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

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% H2, 25% H2O, and 14% CO.

[1]  Suresh V. Garimella,et al.  Optimization Under Uncertainty Applied to Heat Sink Design , 2013 .

[2]  P. Kazempoor,et al.  Novel electrical energy storage system based on reversible solid oxide cells: System design and operating conditions , 2015 .

[3]  Iman Gholaminezhad,et al.  Multi-scale multi-objective optimization and uncertainty analysis of methane-fed solid oxide fuel cells using Monte Carlo simulations , 2017 .

[4]  S. Barnett,et al.  Modeling and experimental performance of an intermediate temperature reversible solid oxide cell for high-efficiency, distributed-scale electrical energy storage , 2015 .

[5]  Ramin Roshandel,et al.  Multi objective optimization of solid oxide fuel cell stacks considering parameter effects: Fuel utilization and hydrogen cost , 2013 .

[6]  Reuven Y. Rubinstein,et al.  Simulation and the Monte Carlo Method , 1981 .

[7]  Robert J. Braun,et al.  A thermodynamic approach for selecting operating conditions in the design of reversible solid oxide cell energy systems , 2016 .

[8]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[9]  Ali Jamali,et al.  A multi-objective differential evolution approach based on ε-elimination uniform-diversity for mechanism design , 2015 .

[10]  Hong Liu,et al.  Analysis and optimization of current collecting systems in PEM fuel cells , 2012 .

[11]  Ajay K. Ray,et al.  Multi-objective optimization in solid oxide fuel cell for oxidative coupling of methane , 2010 .

[12]  Robert J. Braun,et al.  Model validation and performance analysis of regenerative solid oxide cells for energy storage applications: Reversible operation , 2014 .

[13]  Christopher Graves,et al.  Production of Synthetic Fuels by Co-Electrolysis of Steam and Carbon Dioxide , 2009 .

[14]  Gevork B. Gharehpetian,et al.  Nonlinear multivariable modeling of solid oxide fuel cells using core vector regression , 2011 .

[15]  Ali Nazari,et al.  Prediction performance of PEM fuel cells by gene expression programming , 2012 .

[16]  Suresh V. Garimella,et al.  Manifold microchannel heat sink design using optimization under uncertainty , 2014 .

[17]  Amornchai Arpornwichanop,et al.  Neural network hybrid model of a direct internal reforming solid oxide fuel cell , 2012 .

[18]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[19]  Nader Nariman-zadeh,et al.  Modeling, parametric analysis and optimization of an anode-supported planar solid oxide fuel cell , 2015 .

[20]  H. Taghavifar Towards multiobjective Nelder-Mead optimization of a HSDI diesel engine: Application of Latin hypercube design-explorer with SVM modeling approach , 2017 .

[21]  Ali Jamali,et al.  Modelling and prediction of complex non-linear processes by using Pareto multi-objective genetic programming , 2016, Int. J. Syst. Sci..

[22]  Ali Jamali,et al.  Uncertainty quantification and robust modeling of selective laser melting process using stochastic multi-objective approach , 2016 .

[23]  Werner Lehnert,et al.  Parameter extraction and uncertainty analysis of a proton exchange membrane fuel cell system based on Monte Carlo simulation , 2017 .

[24]  Jian Li,et al.  Control-oriented modeling analysis and optimization of planar solid oxide fuel cell system , 2016 .

[25]  Uday Kumar Chakraborty,et al.  Genetic programming model of solid oxide fuel cell stack: first results , 2008, Int. J. Inf. Commun. Technol..

[26]  Xingjian Xue,et al.  Mathematical Modeling Analysis of Regenerative Solid Oxide Fuel Cells in Switching Mode Conditions , 2010 .

[27]  Dennis Y.C. Leung,et al.  Theoretical analysis of reversible solid oxide fuel cell based on proton-conducting electrolyte , 2008 .

[28]  S. Ebbesen,et al.  Co-Electrolysis of Steam and Carbon Dioxide in Solid Oxide Cells , 2012 .

[29]  Peiwen Li,et al.  Effects of geometry/dimensions of gas flow channels and operating conditions on high-temperature PEM fuel cells , 2015 .

[30]  Uday K. Chakraborty,et al.  Static and dynamic modeling of solid oxide fuel cell using genetic programming , 2009 .

[31]  Mohsen Hamedi,et al.  Modeling and Optimization of Anode‐Supported Solid Oxide Fuel Cells on Cell Parameters via Artificial Neural Network and Genetic Algorithm , 2012 .