Design of explicit models for estimating efficiency characteristics of microbial fuel cells
Introduction
Recent years have seen the use of microfluidic microbial fuel cells (MFCs) as the most advanced and competent technology for the generation of electricity from wastes and renewable mass. Deployment of this technology consequently results in economic as well as environmental benefits. Unique features of MFC, its mild operating conditions and ability of generating the power from indigenous sources have increased its usage across the globe. However, its full scale application has not gained much prominence. The reason behind this is due to the low power generation, low energy efficiency and the high material costs involved [1]. As fuel cells are still capital intensive, research to enhance the efficiency of MFCs is in demand.
Research on understanding the mechanism behind the working of MFCs mainly took a trial-and-error experimental approach unveiling the significant input parameters. Two vital features of MFC such as power generation and power density were studied [2]. Input parameters used in the study were microbial activity and anode media. In the similar aspect, the effect of two vital input parameters, namely temperature and hydraulic retention, on the power generation of a two-chambered MFC was studied [3]. Studies reveal that at the high substrate concentrations, the maximum power density was achieved.
Though the studies conducted based on a trial-and-error experimental approach can investigate the vital parameters that influence the power output features of MFC, it is not a reliable option due to limitation of the rising materials costs and time involved in implementing the experiments. In this perspective, researches on micro-sized MFCs such as microfluidic based MFCs were given emphasis, which have an additional advantage when compared to macro-scale MFCs. For example, Choi et al. [4] developed Micro-Electro-Mechanical Systems-based MFC that produces a high power density with an improvement of efficiency over 30 percent. Fan et al. [5] illustrated the study on single-chamber Proton exchange membrane-less MFCs by applying a J-Cloth layer on the water-facing side of air cathode. The experimental validation of his proposed design results in an enhanced Coulombic efficiency of MFCs. Ringeisen et al. [6] designed the miniature MFC with higher power densities of 24 and 10 mW/m2. Richter et al. [7] reported the use of gold electrodes for maximum generation of power density with increased columbic efficiency. Siu and Chiao et al. [8] illustrates work on micro-fabricated polydimethylsiloxane (PDMS) microbial fuel cell. This type of fuel cell is considered as a potential power source suitable for bio Micro-Electro-Mechanical Systems devices. Chen et al. [9] made use of photolithography technique to manufacture the miniature microbial fuel cell. However, these studies involve expensive fabrication methods and are difficult to implement when there is limited availability of materials and expertise knowledge on its design.
Therefore, researchers shifted their focus on developing mathematical models for optimizing the power output features of MFC. Picioreanu et al. [10] performed the derivation of the model for MFC with suspended biomass and added electron-transfer mediator. The simulations show the effect of different parameters (electrical resistance, mass transfer resistance, exchange current, coulombic yields and biomass, substrate and mediator concentrations) on the MFC characteristics. Pinto et al. [11] proposed the two-population model describing the competition of anodophilic and methanogenic microbial populations for a common substrate in a MFC. The coefficients of the model are estimated and validated based on the experiments. The further extension of his work [12] was to develop a multi-population model for MFC for an enhanced efficiency and power generation. Sousa et al. [13] conducted the state-of-the-art studies on mathematical modelling of polymer electrolyte fuel cells. The models ranging from empirical to analytical in two and three dimensions were reported. Fig. 1 shows that the two types of modelling procedures can be adapted in modelling of microbial fuel cells.
Formulated models were differential and algebraic equations which were derived based on the physical phenomenon undertaking in the MFCs. For instance, Oliveira et al. [14] discussed in details the number of biological and engineering aspects related to the improvement of MFC performance. Also, the effect of important parameters, such as pH, temperature, feed rate, shear stress and organic load on the performance characteristics of MFCs were discussed [15]. Esfandyari [16] performed mathematical modelling of two-chamber batch MFC. In his work, three models (Monod, Blackman, and Tessier) were used to describe specific growth rate of microbes. Experiments were also performed to validate the current and voltage output from the two-chamber batch MFC.
Although these models are cost-effective, less time consuming and provide good power output analysis, their formulation requires an expert knowledge on the understanding of working principle of the MFC system. Alternatively, the use of statistical methods such as the response surface methodology (RSM) and computational intelligence (CI) methods including general regression neural network, genetic programming (GP), multi-adapative regression splines (MARS) and support vector regression are becoming increasingly popular in formulation of functional expressions for chemical systems based on only the given data. Zhu et al. [17] proposed the false neighbours filtered based support vector regression to predict the short term natural gas demand. Shamshirband [18] also used support vector regression for wind turbine reaction torque prediction. Both of these studies reported the higher prediction accuracy of their proposed model when compared to the standardized support vector regression model. Wang et al. [19] used response surface methodology to generate a mathematical model for process optimization of aluminium holding furnace. Singh [20] used the same method for thermal and thermohydraulic performance evaluation of a double pass packed bed solar air heater. Response surface methodology is based on the assumption of a polynomial based expression with a specified degree. Hence, this may induce the uncertainty in model assumption and its optimum selection for an effective process modelling and optimization. To counter this, recently Taghavifar et al. [21] proposed a hybrid genetic algorithm and neural network approach to predict the diesel engine spray characteristics. The proposed approach performs better than those of response surface methodology because it does not require any pre-assumption of model structure. Madani et al. [22] optimized the power density of the MFC based on buffer concentration and pH level of catholyte using the RSM. It was found that the buffer concentration significantly affects the power density of MFC. Hosseinpour et al. [23] used input ionic strength in addition to buffer concentration and pH level to optimize the power density of MFC. Esfandyari et al. [24] explored the use of neuro-fuzzy modelling for estimating the power density and columbic efficiency of microbial fuel cell. This shows that the statistical regression methods has been applied to the model and optimizes the characteristics of MFC [25]. However, its framework is based on assumptions such as the normality and un-correlated residuals, which induce ambiguity in the prediction ability of the model [26]. On the other side, CI methods such as GP and MARS without statistical assumptions are good at capturing dynamics of a given complex system of unknown behaviour based on the set of multiple input variables [27]. After conducting a literature review, there is almost no existing research on CI formulated models to simulate the performance features of the micro-sized MFC system [28]. A recent survey on developments in modelling aspects of MFC by Ortiz-Martínez et al. [28] also recommended that an examination on MFC is yet to be explored by the concept of mathematical modelling.
To narrow the knowledge gaps in the literature, this paper aims to investigate the capability of CI methods such as GP and MARS in design of explicit models for the estimation of efficiency characteristics: power density (PD) and voltage output (V) of the micro-sized MFC based on the two sets of operating conditions 1) chemical oxygen demand concentration (CODC) and current density (CD) 2) Anolyte concentration flow rate (AC) and current density. The formulation of problem of modelling the power output features of microfluidic MFC is the research's novelty and is shown in Fig. 2. Performance of the models is evaluated against the actual data obtained from the experiment. The robustness in the best performing models is validated by performing simulation of the models over 8000 samples based on the normal distribution of the operating conditions. 2-D and 3-D surface analysis will be conducted on the models to reveal the main and interactive effect of operating conditions on the two efficiency features of MFCs. Further, the standard optimization of the best models will be performed that shall result in optimum operating conditions responsible for improving the efficiency of MFCs.
The paper is structured as follows. Section 2 discusses the experimental set-up details of the MFC and provides description of the scientific problem. Section 3 discusses the two CI methods: GP and MARS. Section 4 discusses the settings of parameters of the CI methods. Section 5 computes the performance of the developed models against the experimental data based on statistical metrics. Section 6 illustrates the 2-D, 3-D and simulation analysis on the best performing models. Finally, Section 7 discusses the conclusions along with contributions arising from the present work.
Section snippets
Details of experiments on micro sized MFC
The experimental study is referred from the work discussed in Ye D et al. [29]. The data obtained from the experiment comprise two sets of operating conditions: 1) chemical oxygen demand concentration and current density 2) Anolyte concentration flow rate and current density, whose effect on two efficiency features of MFC 1) Power density and 2) Voltage output is measured. The power density and voltage are measured independently based on two sets of operating conditions 1) chemical oxygen
Genetic programming
Evolutionary approach of GP which works on the principle of “Survival of the fittest” is proposed to design the models for estimation of efficiency features of MFCs [30]. The mechanism is similar to that of genetic algorithm (GA), except the fact that GP evolves model structures but GA evolves solutions in crisp form [31]. The steps needed for the implementation of GP (Fig. 5) are outlined as follows.
- 1
The first step involves the definition of functional and terminal set. Functional includes the
Choosing parameter settings for implementation of computational intelligence methods
A trial-and-error process is adopted to adjust the parameter settings of GP. The settings such as the population size, the number of generations and the probabilities for crossover, mutation and reproduction are varied from their minimum to their maximum values (Table 2). The maximum value is chosen based on the minimum RMSE value of the models on the training and testing data, which does not undergo any change in the last 20 consecutive generations. Most of the combinations are designed (
Evaluation of models for efficiency features of MFCs
The models were formulated using the two CI methods GP and MARS based on the two sets of operating conditions 1) chemical oxygen demand concentration and current density 2) Anolyte concentration flow rate and current density. Three statistical metrics (the square of the correlation coefficient (R2), the mean absolute percentage error (MAPE) and the RMSE) are used to assess the models. Their formulas (Equations (A5), (A6), (A7)) are given in the appendix.
It was found that both the models GP and
2-D and 3-D surface analysis of the GP models
Section 5 concludes that the GP models have outperformed the MARS models in estimation of efficiency characteristics of the MFC. Therefore, the GP models are the best performing ones. In this section, the relationships between the efficiency characteristics (power density and voltage output) and operating conditions is extracted from the GP models using the notion of sensitivity and parametric analysis. Sensitivity analysis (SA) determines the percentage impact of individual operating
Conclusions
This study presents a contribution in design of explicit and generalized models for the accurate estimation of two efficiency characteristics (power density and voltage) of MFC. The modelling of MFCs is considered complex and therefore the present work proposed two CI methods GP and MARS in design of explicit models for power density and voltage of MFCs. The statistical analysis found that the GP models outperformed the MARS. The robustness in the GP models was validated by performing the
Acknowledgments
The study was supported by funding from Nanyang Technological University, Singapore, ref. M060030008.
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