Antoine Garnier

Julien Eynard

Matthieu Caussanel

Stéphane Grieu
email: stephane.grieu@promes.cnrs.fr

Low computational cost technique for predictive management of thermal comfort in non-residential buildings

Keywords: non-residential building, energy consumption, zoned HVAC system, thermal comfort, artificial neural networks, model predictive control

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Low computational cost technique for predictive management of thermal comfort in non-residential buildings

Introduction

Within non-residential buildings, almost half of the electricity consumption is due to Heating, Ventilation and Air-Conditioning (HVAC) systems [START_REF] Pérez-Lombard | A review on buildings energy consumption information[END_REF]. As a consequence, new approaches are needed to make HVAC systems more efficient. First, energy efficiency can be improved in central heating systems by introducing zoned heating. This allows a more granular application of heat and HVAC sub-systems can be controlled independently. Another key point is indoor thermal comfort. Thermal comfort is subjective, hard to define and even harder to achieve in a non-residential building. It is mainly related to indoor conditions and impacted in a significant way by the effectiveness of the building envelope and the way the HVAC system is used.

Over the last few years, many studies have been conducted on thermal comfort management. These studies are based on the use of different tools [START_REF] Dounis | Advanced control systems engineering for energy and comfort management in a building environment -a review[END_REF], such as fuzzy logic [START_REF] Gouda | Thermal comfort based fuzzy logic controller[END_REF] [START_REF] Egilegor | A fuzzy control adapted by a neural network to maintain a dwelling within thermal comfort abstract[END_REF] or genetic algorithms [START_REF] Alcalá | Fuzzy control of hvac systems optimized by genetic algorithms[END_REF]. Bermejo et al. [START_REF] Bermejo | Design and simulation of a thermal comfort adaptive system based on fuzzy logic and on-line learning[END_REF] proposed an adaptive system based on fuzzy logic, capable of learning the user thermal sensation to maintain an optimal comfort. Dounis and Manolakis [START_REF] Dounis | Design of a fuzzy system for living space thermalcomfort regulation[END_REF] developed an algorithm to regulate the PMV index using a fuzzy system, capable of controlling both the temperature and humidity in a room. Fraisse et al. [START_REF] Fraisse | Thermal control of a discontinuously occupied building using a classical and a fuzzy logic approach[END_REF] used a self-learning fuzzy controller to find the optimal heating start time. With the exception of the last one, these approaches require to turn on the HVAC system at a fixed time and this can impact negatively thermal comfort if the system is started too late, or energy consumption if triggering happens too soon.

Predictive control [START_REF] Paris | Heating control schemes for energy management in buildings[END_REF][10] [START_REF] Ferreira | Neural networks based predictive control for thermal comfort and energy savings in public buildings[END_REF] is a very good alternative to the above-mentioned approaches. Indeed, predictive algorithms can take advantage of the intermittent use of buildings, whose occupancy is regular and known. In particular, Artificial Neural Networks (ANN) have demonstrated on several occasions their efficiency in control and energy consumption optimization. Huang et al. [START_REF] Huang | A new zone temperature predictive modeling for energy saving in buildings[END_REF] worked on a predictive model based on ANN to forecast temperature inside an area by taking into account the coupling effect between zones. Morel et al. [START_REF] Morel | Neurobat, a predictive and adaptive heating control system using artificial neural networks[END_REF] and Argiriou et al. [START_REF] Argiriou | Development of a neural network heating controller for solar buildings[END_REF] [START_REF] Argiriou | A neural network controller for hydronic heating systems of solar buildings[END_REF] worked on similar predictive control strategies based on outdoor temperature and solar radiation forecasting. In [START_REF] Dounis | Design of a fuzzy system for living space thermalcomfort regulation[END_REF] a water heating system is controlled in isolated rooms while in [START_REF] Fraisse | Thermal control of a discontinuously occupied building using a classical and a fuzzy logic approach[END_REF] an electrical heating system is controlled over individual solar houses. Control was done for only one area, without considering thermal exchanges. Moros ¸an et al. [START_REF] Moros ¸an | Building temperature regulation using a distributed model predictive control[END_REF] developed a distributed predictive approach to control several areas simultaneously while taking into account thermal transfers. In this case, thermal comfort was defined on the basis of a reference temperature. The proposed algorithm is useful but on-line optimization is needed and computation time is extensive. As a result, such a solution cannot be implemented easily in an embedded system. Álvarez et al. [START_REF] Álvarez | Optimizing building comfort temperature regulation via model predictive control[END_REF] developed a predictive approach to control an HVAC system composed of solar collector fields. A key point was to ensure an acceptable thermal comfort in the different areas of the considered building despite limited thermal resources. The PMV index was used as a thermal comfort indicator. Moreover, many solutions are based on controlling local heating systems in small areas [START_REF] Endravadan | Régulation des systèmes de chauffage et de climatisation basée sur la sensation thermique humaine. Impact sur la consommation d'énergie dans les bâtiments[END_REF]. This kind of approaches is not well adapted to changes in human activity but thermal comfort requirements can be met without wasting energy. Moreover, additional heating sub-systems are sometimes needed. Kolokotsa et al. [START_REF] Kolokotsa | Predictive control techniques for energy and indoor environmental quality management in buildings[END_REF] developed a predictive controller using a bilinear model. Comfort has been defined on the basis of both a fixed temperature and a humidity bandgap to satisfy.

Pyrescom Company has developed a monitoring system that carries out meteorological parameters and energy measurements to improve energy efficiency in non-residential buildings (Batnrj project). The collected data are used to find out possible ways to develop an efficient HVAC control strategy. Several buildings are currently instrumented using the Pyrescom monitoring system, including a non-residential building located in the city of Perpignan (south of France). This reference (pilot) building has been modeled using the EnergyPlus software and allowed the strategy about HVAC management we propose to be tested and evaluated. Energy consumption, thermal comfort and computation time are considered as performance indicators. Computation time is a key point to the project. For each instrumented building, an embedded system is used to collect data from various sensors (temperature, humidity, energy consumption, etc.) and these data are sent to a remote server. This server has a significant computational power but the embedded systems have limited capabilities. That is why the main objective of the work we present in this paper is to develop a computationally tractable approach for managing energy resources and satisfying thermal comfort requirements in non-residential buildings. The proposed strategy is based on predictive control and aims at managing thermal comfort in several areas of non-residential buildings equipped with HVAC sub-systems without on-line optimization. Thermal comfort is based on the PMV (Predicted Mean Vote [START_REF] Fanger | Assessment of man's thermal comfort in practice[END_REF]) index, which is a standardized indicator designed to estimate the thermal sensation of the occupants. This criterion allows temperature to be adjusted in a building according to the period of the year, occupant behaviour and activities. Moreover, air temperature set-point may be reduced when the wall temperature increases, while keeping an identical comfort. So, we used first feedforward Artificial Neural Networks (ANN) to model the non-linear behaviour of the PMV index, mainly from solar radiation, outdoor temperature and internal gains (ANN-based PMV models). Then, we considered the PMV index as a control set-point and thermal comfort can be maintained in a desired interval which can be adjusted by people working in a given building.

The present paper is organized as follows: first, the reference (pilot) building we modelled using the EnergyPlus software is described (section 2). Next, section 3 focuses on thermal comfort and the way the PMV index can be used as a relevant comfort indicator. The following section (section 4) is about the development and validation of the ANN-based PMV models (the interaction, i.e. heat transfer, between the three rooms we considered in the non-residential building is taken into account or not). The predictive control strategy we developed for HVAC subsystems is presented in section 5. Finally, the results we obtained are analyzed and compared with the results provided by standard (non-predictive) management strategies. The paper ends with a conclusion and an outlook to future work.

Non-residential (reference) building

To evaluate the proposed strategy, a reference building has been modelled using the EnergyPlus software, which is able to perform accurate building simulations. The considered building is a real two-storey building of 1000 m 2 , built in 2008 and located in Perpignan (south of France). It is facing south and agrees with the French "Thermal Regulation 2005" [START_REF] Franc ¸aise | Arrêté du 24 mai 2006 relatif aux caractéristiques thermiques des bâtiments nouveaux et des parties nouvelles de bâtiments[END_REF]. This non-residential building is divided into three main areas of 340 m 2 each (figure 1), with different uses. About a dozen employees work in offices at the ground and first floors (green and yellow area). The red area in the first floor is a manufacturing zone where about 6 persons work seated or in a standing position. The last room of the ground floor is a warehouse (blue area) that is not heated.

For both the warehouse and the manufacturing area, ceiling is 3.90 m. In the offices, a suspended ceiling stands at 2.70 m. The materials used in the building Table 1: Properties of the materials used in the exterior walls. l is the thickness, λ the conductivity, ρ the density and C the specific heat of a material.

Layer

l λ ρ C (cm) (W•m -1 •K -1 ) (kg•m -3 ) (J•kg -
•K•W -1 .
The south face and a part of the west face of the building are made from glass. Glass has been treated to filter infrared radiation and avoid overheating in summer. The other glasses in the building consist in 3 mm double glazed bays. The present study focuses on the three following (occupied and equipped with sensors) areas: the offices on both floors and the manufacturing area, that is composed of an open space of 230 m 2 and three storage rooms of 110 m 2 (not heated). Heating is handled in the building by a zoned electrical HVAC system consisting in several sub-systems, one for each area, where only the temperature set-point can be adjusted. Each sub-system is managed by a local controller. The characteristics of the different HVAC sub-systems for each area are listed by table 2. All the units have a coefficient of performance (CoP) equal to 3.8. As previously stated, the proposed management approach is based on a model predictive controller that will supervise the HVAC sub-systems (figure 2). Weather data (outdoor temperature, solar radiation, wind speed) are required to perform the simulation process. We used real data from year 2011 provided by the Pyrescom monitoring system. Since atmospheric pressure measurements were missing, we used data from the Perpignan airport which is located 7 km away from the building. Measurements were carried out with a time step of 30 seconds while averaged values were saved every 15 minutes and stored in a database. As a consequence, the simulation time step is 15 minutes, what enables because of the characteristics of the building a reactive control approach to be developed. Let us note that Perpignan benefits from a relatively mild mediterranean climate. Figure 3 shows how outdoor temperature evolves at 6 a.m., from January to December 2011 (during the simulation period).

Thermal comfort

The Predicted Mean Vote (PMV) index is used as a thermal comfort indicator. This indicator was developed by Fanger [START_REF] Fanger | Assessment of man's thermal comfort in practice[END_REF], before to be standardized by inter- [START_REF]ANSI/ASHRAE Standard 55, Thermal environmental conditions for human occupancy[END_REF]. The PMV index quantifies the thermal sensation felt by some people in a room. This sensation is described by a scale ranging from -3 (cold) to +3 (hot) (table 3). The exchange of heat between the human body and its environment strongly governs thermal comfort. It is highly subjective and can be considered as perfect when the sum of exchanges is zero. Equation 1 depicts the way one can compute the PMV index:

P MV = [0.303exp -0.036M + 0.028] × L (1)
with L the difference between the heat produced and the heat lost.

L = M -W -H 1 -H 2 -H 3 -H 4 -H 5 -H 6 (2)
For the room j, ∀j ∈ 1; 3 , M j is the metabolism (described below). W j is the external work and is considered to be null. Interval ICL value (clo) ), relative humidity (HR j ), air speed (v air j ), metabolic activity, and clothing thermal insulation. Let us note that air speed is not calculated by the EnergyPlus software. However, this missing information is not critical because air speed has no influence on the PMV value as long as it remains below 0.1 m•s -1 [START_REF] Nf | Détermination analytique et interprétation du confort thermique par le calcul des indices PMV et PPD et par des critères de confort thermique local[END_REF]. This is mostly the case within the non residential building we considered as a reference building. Moreover, metabolic activity is supposed to be constant and only depends on the considered area. In offices, people work in a sitting position most of the time and, as a result, M is set to 70 W•m -2 (i.e. 1.2 met). Activity in the manufacturing area is more dynamic and M is set higher to 116 W•m -2 (i.e. 2 met).

t 6 < -5 • C 1 -5 • C ≤ t 6 < 5 • C 0.818 -0.0364t 6 5 • C ≤ t 6 < 26 • C 10 -0.
Depending on outdoor temperature, people dress differently. As a result, clothing thermal insulation varies over time. Schiavon and Lee [START_REF] Schiavon | Dynamic predictive clothing insulation models based on outdoor air and indoor operative temperatures[END_REF] developed a predictive model to estimate clothing thermal insulation (noted ICL). So, it is defined, each day, from the outdoor temperature observed at 6 a.m. (t 6 ), as shown in table 4. According to theses equations, clothing thermal insulation varies from 0.58 clo, during winter time, to 0.46 clo, during summer time. Figure 4 depicts the way such a parameter evolves between January and December 2011. Usual clothes for summer are a pant with a short-sleeved shirt, while during winter, usual clothes are a trouser with a long-sleeved shirt. Looking at figure 4, the result seems to be realistic. It can be highlighted that the 2011 winter was mild, so the clothing thermal insulation was moderate. At the end of January, outdoor temperature has strongly decreased and, as a result, the algorithm has automatically adjusted the clothing thermal insulation value.

ANN-based PMV models

Structure of the models

A model of the system to be controlled is required to evaluate the predictive control strategy and check if the PMV index can be maintained into the desired interval during occupancy periods [-0.5; +0.5]. In a first single-area approach, we used a linear state-space model. We obtained good results but the local controller used to regulate the air temperature in the building and whose behaviour is unknown induces nonlinearities. As a consequence, we decided for feedforward Artificial Neural Networks (ANN) [START_REF] Rosenblatt | The Perceptron: a perceiving and recognizing automaton, Project PARA[END_REF] [26] to model the multi-area system. This kind of network consists of a series of layers. The first layer is connected to the network's input vector while each subsequent layer is connected to the previous layer. The final layer produces the network's output. Feedforward artificial neural networks can be used for any kind of input to output mapping. With only one hidden layer and enough neurons in this layer, such networks can approximate any nonlinear continuous function to any desired degree of accuracy [START_REF] Hornik | Multi-layer feedforward networks are universal approximation[END_REF]. A key point in using ANN to describe nonlinear dynamics is to define the right topology of the networks in order to avoid poorly fitted or overfitted models (generalization ability is affected in a significant way by overfitting). In addition, training has to be done using an efficient learning algorithm (for example, the well-known and efficient Levenberg-Marquardt (LM) algorithm [START_REF] Hagan | Training feedforward networks with the marquardt algorithm[END_REF] or, when using self-growing feedforward artificial neural networks, the Cascade-Correlation (CC) algorithm) and an adequate database of examples [START_REF] Charalambous | Conjugate gradient algorithm for efficient training of artificial neural networks[END_REF].

ANN-based PMV model

ANN-based PMV model

The proposed strategy is first designed to manage thermal comfort in the three considered areas (the offices in both floors and the manufacturing area) in a separate way. As a result, no interaction (i.e. heat transfer) is considered between these areas and three models, one per area, are needed. So, a model links the PMV index (at time k + 1) in the room j, ∀j ∈ 1; 3 , with outdoor temperature (T out ), solar radiation (SR) and internal heat gain (IG j ) at time k. The most common sources of internal heat gain are metabolism, appliances, electronic devices, and lighting. In addition, the influence of the heating system of the room j is taken into account through the air temperature set-point (T sp j ). Let us remember that a local controller operates in the three considered areas to regulate the air temperature. Finally, the PMV index in the room j at time k is also considered as a model input (figure 5). Equation 3formulates the PMV index in the room j, without interaction with the two other considered rooms. So, ∀j ∈ 1; 3 :

P MV j (k + 1) = ANN j P MV j (k), T out (k), SR(k), IG j (k), T sp j (k) (3)
In a second time, thermal comfort is managed in the building taking into account the existing interaction (i.e. heat transfer) between the three areas. As a result, the PMV indexes in the rooms j, l and m are simultaneously computed at time k + 1 with an overall model (ANN j,l,m ). This model (figure 6) uses as inputs all the air-temperature set-points (T sp j , T sp l and T sp m ), internal heat gains (IG j , IG l and IG m ) and PMV indexes (P MV j , P MV l and P MV m ) at time k. In equation 4, ANN j,l,m j denotes that P MV j (k +1) is the selected output among the three outputs of the model. So, ∀j, l, m ∈ 1; 3 such as j = l = m:

P MV j (k + 1) = ANN j,l,m j   P MV j (k), P MV l (k), P MV m (k), . . . SR(k), IG j (k), IG l (k), IG m (k), . . . T out (k), T sp j (k), T sp l (k), T sp m (k)   (4)

Training phase and generalization ability

A training phase is needed to identify the parameters of the ANN-based models (the synaptic weights and biases) from examples. So, we generated a database of examples using the EnergyPlus model of the considered non-residential building. Of course, training efficiency is highly related to data relevance. We simulated the behavior of the building during a whole year and turned on and off the HVAC sub-systems randomly every day (2 to 6 hours before people arrive at the building or after they left the building). In addition, we selected randomly temperature set-points in the interval [19 • C; 26 • C]. These set-points remained unchainged during all the day. Let us note that in a real building, the identification process will be carried out from measurements provided by the Pyrescom monitoring system. So, the thermal model of the considered building is not necessary. Using simulated (or measured) data, the training phase is achieved using Matlab R and its neural network toolbox. Because overfitting can be favoured by a badly-sized training subset, we decided to train the networks using different subsets of data randomly picked up among all the available examples. We used the Levenberg-Marquardt algorithm as learning algorithm [START_REF] Hagan | Training feedforward networks with the marquardt algorithm[END_REF]. It is accurate, fast and uses matrix decompositions to limit the amount of memory used. The validation phase has been carried out using new data sets dealing with realistic scenarios.

The parametric study we carried out to model the PMV index in the room j when interaction between the three considered areas is not taken into account (model ANN j , ∀j ∈ 1; 3 ) has highlighted that generalization is very good when using feedforward neural networks with 30 hidden neurons while using about 15% of the available data during the training phase. As a consequence, we selected this configuration. In this case, the Mean Relative Error (MRE) over validation data is about 5%, whatever the room. Figure 7 depicts the impact on generalization of the number of hidden neurons and the quantity of training data used. This figure is related to the manufacturing area. Learning is achieved in about 20 seconds, so it can be easily handled by a remote server without penalizing the other running applications. Taking a look at figure 7, one can also note that when using less than 15 hidden neurons (whatever the quantity of training data used) the PMV model is under-parameterized. In opposition, very good results can also be achieved with 40 to 50 hidden neurons and 25 to 50% of the available data used during the training phase. However, in this case, computation time is higher than it is with the selected configuration.

When taking into account the interaction (i.e. heat transfer) between the three considered areas (model ANN j,l,m , ∀j, l, m ∈ 1; 3 such as j = l = m), generalization is also very good for a feedforward artificial neural network with 30 hidden neurons while using about 10% of the available data during the training phase. Again, the Mean Relative Error (MRE) over validation data is about 5%, whatever the room. Taking a look at figure 8 (manufacturing area), one can note that when using less than 10 hidden neurons (whatever the quantity of training data used) the PMV model is under-parameterized. In opposition, it is over-parameterized when considering about 40 hidden neurons. Finally, figure 9 shows values of the PMV index given by EnergyPlus and the ANN-based models (for a period of five days), for each of the three considered rooms (interaction is taken into account). The HVAC sub-systems are turned on only during occupancy periods, with a temperature set-point set to 22 • C. It clearly appears that the ANN-based models are able to estimate accurately the PMV index in the different areas when taking into account interaction.

Exogenous variables forecasting

In order to estimate the PMV index, forecasting values of the model exogenous variables are needed. Because the internal heat gains are directly related to the building occupation, they can be easily estimated. As a consequence, only outdoor temperature and solar radiation have to be forecasted. Morel et al. [START_REF] Morel | Neurobat, a predictive and adaptive heating control system using artificial neural networks[END_REF] and Argiriou et al. [START_REF] Argiriou | Development of a neural network heating controller for solar buildings[END_REF] developed neural network models to forecast theses variables but such a solution implies more calculation time. As a result, we considered first as a forecasted value, the value measured the previous day at the same time (SR and T out ). Next, with the aim of increasing the accuracy of the forecasted temperature, a correction term has been added by using the difference between the current value and the value of the previous day at the same time (equation 5). k is the present time, and i the forecasting horizon:

0 -1 -2 1 2 3
SR(k + i) = SR(k + i -24h) T out (k + i) = T out (k + i -24h) + T out (k) -T out (k -24h) (5)

Control strategy

Control of thermal comfort

Since our objective is to satisfy thermal comfort requirements in the three considered rooms of the building, the HVAC air temperature set-point T sp j (∀j ∈ 1; 3 ) has to be adjusted as necessary. As a key point, we need a set-point for the PMV index (P MV sp j ) to be reached. From this set-point as well as T wall j , HR j , v air j and M j (figure 10), T sp j is estimated. Because of both the complexity and non-linearities of the PMV equation, one cannot solve it analytically to find the appropriate air temperature set-point. That is why a numerical method has been considered to solve equation 6. T sp j is then set according to this computed value:

P MV (T j , θ j ) = P MV sp (6)
with θ j bringing together T wall j , HR j , v air j and M j and P MV sp j the PMV setpoint value from which we computed the air temperature set-point T sp j . So, the final objective is to find the best value for T sp j (k) such as if T j (k) = T sp j (k) then P MV j (k) = 0.

In order to solve this problem, different iterative methods have been evaluated with the aim of finding the fastest and the most efficient one (the standard algorithms used are detailed in [START_REF] Bonnans | Numerical Optimization: Theoretical and Practical Aspects[END_REF]). The stopping criterion is a tolerance of 0.05 • C on T sp j . First, we used the binary search algorithm. The number of iterations is related to the desired accuracy, given that convergence is linear. The initial values of the minimal and maximal thresholds were set to 15 and 30 • C, respectively. At each iteration, the gap around the solution is reduced until it is lower than the desired accuracy. The second algorithm used is the Newton-Raphson method.

Comfort level controller

The solution is computed on the basis of a correction term defined as the ratio between the function and its derivative. Since it is not possible to find the derivative analytically, it is approximated. The initial value was set to 20 • C. The main advantage of the Newton-Raphson method lies in its quadratic convergence. The third algorithm we considered is the secant method. It is quite similar to the Newton-Raphson method, but uses a specific equation to approximate the derivative, based on the two previous values. The initial values were set to 20 • C and 25 • C. Table 5 summarizes performance results for the three methods we tested. Although the Newton-Raphson method needs three time less iterations to reach the solution than the binary search algorithm, computation time is similar. Slowness is due to the PMV index being calculated three times per iteration instead of just one time with the binary search algorithm. With the secant method, convergence is slightly slower but the PMV index is computed only once per iteration. As a consequence, computation time is reduced by half and the secant method has been chosen among the three tested methods.

Predictive control strategy

The block diagram of the proposed control predictive strategy is presented by figure 11. EnergyPlus is used to simulate the behaviour of the real non-residential building, considered as the reference building. The controlled output is the PMV index. The proposed Model Predictive Controller (MPC) uses the identified ANNbased PMV models to perform some predictions and optimize the way the heating sub-systems will operate (we seach for the optimal time to switch on or off the sub-systems), taking into account the constraints about thermal comfort during occupancy periods. The controller computes the HVAC air temperature setpoint (the manipulated input) for the room j, ∀j ∈ 1; 3 . Based on previous day values, the forecasting unit estimates the exogenous disturbances (T out , SR and IG j ). As previously mentioned, thermodynamic simulations are carried out using EnergyPlus with MPC set-point values computed by Matlab R . These two softwares are interfaced using the MLE+ toolbox [START_REF] Nghiem | MLE+: a Matlab-EnergyPlus co-simulation interface[END_REF]. In real non-residential buildings equipped with HVAC sub-systems, EnergyPlus simulations are no more needed. To assess performance, energy consumption and thermal comfort during occupancy periods are considered. The main objective is to satisfy thermal comfort requirements when the different areas are occupied and avoid energy waste during the rest of the time. The thermal comfort interval is defined on the basis of a PMV value ranging between P MV min j = -0.5 and P MV max j = 0.5. The temperature set-point is computed to obtain a PMV index equal to zero in the room j, ∀j ∈ 1; 3 . In real buildings, these parameters will be adjusted in real time, according to people's feelings. With the proposed strategy, one can optimize the way the HVAC sub-systems switch from one operation mode to another (on/off).

The optimization problem related to the search for the optimal time to switch the HVAC sub-systems on can be formalized in a standard way as a MPC problem. The aim is to minimize the time during which the HVAC sub-systems are on before the arrival of the first occupant (at time p). The criterion to be minimized is defined by equation 7, considering k ∈ N the actual time and p ∈ N the prediction horizon. u j (k + i/k) is the vector of the manipulated variables for the room j. HV AC j (k + i/k) = 1 if the HVAC sub-system is on and HV AC j (k + i/k) = 0 if it is off. Let us note that X(k + i/k) is the forecasted value of X at time k + i, based on the knowledge of X at time k:

min ū∈{0;1} p (p - p i=1 (u j (k + i/k))) (7)
Thus, HV AC j (k

+ i/k) = u j (k + i/k) and if HV AC j (k + i/k) = 1 then T sp j (k + i/k) = T sp j (k)
, with T sp j (k) the set-point temperature computed to ensure P MV j (k) = 0 (see equation 6 and figure 11). Else, if HV AC j (k + i/k) = 0 then T sp j (k + i/k) = 0. So, the vector ū = [u j (k + 1/k), . . . , u j (k + p/k)] ∈ {1; 0} p and u j (k) is a binary variable. One can note that we consider an integer n j ∈ 1; p which exists so that the constraints defined by equation 8 are satisfied. With such an assumption, the HVAC sub-system of the room j is switched on only once:

[u j (k + 1/k), . . . , u j (k + n j -1/k)] = {0} n j -1 [u j (k + n j /k), . . . , u j (k + p/k)] = {1} p-n j +1 (8)
The terminal constraints related to thermal comfort requirements are given by equation 9:

P MV min j ≤ P MV j (k + p/k) ≤ P MV max j (9)
The PMV index in the room j, ∀j ∈ 1; 3 , is forecasted using the ANNbased model we presented in section 4 (equation 10). Equation 11 is about the forecasting of the exogenous variables, with SIG j the function that defines the occupancy of the room j and computes the internal heat gain. Equation 12 deals with the computation of the air temperature set-point:

P MV j (k + i + 1/k) = ANN j   P MV j (k + i/k), T out (k + i/k), . . . SR(k + i/k), IG j (k + i/k), . . . T sp j (k + i/k)   (10)    T out (k + i/k) = T out (k + i -24h) + T out (k) -T out (k -24h) SR(k + i/k) = SR(k + i -24h) IG j (k + i/k) = SIG j (k + i) (11)
T sp j (k + i/k) = T sp j (k) such as if T j (k) = T sp j (k) then P MV j (k) = 0 (12)
As a key point, the criterion to be minimized can be reformulated to avoid searching the solution for each u j (k + i/k). With such a reformulation, we only need to find the best value of n j as an integer parameter (equation 13), which is enough to find the vector of the manipulated variables, as shown in equation 8. The constraints remain unchanged:

min n j ∈ 1;p (p -n j ) (13)
The optimization problem related to the search for the optimal time to switch the HVAC sub-systems off can be formalized in the same way. Our goal is to maximize the time during which the sub-systems are off before people leave the building (at time p). So, the criterion is defined as follows (equation 14):

max n j ∈ 1;p (p -n j ) (14)
Except for thermal comfort requirements, the constraints remain the same as for the first optimization problem (the search for the optimal time to switch the HVAC sub-systems on). So, because thermal comfort has to be maintained until the end of the prediction horizon (p), equation 9 is replaced by equation 15. So ∀i ∈ 1; p :

P MV min j ≤ P MV j (k + i/k) ≤ P MV max j (15)
Finally, with a centralized MPC controller, n j is the same for all the considered areas and is so noted n. Moreover, the constraints related to thermal comfort when searching for the optimal time to switch on or off the HVAC sub-systems (equations 9 and 15) have to be respected in each of the considered rooms at the same time, i.e. ∀i ∈ 1; p . In addition, P MV j is computed for the room j using the model ANN j,l,m j , ∀j, l, m ∈ 1; 3 such as j = l = m, in order to take into account the existing interaction (i.e. heat transfer) between the different areas of interest (equation 16):

P MV j (k + i + 1/k) = ANN j,l,m j     P MV j (k + i/k), P MV l (k + i/k), P MV m (k + i/k), . . . IG j (k + i/k), IG l (k + i/k), IG m (k + i/k), . . . T sp j (k + i/k), T sp l (k + i/k), T sp m (k + i/k), . . . SR(k + i/k), T out (k + i/k)     (16)
In order to avoid on-line optimization that needs computing resources, we propose an algorithm allowing the optimal switching time (i.e. the optimal time to turn on and off the HVAC sub-systems) to be found without optimization. Only one simulation of the prediction model (ANN j or ANN j,l,m j ) for each of the considered rooms is needed. Figure 12 depicts the predictive algorithm used. As mentioned above, the sampling time is 15 minutes. The occupancy schedule (people are present from 8:00 a.m. to 6:00 p.m.) is identical for the three considered areas. First, the air temperature set-points are computed to obtain P MV sp j = 0. Depending on the presence or not of people in the building, two different cases can be highlighted, ∀j ∈ 1; 3 :

(i) When the building is occupied (Z j = 1 for the room j), the objective is to turn off the HVAC sub-systems as soon as possible while ensuring that thermal comfort will meet requirements (equation 15) until all the people leave the different areas, taking into account their thermal inertias. All the HVAC sub-systems are considered to be turned off (HV AC j (k) = 0) along the forecasting horizon p while outdoor temperature and solar radiation (both are exogenous disturbances) are estimated on the basis of the previous day values (equation 11). The PMV index is forecasted using the proposed ANN-based models (equation 10). As long as the building is occupied, the predictive algorithm checks if thermal comfort requirements are satisfied in each area of interest (the ground floor and first floor offices as well as the manufacturing area). If the constraints are not met, it means that the HVAC sub-systems must not be turned off at this time and, as a result, the air-temperature set-points are set to the values we computed initially (equation12). When the building is no more occupied (Z j = 0 for the room j), thermal comfort is necessarily satisfied and all the HVAC sub-systems are turned off (HV AC j (k) = 0).

(ii) When the building is empty (Z j = 0 for the room j), the predictive algorithm searches for the last moment to turn on the HVAC sub-systems. The optimal time to switch the sub-systems on is defined as the time allowing thermal comfort requirements to be met when the first worker arrives at the building. If thermal comfort is ensured at least two time steps before the first worker arrival, decision is delayed and the HVAC sub-systems stay off (HV AC j (k) = 0). If thermal comfort is not ensured at least one time step before the first worker arrival (equation 9), the HVAC sub-systems are switched on (HV AC j (k) = 1) and the air temperature set-points computed initially are used (equation12).

Results

In order to evaluate performance regarding thermal comfort, we considered the percentage of time for which the PMV value remains between -0.5 and 0.5, the building being occupied. This percentage is of course directly related to constraints satisfaction. In addition, calculation of energy consumption is based on an average consumption per day and square meter. With these criteria, one can compare the proposed predictive strategy with non-predictive ones. Finally, the time needed to compute the air temperature set-points is recorded. This allows computation requirements to be evaluated. The results are grouped in table 6.

Standard (non-predictive) strategies

The situation described below is the reference scenario (S1). In the real nonresidential building, the HVAC sub-systems are turned on and the air temperature set-points remain the same (T sp j = 22 • C in the room j, ∀j ∈ 1; 3 ) during daytime, nighttime and week-end periods. With this scenario, thermal comfort is slightly lower than zero and exceeds this value when outdoor temperature and/or solar radiation are high. Figures 13a and14a depict the way both the PMV index (top) and power consumption (bottom) evolves during two characteristic weeks (a cold one and a milder one). Scenario S2 allows the same strategy to be applied but using a PMV set-point, instead of an air-temperature set-point. This time, the average PMV index is very close to zero, but we observe the same problem as previously, that is to say overheating in case of high temperature and/or solar radiation. This explains why the comfort criterion is lower, even with a higher consumption of energy.

As an other option, we used a scheduler to stop the HVAC sub-systems during the night and the week-ends and to turn them on in the morning, two hours

Action to do

Test phase

Yes No

We look if HVAC subsystem should be turned on, right now, to satisfy future thermal comfort constraints

We look if HVAC subsystem could be turned off, right now, but satisfying thermal comfort constraints until the end of occupancy

No

No Yes Yes Figure 12: Predictive control algorithm for the room j, ∀j = 1, 2 or 3 (no interaction between the rooms), or for j = 1, 2 and 3 (with interaction between the rooms). before people arrive in the manufacturing area. Two hours is a standard amount of time to heat a building during the cold period of the year concerned by heating. On this basis, we defined two scenarios: S3 (T sp j = 22 • C in the room j, ∀j ∈ 1; 3 ) and S4 (P MV sp j = 0 in the room j, ∀j ∈ 1; 3 ). Quite logically, the results we obtained highlight a significant decrease in energy consumption: -62.1% (-144 Wh/day•m 2 ) with S3 and -57.8% (-134 Wh/day•m 2 ) S4, taking as a reference the results we obtained with scenario S1. In addition, thermal comfort is improved : turning off the heating systems during periods of vacancy attenuates and delays overheating effects. Figures 13b and14b show that scenario suffers from a lack of flexibility. Indeed, thermal comfort is sometimes reached too early (for example during mild days), which leads to energy waste, while it is reached too late some other days. In this case, thermal comfort requirements are not satisfied.

Predictive control strategy

The next scenario (S5) introduces a predictive control with a single-area approach somewhat conservative because heat transfer between the three considered areas is not taken into accdount. As a result, the HVAC sub-systems are turned on too early and turned off too late. Otherwise, thermal comfort is good, even tough electrical consumption is slightly higher than for both scenarios S3 and S4. As a key point, overheating is limited compared to what is observed when applying the non-predictive strategies. The three last scenarios (S6, S7 and S8) are based on the multi-area predictive algorithm. Due to the forecasting method used for outdoor temperature and solar radiation, they give different results. Scenario S6 is the ideal case because the real values of outdoor temperature and solar radiation are used. For scenario S7, uncorrected previous-day values are used. Finally, scenario S8 uses corrected previous-day values for outdoor temperature (see section 4.3) (figure 13c). These three scenarios allow the impact on the results of the forecasting procedure to be highlighted: with an ideal prediction of outdoor temperature and solar radiation (S6), the comfort criterion is the best. Of course, such a situation is not realistic because forecasting outdoor temperature and solar radiation without error is impossible. So, these results are only given to evaluate the performances of the other strategies in comparison with the ideal case. Using only the previous day values (S7) is efficient, but sometimes leads to sub-systems turned on too soon or too late. With the correction factor (S8), this problem is solved most of the time: the consumption of energy is slightly lower while thermal comfort is better. These results suggest the robustness of the proposed approach. So, an advanced forecasting approach, leading probably to an increase in computation time, seems to be unnecessary. In addition, a study of the robustness of the proposed strategy has been carried out and is presented in section 6.4.

The multi-area predictive strategy allows the problems encountered by the standard strategies to be solved. During cold days or after week-ends, the anticipation time is longer than in case of warm days. The thermal comfort are just met when the first worker arrives at the building in the morning. As a result, energy waste is low and thermal comfort is very good. In addition, the HVAC sub-systems are switched off before the end of the day, allowing energy savings without impacting thermal comfort in a negative way. This avoids the overheating problem encountered when applying the non-predictive strategies. During warm weeks, the predictive strategy has other advantages. The anticipation time is much shorter than when using the scheduler and the HVAC sub-systems are often turned off before the end of the morning, which allows big energy savings during the afternoon. Thermal comfort requirements are met until the last worker leaves the building. In comparison to the strategy currently being pursued in the building (scenario S1), the multi-area approach (scenario S8) allows energy consumption to be reduced of about 65%, while the duration of thermal discomfort is almost halved (-150 Wh/day•m 2 ). In comparison to scenario S3, which is an efficient scenario, energy saving is about 7.3% (-6.4 Wh/day•m 2 ) and thermal comfort is better. As a reminder, the building is occupied by people from 8:00 a.m. to 6:00 p.m. With the scheduler strategy, the HVAC sub-systems are always turned on 2 hours before the beginning of an occupation period and turned off when people leave the non-residential building. Tables 7 and8 highlight the optimal on/off switching times for two simulation periods, when using scenario S8: from January 4 to 11 (figure 13c) and from November 2 to 9 (figure 14c), 2011. On/off switching times are related to outdoor temperature and solar radiation. As a key point, optimization strongly reduces the HVAC sub-systems operating time.

Computation time

Strategies consisting in a direct control of temperature do not require any computation. In opposition, when the temperature set-points to be applied to the HVAC sub-systems are defined on the basis of the PMV indexes, computation is required. Duration is directly related to the resolution process, computation time is then 2.4 ms for each of the considered areas. Of course, predictive control is the slowest strategy. Duration is variable and strongly depends on the number of time steps needed to find the optimal solution of the problem (at each time step the ANN-based models are used to forecast the PMV index). If the stopping criterion is reached soon (i.e. thermal comfort is achieved before occupancy or not maintained while occupancy), computation is done in about 100 ms. Otherwise, computation lasts 400 ms at the maximum. As a consequence, the use of artificial neural networks has to be carefully considered in order for the proposed management solution to be implemented in an embedded system whose memory size and operation capability are limited.

Robustness of the predictive controller

The MPC strategy requires forecasting the exogenous variables. Consequently, evaluating how accuracy impacts on efficiency is necessary. So, we carried out a complementary study about the robustness of the proposed strategy. This study highlights the impact of underestimated or overestimated exogenous variables. We considered scenario S6 and we applied an error ranging between -50% and +50% to forecasted outdoor temperature (T out ) and solar radiation (SR) values. Figure 15 depicts the results about robustness we obtained, considering the manufacturing area as well as both the ground and first floor offices. Figure 15a is about outdoor temperature. When T out is underestimated (outdoor temperature is higher than estimated by the proposed model), energy consumption increases. In this case, the control algorithm decided for a PMV index and more time is needed to reach the desired comfort level at 08:00 a.m. As a result, the HVAC sub-systems are turned on earlier than when outdoor temperature is correctly estimated. In the same way, the predictive controller has estimated that once the HVAC subsystems are shutted down, thermal comfort will decrease in the rooms faster than it really does. As a consequence, the action to turn the HVAC sub-systems off is delayed. Likewise, an overestimation of T out (outdoor temperature is lower than estimated by the model used) generates an opposite behaviour: heating starts too late, what decreases energy consumption but affecting thermal comfort. However, one can note that a forecasting error ranging between -40% and +30% affects only slightly thermal comfort. As a result, the robustness of the model predictive controller with respect to the uncertainty in forecasting T out is quite good. Beyond this interval, thermal comfort deteriorates in a more significant way.

Figure 15b is about solar radiation. Taking a look at this figure, one can clearly note that a forecasting error does not really affect control performance. Changes in both thermal comfort and energy consumption are very low. As a result, the proposed model predictive controller can be considered as consistent. As one can see in the figure, the HVAC sub-systems are turned on early in the morning (at dawn). From this time to the time people arrive at the non-residential building to work, solar radiation is vey low. So, the prediction error impacts in a more significant way when the HVAC sub-systems must be turned off. Let us note that solar radiation and outdoor temperature are linked together: when solar radiation is low, because of clouds, outdoor temperature is also low.

Overall, accuracy in forecasting T out and SR impacts on thermal comfort and energy consumption. The robustness of the proposed predictive control strategy is quite good, even if accuracy is not high. However, if T out (and/or SR) is underestimated, the HVAC sub-systems are turned on too early. If underestimation is moderate, thermal comfort is improved but to the detriment of energy consumption. In opposition, if underestimation is significant, overheating can be highlighted and thermal comfort is deteriorated. An overestimation of T out (and/or SR) reduces energy consumption and thermal comfort. If solar radiation is overestimated, the impact of overestimation can be considered as insignificant. This impact is slightly higher when outdoor temperature is overestimated. However, the predictive controller is still performing in a good way.

Conclusion

The aim of the work presented in this paper was to develop an efficient strategy based on predicitive control to satisfy thermal comfort requirements in nonresidential buildings equipped with zoned HVAC systems and local controllers, while minimizing energy consumption. We used the PMV (Predicted Mean Vote) index as a thermal comfort indicator. With such an indicator, one can estimate the thermal sensation of people in a building. The algorithm we developed allows the air temperature set-points of the HVAC sub-systems to be computed and the PMV set-points to be reached. Energy consumption can be minimized if operation time is reduced. Thus, we proposed a model predictive controller in order to supervise the local controllers and estimate the optimal time to turn on and off the HVAC sub-systems.

Low-order models based on Artificial Neural Networks (ANN) have been identified to forecast the PMV index in the considered rooms of a non-residential building. These ANN-based models are used as internal models of the predictive controller. We evaluated two different approaches: first, we developed one model per room. In this case, interaction (i.e. heat transfer) between the rooms is not taken into account. In a second time, we proposed a global model for all of the rooms we considered. With such a model, interaction is allowed for. In both cases, thermal comfort is improved and comfort constraints are met.

In order to evaluate the proposed strategy, a dedicated software for building simulation has been used to develop a complete model of a real non-residential building located in Perpignan (south of France). This high-order model allowed different strategies and scenarios to be evaluated and compared. As a key point, one can note that the predictive controller based on the global ANN-based model (interaction between the rooms is taken into account) offers a significant improvement in energy efficiency and thermal comfort assessment. This strategy allows saving up to 65% of energy when compared with the current strategy used in the real building. With this strategy, the HVAC sub-systems are turned on and off at the right time, that is turned on a few hours before the next occupation period to satisfy thermal comfort requirements (when people arrive at the building) and turned off to reduce energy consumption before people leave the building.

In comparison to a standard scheduler, the proposed predictive strategy is more flexible, the switching times being automatically adapted to the actual state of the building, occupancy (internal heat gain) and exogenous perturbations (the weather conditions). Moreover, the developped algorithm is computationnaly tractable (it does not need extensive on-line optimization like with standard MPC) and will be implemented in an embedded system. So, one can note that the results we obtained meet the objectives that were defined at the start of the Batnrj project.

Future work will first focus on trying out the proposed predictive strategy in the real non-residential (reference) building. Then, the developed algorithm will be refined in order to compute an optimal and particular switching time for each of the HVAC sub-systems. Finally, the strategy should be improved to optimize the cooling process during summer time.

Figure 1 :

 1 Figure 1: Topology of the considered non-residential (reference) building.

Figure 2 :

 2 Figure 2: The three considered rooms equipped with sensors and HVAC sub-systems. Only the temperature set-points can be adjusted.

Figure 3 :

 3 Figure 3: Evolution of outdoor temperature at 6 a.m., from January to December 2011.

Figure 5 :

 5 Figure 5: ANN-based PMV model for the room j, ∀j ∈ 1; 3 (no interaction between the rooms).

Figure 6 :

 6 Figure 6: ANN-based PMV model for the rooms j, l and m, ∀j, l, m ∈ 1; 3 such as j = l = m (with interaction between the rooms).

Figure 7 :

 7 Figure 7: MRE [%] during validation, according to the number of hidden neurons and the percentage of data used to train the network (ANN j , room of the building: manufacturing area).

Figure 8 :

 8 Figure 8: MRE [%] during validation, according to the number of hidden neurons and the percentage of data used to train the network (ANN j,l,m j , room of the building: manufacturing area).

  Ground floor offices. R 2 = 0.9705, MRE = 3.69%. Manufacturing area. R 2 = 0.9726, MRE = 3.53%. First floor offices. R 2 = 0.9815, MRE = 2.60%.

Figure 9 :

 9 Figure9: Estimation of the PMV index for each of the three considered areas. The red solid line is the PMV given by EnergyPlus and the blue dashed line is the estimation given by the ANN-based PMV models (ANN j,l,m , ∀j, l, m ∈ 1; 3 such as j = l = m).

Figure 10 :

 10 Figure 10: Control of thermal comfort.

Figure 11 :

 11 Figure 11: Block diagram of the predictive control strategy.

  Scenario S1. consumption is 257 Wh/day•m 2 . Scenario S3. consumption is 111.5 Wh/day•m 2 . Scenario S8. Consumption is 108.4 Wh/day•m 2 .

Figure 13 :

 13 Figure 13: The simulation period is from January 4 to 11, 2011. At the top: temperature set-point (dotted line), PMV index (discontinuous line) and thermal comfort constraints (blue dashed line). At the bottom: power consumption. Green, orange and red lines are for the ground floor offices, the first floor offices and the manufacturing area, respectively.

  Scenario S1. Consumption is 131.8 Wh/day•m 2 . Scenario S3. Consumption is 49.6 Wh/day•m 2 . Scenario S8. Consumption is 31.1 Wh/day•m 2 .

Figure 14 :

 14 Figure 14: The simulation period is from November 2 to 9, 2011. At the top: temperature set-point (dotted line), PMV index (discontinuous line) and thermal comfort constraints (blue dashed line). At the bottom: power consumption. Green, orange and red lines are for the ground floor offices, the first floor offices and the manufacturing area, respectively.

Figure 15 :

 15 Figure15: Robustness of the predictive control strategy (considering the manufacturing area as well as both the ground and first floor offices). The simulation is carried out from January to February, 2011. The blue line is for the average energy consumption and the red line is about the comfort criterion (the percentage of time for which the PMV value remains between -0.5 and 0.5).

Table 2 :

 2 Characteristics of the three considered areas.

	Characteristics Ground floor Manufacturing First floor
		offices	area	offices
	Surface (m 2 )	165	230	155
	Volume (m 3 )	450	900	420
	Heating power (W)	5000	10000	5000
	Number of occupants	8	6	5
	Metabolic activity (W•m -2 )	70	116	70
	Lighting power (W)	1000	1400	1000

are listed in table 1. The exterior walls consist of several layers of different materials. From the outside to the inside are juxtaposed a brick layer, heavy weight concrete, an insulation board, and finally a gypsum board. The interior walls are composed of two gypsum boards, for a total thermal resistivity of 2.2 m 2

Table 3 :

 3 Thermal sensation scale.

	PMV value Thermal sensation
	+3	hot
	+2	warm
	+1	slightly warm
	0	neutral
	-1	slightly cool
	-2	cool
	-3	cold
	national organizations [22]

Table 4 :

 4 H 1 , ..., H 6 are the heat losses coefficients (W•m -2 ). H 1 is the heat loss by diffusion through the skin and H 2 is Clothing thermal insulation.

	clo
	0.8
	0.6
	0.4
	0.2
	0
	Feb.	Apr.	Jun.	Aug.	Oct.	Dec.
	Figure 4: Evolution of clothing thermal insulation, from January to December 2011.

Table 5 :

 5 Evaluation of the tested algorithms.

	Method	Number of Computation
		iterations	time (ms)
	Binary search	9	4.6
	Newton-Raphson	2-3	5
	Secant	4-5	2.4

Table 6 :

 6 Performance of the strategies (simulation is from January to February 2011). (C) is for the Continuous strategy, (S) is for the Scheduler operating mode, and (P) is for the Predictive strategy.

	"Occupancy"	"Vacancy"	Consumption	Comfort
	set-point	set-point	(Wh/day•m 2 ) criterion (%)
	S1 (C) T sp j = 22 • C T sp j = 22 • C	232	78.2
	S2 (C) P MV sp j = 0 P MV sp j = 0	253	74.1
	S3 (S) T sp j = 22 • C	Off	88	82.6
	S4 (S) P MV sp j = 0	Off	98	79.3
	S5 (P) P MV sp j = 0	Off	102	84.9
	S6 (P) P MV sp j = 0	Off	82.9	87.2
	S7 (P) P MV sp j = 0	Off	82	86.6
	S8 (P) P MV sp j = 0	Off	81.6	86.8

Table 7 :

 7 On/off switching times using scenario S8 (from January 4 to 11, 2011) and operating time saved in comparison to scenario S3. January 8 (Saturday) and 9 (Sunday), 2011, are weekend days.

	Day	Jan. 4	Jan. 5	Jan. 6	Jan. 7
	Starting time 6:00 a.m. 6:00 a.m. 6:30 a.m.	6:45 a.m.
	Stopping time 4:30 p.m. 4:15 p.m. 12:15 p.m. 12:15 p.m.
	Time saved (h)	1:30	1:45	6:15	6:30
	Day	Jan. 8	Jan. 9	Jan. 10	Jan. 11
	Starting time	n.a.	n.a.	6:15 a.m.	6:15 a.m.
	Stopping time	n.a.	n.a.	2:15 p.m. 12:15 p.m.
	Time saved (h)	n.a.	n.a.	4:00	6:00

Table 8 :

 8 On/off switching times using scenario S8 (from November 2 to 9, 2011) and operating time saved in comparison to scenario S3. November 5 (Saturday) and 6 (Sunday), 2011, are weekend days.

	Day	Nov. 2	Nov. 3	Nov. 4	Nov. 5
	Starting time 7:30 a.m. 7:45 a.m.	7:30 a.m.	n.a.
	Stopping time 9:45 a.m. 10:00 a.m. 10:00 a.m.	n.a.
	Time saved (h)	9:45	9:45	9:30	n.a.
	Day	Nov. 6	Nov. 7	Nov. 8	Nov. 9
	Starting time	n.a.	6:45 a.m.	7:00 a.m. 7:15 a.m.
	Stopping time	n.a.	12:15 p.m. 9:00 a.m. 8:45 a.m.
	Time saved (h)	n.a.	6:30	10:00	10:30

Acknowledgments

The authors want to thanks the Pyrescom company (www.pyres.com) for its financial support. Jean-Michel Cabanat and Cédric Calmon are acknowledged for their technical help and support.


Atef Dorai
email: atef.dorai@univ-st-etienne.fr

Virginie Fresse
email: virginie.fresse@univ-st-etienne.fr

El-Bay Bourennane

Abdellatif Mtibaa

A Novel Architecture for Inter-FPGA Traffic Collision Management

Keywords: Traffic Collision, NoC, Inter-FPGA, Multi-FPGA

with the increasing complexity of various communications and applications, Network-On-Chip (NoC) is one of the most efficient communication structures. Multi-FPGA platforms are considered as the most appropriate experimental solutions to emulate a large size of MPSoCs (Multi-Processor System-on-Chip) based on a NoC. The deployment of the NoC into several FPGAs requires the use of inter-FPGA communication links. The number and performance of external links restrict the bandwidth of communication. Currently, the number of inter-FPGA signals is considered as a substantial problem in NoC implemented on Multi-FPGA architectures.

In this paper, we propose the integration of the collision management architecture connected to the NoC. Two collision avoidance algorithms are proposed in the structure to balance the load injected between all routers connected with one external link. This architecture leads to high timing performances in multi-FPGA system communications. The results demonstrate the efficiency of the collision management structure connected to the NoC. The collision management algorithm is chosen according to the type of inter-FPGA communication requirements.

I. INTRODUCTION

The large-scale integration of embedded cores in MPSoCs design will increase in the future years [START_REF]International Technology Roadmap for Semiconductors (ITRS[END_REF]. For example, Intel has developed a co-processor called knights corner has 50 cores [2], NVIDIA has announced a multicore-chip called Fermi that has over 512 CUDA cores [START_REF]Next Generation Cuda Architecture[END_REF]. To support the numerous parallel data transmission and high bandwidth, communication infrastructure on-chip is needed.

MPSoCs using a NoC are the most efficient architectures for many core applications (i.e. applications with hundreds of cores). The verification of such complex architectures can be handled with prototyping process on programmable devices such as FPGA. The resources of one FPGA are not enough to handle the complete MPSoC based NoC architecture. Multi-FPGA platforms are then required. Implementing a large size of NoC on such platforms requires to partition the NoC into subnetwork and to connect each FPGA with external links. The number of communication protocols (when using a plat-form) or the available I/O pins (when using the FPGA only) is restricted. Several nodes of the NoC must share external links, reducing the bandwidth and creating collisions when several nodes require the access at the same time. For example, the virtex-6 XC6VLX195T FPGA has 600 I/O pins.

Prototyping a NoC can lead to connect 15 routers with 16-bit data or 8 routers with 32-bit data. If the number of routers to connected is higher, sharing the external links is required. This reduces the bandwidth between each FPGA creating collisions. However, network topologies have high impact on the size of NoC prototyped. The mesh topology with the higher level of interconnect is not easily scalable on multi-FPGA [START_REF] Lankes | Hierarchical NoCs foroptimized Access to Shared Memory and IO Resources[END_REF].

In this paper, we propose a collision management structure containing two kinds of collision management algorithm inspired from the computer network. In this structure, the external access is done using an Access Point (AP) and an Access Protocol block. The collision management algorithms are the Backoff algorithm and the weighted round robin algorithm adapted from computer network to NoC on multi-FPGA architectures. Some experiments are conducted to compare both approaches and to help the designer to select the most appropriate algorithm according to the communication requirements.

This paper is organized into five sections. Section II presents the background and related works related to the deployment of the NoC on multi-FPGA platform. Section III presents the proposed architecture dedicated to deal with congestion phenomena. This section also details both types of collision management used and the strategies. Section IV presents the experimental results. Comparisons between the Backoff algorithm and weighted round-robin arbiter are also presented in this section. Finally, Section V concludes the paper.

II. BACKGROUND A. Related work

NoC communication on multi-FPGA architecture provides high scalability, high performances and low power consumption [START_REF] Al-Hashimi | System-on-Chip: Next Generation Electronics[END_REF]. Few works have been achieved to evaluate the performances of a large NoC. Explorations made in [START_REF] Fresse | From Mono-FPGA to Multi-FPGA Emulation Platform for NoC Rerformance Evaluations[END_REF] show the limitation of the size of a basic NoC on a single FPGA. Multi-FPGA platform must be considered in a system containing hundreds of cores. Two different approaches for the deployment have emerged. The first approach consists in partitioning the 2D NoC on each FPGA and replaces inter-FPGA links by external serial or parallel buses [7] [8]. This approach ensures the evaluation of communication performance between two FPGAs as each link remains. However, it is difcult to deploy a large NoC as there is a restricted number of external links. In Fig. 1. Access-protocols in computer network [START_REF] Liua | Building a Multi-FPGA-based Emulation Framework to Support NoC Design and Verification[END_REF] the NoC system contains two parts (the network and the processing system). Each partition is mapped onto different FPGA. This work used the region based partition where each region is composed of a set of processing cores and their routers. The resource chip is composed of four surrounding FPGAs and the network FPGA is the middle FPGA.

The second approach consists in developing a structure dedicated based on a hierarchical 3D concept [START_REF] Seiculescu | SunFloor 3D: A Tool for Networks on Chip Topology Synthesis for 3-D Systems on Chips[END_REF] [START_REF] Feero | Networks-on-Chip in a Three-Dimensional Environment: A Performance Evaluation[END_REF]. Another solution in [START_REF] Stepniewska | Network-on-Multi-Chip (NoMC) for multi-FPGA multimedia systems[END_REF] presents the hierarchical network architecture intended for multi-FPGA. This proposition is based on the tree topology. It consists of three levels of hierarchy (local network, cluster and system). The synthesis results show a loss of 20% of the occupied hardware for the NoC in case of the implementation on the Xilinx Spartan-6 chip. Another methodology is proposed in [START_REF] Fresse | From Mono-FPGA to Multi-FPGA Emulation Platform for NoC Rerformance Evaluations[END_REF] to deploy the 2D NoC onto multi-FPGA platforms with a restricted number of external links. The deployment and the associated adaptations depend on both the number of FPGA routers (NR) to be connected to the external links and the number of inter-FPGA links (NLI). For a large size of NoC, the number of routers to be connected to one external link is huge, creating collision problems when several routers want to send data at the same time in external link.

The collision avoidance and management for large NoC based SoC on FPGA has not been yet proposed in literature. The contribution of the paper is to propose some collision management solutions to distribute the shared external links reducing the collision and increasing the bandwidth.

B. Management of collision in computer network

In the OSI reference model, the Media Access Control (MAC) protocol is positioned at the second layer in computer network. It plays a very important role to control the access for the external users. The MAC protocol can be classified into two majors groups as shown in Figure 1. The first group contains methods access random using ALOHA and Carrier Sense Multiple Access (CSMA) based on Backoff algorithm. The second group contains scheduled access methods. Common access-protocol supporting scheduling mechanisms for computer network are: Time Division Multiplexing, Round-Robin and Weighted Round-Robin [START_REF] Jurdak | A Survery, Classification and comparative Analysis of Medium Access Control Protocols For Ad hoc Networks[END_REF]. Two multiple access protocols will be used in our work, a random access algorithm based on the Backoff algorithm and a scheduled access algorithm based on the Weighted round-robin algorithm.

a) Backoff algorithm (BO): It is one class of collision resolution algorithm used in the medium access control. When

III. COLLISION MANAGEMENT STRUCTURE FOR NOC ON MULTI-FPGA

A large NoC is considered to be deployed on the multi-FPGA platform. Many nodes (i.e. routers) sharing one external link compete to have access to the external link. Some collisions can occur if several routers want to send data to the external link at the same time. A collision management structure is therefore proposed to avoid such collisions and to efficiently distribute the access to the external link. The collision management structure proposed is inserted between the NoC and the external FPGA link. It can control and manage the access several cores connected to one external link. This structure is constituted of two main blocks: the accessprotocol and the Access-Point (AP), as depicted in Figure 2.

A. Access-Point (AP)

The Access Point (AP) is an interface that provides connectivity between the access-protocol and the external link. It integrates unidirectional buffer for send and receive data. If a router wants to send packets to the external link, the Access-Point checks if the external link is free. If the link is free, the packet is sent to the AP for transmission. If several routers want the access to the external link, the AP receives the packet from the router selected by the Access Protocol block.

The AP is adapted to the type to the external link used. The communication between two AP uses the handshake flow control in the experiments conducted in the paper. Reducing the number of APs can lead to the optimization of the number of pins used.

B. Access-protocol

The access-protocol block is inserted between the routers and the AP. It contains one block dedicated to select the router amongst many routers requesting the access. The accessprotocol use packet-switching flow control, this presents an attractive solution for communication intensive when the number of router is as high as 8 [START_REF] Zeferino | A Study on Communication Issues for Systems-on-Chip[END_REF]. This block integrates a collision management algorithm extracted from computer network and adapted to NoC on multi-FGPA. Two algorithms are proposed: the backoff algorithm (BO) and the Weighted Round Robin (WRR) algorithm. Both are used in the experiments for comparisons and to help the designer to select the most appropriate algorithm. The Access Protocol allocates the time for each router when it has access to the AP [START_REF] Stiliadis | Latency-Rate Servers: A general Model for Analysis if Traffic Scheduling Algorithms[END_REF]. The allocated time depends on the algorithm and the packets to be sent. The access-protocol contains an intelligent data allocation for timevarying and for monitoring the real-time load traffic for each packet. The timing vector allocation is first detailed, then the collision management algorithms are presented.

c) Vector allocation time-varying: The flows from the NoC to the AP are time-varying. It is therefore necessary to allocate the time inside AP for each packet incoming from routers. Each packet inside the NoC contains a header and a payload (containing data). Each packet to be sent to the AP has different size (depending on the payload, the header is identical) arriving at different rate. The information in the header of packet is extracted to set the allocation phase. Each packet is stored in the local input port of the router, all the received packets connected to the AP goes first to the Allocation process (given in algorithm 1) for the timing allocation.

The router allocation depends on the algorithm used as depicted in Figure 3. An example of 4 routers connected to the AP is presented (R0 to R3). Each packet has a specific size of packet and the number of packet to be sent is different. The variability of packets depends on the algorithm mapped onto the NoC. The size of packets is extracted and used to allocate the required time in AP (considering that the timing allocation is given to send one complete packet). At a specific time, some routers do not require to send packet to the AP (R2 is in idle state as there are any packet available in the local port), other with different size of packets do. The difference between both algorithm is the scheduling queue in the AP as the allocation value differs from each other.

Algorithm 1: Pseudo code for mechanisms allocation

Require: P: Input packet Ensure: Time: Time allocate for each packet Initialization;

for i ← 0 to n -1 do F litN umber[i] ← ∅; N umberF lit[i] ← ∅; end for i ← 0 to n -1 do if (rx[i]='1') then F litN umber[i] ← F litN umber[i] + 1;; if (FlitNumber[i]=1) then N umberF lit[i] ← conv integer(P [i]) + 2; T ime[i] ← N umberF lit[i]; end if FlitNumber[i]=NumberFlit[i]+2 then F litN umber[i] ← ∅; T ime[i] ← ∅; end end end
The algorithm describes the process of the time allocation as shown in algorithm 1. The array of variables called FlitNumber is initialized to zero. In this example, the routers connected to the AP are numbered 1 to n, i is an index whose value is between 0 and (n-1). A new request maintains the list of routers that are connected to the access-protocol by the input signal (rx). The information is in the header of the packet and is extracted by the process. This algorithm analyzes the data and extracts the size of packet. This time allocation value is sent as an input of the access-protocol. However, if the output port of one router connected to the access-protocol is empty, the FlitNumber variable becomes equal to NumberFlit at the end of the transmission. The FlitNumber is set to zero and the index i is moved to another router that will start transmission.

d) Backoff algorithm: The structure of the accessprotocol using the Backoff algorithm is depicted in Figure 4. It consists of two blocks, one for transmission and another one for reception. The transmission block contains a priority arbiter, a multiplexer, a counter for the flits of packets and the Backoff block. The reception part includes the demultiplexer, the counter and the routing algorithm.

Each router that wants to send packets to the AP, sends a request signal to the access-protocol. If there is only one request from one router, the arbiter receives the request signal and sends the allocation-time associated to the packet to the AP. The time is set using this allocation time to send the full packet to the AP. The accesss-protocol transmits the packet to the AP by configuring the multiplexer. When the counter value reaches zero, the connection between the transmitted node and The Backoff algorithm model contains 2 major modules which are a Random generator and a Backoff-Timer. The Backoff-Timer accepts the values of unsigned integers from Random generator module. If several routers request the access to the AP, the random generator supplies random values to each requesting router. The Backoff-Timer module generates random values of integer from 1 to 255. This module is based on the concept of linear-feedback shift register (LFSR). The total number of random states generated on LFSR depends on the feedback polynomial. As it is a simple counter, so the maximum value is (2 n -1) by using maximum feedback polynomial, where n is the number of shift registers used in this design. Thus, an LFSR is most often a shift register whose its input bit is driven by the exclusive-or (XOR) of some bits of the overall shift registers value.

If the external link is busy while routers request a transmision, their transmissions are deferred until the end of the current transmission and a randomly selected Backoff-Timer period. Figure 5 shows an example of a data transmissions scenario in the proposed Backoff algorithm. The NoC in this example have 3 concurrent routers resquesting accesses to the AP. Multiples routers are deferred and selected according to the random Backoff. The router having the smallest random Backoff-Timer will win the transmission as the waiting time is smaller. Once the current router had finished the transmission, the remained routers start decrementing their Backoff-Timer. The router which finish to decrement its Backoff-Timer, can start its transmission. This mechanism is repeated until all routers have accessed one by one to the external link.

e) weighted round-robin: Each router initiates a request signal to get access to the external link and deactivate the request signal when the transmissions is finished. If more than one router request for the external link at the same time, the Fig. 5. Backoff procedure Fig. 6. Weighted Round-Robin procedure access is granted on the round-robin basis. For each packet, a weight is set, this weight indicates the time allocated to its associated router inside the AP. The weight depends on the size of packets (number of flits inside a packet). The weight 0 is set to routers that do not request to send packet (idle state).

An example is given in Figure 6. All routers resquest the access to the AP. The weights are given according to the position of the router (weight 1 for first router, weight 2 for the second and weight 3 for the third). The access is given to the first router with a time depending on the size of the packet. The first packet contains 3 flits, the counter will count 3 times to send one flit to let the AP to send the complete packet.

This procedure ensures that any independent router is locked out while another router has the continuous access. The continuous access is granted to any router for a period of time. The weighted round-robin scheduler is designed to serve different routers capacities. In WRR, each router-queue has a counter that specifies the number of its that can be sent from it. The use of the AP is optimized as the allocation is based on the size of packets.

IV. EXPERIMENTS

In this section, some results are presented by using the collision management algorithms. They are based on the The minimal latency is the time elapsed from the moment the first message (i.e. all packets) is received by the destination node. The maximal latency is the time required for last router to get the latest message. The average latency for all routers is also defined.

B. Resource results

1) Synthesis results: Figure 8 represents the percentage of resources used on the Virtex-6 FPGA. The number of resources for all three architectures is small compared to the number of resources available on the FPGA. The advantage becomes obvious with the increase of the sub-Network size. The percentage of registers used increases from approx.0.12% to 1.29% and 0.12% to 1.09% for a 1x2 to a 1x16 sub-NoC respectively with the BO and WRR. The percentage of LUTs increases from approx. 0.68% to 6.67% and 0.68% to 9.07% with the Backoff and the weighted Round-Robin. These extra resources are not signicant compared to the total number of the available FPGA resources. The number of resources linearly depends on the size of the NoC whatever the architecture used.

The number of resources added to the NoC when integrating the collision avoidance architecture is depicted in Figure 9. The percentage of added registers to the NoC is from 43% to 58% for the Backoff and is from 30% to 48% for the Weighted Round-Robin (Figure 9.a). The percentage of added registers remains stable for a number of routers higher than 4 and for the WRR architecture. The percentage of added LUTs is 10% and 26% for the 1x4 with the BO and WRR (Figure 9.b). It corresponds to 245 more registers and 185 more LUTs. It uses 54%, 30% of registers and 19%, 62% of LUTs for the size The percentage of LUTs is higher for the WRR algorithm compared to BO. The percentage of registers for the BO compared to the WRR. The percentage of the total added resources is the same for both (the sum of added registers and LUTs is globally the same). Both architectures require more resources than the original NoC itself.

2) NoC partitionning: One access-point is used in the experiments. All routers are connected to this AP. The size of the NoC partitioned can be higher with the use of the AP compared to a traditional link to link connection. Using a NoC partitioned into sub-NoC (without AP), the maximal number of routers that can be connected to external pins is 9 (for 32-bit flits) and 4 (for 64-bit flits) for the ML605 platform. Table I presents the number of routers in the basic partitioning and the number of AP when using a collision avoidance architecture. This is therefore not possible to deploy a large size of NoC without sharing external links. The use of the AP can increase the size of the NoC as several routers can be connected to the AP (in theory the number is unlimited). The limitation is due to the number of FPGA resources and the FPGA communication network. Moreover the number of AP depends on the number of pins available in the FPGA and the size of the external bus connected to the AP. It is therefore possible to increase the number of AP. For the size of flits of 64-bits the maximal number of AP is 4 and 9 for the 32-bit size. The collision management architecture can reduce the number of pins and can increase the number of routers. The use of the AP offers a substantial improvement both compared limitation made by the number of I/O.

C. Timing results

This section analyses the timing performances obtained with both proposed collision management algorithms and compare these results. The timing performances with the NoC only are not considered as it cannot manage collisions. The objectives are to analyze the impact of the two access-protocols, with several load injected and with several lengths and number of packet when several nodes send packets to AP at the same time. Several experiments with different traffics are done using synthetic traffics and real application traffics. In the synthetic traffic analysis, the evaluation of the communication between TGs and TRs for each link is done using synthetic scenarios. The test scenario is the one to one scenario. In this scenario, each router (0, j) in first FPGA communicates only with the router (1, j) in the second FPGA. Experiments are done on homogeneous and heterogeneous packets. Packets are homogenous if all the packets have the same size and the same T idle between two packets for the same destination (and the same data injection rate). Traffics are heterogeneous when the size of packet is different (with fixed or varying T idle ). The detailed experiments in a collision context are given as follows:

• Homogenous traffic: all TGs send the same packet (same size and same number) with the same data injection rate (T idle to). • Heterogeneous traffic: the TGs send the same size of packets, the value of T idle changes and the data injection rate to. • Heterogeneous traffic: T idle is fixed for all packets and the length of packets changes for each TG (the data injection rate is different for each TG). • Heterogeneous traffic based on the real application: the traffic parameters are based on the real-application for multispectral imaging. In this application, the number and size of packets and the T idle vary for each TG.

1) Homogenous traffic: The first scenario using homogenous traffics is done on the regular 1x8 sub-network on each FPGA. The timing evaluation is based on sending 50 packets, each packet containing 100 flits. The T idle and the data injection rate are the same for all routers. Figure 10 and Figure 11 present the obtained results for the minimal and maximal latencies with different data injection rates. The data injection rate varies from 10% to 80%. The time spent by routers to transmit one flit is two clock cycles. The minimal and maximal latency strongly depend on the packet scheduling on the access-protocol, the number of routers connected to the AP and the data injection rate. It is observed that the minimal latency for the BO algorithm converges and becomes constant from 50% data injection rate. The minimal latency is the same whatever the number of the routers connected to the AP for the Backoff architecture. The minimal latency changes according to the number of routers for the WRR architecture. The load injection does not have any impact on the minimal latency. The WRR architecture provides better minimal latencies for a data injection rate below 50%. The BO provides better minimal latencies above 50%. Figure 11 depicts the maximal latencies using the Backoff (a) and the Reighted Round-Robin (b) for different number of routers and for different data injection rate. There is a degradation of the maximal latency for BO, the maximal latencies depend on the number of routers and on the load injected. For most scenarios, the WRR provides a better maximal latency. The maximal latency is identical with 4 routers and for a data injection rate higher than 10%. The maximal latency is also identical for 8 or 12 routers with the 40% data injection rate and for 16 routers with the 30% data injection rate.

The maximal latency for BO for some traffics is higher than the WRR solution because of the value of Backoff-Timer generated by the random generator. For the size of the sub-NoC, the minimal latency for the Backoff does not exceed 120.10 3 cycles, while the maximal latency varies between 160.10 3 and 250.10 3 cycles. This variation does not appear with WRR as the minimal and maximal latencies only depends 2) Heterogenous traffics: Two scenarios using heterogeneous traffics are presented. Both examples exhibit most intensive communications with heterogeneous packets commonly used in most systems. Destinations for packets are chosen to have a point to point connection (similar than the previous experiment), different T idle and different length with bandwidth requirements are randomly selected. In the first example, T idle is set to 100 cycles and the size of packets is randomly chosen for all transmitting routers (the size of packet also varies). In the second example, all routers send packets with the same size and number but with a varying T idle . Three scenarios are used for both examples. For all experiments, the average, minimal and maximal latency are compared. In the first experiment, the position of the load injected changes from router to another one. For each example we apply the time allocation algorithm. Table II and Table III describes both examples with the different values of T idle , the size of packet.

Figure 12 gives the minimal, maximal and average latencies for the three scenarios using the BO and WRR. The T idle is 100 clock cycles and the size of packets changes as shown in Table II. The average, minimal and maximal latencies are similar with the use of the WRR whatever the scenario. The average, minimal and maximal latencies changes according to the scenario used. The average and minimal latencies are better with the BO and the maximal latency is better with the WRR. The first packet arrives faster and the last packet arrives later with the BO. In the average, packets arrive faster with the BO compared to the WRR. The packet distribution is more uniform with the WRR. Timing performances can be optimized with the BO architecture for heterogeneous traffics. Figure 13 gives some experiments with the same size of packets (with different value of T idle for each TGs). The T idle are given in Table III. The average timing performance is close for both solutions (around 3000 clock cycles). The minimal latency is better with BO and the maximal latency is better with WRR.

For both experiments, the maximal latency is worse for 3) Results under applications specific traffic: In the previous scenarios, experiments are done with intensive one to one connections between FPGA with homogeneous and heterogeneous traffics. The evaluation of the proposed architecture is done under a real benchmark application, a multispectral image application developed for art authentication [START_REF] Zhang | Evaluation of NoC Dedicated to Multispectral Image Data Communication[END_REF]. This application contains 14 tasks with communications given in the task graph depicted in Figure 14.a. The communication requirements of each communication are given by a triplet (x,y,z), indicating the size of packets, the number of packets and the T idle . For example, the message from T3 to T6 is [START_REF] Xinyu | Multi-FPGA emulation of a 48-cores multiprocessor with NOC[END_REF]26215,[START_REF] Xinyu | Multi-FPGA emulation of a 48-cores multiprocessor with NOC[END_REF] indicating that 26215 packets with the size 8 is sent and the idle time between packet is 8 clock cycles. The task mapping for each task for the application onto two 1x8sub-NoCs is described in Figure 14-b.

For the application, packets have to be sent from both sides. Two collision avoidance architectures are integrated between both sub-NoC to transmit data for both sides. Figure 15 shows the communication latencies between routers (the routers depicted in the figure are the receivers). The communications between R3-R4 (receiving router R4 in the figure), R2-R5 and R3-R6 are faster with the WRR than BO. The differences between the BO and WRR for the communications give above are high as it represents 50% of added clock cycles. For some communication (receivers R9, R11 and R13), the latency is better with the BO than the WRR. In this case, the WRR architecture is most efficient than the BO architecture (not for all inter-FPGA communications).

V. CONCLUSION

In this paper a novel collision management architecture dedicated to manage collisions between sub-NoC implemented on different FPGA boards is proposed. The proposed collision management consists of two blocs: the Access Point to send packets between inter-FPGA links, and a Access Protocol to manage the collision and schedule the access to the Access Point. This block integrates two algorithms, the Backoff algorithm that distributes randomly the access and the weighted round-robin algorithms. The use of the AP can decrease the number of external IO (and links) and it is possible to deploy a large a size of NoC on multi-FPGA.

The experiments based on synthetic traffics and on a real application evaluated on an existing NoC demonstrate that both congestion algorithms are efficient. The choice of the algorithm depends on the traffics. Both can optimize the schedule on the Access Point with a number of required added resources on the FPGA.

In this case, the WRR architecture is most efficient than the BO architecture (not for all inter-FPGA communications). The values of the idle time should be explored to fully exploit the collision management algorithm (the previous work selected the idle times using the background of the user).

Fig. 2 .

 2 Fig. 2. Collision management algorithm based-NoC on multi-FPGA

Fig. 3 .

 3 Fig. 3. Bandwidth communication for both access-protocol

Fig. 4 .

 4 Fig. 4. Structure of Backoff algorithm based NoC multi-FPGA

Fig. 7 .

 7 Fig. 7. Emulation platform designed on multi-FPGA

Fig. 8 .

 8 Fig. 8. Percentage of resources on virtex-6 FPGA: (a) registers, (b) LUTs

Fig. 9 .

 9 Fig. 9. Added resources compared to NoC only: (a) registers, (b)LUTs

Fig. 10 .

 10 Fig. 10. Minimal latency for : (a) Backoff algorithm (b) Weighted Round-Robin

Fig. 11 .

 11 Fig. 11. Maximal latency for : (a) Backoff algorithm (b) Weighted Round-Robin

Fig. 12 .

 12 Fig. 12. Different scenario based on the variation of the size of packet (with the T idle constant)

Fig. 13 .Fig. 14 .

 1314 Fig. 13. Different scenario with the variation of data injection rate T idle

Fig. 15 .

 15 Fig. 15. The communication latency of the imaging multispectral application between APs

TABLE I INTER

 I -FPGA CONNECTIONS ACCORDING TO THE PARTITIONNING

	Size of flits	32-bits 64-bits
	Maximum number of AP	9	4
	Routers surrounding FPGA before adding AP	8	4

TABLE III VARIED

 III DATA INJECTION RATE T idle

	Path	packet lenght	scenario0	T idle scenario1 scenario2
	R0 → R1	20	10	360	160
	R2 → R3	20	15	160	95
	R4 → R5	20	25	95	15
	R6 → R7	20	40	60	360
	R8 → R9	20	60	40	25
	R10 → R11	20	95	25	60
	R12 → R13	20	160	15	10
	R14 → R15	20	360	10	40

ACKNOWLEDGMENT

The funding for this project was provided by a grant from la Region Rhone-Alpes.