A data-driven methodology to predict thermal behavior of residential buildings using piecewise linear models

doi:10.1016/j.jobe.2020.101523

Journal of Building Engineering

Volume 32, November 2020, 101523

https://doi.org/10.1016/j.jobe.2020.101523 Get rights and content

Highlights

•
Development of a new model based on the data driven method.
•
.The paper conducts a comprehensive review of data-driven modeling.
•
.Data-driven models as ARX, indexed ARX and NARX are critically compared.
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.Methods for model identification and sensitivity analysis are summarized.
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The developed model is validated using on-site data.

Abstract

Nowadays, data-driven approaches are a good way to estimate very efficient black box models for different engineering systems. This class of model is well recognized by its outstanding performances to describe the overall behavior of one system based on its input-output relationships without any physical knowledge. In the context of building modeling, this approach is particularly well suited to predict future temperatures or energy consumption in a building. This paper presents an innovative method that uses input-output data to establish reliable and suitable thermal behavior models for residential buildings, especially for existing buildings where only measurements are available and no numerical models are at the disposal of the facility managers. The main paper contributions consist in the design of a new methodology based on the adaptation of a switched model estimation technique and in its validation to model accurately building thermal behaviors. The paper describes different stages needed to reproduce faithfully complex behaviors: data collection, PieceWise affine Auto-Regressive eXogenous (PWARX) identification technique, sensitivity analysis … It also explains how the procedure and the data-driven estimation algorithm are efficient in extracting sub-model parameters and sequence that give an outstanding ability to reproduce thermal dynamics of buildings, requiring the only collection of available data. The effectiveness of our methodology is discussed through experiments on different buildings located in the North of France. Indeed, through a comparative study between the piecewise ARX model and other existing models such as nonlinear ARX, indexed ARX and ARX models, the PWARX model gives good results in terms of indoor temperature estimation with $78.48 %$ accuracy.

Introduction

Control of energy consumption continues to be the primary concern in all areas of research [9,11,16]. Indeed, the optimization of energy consumption allows for improving the energy performance of the building. Furthermore, to design a set of optimal control, a thermal dynamics modeling step is necessary [20]. However, this task is complicated due to various factors influencing the thermal behavior, particularly by Refs. [19]: (i) climate, (ii) building envelope, (iii) building services and energy systems, (iv) building operation and maintenance, (v) occupant activities and behavior and (vi) indoor environmental quality provided.

Having an accurate thermal model plays a vital role in improving prediction and evaluating energy performance. In the literature, three main categories of modeling approaches have been considered [32]:

•
white box models which are based on physical knowledge of the system and thermal balance equations. These are often obtained through energy simulation software like EnergyPlus [4], TRNSYS [10], etc;
•
black box models which use only measured input/output data and statistical estimation methods (e.g. Ref. [24,26]);
•
grey box models, a mix of the first two categories above. They use input/output data as well as some a priori knowledge on system. A popular grey-box model is the equivalent RC networks [24,34,36].

A comparative study between these different models was done in Ref. [1]. The main conclusions of this study are that: (i) the use of white box model often requires important set-up and computation time; (ii) it also involves a large number of inputs to define the model, such as the composition of the building envelope for example [13]. In some studies, it is difficult, if not impossible, to recover this input [30]. To overcome this problem, data-driven methods have emerged in building framework. We find from the literature that the most commonly used data-driven techniques for building thermal modeling and energy performances prediction are based on the ARX (AutoRegressive eXogeneous) model [21,31]. However, despite its performances, such as quick implementation, a good accuracy …, this model has important limits, mainly due to the estimation of a unique thermal model. A unique model may not consider dynamic changes due to usages, equipment configurations or external factors, such as wind and solar radiation, that influence the thermal dynamics of the building.

Today, we can find several data-driven models derived from the ARX model. One can read the following references for further information [2,15,17,22,27,29,37]. Each of them is mainly differentiated by the parameter estimation techniques and the structure of the model. For instance, in Refs. [22], the authors tested the Fractional order Auto-Regression with eXogenous variable (FARX) model on building integrated energy systems. The model has been validated using the input-output data retrieve of a residential building simulated with software IES $<$ VE $>$ . As a result, it has been shown that the FARX model gives better accuracy than ARX one. Also, the results in Ref. [27,35] show that the Non-linear ARX (NARX) model performance was significantly greater than the one of ARX model. However, each technique has its own advantages and inconveniences, and one of our motivation is to discuss on how to recover the best data-driven model structure for simulating the thermal behavior of the building. Issues that one may remark into the following papers [1,22,33,37]. The first response to this discussion has been presented in Ref. [17] where the best prediction method includes a combination of two separate time-indexed ARX models to improve the prediction accuracy of the cooling load over different forecasting periods. In the following, we will also contribute to this discussion by making a comparison of existing ARX-derived techniques.

In this paper, a black-box identification approach by means of a PieceWise affine auto-Regressive eXogenous (PWARX) model will be developed in the framework of building thermal modeling. This new methodology takes profit from recent advances in the hybrid system identification community. Hybrid and PWARX systems are heterogeneous dynamic systems that combine simultaneously continuous and discrete dynamics. These systems are helpful to introduce expert knowledge in the data-driven models, especially when various behaviors or uses have to be explained. They can be represented by switching models, i.e. by a set of continuous-submodels indexed by a discrete mode or a specific building management system setting. However, the idea of using partially observed regime switching models for building thermal modeling has not received satisfactory solutions apart from a few attempts which do not combine real world learning applications such as: missing data, dependent time series and noisy observations, see Ref. [14,28]. Also, these works mainly highlight the necessity of using different models to represent different sorts of dynamics in a building. It was argued too in Ref. [2] and has been proved in the context of the prediction of buildings energy consumption into [3]. Then, the purpose of this paper will be to highlight the interest of using PWARX systems to model building thermal dynamics, in its 3 aspects: presentation of its scientific foundations, with regard to conventional ARX techniques; discussion around its interest to give explanations on different thermal dynamics; experimental comparison of the results obtained with different state-of-the-art methods.

Besides, this paper also discusses the selection of suitable inputs to define the best model structure. This will be done by performing sensitivity analysis and testing several configurations. This step aims to state on the influence of each input on the accuracy of the model and on the quality of identified parameters. Thus, the PWARX model should be able to explain the true thermal and energy behaviors of the building by identifying the use scenarios. Finally, the effectiveness of our methodology will be shown by presenting thermal modeling results for different building architecture located in the north of France. In particular, we assess the performance of our model through a comparative study between the piecewise ARX model and other existing models such as nonlinear ARX, indexed ARX and ARX models.

The rest of the paper is organized as follows. The formal definitions of the ARX model and its derivatives, as well as PWARX model are introduced in Section 2. The system identification technique used to identify and validate the PWARX model is detailed in Section 3. To illustrate the effectiveness of the proposed method, experimental results obtained from a student residential are provided in Section 4. Finally, conclusions and further works are given in Section 5.

Section snippets

ARX model

Let us first consider an ARX model, using an input/output ( $y, u$ ) representation, writing as follows: $y (t) = - a_{1} y (t - 1) - \dots - a_{n_{a}} y (t - n_{a}) + b_{1} u (t - 1) + \dots + b_{n_{b}} u (t - n_{b}) + e (t)$ where $n_{a}$ and $n_{b}$ are the model order, $a_{i}$ and $b_{i}$ are the model coefficients, and $e (t) \in R^{n_{e}}$ is a white noise process. In other terms, the ARX model can be defined by the following relations: $A (z) y (t) = B (z) u (t) + e (t)$ with $A (z) = 1 + a_{1} z^{- 1} + \dots + a_{n_{a}} z^{- n_{a}}$ and $B (z) = b_{1} z^{- 1} + \dots + b_{n_{b}} z^{- n_{b}}$ where z is a backward shift operator.

So, for available input measurements, we can

PWARX thermal model identification methodology

Iin this paper, we present an original data-based method to identify and estimate a set of models that are able to reproduce the variety of building thermal behaviors (Fig. 2). So, to estimate all parameters of the PWARX model, we adopt an identification procedure defined by the following steps. Firstly, we design the experiment and the system necessary to collect the data. Then, we acquire some measurements from different room parts, without requesting specific usages or functioning

Case studies

To show the effectiveness of our methodology, experiments on the Lavoisier student residential building, located in Douai, in the north of France (Fig. 6) have been made.

The total area of the building is approximately $3500 m^{2}$ and it is subdivided into 2 sub-building parts. The first part is composed by 4 floors and the second one by 5 floors. Each floor has respectively for each sub-building 10 and 32 rooms of $11 m^{2}$ with a double glazed window size ( $135 c m \times 110 c m$ ). Notice that for this building,

Conclusions

In this paper, we present a novel methodology for modeling the thermal behavior of residential buildings by using the PWARX model. The identification procedure is detailed to obtain the model and its parameters. Also, several analyses have been conducted to have a suitable structure for the model, as well as to validate it. The first of them is the sensitivity analysis which is necessary to determine what inputs will be required in order to guarantee the accuracy of the model and the quality of

CRediT authorship contribution statement

M.H. Benzaama: Data curation, Software, Writing - original draft, Validation, Investigation, Formal analysis. L.H. Rajaoarisoa: Data curation, Software, Writing - original draft, Validation, Investigation, Formal analysis, Project administration. B. Ajib: Software. S. Lecoeuche: Methodology, Formal analysis, Software, Writing - original draft, Supervision, Project administration.

Declaration of competing interest

None.

Acknowledgements

This work was supported by the European project “SHINE: Sustainable Houses in Inclusive Neighborhoods”. A project granted by Interreg 2 Seas and the European Regional Development Fund.

References (37)

A. Al-janabi et al.
Comparison of energyplus and ies to model a complex university building using three scenarios: free-floating, ideal air load system, and detailed
J. Build. Eng.
(2019)
K. Amasyali et al.
A review of data driven building energy consumption prediction studies
Renew. Sustain. Energy Rev.
(2018)
M. Benzaama et al.
Investigation of the thermal behavior of a combined geothermal system for cooling with regards to Algeria's climate
Sustain. Cities Soc.
(2018)
D. Bond et al.
Configuring wall layers for improved insulation performance
Appl. Energy
(2013)
D. Crawley et al.
Contrasting the capabilities of building energy performance simulation programs
Build. Environ.
(2008)
P. Fazenda et al.
Context based thermodynamic modeling of buildings spaces
Energy Build.
(2016)
F. Ferracuti et al.
Data-driven models for short-term thermal behaviour prediction in real buildings
Appl. Energy
(2017)
P. Gori et al.
Design criteria for improving insulation effectiveness of multilayer walls
Int. J. Heat Mass Tran.
(2016)
Y. Guo et al.
Hourly cooling load forecasting using time-indexed arx models with two-stage weighted least squares regression
Energy Convers. Manag.
(2014)
K. Liu et al.
The re-optimization strategy of multi-layer hybrid building's cooling and heating load soft sensing technology research based on temperature interval and hierarchical modeling techniques
Sustain. Cities Soc.
(2018)

J. Massana et al.

Identifying services for short-term load forecasting using data driven models in a smart city platform

Sustain. Cities Soc.

(2017)

M. Paulus et al.

Algorithm for automating the selection of a temperature dependent change point model

Energy Build.

(2015)

T. Reddy et al.

Using synthetic data to evaluate multiple regression and principal component analysis for statistical modeling of daily building energy consumption

Energy Build.

(1994)

S. Royer et al.

A procedure for modeling buildings and their thermal zones using co-simulation and system identification

Energy Build.

(2014)

R. Sarwar et al.

Field validation study of a time and temperature indexed autoregressive with exogenous (arx) model for building thermal load prediction

Energy Build.

(2017)

J. Siroky et al.

Experimental analysis of model predictive control for an energy efficient building heating system

Appl. Energy

(2011)

M. Soleimani-Mohseni et al.

Estimation of operative temperature in buildings using artificial neural networks

Energy Build.

(2006)

S. Wang et al.

Simplified building model for transient thermal performance estimation using ga-based parameter identification

Int. J. Therm. Sci.

(2006)

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A data-driven methodology to predict thermal behavior of residential buildings using piecewise linear models

Highlights

Abstract

Introduction

Section snippets

ARX model

PWARX thermal model identification methodology

Case studies

Conclusions

CRediT authorship contribution statement

Declaration of competing interest

Acknowledgements

J. Build. Eng.

Renew. Sustain. Energy Rev.

Sustain. Cities Soc.

Appl. Energy

Build. Environ.

Energy Build.

Appl. Energy

Int. J. Heat Mass Tran.

Energy Convers. Manag.

Sustain. Cities Soc.

Sustain. Cities Soc.

Energy Build.

Energy Build.

Energy Build.

Energy Build.

Appl. Energy

Energy Build.

Int. J. Therm. Sci.