# Bioinspired Hybrid Model to Predict the Hydrogen Inlet Fuel Cell Flow Change of an Energy Storage System

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## Abstract

**:**

## 1. Introduction

## 2. Case Study

#### 2.1. Fuel Cell

#### 2.2. Power System

## 3. Model Approach

#### 3.1. Data Processing

#### 3.2. K-Means Algorithm

- A random set of data samples are chosen as the first set of centroids due to, at the beginning, the center of each group is not known;
- A set of data samples will create a cluster if this set of points are the nearest to this cluster centroid;
- Once the clusters are defined, it is necessary to calculate their associated centroid. These new centroids are chosen as the center of each cluster.

#### 3.3. Artificial Neural Networks

- Number of layers;
- Number of neurons per layer;
- Links between neurons;
- Activation functions.

#### 3.4. Polynomial Regression

#### 3.5. Support Vector Machines for Regression

- ${I}_{n}$ is a vector of n ones;
- T means transpose of a matrix or vector;
- $\gamma $ a weight vector;
- b regression vector;
- ${b}_{0}$ is the model offset.

## 4. Results

#### 4.1. Clustering Results

#### 4.2. Modeling Results

#### 4.2.1. Artifical Neural Networks

#### 4.2.2. Polynomial Regression

#### 4.2.3. Support Vector Machines for Regression

#### 4.2.4. Best Regression Local Models Selection

#### 4.3. Validation Results

- Mean Squared Error −$MSE=23.8121$;
- Normalized Mean Squared Error −$NMSE=0.4438$;
- Mean Absolute Error −$MAE=3.7318$;
- Mean Absolute Percentage Error −$MAPE=110.4193$.

## 5. Conclusions and Future Works

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Cl-1 | Cl-2 | Cl-3 | Cl-4 | |
---|---|---|---|---|

Global | 187 | |||

Hybrid 2 | 92 | 95 | ||

Hybrid 3 | 52 | 67 | 68 | |

Hybrid 4 | 42 | 45 | 47 | 53 |

**Table 2.**Mean Absolute Error (MAE) using Artificial Neural Network (ANN) with 13 neurons in the hidden layer.

Cl-1 | Cl-2 | Cl-3 | Cl-4 | |
---|---|---|---|---|

Global | 7.7725 | |||

Hybrid 2 | 43.6784 | 77.1169 | ||

Hybrid 3 | 17.8174 | 26.0211 | 41.1911 | |

Hybrid 4 | 14.8003 | 25.2539 | 10.7302 | 23.8377 |

Cl-1 | Cl-2 | Cl-3 | Cl-4 | |
---|---|---|---|---|

Global | 4.0405 | |||

Hybrid 2 | 6.5793 | 13.0030 | ||

Hybrid 3 | 29.8819 | 74.4182 | 14.6885 | |

Hybrid 4 | 52.8102 | 50.7558 | 53.4093 | 124.6589 |

Cl-1 | Cl-2 | Cl-3 | Cl-4 | |
---|---|---|---|---|

Global | 4.0405 | |||

Hybrid 2 | 6.5793 | 13.0030 | ||

Hybrid 3 | 29.8819 | 74.4182 | 14.6885 | |

Hybrid 4 | 52.8102 | 50.7558 | 53.4093 | 124.6589 |

Cl-1 | Cl-2 | Cl-3 | Cl-4 | |
---|---|---|---|---|

Global | LS-SVR | |||

Hybrid 2 | LS-SVR | LS-SVR | ||

Hybrid 3 | LS-SVR | LS-SVR | LS-SVR | |

Hybrid 4 | LS-SVR | LS-SVR | LS-SVR | LS-SVR |

Cl-1 | Cl-2 | Cl-3 | Cl-4 | |
---|---|---|---|---|

Global | 18.3348 | |||

Hybrid 2 | 11.0268 | 28.0035 | ||

Hybrid 3 | 20.3464 | 37.9476 | 10.7460 | |

Hybrid 4 | 65.2756 | 15.5356 | 10.2792 | 94.5818 |

Global | Hybrid Model (Local Models) | |||
---|---|---|---|---|

2 | 3 | 4 | ||

MSE | 24.0758 | 33.8591 | 23.8121 | 398.9072 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Alaiz-Moretón, H.; Jove, E.; Casteleiro-Roca, J.-L.; Quintián, H.; López García, H.; Benítez-Andrades, J.A.; Novais, P.; Calvo-Rolle, J.L.
Bioinspired Hybrid Model to Predict the Hydrogen Inlet Fuel Cell Flow Change of an Energy Storage System. *Processes* **2019**, *7*, 825.
https://doi.org/10.3390/pr7110825

**AMA Style**

Alaiz-Moretón H, Jove E, Casteleiro-Roca J-L, Quintián H, López García H, Benítez-Andrades JA, Novais P, Calvo-Rolle JL.
Bioinspired Hybrid Model to Predict the Hydrogen Inlet Fuel Cell Flow Change of an Energy Storage System. *Processes*. 2019; 7(11):825.
https://doi.org/10.3390/pr7110825

**Chicago/Turabian Style**

Alaiz-Moretón, Héctor, Esteban Jove, José-Luis Casteleiro-Roca, Héctor Quintián, Hilario López García, José Alberto Benítez-Andrades, Paulo Novais, and Jose Luis Calvo-Rolle.
2019. "Bioinspired Hybrid Model to Predict the Hydrogen Inlet Fuel Cell Flow Change of an Energy Storage System" *Processes* 7, no. 11: 825.
https://doi.org/10.3390/pr7110825