shetty and Nilsson 2015). Conventionally used single-stage metamodel approaches (Gu et al 2013;Shetty and Nilsson 2015) are simple and efficient.…”

“…Several studies have focused on improving the efficiency of stochastic optimization methods (Parkinson et al 1993;Lee and Park 2001;Wu et al 2001;Du and Chen 2004;Liang et al 2004;Shan and Wang 2008), either by improving the efficiency of the optimization process or by modifying optimization formulations. Some researchers have, in addition, focussed on minimizing computational effort by using metamodels Kim and Choi 2008;Zhao et al 2009;Zhu et al 2009;Lönn et al 2010;Wiebenga et al 2011). The use of metamodels is one of the most promising techniques in order to minimize computational effort in stochastic optimization of large-scale problems.…”

Adaptive Response Surface Method Based Efficient Monte Carlo Simulation

“…the Root Mean Square Error (RMSE), the co-efficient of determination (R 2 ) and the average prediction error ( m ) usually used to check the validity of the meta-models are computed for both the LSM and MLSM based RSM. Details of the expressions of these norms may be seen elsewhere (Bouazizi et al 2009, Lönn et al 2010. Table 2 shows the results of statistical tests for both the SD and CCD based RSM using LSM and the MLSM.…”

Robust optimisation of railway crossing geometry

“…Applications of robust optimisation in solving engineering problems can be found in many publications such as. [8][9][10][11] In the present paper, the robust optimisation approach is proposed in the design of crossing geometry, in which the wing rails are prescribed to the selected turnout design, while the nose rail is adjusted. Based on the previous parametric study [12] on wheel transition behaviour, three design variables are chosen in the optimisation to tune the longitudinal height profile and the B-spline represented cross-sectional shape of the nose rail.…”