Framework based on number of basis functions complexity measure in investigation of the power characteristics of direct methanol fuel cell

• An evolutionary algorithm of GP having two complexity measures is proposed that can assist in selecting optimum operating conditions of air-breathing DMFC.
• 2-D and 3-D plots for power characteristics of air-breathing DMFC are plotted.
• Based on the model analysis, it was found that the methanol concentration influences the power characteristics the most followed by cell temperature and methanol flow rate.

A potential alternative to cell batteries is the air-breathing micro direct methanol fuel cell (μDMFC) because it is environmental friendly, charging-free, possesses high energy density properties and provides easy storage of the fuel. The effective functioning of the complex air-breathing μDMFC system exhibits higher dependence on its operating conditions and the parameters. The main challenge for the experts is to determine its optimum operating conditions. In this context, the mathematical modeling approach based on evolutionary framework of genetic programming (GP) can be applied. However, its successful implementation depends on the complexity chosen in its structural risk minimization (SRM) objective function. In this work, the two measures of complexity based on the standardized number of nodes and the number of basis functions in the splines is chosen. Comparison between the two GP approaches based on these two complexity measures is evaluated on the experimental procedure performed on the μDMFC. The power characteristics considered in this study are power density and open-circuit voltage and the three inputs considered are methanol flow rate, methanol concentration and the cell temperature. The statistical analysis based on cross-validation, error metrics and hypothesis tests is performed to choose the best GP based power characteristics models. Further, 2-D plots for measuring the individual effects and the 3-D plots for the interaction effects of the inputs on the power characteristics is plotted based on the parametric approach. It was found that the methanol concentration influences the power characteristics (power density and OCV) of μDMFC the most followed by cell temperature and methanol flow rate.