Christopher Ha

Analytical Target Cascading for Multi-Mode Design Optimization: An Engine Case Study

Advances in design and information science have enabled the engineering community to look into changeable systems that work under multiple operating scenarios or modes. In this paper, a multidisciplinary design optimization approach for changeable systems is presented, with its focus on sharing a uniform part of system configuration across all the operating scenarios. Compared to the fully adaptive system approach, this approach enables reduction in the computational expense due to the repetitive mode-by-mode optimization, which becomes impractical as the number of modes increases. In the proposed approach, Analytical Target Cascading (ATC), a hierarchical optimization methodology, models the multi-mode design optimization in a two-level structure: the subsystem problems achieve the performance targets through optimizing local copies of the system configuration; and the system problem coordinates system configuration copies at multiple modes to obtain consistency. Local objectives are introduced to accommodate (unattainable) targets assigned locally for the individual systems, and a weight-updating scheme utilizing local objective information is proposed to balance among performance deviations at multiple modes. A case study on industrial engine simulation parameter identification demonstrates the effectiveness of the proposed approach.

Multilevel Optimization Considering Variability in Design Variables of Multidisciplinary System

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.

Subspace-Based Reliability Method (SBRM) for Sequential Improvement of Probability Estimation

Reliability is a critical design criterion in a product development process and it is generally used as a product quality measurement. In a virtual product development environment, reliability can be estimated by conducting a large number of simulations such as Monte Carlo simulations. However, this approach is often impractical to be implemented in an industrial application due to high computational cost. To alleviate the prohibitive cost, point estimation methods, such as FirstOrder Reliability Method (FORM) and Second-Order Reliability Method (SORM), are often used. Such methods approximate a limit state boundary with the fixed order of Taylor series expansion (i.e., linear for FORM). The accuracy of the reliability estimation from the methods depends on the fitness of the simplified limit state boundary to the actual one. Using the point estimation method, a designer is often unable to determine the error or confidence level associated with the analysis result, especially for a complex and unfamiliar problem. In order to address the issues, the Subspace-Based Reliability Method (SBRM) is proposed in this paper. In SBRM, reliability is estimated by considering the failure boundary, as well as the Most Probable Point (MPP). The Moving Least Square (MLS) method is used to avoid the pre-fixed order of failure boundary approximation. A subspace centering MPP is defined with a desired level of accuracy in the assessment result. Within the subspace, the actual integration of failure probability is performed with the approximated boundary. For the efficiency of the integration with a multi-dimensional problem, the Dimension Reduction (DR) method is utilized. By sequentially adding more simulations for the approximation, a convergence history of reliability assessments is obtained and used to check the credibility of the result. The applicability of the proposed method is demonstrated with analytical examples.