Piotr Bilinski

Francois Bremond

Contextual Statistics of Space-Time Ordered Features for Human Action Recognition

The bag-of-words approach with local spatio-temporal features have become a popular video representation for action recognition. Recent methods have typically focused on capturing global and local statistics of features. However, existing approaches ignore relations between the features, particularly space-time arrangement of features, and thus may not be discriminative enough. Therefore, we propose a novel figure-centric representation which captures both local density of features and statistics of space-time ordered features. Using two benchmark datasets for human action recognition, we demonstrate that our representation enhances the discriminative power of features and improves action recognition performance, achieving 96.16% recognition rate on popular KTH action dataset and 93.33% on challenging ADL dataset.

Introduction

Automatic recognition of human actions has gained tremendous interest in recent years. Video surveillance, video data indexing, video retrieving, human-computer interaction or sport event analysis are just few of many applications, in which action recognition plays the main role. In recent years, various methods have been proposed and much progress has been made. However, due to enormous variations in visual and motion appearance of both people and actions, camera view point, occlusions, noise and enormous amount of video data, action recognition still remains a challenging problem.

Over the last few years, many different action recognition techniques have been proposed. Existing techniques could be divided into four categories. The first group of techniques uses silhouette or body contour information to represent an action [START_REF] Davis | Hierarchical motion history images for recognizing human motion[END_REF][START_REF] Ahad | Motion history image: its variants and applications[END_REF][START_REF] Aggarwal | Human motion analysis: a review[END_REF][START_REF] Kim | Silhouette-based Human Activity Recognition Using Independent Component Analysis, Linear Discriminant Analysis and Hidden Markov Model[END_REF][START_REF] Lin | Recognizing actions by shape-motion prototype trees[END_REF]. Such techniques usually require precise algorithms, which is often difficult to achieve, especially in real-world videos. The sec- ond category contains methods analysing motion trajectories [START_REF] Messing | Activity recognition using the velocity histories of tracked keypoints[END_REF][START_REF] Raptis | Tracklet descriptors for action modeling and video analysis[END_REF][START_REF] Kaaniche | Gesture recognition by learning local motion signatures[END_REF][START_REF] Wang | Action recognition by dense trajectories[END_REF]. This group of techniques usually requires either feature point or object tracking. Reliable tracking is also difficult to achieve due to illumination variability, occlusions, noise, low discriminative appearance or drifting problems. The third category of techniques uses local spatio-temporal features [START_REF] Laptev | On space-time interest points[END_REF][START_REF] Rapantzikos | Dense saliencybased spatiotemporal feature points for action recognition[END_REF][START_REF] Klaser | A spatio-temporal descriptor based on 3d-gradients[END_REF][START_REF] Gilbert | Fast realistic multi-action recognition using mined dense spatio-temporal features[END_REF][START_REF] Liu | Learning human action via information maximization[END_REF] which have recently become a very popular video representation method for action recognition. Local spatio-temporal features have shown very good performance in recognition of various action classes. They are able to capture both visual and motion appearance. They are robust to viewpoint and scale changes, they are easy to implement and fast to process. Moreover, they do not require either object localization or tracking and in addition they are robust to background clutter. Over the last few years, many different local interest point detectors (like Harris3D [START_REF] Laptev | On space-time interest points[END_REF], Cuboid [START_REF] Dollar | Behavior recognition via sparse spatio-temporal features[END_REF], Hessian [START_REF] Willems | An efficient dense and scale-invariant spatio-temporal interest point detector[END_REF] or Dense sampling [START_REF] Wang | Evaluation of local spatio-temporal features for action recognition[END_REF]) and many spatio-temporal descriptors (like HOG [START_REF] Laptev | Learning realistic human actions from movies[END_REF], HOG3D [START_REF] Klaser | A spatio-temporal descriptor based on 3d-gradients[END_REF], HOF [START_REF] Laptev | Learning realistic human actions from movies[END_REF], Cuboid [START_REF] Dollar | Behavior recognition via sparse spatio-temporal features[END_REF] or ESURF [START_REF] Willems | An efficient dense and scale-invariant spatio-temporal interest point detector[END_REF]) have been proposed. One of the most commonly used descriptors in the literature showing a high performance over the various datasets [START_REF] Wang | Evaluation of local spatio-temporal features for action recognition[END_REF] are: Histogram of Oriented Gradients (HOG) and Histogram of Oriented Flow (HOF) descriptors [START_REF] Laptev | Learning realistic human actions from movies[END_REF]. The former describes the local visual appearance and the latter characterizes the local motion appearance of the interest point. These descriptors are usually applied with the Harris3D corner detector [START_REF] Laptev | On space-time interest points[END_REF], 1 which is a space-time extension of the Harris operator.

Local spatio-temporal features are mostly used with a bag-of-words model. Together, they have shown to achieve high recognition rate across various datasets [START_REF] Liu | Recognizing realistic actions from videos "in the wild[END_REF][START_REF] Laptev | Learning realistic human actions from movies[END_REF][START_REF] Niebles | Unsupervised learning of human action categories using spatial-temporal words[END_REF]. The bag-of-words model simplifies the structure of 3D video data assuming conditional independence across spatial and temporal domains. It encodes global statistics of features computing histogram of feature occurrences in a video. However, this technique has few limitations: it ignores relative position of features, local density of features, local pairwise relationships among the features and information about the space-time order of features. A common way to overcome these limitations is to use either spatiotemporal grids [START_REF] Laptev | Learning realistic human actions from movies[END_REF] or multi-scale pyramids [START_REF] Lazebnik | Beyond bags of features: spatial pyramid matching for recognizing natural scene categories[END_REF]. Unfortunately, these methods are still limited in terms of detail description providing only a coarse representation. To overcome these limitations, techniques of the fourth category can be used to enhance the discriminative power of features and help in the task of action recognition. The fourth group of method is based on contextual information [START_REF] Galleguillos | Context based object categorization: A critical survey[END_REF] extracting from the video content scene information [START_REF] Li | What, where and who? classifying events by scene and object recognition[END_REF][START_REF] Marszalek | Actions in context[END_REF], spatiotemporal relations between trajectories [START_REF] Sun | Hierarchical spatio-temporal context modeling for action recognition[END_REF], figure-centric features [START_REF] Wang | Action recognition with multiscale spatio-temporal contexts[END_REF][START_REF] Banerjee | Learning neighborhood cooccurrence statistics of sparse features for human activity recognition[END_REF][START_REF] Kovashka | Learning a hierarchy of discriminative space-time neighborhood features for human action recognition[END_REF] or modelling human-object interactions [START_REF] Gupta | Objects in action: An approach for combining action understanding and object perception[END_REF]. Sun et al. [START_REF] Sun | Hierarchical spatio-temporal context modeling for action recognition[END_REF] have proposed to model the spatiotemporal context of trajectories into transition matrix of a Markov process, and then extract its stationary distribution as the final context descriptor. The authors capture the local occurrence statistics of all types of trajectories within figure-centric neighbourhoods. Wang et al. [START_REF] Wang | Action recognition with multiscale spatio-temporal contexts[END_REF] have proposed a representation that captures contextual interactions between interest points, based on the density of all features observed in each interest point's multiscale spatio-temporal contextual domain. However, both these methods are restricted to aggregate statistics over the video volume and ignore local pairwise relationships between features. Banerjee et al. [START_REF] Banerjee | Learning neighborhood cooccurrence statistics of sparse features for human activity recognition[END_REF] have proposed to learn the local neighbourhood relationships between local features, and train a CRF based human activity classifier. The neighbourhood relationships are modelled in terms of pairwise co-occurrence statistics. Kovashka et al. [START_REF] Kovashka | Learning a hierarchy of discriminative space-time neighborhood features for human action recognition[END_REF] have proposed to learn the shapes of space-time feature neighbourhoods that are the most discriminative for a given action category. The authors have proposed figure-centric statistics that capture the orientation between features. However, despite that these methods capture relationships between local features, they are still limited ignoring important information about the spatio-temporal order of features.

To differ from those ideas, we propose a novel representation based on quantized local spatio-temporal features. We enhance the discriminative power of features incorporating figure-centric information about the local spatiotemporal distribution and order of features. For each detected local feature, we define its neighbourhoods and com-pute statistics of pairwise co-occurring visual words within such neighbourhoods. Our representation captures not only, local density of features but also, local pairwise relationships among the features and information about the spacetime order of features. We evaluate our approach on two publicly available datasets for human action recognition (KTH and ADL). We show that the proposed representation enhances the discriminative power of features and improves action recognition performance.

Proposed Approach

Local spatio-temporal features used with bag-of-words model have shown to achieve high action recognition performance. Recent methods have typically focused on capturing global and local statistics of features. However, existing approaches ignore relations between the features, particularly space-time arrangement of features, and thus may not be discriminative enough. Therefore, we propose a novel figure-centric representation which captures local density of features and local pairwise relationships among the features with information about the space-time order of features. The technique presented in this section enhances discriminative abilities of features and improves action recognition performance.

Interest Point Quantization

Firstly, we extract local interest points P = {P 1 , ..., P n } and their descriptors for each video sequence. Then, we cluster all the descriptors extracted from the training videos into k classes, called visual words. Finally, for each video sequence V, we map the extracted interest points to the closest visual words using associated local descriptors:

V = {(P 1 , c 1 ), . . . , (P n , c n )}, (1)
where point P i is represented as

P i = [P (x) i , P (y)
i , P

i ] T and c i is an index of the closest visual word from the P i .

Figure-Centric Neighbourhoods

To specify Space-Time Ordered Contextual Features (STOCF), we initially define the neighbourhoods of detected points.

For each detected interest point P i , we compute a set S = {S 1 , ..., S |S| } of multi-scale blocks around it. For simplicity, we define s-th scale neighbourhood of the point P i as cuboid with side lengths G

(x) s , G (y)
s and G (t) s (Figure 1). The points that belong to such s-th scale cuboid can be defined as:

N i,s = {P j ∈ P : d∈{x,y,t} |P (d) j -P (d) i | ≤ W (d) s }, (2)
where ∀ d∈{x,y,t} G In the previous section, we have explained that each point is assigned to a certain visual word v. Therefore, we define N (v) i,s as a set of points in neighbourhood N i,s , which are assigned to the codebook element v:

(d) s = 2W (d) s + 1. N 3,s = {P 1 , P 2 , P 3 , P 4 }, C = {C 1 , C 2 }, N (C1) 3,s = {P 1 , P 3 }, N (C2) 3,s = {P 2 , P 4 }, M (F ) 3,s = P 1 P 2 P 3 P 4       P 1 0 1 1 1 P 2 0 0 1 1 P 3 0 0 0 1 P 4 0 0 0 0 , M (C) 3,s = C 1 C 2 C 1 1 3 C 2 1 1 , CF 3,s = [1, 3, 1, 1] T , Table 1: STOCF feature -
N (v) i,s = {P j ∈ N i,s : c j = v}, (3)
where c j is the index of the visual world assigned to the point P j (defined in Equation 1).

Space-Time Ordered Contextual Features (STOCF)

Given computed local interest points and their neighbourhoods, we show how to compute the Space-Time Ordered Contextual Features (STOCF) for a specified point P i and its neighbourhood N i,s .

We define STOCF as figure-centric statistics of features within 3D video patches. STOCF features are represented as histograms of pairwise co-occurring visual words. Each element of the histogram contains information about the relationship between two visual wordse.g. the value of x for pair of visual words (C a , C b ) means that there is x pairs of points where the first point is assigned to the visual word C a and the second to the C b . More precisely, we compute non-negative matrix M (C) i,s :

M (C) i,s =     R (1,1) i,s . . . R (1,k) i,s . . . . . . . . . R (k,1) i,s . . . R (k,k) i,s     , (4)
where

R (a,b) i,s
is the cardinality of the set R ( Parameter w d , which is explained later, is the weight for the dimension d and sgn(x) is the signum function 1 .

Finally, we define the STOCF features -CF i,s , computed for the point P i in the s-th scale neighbourhood N i,s , as matrix M (C) i,s reshaped to a single dimensional vector:

CF i,s = [R (1,1) i,s , . . . , R (1,k) i,s , R (2,1) i,s , . . . , R (k,k) i,s ] T , (6)
If necessary, the size of the STOCF features can be reduced using e.g. PCA or LDA technique. However, due to the efficiency of small codebooks, methods for dimension reduction were not applied during our experiments. A calculation example of STOCF features is given in Table 1.

Action Recognition using STOCF features

To represent videos, we apply the bag-of-words model for each feature class (HOG-HOF and STOCF) independently. We construct visual vocabularies from training videos clustering computed features. Then, we assign each feature to its closest visual world. The concatenated histograms of visual world occurrences over video forms the final representation.

To classify a video, we use multi-class non-linear Support Vector Machines (SVM). We apply a χ2 distance to compare two n-bins histograms H i = [H i (1), ..., H i (n)] T and H j = [H j (1), ..., H j (n)] T :

χ 2 (H i , H j ) = 1 2 n k=1 (H i (k) -H j (k)) 2 H i (k) + H j (k) ( 7
)
This distance is then converted into SVM multi-channel χ 2 kernel using a multi-channel generalized Gaussian kernel:

K(H i , H j ) = exp(- 1 A χ 2 (H i , H j )) ( 8
)
where A is the normalization parameter set as in [START_REF] Laptev | Learning realistic human actions from movies[END_REF].

Experiments

Our experiments demonstrate the effectiveness of the proposed representation for a various of action categories. We evaluate our approach on two benchmark datasets for human action recognition -KTH and ADL datasets. Sample frames from video sequences of these datasets are presented in Figure 2. We show that using a small codebook (Section 2.1), we are able to enhance the discriminative power of features and improve action recognition performance.

Implementation Details

To detect interest points in a video, we use the sparse Harris3D corner detector [START_REF] Laptev | On space-time interest points[END_REF]. We detect points in multiple spatial and temporal scales. Then, for each 3D video patch in the neighbourhood of a detected point, we compute HOG (Histogram of Oriented Gradient) and HOF (Histogram of Optical Flow) descriptors [START_REF] Laptev | Learning realistic human actions from movies[END_REF]. The detector and descriptors were selected based on their use in the literature and provide a good baseline for comparison with the state-of-theart techniques. However, our action representation method is independent of the type of detector and descriptor, and can be used together with any other algorithm.

In order to quantize local features, we use the kmeans clustering technique and nearest neighbour algorithm. To compute the bag-of-words representation, features are quantized to the codebook size of 1000, which has shown empirically to give good results. As a metric to calculate a distance between features and visual words, we use the L 2 norm. Since Harris3D corner detector calculates sparse spatio-temporal features, we set the weights w as w (x) = 1, w (y) = 2, w (t) = 4 (Equation 5). To compute STOCF features, the HOG-HOF descriptors are quantized to small codebook sizes (10, 15, 20 and 25) and

s , W

∈ {4, 8, ..., 32}). The proper selection of neighbourhood size is important. Too small neighbourhood can contain only a few points and might not be discriminative. Too large volume may employ too many points and might also result in being not discriminative. Choosing an appropriate scale can be done in two ways: using Multiple Kernel Learning or cross-validation. In all our experiments, we calculate several codebooks to quantize local points (Section 2.1), and several multi-scale neighbourhoods to compute STOCF features. Then, we apply the cross-validation technique to both gauge the generalizability of the proposed approach, and select the most discriminative parameters. We use the Leave-One-Out Cross-Validation (LOOCV) technique, where videos of one person are used as the validation data, and the remaining videos as the training data. This is done repeatedly so that videos of each person are used once as the validation data.

KTH Dataset

The KTH [START_REF] Schuldt | Recognizing human actions: A local svm approach[END_REF] 2 dataset contains six types of human actions: walking, jogging, running, boxing, hand waving and hand clapping. Each action is performed several times by 25 different subjects in four different scenarios: outdoors (s1), outdoors with scale variation (s2), outdoors with different clothes (s3) and indoors (s4). The dataset contains 599 video files. All sequences were recorded with 25 fps frame rate.

The dataset contains a set of challenges like: scale changes, illumination variations, shadows, different scenarios, cloth variations, inter and intra action class speed variations and low resolution (160 × 120 pixels spatial resolution).

We follow recent evaluations on the KTH dataset [START_REF] Liu | Recognizing realistic actions from videos "in the wild[END_REF][START_REF] Wu | Action recognition using context and appearance distribution features[END_REF][START_REF] Kim | Tensor canonical correlation analysis for action classification[END_REF][START_REF] Wu | Action recognition in videos acquired by a moving camera using motion decomposition of lagrangian particle trajectories[END_REF][START_REF] Jiang | Recognizing human actions by learning and matching shape-motion prototype trees[END_REF] using LOOCV scheme. In general, LOOCV assesses the performance of an approach with much more reliability than splitting-based evaluation schemes because it is much more comprehensive. Results from the exper-iments are presented in Table 2. Comparison of our approach with state-of-the-art methods in the literature using LOOCV technique is presented in the Table 3. For scenarios s1, s2, s3 and s4, our approach obtains the recognition rate of 98.67%, 95.33%, 92.62% and 98.00% respectively (selecting codebook size of 15, 25, 10 and 10 respectively). Overall, our approach obtains 96.16% recognition rate. The results clearly show that our representation enhances the discriminative power of features and outperforms state-ofthe-art techniques.

Moreover, given quantized local interest points, we examine the average computation time of STOCF features using various codebooks (Section 2.1) and neighbourhoods. Results are presented in Table 4. We observe, that using small codebooks, STOCF features are very fast to calculate and achieve high action recognition rate. s1 s2 s3 s4 s1-s4 98.67% 95.33% 92.62% 98.00% 96.16%

(x) = W (y) = W (t) ).

ADL Dataset

The ADL (University of Rochester Activities of Daily Living) [START_REF] Messing | Activity recognition using the velocity histories of tracked keypoints[END_REF] 3 dataset contains ten types of human activities 3 http://www.cs.rochester.edu/˜rmessing/uradl/ of daily living selected to be useful for an assisted cognition task. The full list of activities is: answering a phone, dialling a phone, looking up a phone number in a telephone directory, writing a phone number on a whiteboard, drinking a glass of water, eating snack chips, peeling a banana, eating a banana, chopping a banana, and eating food with silverware. Each action is performed three times by five different people. In total, the dataset contains 150 video sequences recorded with 30 fps frame rate and 1280 × 720 pixel resolution. The videos were down-sampled to the spatial resolution 640 × 360 pixels.

The dataset contains a set of challenges like: different shapes, sizes, genders and ethnicities of people, and difficulty to separate activities on the basis of a single source of information (e.g. eating banana and eating snack or answering a phone and dialling a phone).

The results from the experiments, together with a comparison of our approach with state-of-the-art methods in the literature, are presented in Table 5. Our approach obtains 93.33% recognition rate, which is comparable to [START_REF] Wang | Action recognition with multiscale spatio-temporal contexts[END_REF] (where the authors use more efficient but more timeconsuming and complex learning algorithms; also, [START_REF] Wang | Action recognition with multiscale spatio-temporal contexts[END_REF] reaches 93.8% accuracy for the KTH dataset while our approach achieves 96.16% accuracy) and outperforms all other state-of-the-art methods [START_REF] Matikainen | Representing pairwise spatial and temporal relations for action recognition[END_REF][START_REF] Satkin | Modeling the temporal extent of actions[END_REF][START_REF] Benabbas | Action recognition using direction models of motion[END_REF][START_REF] Raptis | Tracklet descriptors for action modeling and video analysis[END_REF][START_REF] Messing | Activity recognition using the velocity histories of tracked keypoints[END_REF]. The results clearly show that our representation enhances the discriminative power of features and improves the action recognition performance.

Method

Year Recognition Rate (%) Matikainen et al. [START_REF] Matikainen | Representing pairwise spatial and temporal relations for action recognition[END_REF] 2010 70% Satkin et al. [START_REF] Satkin | Modeling the temporal extent of actions[END_REF] 2010 80% Banabbas et al. [START_REF] Benabbas | Action recognition using direction models of motion[END_REF] 2010 81% Raptis et al. [START_REF] Raptis | Tracklet descriptors for action modeling and video analysis[END_REF] 2010 82.67% Messing et al. [START_REF] Messing | Activity recognition using the velocity histories of tracked keypoints[END_REF] 2009 89% Wang et al. [START_REF] Wang | Action recognition with multiscale spatio-temporal contexts[END_REF] 2011 96% (93.8% for KTH) Our method 93.33%

Conclusions and Future Work

We have proposed a novel figure-centric representation which captures statistics of space-time ordered features. This representation has been evaluated on two public benchmark datasets for human action recognition. We have obtained 96.16% recognition rate for the KTH dataset and 93.33% for the ADL dataset. This shows that our approach enhances the discriminative power of features and improves action recognition performance. In the near future work, we intend to examine more efficient learning algorithms (like Multiple Kernel Learning) to combine STOCF features from different neighbourhoods, and to evaluate our representation using various interest point detectors and descriptors. We also intend to examine the proposed representation in a hierarchical manner, i.e. using STOCF features as descriptors in the interest point quantization process.

Figure 1 :

 1 Figure 1: Multi-scale figure-centric neighbourhoods used to calculate Space-Time Ordered Contextual Features.

  sample of computation. The red cuboids represent a figure-centric s-th scale neighbourhood of the point P 3 . The set of points belonging to this neighbourhood is marked as N 3,s . C represents the set of visual words and N (Cj ) 3,s is the set of points (belonging to the N 3,s ) that are assigned to the visual word C j . An order of points is represented by binary matrix M (F ) 3,s , where M (F ) 3,s (P a , P b ) = 1 means that point P a occurs before point P b . The matrix M (C) 3,s is obtained from corresponding points from the matrix M (F ) 3,s using point to codebook mapping. Finally, the STOCF feature is marked as CF 3,s . Related elements of the matrices M (F ) 3,s and M (C) 3,s , and vector CF 3,s are indicated by identical colours.

  |), and the set R (a,b) i,s represents pairs of co-occurring points which are organized in space-time: R (a,b) i,s = {(P j , P k ) ∈ N

Figure 2 :

 2 Figure 2: Sample frames from video sequences of the KTH (first row) and ADL (second row) datasets.

Table 2 :

 2 KTH dataset: Evaluation of STOCF features. The table shows the action recognition rate.

	Method	Year Accuracy
	Liu et al. [21] 2009	93.8%
	Wu et al. 2011	94.5%
	Kim et al. [12] 2007	95.33%
	Wu et al. [36] 2011	95.7%
	Lin et al. [10] 2011	95.77%
	Our method		96.16%

Table 3 :

 3 KTH dataset: Comparison of our approach with state-of-the-art methods in the literature.

			Neighbourhood
	Codebook	4	12	20
	10	1.82ms 3.09ms 5.63ms
	20	1.87ms 3.22ms 6.36ms
	Table 4: KTH dataset: Average computation time of
	STOCF features using various codebooks and neighbour-
	hoods (W

Table 5 :

 5 ADL dataset: Comparison of our approach with state-of-the-art methods in the literature.

The signum function of a real number x is defined as follows: 1 if x > 0, 0 if x = 0, and -1 otherwise.

http://www.nada.kth.se/cvap/actions/

Acknowledgements.

This work was supported by the Région Provence-Alpes-Côte d'Azur. However, the views and opinions expressed herein do not necessarily reflect those of the financing institutions.


Delphine Battistelli
email: delphine.battistelli@paris-sorbonne.fr

Marcel Cori
email: mcori@u-paris10.fr

Jean-Luc Minel
email: jminel@u-paris10.fr

Charles Teissèdre
email: charles.teissedre@mondeca.com

Information Retrieval: Ranking Results according to Calendar Criteria

Our work deals with calendar information as it is expressed in natural language (NL), that is to say through textual units such as prepositional phrases or noun phrases (e.g. in the 90s, at the beginning of the XVth century). We call these textual units Calendar Expressions (CE). Our work aims at showing how Information Retrieval systems can benefit from dealing with CE. In this paper we describe our overall approach which consists in a formal analysis of CEs that leads to a semantic representation. We then detail an algorithm that uses this representation to filter and rank CEs embedded in texts, according to a query containing a CE. The algorithm is integrated in an experimental search engine (called CaSE). Our representation of calendar information as it is expressed in NL and the function which computes the proximity between the two CEs, one in the text and the other in the query, provides a mean to process a query without any overlapping.

Introduction

Our work deals with the issue of searching for information according to calendar criteria, as they are expressed in natural language. Considering for example a corpus related to the history of the United States, a user could be interested in finding information such as "prohibition at the beginning of the 30s". There could be several more or less relevant answers to such a query in documents. One of the best answers could be "In 1931, shortly before the end of Prohibition, Madden got out of bootlegging", but an answer such as "By the end of the 20s, Bureau of Prohibition agent Eliot Ness began an investigation of Capone and his business" may also satisfy the user.

Leaving aside the issue of processing keywords such as "prohibition", our work focuses on the problem of linking the calendar information contained in the query with the calendar information we can find in the corpus. This requires a linguistic analysis of textual units conveying calendar information. It also requires being able to rank the set of units that are considered as relevant answers. We define a Calendar Expression (CE) as a more or less complex adverbial unit, including prepositions and/or other elements interacting directly with an explicit calendar reference. For example (the calendar references, which can be of different granularity levels, are underlined):

(E0) in 1931 (E1) at the beginning of the 30s (E2) three months before the beginning of the year 1985 (E3) until three months before the beginning of the 30s (E4) between the end of the year 2007 and the beginning of March 2009 One originality of our approach is that it is based on a theoretical modelling of CEs underpinned by a linguistic analysis. This approach is implemented and integrated in an experimental search engine (called CaSE). The CaSE system is divided into multiple steps for documents and query analysis (see figure 1): (1) CE annotation (parsing step);

(2) a transduction step to transform the annotation outputs into Calendar Intervals; and

(3) the core retrieval process. Based on the resources for annotation described in [START_REF] Teissèdre | Resources for Calendar Expressions Semantic Tagging and temporal Navigation through Texts[END_REF], the first step of the processing chain annotates the CEs embedded in documents. As presented in Section 2, this first step delivers a linguistic analysis of these expressions, named Functional Representation (see section 2.1). Based on the formal transduction processing described in [START_REF] Battistelli | Semantics of Calendar Adverbials for Information Retrieval[END_REF], the second step transforms this Functional Representation into what we name a Referential Representation, or Calendar Intervals (see sections 2.2 and 2.3). The retrieval algorithm used during the search process is described in section 3. It relies on an empirical function that computes a semantic distance evaluation between the Referential Representation of the CE embedded in the query and the Referential Representations of CEs found in documents. In section 4, we compare our approach to related work. We stress the fact that analysing calendar information within texts via textual units such as CEs (called "temporal adverbials" in theoretical linguistics, see [START_REF] Klein | Time in Language[END_REF] for instance) is an innovative and intuitive way for IR systems that require some calendar criteria. It distinguishes our approach from all existing approaches in this area.

Formal Representation of Calendar Expressions

In this section, we describe our two-step approach to CE semantics. As detailed in [START_REF] Battistelli | Representing and Visualizing Calendar Expressions in Texts[END_REF], the first step provides a functional analysis of the different CE component units. The second step transforms functional representations of CEs into referential ones. This transformation is useful for the last step of the processing chain: the ranking of CEs embedded in documents in response to a CE embedded in a user's query.

Functional Representation of Calendar Expressions

The Functional Representation of a CE is defined as a sequence of operations that act on a Calendar Base (CB) -see [START_REF] Battistelli | Representing and Visualizing Calendar Expressions in Texts[END_REF] for more details. The Calendar Base is the core calendar reference indicated by a textual unit (such as "17th century", "June 6, 1897", for instance). Several operators can successively apply upon the CB: (i) Zooming and Shifting Operators (corresponding to textual units such as "mid", "three months before"), (ii) Zoning Operators (corresponding to textual units such as "at", "before", "until") and (iii) Composition Operators (involved in CEs such as "from the mid 80s to the mid 90s"). More precisely, we consider four sets of operators:

OpZooming = {ZoomID,

Referential Representation

In this section we describe a method, improved and augmented from [START_REF] Battistelli | Semantics of Calendar Adverbials for Information Retrieval[END_REF], to transform the Functional Representation of CEs into its referential counterpart, also named Calendar Intervals (CI). This step is useful to perform similarity comparisons between several CEs.

Calendar Units. We take a finite set of units U = {u, v, w, ...}, e.g. {millennium, century, decade, year, month, day, . . . }. To each unit u is associated an infinite sequence:

S(u) = . . . , u -n , . . . , u -1 , u 0 , u 1 , . . . , u m , . . .
which describes the succession of dates according to a given unit. For example, if u is month, S(u) is a sequence such as . . ., 2010-11, 2010-12, 2011-1, 2011-2, . . . . We also take an order relation between units: we say that unit v is smaller than unit u, and we write v ≤ u (e.g. day ≤ year). When v ≤ u, we define two mappings b u→v and e u→v such that:

(i) ∀i b u→v (i) ≤ e u→v (i) (ii) if i 1 < i 2 e u→v (i 1 ) < b u→v (i 2 ) If b u→v (i) = j and e u→v (i) = k, it
means that v j is the beginning of u according to v and that v k is the end of u according to v. In particular, for each u and for each i, b u→u (i) = i and e u→u (i) = i.

Calendar Intervals A Calendar Interval (CI) is given by an ordered pair of elements taken from one of the sequences S(u) : u i , u j (with i ≤ j). We can also write: i, j, u . u i represents the date of the beginning of the CI, u j represents the date of the end and u is the unit. Particular cases where i = -∞ or j = +∞ are admitted. The case of the empty CI, written ∅, is also admitted. For each CI i, j, u where the unit is u and for each v smaller than u we can associate its image according to v:

f u→v ( i, j, u ) = b u→v (i), e u→v (j), v
For instance, the image of the CI 1995-3, 1996-5 according to the day is the CI 1995-3-1, 1996-5-31 .

Properties Given two CIs A and B whose units are respectively u and v, let w be the smallest unit among u and v, f

u→w (A) = i, j, w , f v→w (B) = k, l, w .
The intersection of A and B is the CI A ∩ B = max(i, k), min(j, l), w except if max(i, k) > min(j, l). In this case A ∩ B = ∅. We will say that A is included in B (or

B contains A) iff i ≥ k and j ≤ l. A equals B iff A is included in B and B is included in A.
The relative length of A and B (B = ∅) is the value: rl(A/B) = j-i+1 l-k+1

If A = ∅, rl(A/B) = 0 for each B = ∅.
If B is an infinite CI and A = ∅ we say that rl(A/B) = ε, a value greater than 0 but smaller than all other positive numbers.

If A and B are infinite CIs:

-if A is strictly included in B, rl(A/B) = 1 -ε -if B is strictly included in A, rl(A/B) = 1 + ε -if B equals A, rl(A/B) = 1

Calendar Intervals associated to Calendar Expressions

Given the Functional Representation of a CE, a translation process transforms it into a Calendar Interval. Remember that a Functional Expression is obtained by the successive application of four kinds of operators to a Calendar Base. Simultaneously, we consider four kinds of successive operations that are applied to the CI associated to a calendar base. This translation process enables us to associate a computed CI with each CE.

(1) To each CB we associate a CI for which the beginning is equal to the end, such as u i , u i . For instance: (2) Let us consider an FE α with which a CI i, j, u is associated.

(2.1) If Ω is an operator of OpZooming we associate a CI to Ω(α) for each unit v strictly smaller than u.

ZoomBegin b u→v (i), b u→v (i) + τ (e u→v (j) -b u→v (i) + 1) , v ZoomEnd e u→v (j) -τ (e u→v (j) -b u→v (i) + 1) , e u→v (j), v ZoomMiddle b u→v (i) + µ(e u→v (j) -b u→v (i) + 1) , e u→v (j) -µ(e u→v (j) -b u→v (i) + 1) , v
Here τ , τ and µ are coefficients taken between 0 and 1 (or between 0 and 1 2 ). In the following we will take τ = τ = µ = 0.25. Thanks to the floor function 4 , we always obtain integers. Consequently, the results will differ depending on the unit taken into account. (2.2) If Ω is an operator of OpShifting where v is a unit of U smaller than u (or equal to u), we associate a CI to Ω(α).

ShiftBefore(v, -n) b u→v (i) -n, b u→v (i) -n, v ShiftAfter(v, +n)
e u→v (j) + n, e u→v (j) + n, v For instance, for the CE (E2), we obtain: 1984-10, 1984-10 .

(2.3) If Ω is an operator of OpZoning we obtain for Ω(α): Before -∞, i -1, u After j + 1, +∞, u Until -∞, j, u . Since i, +∞, u . For instance, for the CE (E3) we obtain -∞, 1929-10 .

(3) Let us consider two FEs α and β with which two CIs i 1 , j 1 , u and i 2 , j 2 , v are associated. We take w, the largest unit smaller than u and v. To Between(α, β) we associate e u→w (j 1 ) + 1, b v→w (i 2 ) -1, w .

For instance, in order to represent (E4), we obtain: 2008-1-1, 2009-2-28

3 Filtering and Ranking Answers for Retrieval Purposes

The Issue

We assume that we have a set A = {A 1 , A 2 , . . . , A n } of CEs translated into CIs. The CE used in a query is also translated into a CI, called Q. The goal is to extract a relevant subset A(Q) = {A i1 , A i2 , . . . , A ip } from A and to order it from the most to the least relevant. To evaluate the relevance of CEs, we first consider an adequacy criterion, then, if necessary, an order criterion, in the event of equal adequacy.

Adequacy Criteria

We take into account four kinds of criteria, from the best to the worst. These criteria can be described in terms of Allen relations [START_REF] Allen | Maintaining Knowledge about Temporal Intervals[END_REF].

(1) Equality: if any A i is equal to Q, it is the best match of the query.

(2) Inclusion: if any A i is included in Q, it also matches the query. It corresponds to (4) In all other cases, there is no matching between Q and A i . Nevertheless we may keep some A i according to proximity criteria.

A i during Q or A i starts Q or A i finishes Q: for instance, if Q corresponds to

Scoring the Answers

We first have to order several answers which satisfy the Inclusion criterion. The greater the coincidence area is, the better the answer will be. To do this, we take into account the value of rl(A/Q) for an answer A to a query Q. For instance, A 1 corresponding to from February to November 1980 will be better than A 1 (see table 1). To order answers A contained in Q, we take into account rl(Q/A). For instance A 2 corresponding to from October 1979 to March 1981 is better than A 2 .

In the case of Overlapping, we take into account two factors: the part of A included in Q relative to Q and the part of A included in Q relative to A. These two factors lead us to define two types of quantities: the pertinence of an answer A relative to a query Q, written pert(A/Q), and the precision of an answer A relative to Q, written prec(A/Q):

pert(A/Q) = rl((A ∩ Q)/Q) prec(A/Q) = rl((A ∩ Q)/A)
These two types of values are not of equal importance however. We therefore introduce a new coefficient, α, lower than 1 in order to compute a score for an answer relative to a query:

score(A/Q) = prec(A/Q) + α pert(A/Q) 1 + α
Several series of experiments led us to take α = 0.4 but this value may be adjusted. Note that in the Equality case we have score(A/Q) = 1. In the Inclusion case we have a value depending only on rl(A, Q). In the Containing case we find a value depending only on rl(Q, A). And in the No matching case we find score(A/Q) = 0.

This score can then be applied to all cases. This allows us to compare answers satisfying distinct criteria, and it can happen that an answer satisfying the Overlapping criterion or the Containing criterion has a better score than an answer satisfying the Inclusion criterion.

Table 1 shows some scores found for the query in 1980. We can see that an infinite CI is a possible answer, and its score can be compared to scores of finite CIs. We can also see that an answer satisfying the Inclusion criteria such as A 1 can sometimes be assigned a lower score than an answer satisfying the Containing criterion such as A 2 , because its coincidence area with the query is too small.

Ordering the Answers

Let us define the pole of a CI. For i, ∞, u the pole is i, for -∞, j, u the pole is j. If i, j, u is obtained by a ZoomBegin, the pole is i. If it is obtained by a ZoomEnd, the pole is j. Otherwise the pole is i+j 2 . The distance of two CIs A and B having the same unit u is defined as being the absolute value of the difference between the poles: |pole(A) -pole(B)|.

If two answers have the same score, we order them according to their distance from the query. The distance allows us to keep some answers with the score of zero if their distance from the query is not too great.

We also use the distance for ordering answers to an infinite query. If Q is an infinite CI, we do not consider the score but only the precision. If two answers have the same precision, those having the smallest distance from the query are preferred. The process is illustrated in table 1. The answers are presented from the best to the worst. ε is the symbol introduced in 2.2, representing a number smaller than all other numbers.

Implementation

This Retrieval model is integrated in a Lucene 5 based Search Engine with a standard Keyword Analyzer, for French and English documents. The system can handle queries that combine keywords and calendar expressions, such as prohibition at the beginning of the 30s, Luther King around 1963 or constitution 18 th century 6 .

The processing chain annotates Calendar Expressions, computes Calendar Intervals, indexes the results and analyses queries during the retrieval process.

Calendar Expression annotation is performed thanks to the annotator described in [START_REF] Teissèdre | Resources for Calendar Expressions Semantic Tagging and temporal Navigation through Texts[END_REF]. It provides Functional Representations of CEs, as described in section 3.1 (for this task, the authors report a recall rate of 84.4% and a precision rate of 95.2% for French). The Calendar Intervals transducer module is fed with the annotator's output. It delivers Calendar Intervals as output. Once computed, Calendar Expressions are indexed along with the sentences in which they are embedded.

Documents in this context are seen as a set of sentences containing Calendar Expressions. The documents returned to a query are those that contain the best ranked sentences. Instead of the regular snippets provided by common search engines in the result list, the system displays the most relevant sentences for each document. The relevant extracts are sentences in order to ensure that the distance between the Calendar Expression and the keywords being searched is not too great. This is a provisional simplification of a complex linguistic problem, namely the scope of temporal adverbials, that is to say, how temporal adverbials are involved in discourse structuring and can thus contribute to the calendar anchoring of situations that are described in sentences following the one containing a temporal adverbial ( [START_REF] Van Raemdonck | Est-il pertinent de parler d'une classe d'adverbes de temps ? Actes de CLAC[END_REF], [START_REF] Draoulec | Time Travel in Text: Temporal Framing in Narratives and Non-narratives[END_REF], [START_REF] Charolles | Les adverbiaux en position préverbale : portée cadrative et organisation des discours[END_REF]).

The query processor we implemented analyses queries submitted by users and separates the set of keywords (the thematic query) from the calendar criterion. The calendar criterion of the query is then used by the temporal retrieval module to provide a ranked list of documents.

4 Related Work [START_REF] Alonso | On the Value of Temporal Information in Temporal Information Retrieval[END_REF] highlight the importance of temporal information in Information Retrieval and note the scarcity of work in this area. Our work aims to contribute to filling this gap by showing two main points: 1) how IR systems (e.g. search engines) can benefit from taking into account calendar information, embedded both in documents and in queries; 2) how this applicative area can benefit from taking into account the way language expresses reference to calendar time via what is named in theoretical linguistics "temporal adverbials" (e.g. "in 1998", "at the beginning of 1998", "since 1998", "two months before the end of 1998").

Let us consider point 1). As mentioned in [START_REF] Berberich | A Language Modeling Approach for Temporal Information Needs[END_REF], calendar information as it is encoded in an expression such as "in 1998" is frequent across many kinds of documents and can be extracted with relative ease. However, it is not so immediately clear how it should be integrated into a retrieval model. Indeed, we can observe that almost all the approaches are based only on the publication dates of documents. For example, both [START_REF] Li | Time-Based Language Models[END_REF] and [START_REF] Dakka | Answering General Time-Sensitive Queries[END_REF] propose language models that take into account the publication date of documents, in order to favor, for instance, the most recent documents. [START_REF] Jones | Temporal Profiles of Queries[END_REF] focus on constructing query-specific temporal profiles based on the publication date of relevant documents.

Among the very few approaches dealing with calendar information embedded in documents, we can first mention [START_REF] Jin | TISE: A Temporal Search Engine for Web Contents[END_REF], which developed a temporal search engine supporting a Web search on temporal information embedded in Web pages. Secondly, and the closest to our approach, we can mention [START_REF] Alonso | Clustering and Exploring Search Results using Timeline Constructions[END_REF] which proposes a search engine capturing calendar information in documents. Their goal is to build clusters of documents and then rank documents in each cluster according to the calendar information that the documents contain. Like the other experimentations mentioned, they do not provide a means to express queries containing a Calendar Expression. In this sense, expressiveness is limited.

Our approach differs from all these approaches mainly by the fact that we consider temporal adverbial units, called here Calendar Expressions. Regarding point 2), with the exception of the approach adopted in [START_REF] Schilder | From Temporal Expressions to Temporal Information: Semantic Tagging of News Messages[END_REF], none of the approaches conducted in NLP (see [START_REF] Pustejovsky | The Specification Language TimeML. The Language of Time[END_REF]) and IR consider this kind of textual unit as a temporal expression in itself. This is mainly because the issue of analysing temporal information in texts by a named-entities approach has influenced (and is still influencing) a lot of studies. In a named-entities approach, only strict calendar reference is considered and analysed, e.g. "1998" in the previous examples. This is what is named a "Temporal Expression" (or a "Date") in the most popular annotation schemata (TIMEX2 [START_REF] Ferro | TIDES 2005 Standard for the Annotation of Temporal Expressions[END_REF] and TIMEX3 [START_REF] Pustejovsky | TimeML: Robust Specification of Event and Temporal Expressions in Text[END_REF][START_REF] Pustejovsky | The Specification Language TimeML. The Language of Time[END_REF]). All the approaches cited above use this kind of approach to calendar information in texts.

For a retrieval purpose (such as developing a search engine for instance), we believe that our approach is more intuitive and can lead to better performance from a user's point of view concerning the semantic relations between calendar information as it is expressed in a query and in a collection of documents. Indeed, our approach makes it possible, in a unified formal manner, to exploit (as pursued for example in [START_REF] Alonso | Clustering and Exploring Search Results using Timeline Constructions[END_REF]), the multi granularity of calendar information (e.g. "on May, 25 1980", "in May 1980"), and also the semantics of units that appear in a calendar expression (e.g. "around/after/in May 1980"). Let us imagine a user who is searching for events that occurred "in May 1980". Our system will establish a relation between the query and possible answers such as "around May 1980" and "after May 1980" given in this order. None of the above-mentioned approaches can currently deal with this kind of scenario.

Conclusion

We have described the main theoretical principles of our approach and a processing chain based on these principles which identifies Calendar Expressions in French or English texts and parses them in order to build functional representations. These representations are then transformed into referential representations. The whole process provides a way to compute a distance between a temporal query and these expressions. We have presented a heuristic function which provides a means to score and order all the answers. We have shown that this approach is able to process queries which contain different levels of calendar granularity.

We are currently extending Calendar Expression modelling so that the system can cope with expressions that refer to several areas on the Calendar system, such as iterative expressions (e.g.: "every Monday in February 2011") or aggregates (e.g. :"April, 11, 12, 15 and 22, 2011").

Fig. 1 .

 1 Fig. 1. Querying Process

  January 1985 : 1985-1, 1985-1 10th of January 1985 : 1985-1-10, 1985-1-10 80s : 198 , 198

  For instance, for the CE (E1) given in the Introduction, we obtain 1930, 1933 or 1930-1, 1933-4 or 1930-1-1, 1933-4-20 .

  in 1980 and A 1 corresponds to from March to May 1980. (3) Partial matching: if Q is included in any A i , i.e. if Q occurs during A i or Q starts A i or Q finishes A i we say that A i contains Q (Containing criterion).For instance, if A 2 corresponds to from 1978 to 1982, A 1 is a better answer than A 2 to Q because all A 1 matches the query and not all A 2 . If A i overlaps Q or Q overlaps A i , we say that the Overlapping criterion holds: for instance, if A 3 corresponds to from November 1979 to May 1980. We do not consider that this kind of adequacy is better or worse than the Containing case.

Table 1 .

 1 Scores and distances for answers to two queries

	answers to the query in 1980	score	answers to the query
	A0 in 1980	1.	since 1980	prec distance
	A 1 from February to November 1980 0.952	since 1980	1.	0 year
	A1 from March to May 1980	0.785	year 1982	1.	2 years
	A 2 from October 1979 to March 1981 0.762	since 1983	1.	3 years
	A 1 on May 25, 1980	0.715	from 1983 to 1986	1.	4 years
	A3 from November 1979 to May 1980 0.629	since 1978	1 -ε 2 years
	A2 from 1978 to 1982	0.428	since 1975	1 -ε 5 years
	A 3 since January 1980	0.285	from 1979 to 1981	0.666 0 year
	A 3 since May 1980	0.190	until 1984	ε	4 years
	A 2 from July 1980 to June 2010	0.154	until 1975	0	5 years

x designates floor(x).

http://lucene.apache.org/

The system can be tested at the following address: http://client1.mondeca.com/TemporalQueryModule/?locale=en

Acknowledgments. This project is partially granted by Chronolines ANR project (ANR-10-CORD-010).


Paul Byrne
email: paul.byrne@univ-rennes1.fr

Jacques Miriel

Yves Lenat

Design and simulation of a heat pump for simultaneous heating and cooling using HFC or CO 2 as a working fluid

Keywords: design, simulation, heating, cooling, domestic hot water, HFC, R407C, CO 2

come

Design and simulation of a heat pump for simultaneous heating and cooling using HFC or CO2 as a working fluid

Paul Byrne, Jacques Miriel, Yves

NOMENCLATURE

Context and objectives

Nowadays, global warming being a major concern for the environment, researchers are focussing more and more on energy efficiency in buildings. In developed countries, commercial and residential buildings account for around 40% of national energy consumption and 25% of green house gas emissions. This is the sector in which energy savings can be the highest and building companies are proposing new environmentally-friendly constructions. Thermal performance of buildings is thus continuously improving. Moreover, comfort requirements demand more and more energy. Indeed, whilst domestic hot water (DHW) demands continue to increase, the demand for cooling is rising to compensate internal heat gains caused by more and more household electrical equipment. Also a better thermal envelope implies that new buildings need less energy for heating and more for cooling. Therefore thermal needs of new buildings are more balanced between heating and cooling over the year.

During winter, energy is demanded exclusively for space heating and DHW production. Between winter and summer, some buildings can demand simultaneously cooling in rooms facing south and heating in rooms facing north. During summer, energy is needed for DHW production and space cooling at the same time. An answer to a dual energy demand is the heat pump, since it has simultaneously a heating capacity at the condenser and a cooling capacity at the evaporator.

This study presents the reasoning behind the design of a heat pump that can satisfy fluctuating needs, simultaneous or not, in heating and cooling. This heat pump is named HPS (Heat Pump for Simultaneous heating and cooling) and can be installed in hotels where DHW demands are high and glass fronted buildings where simultaneous needs in space heating and space cooling are more frequent. The first objective is to produce, as much as possible, heat and cold using the same energy input at the compressor.

The second objective is to limit the performance loss of air-source heat pumps during winter due to low air temperatures and frosting [START_REF] Liu | Frosting of heat pump with recovery facility[END_REF].

The design depends on the working fluid. The refrigerants used in new heat pumps are HFCs and natural fluids. HFCs provide good performances, but these fluids are classified by the Kyoto Protocol (1997) in the category of green house gases. That is why they are likely to be banned in the future. As far as mobile air conditioning is concerned, European Directives already plan the phase-out of refrigerants having a 100-year GWP (Global Warming Potential) over 150 kg CO2 by 2011. Among natural fluids (GWP ≤ 1 kg CO2 over 100 years) carbon dioxide (CO 2 , R744) seems one of the most adapted to residential applications or offices because it fulfils the requirements of low toxicity and low flammability.

According to [START_REF] Lorentzen | Revival of carbon dioxide as a refrigerant[END_REF][START_REF] Lorentzen | The use of natural refrigerants: a complete solution to the CFC/HCFC predicament[END_REF], author of "Revival of carbon dioxide as a refrigerant", CO 2 is the most promising natural refrigerant as a substitute for HCFCs and HFCs. In Japan, CO 2 heat pump water heaters called "Ecocute" are now commonly used [START_REF] Kusakari | The spread situation and the future view of the CO 2 refrigerant heat pump water heater in Japan[END_REF]. According to [START_REF] Nekså | CO 2 heat pump systems[END_REF][START_REF] Nekså | CO 2 as refrigerant, a way to reduce greenhouse gas emissions[END_REF], carbon dioxide is a very promising fluid for space heating applications.

Faced with this context, we have built numerical models and run simulations with highly efficient compressors and heat exchangers models to evaluate the performance of a HPS and compared the results to those of a standard reversible heat pump. Also, the possibility of using carbon dioxide instead of a HFC has been examined. The comparisons have been led from technical and environmental points of view. The HFC chosen for the simulation study is R407C, a working fluid widely used in heat pumping technology.

Design of the HPS

Heat exchangers

The HPS (Fig. 1 and Fig. 2) has three main heat exchangers: a condenser (or a gas cooler for carbon dioxide) that heats a water tank for space heating; an evaporator that cools a second water tank for space cooling; and a balancing air coil that works either as a condenser in a cooling mode or an evaporator in a heating mode. The latter is a three-fluid heat exchanger working with air on one side and on the other side, refrigerant flowing through two separate networks of tubes for high and low pressure. A subcooling heat exchanger is added to the three heat exchanger configuration. It enables energy storage on the cold water loop when it is not used for cooling, mainly during winter. The amount of energy stored is used to run the water evaporator during a subsequent mode of operation. Most of the time during winter, working on water instead of air at evaporation lifts up the evaporating temperature as well as the low pressure and so, it improves the performance of the heat pump. Moreover this technique liberates the air coil for defrosting without stopping the heat production.

Operating modes

The operation of the HPS is based upon three main modes: a cooling mode using the water evaporator and the air heat exchanger as a condenser; a dual mode preparing simultaneously hot and cold water using the water heat exchangers (condenser and evaporator); and a heating mode using the water condenser, the subcooler for heat storage on the cold water loop and the air coil as an evaporator. Commutation of modes is managed by a programmable controller that opens or closes the appropriate on-off electronic valves.

HFC configuration

The HFC HPS (Fig. 1) is equipped with a standard plate condenser producing hot water for space heating. The controller does not adapt the condensing temperature to DHW preparation since the priority application of the HPS is space heating and because it would degrade too much the performance. Thus domestic hot water is prepared using an extra heat exchanger placed on the pipe between the outlet of the condenser and the hot water tank. Then an auxiliary heater brings the water to the appropriate temperature for domestic use. Graphs a1, a2 and a3 of Fig. 3 show the HFC HPS heat production processes on temperature -enthalpy charts. Each graph shows the temperature evolutions of the refrigerant (plain lines), of the hot or cold tank water (dotted lines) and the DHW (doubled and dotted lines) in the high pressure heat exchangers. Enthalpy is only linked to the refrigerant state at inlets and outlets of heat exchangers. Heat exchangers being counter-flow, the water inlet (respectively outlet) corresponds to the refrigerant outlet (resp. inlet). On the chart, the inlet (or outlet) point for water corresponds to the water temperature and to the refrigerant enthalpy at that point of the heat exchanger. For HFC charts, DHW is not produced by the condensers. DHW temperature evolutions are represented under the outlet of the condenser. In all modes, condensation energy is used to heat the hot water tank. The DHW is first preheated through an exchanger by the hot water for space heating and then reheated by an auxiliary heater. The cold water tank is heated using the subcooling energy of the refrigerant in the heating mode (graph a1). The cooling mode is standard. It uses the water evaporator and the air coil as a condenser.

CO 2 configuration

The main difference between the HFC and CO 2 machines resides in the heat exchangers technology so that it can withstand operating pressures above 100 bar. The CO 2 HPS (Fig. 2) uses the transcritical cycle of carbon dioxide in which heat rejection occurs at a pressure above the critical point. The water condenser in the HFC configuration corresponds to a gas cooler in the CO 2 configuration. The most efficient CO 2 heat exchangers are made up of microchannels. They can handle high pressures and provide higher heat transfer coefficients [START_REF] Zhao | Microchannel heat exchangers with carbon dioxide[END_REF]. The gas cooler is divided into three sections. The top section is used for domestic hot water preparation at 55-60°C. The middle section is dedicated to the production of hot water for space heating at temperatures between 25 and 45°C. Finally, the lower section is connected to the cold water tank for energy storage during winter. [START_REF] Stene | Residential CO 2 heat pump system for combined space heating and hot water heating[END_REF] proposes to use the lower part of the gas cooler (at the lower temperature) to preheat DHW, the middle part to heat water for space heating and the upper part to reheat DHW. This could not be done simply with the CO 2 HPS since the energy storage on the cold loop, by subcooling of the refrigerant, is a key feature of the machine.

Graphs b1, b2 and b3 of Fig. 3 show the heat production processes of the CO 2 HPS. The DHW is heated using the top section of the gas cooler in which the temperatures are the highest. During summer in the dual mode, this section of the gas cooler is the only one used (graph b3). The middle section is dedicated to space heating in the heating mode and the winter dual mode (graphs b1 and b2). The cold water tank is heated using the subcooling energy of the refrigerant in the heating mode (graph b1).

The transcritical cycle of CO 2 provides a high temperature at the gas cooler inlet and a continuous temperature glide along the gas cooler, which enables the production of hot water for domestic use as required for the HPS. For this reason, even if it provides poorer performance than standard cycles with HFCs, the CO 2 transcritical cycle seems to suit the residential and office applications selected for the HPS. Also, the defrosting technique benefits from the high amount of energy recoverable by subcooling (about 30% of the total energy available at heat rejection).

Cooling and dual mode during summer

During summer, the dominant mode is the cooling mode. When there are needs for DHW, the dual mode is run until the demand is satisfied. The HPS then switches back to the cooling mode.

All modes during in-between seasons

Between summers and winters, the heating and cooling needs are lower and fluctuating. The HPS produces hot and cold water mainly in the dual mode to be able to provide energy for any demand.

Alternated sequence during winter period

During winter, the HPS alternates between heating mode and dual mode in order to use to a maximum the water evaporator instead of the air evaporator. In the heating mode, the subcooling of the refrigerant is used to heat the cold tank. The cold tank temperature increases from 5 to 15°C. The HPS then changes mode and operates in the dual mode. The controller stops the fan of the air evaporator and switches the on-off electronic valves in order to use the water evaporator instead of the air evaporator. The subcooler is bypassed by changing the position of the three-way valve and becomes inactive. The cold tank being the cold source for the water evaporator, its temperature decreases from 15 to 5°C. Then the controller switches the HPS back to the heating mode and a new sequence starts again. This alternated sequence enables a continuous production of heat for space heating using, during part of the time, a cold source at a temperature higher than that of a standard heat pump. Using this alternated sequence, the average performance can be improved during winter.

Defrosting technique

Defrosting is carried out during the second part of the alternated winter sequence. In the heating mode, under cold outside air temperatures, the fins of the air evaporator get frosted. Before the frost thickness becomes critical, the cold tank temperature has raised 15°C and the dual mode has been engaged. In the dual mode, the air coil is automatically defrosted. After flowing through the water condenser, the refrigerant enters the three-fluid heat exchanger at a temperature around 30°C and is subcooled by heat exchange with the frosted fins. At the same time, a thermosiphon forms between the two evaporators. Part of the vapour coming out of the water evaporator migrates towards the air evaporator where the temperature, and thus the pressure, is lower. The gas exchanges heat with the frosted fins and condenses. Finally, it flows back to the water evaporator by gravity. The sequence finishes in the dual mode until the cold tank temperature decreases back to 5°C.

A major advantage of this operating sequence is to carry out defrosting without stopping or even degrading the heat production. Frost thickness can thus be minimized and mean convection heat transfer coefficients at the evaporator can be maximized [START_REF] Xia | defrost, and refrost and its impact on the air-side thermal-hydraulic performance of louvered-fin, flat-tube heat exchangers[END_REF]. The average efficiency in heating is improved compared to the performance of heat pumps that use hot gas or reversed cycle defrosting methods.

High pressure control

As pressures and temperatures are linked during condensation, high pressure control ensures that condensation occurs in the appropriate condenser. Moreover it is able to control the condensation temperature and thus the heating capacity. A special liquid receiver is placed on the liquid line. It is connected to the compressor discharge line and the inlet of the air evaporator by pipes of smaller diameter on which electronic on-off valves are located (Evr1 and Evr2 on Fig. 1 and Fig. 2).

The high pressure control system indirectly controls the volume of liquid in the receiver. The volume of liquid in the different condensers depends on the mode. If the chosen mode is the heating mode, condensation occurs in the water condenser. The controller calculates the set point for high pressure so that condensation is completed in the condenser. The receiver is filled up with gas coming from the compressor discharge line at a pressure higher than the pressure in the receiver until the calculated pressure is reached. The gas entering the receiver drives the liquid towards the air condenser, the subcooling heat exchanger and the bottom part of the water condenser. If however the chosen mode is the cooling mode, the condenser becomes the air heat exchanger. The set point for pressure is then the lowest possible. The pressure is reduced by driving the gas out of the receiver towards the inlet of the air evaporator. The refrigerant in a liquid phase is sucked out of the water condenser and the subcooler and enters the receiver.

This system is essential to ensure that the air coil and the subcooling heat exchanger are full of liquid and that the condensation is completed in the water condenser during a heating or a dual mode. Otherwise part of the refrigerant could condense in the subcooling heat exchanger and all the energy available from the condensation would not be transferred to the hot water tank for space heating.

The proper operation of the control system depends upon a special liquid receiver being designed quite high and quite narrow with the main objective to enhance temperature stratification and to limit as far as possible thermal transfer between the gas and the liquid. When the gas is injected, part of it condenses. When gas is rejected to the low pressure, part of the liquid evaporates. Although these phenomena can reduce the efficiency of the liquid variation in the receiver, it can stabilize the control system. The receiver is also thermally insulated to reduce the heat transfer with the ambience.

Numerical model

Simulation Tools

The numerical approach is carried out in four steps. A first simulation using TRNSYS software is run to obtain the heating, cooling and DHW demands of a standard hotel of 45 bedrooms. In parallel, the steady state performance in heating and cooling is calculated for each mode (heating, cooling and dual modes). The simulation tool used for this calculation is also TRNSYS. Every component of the machine is programmed as a model in FORTRAN and the refrigeration cycle is modelled as the connection of the different components using the input and output variables. The heating sequence alternating heating and dual mode is then studied. Operating times for each mode were calculated during a frosting -defrosting sequence. The last step consists in coupling the demands with the heating and cooling capacities of the heat pump depending on the outside air temperature. This simulation enables to calculate the daily operating times of each working mode and the average daily and annual performance.

Building model

A hotel of 45 bedrooms was modelled. High domestic hot water consumption, thermal zones, wall materials, glazed surfaces, solar protections and ventilation, occupancy and lighting schedules were defined using the building module of TRNSYS so as to calculate the hotel's daily needs in heating and cooling. This simulation was run using the annual weather data file of Paris.

Heat pump models

Four models corresponding to four operating modes (heating mode, cooling mode and dual mode with and without defrosting) were defined to calculate the steady state heating and cooling capacities and coefficients of performance. Pressure drops and heat losses to the environment are assumed negligible and compressors are modelled using high efficiency factors.

Each mode establishes the performance of the cycle for ambient temperatures varying from -15 to 15°C in heating and from 25 to 40°C in cooling. The cold water is cooled from 10 to 5°C. The set point for space heating water temperature follows a heating curve depending on ambient temperature (Fig. 4).

Because of the heating curve, the system performance is always linked to the ambient air temperature, even in the dual mode.

Heat exchanger models

The HFC heat exchangers models use the Log Mean Temperature Difference (LMTD) method. The heat transfer coefficients and the steady state capacities are calculated using the geometrical characteristics of existing heat exchangers (Table 1), the McAdams correlations described in the ASHRAE Handbook Fundamentals (1989) for sensible heat transfers and condensation and the Tran et al.

(1996) correlation for boiling heat transfer in the evaporator. The heating and cooling capacities are deduced from the heat transfer coefficients.

The Number of Transfer Units (NTU) and the LMTD calculation methods are used respectively in the CO 2 gas cooler and evaporator. The correlations used to calculate the heat transfer coefficients for carbon dioxide are the Gnielinski correlation [START_REF] Sarkar | Simulation of a transcritical CO 2 heat pump cycle for simultaneous cooling and heating applications[END_REF] in the gas cooler and the Bennet-Chen correlation in which the nucleate boiling coefficient has been modified by Hwang et al. for carbon dioxide in the evaporator (Haberschill et al., 2007). To calculate heat transfer coefficients for water and CO 2 sensible heat transfer, the McAdams correlations are used (ASHRAE, 1989). As flow boiling for CO 2 is still an issue, another heat transfer correlation, the Wattelet-Carlo correlation [START_REF] Sarkar | Simulation of a transcritical CO 2 heat pump cycle for simultaneous cooling and heating applications[END_REF] has been tested and showed a negligible variation in the temperature chart (Fig. 5) and the cooling capacity (less than 10% difference).

Condensers and evaporators are divided into zones. Each zone is related to a fraction of the total surface of the exchanger. HFC and CO 2 evaporators have a two-phase zone for evaporation and a singlephase zone for superheating. The HFC condenser has a single-phase zone for desuperheating, a two-phase zone for condensation and another single-phase zone for subcooling. The CO 2 gas cooler and evaporator are divided into 50 sections to take into account the dramatic variations of thermodynamic properties in supercritical conditions. Fig. 6 shows the influence of the number of sections on the simulated temperature evolutions along a CO 2 evaporator. The temperatures calculated for a 50-section evaporator are near to the temperatures of a 75-section one while significantly diminishing the calculation time.

For all heat exchangers, iterative calculation progresses from section to section from one end of the exchanger to the other. Fig. 7 shows an example of the calculation strategy for an evaporator. In the beginning, on each section or zone, outlet temperatures are set at the inlet values. Then, the calculations use the inlet and outlet temperatures and the structural parameters of the heat exchanger (hydraulic diameter, plate thickness…) to determine the heat transfer coefficients, the new outlet temperatures, the heating and cooling capacities. The outlet variables of a zone are the inlet variables of the next zone.

Once the calculation has reached the last zone, it starts again in the other way to the first zone. The whole calculation is iterated until the outlet temperatures of the refrigerant and the other fluid (water or air) have converged for the entire heat exchanger.

Compressor model

The compressor model calculates the mass flow rate and the compression work knowing the input and output pressures (Eq. ( 1) to ( 4)) and using the Refprop database ( 2002). The volumetric efficiency (Eq.

(1)) is calculated using a constant polytropic exponent of 1.076 for R407C. This value of the polytropic exponent has been calculated using experimental results carried out in our laboratory on a Copeland ZB38KCE scroll compressor. A brief sensitivity analysis showed that a variation of ± 0.1 of the polytropic exponent value would provoke a variation of the heating COP inferior to 1.4% on a range of pressure ratios from 1.5 to 5. For CO 2 , the volumetric efficiency is obtained by a polynomial correlation estimated by [START_REF] Sarkar | Simulation of a transcritical CO 2 heat pump cycle for simultaneous cooling and heating applications[END_REF] from experimental results presented by [START_REF] Ortiz | Evaluation of the performance potential of CO2 as a refrigerant in airto-air air conditioners and heat pumps: system modelling and analysis[END_REF]. The output pressure is assumed to be calculated by the high pressure control system in accordance with the hot water inlet temperature. For carbon dioxide transcritical cycles, there exists an optimal high pressure that gives a maximum COP [START_REF] Lorentzen | Revival of carbon dioxide as a refrigerant[END_REF]. The high pressure is given by a correlation from [START_REF] Liao | A correlation of optimal pressures in transcritical carbon dioxide cycles[END_REF].

The isentropic efficiency of the CO 2 compressor is based on the correlation of [START_REF] Brown | Comparative analysis of an automotive air conditioning system operating with CO 2 and R134a[END_REF] who curve-fitted the results presented by [START_REF] Rieberer | CO 2 heat pumps in controlled ventilation systems[END_REF]. The isentropic efficiency for R407C is calculated using a correlation based on curve-fitted results of experiments carried out in our laboratory on the Copeland ZB38KCE compressor (Fig. 8). Isentropic efficiency is higher for CO 2 because of the lower compression ratio. For the R407C model, the relative clearance volume is set to 2%. Mechanical and electrical efficiencies are respectively 0.8 and 0.95. These values are deliberately high in order to simulate highly efficient compressors. Finally, the discharge temperature is calculated thanks to the Refprop database (2002) for the outlet values of enthalpy (Eq. ( 5)) and high pressure.

        -       ⋅ - = 1 1 1 n vol LP HP c η (1) s vol V m ⋅ ⋅ = η ρ & (2) ( ) i ideal o carnot h h m W - ⋅ = - & & (3) el mec is carnot W W η η η ⋅ ⋅ = & & (4) is i ideal o i o h h h h η - + = - (5)

Frosting -defrosting model

Once the capacities are calculated, the frost mass variations on the air coil and the temperature variations of the cold tank are calculated using Eq. ( 6) to (9). The frost layer is assumed to be very thin and continuous so that it does not affect the cooling capacity. This implies that the cold tank water temperature varies rather quickly. The frosting-defrosting sequence lasts around 20 minutes. This rather short time of sequence ensures a low frosting level. x L (= 0.25) is the estimated percentage of the cooling capacity used by frost formation in latent heat transfer. η df (= 0.5) is the estimated efficiency of the defrosting system. This means that 50% of the cooling capacity is used to carry out defrosting. The frosting -defrosting sequence is modelled using a time step of 0.5 second. Fig. 9 shows the little influence (less than 5.4%) of parameters x L , η df and the time step value dt on the relative difference between the dual mode time ratios (Eq. ( 10) and ( 11)) of R407C and CO 2 . The coupling of the parameters has also been investigated and does not affect further the ratio difference. The difference in the overall operation of the HFC and CO 2 heat pumps will only be very slightly affected by a variation of these parameters.

Frost mass variation during frosting:

S L c f L x Q dt dm . & = (6)
Frost mass variation during defrosting:

F df c f L Q dt dm η . & - = (7)
Cold tank temperature increase:

w w sc cs Cp m Q dt dT . & = (8)
Cold tank temperature decrease:

w w c cs Cp m Q dt dT . & = (9)
Time ratios were calculated in order to take into account the alternation of the two modes with and without frosting (Eq. ( 10) and ( 11)). These ratios are used in the coupling of the HPS with the building. A third time ratio was calculated to estimate the time of frosting conditions during each day of the year (Eq. ( 12)). It is assumed that frost appears when the ambient temperature is below 6°C. This assumption depends on the ambient air conditions. The value of this threshold is negligible for our comparison. It is a matter of component design.

Operating strategy

The coupling of the HPS with the building is a simulation based on daily energy balances. For each day of the year, the heating and cooling demands and the heating and cooling capacities in each mode are confronted. The operating times per mode are obtained by dividing demands by capacities. The demands can be satisfied under several modes. The HPS starts to work in the dual mode as this mode is the most efficient. Then it continues in the heating or the cooling mode depending on the remaining thermal demands. Domestic hot water production is not simulated in the same way for the HFC and CO 2 heat pumps.

For the HFC heat pump, DHW production is carried out by the heat pump up to 40°C and then by an electric auxiliary heater from 40 to 55°C. For CO 2 , all the DHW demand is satisfied by the heat pump thanks to the progressive temperature decrease in the gas cooler.

The times of operation in each mode are calculated following the operating strategy. Dual mode is run first, until the minimum between heating and cooling demands are satisfied (Eq. ( 13)). The second part of the equation corresponds to the alternation between dual and heating mode during a heating period.

(

)

[ ]                       ⋅ - × - + +         = - °< - °< hDM cDM c hDM h hDM h nof DM C T f DM C T cDM c hDM h DM Q Q q Q q Q q r r r r Q q Q q t , min . 1 . , min 6 6 (13)
where q h is the daily demand in heating, q c , the daily demand in cooling and hDM Q & , the heating capacity in dual mode.

In heating mode, the operating time is the time needed to cover all the heating needs minus the dual mode time.

( ) ( ) [ ]                       ⋅ - × - + - = - °< - °< hHM cDM c hDM h hDM h nof DM C T f DM C T HM Q Q q Q q Q q r r r r t & & & & , min . 1 . 1 6 6 (14)
where HM stands for heating mode.

In cooling mode, the operating time is the time needed to cover all the cooling needs minus the time needed for cooling in the dual mode.

cCM cDM c hDM h cDM c CM Q Q q Q q Q q t &
sequence, the cooling energy is not taken into account because it is not used for space cooling. If the heating and cooling capacities are useful in a dual mode, the first law coefficient of performance is given by the sum of heating and cooling COPs. The daily and annual coefficients of performance are calculated in proportion to the operating times per mode.

The Carnot COPs have also been calculated on each time step. The Carnot COPs in heating, dual and cooling modes are expressed in terms of temperatures of sources by the combination of first and second laws of thermodynamics and by imposing a zero entropy generation in the second law. The annual Carnot COP is calculated in proportion to the operating times obtained by the calculation using the first law COP.

Second law (exergy) efficiency is calculated using equations presented by Sarkar et al. (2004) as the ratio of the net exergy output to the work input to the compressor. Exergy outputs are calculated for the useful heat exchangers.

Electricity consumptions are deduced from the daily calculations. They include the consumption of an eventual auxiliary heater for DHW production. The consumptions of other auxiliaries like fans, pumps or control equipment are not taken into account.

Hypotheses for standard heat pumps

The calculations were also carried out for standard reversible HFC and CO 2 heat pumps that have the same heating and cooling capacities as the HFC and CO 2 HPSs: the standard heat pump models have the same steady state performances depending on the temperature than the ones calculated for the HPS.

During summer, the standard heat pumps are supposed to be in a cooling mode and so, not to be able to produce domestic hot water. All the heat needed for this purpose is then provided by the electric heater.

The defrosting sequence is supposed to last the same time for both machines. This means that the dual mode time of the HPS equals the defrosting time of the standard heat pump. At first this assumption seems penalizing for the standard heat pump but it gives actually a fair estimation of the performance loss during defrosting. The standard heat pump is supposed to use a reversed cycle defrosting method. So there is a loss of performance due to two contributions: the shutdown of heat production and the drawing on the stock for space heating for the evaporation of the reversed cycle. The electricity consumption of a standard heat pump in a heating mode is given by Eq. ( 16).

( )

HM h f DM C T HP standard COP q r r C ⋅ ⋅ + = - °<6 1 (16)

Results and discussion

Building simulation

The annual simulation of the hotel shows the variation of daily heating and cooling demands all year round (Fig. 10). Annual needs amount to 25 322 kWh for DHW production, 68 640 kWh for space heating and 30 146 kWh for space cooling. A heat pump of 50 kW heating capacity is installed in the building to satisfy these needs.

It can also be pointed out that during spring and autumn heating and cooling demands appear during the same days. During summer the plateau in the heating curve corresponds to the domestic hot water demand and is quite constant. From the end of April to the end of October a significant part of the total heating and cooling needs can be satisfied by a simultaneous production.

Steady state performance

Fig. 11 shows the first law COPs, the Carnot COPs and the second law efficiencies calculated in steady state simulations in the heating mode for lower air temperatures, in the cooling mode for higher air temperatures and in the dual mode for an average temperature of 20°C. The heating mode is less efficient for CO 2 than for R407C from 18% at -15°C to 43% at 15°C. The CO 2 cooling mode is 28% less efficient at 40°C but 7% more efficient at 25°C. The dual mode is 22% less efficient in terms of a COP integrating heating and cooling energies at an ambient temperature of 20°C. The dual mode is also used at other ambient temperatures. Additional calculations showed a heating and cooling integrated first law coefficient of performance decrease of between 43% at -15°C and 15% at 15°C. These results are based only on the thermodynamic cycles. CO 2 is clearly less efficient in terms of first law COP than R407C when used in classic space heating or cooling applications. The standard heat pump models also use these first law COPs in the coupling with the building. The Carnot COPs are based on temperatures of sources.

The difference between HFC or CO 2 COPs and Carnot COPs represent the degree of irreversibility within each cycle. It seems clear that the carbon dioxide transcritical cycle introduces more irreversibilities than the standard HFC refrigeration cycle.

The second law efficiency curves are linked to output energies and mean source temperatures. CO 2 values are between 25.8% and 12.0% in heating and 24.4% and 28.3% in cooling. R407C values are between 38.1% and 30.8% in heating and 25.9% and 34% in cooling. Globally carbon dioxide second law efficiency shows a little less dependency to temperature than R407C. At 25°C in cooling mode, first law COP and second law efficiency are higher for CO 2 than for R407C. This tendency is in accordance with some results published by [START_REF] Kim | Fundamental process and system design issues in CO 2 vapour compression systems[END_REF]. In dual mode, CO 2 is nearly as efficient as R407C in terns of exergy (42.0% for CO 2 and 45.3% for R407C).

Frosting -defrosting model

Time ratios were calculated according to Eq. ( 9) and (10) (Table 3) and proved different with and without frosting because they depend on the cooling capacity. The dual mode time ratio is quite near 15% for both fluids when there is frosting conditions. The defrosting acts upon the refrigerant like a subcooling. Therefore, there is an additional capacity at heat rejection that is compensated by an additional cooling capacity at the evaporator. Nevertheless the carbon dioxide HPS works longer under the dual mode than the R407C HPS, especially when there is no frosting: 0.166 for R407C against 0.221 for CO 2 . This can be explained by the higher amount of energy recoverable by subcooling. This characteristic shortens the time of temperature rise between 5 and 15°C in the cold tank during the heating mode. Therefore the dual mode time takes a greater part of the sequence. The coefficients of performance are higher when operating on a dual mode because of the higher temperature source at the evaporator. A higher COP during a longer time in dual mode increases the average COP. The CO 2 HPS takes more benefit from the alternated sequence than the HFC HPS.

Annual performance

Table 4 presents first law COPs, Carnot COPs and second law efficiencies for R407C and carbon dioxide. The first law COP corresponds to the ratio of overall useful thermal energy to used energy. As expected, CO 2 has a lower first law COP than R407C. However, the HPS annual first law COPs are 3.57 for R407C and 3.26 for carbon dioxide which corresponds to a 8.7% reduction whereas the steady state performance calculations led to an average larger difference. This means that, considering the whole system operation and not only the steady state COPs, the decrease in performance between R407C and CO 2 becomes lower because of the higher subcooling energy. This conclusion is confirmed by the Carnot COPs that depend only on the times of operation in the different modes and by the operating strategy concerning alternated winter sequences between heating and dual modes and DHW production. Globally, Carnot COP is higher for CO 2 than HFC because of the enhanced use of the dual mode. The annual Carnot COPs are 11.06 for R407C and 12.10 for CO 2 . Second law efficiencies also follow this tendency.

Using carbon dioxide, the dual mode operates during a longer time than with a HFC when running the winter alternated sequences and producing DHW during summer.

When compared to a standard heat pump, the R407C HPS proved more efficient in terms of first law COP and second law efficiency. However the annual Carnot COP is lower because of the lower source temperature in a dual mode than in a heating mode with an ambient temperature higher than 10°C, which occurs rather often under the climatic conditions of Paris. The CO 2 HPS shows an improvement in first law COP, Carnot COP and second law efficiency compared to a standard heat pump thanks to the enhanced operation in the dual mode.

Electricity consumptions

The electricity consumptions of the HPS and of a standard reversible heat pump using HFC or CO 2 are detailed on Table 5. Because of the type of climate of Paris, colder during winter than hot during summer as far as thermal demands are concerned, each system consumes more electricity in the heating mode than in the cooling mode. Comparing heat pumps to HPSs, it can be observed that the use of the dual mode, producing simultaneously hot and cold water, diminishes the electricity consumptions of the heat pumps in heating and cooling modes and of the auxiliary heater. During winter, part of the heating demand is satisfied with COPs improved by alternating heating and dual modes. During spring and autumn, depending on the major thermal demand, "free" cooling or "free" heating is performed in the dual mode. The auxiliary heater consumption is also lower for the HPS because during summer, the DHW is partly (or completely for CO 2 ) produced in a dual mode while for the standard heat pump, switched in a cooling mode for the hot season, it is entirely produced by the electric heater. Therefore electricity consumptions in heating, cooling and dual modes of the HPSs are lower than that of the heat pumps in heating and cooling modes. The HPS working with R407C consumes 16.6% less electricity than a standard heat pump. With carbon dioxide, the improvement reaches 27.4% thanks to the direct DHW production and to the favourable winter alternated sequence. The electricity consumption of the CO 2 HPS is lower than that of the HFC standard heat pump. The replacement of a standard heat pump by a HPS leads to a higher increase in performance with carbon dioxide than with a HFC.

TEWI calculations

The Total Equivalent Warming Impact (TEWI) is calculated for the four heat pump systems (Table 6) using the greenhouse gas emission ratio of electricity production of France (0.13 kg CO2 /kWh). The refrigerant charge of the HPS is higher than that of a standard heat pump because of the implementation of a variable volume receiver, a secondary condenser and a subcooler at high pressure. A R407C HPS prototype having a heating capacity of 15 kW is currently under testing. Its refrigerant charge amounts to 9 kg whereas the conventional charge ratio would be around 0.2 kg per kW in heating. The refrigerant charge of the 50 kW R407C and CO 2 HPSs and standard heat pumps is respectively 18 kg and 6 kg. For a life time of 20 years, a leakage rate of 3% per year and a recovery rate of 75%, the TEWI is lower for the HPSs than for the standard heat pumps even if the refrigerant charge is increased. The savings in energy consumption have a much more significant impact than the increase of the refrigerant charge. The carbon dioxide HPS has the lowest TEWI with 95 359 kg of CO 2 . There is a relative environmental benefit to use carbon dioxide instead of R407C as a working fluid for this concept of HPS with a saving of around 4 000 kg of CO 2 , which represents 4% of the total equivalent warming impact.

Conclusion

A Heat Pump for Simultaneous heating and cooling has been designed in the aim of heating and cooling luxury dwellings, hotels and smaller office buildings and also producing domestic hot water.

Running costs and greenhouse gas emissions can be diminished by using the same electric energy to produce hot and cold water simultaneously. This machine also proposes an answer to reduce the performance loss of air-to-water heat pumps under low ambient temperatures and especially during defrosting sequences by alternation between an air evaporator and a water evaporator.

The HPS has been designed for HFCs and CO 2 . The results are obtained for highly efficient compressors and perfect heat exchangers and are closely linked to these assumptions. Today, HFCs are the most efficient and "secure" fluids on the market but they are greenhouse gases. Carbon dioxide is environmentally friendly but it is less efficient and its technology needs more development to be really competitive in space heating applications [START_REF] Kim | Fundamental process and system design issues in CO 2 vapour compression systems[END_REF]. Nevertheless its thermodynamic properties enable domestic hot water production. The alternated winter sequence offers a new solution for defrosting. Especially, it increases the average performance in heating, and increases further with a high subcooling capacity available with CO 2 . The CO 2 HPS outperforms the HFC standard heat pump in terms of first law COP and annual electricity consumption and this opens the door to carbon dioxide as a working fluid for space heating applications. The properties of the carbon dioxide transcritical cycle enhance the operation of the HPS in the dual mode as shown through the Carnot COP and second law efficiency annual values.

TEWI calculations conclude to a reduction of green house gas emissions by the use of carbon dioxide instead of R407C as a working fluid for this concept of HPS. Also, the environmental analysis could be extended to the life cycle cost (LCC) which could advantage more carbon dioxide because of the difference between the synthesis of R407C and the capture of CO 2 and because of smaller (thus probably cheaper in terms of CO 2 emissions) components for CO 2 .

In conclusion, transcritical CO 2 technology is improving day after day and offers a slightly lower impact on global warming. However, HFC heat pumps for space heating and cooling still remain more efficient and less costly in terms of energy consumption.

Fig. 3 -

 3 Fig. a1

Table 3 -Time ratios of the dual mode with and without frosting during winter alternated sequences

 3

	Time ratio	R407C	CO 2
	r DM-nof	0.166	0.221
	r DM-f	0.145	0.165

Table 4 -Annual first law COP, Carnot COP and second law efficiency of a HPS and a reversible heat pump working with R407C or carbon dioxide

 4

	System	Refrigerant	First law COP	Carnot COP	Second law efficiency
	HPS	R407C	3.57	11.06	26.40%
		CO 2	3.26	12.10	27.48%
	Standard	R407C	3.06	11.49	23.78%
	heat pump	CO 2	2.70	10.95	18.38%

Table 5 -Electricity consumption (kWh) in different modes, for a HPS and a reversible heat pump, and for R407C and carbon dioxide

 5

	Fluid		HFC		CO 2
	System	HPS	standard heat pump	HPS	standard heat pump
	cooling mode	5 031	5 946	4 593	5 604
	heating mode	16 750	21 573	26 343	36 634
	dual mode	3 959	0	5 739	0
	auxiliary heater for DHW	9 536	14 753	0	8 248
	total	35 275	42 272	36 675	50 487

& & & & &

& & &

where CM stands for cooling mode.

Performance evaluation and electricity consumptions calculations

Three performance factors are used: the first law COP, the Carnot COP and the second law efficiency.

The corresponding equations are reported in table 2.

The first law coefficients of performance are defined as the useful energies provided at the water heat exchangers divided by the electricity consumption of the compressor. During a heating mode, the heating energy provided at the water condenser is the only considered. During a cooling mode, the cooling energy provided at the water evaporator is the only considered. During the dual mode of an alternated winter