# Estimation of Heat Loss Coefficient and Thermal Demands of In-Use Building by Capturing Thermal Inertia Using LSTM Neural Networks

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## Abstract

**:**

## 1. Introduction

_{2}concentration) and outdoor variables (temperature, relative humidity, and solar radiation). The accuracy of the models developed is quantified using the Coefficient of Variation of the Root Mean Squared Error (CV(RMSE)) and the Mean Bias Error (MBE). These error measures were both recommended by the American Society of Heating, Refrigerating and Air-Conditioning engineers (ASHRAE) and validated on Guideline 14 [22].

## 2. Materials and Methods

#### 2.1. LSTM Architecture

#### 2.2. Heat Loss Coefficient (HLC)

#### 2.3. Validation and Error Measurement

## 3. Experimental Case of Study

#### 3.1. Building and Heating System Description

#### 3.2. Pre-Processing Data

#### 3.3. Neural Network Setup

## 4. Results and Discussion

#### 4.1. Time-Lag Selection

#### 4.2. Error Measurement and Performance Analysis

#### 4.3. HLC Comparison

^{2}, provided by Erkoreka et al. [25]. The thermal conditions of these three periods are summarized in Table 4.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 2.**Rectorate building of the UPV/EHU located on Leioa, Vizcaya, in the north of Spain. (

**a**) Plan view of the building of the blocks: 1-west block; 2-central block; 3-east block. (

**b**) Façade view of the west block.

**Figure 3.**Sensor distribution on each floor. Temperature, humidity, and CO

_{2}sensors are marked as green squares, while blue and red squares indicate the electric consumption and thermal demand sensors, respectively. (

**a**) Ground Floor, (

**b**) First Floor, (

**c**) Second Floor, (

**d**) Third Floor.

**Figure 5.**Results of thermal demand predictions on GF (

**top left**), 1F (

**top right**), 2F (

**bottom left**) and 3F (

**bottom right**).

Variable | Lower Filter | Upper Filter |
---|---|---|

Indoor TA | 15 °C | 32 °C |

Indoor RH | 0% | 100% |

CO_{2} | 200 ppm | 1000 ppm |

Elec. consumption | 25 W | 5000 W |

Outdoor TA | −15 °C | 45 °C |

Outdoor RH | 0% | 100% |

Radiation | 3.5 W/m^{2} | 1500 W/m^{2} |

Time-Lag | GF | 1F | 2F | 3F |
---|---|---|---|---|

3 h | 42.43 | 15.54 | 28.39 | 22.64 |

6 h | 39.74 | 14.37 | 19.94 | 20.65 |

12 h | 21.12 | 12.71 | 15.92 | 19.50 |

24 h | 33.95 | 13.13 | 20.19 | 25.32 |

**Table 3.**Monthly calculation (Mean) and Standard Deviation (SD) of CV(RMSE) and MBE errors for heat demand prediction for each floor.

CV(RMSE) [%] | MBE | |||
---|---|---|---|---|

Floor | Mean | SD | Mean | SD |

GF | 21.12 | 4.33 | 11.92 | 4.79 |

1F | 12.71 | 4.13 | 3.65 | 5.21 |

2F | 15.92 | 5.38 | −1.04 | 8.81 |

3F | 19.50 | 4.52 | −5.01 | 11.96 |

**Table 4.**Thermal conditions for the three periods analyzed. All variables are averaged for the period.

Period | T_In-T_Out [K] | Q [kW] | Q + K [kW] | Rad/(Q + K) [%] |
---|---|---|---|---|

Sample 1 | 14.98 | 33.72 | 49.53 | 9.73% |

Sample 2 | 19.68 | 42.12 | 56.64 | 5.70% |

Sample 3 | 17.70 | 26.55 | 41.54 | 9.79% |

Period | GF [kW/K] | 1F [kW/K] | 2F [kW/K] | 3F [kW/K] | Building (Predicted) [kW/K] | Building (Real) [kW/K] |
---|---|---|---|---|---|---|

Sample 1 | 0.61 | 1.01 | 0.71 | 0.80 | 3.13 | 3.27 |

Sample 2 | 0.56 | 0.87 | 0.67 | 0.71 | 2.81 | 2.85 |

Sample 3 | 0.46 | 0.79 | 0.55 | 0.64 | 2.44 | 2.35 |

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**MDPI and ACS Style**

Pensado-Mariño, M.; Febrero-Garrido, L.; Pérez-Iribarren, E.; Oller, P.E.; Granada-Álvarez, E.
Estimation of Heat Loss Coefficient and Thermal Demands of In-Use Building by Capturing Thermal Inertia Using LSTM Neural Networks. *Energies* **2021**, *14*, 5188.
https://doi.org/10.3390/en14165188

**AMA Style**

Pensado-Mariño M, Febrero-Garrido L, Pérez-Iribarren E, Oller PE, Granada-Álvarez E.
Estimation of Heat Loss Coefficient and Thermal Demands of In-Use Building by Capturing Thermal Inertia Using LSTM Neural Networks. *Energies*. 2021; 14(16):5188.
https://doi.org/10.3390/en14165188

**Chicago/Turabian Style**

Pensado-Mariño, Martín, Lara Febrero-Garrido, Estibaliz Pérez-Iribarren, Pablo Eguía Oller, and Enrique Granada-Álvarez.
2021. "Estimation of Heat Loss Coefficient and Thermal Demands of In-Use Building by Capturing Thermal Inertia Using LSTM Neural Networks" *Energies* 14, no. 16: 5188.
https://doi.org/10.3390/en14165188