10.1007/s40095-018-0269-5

Multi-objective modeling, uncertainty analysis, and optimization of reversible solid oxide cells

  1. Department of Materials Science and Engineering, School of Engineering, Shiraz University, Shiraz, IR
  2. Department of Materials and Life Chemistry, Kanagawa University, Yokohama, Kanagawa, 221-8686, JP
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Published in Issue 2018-03-19

How to Cite

Salehi, Z., & Gholaminezhad, I. (2018). Multi-objective modeling, uncertainty analysis, and optimization of reversible solid oxide cells. International Journal of Energy and Environmental Engineering, 9(3 (September 2018). https://doi.org/10.1007/s40095-018-0269-5

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Abstract

Abstract Reversible solid oxide cells can provide efficient and cost-effective scheme for electrical-energy storage applications. However, this technology faces many challenges from material development to system-level operational parameters , which should be tackle for practical purposes. Accordingly, this study focuses on developing novel robust artificial intelligence-based black-box models to optimize operational variables of the system. A genetic-programming algorithm is used for Pareto modeling of reversible solid oxide cells in a multi-objective fashion based on experimental input–output data. The robustness of the obtained optimal model evaluated using Monte Carlo simulations technique. An optimization study adopted to optimize the operating parameters, such as temperature and fuel composition using a differential evolution algorithm. The objective functions that have been considered for Pareto multi-objective modeling process are training error and model complexity. In addition, the discrepancy between maximum and minimum output voltage in the whole operation of the system is chosen as the optimization process objective function. The robustness of the optimal trade-off model is shown in terms of statistical indices for varied uncertainty levels from 1 to 10%. The optimized operational condition based on the suggested model reveals optimal intermediate temperature of 762 °C and fuel mixture of about 29% H 2 , 25% H 2 O, and 14% CO.

Keywords

  • Reversible solid oxide cell,
  • Multi-objective,
  • Genetic programming,
  • Pareto,
  • Monte Carlo simulations

References

  1. Kazempoor and Braun (2014) Model validation and performance analysis of regenerative solid oxide cells for energy storage applications: reversible operation (pp. 5955-5971) https://doi.org/10.1016/j.ijhydene.2014.01.186
  2. Wendel et al. (2015) Novel electrical energy storage system based on reversible solid oxide cells: system design and operating conditions (pp. 133-144) https://doi.org/10.1016/j.jpowsour.2014.10.205
  3. Wendel et al. (2015) Modeling and experimental performance of an intermediate temperature reversible solid oxide cell for high-efficiency, distributed-scale electrical energy storage (pp. 329-342) https://doi.org/10.1016/j.jpowsour.2015.02.113
  4. Wendel et al. (2016) A thermodynamic approach for selecting operating conditions in the design of reversible solid oxide cell energy systems (pp. 93-104) https://doi.org/10.1016/j.jpowsour.2015.09.093
  5. Jin and Xue (2010) Mathematical modeling analysis of regenerative solid oxide fuel cells in switching mode conditions (pp. 6652-6658) https://doi.org/10.1016/j.jpowsour.2010.04.018
  6. Ni et al. (2008) Theoretical analysis of reversible solid oxide fuel cell based on proton-conducting electrolyte (pp. 369-375) https://doi.org/10.1016/j.jpowsour.2007.11.057
  7. Chaichana et al. (2012) Neural network hybrid model of a direct internal reforming solid oxide fuel cell (pp. 2498-2508) https://doi.org/10.1016/j.ijhydene.2011.10.051
  8. Cheng et al. (2016) Control-oriented modeling analysis and optimization of planar solid oxide fuel cell system (pp. 22285-22304) https://doi.org/10.1016/j.ijhydene.2016.08.213
  9. Mohammadi et al. (2011) Nonlinear multivariable modeling of solid oxide fuel cells using core vector regression (pp. 12538-12548) https://doi.org/10.1016/j.ijhydene.2011.06.108
  10. Li et al. (2012) Analysis and optimization of current collecting systems in PEM fuel cells https://doi.org/10.1186/2251-6832-3-2
  11. Liu et al. (2015) Effects of geometry/dimensions of gas flow channels and operating conditions on high-temperature PEM fuel cells 6(1) (pp. 75-89) https://doi.org/10.1007/s40095-014-0153-x
  12. Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press. ISBN 0-262-11170-5 (1992)
  13. Chakraborty (2009) Static and dynamic modeling of solid oxide fuel cell using genetic programming (pp. 740-751) https://doi.org/10.1016/j.energy.2009.02.012
  14. Chakraborty (2008) Genetic programming model of solid oxide fuel cell stack: first results 1(3/4) (pp. 453-461)
  15. Nazari (2012) Prediction performance of PEM fuel cells by gene expression programming (pp. 18972-18980) https://doi.org/10.1016/j.ijhydene.2012.08.101
  16. Bozorgmehri and Hamedi (2012) Modeling and optimization of anode-supported solid oxide fuel cells oncell parameters via artificial neural network and genetic algorithm 12(1) (pp. 11-23) https://doi.org/10.1002/fuce.201100140
  17. Forough (2013) A., Roshandel, R.: Multi-objective optimization of solid oxide fuel cell stacks considering parameter effects: fuel utilization and hydrogen cost 5(5) https://doi.org/10.1063/1.4822253
  18. Quddus et al. (2010) Multi-objective optimization in solid oxide fuel cell for oxidative coupling of methane (pp. 639-648) https://doi.org/10.1016/j.cej.2010.09.041
  19. Borji, M., Atashkari, K., Nariman-zadeh, N., Masoumpour, M.: Modeling, parametric analysis and optimization of an anode-supported planar solid oxide fuel cell. Proc IMechE Part C: J Mech. Eng. Sci. 1–16 (2015)
  20. Gholaminezhad et al. (2017) Multi-scale multi-objective optimization and uncertainty analysis of methane-fed solid oxide fuel cells using Monte Carlo simulations (pp. 175-187) https://doi.org/10.1016/j.enconman.2017.10.011
  21. Rubinstein (1981) Wiley https://doi.org/10.1002/9780470316511
  22. Xu et al. (2017) Parameter extraction and uncertainty analysis of a proton exchange membrane fuel cell system based on Monte Carlo simulation (pp. 2309-2326) https://doi.org/10.1016/j.ijhydene.2016.11.151
  23. Taghavifar (2017) Towards multiobjective Nelder-Mead optimization of a HSDI diesel engine: application of Latin hypercube design-explorer with SVM modeling approach (pp. 150-161) https://doi.org/10.1016/j.enconman.2017.04.008
  24. Jamali, A., Khaleghi, E., Gholaminezhad, I., Nariman-zadeh, N.: Modelling and prediction of complex non-linear processes by using Pareto multi-objective genetic programming. Int. J. Syst. Sci.
  25. https://doi.org/10.1080/00207721.2014.945983
  26. Gholaminezhad, I., Assimi, H., Jamali A., Vajari, D.A.: Uncertainty quantification and robust modeling of selective laser melting process using stochastic multi-objective approach. Int. J. Adv. Manuf. Technol.
  27. https://doi.org/10.1007/s00170-015-8238-0
  28. Ebbesen et al. (2012) Co-electrolysis of steam and carbon dioxide in solid oxide cells 159(8) (pp. F482-F489) https://doi.org/10.1149/2.076208jes
  29. Ebbesen et al. (2009) Production of synthetic 24 by co-electrolysis of steam and carbon dioxide 6(6) (pp. 646-660) https://doi.org/10.1080/15435070903372577
  30. Storn and Price (1997) Differential evolution: a simple and efficient heuristic scheme for global optimization over continuous spaces (pp. 341-359) https://doi.org/10.1023/A:1008202821328
  31. Sarangi et al. (2014) Manifold microchannel heat sink design using optimization under uncertainty (pp. 92-105) https://doi.org/10.1016/j.ijheatmasstransfer.2013.09.067
  32. Bodla et al. (2013) Optimization under uncertainty applied to heat sink design 135(1) https://doi.org/10.1115/1.4007669
  33. Gholaminezhad, I., Jamali, A.: A multi-objective differential evolution approach based on ε-elimination uniform-diversity for mechanism design. Struct. Multidisc. Optim.
  34. https://doi.org/10.1007/s00158-015-1275-3