M Rubio

M Sonebi
email: m.sonebi@qub.ac.uk

S Amziane

3D PRINTING OF FIBRE CEMENT-BASED MATERIALS: FRESH AND RHEOLOGICAL PERFORMANCES

Keywords: 3D printing, polypropylene fibres, penetration, slump flow, superplasticiser, viscosity modifying agent EcoGRAFI

The aim of this paper is to investigate the effect of different mix composition on fresh and rheological properties of a printable mortar. For the mix design, two binders such as fly ash (FA), and silica fume (SF) were used with cement and sand for a water/binder ratio of 0.50. Polypropylene fibres (PP), superplasticizer (SP), and viscosity modifying agents VMA (Diutan gun and nano-clay) were used in the investigation. The results show that adding 24% of fly ash and 8% Silica fume increased the yield stress, cohesiveness, and improved the structure homogeneity and stability which appeared to be an advantage to print layers. Indeed it reduced the fluidity, bleeding and the blockage of layers. Additionally, it also improved the passing ability through the extruder and showed a greater resistance to penetration. The addition polypropylene fibres (0.2% to 0.6%) led to a higher yield stress, and cohesiveness of the mix. This is led to a stable mortar and kept the shape of layer under its own weight and sustained weight of successive layers. The incorporation of PP fibres reduced the time gap. Furthermore, high dosage of fibres can create more difficulties to extrude layers and led more drainage phenomenon which increased the stiffening of the mix. PP fibres might be efficient to print layers due to their small length and diameter which resulted in a dense and efficient network.

VMAs cause an important loss of workability and time gap which influenced the passing ability of the mix through the extruder. However a high dosage of SP increased also bleeding and segregation and may affect the stability and shape of the printable layers. Good correlations existed between slump flow results, penetration results and also yield stress.

INTRODUCTION

Inspired by the 3D printing with polymer materials, 3D printing opens new horizons to cement-based materials of the construction industry. As formworks represent 35-60% of the overall costs of concrete structures, it would be an important financial advantage to use this new technology. Besides, 3D printing in building structures without formworks permits to improve the construction rate and open to new architectural liberties. Replacing humans work by additive technology automated allows building in polluted zones or on planets as reported in the project of contour crafting with the construction of bases on the moon for the NASA [P. 3D 2015].

Several applications were reported on applications and prototypes of 3D printing [Khoshenevis 2006] [Le 2012[START_REF] Amziane | Alec , Exquisite 400 m2 villa 3D printed onsite in Beijing in just 45 days[END_REF][START_REF] Scott | Chinese Construction Company 3D Prints an Entire Two-Story House On-Site in 45 Days, Article from the 3DPrint website[END_REF][START_REF] Amziane | Alec , Exquisite 400 m2 villa 3D printed onsite in Beijing in just 45 days[END_REF]] [Lloret 2015]. Contour Crafting is currently the most effective method researchers have found so far. The concrete layers are poured out by robotic machines and can be used for small-scale industrial parts and building structures [START_REF] Malaeb | 3D Concrete printing: machine and mix design[END_REF]]. The two previous pioneers of 3D printing concrete as companies were the Shanghai Company, WinSun [START_REF] Wangler | [END_REF]]. It was reported that to 10 full scale houses have been printed in less than 24 hours with 3D printing concrete. The method is appealing by the low cost of each house, around 5000$ [START_REF] Malaeb | 3D Concrete printing: machine and mix design[END_REF]]. The largest 3D printer has been created by the World's Advanced Saving Project launched in 2010 by the Italian Centro Sviluppo Progetti Company. It was 12 meters tall in a hexagonal shape [START_REF] Wangler | [END_REF]]. Finally, HuaShang Tengda Company (China) has recently managed to incorporate reinforcements to its 3D printed concrete structure. In fact, they have printed a 400 m² villa around iron frameworks by using an original nozzle design. They first raised the complete steel bars and pipes complex of the house. Then, concrete has been printed over it with big scale 3D printer [START_REF] Scott | Chinese Construction Company 3D Prints an Entire Two-Story House On-Site in 45 Days, Article from the 3DPrint website[END_REF]]. The printability of fresh cement based materials is the ability of the layer to maintain itself and the weight of the layers subsequently deposited. The time gap between two deposited layers must be sufficiently long to provide adequate mechanical strength capable of sustaining the weight of the subsequently deposited layers and also short enough to provide an optimized bond strength and building rate. It appears that it's the shortest time gap which allows the stability of the structure during construction. The ability of the first layer to support itself and others layers is link to its rheology and more precisely to its yield stress [Perrot 2015]. The aim of this study is to evaluate the effect of different mix composition parameters included dosage of superplasticizer (SP), addition of fly ash (FA) and silica fume (SF), the dosage of polypropylene fibres (PP) and type of viscosity modifying agent (VMA) on fresh and rheological properties of a printable mortar.

EXPERIMENTAL PROGRAMME

Fresh properties of printed cement-based mortar compose of fly ash and silica fume, incorporating fibers (PP), viscosity modifying agent (VMA such as diutan gum, nano-clay) and superplasticizer were investigated.

The following properties of the mortars were examined: the slump flow, the penetration test, the rheological properties (yield value), and the extruded property. Moreover, the relationships between the fresh properties were evaluated.

Materials

The mortars were prepared with a fixed water-to-binder ratio (w/b) of 0.50. Portland cement CEMI 42.5N specified by BS EN 197-1: 2000 (specific gravity of 3.13) was used in all mixes. Fly ash from Scot ash ltd was added and conformed to BS EN 450-1:2005. Undensified silica fume (SF) were used with a percentage of 8% relative to the mass of cement. The percentage of SiO2 was more than 90% and the specific surface area of SF was 17500 m 2 /kg with a specific gravity of 2.2. A synthetic polycarboxylate polymer-based superplasticiser (SP) with solid content of 30% and specific gravity of 1.05 was used. Diutan gum was supplied by Kelco-crete which is an anionic polysaccharide gum as used as viscosity modifying agent (VMA1). It was used as powder at 0.05% (by mass of binder). A second VMA Acti-gel208 nano-clay based composed of attapulgite-clay small needles with negative charges (VMA2) is used at 0.10% (by mass of binder). Sand with maximum particle size of 1.18 mm was obtained by sieving oven-dried (at 105 ±5 °C) sand with particle size of 0-5 mm. Polypropylene fibres (PP) having length 6 mm was used to improve cohesion, holding, mould-ability, and to limit the cracking of cementitious composites.

Mixing and testing procedure

The mortars were prepared with high-shear Hobart mixer in 2-L batches. Premixed solid components, i.e. cement, fly ash (if any), silica fume (if any) and sand, were mixed for 30 seconds at low speed (140 rpm). Next, water at temperature of 16 ±0.5 °C and SP were added together to the mixer and mixed for 30 seconds at a low speed (140 rpm). Then the mixer was stopped, any lumps of solids were crushed, fibres (if any) and VMA1 or VMA2 (if any) were added (within 1 min), and the mortar was mixed again for 2 min (4 min when VMA2 is added) at a high speed (285 rpm). Then VMA1 (if any) is added and the mortar is mixed 1 min at a low speed (140 rpm). The temperature of the mortar after mixing was 20 ± 1 °C. For all tests the timing is given from zero timethat is, the time when the cement particles first touch the mixing water.

The penetration test (cone plunger) was started at 6 min (immediately after the end of mixing -Fig. 1). After filling the cone mould with mortar in two layers, the cone plunger is adjusted in order to allowing the cone to just touch the surface of the mortar sample. Then the cone plunger is released allowing the plunger to penetrate into mortar paste under its own weight for 5 seconds. After 5 seconds, the penetration value is noted to the nearest millimetre. Then the slump flow test was started at 10 min (Fig. 2). The dimensions of cone were 100 x 70x 60 mm. The cone-shaped mould was placed in the centre of a jolting table. After filling with mortar in two layers, the cone was gently lifted 15 times (approximately 30 s after finishing of placing of the grout). When the flow stopped, the spread of the mortar was measured with a ruler in two perpendicular directions. Finally, extrudability of mortar mixes is tested with the simple modified joint gun described in Fig. 3. Rheological measurement was carried out with a computer-controlled vane viscometer (Haake VT550). At 6 ± 1 min, approx. 800 ml of the sample was introduced into a plastic container where the vane was plunged. After 30 s rest, the test was started and the mortar was sheared at different shear rates. The two rheological parameters, yield stress (τ0) and plastic viscosity (μp), were obtained from the modified Bingham model fitted to the experimental data (downcurve). The yield stress at a zero shear rate was extrapolated from the Bingham model. Unfortunately, as mortar mixes were too stiff to be characterized with the viscometer, a semi-empirical alternative is used to determine the yield stress using cylinder measurement (slump -Fig. 4, [Pashias 1996]) : s' = 1 -2τ′ y ( 1 -2ln(2τ′ 0 ))

where:  Cylinder dimensions : h 0 = 138 mm and d 0 =64 mm  s = h 0 -h with h 0 the initial height and h the final height  s' = s/h deformation quantities are dimensionless  τ′ 0 = τ 0 /ρm.g. h 0 stress quantities are dimensionless

The test procedure is detailed in the following steps.

The mould is placed centrally on the flow table and the mortar is introduced in two layers. Each layer is compacted with ten short strokes in order to have a uniform filling of the mould. The mould is maintained in place firmly during the filling. The excess of mortar is remove with the help of a palette knife. After 15 seconds the cone is gently and vertically lifted and the height of the spread mortar is measured (Fig. 4).

The weight of the mortar was measured in constant volume and the fresh density of the mortar was calculated.

The workability life is a crucial parameter which is influenced by the build-up rate of layers. It was measured by the time at which it reached a defined limit of stiffness or workability during the gun extrusion test.

The workability life test measuring the evolution of the consistency, yield stress and extrudability during time was performed beginning with the first measurement of the flow table test and penetrometer test, and then cylindrical slump test and extrudability test. After, these tests were repeated every fifteen minutes until the mortar was too stiff. These tests are interesting because it can indicate the printable length of the layer which influences the overlaying time gap between two layers.

MIX PROPRTIONS

Table 1 summaries the mix proportions of 3D mortars tested in this investigation. w/b ratio used was 0.50 and binder-to-sand ratio was 0.50. Four parameters were investigated: effects of fly ash as replacement of 24% (by mass of cement) and silica fume (8% replacement of cement), dosage of SP (0.275(1/2 SP) and 0.55% (SP) of binder), dosage of PP fibres (0.2% to 0.6%), and effect of type of VMA (% of binder by mass, VMA1, VMA2). The diutan gum based VMA was added at 0.05% and the nano-clay based VMA was added at 0.1%. Then polypropylene micro fibres were added with a varying percentage at 0.2%(PP), 0.4%(2PP) and 0.6% (3PP) relative to the total batch volume in order to reduce the shrinkage and the deformation in plastic state.

RESULTS AND DISCUSSION

The purpose of the experimental program is to analyse the effect of different mix compositions on the rheological behaviour and fresh properties of a printable mortar by using simple tests (flow table test, cylindrical slump test, penetrometer test). The rheological parameters were evaluated by yield stress.

In this investigation, stiff mixes were tested by the rheometer and it caused some difficulties which due to the limitation of the rheometer. Therefore, the slump test as a simplified rheological test is adopted in order to estimate the static yield stress.

Tab. 1: Compositions of all mixes (kg/m 3 )

Effect of binder on fresh and rheological properties of printed layers

Results of penetration and slump flow, obtained by flow table, composed of 100% of cement, 76% of cement and 24% of fly ash are plotted in Fig. 5. Fig. 5 indicates a decrease of the slump flow values with the addition of fly ash. The surface area of fly ash is equal to 420 m²/kg which is slightly greater than the cement (370 m²/kg). Consequently, bleeding and segregation were reduced as more water is needed to cover the surface of these particles. A Higher amount of unburned carbons from FA might lead to a reduction of workability linked to the adsorption of SP [Sonebi 2006].

The results of the penetrometer (Fig. 5) indicate basically the same penetration with the addition of fly ash. There was no significant effect on penetration and the maximum of value of 39mm represents the limit of the penetration test; consequently it's difficult to observe the influence of fly ash on the penetration results. In this case the consistency mortar was too soft to be analysed with the penetrometer. Fig. 6 shows that adding FA improved the shape of printed layers. /kg) which is really greater than the cement and fly ash (respectively equal to 370 m²/kg and 370m²/kg). Furthermore, at the fresh state, silica fume permits also to the cement based material to be more cohesive (less segregation and bleeding) which increases the yield stress and the fluidity of a portion of the mix isn't altered and doesn't allowed a greater spread compared to a mix containing fly ash [Sonebi 2010] [Sonebi 2015]. Additionally, as silica fume is a very reactive pozzolanic material, it reduces delay in setting [Sonebi 2015]. Silica fume counterbalances the addition of superplasticiser and fly ash (retarder effect). It seems that SF permits to obtain quickly a stable structure of extrudable mortar which is very interesting for the 3D printing. This resulted to keep after the extrusion, the shape of the layer under its own weight and under successive layers weight without degrading the extrudability (Fig. 8). The results of the penetrometer have the same trend compared to the results of slump flow values as it can be noticed in Fig. 7. A reduction of the penetration with the addition of SF is highlighted (for both mixes SP-PP and SP-2PP).

The penetrometer results indicated that there was an improvement of the cohesiveness of the mix containing SF and improving the shape of 3D printing layers (Fig. 8).

Effect of fibres on fresh and rheological properties of printed layers

Fig. 9 shows a reduction of the slump flow with the increase of the percentage of fibres (PP) from 0.2% to 0.6%. Furthermore, the results also indicate an increase of the static yield stress by increasing percentage of PP (particularly from 2PP to 3PP). It can be noticed that increasing the fibres enhanced the cohesiveness which limits significantly the flow of the mix and has an influence on its workability [Martinie 2009[START_REF][END_REF]]. With addition of 0.6%PP fibres, its volume becomes important due to its low specific gravity and has an impact on the consistency and on the flowability of the mix. Indeed fibres begin to connect and a process of percolation can occurs [Peled 2003].

The results of the penetrometer might indicate basically the same penetration with the addition of 0.4% fibres (2PP). However, a significant difference can be noticed when 0.6% of PP fibres (3PP) was added (Fig. 9). The results of the penetrometer might highlight that the network of PP fibres begin to be efficient at 0.6%PP (3PP) fibres to resist to this type of load due to the penetration of plunger.

Adding fibres permitted to the mix to have a better cohesiveness and have a more stable structure to not collapse under layer own weight and other successive layers.

Fig. 9: Effect of PP fibres on slump flow diameter, on penetration and estimated yield stress

Effect of chemical admixtures on fresh and rheological properties of printed layers 4.3.1 -Superplasticiser

As expected, Fig. 10 shows a decrease of the slump flow with the reduction of % of SP from 0.55% (SP) to 0.275% (1/2SP). Additionally, it can be noticed an increase in a static yield stress (247-967 and 587-1079 Pa) with the reduction of SP for both mixes made with 2PP and 3PP, respectively. The very high value of spread diameter (around 240mm) is due to the addition of 0.55% of superplasticiser. An increase of SP has a significant influence on consistency and workability due the steric repulsion mechanism of SP. Indeed The results of the penetrometer have the same trend compared to the results of slump flow as it can be noticed in Fig. 10. The penetrometer decreased when SP reduced from 0.55 to 0.275%. Penetrometer results confirm the influence of the effect of superplasticiser on consistency and flow ability.

Fig. 10: Effect of SP on slump flow diameter, penetration test and estimated yield stress

-Effect of VMAs

The results in Fig. 11 show that the addition of diutan gum VMA1 at 0.05% for a given dosage of SP (0.5%) decreased significantly the slump flow. In parallel, an increase of the static yield stress with the addition of 0.05% of VMA1 can be noticed (Fig. 12, almost from zero to 900 Pa). The flow ability and segregation are reduced and the cohesion is enhanced due to the entanglement and intertwining of VMA1 polymer chains at low shear rate. The association of water between adjacent chains allows the decrease of the bleeding. At a dosage of 0.05%, VMA1 influenced radically the consistency, the yield stress, the cohesiveness and increase the viscous behaviour of the mortar [START_REF] Schmidt | [END_REF]] [Sonebi 2006] [Sonebi 2003].

The results of the penetrometer have the same trend compared to the results of slump flow as it can be noticed in Fig. 11. It indicates a reduction in the penetration values with the addition of VMA1.

Penetrometer results confirm the influence of the effect of diutan gum on consistency and flowability. Additionally, an increase of the static yield stress (almost from zero to 131 Pa) with the addition of 0.1% of VMA2 can be observed (Fig. 12). Indeed, the particle size of nano-clay is significantly finer than those of cement and fly ash. Consequently, particles are inter mingle with the binder which increase the number of physical contact points and lead to enhance shear resistance. In addition, nano-clay increases the flocculation strength of the suspension which improved the structural stability. Additionally, cohesiveness of the mix is improved with the addition of nano-clay [Nathan 2010] [Kim 2010].

The reduction of the slump flow was about 41% with VMA1 compared to 15% with VMA2. Therefore, VMA1 is more powerful of reducing the fluidity. This difference could be explained by the type of mechanism and dosage of VMA. VMA1 caused an important loss of workability which influences the passing ability of the mix through the extruder. Therefore, VMA2 might be better solutions which improved the stability of the structure without decreasing dramatically the workability. The results of the penetrometer indicate slightly the same penetration with the addition of VMA2.

Correlation

Both slump flow and penetrometer test can measure the consistency of mortar. Consistency of mortar is a measure of its deformability when subjected to a certain type of stress. A correlation between slump flow and the penetrometer values were established for similar mortar. Fig. 13 shows a very good linear correlation between the slump flow and the penetrometer tests (R 2 = 0.86 and 0.89) of mixes made with different dosages of PP and SP (Fig. 13 without SF) Additionally, as it can be observed in Fig. 14, the coefficients of correlation R² between slump flow and the estimated yield stress were about 0.88 and 0.81 for similar mortars. The relationship seemed to follow the linear model and showed that when the spread diameter decreased, the static yield stress increased. Even if the effect a constant energy was supplied to the mix, a good correlation between estimated static yield stress and slump flow was highlighted.

Opening time

Time gap represents the time period in which the mortar is still reasonably workable and extrudable in layers. The change of workability with time was measured using the flow table test and slump of cylinder test (to estimated yield stress). The extrudability was tested in extruding layers with a simple modified joint gun.

-Effect of fly ash

The open time was investigated mortar made with FA compared to NO-FA. As expected Fig. 15 shows that the addition of fly ash affect the time gap of the mix due to the pozzolanic behaviour of fly ash which didn't react in early hours. The consistency of the mix made with fly ash maintained the opening time after two hours compared to NO-FA (9% drop for fly ash compare to 24% for NO-FA). A drainage occurred during the extrusion for mix 100%C which had the consequence to not be extrudable after 55 min while it was still fluid. Adding fly ash improved the extrusion ability; maintain the consistency and the workability of the mix.

-Effect of SP

Opening time was investigated with variation of SP 0.275 to 0.55% (1/2SP & SP). Fig. 19 shows that the increase of SP influenced significantly the slump flow and the time gap of the mix. Indeed, it can be noticed a reduction of 30 min (PP) and 60 min (2PP) when SP increased from 0.55 to 0.275%. The decrease of SP led to an increase in the estimated yield stress and a reduction of time gap of 60 min (Fig. 19). Indeed SP which cause segregation, bleeding of water content and at this dosage might has a slight initial retardation of cement hydration might be the cause of this increase of time gap when superplasticiser dosage is increased (19% drop with SP vs. 21% with 1/2SP) [Puertas 2015]. In addition, nano-clay increased the viscosity and the flocculation of the suspension which improve the structural stability. Therefore, VMA2 behaviour combined with built up rate of the cementitious mix reduced the time gap.

Due to the round shape and small particle size distribution of VMA2, it allowed a better flowability and passing ability through the orifice of the gun than VMA2 and permitted a better extrusion and greater open time.

Fig. 20: Effect of VMA1 and VMA2 on the opening time

CONCLUSION

The objective of this paper was to study the effect of different mix compositions on the rheological behaviour and fresh properties of a printable mortar. Layers are extruded with a simple modified joint gun. This tool permitted in association with the slump test to determine the time gap and the extrudability of the different mixes. Based on the results from this study, the following conclusions can be made: 

The addition of 24% of fly ash (FA) and 8% of silica fume (SF) increased significantly the yield stress, cohesiveness, structure homogeneity and the stability appeared to be an advantage to print layers. Indeed it also reduced significantly the fluidity, the bleeding and the segregation of layers.

Similarly, FA and SF reduced the slump flow. Additionally, it improved the passing ability through the extruder and showed a greater resistance to penetration. Using SF and FA led a reduction of time gap.  Adding polypropylene (PP) fibres (0.2% to 0.6%) permitted to the mix to have a higher yield stress, cohesiveness and resulted in more stable structure to not collapse under own weight of layer and successive layers weight. With the incorporation of fibres the time gap is reduced. Furthermore, positive effect of fibres can be reversed when the percentage is too high (difficulties to extrude and drainage phenomenon which led to a stiffening of the mix). Polypropylene fibres might be efficient to print layers due to their length and diameter which led to a dense and efficient network. 

The addition of VMA permits to the mortar to gain in cohesiveness, in shear strength avoiding bleeding and segregation which is an advantage for 3D printing. However, the type and dosage of VMA is very important. VMA1 caused an important loss of workability and time gap which influenced the passing ability of mortar through the extruder. Therefore, VMA2 demonstrated a better performance which improved the stability of the structure without decreasing dramatically the workability and time gap. Moreover increasing SP improved the workability, the passing ability through the extruder and led to a greater workability and penetration. However high dosage of SP increased risk of bleeding and segregation of the mix.



A good linear correlation (R²> 0.86) between penetrometer and flow table results was obtained.

In addition, it might be noticed a good correlation (R²>0.81) between the flow table and the estimated yield stress. Correlations showed that when the workability reduced, the static yield stress increased.

Fig. 1 :

 1 Fig. 1: Penetration test.

Fig. 5 :

 5 Fig. 5: Effect of FA on slump flow and penetration

Fig. 7 :

 7 Fig. 7: Effect of SF on slump flow diameter, penetration and estimated yield stress

  SP can induced mixes segregation and bleeding[Sonebi 2015] [Puertas 2015] [Sonebi 2003].

Fig. 11 :

 11 Fig. 11: Effect of VMAs on slump flow and penetration

  (a) and with SF (Fig. 13 (b)). It can be Relationship between slump flow and penetrometer (a) (different PP and SP), (b) (with and

  Relationship between yield stress and slump flow (a) (different PP and SP), (b) (with and without SF)

Fig. 15 :

 15 Fig. 15: Effect of FA on the opening time

Fig. 16 :Fig. 18 :

 1618 Fig. 16: Effect of SF on opening time (Slump flow vs. time)

Fig. 19 :

 19 Fig. 19: Effect of SP on the opening time


M Rubio

M Sonebi
email: m.sonebi@qub.ac.uk

S Amziane

FRESH AND RHEOLOGICAL PROPERTIES OF 3D PRINTING BIO-CEMENT-BASED MATERIALS

Keywords: 3D printing, flax fibres, opening time, penetration, slump flow, yield stress EcoGRAFI

The aim of this study is to investigate the effect of different mix composition on fresh and rheological properties of a bio-printable mortar. Different binders were tested such as fly ash (FA), silica fume (SF), and used with CEMI and sand for a water/binder ratio of 0.50. Then, superplasticizer (SP) and natural flax fibres 15 mm (FL) were used in the investigation at varying percentage for a given binder. Two viscosity modifying agents were also tested. Adding flax fibres (0.2% to 0.6%) led to a greater yield stress, higher cohesiveness of the mix. It also demonstrated more stable structure of layers which allowed to not collapse under layer own weight and other successive layers. With the incorporation of fibres the time gap is reduced. Furthermore, positive effect of fibres can be reversed when the dosage in fibres is too high (difficulties to extrude and drainage phenomenon which led to a stiffening of the mix). VMA caused an important loss of workability and time gap which influenced the passing ability of the mix through the extruder. Increase SP led to an increase in slump flow and penetration values which can affect the stability of the shape of printed layers. Good linear correlation between slump flow and penetrometer was established.

INTRODUCTION

Contour Crafting is currently the most effective method researchers have found so far. The concrete layers are poured out by robotic machines and can be used for small-scale industrial parts and building structures [START_REF] Malaeb | 3D Concrete printing: machine and mix design[END_REF]]. Inspired by the 3D printing with polymer materials, 3D printing opens new horizons to cement-based materials of the construction industry. As formworks represent 35-60% of the overall costs of concrete structures, it would be an important financial advantage to use this new technology. Besides, 3D printing in building structures without formworks permits to improve the construction rate and open to new architectural liberties. Replacing humans work by additive technology automated allows building in polluted zones or on planets as reported in the project of contour crafting with the construction of bases on the moon for the NASA [P. 3D 2015].

Several applications were reported on applications and prototypes of 3D The two previous pioneers of 3D printing concrete as companies were the Shanghai Company, WinSun [START_REF] Wangler | [END_REF]]. It was reported that to 10 full scale houses have been printed in less than 24 hours with 3D printing concrete. The method is appealing by the low cost of each house, around 5000$ [START_REF] Malaeb | 3D Concrete printing: machine and mix design[END_REF]]. The largest 3D printer has been created by the World's Advanced Saving Project launched in 2010 by the Italian Centro Sviluppo Progetti Company. It was 12 meters tall in a hexagonal shape [START_REF] Wangler | [END_REF]]. Finally, HuaShang Tengda Company (China) has recently managed to incorporate reinforcements to its 3D printed concrete structure. In fact, they have printed a 400 m² villa around iron frameworks by using an original nozzle design. They first raised the complete steel bars and pipes complex of the house. Then, concrete has been printed over it with big scale 3D printer [START_REF] Scott | Chinese Construction Company 3D Prints an Entire Two-Story House On-Site in 45 Days, Article from the 3DPrint website[END_REF]]. The printability of fresh cement based materials is the ability of the layer to maintain itself and the weight of the layers subsequently deposited. The time gap between two deposited layers must be sufficiently long to provide adequate mechanical strength capable of sustaining the weight of the subsequently deposited layers and also short enough to provide an optimized bond strength and building rate. It appears that it's the shortest time gap which allows the stability of the structure during construction. The ability of the first layer to support itself and others layers is link to its rheology and more precisely to its yield stress [Perrot 2015]. The aim of this study is to evaluate the effect of different mix composition parameters included dosage of superplasticizer (SP), addition of fly ash (FA) and silica fume (SF), the dosage of flax fibres (FL) and type of viscosity modifying agent (VMA) on fresh and rheological properties of a printable mortar.

EXPERIMENTAL PROGRAMME

Fresh properties of printed cement-based mortar compose of fly ash and silica fume, incorporating fibers (FL), VMAs (diutan gums, nano-clay) and superplasticizer were investigated. The following properties of the mortars were examined: the slump flow, the penetration test, the rheological properties (yield value), and the extruded property. Moreover, the relationships between the fresh properties were evaluated.

Materials

The mortars were prepared with a fixed water-to-binder ratio (w/b) of 0.50. Portland cement CEMI 42.5N specified by BS EN 197-1: 2000 (specific gravity of 3.13) was used in all mixes. Fly ash from Scot ash ltd was added and conformed to BS EN 450-1:2005. Undensified silica fume (SF) were used with a percentage of 8% relative to the mass of cement. The percentage of SiO2 was more than 90% and the specific surface area of SF was 17500 m 2 /kg with a specific gravity of 2.2. A synthetic polycarboxylate polymer-based superplasticiser (SP) with solid content of 30% and specific gravity of 1.05 was used. Diutan gum was supplied by Kelco-crete which is an anionic polysaccharide gum as used as viscosity modifying agent (VMA1). It was used as powder at 0.05% (by mass of binder). A second VMA Acti-gel208 nano-clay based composed of attapulgite-clay small needles with negative charges (VMA2) is used at 0.10% (by mass of binder). Sand with maximum particle size of 1.18 mm was obtained by sieving oven-dried (at 105 ±5 °C) sand with particle size of 0-5 mm. Flax fibres supplied by Azichem Ltd (Italy) were used for this investigation have a length of 15 mm. Monofilament flax fibres are used to improve cohesion, holding, mould-ability, and to limit the cracking of cementitious composites.

Mixing and testing procedure

The mortars were prepared with high-shear Hobart mixer in 2-L batches. Premixed solid components, i.e. cement, fly ash (if any), silica fume (if any) and sand, were mixed for 30 seconds at low speed (140 rpm). Next, water at temperature of 16 ±0.5 °C and SP were added together to the mixer and mixed for 30 seconds at a low speed (140 rpm). Then the mixer was stopped, any lumps of solids were crushed, fibres (if any) and VMA1 or VMA2 (if any) were added (within 1 min), and the mortar was mixed again for 2 min (4 min when VMA2 is added) at a high speed (285 rpm). Then VMA1 (if any) is added and the mortar is mixed 1 min at a low speed (140 rpm). The temperature of the mortar after mixing was 20 ± 1 °C. For all tests the timing is given from zero timethat is, the time when the cement particles first touch the mixing water. The penetration test (cone plunger) was started at 6 min (immediately after the end of mixing -Fig. 1). After filling the cone mould with mortar in two layers, the cone plunger is adjusted in order to allowing the cone to just touch the surface of the mortar sample. Then the cone plunger is released allowing the plunger to penetrate into mortar paste under its own weight for 5 seconds. After 5 seconds, the penetration value is noted to the nearest millimetre. Then the slump flow test was started at 10 min (Fig. 2). The dimensions of cone were 100 x 70x 60 mm. The cone-shaped mould was placed in the centre of a jolting table. After filling with mortar in two layers, the cone was gently lifted 15 times (approximately 30 s after finishing of placing of the grout). When the flow stopped, the spread of the mortar was measured with a ruler in two perpendicular directions. Finally, extrudability of mortar mixes is tested with the simple modified joint gun described in Fig. 3. Rheological measurement was carried out with a computer-controlled vane viscometer (Haake VT550). At 6 ± 1 min, approx. 800 ml of the sample was introduced into a plastic container where the vane was plunged. After 30 s rest, the test was started and the mortar was sheared at different shear rates. The two rheological parameters, yield stress (τ0) and plastic viscosity (μp), were obtained from the modified Bingham model fitted to the experimental data (downcurve). The yield stress at a zero shear rate was extrapolated from the Bingham model. Unfortunately, as mortar mixes were too stiff to be characterized with the viscometer, a semi-empirical alternative is used to determine the yield stress using cylinder measurement (slump -Fig. 4, [Pashias 1996]) : s' = 1 -2τ′ y ( 1 -2ln(2τ′ 0 ))

where:  Cylinder dimensions : h 0 = 138 mm and d 0 =64 mm  s = h 0 -h with h 0 the initial height and h the final height  s' = s/h deformation quantities are dimensionless  τ′ 0 = τ 0 /ρm.g. h 0 stress quantities are dimensionless

The test procedure is detailed in the following steps.

The mould is placed centrally on the flow table and the mortar is introduced in two layers. Each layer is compacted with ten short strokes in order to have a uniform filling of the mould. The mould is maintained in place firmly during the filling. The excess of mortar is removing with the help of a palette knife. After 15 seconds the cone is gently and vertically lifted and the height of the spread mortar is measured (Fig. 4).

The weight of the mortar was measured in constant volume and the fresh density of the mortar was calculated.

The workability life is a crucial parameter which is influenced by the build-up rate of layers. It was measured by the time at which it reached a defined limit of stiffness or workability during the gun extrusion test.

The workability life test measuring the evolution of the consistency, yield stress and extrudability during time was performed beginning with the first measurement of the flow table test and penetrometer test, and then cylindrical slump test and extrudability test. After, these tests were repeated every fifteen minutes until the mortar was too stiff. These tests are interesting because it can indicate the printable length of the layer which influences the overlaying time gap between two layers.

MIX PROPRTIONS

Table 1 summaries the mix proportions of 3D mortars tested in this investigation. The w/b ratio used was 0.50 and binder-to-sand ratio was 0.50. Four parameters were investigated: effects of fly ash as replacement of 24% (by mass of cement) and silica fume (8% replacement of cement), dosage of SP (0.275(1/2 SP) and 0.55% (SP) of binder), dosage of PP fibres (0.2% to 0.6%), and effect of type of VMA (% of binder by mass, VMA1, VMA2).

The diutan gum based VMA was added at 0.05% and the nano-clay based VMA was added at 0.1%. Then flax fibres were added with a varying percentage from 0.2 to 0.6% relative to the total batch volume in order to reduce the shrinkage and the deformation in plastic state.

RESULTS AND DISCUSSION

As previously stated, the purpose of the experimental program is to analyse the effect of different mix compositions on the rheological behaviour and fresh properties of a printable mortar in using basic tests (penetrometer test, flow table test, cylindrical slump test). The rheological parameters were evaluated by yield stress. In this investigation, stiff mixes are used and it causes some difficulties in applying a rheometer test for mortar mixtures. Therefore, the slump test as a simplified rheological test is adopted in order to estimate the static yield stress.

Tab. 1: Compositions of all mixes made with flax fibres (kg/m 3 )

Effect of binder on fresh and rheological properties of printed layers

Results of penetration and slump flow, obtained by flow table, composed of 100% of cement, 76% of cement and 24% of fly ash are plotted in Fig. 5. Figure 5 indicates a decrease in the slump flow diameter and in parallel an increase in the static yield stress (from 789 to 913 Pa and 656 to 887 Pa) with the addition of silica fume. Silica fume improved the cohesiveness, reduces bleeding and the setting delay.

The surface area of SF was 17500 m²/kg which is really higher than those of cement and fly ash (370 m²/kg and 370m²/kg, respectively). Consequently, bleeding and segregation is reduced as more water is needed to cover the surface of these particles [Sonebi 2010] [Sonebi 2015]]. Silica fume counterbalances the addition of SP and fly ash (retarder effect) which decreases the spread diameter and increases the yield stress.

The results of the penetrometer have the same trend compared to the results of slump flow as it can be noticed in Fig. 5. The penetrometer results indicate a decrease in the penetration for the mix made with FL and the addition of fly ash. Similarly, penetrometer values also decreased when a high dosage of flax used (3FL) normal quantity of flax. SF permitted to obtain a stable structure which is very interesting for the 3D printings which need to keep after the extrusion the shape of the layer under its own weight and under successive layers without degrading the extrudability (Fig. 6).

It can be noticed a greater slump flow for the mix 1/2 SP 3FL compared to 1/2SPFL mix. It can be explained by a technical imprecision during the measurement or the compaction of these very stiff mortar mixes. Indeed as the mix is stiff, some air might be entrapped during the compaction in the cone.

Effect of fibres on fresh and rheological properties of printed layers

Fig. 7 indicates a slight decrease in the slump flow with the increase of the percentage of flax fibres from 0.2% to 0.6% (FL to 3 FL). It can be noticed that increasing the percentage of fibres enhanced the cohesiveness which limited significantly the flow of the mix and has an influence on its workability [Martinie 2009[START_REF][END_REF]]. Adding fibres resulted in a better cohesiveness and more stable structure of mortar to not collapse under layer own weight and sustained successive layers weight. The flax fibres network might be noticeably less dense than other polypropylene mesh due to the length [Marine 2017]. As mix with a dosage of 0.55%SP was too fluid, the semi-empirical formula used wasn't able to calculate the static yield stress. But referring to the results of the slump flow, the increase of the flax fibres to 3FL might not affect significantly the yield stress and the workability of the mix.

The results of the penetrometer (Fig. 7) indicate the same penetration with the addition of 3FL fibres. The results of the penetrometer might confirm the results of the slump flow and the hypothesis that 0.2 or 0.6%FL did not have an influence on penetration of plunger. A higher dosage in flax might be tested in further research.

Fig. 7: Effect of dosage of flax fibres on slump flow and penetration

Effect of chemical admixtures on fresh and rheological properties of printed layers

-Superplasticiser

As expected the reduction of SP (0.55 to 0.275%) led to decrease in a slump flow (Fig. 8). Addition of 0.55% SP led to a higher of slump flow (around 268mm).

Unfortunately, as mixes with 0.55% of SP were too fluid (Fig. 8), the semi-empirical formula used wasn't able to calculate the static yield stress of these flax mixes. Thus a conclusion about the influence of the superplasticiser dosage on the workability of the mortar mix can't be done. But referring to the results of the slump flow, the decrease of the dosage of SP might not affect significantly the yield stress and the workability of the mix. The results of the penetrometer have the same trend compared to the results of slump flow as it can be noticed in Fig. 8. The results of the penetrometer indicate a reduction in the penetration values with the decrease of SP from 0.55 to 0.275% (SP to 1/2SP).

Penetrometer results confirmed the influence of the effect of superplasticiser on consistency and flowability. Fig. 9 presents the shape of 2 printed layers made with SP (0.55%) and 1/2SP (0.275%).

SP 3FL

1/2 SP 3FL Fig. 11: Effect of VMA1 on shape of 2 printed layers Fig. 12 shows that the addition of nano-clay gel VMA2 for a given dosage of SP decrease significantly the slump flow. However, the impact of VMA2 on the static yield stress can't be noticed (Fig. 12) because of the semi-empirical formula which wasn't able to determine the static yield stress of this fluid mortar mix.

As the slump flow decreased with VMA2, it might be expected an increase of the static yield stress. Indeed, the particle size of nano-clay is significantly finer than those of cement and fly ash. Consequently, particles are inter mingle with the binder which increase the number of physical contact points and lead to enhance shear resistance. In addition, nano-clay increased the flocculation strength of the suspension which improves the structural stability. Additionally, cohesiveness of the mix is improved with the addition of nano-clay. [Nathan 2010] [Kim 2010] The addition of silica fume characterized by a small particle size distribution seems to combine its effects with VMA2 ones and led to decrease further in slump flow (221 with VMA2 to 205mm with VMA2 and SF).

It can be noticed that in the reduction of the slump flow diameter, the effect of VMA1 with a reduction of about 49% is more efficient than the effect of VMA2 with a reduction about 18%. This difference could be explained by the type of mechanism and dosage.

VMA1 cause an important loss of workability which influences the passing ability of the mix through the extruder. Therefore, VMA2 might be a better solution which improves the stability of the structure without decreasing dramatically the workability.

The results of the penetrometer haven't the same trend compared to the results of slump flows as it can be noticed in Fig. 12. The results of the penetrometer indicate slightly the same penetration with the addition of VMA2. These results might indicate that VMA2 isn't able to resist to this type of load of plunger. Nevertheless, it can be noticed that the addition of silica fume led to a decrease in the penetration values as stated before in the part concerning the influence of silica fume on consistence of mortar. Fig. 13 shows the effect of VMA 2 on printable layers.

Correlation

Both flow table and penetrometer can measure the consistency of mortar. Consistency is the deformability of mortar when subjected to a certain type of stress. A correlation between slump flow and the penetrometer for the same type of mortar was established for mixes without Sf and VMA (Fig. 14).

-Effect of silica fume

It can be observed on that adding SF in mixes containing flax fibres reduced the consistency and workability due to the increase of the cohesiveness and high reactivity of silica fume (Fig. 16). The mix without silica fume was already not extrudable after 10 min, and adding silica fume accentuate the difficulty to extrudability.

Fig. 16: Effect of SF on extrudability

-Effect of superplasticiser

Open time was investigated with varying SP from (1/2SP to SP) by weight of binder (Fig. 17). As previously reported, the decrease of SP influences significantly the spread diameter, the yield stress and the time gap of the mix. Indeed, it can be noticed a decrease of 60 min with the addition 1/2SP. Indeed high dosage of SP can cause segregation; bleeding and retardation of cement hydration might be the cause of this increase of time gap.

-Effect of VMAs

The results show that the addition of diutan gum for a given dosage of SP (0.55%) decreased significantly the open time of the mortar (Fig. 18). It can be noticed a decrease of 30 min with the addition of 0.05% by weight of cement of VMA1. Action of VMA1 combined with built up rate of the cementitious mix reduced the time gap.

In addition, the slope of the VMA1 curve is lower than the slope of the mix without VMA which means that the mix is very stiff and can't spread anymore (19% drop without VMA1 compare to 9% with VMA1)-Fig. 17. Flax fibres have a fibres network less dense than the one of polypropylene fibres due to its length; it allows a greater time gap. The addition of 0.1% of nano-clay shows a decrease in the open time of 15 min which is half lower compared to the results with the addition of VMA1. As previously reported with the addition of VMA1, VMA2 curve is lower than the slope of the mix without VMA which means that the mix is very stiff and can't spread anymore (27% drop without VMA compare to 16% with VMA2, Fig. 18). VMA2 increased the cohesiveness, viscosity, and flocculation of the suspension. Action of VMA2 combined with built up rate of the cementitious materials reduced the time gap. VMA2 allowed a better flowability, cohesion and passing ability through the orifice of the gun than VMA2 and its steric repulsion and permit a better extrusion and greater open time.

CONCLUSION

This study was focused to investigate the effect of different mix compositions on the rheological behaviour and fresh properties of a printable mortar in using basic tests like the penetrometer test, the flow table test and the cylindrical slump test. Layers are extruded with a simple modified joint gun. This tool permitted in association with the slump test to Concerning the binder composition, regarding the analyse of results it can be observed that adding 24% of fly ash (FA) and 8% of silica fume (SF) increasing yield stress, cohesiveness, structure homogeneity and stability appeared to be an advantage to print layers. Indeed it reduced the too important fluidity, bleeding and the segregation of layers as it was previously noticed with a reduction of the flow table diameter. Additionally, it improves the pass ability through the extruder and shows a greater resistance to penetration. A decrease of the time gap can be noticed. 

The addition of flax fibres (FL) fibres (0.2% to 0.6%) permitted to the mortar to have a greater yield stress, cohesiveness and have a more stable structure to not flow under layer own weight and successive layers weight. With the incorporation of fibres the time gap is reduced. Additionally results might highlight the influence of the type, length and diameter of fibres. Furthermore, positive effect of fibres can be reversed when the dosage in fibres is too high (difficulties to extrude and drainage phenomenon which led to a stiffening of the mix).



The incorporation of VMAs permitted to gain in cohesiveness, viscosity avoiding bleeding and segregation which is an advantage for 3D printing. However, the type and dosage of VMA is very important. As it was previously stated, VMA1 cause an important loss of workability and time gap which influences the pass ability of the mix through the extruder. Therefore, VMA2 might be a better solution which improves the stability of the structure without decreasing dramatically the workability and time gap. Moreover increasing the dosage of SP improved the workability, the passing ability trough the extruder and led to a greater slump flow diameter and penetration. However a too high dosage of SP increased also risk of bleeding and segregation of the mix.



A good correlation between penetrometer and flow table results was obtained.

  printing [Khoshenevis 2006] [Le 2012] [Alec 2016] [Scott 2016] [Alec 2016] [Lloret 2015].

Fig. 1 :

 1 Fig. 1: Penetration test

Fig. 5 :

 5 Fig.5: Effect of silica fume on slump and penetration, and estimated yield stress

Fig. 8 :

 8 Fig. 8:.Effect of dosage of SP and slump and penetration

Fig. 10 :

 10 Fig.10: Effect of VMA1 on slump flow and penetration and estimated yield stress

Fig. 12 :

 12 Fig. 12: Effect of VMA2 on slump flow, penetrometer and estimated yield stress

Fig. 14 :

 14 Fig. 14: Correlation between slump flow andpenetrometer(No VMA and No SF)

Fig. 15 :

 15 Fig. 15: Extrudability of layers in function of time

Fig. 17 :

 17 Fig. 17: Effect of SP on slump flow in function of opening time

Fig. 17 :

 17 Fig. 17: Effect of VMA1 and VMA2 on slump flow in function of opening time of mix with flax fibres

Fluid

  gap and the extrudability of the different mixes. Conclusions can be drawn: 


Alzouhri Amr
email: amr.alzouhri-alyafi@imag.fr

Alyafi

Monalisa Pal
email: monalisap90@gmail.com

Stephane Ploix
email: stephane.ploix@grenoble-inp.fr

Patrick Reignier
email: patrick.reignier@inria.fr

Sanghamitra Bandyopadhyay

Felix Viallet

Differential Explanations for Energy Management in Buildings

Keywords: building, efficient energy use, exploration of differential explanations, causality, multi-objective optimization, differential evolution, Paretooptimality, ambient intelligence, user advice generation

In the field of building energy efficiency, researchers generally focus on building performance and how to enhance it. The objective of this work is to empower the building occupants by putting them in the loop of efficient energy use, supporting them to achieve their objectives by pointing out how far their actions are from an optimal set of actions. Different levels of explanation are investigated. Indicators measuring the distance to optimality are, firstly, proposed. An algorithm that generates deeper explanations is then presented to determine how changing some actions impacts comfort. The paper emphasizes the importance of explanations with a real case study. It identifies the type and level of explanations needed for different occupants. The concept of replay is presented. An occupant can replay his past actions and learn from them.

Introduction

Considering the massive increase in energy demands, building consumption is a very fundamental domain as it constitutes more than 40% of the globally sup-plied energy [START_REF] France | Le btiment, premier poste de consommation dnergie en france[END_REF]. It illustrates the importance to decrease or limit the emissions from buildings. Enhancements in construction techniques, insulation and building regulations have increased the relative energy impact of occupant's actions in the energy consumption. It is therefore important that occupants understand the impact of their actions in order to reduce the energy consumption while meeting their demands on expected comfort. An energy management system with explanatory capabilities relies on physical models. These models are used to simulate and predict the evolution of various variables (temperature, air quality, consumption, etc.) according to actions. Depending on the service provided by the occupants, the models can be used in a direct way for simulating an action's impact, or in an indirect way to compute the best actions according to some criteria. Due to their complexity and mathematical formalism, models and optimization results are however not suitable for direct interactions with inhabitants: the intrinsic knowledge they contain is not directly intelligible. Human beings are trained, since elementary school, to think and to understand the world through causal representations like: what happens, when does it happen, what affects it, and what does it affect? [START_REF] Bredeweg | Qualitative Modeling in Education[END_REF]. This causal knowledge is hidden inside the equations and should be explicit.

The paper focuses on the generation of explanations about energy impact of user actions. Explanations occur in different ways [START_REF] Keil | Explanation and Understanding[END_REF] and for different reasons. One of the main motivation for having explanations is to be able to manage in a better way if similar events or scenarios arise in future [START_REF] Heider | The Psychology of Interpersonal Relations[END_REF]. Explanations usually rely on causal relationships. There are at least four kinds of causal explanations: common cause, common effect, linear causal chains, and causal homeostasis (cyclic causal relationships) [START_REF] Sober | Common Cause Explanation[END_REF]. According to [START_REF] Wilson | The Shadows and Shallows of Explanation[END_REF], explanations are ubiquitous, come in a variety of forms and formats, and are used for a variety of purposes. Still, the common feature about most explanations is their limitation. For most natural phenomena and many artificial ones, the full set of relations to be explained is complex and far beyond the grasp of any one individual.

The paper focuses on a real case of study: an office, where 4 persons work. It is equipped with 27 sensors collecting information about CO 2 concentration, humidity, electrical consumption, luminescence, temperature, presence, occupancy etc. It is also equipped with 2 cameras to verify the occupant's actions and their routines in historical data. A panoramic photo of the office with sensors is presented in Fig. 1.

The comfort criteria for this office are the thermal comfort and the air quality based on CO 2 . The office does not contain any controllable HVAC system. This work proposes a method for occupants to better understand and learn how to improve their actions. In this scenario or similar ones, changing the door and window positions are the only possible actions occupants may perform. Such an application in energy building is first of its kind, as par the author's knowledge, and here lies the novelty of the proposed work.

The next section shows a brief description of the problem and a general approach to resolve it. Section 3 describes the motivation for generating explanations for energy management systems while presenting the physical models. Section 4 proposes a new indicator that helps the occupants to understand the gap between their actions and optimal actions according to comfort criteria. Section 5 focuses on how to show to the occupants the consequences of their actions as compared to optimal actions, by generating differential explanations and influences.

Problem Statement

The main objective of the paper is to propose solutions to assist occupants to better understand how they can modify their behavior and make better decisions with respect to their own comfort criteria. Due to the complexity of the building physics and unconscious routines, occupants face difficulties while trying to understand what is happening and why they need to change their daily routines to obtain better comfort, or to better compromise between comfort and cost. Generation of contextual explanation is therefore at stake. Explanations should rely on causal relationships i.e on an ordering in phenomena modeled by variables: the causes, i.e. the occupant actions (A) or contextual (C) phenomena, the final effects (E) and the intermediate effects (I). It is summarized in Fig. 2 for the studied office. The arrows in the figure represent the cause-effect relation between these groups.

The different groups of variables are given by:

1. Context group: it contains all the uncontrollable variables that the system needs to take into consideration like the outside temperature T out , the humidity, the temperatures in the neighbor zones T cor , the number of occupants, etc.

2. Actions group: it contains all the different actions that the system can propose to the occupants to enhance their comfort levels (like opening the window ζ w , and opening the door ζ D ). All of this can be reformulated as: A, C

I

-→ E where: A is the set of variables modeling occupant's actions, C is the set of contextual variables, I represents the intermediate variables, and E represents the effect variables.

The effects resulting from the best actions according to some given criteria can be computed. It is denoted by: A * , C I * -→ E * where: A * is the optimal set of actions, I * represents the intermediate variables generated from optimal actions, and E * is the optimal effects that can be achieved.

To generate the explanations, a concept of a qualitative distance is defined by comparing the actual scenario (x) to the optimal one (x ), which is given by:

Π v-3,v-2,v-1,v1,v2,v3 (x -x) : x -x < v -3 → very low v -3 ≤ x -x < v -2 → low v -2 ≤ x -x < v -1 → slightly low v -1 ≤ x -x < v 1 → no change v 1 ≤ x -x < v 2 → slightly high v 2 ≤ x -x < v 3 → high x -x ≥ v 3 → very high (1)
This mapping is done to show the occupants the impact of their actions on the comfort criteria, and to convince them why do they need to change their behavior when it is far from optimality.

These concepts are going to be used firstly to explain how far actions are from the optimal actions, then to compute what can be gained by changing the actions.

Physical Knowledge Model

Advanced energy management systems rely on one or more physical models. For example, the physical model for predicting the inside temperature for the office is the following [START_REF] Lisa | Mthodologie pour la comparaison de structures de modles simplifis[END_REF]:

T n , T in and T out represent respectively the temperatures of the adjacent corridor, the office and outdoor.

R D and R W represent respectively the thermal resistances of the door and the window when they are closed.

ζ D and ζ W are 1 if the door or the window is opened, 0 otherwise. R i and C i represent respectively the resistance and the capacitance of walls. φ in represents the internal thermal gains: solar gains, gains of electric devices and gains due to occupancy.

Let 1 R = 1 R i + 1 R out + ζ W R W + 1 R n + ζ D R D (2)
where:

R D = 1 ρ air c p,air Q D ( 3
)
ρ air is the air volume in the zone. c p,air is a specific mass heat of air. Q D is the air speed traversing the door.

R W = 1 ρ air c p,air Q W ( 4
)
Q W is the air speed traversing the window.

dτ dt = R -R i R 2 i C i + R R i C i φ in + R R i C i ( 1 R out + ζ W R W )T out + R R i C i ( 1 R n + ζ D R D )T n (5)
T in = R R i τ + R( 1 R out + ζ W R W )T out + R( 1 R n + ζ D R D )T n (6)
with R n , R out , R i and C i being time-invariant. Equation ( 6) serves as a model to predict the inside temperature. By observing the variables included in it, it is clear that the inside temperature is related to different phenomena like outdoor temperature, corridor temperature, the different sources of heat inside the office, and actions that are taken by occupants regarding the position of the door and the window.

Determination of the air quality is usually done by measuring the concentration of CO 2 in the air. The following air quality model has been used:

C cor , C in and C out represent respectively the CO 2 concentration of the corridor, the office and outdoor. V stands for the volume of the office and n(t) for the number of occupants [START_REF] Amayri | Estimating occupancy in an office setting[END_REF].

V dC in dt = -(Q out (t) + Q cor (t))C in + Q out (t)C out +Q cor (t)C cor + S CO2 × n(t) (7)
Assumptions :

Q out (t) = Q 0 (t) out + ζ W (t)Q W (8) Q cor (t) = Q 0 (t) cor + ζ D (t)Q D (9)
Then, it yields to:

V dC in dt = -(Q 0 (t) out + Q 0 (t) cor + ζ W (t)Q w + ζ D (t)Q D )C in + (Q 0 (t) out + ζ W (t)Q W )C out + (Q 0 (t) cor + ζ D (t)Q D )C cor + S CO2 × n(t) (10)
Further details of the physical model can be found in [START_REF] Lisa | Mthodologie pour la comparaison de structures de modles simplifis[END_REF]. From Eq. ( 2) to [START_REF] Robič | Demo: Differential evolution for multiobjective optimization[END_REF], it is clearly noticeable that the desired criteria, thermal comfort and air quality, are dependent on many different phenomena from different zones and from different actions.

Another very important element in an energy management system is the optimizer [START_REF] Ha | An optimal approach for electrical management problem in dwelings[END_REF]. The optimizer acquires the available data and the output of various models to compute the optimal scenario according to the chosen comfort criteria and the occupant's preferences. The details on the optimizer used for this paper is provided in Section 4.

The output of the model and the optimizer are used to compute the best set of actions by optimizing the occupant's comfort criteria. Figure 3 represents the different measured temperature that were taken from different thermal zones on a random day from the database of last year (e.g. 05/June/2015) with a red box marking the zone from 2pm to 3pm. Here the output of the system optimizer is depicted as 'office temperature best'. Same is done in Fig. 4 for the air quality (CO 2 concentration). Figures 5 and6 correspond respectively to the door and the window positions manually controlled by the inhabitant and the recommended actions. Observing the zone between 2pm and 3pm, it can be seen that the system recommends to close the window and open the door. This would prevent the inside temperature from reaching the outdoor temperature and opening the door would help keeping the temperature closer to the corridor temperature, which is below the outside temperature. However, doing these recommended actions would cause an acceptable degradation in the air quality.

Based only on these observations, it is very complex to correlate all these different data to understand why the energy management system is recommending some actions. If the user's behavior is not the same as the proposed optimal scenario, he will have to change his habits. To help him change his habits, it is important to explain him what are the consequences of each of his non optimal action so that he can decide which one he will really change. The proposed approach tries to benefit from the physical model then figures out how to extract useful information from different measured and calculated data, and represent them in a way that makes more meaning for the inhabitants.

Distance to Best Compromises

This section deals with the assessment of how far is the actual behavior from the optimal one. There are different comfort criteria, such as reduction of the CO 2 concentration, maintaining the office temperature within preferred levels, reducing the humidity level and other possible cost criteria such as minimizing energy consumption, minimizing energy cost taking into account possible variable tariffs. Hence, the problem is a multi-criteria problem. For computing the distance to best compromises, the distance to the Pareto-front is to be calculated. There is a need for an indicator showing the occupant how much the degradation in their comfort levels generated by their actions is far or close to the achievable optimal solution.

This work presents a case study which considers optimal scheduling of actions according to the minimization of thermal (σ T ) and air quality dissatisfactions (σ air ) which stand for final effect variables in Fig. 2. Quantitatively, thermal and air quality dissatisfaction are given by Eq. ( 12) and [START_REF] De Souza | Clustering of interval data based on city-block distances[END_REF]. The thermal dissatisfaction is based on a preferred office temperature range from 21 • C to Following this, the section describes how the distance to best compromises is calculated. It also presents a brief description of the optimization algorithm which acts as the tool to obtain the optimized schedule of actions.

Criteria and Compromises

The dissatisfaction minimization problem can be formulated as shown in Eq. [START_REF] Ishibuchi | Evolutionary many-objective optimization: A short review[END_REF] where the solution vector A, for actions (Fig. 2), is a 24-dimensional binary sequence representing the status (open = 1 / close = 0) of door and window over 12 hours (8 am to 8 pm) which influences temperature and CO 2 concentration and in turn influences the dissatisfaction levels (as quantified in Eq. ( 12) and ( 13)).

Minimize:

D(A) = [σ T (A), σ air (A)] =     12 k=1 σ k T (A) 12 , 12 k=1 σ k air (A) 12     (11)
The dissatisfaction for the thermal comfort at the k-th time period is given by:

σ k T (T in ) =      21-Tin 21-18 , if T in < 21 0, if 21 ≤ T in ≤ 23 Tin-23 26-23 , if T in > 23 ( 12
)
where T in stands for the office temperature and is a function of the occupant's actions A.

Similarly, the air quality dissatisfaction for the air quality at the k-th time period is given by:

σ k air (C in ) = 0, if C in ≤ 400ppm Cin-400 1500-400 , if C in > 400ppm (13)
where C in stands for the CO 2 office concentration and is also a function of A.

The data recorded by the sensors correspond to some states of door and window positions. Based on the recorded data, the set of 12 temperatures (T k in (A), recorded in • C) and the set of 12 CO 2 concentrations (C k in (A), recorded in ppm) where each value is the average for the k-th hour, helps in quantifying the thermal and air quality dissatisfaction. The aim of the optimization is to minimize daily average of the thermal and the air quality dissatisfaction levels for the occupant and thereby determine the ideal scenario (A ) of door and window position over the 12 hours of the day which will help achieve these minimal dissatisfaction levels (E ). The occupant when provided with these optimal actions (A ) is expected to learn the scope of possible enhancement as compared to their past actions ( Ã). This learning takes place with the help of the differential explanations and influences which is explained in detail in Section 5.

For optimization, the multi-objective version of differential evolution (DEMO) [START_REF] Robič | Demo: Differential evolution for multiobjective optimization[END_REF] has been employed. The thermal and air quality dissatisfaction are conflicting in nature. For example, when outdoor temperature is lower than the preferred temperatures, opening the window can decrease the office temperature and hence increasing thermal dissatisfaction while on the other hand, it will decrease the CO 2 concentration and hence decrease air quality dissatisfaction. Thus, a set of trade-offs is obtained which represents the different levels of thermal and air quality dissatisfaction as a solution for the multi-objective optimization problem.

Compromises of Interest

The set of trade-offs gives rise to a surface in the objective space which is popularly known as Pareto-Front. In other words, for this work, the Pareto-Front is an approximated curve based on the optimization results when plotted as thermal dissatisfaction versus air quality dissatisfaction or vice-versa. From the recorded data, the thermal and air quality state can also be marked and hence, present the system state compared to optimal state in a graphical format as shown in Fig. 7. The system state depicts the aggregate result of a nonoptimal scenario as it is played by the occupants and thus reflects the quality of their behavior.

Based on each criteria, several points on the approximated Pareto-front are selected and the occupant is presented with a set of four possibilities which are as follows:

1. The state of the house or the actions (opening/closing of doors/windows) that can be considered by the occupant for achieving minimum air quality dissatisfaction (or equivalently maximum air quality comfort) while suffering some losses on the thermal comfort. This is marked by a blue circle on Fig. 7.

2. Like the previous case, the actions that can be considered by the occupant for achieving maximum thermal comfort while suffering some losses on the air quality comfort. This is marked by a green square on Fig. 7.

3. The actions that can be considered by the occupant for obtaining maximum improvement on the air quality comfort while sacrificing minimal amount of thermal comfort. This is marked by a magenta triangle on Fig. 4. Like the previous case the actions that can be considered by the occupant for obtaining maximum improvement on the thermal comfort while sacrificing minimal amount of air quality comfort. This is marked by a yellow diamond on Fig. 7.

It is further emphasized that each of these vectors (black points) in the Pareto-front as shown in Fig. 7 corresponds to some scenario and thus, represents a behavior of the occupant in terms of openings and closings of doors and windows over 12 hours on a particular day.

Multi-objective Differential Evolution

The goal is to provide the occupant with support to improve his behavior by understanding how far he is from optimal behavior. The optimal behavior is a set of solutions consisting each in a scenario of openings and closings . This optimization problem is addressed with the multi-objective version of differential evolution (DEMO) algorithm [START_REF] Robič | Demo: Differential evolution for multiobjective optimization[END_REF]. The algorithm is briefly described next. It consists of the following steps: initialization, mutation, recombination and selection.

Initialization

For the first generation, several numbers (20, for this work) of population candidates are randomly initialized where each candidate is a 24-dimensional vector (A) whose each element is either open (1) or close (0) status of door or window.

Mutation

In this step, for every i-th candidate in the population, three candidates and random indices r 1 , r 2 and r 3 are chosen such that i, r 1 , r 2 and r 3 are mutually exclusive. The donor vectors, V i,G , are generated at the mutation step for generation G by Eq. ( 14) where F is called the scale factor which is randomly selected such that F ∈ [0, 2]. To ensure that the constituents of the vectors are binary, the floor function ( . ) has been employed.

V i,G = A r1,G + F × (A r2,G -A r3,G ) (14)

Recombination

The constituent of donor solutions and candidate solutions are chosen to construct the trial solutions, U i,G , based on the crossover ratio, CR ∈ [0, 1] which is a random value. Recombination follows Eq. ( 15) which suggests that higher value for CR favors selection of donor solutions and hence, CR was chosen to be 0.8. A random index I rand is selected for which the constituent of the donor is considered so that the trial vector is always new.

u ij,G = v ij,G , if rand ij ≤ CR or j = I rand a ij,G , if rand ij > CR and j = I rand (15)

Selection

The fitness evaluation of a solution is dictated by Eq. [START_REF] Ishibuchi | Evolutionary many-objective optimization: A short review[END_REF]. Since there are multiple criteria for selection, Pareto-dominance relation between the fitnesses of the trial and candidate solutions helps to decide which solution is chosen for the next generation. Selection is governed by Eq. ( 16) whereas Eq. ( 17) demonstrates Pareto-dominance relation [START_REF] Ishibuchi | Evolutionary many-objective optimization: A short review[END_REF] where A 1 Pareto-dominates A 2 i.e. A 1 A 2 . Since, the aim of this optimization problem is to increase the comfort of the occupant, minimization of dissatisfaction defined in Eq. ( 12) and Eq. ( 13) are to be considered.

A i,G+1 = A i,G , if D(A i,G ) D(U i,G ) U i,G , otherwise (16)
∀i ∈ {1, 2},

d i (A 1 ) ≤ d i (A 2 )
and ∃j ∈ {1, 2},

d j (A 1 ) < d j (A 2 ) (17)
At the end of a large number of generations (300 for this work) by which the optimization is believed to have converged to some optima, a set of solutions and the associated set of criteria are obtained. At the termination of the optimization algorithm, the subset of solutions is selected such that no other solution Pareto-dominates any solution of this subset. This subset is known as the Pareto-optimal set and the corresponding criteria forms a set known as Pareto-Front.

Pareto-Front represents the set of the optimal possible solutions that the occupant can take depending on his preferences. Based on this Pareto-Front, the suggestions illustrated in Fig. 7 are obtained. The assessment of the best candidate solution proceeds as follows. The city-block distance, as given by Eq. ( 18), (representing the net dissatisfaction) [START_REF] Melter | Some characterizations of city block distance[END_REF][START_REF] De Souza | Clustering of interval data based on city-block distances[END_REF] of every objective vector, D i , from the reference objective vector, D 0 , is used as an indicator. The origin (coordinate (0, 0)) of the objective space is considered as the reference objective vector because it is the minimum possible value either of the thermal or air quality dissatisfaction can attain. Hence, this quality indicator is used for ranking solutions at every generation of optimization and also for reporting the best candidate solution after termination of the optimization algorithm. Best candidate solution is that solution whose objective vector is closest to the origin of the objective space. This objective vector represents the best trade-off among all the conflicting objectives (considering equal preference of the different objectives) and its corresponding solution is the approximation of the optimal schedule of door and window opening/closing (A * ) that the occupant can consider. The indicator, given by Eq. ( 18), can also be used to measure the distance between the a Pareto-optimal solution and the user position by replacing D 0 with the dissatisfaction values obtained from the historical data.

Dist(D i , D 0 ) = 2 k=1 |d ik -d 0k | (18)
To assess the problem at hand, the solution from the optimization problem obtained using the data of a random day from last year (i.e. recordings of 05/May/2015) is depicted in Fig. 8. The user position or the dissatisfaction on 05/May/2015 obtained from historical data is marked as a blue cross on Fig. 8. The solution corresponding to the nearest objective vector of the Pareto-Front from the origin is the best schedule proposed to the occupant. From the set of different solutions the four compromises of interest as mentioned in Section 4.2 are chosen. Based on this example, solutions 1 and 2 merges with solutions 3 and 4, respectively, and forms the end coordinates of the curve representing the Pareto-Front. Hence, two solutions at both the ends of the Pareto-front along with the solution nearest to the ideal objective vector (origin) are the schedules to be analyzed further. These proposed schedules along with the schedule of actions performed by the occupant results in a set of 12 temperatures and CO 2 concentrations, which are shown in Fig. 9 and 10 respectively. The observations made from Fig. 8 is not so much evident for the occupant. However, from Fig. 9 and 10 the occupant can understand how much gain in thermal comfort can be achieved in different hours using the proposed optimal set of actions. Moreover, from this optimal set of actions the physical model can generate its associated state, which can be compared with the occupant's state to generate the differential explanations and influences (explained in Section 5) and thus present to the inhabitant the possible changes in actions to improve his comfort. From these results, it can be observed that the usual schedule of actions followed by the occupants is worse with respect to all the three proposed schedules. Following any of the proposed schedules of actions will lead to decrease in the dissatisfaction with respect to both air quality and office temperature. This is consistent with both the temporal results (Fig. 9 and 10) and the resultant Pareto-Front (Fig. 8).

As an example scenario, the temperature and CO 2 concentrations based on the occupants behavior peaks between 3pm to 4pm as shown in Fig. 9 and10.

From Fig. 9, during 3pm to 4pm, it can be observed that if the scenario for optimal air quality is chosen, the temperature decreases but it decreases much more if the scenario for optimal thermal quality is chosen. Even at times like the period between 11am to 12pm in Fig. 9, reaching optimal air quality comfort can lead to increase in room temperature i.e. loss in thermal comfort.

Similarly, from Fig. 10, during 3pm to 4pm, it can be observed that if scenario for optimal thermal quality is chosen, the CO 2 concentration in the room decreases but it decreases much more if the scenario for optimal air quality is chosen.

With further analysis, it can be seen from Fig. 9 and 10 that for most of Figure 9: Average office temperatures at different hours showing the proposed temperatures and the recorded temperatures the hours, the curve corresponding to best schedule of actions (average dissatisfaction nearest to the origin) lies between the curves which originates from the end points of the Pareto-Front. This is not the case at the end hours of the day. However, it can be addressed to the fact that the minimization is performed on the average dissatisfaction measured across the entire day and not at every hour. Hence, using this proposed method optimal schedules can be generated for comparison with the historical schedule of the occupants. Among the several schedules generated from the Pareto-front, based on the solutions discussed in Section 4.2, a few solutions are chosen for comparison. The user can prefer any of these schedules to compare his past schedule and learn the impact of his actions. The information on impact of his actions is generated using differential explanations as described in the next section. Thus, in order to compare his past actions, a single schedule has to be rendered. Considering equal preferences of the occupants with respect to thermal and air quality dissatisfaction, the schedule generated from the point on the Pareto-Front which is closest to the origin of the objective space (Eq. ( 18)) is presented for generating the differential explanations.

Based on these results, occupants can get an indicator of the amount of gain or loss in temperatures and CO 2 concentrations to be achieved by them while following the actions proposed by the system for the entire day. The differential explanations, explained in Section 5, will lead the occupants to understand what actions are to be taken to achieve these best comfort levels. Differential explanations are constructed by analyzing the difference between two scenarios (the historical one and the optimal one calculated by the system) to assist the occupants to understand the impact and the effect of their daily actions on the optimality of their desired criteria.

From the optimization results, occupants can understand their position according the possible set of the optimal solutions for the entire day. Differential explanations will help them to understand how and what needs to be done to reach the chosen optimal solution according to their objectives. This comparison includes the set of actions, the intermediate variables, and the effects. The variables are concerned with the consequences of the difference between the users' actions and the optimal actions, and form the basis for the explanations. With this, it is possible to generate an indicator for the impact of those actions on the optimality. It also requires evaluation of the different criteria and represents them in the form of cause-effect relation to make them more clear for occupants.

In Fig. 11, the differential explanations are illustrated in a table where the first column represents the distance of optimality for actions with what the occupant should have done according to the optimal plan, as shown in Eq. ( 19).

A k -Ãk = ∆A k (19)
where A k represent the action (Fig. 2) calculated by the optimizer at instant k while Ãk represents a measured occupant's action at the same instant. The variable, k, can take any value in [0, 23]. In this paper, k = [START_REF] Amayri | Estimating occupancy in an office setting[END_REF]20] , ∀k, because it focuses on the time where occupants are present (daytime period). At 8am, for instance, the inhabitant should have opened the window more. At 4pm, the user behaves according to best scenario.

The second column presents the effects (Fig. 2), like in the thermal comfort and the air quality. This is given by Eq. ( 20).

E k -Ẽk = ∆E k (20)
where E k represent the calculated effect by system at instant k while Ẽk represents the measured effect. The right-hand-side of Eq. ( 19) and (20) denotes the difference in actions of the occupants and its resulting difference in the effect at the k-th instant, respectively.

To better represent the causality in the explanations and extract the knowledge from the system, the intermediate variables are added in the third column of Fig. 11. Those variables are extracted to render the knowledge from the system explicitly.

The last row labeled ALL represents the overall gain or loss in the comfort criteria throughout the day. To generate a small summary and give the inhabitant an indicator to optimality in general, for the entire day.

When computing the differential explanation, it is necessary to transform quantitative variable values into qualitative ones for a better understanding Figure 11: Differential explanations help the inhabitants to understand their actions like at 4pm, the user behaves correctly (its action was similar to the proposed optimal plan); at 12am, the inhabitant should have opened the door for much longer time, this would helped him getting a high improvement in his thermal comfort and slight enhancement in the air quality.

for the occupants and defines the qualitative distance. For instance, telling the occupant that closing the door at 2pm will cause a lot of decrease in the airflow and that he will obtain a significant decrease in the air quality level is easier to understand rather than telling that a difference in airflow of 30% will lead to a difference in CO 2 concentration of 400 ppm. The transformation from quantitative to qualitative here is done by dividing the value domain of a variable into 7 sub-domains (3 positive, 3 negative and 1 no-change levels). Those levels were chosen from the physical world according to their impact on the model and the occupant.

The levels for the variations in thermal dissatisfaction are given by: Π T -0.25,-0.15,-0.05,0.05,0.15,0.25 (∆σ k T (T in ))

The levels for the variations in air quality dissatisfaction are given by: Π

C CO 2 -0.2,-0.1,-0.05,0.05,0.1,0.2 (∆σ k air (C in ))
The levels for the variations in the opening of the door and the window are given by: Π opening -0.7,-0.5,-0.2,0.2,0.5,0.7 (∆ζ D )

Π opening -0.7,-0.5,-0.2,0.2,0.5,0.7 (∆ζ w )

The arguments of each of these discretization functions is the difference of the measured quantity with the proposed optimal value of the quantity.

Except for the no-change level, where arrows are omitted, 1 to 3 arrows have been used to represent the associated sign of variation (arrows direction) and intensity (number of arrows). For instance, in Fig. 11, the logo of window with three adjacent upward arrows means that the occupant should have opened the window for a much longer period of time during the corresponding time period.

As it can be seen, the differential explanations are much easier to understand than the analysis of the 11 plotted curves (Fig. 3 to 6) where the inhabitant has to correlate the different actions, effects and intermediate variables. With differential explanation, it is thus easy for an occupant to identify the actions that needs to be modified, monitor the difference gained with respect to different criteria while at the same time use the intermediate variables as elements of understanding.

The differential explanation is providing a list of behavior modifications (opens the door for a longer period, for instance) with the associated impact. However, there are two limitations with such a description.

First, there is not a direct link between an action modification and its impact. Buildings have inertia i.e. energy dynamically stored in their structure. This inertia causes a delay and has a smoothing effect on different changes in the building preventing a rapid degradation or augmentations in temperature. Inertia is also present in the room volume for the CO 2 concentration. Thus, occupant actions might have a delayed impact. In Fig. 12, closing the door at 10am does not have an immediate impact but it has a strong influence on the air quality at 12pm: it is a calculated delayed impact.

Second, all the proposed action modifications does not have the same impor-tance: some of them have a limited influence and could be skipped if necessary (the inhabitant might not want for instance to interrupt his current activity to close the window). But some of them should be followed because of their high influence on the selected criteria (like the previous door example having a strong influence on the air quality). Lets consider à = { Ãi,k ; ∀k}

A = {A i,k ; ∀k} (21)
where i stands for the different actions (window and door) and k for the time period. The influence of each action is determined by changing one action at a time like in Eq. ( 22). In a specific instant the calculated action will be equal to the measured action.

A t = {A k ; ∀k = t} ∪ Ãt (22)
The physical model is then used to re-simulate the effects.

Physical model:

A t =⇒ E t (23)
By comparing the optimal scenario with a scenario calculated by replacing one optimal action by the action that has been really done, it is possible to evaluate the impact of occupants behaviors that they may have on the comfort level and how it is preventing them from reaching the optimal level. For instance, on Fig. 12, occupant might discover that opening the window for longer time requested by the system at 8:00 will not change much the air quality at 12:00 but not closing the door at 10:00am could dramatically change the level of the air quality at 12:00pm.

E t -E k = ∆E (24)
Thus, the proposed method allows the occupants to have an explanation based on the cause-effect relations of their actions and they may decide to change their routines, learning from their historical actions.

Conclusion

The main objective of this paper is to help the occupants to get a better understanding of their energy management system and their actions. This work discusses and presents why explanations are needed and why they are important for occupants apprehension of the energy management system and the impact of their actions. It presents the concept of differential explanations i.e. a type of cause-effect explanations and also presents the concept of influence of the inhabitant's actions to clarify for him/her the long term effect of his/her actions. This study uses the multi-objective version of differential evolution (DEMO) for proposing optimal actions to the occupant based on his/her past actions. This is preliminary work dealing with thermal and air quality comfort criteria.

In future, this work will examine different methods to build and generate qualitative models to define causality between actions and their causal chain of impacts. This can be done by using causal physical models like bond graphs [START_REF] Ghiaus | Fault diagnosis of air conditioning systems based on qualitative bond graph[END_REF] and try to profit from the techniques of the causal graph to formalize the causal explanations like by using GARP3 [START_REF] Bredeweg | Garp3: A new workbench for qualitative reasoning and modelling[END_REF] as workbench for qualitative reasoning and modeling.

Another aspect to be explored is the optimal schedule obtained when other criteria such as humidity, consumption of energy, price of electricity, etc. come into play. Besides having multiple criteria, the occupant may be biased towards certain criteria. Hence, the preference of the occupant plays a crucial role in decision making. Incorporating such user preferences is another open area of research. As the only machine learning tool used in this work is the optimization algorithm, the comparison of the performance of the proposed approach using other optimization algorithms is to be studied further.

Figure 1 :

 1 Figure 1: Panoramic photo of the office with sensors

Figure 2 :

 2 Figure 2: General schema of explanations

Figure 3 :

 3 Figure 3: Different temperature measurements and system output

Figure 5 :Figure 6 :

 56 Figure 5: Actual and recommended door position

  thermal comfort maximum gain in air quality comfort maximum gain in air quality comfort with minimal change in thermal comfort maximum gain in thermal comfort with minimal change in air quality comfort best position for thermal comfort best position for air quality comfort nearest position for best air quality comfort nearest position for best thermal comfort

Figure 7 :

 7 Figure 7: Optimal scenario and consequences of occupant's historical actions.

Figure 8 :

 8 Figure 8: Results from Multi-objective Differential Evolution for comparison with User Position

Figure 10 :

 10 Figure 10: Average concentrations of CO 2 at different hours showing the proposed concentrations and the recorded concentrations

Figure 12 :

 12 Figure 12: Differential Explanations with Influences

Acknowledgment

This study has been supported by the Indian side of the project sanctioned vide DST-INRIA/ 2015-02/ BIDEE/ 0978 by the Indo-French Centre for the Promotion of Advanced Research (CEFIPRA -IFCPAR).

This work benefits from the support of the INVOLVED ANR-14-CE22-0020-01 project of the French National Research Agency [16] which aims at implementing new occupant interactive energy services, like MIRROR, WHAT-IF and SUGGEST, into a positive energy building constructed at Strasbourg in France by Elithis.