# A new approach for "Smart Heating"

Améni Makhlouf, Bruno Marhic, Laurent Delahoche, Jean-Baptiste Masson, Hassani Messaoud

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Améni Makhlouf, Bruno Marhic, Laurent Delahoche, Jean-Baptiste Masson, Hassani Messaoud. A new approach for "Smart Heating". 2017 International Conference on Control, Automation and Diagnosis (ICCAD), Jan 2017, Hammamet, Tunisia. 10.1109/ICCAD40157.2017. hal-04322082

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# A new approach for “Smart Heating”

Conference Paper · January 2017

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3 authors, including:

<figure><img src="image_2.png" /><figcaption>Améni Makhlouf</figcaption></figure>

Université de Picardie Jules Verne

4 PUBLICATIONS

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<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /><figcaption>Bruno Marhic</figcaption></figure>

Université de Picardie Jules Verne

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809 CITATIONS

<figure><img src="image_5.png" /></figure>
A new approach for “Smart Heating”

Améni Makhlouf<sup>a,b</sup>, Bruno Marhic<sup>a</sup>, Laurent Delahoche<sup>a</sup>, Jean-Baptiste Masson<sup>a</sup>

<sup>a</sup> Laboratoire des Technologies Innovantes (LTI) EA 3899, Département. Informatique, Avenue des Facultés le Bailly, 80000 Amiens Cedex 1, France.

makhouf.ameni@gmail.com

*Abstract*— This paper presents a heating management algorithm that models and handles uncertainties in buildings, in order to design and produce a temperature trend that will be inserted in the Smart an Predictive Heating System (SPHS). The aim of this system is to reduce energy consumption in the building whilst maintaining a comfortable ambiance for the occupant. In this paper we propose two different mass distribution designs, we compare them and we present and discuss different experimental results in order to show the reliability of our proposed solution.

*Keywords*— Heating management system; belief function theory; mass distribution

# I. Introduction

Works of research aim to develop methods to reduce energy consumption and decrease its cost in the building. In fact, different elements have a direct influence on the heating management systems; amongst them the occupancy, the weather forecast and the thermal comfort. Works of research study these aspects separately for public buildings and residential buildings.

The first aspect that energy management models should consider is the occupancy as it strongly contributes to reducing the building's energy consumption. Some works of research study use the occupancy profile, for example, [1, 2] demonstrate that a personalized occupancy profile on the HVAC start/stop schedule could save up to 9% energy compared to the conventional schedules. In addition, the occupant's activity or user's behavior is as important as the occupancy because it gives indications for the occupancy schedule. Therefore, this research [3] concentrates on studying the occupant's behavior to define occupancy patterns in order to reduce energy consumption in residential buildings. The second aspect is the influence of the weather forecast on buildings, which was the topic for numerous papers. For example, in [4] they developed a model to analyze the thermal performance of a double skin façade with buoyancy-driven airflow. The third aspect is the thermal comfort which is related to the two aspects quoted previously and it cannot be determined if the occupancy state is not clear because we usually try to establish a comfort ambiance when the occupant is at home or before he arrives (preheating period).

Hassani Messaoud<sup>b</sup>

<sup>b</sup>Laboratoire de Recherche en Automatique, Traitement du Signal et Image (LARATSI) LR13ES13, ENIM, Rue Ibn El Jazzar,

5000 Monastir, Tunisia

Different studies integrate different methods to maintain a reasonable thermal comfort state in the building. For example, a new control strategy for commercial buildings is introduced in [6], which aims to maintain internal thermal comfort by regulating the chilled water flow distribution.

A smart building is a building that incorporates smart technology, which refers to automated systems, sensors, building management systems and data gathering devices. To collect information and to process it, we need to use a data fusion algorithm. In fact, different studies on heat management in buildings rely on the fusion of different information provided by the multiple sensors planted in the smart building. For example in [7] they propose an indoor energy and comfort management model based on information fusion using ordered weighted averaging (OWA) aggregation that was associated to a multi-agent building control system with particle swarm optimization (PSO) in order to achieve a high level of comfort with minimum power consumption.

The Dempster-Shafer method has proved its efficiency in different fields despite the risk of generating a conflict mass in the case of numerous and heterogeneous sources of information. In a previous work [8], we proposed an approach based on the Dempster-Shafer theory and we obtained encouraging results; however, since we aggregate heterogeneous and numerous sources we obtain an important conflict mass.

In this paper, we aim to reduce the conflict mass but we didn't use a conflict management algorithm and we didn't reduce the number of sources of information. We tried to contextualize the different mass distributions for certain sources and by doing so we tried to obtain the suitable decision with an acceptable conflict mass. In fact in the current work we will unify the different frames of discernment to reduce the conflict mass even more.

In fact, in different works researchers use the vacuous extension to unify the frames of discernment as in [5] where they use it to obtain the suitable address in the process of address recognition. Our main contribution is to generate the temperature trend to control the SPHS without generating an important conflict mass and the contribution is to demonstrate the flexibility of our algorithm as we test it on realistic scenarios as presented in the simulation section.
This paper is organized as follows: Section 2 briefly introduces the belief theory and the TBM model. In section 3 our approach is explained in detail. Several simulation case studies are presented and discussed in section 4. Finally in section 5 we conclude the paper.

## II. Preliminary notion

### A. Belief function theory

The Dempster-Shafer theory, known as the evidence theory, is a powerful mathematical tool to model and fuse uncertain and inaccurate data. It was introduced by Dempster in 1967 and improved by Shafer in 1976 [13]. The assets of this theory are its flexibility to model the information and its ability to represent the ignorance with a clearer and more efficient method than the probabilistic functions [12].

We define the Frame of Discernment (FoD) $\Omega$ as a set of N hypotheses that represent the exhaustive and exclusive solutions to the problem.

$$ \Omega = \{H_1, H_2, \dots, H_N\} \qquad (1) $$
with $H_i \cap H_j = \emptyset; \forall i, j \in N \text{ and } i \neq j $$

Therefore, we can define the power set $2^\Omega = \{A | A \subseteq \Omega\}$. This set presents the singletons hypothesis and all disjunctions of hypothesis $2^\Omega = \{\emptyset, H_1, \dots, H_N, H_1UH_2, \dots, \Omega\}$. Thus we present the element that characterises the theory of evidence i.e. the mass function or the basic belief assignment (BBA) of each element of $2^\Omega$ by the following relation.

$$ m : 2^\Omega \to [0,1] \qquad (2) $$
$$ A \to m(A) $$
$$ \text{with } \sum_{A \subseteq \Omega} m(A) = 1 $$

The main combination rule of two mass functions is the orthogonal combination known as the Dempster rule of combination. For two sources S1 and S2 having respectively m1 and m2 as bba, the Dempster rule is defined by:

$$ m_1 \oplus m_2(A) = \frac{1}{1-k} \sum_{B \cap C = A} m_1(B)m_2(C) \qquad (3) $$

Where K presents the conflictual mass between the combined evidence function and defined by:

$$ k = \sum_{B \cap C = \emptyset} m_1(B)m_2(C) \qquad (4) $$

### B. The Transferable Belief Model (TBM)

The Transferable Belief Model (TBM) is a model for quantified belief based on the use of belief functions. This formalism can model and manage doubt independently of the hypotheses. This is a major advantage of this theory compared to probabilistic one [11]. The TBM is based on a two-level model: the first level is the credal level and the second level is the pignistic level. The TBM conjunctive rule consists in combining beliefs linked to each expert with a conjunctive combination. We associate the mass m1 to the source 1 of

information (i.e. expert 1) and the m2 to the source 2, the combination is as follows:

$$ m_1 \oplus m_2 = m_{1,2}(A) - \sum_{B \cap C = A} m_1(B)m_2(C) \qquad (5) $$

In addition, the following relation presents the pignistic probability, which is defined for each single hypothesis of $\Omega$:

$$ \mathrm{BetP}(Y) = \sum_{A \subseteq \Omega, Y \in A} \frac{m(A)}{|A|(1-m(\emptyset))} \qquad (6) $$

For the different simulations and combinations we will use the Transferable Belief Model (TBM); consequently the decision will be taken according to the maximum of the pignistic criterion.

### C. Discounting

To define the reliability of a final decision about a singleton hypothesis, it is possible to weigh the influence of a sensor in the final fusion process without completely removing it. The discounting proposed by Shafer [13], associates a reliability index $\alpha \in [0, 1]$, and the new mass functions are presented as follows:

$$ \begin{cases} m(A) = (1 - \alpha)m(A) \\ m(\Omega) = \alpha + m(\Omega)(1 - \alpha) \end{cases} \qquad (7) $$

### D. The vacuous extension

The combination of two sources of information requires that combined mass functions share the same FoD, but in our case study, the experts state information on different FoD. However, it is possible to aggregate information that does not share the same FoD by translating it to the frame product [5]. This principle is known as the vacuous extension in the belief functions theory.

Let $\Theta$ and $\Omega$ represent two FoD. A mapping $\rho: 2^\Theta \to 2^\Omega$ is a refinement of $\Theta$ if it verifies the following properties [5]:

1. The set $\{\rho(\{\theta\}), \theta \in \Theta\} \subseteq 2^\Omega$ is a partition of $\Omega$.

2. For all $A \subseteq \Theta: \rho(A) = \bigcup_{\theta \in A} \rho(\{\theta\})$ \qquad (8)

Then the vacuous extension of $m^\theta$ to $\Omega$ is represented as follows: a bba $m^\theta$ on $\Theta$ may be transformed without any loss of information into a bba $m^\Omega$ on a refinement $\Omega$ of $\Theta$ by transferring each mass $m^\theta(A)$ for $A \subseteq \Theta$ to
$$ B = \rho(A): m^\theta(A) = m^\Omega(\rho(A)) $$

## III. Method description

Our method has for objective to aggregate different and uncertain information provided by the sources of our three experts (Occupancy, Thermal comfort and Weather forecast). The fusion model we propose is subdivided into two parts; the first one where information is collected and treated and, the second one where we aggregate information to make a decision. The algorithm will produce a temperature trend,
which will be inserted in the Smart and Predictive Heating System (SPHS).

<figure><img src="image_6.png" /><figcaption>Fig. 1. Fusion method diagram</figcaption></figure>

### A. Block B1: Occupancy

The Block B1 is the occupancy fusion part; it has three independent information sources or experts as in Fig.1: the in/out sensor, and the weekly schedule of occupant sensors known as expert occupancy 1, and 2 respectively. The fusion of the two experts gives a decision on the occupancy state of the room.

* Source occupancy 1: the presence sensor (Ps)

* Source occupancy 2: the daily Schedule(Sc) fixed by the occupant.

The occupancy expert has for $F_oD \Omega 1 = \{Sun, So\}$; meaning $\Omega 1 = \{Soon unoccupied, Soon occupied\}$.

### B. Block B2: Thermal comfort

The thermal comfort is defined in [10] as “a state of satisfaction of the body against the thermal environment”. However, the concept of comfort varies from one person to another and different statistic studies were elaborated on representative samples of people to establish the different aspects of the thermal comfort criteria. Thus, in ISO 7730-2005 « Ergonomics of the thermal environment -- Analytical determination and interpretation of thermal comfort using calculation of the PMV (Predicted Mean Vote) and PPD (Predicted Percentage of Dissatisfied) indices and local thermal comfort criteria » we can distinguish the intervals of different environmental characteristics that define the state of comfort or discomfort of a person in a specific ambience. We use different sensors to gather the information for each source. For instance the room temperature is measured by a thermometer and the relative velocity and humidity is given by the controlled mechanical ventilation (CMV) installed in the room. While the clothing expert is defined according to the

seasons and the information for the activity is provided by different sensors. The $F_oD$ for the B2 is $\Omega 2 = \{TC, Comf, TH\}$, meaning $\{Too-Cold, Comfortable, Too-Hot\}$. In our study, we will consider the following characteristics as the inputs (i.e. experts) of the block B2:

* The temperature of comfort (Tc) in Celsius

* The relative humidity (Rh) in percentage

* The relative air velocity (Rv) in m/s

* The clothing (Clo) in Clo index from clothing (ISO 7730-2005)

* The activity (Ac) in met index from human metabolic activity (ISO 7730-2005)

During the process of designing the fusion model we elaborate different mass distributions to improve the final decision and obtain reliable results. So in this section we will present in figure 2 and 3 the mass distribution as an example of the relative Air velocity.

<figure><img src="image_7.png" /><figcaption>Fig. 2. First Mass distribution for the expert Relative air velocity (MdRv1)</figcaption></figure>

The first mass distribution represents the three hypothesis, their intersection between them and the mass of ignorance ($m(\Omega)$). However in the second distribution we eliminate the assignment on the comfort and replace it with a mass of ignorance, because we know for certain when it is hot or cold but the concept of comfort is relative from one person to another. So the difference between the two mass distributions is in the second one the masses are less comitted, but that doesn't affect the reliability, on the contrary it provides better results.

<figure><img src="image_8.png" /><figcaption>Fig. 3. Second Mass distribution for the expert Relative air velocity (MdRv2)</figcaption></figure>

We will present a simulation for different scenarios in section IV for the two distributions and we will compare their results.
### C. Block B3: Weather forecast

We will use the data, provided by the latest version of the weather model AROME [14] for the fusion of block B3. The nebulosity influences the temperature in the building and outdoors during the day and the night. Thus, our << expert temperature >> will depend on the variation of the nebulosity. We specify an interval for each temperature value and we attribute a function to define the masses in that interval. Since AROME gives new prediction values every 3 hours, the fusion for block B3 will be repeated every 3 hours to update our information. The sources for this block B3 are: the external temperature (T), the wind (W), the nebulosity (N) and the precipitation (P). The thermal comfort expert has for $FoD \Omega2 = \{TH, C, TC\}$; meaning $\Omega2 = \{Too Hot, Comfortable, Too Cold\}$.

We integrate the result of the weather forecast aggregation as a source of information associated to the thermal comfort expert and not as an independent expert for two reasons. The first one is to minimize the conflict mass in the final result and the second one is to simplify the calculation process.

### D. The frame of discernement for the fusion algorithm

Each expert gives its opinion on a different FoD, so we have two different FoDs, $\Omega1 = \{Sun, So\}$ and $\Omega2 = \{TH, C, TC\}$. We use the vacuous extension to create an efficient fusion model we need to combine these two FoDs in order to obtain one FoD that gives us the necessary information; Thus the frame product, which we will use to make our decision rule for the different scenarios, will be $\Omega1 \times \Omega2 = \{(Bi, TH), (Bi, C), (Bi, TC), (Bo, TH), (Bo, C), (Bo, TC)\}$.

## IV. Simulation results

We will present different real-life scenarios to prove the efficiency and reliability of the proposed approach to fuse heterogeneous, erroneous and uncertain data. The final decision provides a contextual temperature trend, which is a kind of predictive temperature reference, in order to manage the SPHS.

For each scenario, we will give the simulation results with the first and the second mass distribution for each scenario and we will make the decision concerning the heating system.

### A. First scenario

The first scenario presents the case of a regular working day morning. The occupant is getting ready to go to work at 8:30 am and meanwhile he opens a window to freshen the room.

<table><caption>TABLE I. DATA FOR THE FIRST SCENARIO</caption><thead><tr><th>B1: Occupancy</th><th>B2: Thermal comfort</th><th>B3: Weather forecast</th></tr></thead><tbody><tr><td>Day : Wednesday</td><td>Tc = 22 °C</td><td>T = -5°C</td></tr><tr><td>Time : 07:45-08:15 am</td><td>Rh = 45 %</td><td>W=20 km/h</td></tr><tr><td>Presence sensor:</td><td>Rv= 0.2 ms<sup>-1</sup></td><td>N = 45 %</td></tr><tr><td>E=1</td><td>Clo = 0.7clo</td><td>P = 4.5 mm</td></tr><tr><td>Ac=1.2 met</td><td>Ac = 1.2 met</td><td></td></tr></tbody></table>

### a. Result with the first mass distribution

<table><caption>TABLE II. PIGNISTIC PROBABILITIES FOR THE FIRST SCENARIO WITH THE FIRST MASS DISTRIBUTION</caption><tr><td>BetP(Sun, TH)= 0.0024</td><td>BetP(Sun, C)= 0.7721</td><td>BetP(Sun, TC)= 0.1455</td><td>BetP(So, TH)= 0.0002</td></tr><tr><td>BetP(So, C)= 0.0671</td><td>BetP(So, TC)= 0.0127</td><td>m(Ø)=0.5599</td><td></td></tr></table>

For the first mass distribution the results indicate that the internal comfort is established and that the occupant is leaving soon (BetP(Sun, C) = 0.7721), however the conflict mass ($m(Ø)=0.5599$) is very important and can influence the final decision since the reliability of the system can be questioned. The final decision to make is to decrease the heating because the occupant is leaving, but we can notice that this slight modification (the window is open for fifteen minutes), disturbs the fusion system for the first mass distribution.

### b. Result with the second mass distribution

<table><caption>TABLE III. PIGNISTIC PROBABILITIES FOR THE FIRST SCENARIO WITH THE SECOND MASS DISTRIBUTION</caption><tr><td>BetP(Sun, TH)= 0.0038</td><td>BetP(Sun, C)= 0.7471</td><td>BetP(Sun, TC)= 0.1691</td><td>BetP(So, TH)= 0.0003</td></tr><tr><td>BetP(So, C)= 0.0650</td><td>BetP(So, TC)= 0.0147</td><td>m(Ø)=0.0986</td><td></td></tr></table>

It seems that the results for the second mass distribution are conform to the results of the first mass distribution (BetP(Sun, C) = 0.7471), nevertheless we can notice that the pignistic probability on "Too Cold" increases (BetP(Sun, TC) = 0.1691 > 0.1455 (Table.II)), which is totally justified because the window is open and the temperature decreases quickly. Also we can notice that the conflict mass decreases with the second mass distribution ($m(Ø) = 0.0986 << m(Ø) = 0.5599$ (Table II)) This shows that the second mass distribution is more realistic and reliable than the first one and can adapt to minor and sudden variations in the room, which is very important for the real-time heating management system.

### B. Second scenario

In this second scenario we will present the influence of a major unexpected event, when the occupant comes home earlier than expected (according to the planning he was supposed to return home between 6:30 – 7:00 pm)

<table><caption>TABLE IV. DATA FOR THE SECOND SCENARIO</caption><thead><tr><th>B1: Occupancy</th><th>B2: Thermal comfort</th><th>B3: Weather forecast</th></tr></thead><tbody><tr><td>Day : Wednesday</td><td>Tc = 16 °C</td><td>T = 5°C</td></tr><tr><td>Time : 05:00-05:30 am</td><td>Rh = 55 %</td><td>W=15 km/h</td></tr><tr><td>Presence sensor:</td><td>Rv= 0.24 ms<sup>-1</sup></td><td>N = 40 %</td></tr><tr><td>E=1</td><td>Clo = 1clo</td><td>P = 1.5 mm</td></tr><tr><td>Ac=1 met</td><td>Ac = 1 met</td><td></td></tr></tbody></table>

### a. Result with the first mass distribution

<table><caption>TABLE V. PIGNISTIC PROBABILITIES FOR THE SECOND SCENARIO WITH THE FIRST MASS DISTRIBUTION</caption><tr><td>BetP(Sun, TH)= 0.0002</td><td>BetP(Sun, C)= 0.1491</td><td>BetP(Sun, TC)= 0.3507</td><td>BetP(So, TH)= 0.0002</td></tr><tr><td>BetP(So, C)= 0.1491</td><td>BetP(So, TC)= 0.3507</td><td>m(Ø)=0.5328</td><td></td></tr></table>
We are in the “Eco-Mode” (16° C), so the pignistic probabilities indicate that the ambiance in the room is uncomfortable; it is the “Too Cold” sensation (BetP(Sun, TC) = BetP(So, TC) = 0.3507) but we cannot decide on the state of occupancy, because in this case the occupant came home earlier than expected. Therefore, we do not consider the schedule as a source of information and the priority will be given to the presence sensor to decide on the occupancy. Since (E = 1) it confirms that the room is occupied and that the temperature trend will be to “Increase” the temperature immediately, to achieve a comfortable ambiance in a short time.

b. Result with the second mass distribution

<table><caption>TABLE VI. PIGNISTIC PROBABILITIES FOR THE SECOND SCENARIO WITH THE SECOND MASS DISTRIBUTION</caption><tr><td>BetP(Sun, TH)=<br>0.0092</td><td>BetP(Sun, C)=<br>0.2115</td><td>BetP(Sun, TC)=<br>0.2793</td><td>BetP(So, TH)=<br>0.0092</td></tr><tr><td>BetP(So, C)=<br>0.20115</td><td>BetP(So, TC)=<br>0.2793</td><td colspan="2">m(Ø)=0.0030</td></tr></table>

The results with the second mass distribution indicates that the heating must “Increase” even if we lose more energy to achieve a comfortable ambiance for the occupant as we did find with the first mass distribution, which is conform to the decision rule. However, we can notice that, with the second mass distribution, the value of the pignistic probabilities are more important (BetP(Sun, TC) = 0.4559 > BetP(Sun, TC) = 0.3507 (Table.V)) and the conflict mass is much lower with this mass distribution (m(Ø) = 0.0132 << m(Ø) = 0.5328 (Table.V)). We can conclude that once again the second mass distribution proved its efficiency, we obtain the suitable decision without an important conflict mass.

v. Conclusion

We can conclude that the method presented in this paper based on the belief function theory is reliable. Indeed, it proved its efficiency through the different real-life scenarios. We obtained a coherent decision for each scenario; the necessary ‘tempera ture trend’ was inserted in the ‘Smart and Predictive Heating System’, even in the case of an unexpected event. In addition, we succeed to minimize the conflict mass generated when the data was aggregated without using a conflict management algorithm but whilst solving the origin of the problem which was the mass distribution and the

heterogeneity of the frame of discernment. In further works we will integrate a management conflict algorithm and a contextual discounting in order to minimize the conflict mass even more.

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