# A Novel Interval Energy-Forecasting Method for Sustainable Building Management Based on Deep Learning

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Related Work for Point Forecasting

#### 2.2. Related Work for Interval Forecasting

## 3. Methodology

#### 3.1. Data Description

#### 3.2. Research Outline

- (1)
- BPNN

- (2)
- SVM

- (3)
- RF

- (4)
- LSTM

- (5)
- Penalized quantile regression

#### 3.3. Optimizing Hyperparameters for Machine-Learning Methods

#### 3.4. Evaluation Metrics

## 4. Results and Discussion

#### 4.1. Model Training

#### 4.2. Point Prediction Results

#### 4.3. Interval Prediction Results

## 5. Conclusions

- The proposed LSTM-PQR model has better performance than BPNN, SVM, and RF for interval indoor load forecasting in an office building.
- For point prediction performance, the distribution of MAE and RMSE in different models are quite different. Generally, the LSTM model maintains optimal performance, while the SVM and RF models have relatively poor prediction results.
- For interval prediction performance, the LSTM-PQR model is still the most suitable choice, especially in daily interval load forecasting, and it has improvements ranging from 6.4% to 20.9% for PICP comparing with the other three models.

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

ANN | Artificial neural network |

SVM | Support vector machine |

DT | Decision tree |

PSO | Particle swarm optimization |

PCA | Principal component analysis |

MAE | mean absolute error |

RMSE | root mean square error |

AIC | Akaike Information Criterion |

BIC | Bayesian Information Criterion |

CV(RMSE) | Coefficient of variation of the RMSE |

PQR | Penalized quantile regression |

RF | Random forest |

PICP | Prediction interval coverage probability |

PINAW | Prediction interval normalized average width |

DE | Differential evolution |

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**Figure 8.**PICP results of proposed models for daily and weekly interval load forecasting with 95% prediction interval.

**Figure 9.**PINAW results of proposed models for daily and weekly interval load forecasting with 95% prediction interval.

References | Temporal Granularity | Time Horizon | Method |
---|---|---|---|

[22,23,24] | Hourly | 24 h | ARX, SRWNN, LSTM |

[25] | 15 min | 24 h | ANN |

[26] | 5 min | 24 h | mbCRT |

[27] | 15 min | 15–60 min | Markov model, ANN, SVR |

[28] | Hourly | 6 h | AR, WT-AR, NM-AR |

Data | Distribution | Parameters |
---|---|---|

Energy consumption | Lognormal | Mean of logarithmic values: 4.284 |

Standard deviation of logarithmic values: 0.706 | ||

Ambient temperature | Normal | Mean:18.481 |

Standard deviation: 9.451 | ||

Relative humidity | Extreme value | Location parameter: 77.860 |

Scale parameter:14.660 | ||

Wind speed | Weibull | Scale parameter: 4.564 |

Shape parameter: 2.473 | ||

Model | Hyperparameters | Range | Step Size | Optimal Value |
---|---|---|---|---|

BPNN | Number of neurons | [10, 100] | 5 | 40 |

Activation function | ‘sigmoid’, ‘tanh’, ‘relu’ | None | ‘sigmoid’ | |

Initial learning rate | [0.001, 0.01] | 0.001 | 0.002 | |

SVM | Kernel function | ‘Gaussian’, ‘linear’, ‘poly’ | None | ‘Gaussian’ |

C | [1, 5] | 0.5 | 3 | |

Epsilon | [0.1, 1] | 0.1 | 0.2 | |

RF | Number of the trees | [5, 100] | 5 | 50 |

Depth of the trees | [10, 120] | 10 | 50 | |

Minimum sample number in leaf node | [1, 5] | 1 | 1 | |

LSTM | Number of neurons | [10, 100] | 5 | 40 |

Activation function | ‘softsign’, ‘sgdm’, ‘tanh’ | None | ‘sgdm’ | |

Initial learning rate | [0.001, 0.01] | 0.001 | 0.002 |

Model | Composite Score for Daily Load Forecasting | Composite Score for Daily Load Forecasting |
---|---|---|

LSTM | 99.60 | 99.60 |

RF | 16.52 | 60.59 |

BPNN | 57.32 | 81.14 |

SVM | 8.94 | 0.20 |

Model | PICP (mean) | PICP (max) | PICP (min) | PICP (SD) | PINAW (mean) | PINAW (max) | PINAW (min) | PINAW (SD) |
---|---|---|---|---|---|---|---|---|

LSTM | 0.739 | 0.988 | 0.450 | 0.171 | 0.565 | 0.757 | 0.386 | 0.123 |

RF | 0.646 | 0.982 | 0.400 | 0.179 | 0.637 | 1.004 | 0.411 | 0.194 |

BPNN | 0.687 | 0.964 | 0.470 | 0.158 | 0.618 | 0.963 | 0.399 | 0.192 |

SVM | 0.669 | 0.949 | 0.523 | 0.127 | 0.659 | 1.063 | 0.413 | 0.186 |

Model | PICP (mean) | PICP (max) | PICP (min) | PICP (SD) | PINAW (mean) | PINAW (max) | PINAW (min) | PICP (SD) |
---|---|---|---|---|---|---|---|---|

LSTM | 0.781 | 0.935 | 0.522 | 0.113 | 0.356 | 0.519 | 0.184 | 0.121 |

RF | 0.731 | 0.913 | 0.504 | 0.111 | 0.414 | 0.608 | 0.207 | 0.142 |

BPNN | 0.694 | 0.978 | 0.402 | 0.197 | 0.403 | 0.592 | 0.218 | 0.126 |

SVM | 0.618 | 0.911 | 0.413 | 0.151 | 0.410 | 0.766 | 0.209 | 0.158 |

Model | Composite Score for Weekly Interval Load Forecasting | Composite Score for Daily Interval Load Forecasting |
---|---|---|

LSTM | 99.60 | 99.60 |

RF | 11.95 | 21.27 |

BPNN | 43.78 | 27.45 |

SVM | 12.37 | 4.96 |

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**MDPI and ACS Style**

Duan, Y.
A Novel Interval Energy-Forecasting Method for Sustainable Building Management Based on Deep Learning. *Sustainability* **2022**, *14*, 8584.
https://doi.org/10.3390/su14148584

**AMA Style**

Duan Y.
A Novel Interval Energy-Forecasting Method for Sustainable Building Management Based on Deep Learning. *Sustainability*. 2022; 14(14):8584.
https://doi.org/10.3390/su14148584

**Chicago/Turabian Style**

Duan, Yun.
2022. "A Novel Interval Energy-Forecasting Method for Sustainable Building Management Based on Deep Learning" *Sustainability* 14, no. 14: 8584.
https://doi.org/10.3390/su14148584