Mixed uncertainty based analytical target cascading: an approach for hierarchical multilevel optimization under probabilistic and interval mixed uncertainties

Analytical target cascading (ATC) has been extended to the probabilistic formulation to deal with the hierarchical multilevel optimization problem under uncertainty. However, only aleatory uncertainties can be handled by the probabilistic theory. Considering both aleatory and epistemic uncertainties exist in engineering design, a mixed uncertainty based analytical target cascading (MUATC) approach is proposed in this paper. The probability distribution and interval are used to represent the aleatory uncertainties and epistemic uncertainties, respectively. To figure out the mixed uncertainty propagation(MUP) problem, the reliability index approach based MUP (RIA-MUP) and performance measurement approach based MUP (PMA-MUP) are proposed firstly. Based on PMA-MUP, the MUATC method is established. MUATC firstly decouples the mixed uncertainty all-in-one (MUAIO) problem into deterministic optimization problem and mixed uncertainty analysis, and then hierarchically decomposes them into subproblems. All-in-one (AIO) mixed uncertainty analysis and hierarchically mixed uncertainty analysis methods are established to calculate the characteristic of the interrelated responses and shared variables. The accuracy and effectiveness of MUATC are demonstrated with three examples.