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Optimization of a Stirling Engine by Variable-Step Simplified Conjugate-Gradient Method and Neural Network Training Algorithm

Author

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  • Chin-Hsiang Cheng

    (Department of Aeronautics and Astronautics, National Cheng Kung University, No.1, University Road, Tainan 70101, Taiwan)

  • Yu-Ting Lin

    (Department of Aeronautics and Astronautics, National Cheng Kung University, No.1, University Road, Tainan 70101, Taiwan)

Abstract

The present study develops a novel optimization method for designing a Stirling engine by combining a variable-step simplified conjugate gradient method (VSCGM) and a neural network training algorithm. As compared with existing gradient-based methods, like the conjugate gradient method (CGM) and simplified conjugate gradient method (SCGM), the VSCGM method is a further modified version presented in this study which allows the convergence speed to be greatly accelerated while the form of the objective function can still be defined flexibly. Through the automatic adjustment of the variable step size, the optimal design is reached more efficiently and accurately. Therefore, the VSCGM appears to be a potential and alternative tool in a variety of engineering applications. In this study, optimization of a low-temperature-differential gamma-type Stirling engine was attempted as a test case. The optimizer was trained by the neural network algorithm based on the training data provided from three-dimensional computational fluid dynamic (CFD) computation. The optimal design of the influential parameters of the Stirling engine is yielded efficiently. Results show that the indicated work and thermal efficiency are increased with the present approach by 102.93% and 5.24%, respectively. Robustness of the VSCGM is tested by giving different sets of initial guesses.

Suggested Citation

  • Chin-Hsiang Cheng & Yu-Ting Lin, 2020. "Optimization of a Stirling Engine by Variable-Step Simplified Conjugate-Gradient Method and Neural Network Training Algorithm," Energies, MDPI, vol. 13(19), pages 1-18, October.
    • Handle: RePEc:gam:jeners:v:13:y:2020:i:19:p:5164-:d:423499
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    References listed on IDEAS

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    1. Cheng, Chin-Hsiang & Huang, Yu-Xian & King, Shun-Chih & Lee, Chun-I & Leu, Chih-Hsing, 2014. "CFD (computational fluid dynamics)-based optimal design of a micro-reformer by integrating computational a fluid dynamics code using a simplified conjugate-gradient method," Energy, Elsevier, vol. 70(C), pages 355-365.
    2. Kongtragool, Bancha & Wongwises, Somchai, 2003. "A review of solar-powered Stirling engines and low temperature differential Stirling engines," Renewable and Sustainable Energy Reviews, Elsevier, vol. 7(2), pages 131-154, April.
    3. Huang, Yu-Xian & Wang, Xiao-Dong & Cheng, Chin-Hsiang & Lin, David Ta-Wei, 2013. "Geometry optimization of thermoelectric coolers using simplified conjugate-gradient method," Energy, Elsevier, vol. 59(C), pages 689-697.
    4. Jörg Fliege & Benar Fux Svaiter, 2000. "Steepest descent methods for multicriteria optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(3), pages 479-494, August.
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    1. Chin-Hsiang Cheng & Duc-Thuan Phung, 2021. "Numerical Optimization of the β-Type Stirling Engine Performance Using the Variable-Step Simplified Conjugate Gradient Method," Energies, MDPI, vol. 14(23), pages 1-14, November.
    2. Chin-Hsiang Cheng & Yu-Ting Lin, 2022. "Computational Optimization of Free-Piston Stirling Engine by Variable-Step Simplified Conjugate Gradient Method with Compatible Strategies," Energies, MDPI, vol. 15(10), pages 1-16, May.

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