Research On The Improved Probabilistic Analytical Target Cascading Method For UMDO Problem

For the Multidisciplinary Design Optimization (MDO) problems under uncertainty,researchers usually adopt the MDO methods to decompose the whole system into subsystemsand use the uncertainty based optimization method to solve the problem in each subsystem,which is called Uncertainty based Multidisciplinary Design Optimization (UMDO) method.Probabilistic Analytical Target Cascading (PATC) is a promising approach for designoptimization under uncertainty which inherits the features of the ATC and has strictconvergence property. However, in the original PATC approach, each subproblem is solved bythe worst case uncertainty analysis method with the nested double loop structure，and theoutputs are coordinated in a traditional way. Thus, the efficiency of uncertainty optimizationand system coordination for PATC is low.To overcome this disadvantage, we have studied the PATC method intensively andimproved the uncertainty optimization procedure and the system coordination strategy.First, for the uncertainty optimization process, the Sequential Optimization andReliability Assessment based on the Hybrid Mean Value (HMV) method has been studied andemployed to solve the uncertainty analysis in PATC. The proposed method is calledHMV-PATC. The feasibility and efficiency of the HMV-PATC are proved by twomathematical examples.Second, for the coordination strategy, Lagrangian Duality Function (LDF) and QuadraticExterior Penalty Function (QEPF) strategy have been employed respectively to coordinate theresponse and link variables. One geometric programming problem is solved by LDF-HMV-PATC and QEPF-HMV-PATC respectively, the results show that QEPF strategy ismore efficient than LDF. The relationship between updating step and convergenceperformance in QEPF-HMV-PATC method has also been studied, which providesinformation on the selection of the updating step penalty parameter.At last, the proposed QEPF-HMV-PATC method is applied to solve an engineeringexample and obtains a good result.