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Research Papers

Robust Tolerance Optimization for Internal Combustion Engines Under Parameter and Model Uncertainties Considering Metamodeling Uncertainty From Gaussian Processes

[+] Author and Article Information
Yanjun Zhang

Joint Institute Shanghai Jiao Tong University,
University of Michigan—Shanghai
Jiao Tong University,
Shanghai 200240, China

Mian Li

Joint Institute Shanghai Jiao Tong University,
University of Michigan—Shanghai
Jiao Tong University,
Shanghai 200240, China
e-mail: mianli@sjtu.edu.cn

1Corresponding author.

Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received January 22, 2018; final manuscript received June 12, 2018; published online August 6, 2018. Assoc. Editor: Kristina Wärmefjord.

J. Comput. Inf. Sci. Eng 18(4), 041011 (Aug 06, 2018) (13 pages) Paper No: JCISE-18-1025; doi: 10.1115/1.4040608 History: Received January 22, 2018; Revised June 12, 2018

As the core component of an automobile, the internal combustion engine (ICE) nowadays is still a typical complex engineering system. Tolerance design for ICEs is of great importance since small changes in the dimensions and clearances of ICE components may result in large variations on the performance and cost of manufactured products. In addition, uncertainty in tolerance design has great impact on the engine performance. Although tolerance optimization for the key components of ICEs has been discussed, few of them take uncertainty into consideration. In this regard, robust optimization (RO) for the tolerances of ICEs remains a critical issue. In this work, a novel RO approach is proposed to deal with the tolerance optimization problem for ICEs under parameter and model uncertainties, even considering metamodeling uncertainty from Gaussian processes (GP). A typical parameter uncertainty in ICEs exists in the rotation speed which can vary randomly due to the inherent randomness. AVL EXCITE software is used to build the simulation models of ICE components, which brings in model uncertainty. GP models are used as the analysis model in order to combine the corresponding simulation and experimental data together, which introduces metamodeling uncertainty. The proposed RO approach provides a general and systematic procedure for determining robust optimal tolerances and has competitive advantages over traditional experience-based tolerance design. In addition to the ICE example, a numerical example is utilized to demonstrate the applicability and effectiveness of the proposed approach.

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Figures

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Fig. 2

Flow chart of the proposed RO approach

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Fig. 3

Gaussian process prediction for the real output with six samples

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Fig. 4

Deterministic and robust objective functions fd, fWM, fWMG: fWMG considering parameter, model, and metamodeling uncertainties W, M, G, while fWM considering W, M ignoring G: (a) objective functions and (b) compound means and STDs

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Fig. 5

Robust objective function fWM-fun considering parameter and model uncertainties W, M using real models

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Fig. 6

Gaussian process models for the real output with six samples and nine samples

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Fig. 7

Design space of simulation and experimental samples

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