Multilevel Optimization Considering Variability in Design Variables of Multidisciplinary System

Abstract

The objective of this paper is to investigate the reliability-based design optimization (RBDO) for a multidisciplinary system (RBMDO). RBMDO has drawn attention recently because a system level analysis is usually needed in realistic engineering application and, in most cases, variability exists in design variables. However, the forward and feedback calculations among each sub-system and the reliability analysis within an optimization loop are very expensive, thus the RBMDO problem is computationally prohibited and has become one of the research topics in these days. Many researchers have focused on avoiding the system level analysis without sacrificing the accuracy. For this, Analytical Target Cascading (ATC) is used here to decompose the multidisciplinary system. As a result, RBMDO becomes several individual sub-system optimizations thus no system level analysis is required. ATC is a multi-level optimization framework and possesses the characteristic of distributed system. One of the key characteristics of ATC is the original problem is decomposed hierarchically at multiple levels, while the inconsistency among subsystems at each level is coordinated at one level above. ATC has been proven to be a robust approach for multidisciplinary optimization (MDO) problem. To accelerate the reliability-based optimization in each sub-system, the methodology of Sequential Optimization and Reliability Assessment (SORA) is utilized here. SORA is a single loop process wherein the RBO problem, a double-loop process in nature, is converted into a series of deterministic optimizations and reliability analyses, and therefore, the computational cost is reduced. Note that in the proposed ATC approach, the linking variables among each sub-system are the reliability-based optimal design variables. The formulation of the proposed method is then remains same as the ATC although the problem now is more complicated (probabilistic vs. deterministic). A numerical example is given to demonstrate the proposed process. Results are compared to the Fully Integrated Optimization (FIO) or All-In-One (AIO) method to verify the accuracy of the proposed process. Efficiency is also examined by comparing the method of Probabilistic Analytical Target Cascading (PATC). Results shown here indicate the proposed method can provide an optimal design in a very efficient way for a multidisciplinary system that usually involves extreme high computation costs.