# Building Energy Models at Different Time Scales Based on Multi-Output Machine Learning

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## Abstract

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## 1. Introduction

_{2}emissions [1]. The energy use of the construction industry has a significant impact on the environment and the economy. Hence, it is important to reduce the energy use of buildings reasonably and efficiently [2,3]. The key to building energy conservation is to accurately compute building energy use, so as to formulate a reasonable energy conservation plan according to the characteristics of energy use [4,5].

- (1)
- This study compares the predictive performance of single-output and multi-output learning models in building energy analysis. This would provide guidelines on how to choose the single-output and multi-output models in creating machine learning models for building energy assessment.
- (2)
- This study explores the performance of two multi-output models (BASS and DNN) in which the main difference of the two models is whether to maintain output correlation. This would provide the guidelines on how to choose the learning models with or without considering output correlation.
- (3)
- The additive or accumulative features are investigated in creating various time scale models for building energy analysis. This would provide insight on the methods of obtaining building energy use from a smaller time scale to a larger time scale.

## 2. Method

#### 2.1. Data Preparation

^{2}. The fan coil unit is set to provide ventilation, heating, and cooling for the building. The air-cooled chiller and gas boiler provide cold water and hot water, respectively [29]. The internal heat gain schedule of the building is derived from the China national standards of buildings [30]. The building used in this research is located in Tianjin, China. Therefore, the meteorological data of Tianjin in the Chinese standard weather data (CSWD) is used for the calculation of the building energy model.

#### 2.2. Multi-Output Models

#### 2.3. Performance Evaluation

^{2}(coefficient of determination). The calculation formulas for these three indicators are as follows:

^{th}sample, ${y}_{i}$ represents the i

^{th}true value, and ${\widehat{y}}_{i}$ represents the i

^{th}predicted value. The CV(RMSE), MAPE, and R² values are all dimensionless numbers, which are not affected by the order of magnitude of the data and can more effectively express the accuracy of the model. CV(RMSE) and MAPE reflect the error of the model–the smaller, the better. The value of R² ranges from 0 to 1, which reflects the relative error of the model relative to the direct average value. The closer to 1, the better.

## 3. Results and Discussion

#### 3.1. Results of Model Hyperparameter Tuning

#### 3.2. Results of Multi-Output Cooling Energy Models

#### 3.2.1. Daily Cooling Energy Models

^{2}) are very high, except for three data points in SO-BASS. Most of the R

^{2}values are l greater than 0.9 to indicate that all these four models have good performance. Among them, the two models with the largest R

^{2}are MO-BASS and SO-DNN. Further comparison of the median and interquartile range shows that the R² from the MO-BASS model is larger than that of SO-DNN. From the above analysis, the MO-BASS model is the best daily cooling energy model in this case study.

#### 3.2.2. Monthly Cooling Energy Models

#### 3.2.3. Multi-Time Scale Cooling Energy Models

#### 3.2.4. Performance Analysis of 10 Models for Monthly and Annual Cooling Energy

^{2}. The SOB-M performs better than the SOB-D and the MOB-M has better predictive capability compared to the MOB-D. The multi-time scale BASS model has very good performance compared to the monthly and daily BASS models for cooling energy prediction. As for the DNN models, the best prediction model of cooling energy is the monthly summation from the daily SOD-D models. The multi-time scale MOD-Mu model has moderate performance compared to the other four DNN models. The BASS models have better prediction performance in comparison with the DNN models for monthly cooling energy. All the R

^{2}values for the BASS models are above 0.99, which indicates that the BASS has very high predictive capability for monthly cooling energy.

^{2}values, above 0.997. The worst model is the single-out monthly DNN models (SOD-M), in which the CV(RMSE), MAPE, and R² values are 0.016, 0.013, and 0.970, respectively. The remaining nine models’ CV(RMSE) values are less than 0.008, MAPE values less than 0.0078, and R² values greater than 0.995, indicating that these models have good predictive performance.

#### 3.3. Results of Multi-Output Heating Energy Models

#### 3.3.1. Daily Heating Energy Models

#### 3.3.2. Monthly Heating Energy Models

#### 3.3.3. Multi-Time Scale Heating Energy Models

#### 3.3.4. Performance Analysis of Ten Models for Monthly and Annual Heating Energy

^{2}values–close to 1. The following two models are single-output monthly BASS models (SOB-M) and single-output daily DNN models (SOD-D). The remaining three models do not have good predictive performance compared to the other seven models. The multi-output models have better performance compared to the single-output models for monthly heating energy.

#### 3.4. Guide and Application of Building Multi-Output Energy Models

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ANN | artificial neural network |

BASS | Bayesian adaptive spline surface |

BIPV | building integrated photovoltaic |

BMARS | Bayesian multivariate adaptive regression splines |

CSP | cooling set-point |

CSWD | Chinese standard weather data |

CV(RMSE) | coefficient of variation of the root mean square error |

DNN | deep neural network |

DT | decision tree |

ENMIM | ensemble model named evolutionary neural machine inference model |

EPD | equipment power density |

EWU | exterior wall U-value |

GA-NMM | genetic algorithm-based numerical moment matching |

GB | gradient boosting |

HSP | heating set-point |

HVAC | heating, ventilation, and air conditioning |

INF | infiltration rate |

KNN | K-nearest neighbor |

lightGBM | light gradient boosting machine |

LPD | lighting power density |

LR | linear regression |

LSSVR | least squares support vector regression |

MAPE | mean absolute percentage error |

MARS | multivariate adaptive regression splines |

MIMO | multi-input multi-output |

MO | multiple outputs |

OPD | occupancy density |

PCA | principal component analysis |

PCC | Pearson’s correlation coefficient |

PV | photovoltaic |

R² | coefficient of determination |

RBFNN | radial basis function neural network |

RF | random forest |

RU | roof U-value |

SARIMA | seasonal autoregressive integrated moving average |

SHGC | solar heat gain coefficient |

SO | single output |

SVM | support vector machine |

WU | window U-value |

## References

- UN Environment Programme (UNEP). 2021 Global Status Report for Buildings and Construction; UNEP: Nairobi, Kenya, 2021. [Google Scholar]
- Zhang, Y.; Teoh, B.K.; Wu, M.; Chen, J.; Zhang, L. Data-driven estimation of building energy consumption and GHG emissions using explainable artificial intelligence. Energy
**2023**, 262, 125468. [Google Scholar] [CrossRef] - Al-Shargabi, A.A.; Almhafdy, A.; Ibrahim, D.M.; Alghieth, M.; Chiclana, F. Buildings’ energy consumption prediction models based on buildings’ characteristics: Research trends, taxonomy, and performance measures. J. Build. Eng.
**2022**, 54, 104577. [Google Scholar] [CrossRef] - Guo, Y.-Y. Revisiting the building energy consumption in China: Insights from a large-scale national survey. Energy Sustain. Dev.
**2022**, 68, 76–93. [Google Scholar] [CrossRef] - Mohapatra, S.K.; Mishra, S.; Tripathy, H.K.; Alkhayyat, A. A sustainable data-driven energy consumption assessment model for building infrastructures in resource constraint environment. Sustain. Energy Technol. Assess.
**2022**, 53, 102697. [Google Scholar] [CrossRef] - Fathi, S.; Srinivasan, R.; Fenner, A.; Fathi, S. Machine learning applications in urban building energy performance forecasting: A systematic review. Renew. Sustain. Energy Rev.
**2020**, 133, 110287. [Google Scholar] [CrossRef] - Zhang, L.; Wen, J.; Li, Y.; Chen, J.; Ye, Y.; Fu, Y.; Livingood, W. A review of machine learning in building load prediction. Appl. Energy
**2021**, 285, 116452. [Google Scholar] [CrossRef] - Lei, L.; Chen, W.; Wu, B.; Chen, C.; Liu, W. A building energy consumption prediction model based on rough set theory and deep learning algorithms. Energy Build.
**2021**, 240, 110886. [Google Scholar] [CrossRef] - Liu, Y.; Chen, H.; Zhang, L.; Wu, X.; Wang, X.-J. Energy consumption prediction and diagnosis of public buildings based on support vector machine learning: A case study in China. J. Clean. Prod.
**2020**, 272, 122542. [Google Scholar] [CrossRef] - Alobaidi, M.H.; Chebana, F.; Meguid, M.A. Robust ensemble learning framework for day-ahead forecasting of household based energy consumption. Appl. Energy
**2018**, 212, 997–1012. [Google Scholar] [CrossRef] [Green Version] - Wang, Z.; Hong, T.; Li, H.; Piette, M.A. Predicting city-scale daily electricity consumption using data-driven models. Adv. Appl. Energy
**2021**, 2, 100025. [Google Scholar] [CrossRef] - Jetcheva, J.G.; Majidpour, M.; Chen, W.-P. Neural network model ensembles for building-level electricity load forecasts. Energy Build.
**2014**, 84, 214–223. [Google Scholar] [CrossRef] - Ferrantelli, A.; Kuivjogi, H.; Kurnitski, J.; Thalfeldt, M. Office Building Tenants’ Electricity Use Model for Building Performance Simulations. Energies
**2020**, 13, 5541. [Google Scholar] [CrossRef] - Wang, W.; Hong, T.; Xu, X.; Chen, J.; Liu, Z.; Xu, N. Forecasting district-scale energy dynamics through integrating building network and long short-term memory learning algorithm. Appl. Energy
**2019**, 248, 217–230. [Google Scholar] [CrossRef] [Green Version] - Tran, D.-H.; Luong, D.-L.; Chou, J.-S. Nature-inspired metaheuristic ensemble model for forecasting energy consumption in residential buildings. Energy
**2020**, 191, 116552. [Google Scholar] [CrossRef] - Tian, W.; Yang, S.; Li, Z.; Wei, S.; Pan, W.; Liu, Y. Identifying informative energy data in Bayesian calibration of building energy models. Energy Build.
**2016**, 119, 363–376. [Google Scholar] [CrossRef] - Zhu, C.; Tian, W.; Yin, B.; Li, Z.; Shi, J. Uncertainty calibration of building energy models by combining approximate Bayesian computation and machine learning algorithms. Appl. Energy
**2020**, 268, 115025. [Google Scholar] [CrossRef] - Koschwitz, D.; Frisch, J.; van Treeck, C. Data-driven heating and cooling load predictions for non-residential buildings based on support vector machine regression and NARX Recurrent Neural Network: A comparative study on district scale. Energy
**2018**, 165, 134–142. [Google Scholar] [CrossRef] - Jahani, E.; Cetin, K.; Cho, I.H. City-scale single family residential building energy consumption prediction using genetic algorithm-based Numerical Moment Matching technique. Build. Environ.
**2020**, 172, 106667. [Google Scholar] [CrossRef] - Lin, Q.; Liu, K.; Hong, B.; Xu, X.; Chen, J.; Wang, W. A data-driven framework for abnormally high building energy demand detection with weather and block morphology at community scale. J. Clean. Prod.
**2022**, 354, 131602. [Google Scholar] [CrossRef] - Olu-Ajayi, R.; Alaka, H.; Sulaimon, I.; Sunmola, F.; Ajayi, S. Building energy consumption prediction for residential buildings using deep learning and other machine learning techniques. J. Build. Eng.
**2022**, 45, 103406. [Google Scholar] [CrossRef] - Tian, W.; Zhu, C.; Sun, Y.; Li, Z.; Yin, B. Energy characteristics of urban buildings: Assessment by machine learning. Build. Simul.
**2020**, 14, 179–193. [Google Scholar] [CrossRef] - Tian, W.; de Wilde, P.; Li, Z.; Song, J.; Yin, B. Uncertainty and sensitivity analysis of energy assessment for office buildings based on Dempster-Shafer theory. Energy Convers. Manag.
**2018**, 174, 705–718. [Google Scholar] [CrossRef] [Green Version] - Wang, L.; Lee, E.W.M.; Hussian, S.A.; Yuen, A.C.Y.; Feng, W. Quantitative impact analysis of driving factors on annual residential building energy end-use combining machine learning and stochastic methods. Appl. Energy
**2021**, 299, 117303. [Google Scholar] [CrossRef] - Singh, M.; Sharston, R. Quantifying the dualistic nature of urban heat Island effect (UHI) on building energy consumption. Energy Build.
**2022**, 255, 111649. [Google Scholar] [CrossRef] - Luo, X.J.; Oyedele, L.O.; Ajayi, A.O.; Akinade, O.O. Comparative study of machine learning-based multi-objective prediction framework for multiple building energy loads. Sustain. Cities Soc.
**2020**, 61, 102283. [Google Scholar] [CrossRef] - Liu, J.; Zhang, Q.; Dong, Z.; Li, X.; Li, G.; Xie, Y.; Li, K. Quantitative evaluation of the building energy performance based on short-term energy predictions. Energy
**2021**, 223, 120065. [Google Scholar] [CrossRef] - Li, G.; Li, F.; Ahmad, T.; Liu, J.; Li, T.; Fang, X.; Wu, Y. Performance evaluation of sequence-to-sequence-Attention model for short-term multi-step ahead building energy predictions. Energy
**2022**, 259, 124915. [Google Scholar] [CrossRef] - U.S. Department of Energy. EnergyPlus V22.1.0; U.S.Department of Energy: Washington, DA, USA, 2021.
- MOHURD (Ministry of Housing and Urban-Rural Development). China, Energy-Saving Design Standards for Public Buildings; China Building Industry Press: Beijing, China, 2015. [Google Scholar]
- MOHURD (Ministry of Housing and Urban-Rural Development). China, Technical Standards for Near-Zero Energy Buildings; China Building Industry Press: Beijing, China, 2019. [Google Scholar]
- Francom, D.; Sansó, B. BASS: An R Package for Fitting and Performing Sensitivity Analysis of Bayesian Adaptive Spline Surfaces. J. Stat. Softw.
**2020**, 94, 1–36. [Google Scholar] [CrossRef] - An, N.; Zhao, W.; Wang, J.; Shang, D.; Zhao, E. Using multi-output feedforward neural network with empirical mode decomposition based signal filtering for electricity demand forecasting. Energy
**2013**, 49, 279–288. [Google Scholar] [CrossRef] - Cohen-Addad, V.; Kanade, V.; Mallmann-Trenn, F.; Mathieu, C. Hierarchical Clustering: Objective Functions and Algorithms. J. Acm.
**2019**, 66, 1–42. [Google Scholar] [CrossRef] - Kaminskyy, R.; Shakhovska, N.; Kryvinska, N.; Younas, M. Dendrograms-based disclosure method for evaluating cluster analysis in the IoT domain. Comput. Ind. Eng.
**2021**, 158, 107402. [Google Scholar] [CrossRef] - Varshney, A.K.; Muhuri, P.K.; Lohani, Q.M.D. PIFHC: The Probabilistic Intuitionistic Fuzzy Hierarchical Clustering Algorithm. Appl. Soft Comput.
**2022**, 120, 108584. [Google Scholar] [CrossRef]

**Figure 1.**A flow chart of multi-output models of building energy at daily, monthly, and annual scales based on machine learning.

**Figure 4.**Prediction performance of machine learning models for daily cooling energy (SO, single output; MO, multiple output).

**Figure 5.**Dendrogram of July daily cooling energy for the training set and four machine learning models.

**Figure 7.**Prediction performance of four machine learning models for monthly cooling energy (SO, single output; MO, multiple output).

**Figure 8.**Dendrogram of monthly cooling energy for the training set and four machine learning models.

**Figure 9.**Prediction performance of two machine learning models for multi-time scales cooling energy.

**Figure 10.**Performance of 10 models for monthly cooling energy (refer to Table 4 for model explanation).

**Figure 11.**Performance of 10 models for annual cooling energy (refer to Table 4 for model explanation).

**Figure 12.**Correlation coefficient of daily heating energy in January (2, 2 January; … ; 30, 30 January).

**Figure 13.**Prediction performance of four machine learning models for daily heating energy (SO, single output; MO, multiple output).

**Figure 14.**Dendrogram of January daily heating energy for the training set and four machine learning models.

**Figure 17.**Dendrogram of monthly heating energy for the training set and four machine learning models.

**Figure 18.**Prediction performance of two machine learning models for multi-time scales heating energy.

**Figure 19.**Performance of 10 models for monthly heating energy (refer to Table 4 for model explanation).

**Figure 20.**Performance of 10 models for annual heating energy (refer to Table 4 for model explanation).

No. | Parameters | Short Names | Range | Unit |
---|---|---|---|---|

1 | Exterior wall U-value | EWU | 0.1–0.25 | W/(m^{2}K) |

2 | Roof U-value | RU | 0.15–0.3 | W/(m^{2}K) |

3 | Window U-value | WU | 1–2.4 | W/(m^{2}K) |

4 | Solar heat gain coefficient | SHGC | 0.2–0.48 | - |

5 | Infiltration rate | INF | 0.5–0.8 | ACH |

6 | Lighting power density | LPD | 5–10 | W/m^{2} |

7 | Equipment power density | EPD | 9–15 | W/m^{2} |

8 | Occupancy density | OPD | 9–14 | m^{2}/person |

9 | Heating set-point | HSP | 20–22 | °C |

10 | Cooling set-point | CSP | 24–26 | °C |

Model | Hyperparameters | Daily | Monthly | Multi-Time | |||
---|---|---|---|---|---|---|---|

Cooling | Heating | Cooling | Heating | Cooling | Heating | ||

SO-BASS | degree | 3 | 4 | 4 | - | ||

nmcmc | 10,000 | ||||||

MO-BASS | n.pc | 7 | 10 | 5 | 7 | ||

degree | 3 | 4 | 4 | 3 | |||

nmcmc | 10,000 | ||||||

SO-DNN | activation | tanh,relu,liner | tanh,elu,relu,liner | - | |||

number of hidden layers | 3 | ||||||

output layer neurons | 1 | ||||||

MO-DNN | activation | tanh,elu,relu,liner | |||||

number of hidden layers | 4 | 3 | 4 | ||||

output layer neurons | 105 | 102 | 5 | 111 | 108 |

Models | Daily | Monthly | Multi-Time Scale |
---|---|---|---|

SO-BASS | 2032.2 | 98.7 | - |

MO-BASS | 103.9 | 81.1 | 197.2 |

SO-DNN | 3807.2 | 361.7 | - |

MO-DNN | 137.3 | 72.2 | 236.3 |

Machine Learning | Model | Description |
---|---|---|

BASS | SOB-D | Sum the daily energy from the single-output daily BASS models to obtain the monthly or annual energy |

MOB-D | Sum the daily energy from the multi-output daily BASS models to obtain monthly or annual energy | |

SOB-M | Monthly predictions or annual prediction (sum of monthly predictions) from the single-output monthly BASS models | |

MOB-M | Monthly predictions or annual prediction (sum of monthly predictions) from the multi-output monthly BASS models | |

MOB-Mu | Monthly or annual predictions from the multi-output multi-time scale BASS models | |

DNN | SOD-D | Sum the daily energy from the single-output daily DNN models to obtain the monthly or annual energy |

MOD-D | Sum the daily energy from the multi-output daily DNN models to obtain monthly or annual energy | |

SOD-M | Monthly predictions or annual prediction (sum of monthly predictions) from the single-output monthly DNN models | |

MOD-M | Monthly predictions or annual prediction (sum of monthly predictions) from the multi-output monthly DNN models | |

MOD-Mu | Monthly or annual predictions from the multi-output multi-time scale DNN models |

Model | Daily | Monthly | Multi-Time Scale |
---|---|---|---|

SO-BASS | 2293.0 | 128.8 | - |

MO-BASS | 216.6 | 101.6 | 150.4 |

SO-DNN | 3722.6 | 373.6 | - |

MO-DNN | 69.7 | 65.4 | 165.9 |

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**MDPI and ACS Style**

Li, G.; Tian, W.; Zhang, H.; Chen, B.
Building Energy Models at Different Time Scales Based on Multi-Output Machine Learning. *Buildings* **2022**, *12*, 2109.
https://doi.org/10.3390/buildings12122109

**AMA Style**

Li G, Tian W, Zhang H, Chen B.
Building Energy Models at Different Time Scales Based on Multi-Output Machine Learning. *Buildings*. 2022; 12(12):2109.
https://doi.org/10.3390/buildings12122109

**Chicago/Turabian Style**

Li, Guangchen, Wei Tian, Hu Zhang, and Bo Chen.
2022. "Building Energy Models at Different Time Scales Based on Multi-Output Machine Learning" *Buildings* 12, no. 12: 2109.
https://doi.org/10.3390/buildings12122109