#
Short-Term Energy Demand Forecast in Hotels Using Hybrid Intelligent Modeling^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Energy Management in the Hotel Industry

## 3. Methods

#### 3.1. Data

#### 3.2. ARIMAX Modeling

#### 3.3. Bagged Decision Trees Modeling

- Root node: this node has no incoming edges and several (or zero) outgoing edges.
- Internal node: characterized by one incoming edge and two or more outgoing edges.
- Leaf: it has one incoming edge and no outgoing edges.

#### 3.4. Hybrid Intelligent Modeling

#### 3.4.1. K-Means Clustering Algorithm

- Determine the cluster for each sample data based on the distance to the centroids. The cluster assigned should be the closest one to the sample.
- Calculate new centroids as the center of the clusters, taking into account all the samples per cluster.

#### 3.4.2. Multi-Layer Perceptron

- $x={(x\left(1\right),\dots ,x\left(d\right))}^{T}\in {\Re}^{d}$ is the inputs vector
- k is the hidden layers number
- $\varphi $ is a bounded transfer function
- $\theta =(\beta ,{a}_{1},\dots ,{a}_{k},{b}_{1},\dots ,{b}_{k},{w}_{11},\dots ,{w}_{kd})$ is the model parameter vector
- ${w}_{i}={({w}_{i1},\dots ,{w}_{id})}^{T}\in {\Re}^{d}$ is the parameter vector for the hidden unit i

#### 3.4.3. 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. An Intelligent Model for Power Demand

- Clustering training. This phase is the same for all the hybrid models, as they share the same inputs.
- Regression training. For each cluster, two different regression algorithms (MLP and SVR) were evaluated. In the case of ANN, different internal configurations were considered.
- Performance calculation. As the number of clusters for each model is not a predefined, it is necessary to calculate the best cluster assignment based on the achieved error.

#### 4.1. Clustering Training

#### 4.2. Regression Training

#### 4.3. Hybrid Model Performance Calculation

## 5. Results and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Energy and occupancy in 2017 in the hotel under study. (

**A**) Power demand profile in hospitality sector. Elaborated with information provided by ENDESA and a luxury 5-star hotel. (

**B**) Energy consumed and occupancy in 2017 in the hotel, and exterior temperature variation along 2017 from the nearest meteorological station, i.e., at the Tenerife South Airport (GCTS) (Source www.wunderground.com).

**Figure 2.**Demanded power by a hotel. (

**A**) Demanded power by a hotel for 31 days. (

**B**) Auto-Correlation Function and Partial Auto-Correlation Function of demanded power in (

**A**); dashed blue lines indicate significance bounds. (

**C**) Occupation ratio of the hotel during same period.

**Figure 7.**Predicted power demand by the model. Validation of the hybrid intelligent model, the ARIMAX model and the bagged decision tree model.

ARIMAX | MAPE (%) | Box-Ljung Test, p-Value | |
---|---|---|---|

Day 1 (31 December) | ARIMAX(4,0,1) | 2.55 | 2.7 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-5}$ |

Day 2 (3 January) | ARIMAX(4,0,1) | 2.51 | 1.2 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-7}$ |

Day 3 (11 February) | ARIMAX(4,0,1) | 2.43 | 1.1 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-5}$ |

Day 4 (1 August) | ARIMAX(4,0,1) | 3.22 | 9.5 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-7}$ |

Day 5 (29 September) | ARIMAX(3,0,1) | 2.88 | 5.4 $\times \phantom{\rule{3.33333pt}{0ex}}{10}^{-2}$ |

Cl-1 | Cl-2 | Cl-3 | Cl-4 | Cl-5 | Cl-6 | Cl-7 | |
---|---|---|---|---|---|---|---|

Global | 354 | ||||||

Hybrid 2 | 147 | 207 | |||||

Hybrid 3 | 91 | 91 | 172 | ||||

Hybrid 4 | 52 | 65 | 97 | 140 | |||

Hybrid 5 | 40 | 43 | 65 | 87 | 119 | ||

Hybrid 6 | 36 | 43 | 59 | 60 | 76 | 80 | |

Hybrid 7 | 21 | 39 | 47 | 57 | 60 | 61 | 69 |

Cl-1 | Cl-2 | Cl-3 | Cl-4 | Cl-5 | Cl-6 | Cl-7 | |
---|---|---|---|---|---|---|---|

Global | LS-SVR | ||||||

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

Hybrid 3 | MLP-11 | LS-SVR | LS-SVR | ||||

Hybrid 4 | MLP-15 | LS-SVR | LS-SVR | LS-SVR | |||

Hybrid 5 | LS-SVR | LS-SVR | LS-SVR | LS-SVR | LS-SVR | ||

Hybrid 6 | MLP-15 | MLP-14 | MLP-12 | MLP-11 | MLP-12 | LS-SVR | |

Hybrid 7 | LS-SVR | MLP-14 | LS-SVR | MLP-13 | MLP-13 | MLP-11 | LS-SVR |

Cl-1 | Cl-2 | Cl-3 | Cl-4 | Cl-5 | Cl-6 | Cl-7 | Hybrid MSE | |
---|---|---|---|---|---|---|---|---|

Global | 0.9454 | 0.9454 | ||||||

Hybrid 2 | 0.8620 | 0.7596 | 0.8021 | |||||

Hybrid 3 | 1.0792 | 1.3943 | 0.8693 | 1.0582 | ||||

Hybrid 4 | 2.5665 | 0.8984 | 0.9411 | 0.7035 | 1.0780 | |||

Hybrid 5 | 1.2082 | 2.1560 | 1.0623 | 0.9041 | 0.8080 | 1.0873 | ||

Hybrid 6 | 1.0036 | 2.3759 | 1.1940 | 0.5146 | 1.3799 | 0.9011 | 1.1768 | |

Hybrid 7 | 0.8151 | 2.2792 | 1.4413 | 0.5952 | 1.6359 | 1.6617 | 1.6345 | 1.4689 |

**Table 5.**Errors achieve by the models. (Mean Absolute Percentage Error (MAPE), the Mean Absolute Error (MAE), the Mean Square Error (MSE), and the Maximum Error (Max.)).

ARIMAX Model | Bagged Tree Model | Hybrid Model | |||||||
---|---|---|---|---|---|---|---|---|---|

MAPE (%) | MAE (${\mathbf{10}}^{-\mathbf{3}}$ MW) | MSE (${\mathbf{10}}^{-\mathbf{3}}$ MW${}^{\mathbf{2}}$) | MAPE (%) | MAE (${\mathbf{10}}^{-\mathbf{3}}$ MW) | MSE (${\mathbf{10}}^{-\mathbf{3}}$ MW${}^{\mathbf{2}}$) | MAPE (%) | MAE (${\mathbf{10}}^{-\mathbf{3}}$ MW) | MSE (${\mathbf{10}}^{-\mathbf{3}}$ MW${}^{\mathbf{2}}$) | |

Day 1 | 6.27 | 107.73 | 16,402 | 2.70 | 46.73 | 3167 | 2.98 | 53.94 | 4515 |

Day 2 | 4.73 | 82.80 | 9027 | 3.53 | 64.05 | 6473 | 3.74 | 68.36 | 6661 |

Day 3 | 6.01 | 103.46 | 14,832 | 2.43 | 41.88 | 2944 | 1.97 | 33.75 | 2052 |

Day 4 | 8.36 | 138.87 | 21,808 | 4.02 | 70.24 | 7388 | 2.96 | 49.76 | 3773 |

Day 5 | 5.73 | 98.93 | 15,173 | 2.98 | 52.99 | 4015 | 2.43 | 41.76 | 3035 |

Mean | 6.22 | 106.36 | 15,449 | 3.13 | 55.18 | 4797 | 2.81 | 49.51 | 4007 |

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## Share and Cite

**MDPI and ACS Style**

Casteleiro-Roca, J.-L.; Gómez-González, J.F.; Calvo-Rolle, J.L.; Jove, E.; Quintián, H.; Gonzalez Diaz, B.; Mendez Perez, J.A. Short-Term Energy Demand Forecast in Hotels Using Hybrid Intelligent Modeling. *Sensors* **2019**, *19*, 2485.
https://doi.org/10.3390/s19112485

**AMA Style**

Casteleiro-Roca J-L, Gómez-González JF, Calvo-Rolle JL, Jove E, Quintián H, Gonzalez Diaz B, Mendez Perez JA. Short-Term Energy Demand Forecast in Hotels Using Hybrid Intelligent Modeling. *Sensors*. 2019; 19(11):2485.
https://doi.org/10.3390/s19112485

**Chicago/Turabian Style**

Casteleiro-Roca, José-Luis, José Francisco Gómez-González, José Luis Calvo-Rolle, Esteban Jove, Héctor Quintián, Benjamin Gonzalez Diaz, and Juan Albino Mendez Perez. 2019. "Short-Term Energy Demand Forecast in Hotels Using Hybrid Intelligent Modeling" *Sensors* 19, no. 11: 2485.
https://doi.org/10.3390/s19112485