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

Highlights

• 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.

Abstract

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.

Introduction

The usage of conventional batteries is dying because of the disadvantages it possesses such as self-discharge and negative environmental implications [1]. This has led to the emergence and origin of fuel cell, which have now become a potential alternative source of energy in the arising scenarios of shortage of natural and energy resources and environmental degradation over the years in emerging economies [2]. Among the categories of the fuel cells, air-breathing micro-direct methanol fuel cell (μDMFC) has received significant attention because of its higher energy density properties, easy storage of the fuel, quick refueling and environmental friendly. Working mechanism of the μDMFC is shown in Fig. 1, where the electrons flow the outside circuit towards cathode and protons move towards cathode via a proton exchange membrane. The chemical reaction of the methanol in the presence of protons and electrons triggers and generates the water. There is a good amount of progress [2], [3], [4] made in improving the performance of the fuel cell, however still some gaps exists which limits its wider scale commercial applications. Further, with an advent of capital intensive fuel cells and its complex operating mechanism, the motivation for conducting research in improving its energy and working performance is strengthened.

Past studies mainly focus on the experimental procedures in finding the operating conditions (temperature, concentration of methanol in fuel cells, etc.) for improving the energy efficiency of μDMFC. Johan et al. [5] formulated the two phase steady-stage analytical model to study the effect of the operating conditions such as the fuel cell temperature, methanol feed concentration and the energy properties of DMFC. The results conclude that the anode backing layer is a vital design parameter for its efficient implementation. The effect of the five operating conditions such as fuel cell temperature, anode flow rate, cathode humidification, air flow rate and concentration of methanol on the performance efficiency of the DMFCs was studied by Ge and Liu [6]. It was found that among these five inputs, four (operating temperature, anode flow rate, air flow rate and concentration of methanol) were found to have the dominant effect on the power characteristics of the cell. Similarly, the study conducted by Jung et al. [7] investigates the influence of fuel cell operating temperature and methanol concentration on the cell performances. Findings reported that the performance of DMFCs improves with temperature and is optimized when the methanol concentration reaches a value of 2.5 M. Nakagawa and Xiu [8] conducted the quantitative analysis on liquid based DMFC by varying the cell operating temperature till 100 °C and the oxidant gas flow rate. It was found that both these inputs have impact on the power density with the performance becoming optimum at 80 °C and 900 °C respectively. In a study conducted by Surampidi et al. [9], the performance of the liquid based DMFC was found to be increased with cell operating temperature and became optimized at a methanol concentration of 2 M. K. A thorough analysis was conducted on the small scale DMFC to study the effect of three inputs (concentration of methanol in the cell, methanol solution flow rate and air pressure) on the voltage output under varying conditions of current [10]. It was found that the rate and direction of load influences the performances of DMFC the most. Several other experimental studies illustrating the investigation of output characteristics of DMFC is given in [11], [12], [13], [14].

With limitations of rising materials costs and time involved in implementing the experiments, a novel strategy of conducting the quantitative analysis needs a significant attention. In this context, mathematical modeling based on the soft computing methods (general regression neural network, genetic programming (GP) and support vector regression) seems a potential alternative for researchers in optimizing the power output features of μDMFC because of their ability to formulate the models based on only the limited information (input–output data). Thorough literature studies (Fig. 2) suggest that hardly any research that discusses the ability of these methods in simulating the performance features of DMFC was noticed. Recent survey studies on developments in modeling of DMFC by Taymaz et al. [15] also suggested that a more thorough investigation on working of fuel cells is yet to be explored by the notion of mathematical modeling.

Among these methods, GP is well known for formulating functional expressions and capturing dynamics of a given complex system. Past quantitative studies [16], [17], [18], [19], [20] involving the applications of GP in modeling of complex systems have reported that the performance of the GP models includes the search mechanism for solutions and convergence of the optimum solutions depends on the complexity measures used in its objective functions. Thus, it will be interesting to explore the performance of the complexity measures in the objective functions of GP in evolving the generalized models that accurately simulate the power characteristics of μDMFC.

Therefore, in this work, the experimental work followed by an evolutionary algorithm of GP is proposed to derive the functions for the two power characteristics (power density and open-circuit voltage) of air-breathing μDMFC with respect to the three inputs (methanol flow rate (1 ×), methanol concentration (2 ×) and the cell temperature (3 ×)). The procedure involving the experimentation planning and the evolutionary based modeling of the two power characteristics with respect to the three inputs is shown in Fig. 3. The two power characteristics of air-breathing μDMFC are evaluated first by performing the experiments and the data including the three-inputs is processed into the GP framework for the analysis. The two complexity measures such as the number of nodes and the number of basis functions based on the regression splines in objective function of structural risk minimization (SRM) [21] are used to investigate the generalization ability of the four GP power characteristics models. Cross-validation, statistical error metrics and hypothesis tests are used to validate the comparison of the performance of two complexity measures in SRM objective function of the formulated GP models. The two complexity measures in the objective function that gives the best performance of the GP models are plotted against the experimental data to determine its goodness of fit. The main (2-D), interactive effect (3-D) relationships and amount of influence of each input on the two power characteristics are determined based on the sensitivity and parametric approach on the formulated models. The information mined from the statistical analysis and the sensitivity and the parametric approach will be useful for the experts for the effective monitoring of the air-breathing μDMFC and thus resulting in higher energy performance.