# Performance Prediction of Proton Exchange Membrane Fuel Cells (PEMFC) Using Adaptive Neuro Inference System (ANFIS)

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Analysis

#### 2.1. Fuel Cell Testing Procedure

^{2}was used in this investigation. The bipolar plate channel designs were serpentine, and according to the manufacturer’s specifications, the membrane for these types of fuel cells had to be well humidified to reduce any form of resistance on the membrane. The operating parameters used in the investigation are depicted in Table 1.

#### 2.2. Experimental Set-Up

#### 2.3. Adaptive Neuro-Fuzzy Inference System (ANFIS)

#### 2.4. Multiple Linear Regression (MLR)

#### 2.5. Model Implementation

## 3. Results and Discussion

#### 3.1. Results from Experiment

#### 3.2. Analysis of Experimental Data Using Statistical Technique

#### 3.3. Adaptive Neuro-Fuzzy Inference System Results

^{2}into consideration, the model prediction for the current was slightly better compared to the voltage for both the training and the testing.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Performance of proton exchange membrane fuel cell at lower pressure and flow rate of the reactant.

Level of numerical design | −1 | +1 |

Input variable level | Minimum | Maximum |

${H}_{2}$ pressure | 1 bar | 2.5 bar |

${O}_{2}$ pressure | 0.8 bar | 2.3 bar |

${H}_{2}$ flow rates | 15 mL/min | 150 mL/min |

${O}_{2}$ flow rates | 15 mL/min | 150 mL/min |

Fuel Cell Component | Material | Characteristics |
---|---|---|

Housing | Acetyl | Supplier: (Fuel Cell Store) |

Membrane electrode assembly | Nafion 212 | Active area: 3.4 × 3.4 cm Catalyst loading 0.4 mg/cm ^{2} Pt/c.0.55 g cm^{3} bulkSupplier: Fuel cell store |

Bipolar plate | Graphite | 24 pores/cm Thickness: 0.65 mm Supplier: Fuel Cell Store |

Sealing | Silicon | Thickness: 0.8 mm Supplier: Fuel Cell Store |

Data | N | Mean | Standard Deviation | Sum | Minimum | Median | Maximum |
---|---|---|---|---|---|---|---|

Hydrogen Pressure | 22 | 1.71591 | 0.48975 | 37.75 | 1 | 1.75 | 2.5 |

Oxygen Pressure | 22 | 1.51591 | 0.4316 | 33.35 | 0.8 | 1.55 | 2.3 |

Hydrogen flow rate | 22 | 85.56818 | 48.75187 | 1882.5 | 15 | 82.5 | 150 |

Oxygen Flow Rate | 22 | 85.56818 | 44.07739 | 1882.5 | 15 | 82.5 | 150 |

Current | 22 | 0.50955 | 0.44897 | 11.21 | 0.065 | 0.339 | 1.464 |

Voltage | 22 | 0.62314 | 0.12953 | 13.709 | 0.357 | 0.6645 | 0.768 |

DF | Sum of Squares | Mean Square | F Value | Prob > F | |
---|---|---|---|---|---|

Model | 4 | 1.38408 | 0.34602 | 2.06468 | 0.13053 |

Error | 17 | 2.84904 | 0.16759 | ||

Total | 21 | 4.23312 |

DF | Sum of Squares | Mean Square | F Value | Prob > F | |
---|---|---|---|---|---|

Model | 4 | 0.10697 | 0.02674 | 1.85269 | 0.16532 |

Error | 17 | 0.24538 | 0.01443 | ||

Total | 21 | 0.35235 |

Current | Voltage | ||||
---|---|---|---|---|---|

Variable | Value | Std. Error | Variable | Value | Std. Error |

Constant | 1.5481 | 0.48767 | Constant | 0.33199 | 0.14312 |

Hydrogen Pressure | −0.36593 | 0.18367 | Hydrogen Pressure | 0.09843 | 0.0539 |

Oxygen Pressure | −0.14583 | 0.20849 | Oxygen Pressure | 0.04059 | 0.06119 |

Hydrogen flow rate | −0.00336 | 0.00185 | Hydrogen flow rate | 9.722 × 10^{−4} | 5.42 × 10^{−4} |

Oxygen Flow Rate | 0.00114 | 0.00204 | Oxygen Flow Rate | −2.62 × 10^{−4} | 5.989 × 10^{−4} |

Adjusted R^{2} | 0.1686 | Adjusted R^{2} | 0.1397 |

Variable | Current | Voltage |
---|---|---|

Value | Value | |

Number of nodes | 55 | 193 |

Number of linear parameters | 80 | 405 |

Number of nonlinear parameters | 16 | 24 |

Total number of parameters | 96 | 429 |

Number of training data pairs | 18 | 19 |

Number of checking data pairs | 0 | 0 |

Number of fuzzy rules | 16 | 16 |

Training Time (s) | RMSE | R^{2} | ||||
---|---|---|---|---|---|---|

Training | Testing | Training | Testing | Training | Testing | |

Current | 8.04 | 8.32 | 0.028235 | 0.42473 | 0.99193 | 0.9998 |

voltage | 9.92 | 8.620 | 0.006513 | 0.078608 | 0.99069 | 0.99958 |

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**MDPI and ACS Style**

Wilberforce, T.; Olabi, A.G. Performance Prediction of Proton Exchange Membrane Fuel Cells (PEMFC) Using Adaptive Neuro Inference System (ANFIS). *Sustainability* **2020**, *12*, 4952.
https://doi.org/10.3390/su12124952

**AMA Style**

Wilberforce T, Olabi AG. Performance Prediction of Proton Exchange Membrane Fuel Cells (PEMFC) Using Adaptive Neuro Inference System (ANFIS). *Sustainability*. 2020; 12(12):4952.
https://doi.org/10.3390/su12124952

**Chicago/Turabian Style**

Wilberforce, Tabbi, and Abdul Ghani Olabi. 2020. "Performance Prediction of Proton Exchange Membrane Fuel Cells (PEMFC) Using Adaptive Neuro Inference System (ANFIS)" *Sustainability* 12, no. 12: 4952.
https://doi.org/10.3390/su12124952