Sequential probabilistic analytical target cascading method for hierarchical multilevel optimization under uncertainty

Probabilistic Analytical Target Cascading (PATC) is a methodology for hierarchical multilevel optimization under uncertainty. In PATC, the statisticalmoments of the stochastic interrelated responses are matched between neighbouring levels to ensure the consistency of the solution. When the interrelated response is far from normal distribution, high order moments may need to be matched in the PATC formulation, which results in great computational difficulty. To overcome this disadvantage, a sequential PATC (SPATC) approach is proposed in this paper. SPATC firstly decouples the original probabilistic design problem into deterministic optimization problem and probabilistic analysis, and then hierarchically decomposes them into subproblems. The statistical information matching between neighbouring levels in the existing PATC framework is eliminated in SPATC. All in one probabilistic analysis and hierarchical probabilistic analysis are established to calculate the probabilistic characteristic of the interrelated responses and linking variables. Three examples are used to demonstrate the effectiveness and efficiency of the proposed SPATC approach. The results show that the SPATC approach is more efficient and accurate than PATC, especially for the multilevel design problem with non-normal interrelated responses.