# Regarding Solid Oxide Fuel Cells Simulation through Artificial Intelligence: A Neural Networks Application

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## Abstract

**:**

## Featured Application

**Simulation of fuel cell systems.**

## Abstract

^{−2}). Therefore, the neural tool is suitable for system simulation codes/software whether SOFC operating parameters agree with the input ranges (anode feeding composition 0–48%

_{vol}H

_{2}, 0–38%

_{vol}CO, 0–45%

_{vol}CH

_{4}, 9–32%

_{vol}CO

_{2}, 0–54%

_{vol}N

_{2}, specific equivalent hydrogen flow-rate per unit cell active area 10.8–23.6 mL·min

^{−1}·cm

^{−2}, current density 0–1300 mA·cm

^{−2}and temperature 700–800 °C).

## 1. Introduction

_{4}/CO

_{2}gas mixtures is taken into account. Whilst that study provides thorough insight on complex competitive reactions (steam and dry reforming), its applicability is limited to a narrow range of fuels and does not consider other gas species. Regarding some promising SOFC applications, the fuel gas (hydrocarbon reformate, coal and biomass syngas) has non-negligible amounts of H

_{2}and CO. This substantially modifies the reaction rates associated to methane decomposition. A slightly more complex fuel mixture (28.1% CH

_{4}, 56.7% H

_{2}O, 0.5% CO, 12% H

_{2}and 2.7% CO

_{2}) is considered in Reference [27]. Nonetheless, in that paper, gas components fractions do not vary in the data-set used to develop the ANN. Again, the results obtained do not show a high generalization capability with regard to any operative conditions.

_{4}, H

_{2}, CO and CO

_{2}and it predicts voltage losses from a few input parameters (temperature, fuel main components partial flow rates, electric load). Such algorithm is suitable to calculate quickly the SOFC electric power output in a wide range of applications, resulting flexible for many system integration designs, which show promising potentialities (e.g., biogas-fed small-scale SOFC units [33], integrated-gasifier fuel cell systems [34] etc.). The data-set for the network training are collected experimentally on SOFC materials representing the current state-of-the-art, regarding thickness and material composition.

## 2. Materials and Methods

#### 2.1. Artificial Neural Network Development

#### 2.1.1. Architecture Definition

#### 2.1.2. Training

- The first subset (70% of samples) is used for the training itself and it is fed to the network algorithm in order to calculate the values associated to the weight and bias matrix elements;
- The second subset (15% of samples) is used as validation basis. This is employed to measure the generalization capability of the network and to abort the training process early if the network performance on this subset does not improve. (i.e., before the target value for the error function is reached). The validation subset does not influence the network generalization capabilities.
- The third subset (15% of samples) is used for the test, that is to say for a further generalization capability check having no effect on the training phase.

_{inc}. During training, if the nth-step error is less than (n − 1)th-step error, the learning rate is increased. Otherwise, in the event of abnormal performance enhancement, the learning rate is decreased by the learning rate decreasing ratio, LR

_{dec}. If the nth-step error exceeds the error calculated at the preceding iteration, the learning rate is decreased accordingly. With regard to the network training, Table 2 shows the value assigned to the main parameters of the process, managing learning speed and aborting the process when needed. The other parameters in Table 2 are: “minimum performance gradient” represents the minimum accepted value of performance improvement; “maximum validation failures” is the maximum number of failures allowed along the network improvement and “performance goal” is the target of the performance function. During the training phase, simulation performances are checked on the Mean Squared normalized Error (MSE, Equation (1)) and Root Mean squared Error (RMS, Equation (2)), both based on the sum of squared errors (the difference between the ANN output θ

_{ann,i}and the corresponding experimental results θ

_{exp,i}).

#### 2.2. Experimental Data Collection

#### 2.2.1. Materials and Experimental Set-Up

^{2}, thickness anode/electrolyte/cathode: 240/8/50 μm). The sealing used is Aremco Ceramabond

^{®}552. The test rig and related equipment are fully described in Reference [36]. The cell is connected to an electronic load, simulating the user. Raw data are sampled at 1 Hz and processed with an average filter to remove measurement noise (on a 120-sample basis).

#### 2.2.2. Design of Experiments

_{2}, CO

_{2}, CH

_{4}, CO and N

_{2}, the total flow rate is expressed with an auxiliary variable, defined as “equivalent hydrogen” (definition given at Equation (3). Equivalent hydrogen flowrate is set to three levels and expressed per unit cell active area (10.8, 14.7, 23.2 mL·min

^{−1}·cm

^{−2}) to vary the fuel utilization (see the relation between the fuel utilization coefficient U

_{f}and the flowrate of equivalent hydrogen at Equation (4).

_{f}and the fuel mixture dilution fraction (DF, see Equation (6).

#### 2.2.3. Tests Execution: Methods

^{−2}. The waiting time between two consecutive tests is reduced to the minimum duration (average 2 h), to lower the likelihood of cumulative damage and to sort a consistent data-set, suitable for the ANN training.

## 3. Results

#### 3.1. Experimental

_{2}, CO

_{2}, CH

_{4}, CO and N

_{2}volume flowrates. As output section, the matrix shows voltage outputs related to each combination of the previous parameters. Hereinafter, Figure 2 presents a couple of examples regarding SOFC performance maps obtained experimentally. In detail, performances maps are represented for two load conditions, 100 mA·cm

^{−2}and 250 mA·cm

^{−2}. On the y-axis, measured voltage is shown, while on the primary and secondary x-axis the fuel total indicator (Equation (5)) and the temperature are shown. As explained above, the fuel total indicator is a useful dimensionless parameter to sum up the information relative to the kind of fuel mixture and the way it is employed (that is to say the current load and the anode feeding flow rate).

#### 3.2. Neural Network Development

#### 3.3. Neural Network Application

^{−2}).

^{−2}) and the ANN5 tool can be used with a good approximation also to predict results related to the operation of SOFC cells as in Reference [42]. In addition to that, it is worth highlighting the distribution of forecast error in the current density range observed (grey dotted lines in Figure 6). Both simulated curves fit well the real voltage at open circuit and in a current density range, which recalls real applications. In fact, the relative error on the single measurement is significantly lower (<2% Exp synF, <3% Exp synG) at 0 mA·cm

^{−2}and in the current density range 300–500 mA·cm

^{−2}. In terms of RMS, the result scored is 0.93% and 1.6% for the Exp synF curve simulation and Exp synF curve simulation respectively.

## 4. Conclusions

^{−2}) is observed.

_{vol}H

_{2}, 0–38%

_{vol}CO, 0–45%

_{vol}CH

_{4}, 9–32%

_{vol}CO

_{2}, 0–54%

_{vol}N

_{2}, with an equivalent hydrogen area-specific flow-rate between 10.8 and 23.2 mL·min

^{−1}·cm

^{−2}and temperature from 700 °C to 800 °C.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Feedforward-backpropagation ANN structure: in each HL a number #n

_{k}of artificial neurons are connected and correlated through the weight matrix (W

_{k}) and the bias matrix (B

_{k}).

**Figure 6.**ANN5 application: comparison of simulated and experimental polarization curves (

**a**) under Exp synF and (

**b**) Exp synG operating conditions.

ID | Architecture | Number of HL | Neurons in HL 1 | Neurons in HL 2 | Neurons in HL 3 | Neurons in HL 4 | Training Function | Transfer Function |
---|---|---|---|---|---|---|---|---|

ANN1 | L1 | 2 | 10 | 10 | - | - | TrainGDA | LogSIG |

ANN2 | 2 | 16 | 12 | - | - | TrainGDM | ||

ANN3 | 2 | 20 | 16 | - | - | |||

ANN4 | L2 | 3 | 20 | 18 | 14 | - | TrainGDA | TanSIG |

ANN5 | 3 | 25 | 22 | 18 | - | |||

ANN6 | 3 | 15 | 10 | 10 | - | |||

ANN7 | 3 | 25 | 20 | 22 | - | LogSIG | ||

ANN8 | 3 | 30 | 28 | 26 | - | |||

ANN9 | L3 | 4 | 12 | 10 | 8 | 6 | TanSIG | |

ANN10 | L2 | 3 | 30 | 28 | 26 | - |

Description | Symbol | Value |
---|---|---|

Minimum performance Gradient | - | 0.00001 |

Maximum validation failures | - | 600 |

Performance Goal | - | 0 |

Learning rate | LR | 0.01 |

Learning rate increasing ratio | LR_{inc} | 1.05 |

Learning rate decreasing ratio | LR_{dec} | 0.7 |

Temperature | Gas Mixture Volume Fraction on Dry Basis | ${\dot{\mathit{n}}}_{{\mathit{H}}_{2\mathit{e}\mathit{q}}}$ | j | ||||||
---|---|---|---|---|---|---|---|---|---|

°C | MIX | Ref. | H_{2} | CO | CH_{4} | CO_{2} | N_{2} | mL·min^{−1}·cm^{−2} | mA·cm^{−2} |

700 750 800 | synA | [37] | 10% | 13% | 4% | 19% | 54% | 10.8 14.7 23.6 | 0 A → I (0.6 V) (Δj = 50 mA·cm ^{−2}) |

synB | [38] | 48% | 0% | 14% | 9% | 29% | |||

synC | [39] | 22% | 26% | 30% | 22% | 0% | |||

synD | [40] | 32% | 38% | 0% | 30% | 0% | |||

synE | [41] | 0% | 0% | 45% | 32% | 45% |

ANN | Training | Validation | Test | Number of Learning Epochs | |
---|---|---|---|---|---|

ID | RMS % | MSE | RMS % | RMS % | |

ANN1 | 10.75% | 0.0117 | 10.8% | 10.97% | 42 |

ANN2 | 12.92% | 0.0169 | 13.0% | 12.86% | 31,000 |

ANN3 | 13.02% | 0.0171 | 13.1% | 13.01% | 100,000 |

ANN4 | 1.36% | 0.0002 | 1.4% | 1.21% | 10,600 |

ANN5 | 0.80% | <0.0001 | 0.7% | 0.67% | 120,000 |

ANN6 | 0.99% | <0.0001 | 1.0% | 1.05% | 100,000 |

ANN7 | 1.01% | 0.0001 | 1.0% | 1.12% | 100,000 |

ANN8 | 0.98% | <0.0001 | 1.0% | 1.07% | 100,000 |

ANN9 | 1.10% | 0.0001 | 1.1% | 1.05% | 100,000 |

ANN 10 | 0.75% | <0.0001 | 0.8% | 0.78% | 112,000 |

Variables | Exp synF Settings | Exp synG Settings | ANN5 Input Range | ||||
---|---|---|---|---|---|---|---|

Min | Max | ||||||

Temperature (°C) | 765 | 800 | 700 | 800 | |||

Equivalent hydrogen flowrate (mL·min^{−1}·cm^{−2}) | 18.34 | 15.48 | 10.80 | 23.56 | |||

Area Specific partial flowrates (mL·min ^{−1}·cm^{−2}) | H_{2} | 3.67 | (20.0%_{vol}) | 5.16 | (20.0%_{vol}) | 0 | 10.51 |

CO | 7.34 | (40.0%_{vol}) | 5.16 | (20.0%_{vol}) | 0 | 12.74 | |

CO_{2} | 2.75 | (15.0%_{vol}) | 3.87 | (15.0%_{vol}) | 0 | 5.73 | |

CH_{4} | 1.83 | (10.0%_{vol}) | 1.29 | (5.0%_{vol}) | 1.27 | 11.46 | |

N_{2} | 2.75 | (15.0%_{vol}) | 10.32 | (40.0%_{vol}) | 0 | 32.17 | |

Current density (mA·cm^{−2}) | 0–500 | 0–500 | 0 | 1300 |

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## Share and Cite

**MDPI and ACS Style**

Baldinelli, A.; Barelli, L.; Bidini, G.; Bonucci, F.; Iskenderoğlu, F.C.
Regarding Solid Oxide Fuel Cells Simulation through Artificial Intelligence: A Neural Networks Application. *Appl. Sci.* **2019**, *9*, 51.
https://doi.org/10.3390/app9010051

**AMA Style**

Baldinelli A, Barelli L, Bidini G, Bonucci F, Iskenderoğlu FC.
Regarding Solid Oxide Fuel Cells Simulation through Artificial Intelligence: A Neural Networks Application. *Applied Sciences*. 2019; 9(1):51.
https://doi.org/10.3390/app9010051

**Chicago/Turabian Style**

Baldinelli, Arianna, Linda Barelli, Gianni Bidini, Fabio Bonucci, and Feride Cansu Iskenderoğlu.
2019. "Regarding Solid Oxide Fuel Cells Simulation through Artificial Intelligence: A Neural Networks Application" *Applied Sciences* 9, no. 1: 51.
https://doi.org/10.3390/app9010051