A general integrated procedure for uncertainty-based design optimization of multilevel systems by hierarchical decomposition framework

Several subsystems with hierarchical relationship compose a multilevel system, each of which may have uncertainties in material properties and structural geometric parameters. Compared with the integrated strategy, hierarchical decomposition method is more effective in the investigation of the performance of multilevel systems. However, the process of hierarchical propagation of uncertainty may result in many challenging problems, such as multidimensional correlations and complex coupling of uncertainties. In this paper, a general integrated procedure of multilevel system design optimization by means of the integration of the hierarchical uncertainty analysis (HUA), hierarchical sensitivity analysis (HSA) and uncertainty-based design method is innovatively proposed. Firstly, a hierarchical framework combining R-vine copula with sparse polynomial chaos expansions is adopted to solve the problems of uncertainty quantification and propagation. After that, a mapping-based hierarchical sensitivity analysis (MHSA) method is employed to obtain sensitivity indexes of multilevel systems with multidimensional correlations. At last, the probabilistic target cascade analysis method is used to accomplish the multilevel design optimization considering multilevel uncertainty. The proposed procedure is then applied to solve the material–structure integrated design problem of an automotive fiber composite shock tower. Results show that the proposed procedure can achieve a weight reduction compared with the initial design under the premise of meeting the structural performance requirements.