<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In order to solve the problem of the traditional gray prediction model (GM) during determination of the accuracy of buildings’ energy savings and its poor fitting of data, the idea of a fractional model based on the traditional first-order one-variable GM(1,1) model is applied. We use the GM–backpropagation (GM-BP) neural network to solve the optimal fractional order and establish a fractional GM(1,1) model based on the GM-BP neural network. Example calculation shows that the fractional GM(1,1) model can improve the prediction accuracy of buildings’ energy savings, and selecting the optimal order can further improve the prediction accuracy and decrease the error level when using the GM-BP neural network. This work shows that the fractional GM(1,1) model based on the GM-BP neural network has an important guiding role in the energy savings of buildings.</p>
</abstract>

In order to solve the problem of the traditional gray prediction model (GM) during determination of the accuracy of buildings’ energy savings and its poor fitting of data, the idea of a fractional model based on the traditional first-order one-variable GM(1,1) model is applied. We use the GM–backpropagation (GM-BP) neural network to solve the optimal fractional order and establish a fractional GM(1,1) model based on the GM-BP neural network. Example calculation shows that the fractional GM(1,1) model can improve the prediction accuracy of buildings’ energy savings, and selecting the optimal order can further improve the prediction accuracy and decrease the error level when using the GM-BP neural network. This work shows that the fractional GM(1,1) model based on the GM-BP neural network has an important guiding role in the energy savings of buildings.

Energy-saving technology of BIM green buildings using fractional differential equation

Chongqing Vocational Institute of Engineering

Department of Information Technology, Faculty of Computing and Information Technology

Department of Accounting and Finance, Faculty of Administrative Sciences

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

In order to solve the problem of the traditional gray prediction model (GM) during determination of the accuracy of buildings’ energy savings and its poor...

	Building life				Building type
	<2016	2016–2017	2017–2018	>2018	Detached house	Semidetached dwelling	Row house	Villa
Energy-saving rate, %	56	24	17	3	3	12	20	29

Error	GM(1,1) model	GM-BP neural network model

Maximum relative error, absolute value, E_max, %	46.12	0.47
Average relative error, ε_ave, %	7.69	0.08
RMSE (×10⁶)	66.10	1.46

Energy-saving technology of BIM green buildings using fractional differential equation

Published Online: Dec 13, 2021

Page range: 481 - 490

Received: Jun 17, 2021

Accepted: Sep 24, 2021

DOI: https://doi.org/10.2478/amns.2021.2.00085

Keywords
buildings’ energy savings prediction, GM(1,1) model, fractional GM(1,1) model

© 2021 Ya Qin et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

Fig. 3

Energy-saving potential after residential renovation of different years and types of buildings.

Calculation results of the evaluation indexes of each model.

Energy-saving technology of BIM green buildings using fractional differential equation

Published Online: Dec 13, 2021

Page range: 481 - 490

Received: Jun 17, 2021

Accepted: Sep 24, 2021

DOI: https://doi.org/10.2478/amns.2021.2.00085

Keywordsbuildings’ energy savings prediction, GM(1,1) model, fractional GM(1,1) model

© 2021 Ya Qin et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

Fig. 3

Energy-saving potential after residential renovation of different years and types of buildings.

Calculation results of the evaluation indexes of each model.

Keywords
buildings’ energy savings prediction, GM(1,1) model, fractional GM(1,1) model