MICROBIAL FUEL CELLS PERFORMANCE EVALUATION THROUGH THE APPLICATION OF FUZZY LOGIC

Objective: This work aimed to employ fuzzy logic combined with the design of experiments technique to statistically evaluate how the microbial fuel cells operating parameters influence their performance. Theoretical Framework: Microbial fuel cells (MFC) are a technology of interest in the current scenario as they allow simultaneously promoting the biotreatment of waste and the bio generation of electrical energy. Methodology: Through a bibliographical search based on publications on Google Scholar platform over the last 10 years, it was noticed that anode area, external electrical resistance and reactor volume are the most reported input parameters in MFC research and current density and power density are the output parameters most frequently portrayed in these studies, which is why these variables were selected for statistical investigation. Results and Discussion: The results showed that, for both outputs studied, reactor volume and anode area showed a positive effect, while the external electrical resistance showed a negative effect. It was also possible to develop mathematical models that indicated the relationship between the input and output variables studied, with statistical significance for power density model (R 2 = 86%). Originality: Applying computational simulations and subsequent design of experiments to obtain results in accordance with those obtained experimentally in the laboratory.

Originalidad: Se pudo observar la aplicación de simulaciones computacionales a través de Lógica Difusa y posterior planificación experimental para obtener resultados acordes a los obtenidos experimentalmente en el laboratorio.3 biotreatment of waste and the biogeneration of electrical energy.Furthermore, CEM are capable of reducing the operational cost of effluent treatment compared to conventional systems, which proves their high potential as a sustainable alternative for wastewater treatment (Gude, 2015;Hidalgo et al., 2014;Salazar et al., 2023;Grejo & Lunkes, 2022).

Palabras
In general, microbial energy cells can be understood as electrochemical devices in which the chemical energy contained in organic compounds is converted into electrical energy through the metabolism of microorganisms that grow in anaerobic conditions on electrodes (Hidalgo et al., 2014).The general structure of a CEM is made up of two compartments: the first is anaerobic and houses an anode, and the second is aerobic and contains a cathode; These electrodes are separated internally by a barrier that prevents the diffusion of oxygen gas (O2), but are connected externally by an electrical circuit (Rahimnejad et al., 2015).
The operating mechanism of EMFs is based on the process of cellular respiration, so that microorganisms that grow in the anode compartment of these devices oxidize substrates and generate electrons, which are picked up by electron mediators, transported to the outside of the cell and taken directly to the anode. .Then, the electrons are transferred to the cathode through the external electrical circuitwhich creates a potential difference in the system, which can be recovered in the form of electrical energy.Finally, the electrons are generally transferred to the O2 present in the cathode chamber, which is reduced (Hidalgo et al., 2014;Fung, 2016).
For this process to be carried out, it is necessary that the oxidation of the organic material takes place in the absence of electron acceptors, since the anode must be the final electron acceptor in this stage, as this is the only way there is a flow of electronswhich is why it is necessary These devices contain a barrier that prevents the diffusion of O2 from the cathode compartment, which is aerobic, to the anode, which must remain in anaerobic conditions (Logan et al., 2008).
Figure 1 presents the general structure of a CEM.

Figure 1
General structure of a microbial energy cell Analyzing the functioning mechanism of EMFs, it is clear that these are complex systems, in which biological, chemical and physical processes are involved (Oliveira et al., 2013).Thus, in the context in which this technology is still in the development phase, it is clear that studies that seek to acquire and update knowledge on this topic are relevant.(Trapero et al., 2017;Rachinski, 2010).In circumstances like this, mathematical techniques, such as fuzzy logic, are able to help, as they can be used to optimize the operation and design of the system and identify the main factors involved in the process (Picioreanu et al., 2010;Gadkari;Gu;Sadhukhan, 2018).
Fuzzy logic was developed by Zadeh (1965) as an alternative to the technological resources available at the time, which were incapable of dealing with situations that included circumstances that could not be processed through Boolean logic.Thus, the fuzzy approach is capable of combining multivalued logic, probabilistic theory, artificial intelligence and networks, while linking linguistics and human intelligence, as many concepts are better defined by words than by mathematics (Afonso, 2009) .It is also worth highlighting that fuzzy logic can be combined with the experiment planning technique¸ since this combination of tools makes it possible to observe the effects of variables involved in a monitored processas well as their interactions -, determine the best operating conditions and carry out simultaneous optimization of all factors involved in the system, requiring fewer experiments and greater speed and efficiency (Pereira;Pereira-Filho, 2018).

GOALS
The general objective of the work was to optimize the performance of CEM by identifying and investigating the main variables that interfere in their performance, applying computational and statistical tools to improve and predict their functioning, evaluate conditions that are difficult to test experimentally and reduce expenses in terms of resources and research time.As specific objectives, it was postulated to raise the main operating parameters and results in research with EMF reported in the literature through a bibliographical review, apply fuzzy logic to simulate EMF performance in different operational conditions and use the results obtained by the application of fuzzy logic for subsequent use of the experimental planning technique with the purpose of statistically evaluating the operating parameters that most significantly influence the performance of these devices.

METHODS
Initially, to carry out the bibliographic surveywhich aimed to observe the main operating parameters and the results achieved in research with EMF reported in the literature and their magnitudesthe methodology suggested by Galvão (2011) was adopted.To do this, with the research topic in hand, the bibliographic database that would be consulted was selected.
For this research, the Google Scholar platform was chosen as a source of information, based on the perception that this is a popular access tool and that it can be of great relevance when used paying attention to the conditions in which the information content available , authorship, year of publication, association with a credible scientific institution and bibliographic references.
Afterwards, the appropriate search terms were selected to develop the search strategy for the subject field.For this stage, the Health Sciences Descriptors (DeCS) were used, in which, for the research topic, the descriptor in English is "Bioelectric Energy Sources", the descriptor in Spanish is "Fuentes de Energía Bioeléctrica", the descriptor in Portuguese it is "Bioelectric Energy Sources" and there are 10 other alternative terms.Thus, the 13 termsdescriptors in English, Spanish and Portuguese and the alternative termswere selected for the search on the Google Scholar platform.the period and language of the publications that would be analyzed: materials in Portuguese, English or Spanish published between 2013 and 2023.
Finally, the materials were selected and organized for reading and information collection.In this phase, the bibliographic documentswhich totaled 327.publicationshad their abstracts evaluated, with the aim of determining whether they were in line with the purpose of the research project.Those deemed to be in line had their content analyzed and their information recorded.
Of the total number of works that made up the bibliographic database, 59 publications were included in the survey of the main operating parameters and results achieved in CEMthe rest of the works, according to the initial assessment, were not in accordance with the research guidelines, as it corresponded to works that did not specifically deal with CEM, corresponded to bibliographic reviews, presented methodologies that did not suit the objective of the study and similar issues.Table 1 presents the main parameters found in the survey, as well as information related to these data.Such information was used in the methodology for developing the computational simulations, with the parameters power density and electric current density being output variables (responses or results of experiments), and the other parameters being input (or operational) data.Based on the bibliographic search, the parameters, work levels and relevance functions (triangular) were determined for carrying out the study.Thus, the research was based on 3 input variables and 2 output variables.Then, these parameters and their working ranges were used to constitute a set of simulations using the InFuzzy software.To do this, initially, work variables were added and configured with their names, ranges and work functions and units.
Furthermore, the list of linguistic terms was defined for each of them according to the survey data and the programmer's knowledge, as shown in table 2. After configuring the input and output variables, the stage of defining the project rules took place.To this end, 2 rule blocks were created, with all inputs being connected to each of the rule blocks, and each output being connected to only one of the blocks.After their creation, each of the rule blocks was configured according to its inputs and output, considering literature and programmer knowledge.
Tables 3 and 4 present, respectively, the configurations used in the rule blocks relating to current density and power density at this stage of the project.
After building the rule blocks, computational simulations were carried out in the InFuzzy software based on literature data with the aim of obtaining computational responses for the power density and current density outputs and, subsequently, executing a factorial planning of the design type.rotational central composite (DCCR), in addition to defining the statistical significance of the work variables.

RESULTS AND DISCUSSION
From the computer simulations, which were applied to the DCCR planning carried out in electronic spreadsheets, coefficient, error, t-test and p-value values were obtained for each of the variables studied in the planning, which are presented in table 5. -745,81 ±0,18 4217,79 6E-08 -0,03 ±0,04 0,95 0,441 X1: device volume; X2: anode area; X3: external electrical resistance; X11: volume factor square; X22: square of the anode area factor; X33: square of the external electrical resistance factor; X12: interaction between the factors device volume and anode area; X13: interaction between device volume factors and external electrical resistance; X23: interaction between the factors anode area and external electrical resistance From the coefficient data from the set of computational simulations and the fractional factorial planning referring to current and power densities, presented in Table 5, it was verified that working conditions in which the input variables X1 and X2 (device volume and anode area) are at their highest levels positively influenced the production of these outputs.On the other hand, working conditions in which the variable external electrical resistance is at its highest level negatively impacted the outputs.Also analyzing the statistical information presented in table 5 for current density under a confidence level of 95% (α = 0.05), it is clear that all input variablesanode area, external electrical resistance and volume of the device -, as well as its squares and interactions, were statistically significant, since all of these factors had a p-value < α.Under the same analysis for power density, anode area and device volumeas well as their squares and interactionswere statistically significant.In the case of electrical resistanceas well as its interactions, except for its squarethere was no statistical significance.
Considering theoretical information regarding the relationship between power density generated in the EMF and the applied electrical resistance, it is observed that the observed presentation of non-statistical significance for the electrical resistance may be linked to the circumstance that there is no direct mathematical relationship between these variables .In other words, the fact that the maximum power of an EMF is obtained only when the external resistance of the electrical energy source is equal to the internal resistance of the device may have influenced the negative indication of fixed significance for the electrical resistance values used (González del Field, 2014).However, despite the non-statistical significance of external electrical resistance in relation to the power generated in the EMC obtained from the programmer's knowledge and literature, which indicate and confirm its influence, this variable was considered when obtaining models.
Table 6 presents quadratic model equations obtained that demonstrate the relationship between each of the input variables and the outputs studieda relevant result in the field of study of EMF, since these are complex systems that comprise mass and energy balances, in addition of biological, electrical and chemical processes, and that it is still necessary to better understand and predict the dynamic behaviors of such systems (Yao et al., 2016).y1 = 3908,52 + 66970,7x1 + 509,99x2 -968,37x3 + 1375,22x11 + 673,25x22 + 1329,48x33 + 745,81x12 -745,26x13 -745,81x23 Power Density y2 = 1758,87 + 400,57x1 + 368,70x2 -0,02x3 -74,5x11 -33,11x22 -230,80x33 -231, The data that make up the analysis of variance for the study of each of the output variables, used to evaluate the quality of adjustment of the models obtained, are presented in Tables 7 and 8.

Quadratic Equation Current Density
The R2 values obtained from spreadsheet calculations indicate that the models generated present promising results.This observation is reinforced when it is noted that the working ranges of the analyzed variables are quite wide, which would be difficult to replicate in practical conditions, since dealing with such extensive operating ranges complicates working conditions and makes it difficult to achieve very high adjustments.well defined.Furthermore, it is important to remember that the models can be even better adjusted in subsequent research, so that they can achieve even more favorable results.Considering the lack of adjustments presented in the models, it is clear that there was statistical significance for both.However, for the output variable power density, a Fcacl value of 4.91 was obtained, while the Ftab value was 3.79, indicating that the model for this output variable is significant.As for the current density output variable, the Fcalc value was lower than the Ftab and, therefore, its model was not significant.
The non-statistical significance indicated for the model generated regarding electric current may be linked to the fact that measuring current in EMFs is complex and quite susceptible to errors, since these devices, especially on laboratory scales, generate low electric current, which makes the selection and use of the method for evaluating and measuring this magnitude difficult.Furthermore, the leakage of electrical current in these devices is considerable and, consequently, the precision of measurementsof electrical voltage and currentis not that high, causing difficulty in generating and adjusting theoretical models in this area of study (Tavakolian et al. , 2020).Thus, considering that the model generated for electric current was not significant from a statistical point of view, comparisons of planned and simulated data were carried out only for the model referring to power density.Table 9 presents    Analysis of Table 9 and Figure 2 indicates that the data obtained by the model generated through experimental planning are very close to those obtained through fuzzy logic computer simulations.This analysis reinforces the good adjustment of the generated model, especially when considering, as already discussed, the wide working ranges of the variables under examination and the fact that the CEM system is complex and multivariable.For a better investigation of the results obtained, in addition to comparing the data obtained in the computational simulations and in the experimental planning, it is considered pertinent to compare the data generated by the mathematical model and those obtained in the laboratory tests, in order to observe the level of adequacy of these to real systems.Analyzing the dispersion of the data in question, it is possible to notice that the two highest values of average power density are distant from the others, which may indicate inconsistency regarding these.This fact may be related to measurement errors, human or execution, to the inherent variability of population elements, to miscalibration of measuring devices -especially when considering that, in the tests in question, very simple meters were used -or to -previously already discussedsensitivity in the electrical current and density of EMFs, which hinders the precision of these measurements and the adequacy of theoretical models to real systems (Tavakolian et al., 2020).

Figure 3
Average power density measurements generated depending on the days the experiment was conducted On the other hand, the third highest average power density obtained (860.69 mV/m2) in the 26th.day, despite still being greater than the other datawhich is to be expected, since it is the taking of a maximum measurement -, it does not present an inconsistent departure from the other values obtained.Thus, if this point is accepted as the comparison data, a relevant adjustment of its value can be seen in comparison with the prediction of the developed mathematical model (802.53mV/m2).

FINAL CONSIDERATIONS
This work applied fuzzy logic to simulate the performance of microbial energy cells and used the experimental design technique to statistically evaluate how such parameters influence the performance of these devices.Using this methodology, it was concluded that, for both outputs studied, device volume and anode area had a positive effect, while the external electrical resistance variable had a negative effect.
Regarding the significance of the input variables for current density, all input variables, as well as their squares and interactions, were statistically significant.In the case of power density, only electrical resistanceas well as its interactions, except for its squaredid not show statistical significance.From this development, it was possible to obtain mathematical models that indicated the relationship between each of the input variables and the outputs 15 studied, which is of great interest from the point of view of simplification and better understanding of the complex EMF system.Still analyzing the generated models statistically, it was noticed that the one referring to power density was significant, a result reinforced by the proximity between the simulation data and the data predicted by the model, which is of great relevance when considering the wide working ranges of the variables under study.
The advances achieved through this study are of significant value for the study of microbial energy cells, as they are capable of contributing to the investigation of the influence of some of the most important operating variables of CEM and the improvement of the system.
The good fit obtained for the power density model is also noteworthy, especially when considering the combined application of two mathematical techniques, which can make it difficult to adapt to real systems.For future studies, it is suggested to identify, analyze and generate mathematical models for other EMF operating variables that influence their performance in the generation of electrical energy, since numerous variables are involved in the production of electricity in microbial energy cells.Furthermore, it is also suggested to develop studies of the same type to identify and analyze the main operational variables of CEM that influence their performance for organic matter degradation and effluent treatment.
92x12 + 0,03x13 -0,03x23 y1: current density; y2: power density; x1: device volume; x2: anode area; x3: external electrical resistance; x11: square of the volume factor; x22: square of the anode area factor; x3: square of the external electrical resistance factor; x12: interaction between the factors device volume and anode area; x13: interaction between the factors device volume and external electrical resistance; x23: interaction between the factors anode area and external electrical resistance the power density response values generated in the computational simulations for the data sets referring to the data encoded in the DCCR in comparison with the responses estimated by the model obtained in the experimental planning.

Figure 2
Figure 2Graphical representation of the comparison between the results of the set of computational simulations and experimental planning Performance Evaluation through the Application of Fuzzy Logic ___________________________________________________________________________ Rev. Gest.Soc.Ambient.| Miami | v.18.n.1 | p.1-16 | e06712 | 2024.

Table 1
Parameters, numbers of occurrences and their magnitude limits identified in the bibliographic survey

Table 2
Parameters and ranges of their respective linguistic terms used in the set of simulations in theInFuzzy software

Table 5
Coefficient, error, t-test and p-value values for DCCR planning variables

Table 7
Analysis of variance (ANOVA) data for the experimental design of the DCCR type of the current density output variableSource of Variation; SQ: Sum of Squares; nGL: Number of Degrees of Freedom; MQ: Mean Squares

Table 8
Analysis of variance (ANOVA) data for the experimental design of the DCCR type of the power density output variable