# Deep Highway Networks and Tree-Based Ensemble for Predicting Short-Term Building Energy Consumption

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions [1]. According to the current European Union (EU) roadmap, the EU is committed to reducing greenhouse gas emission by 20%, reaching a share of renewable energy in gross final energy by 20%, and reducing total primary energy consumption by 20%—by 2020 as compared to the 1990 levels [2]. In the non-domestic sector, hotels and restaurants are the third largest consumers of energy, accounting for 30%, 18%, 16% and 14% in Spain, France, the UK and the USA, respectively [3,4]. In Greece and Spain, hotels are responsible for about 1/3 of the total energy demand [5]. In hotels, nearly half of the electricity is used for space conditioning purposes [6]. Because of a significant amount of energy consumption, there have been increasing concerns on hotels’ energy use and efforts to effectively manage energy consumption. Predicting energy consumption over a wide range of time horizons is one of the key features of smart girds. It allows for building managers/owners to make informed decisions; e.g., increasing share of renewable energy sources and shifting energy use to off-peak times.

#### 1.1. Context and Objectives

#### 1.2. Related Work

- The use of tree-based ensemble techniques and deep highway networks for predicting HVAC energy consumption from contextual data;
- Studying the impact of networks’ depth on prediction performance of DHN models;
- Demonstrate a prediction error of nearly 6% (normalised root mean square error)on hourly data for two of the best currently known machine learning algorithms (tree-based ensembles and deep learning).

## 2. Materials and Methods

#### 2.1. Machine Learning Algorithms

#### 2.1.1. Support Vector Regression

#### 2.1.2. Deep Highway Networks

#### 2.1.3. Extremely Randomized Trees

#### 2.2. Data Description

#### 2.3. Model Evaluation Metrics

^{2}) and normalised root mean squared error (NRMSE) were used. Determination coefficient is used to measure the correlation between the actual and predicted HVAC energy consumption values. The remaining three metrics are described as below:

## 3. Results

#### 3.1. DHN Hyper-Parametric Tuning

^{2}value of 0.84. It was found that several combinations of networks can achieve best performance, and generally no hyper-parameter drives the predictive performance of the models. Experimental results showed that best performance was obtained with an input dimension of 73 i.e., taking as input the previous 24 h of outdoor dry-bulb air temperature, air relative humidity and HVAC energy consumption and only the past value of the number of guests. However, it is worth mentioning that the increase in performance is small as compared to the increase in the complexity of the model. Results depict that a higher number of layers does marginally improve the performance; however, the best five performances were obtained by using one-layered networks. In order to further investigate the influence of model complexity, Table 4 shows the best performances achieved by the least complex models. The results clearly show that a model with only five input units and one layer, taking as input only one or two past values of input variables can achieve an NRMSE value of nearly 6%, with an error increase of 0.1% as compared to the best performing models.

#### 3.2. SVR Hyper-Parametric Tuning

^{5}, various values of $\u03f5$ were tried to find its optimal value. From the results, it was found that smaller values of $\u03f5$ did not have a significant influence on the performance on SVR model. The performance significantly reduced for values larger than 4. From results, a value of 2 was chosen for $\u03f5$. Table 5 and Table 6 show the results of different experiments for select C and $\u03f5$.

#### 3.3. ET Hyper-Parametric Tuning

^{2}value of 0.7485. The influence of tree depth on predictive accuracy shows that deeper trees resulted in better performance. The performance started to deteriorate for ${d}_{\mathrm{max}}$ greater than 10. The trees with ${d}_{\mathrm{max}}$ = 1 resulted in higher values of RMSE, MAE and MSE, and lower value of R

^{2}. From these results, it is clear that, on the studied dataset, extremely randomized trees’ performance was more influenced by parameter ${d}_{\mathrm{max}}$ instead of ${n}_{\mathrm{min}}$ and K. This may vary from dataset to dataset; however, for most of the cases, default values of the parameters may result in acceptable performance. Table 7, Table 8 and Table 9 show the results of various experiments for selecting ET hyper-parameters.

## 4. Comparison and Discussion

^{2}value is higher than 0.84 and RMSE values were in the range of 3.08 and 4.28 for both training and testing datasets. From these results, it can be concluded that the developed models have the capabilities to accurately predict the hourly HVAC energy consumption.

- The obtained performance is optimal and no further improvement could be achieved;
- The complexity may not have been increased enough to show significant changes in the performance of the model;
- Some variables of interest may not have been taken into account;
- The historical data used in this study is not sufficient to ensure the reliable training of a deep learning models’ deep highway network in our case.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Building electricity consumption of (

**a**) a school; (

**b**) a hotel. Reproduced from Ahmad et al. [3], 2017.

**Figure 3.**Actual hourly HVAC energy consumption. The data shown in the figure is from 15 January 2015 to 15 January 2016.

**Figure 4.**Results from extremely randomized trees model. (

**a**) comparison between actual and predicted energy consumption from the extremely randomized trees (ET) model; (

**b**) scatter chart illustrating the relationship between predicted and actual energy consumption.

**Figure 5.**Violin plot showing probability distribution shapes for ET model during different testing hours, with quartiles and median indicated.

Input/Output Variables | Min | Max | Mean | Median |
---|---|---|---|---|

Outdoor air temperature (°C) | −5.5 | 40.5 | 14.65 | 13 |

Dew point air temperature (°C) | −12 | 20 | 4.84 | 5 |

Outdoor air Relative Humidity (%) | 7.95 | 100 | 58.69 | 58.53 |

Wind speed (mph) | 0 | 33.65 | 6.35 | 4.6 |

No. of rooms booked (-) | 23 | 111 | 79.50 | 83 |

No of guests (-) | 40 | 201 | 124.71 | 127 |

HVAC hourly energy consumption (kWh) | 9.3 | 167.8 | 47.78 | 40.2 |

Decision Variable | Possible Values |
---|---|

Number of hidden layer neurons | [5, 10, 20, 30] |

Number of hidden layers | [1, 5, 10, 20, 50] |

Epochs | [150, 200, 500, 1000, 2000] |

Learning Rate | [0.005, 0.05, 0.01] |

Momentum | [0.95, 0.99, 0.995] |

Activation function | [’VlReLu’, ’Sigmoid’, ’Linear’, ’ReLu’] |

Bias | [−4.0, −3.0, −2.0, −1.0, 0.0, 1.0] |

Model Inputs | [[ 1, 1, 1, 2], [1, 1, 1, 24], [24, 24, 1, 24]] |

Model Inputs | Number of Neurons | Activation Function | Number of Layers | Training Epochs | Bias | Learning Rate | Momentum | R^{2} | NRMSE (%) |
---|---|---|---|---|---|---|---|---|---|

$[24,24,1,24]$ | $30$ | ReLu | 1 | 150 | $-3.0$ | $0.01$ | $0.95$ | 0.84 | $6.007$ |

$[1,1,1,24]$ | $20$ | VlReLu | 1 | 500 | $-3.0$ | $0.05$ | $0.95$ | 0.8492 | $6.008$ |

$[1,1,1,24]$ | $10$ | Linear | 1 | 500 | $-3.0$ | $0.05$ | $0.95$ | 0.8490 | $6.011$ |

$[1,1,1,24]$ | $10$ | Linear | 1 | 500 | $1.0$ | $0.05$ | $0.95$ | 0.8490 | $6.013$ |

$[1,1,1,24]$ | $5$ | Linear | 1 | 500 | $-3.0$ | $0.05$ | $0.95$ | 0.8489 | $6.014$ |

$[1,1,1,24]$ | $20$ | VlReLu | 50 | 1000 | $-2.0$ | $0.005$ | $0.95$ | 0.8484 | $6.024$ |

$[1,1,1,24]$ | $5$ | VlReLu | 1 | 1000 | $-3.0$ | $0.05$ | $0.95$ | 0.8482 | $6.028$ |

$[1,1,1,24]$ | $5$ | Linear | 50 | 1000 | $-2.0$ | $0.005$ | $0.95$ | 0.8482 | $6.029$ |

$[1,1,1,24]$ | $20$ | Linear | 20 | 500 | $-1.0$ | $0.005$ | $0.95$ | 0.8481 | $6.029$ |

$[1,1,1,24]$ | $10$ | VlReLu | 1 | 1000 | $-3.0$ | $0.05$ | $0.95$ | 0.8481 | $6.030$ |

$[1,1,1,24]$ | $5$ | VlReLu | 50 | 2000 | $-2.0$ | $0.05$ | $0.95$ | 0.8481 | $6.030$ |

Model Inputs | Number of Neurons | Activation Function | Number of Layers | Training Epochs | Bias | Learning Rate | Momentum | R^{2} | NRMSE (%) |
---|---|---|---|---|---|---|---|---|---|

$[1,1,1,2]$ | 10 | VlReLu | 1 | 1000 | $0.0$ | $0.05$ | $0.95$ | $0.8444$ | $6.10$ |

$[1,1,1,2]$ | 10 | ReLu | 1 | 150 | $-2.0$ | $0.05$ | $0.99$ | $0.8416$ | $6.16$ |

$[1,1,1,2]$ | 30 | VlReLu | 1 | 200 | $-4.0$ | $0.05$ | $0.95$ | $0.8431$ | $6.13$ |

$[1,1,1,24]$ | 5 | Linear | 1 | 500 | $-3.0$ | $0.05$ | $0.95$ | $0.8489$ | $6.014$ |

$[1,1,1,24]$ | 5 | Linear | 1 | 200 | $-2.0$ | $0.005$ | $0.95$ | $0.8445$ | $6.10$ |

$[1,1,1,24]$ | 5 | ReLu | 1 | 1000 | $1.0$ | $0.01$ | $0.95$ | $0.8425$ | $6.14$ |

C | R^{2} (–) | RMSE (kWh) | MAE (kWh) |
---|---|---|---|

${2}^{-7}$ | −0.336 | 12.501 | 10.601 |

${2}^{-6}$ | −0.307 | 12.362 | 10.448 |

${2}^{-5}$ | −0.259 | 12.132 | 10.188 |

${2}^{-4}$ | −0.176 | 11.726 | 9.752 |

${2}^{-3}$ | 0.021 | 10.700 | 8.795 |

${2}^{-2}$ | 0.380 | 8.518 | 6.912 |

${2}^{-1}$ | 0.670 | 5.926 | 4.658 |

${2}^{0}$ | 0.801 | 4.821 | 3.644 |

${2}^{1}$ | 0.829 | 4.472 | 3.316 |

${2}^{2}$ | 0.839 | 4.343 | 3.188 |

${2}^{3}$ | 0.843 | 4.288 | 3.123 |

${2}^{4}$ | 0.844 | 4.274 | 3.102 |

${2}^{5}$ | 0.844 | 4.269 | 3.091 |

${2}^{6}$ | 0.844 | 4.268 | 3.088 |

${2}^{7}$ | 0.844 | 4.269 | 3.087 |

$\mathit{\u03f5}$ | R^{2} (–) | RMSE (kWh) | MAE (kWh) |
---|---|---|---|

${2}^{-10}$ | 0.84427 | 4.2675 | 3.0924 |

${2}^{-9}$ | 0.84428 | 4.2673 | 3.0922 |

${2}^{-8}$ | 0.84429 | 4.2671 | 3.0920 |

${2}^{-7}$ | 0.84427 | 4.2674 | 3.0922 |

${2}^{-6}$ | 0.84421 | 4.2682 | 3.0928 |

${2}^{-5}$ | 0.84416 | 4.2690 | 3.0927 |

${2}^{-4}$ | 0.84418 | 4.2686 | 3.0916 |

${2}^{-3}$ | 0.84426 | 4.2675 | 3.0903 |

${2}^{-2}$ | 0.84453 | 4.2639 | 3.0881 |

${2}^{-1}$ | 0.84467 | 4.2619 | 3.0849 |

${2}^{0}$ | 0.84477 | 4.2606 | 3.0877 |

${2}^{1}$ | 0.84536 | 4.2525 | 3.0896 |

${2}^{2}$ | 0.84027 | 4.3219 | 3.2041 |

${2}^{3}$ | 0.79878 | 4.8508 | 3.8013 |

${2}^{4}$ | 0.55341 | 7.2267 | 6.1642 |

${2}^{5}$ | −0.44957 | 13.0200 | 11.2723 |

${\mathit{n}}_{\mathbf{min}}$ | R^{2} (–) | RMSE (kWh) | MAE (kWh) |
---|---|---|---|

2 | 0.819 | 4.601 | 3.405 |

3 | 0.822 | 4.564 | 3.377 |

5 | 0.828 | 4.485 | 3.312 |

7 | 0.832 | 4.427 | 3.266 |

10 | 0.837 | 4.372 | 3.223 |

K | R^{2} (–) | RMSE (kWh) | MAE (kWh) |
---|---|---|---|

1 | 0.7485 | 5.423 | 4.200 |

2 | 0.8091 | 4.724 | 3.555 |

3 | 0.8226 | 4.555 | 3.385 |

4 | 0.8246 | 4.529 | 3.353 |

5 | 0.8219 | 4.564 | 3.377 |

**Table 9.**Results of different ${d}_{\mathrm{max}}$, where ${n}_{\mathrm{min}}$ = 3, K = 4 and M = 1000.

${\mathit{d}}_{\mathbf{max}}$ | R^{2} (–) | RMSE (kWh) | MAE (kWh) |
---|---|---|---|

1 | −0.3242 | 12.445 | 10.578 |

3 | 0.5323 | 7.396 | 6.128 |

5 | 0.7629 | 5.265 | 4.199 |

7 | 0.8281 | 4.484 | 3.413 |

9 | 0.8424 | 4.292 | 3.184 |

10 | 0.8427 | 4.288 | 3.167 |

15 | 0.8353 | 4.389 | 3.227 |

20 | 0.8262 | 4.508 | 3.331 |

**Table 10.**Comparison of extremely randomized trees (ET), support vector regression (SVR) and deep highway network (DHN) models.

Model | Training Dataset | Testing Dataset | ||
---|---|---|---|---|

RMSE (kWh) | R^{2} (–) | RMSE (kWh) | MAE (kWh) | |

ET | 4.284 | 0.8427 | 4.288 | 3.167 |

SVR | 4.252 | 0.8453 | 4.253 | 3.090 |

DHN | 3.087 | 0.8491 | 4.200 | 3.027 |

Factor/Variable | Actual E.C. Data | DHN | ET | SVR |
---|---|---|---|---|

Mean | 37.08 | 37.16 | 37.48 | 37.09 |

Median | 35.2 | 35.46 | 35.88 | 35.68 |

Standard Deviation | 10.82 | 9.88 | 9.51 | 9.82 |

Sample Variance | 116.98 | 97.68 | 90.51 | 96.51 |

Kurtosis | 1.14 | 0.62 | 1.10 | 0.97 |

Skewness | 0.96 | 0.82 | 0.93 | 0.88 |

Range | 69.90 | 64.30 | 58.25 | 63.88 |

Minimum | 17.2 | 16.84 | 22.87 | 18.31 |

Maximum | 87.1 | 81.14 | 81.12 | 82.19 |

Sum | 121,981.7 | 122,245.60 | 123,308.75 | 122,015.85 |

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**MDPI and ACS Style**

Ahmad, M.W.; Mouraud, A.; Rezgui, Y.; Mourshed, M. Deep Highway Networks and Tree-Based Ensemble for Predicting Short-Term Building Energy Consumption. *Energies* **2018**, *11*, 3408.
https://doi.org/10.3390/en11123408

**AMA Style**

Ahmad MW, Mouraud A, Rezgui Y, Mourshed M. Deep Highway Networks and Tree-Based Ensemble for Predicting Short-Term Building Energy Consumption. *Energies*. 2018; 11(12):3408.
https://doi.org/10.3390/en11123408

**Chicago/Turabian Style**

Ahmad, Muhammad Waseem, Anthony Mouraud, Yacine Rezgui, and Monjur Mourshed. 2018. "Deep Highway Networks and Tree-Based Ensemble for Predicting Short-Term Building Energy Consumption" *Energies* 11, no. 12: 3408.
https://doi.org/10.3390/en11123408