Céline Craye

David Filliat

Jean-Franc ¸ois Goudou

RL-IAC: An Exploration Policy for Online Saliency Learning on an Autonomous Mobile Robot

In the context of visual object search and localization, saliency maps provide an efficient way to find object candidates in images. Unlike most approaches, we propose a way to learn saliency maps directly on a robot, by exploring the environment, discovering salient objects using geometric cues, and learning their visual aspects. More importantly, we provide an autonomous exploration strategy able to drive the robot for the task of learning saliency. For that, we describe the Reinforcement Learning-Intelligent Adaptive Curiosity algorithm (RL-IAC), a mechanism based on IAC (Intelligent Adaptive Curiosity) able to guide the robot through areas of the space where learning progress is high, while minimizing the time spent to move in its environment without learning. We demonstrate first that our saliency approach is an efficient tool to generate relevant object boxes proposal in the input image and significantly outperforms the state-of-the-art EdgeBoxes algorithm. Second, we show that RL-IAC can drastically decrease the required time for learning saliency compared to random exploration.

I. INTRODUCTION

Object localization has received a lot of attention in the recent years. Today, deep learning-based methods [START_REF] Shaoqing Ren | Faster rcnn: Towards real-time object detection with region proposal networks[END_REF] provide efficient ways to localize and identify a large set of objects in a wide variety of complex environments, but, they generally require hours or days of offline training, high GPU resources, thousand to millions of training images, and are not really flexible to novelty. On the other hand, domestic mobile robots are meant to evolve essentially in indoor environments, interacting with a limited amount of objects, for specific tasks and thus do not require such wide scope capacity. Moreover, they should be able to adapt to novelty by quickly updating the representation of their environment, while dealing with limited computational resources. Lastly, the displacement of the robot makes it possible to move to favorable observation conditions in order to improve recognition performances. In that regard, providing the robot a way to explore, actively learn and update online its representation and knowledge is a very desirable property.

Visual analysis of the environment by mobile robots is generally associated with a way to localize areas of interest on which the robot should focus on. This localization mechanism is typically driven by visual saliency maps [START_REF] Frintrop | VOCUS: A visual attention system for object detection and goal-directed search[END_REF], [START_REF] Meger | Curious george: An attentive semantic robot[END_REF] or, if depth information is available, geometrical segmentation [START_REF] Ali | Contextual object category recognition for rgb-d scene labeling[END_REF], [START_REF] Caron | Neural network fusion of color, depth and location for object instance recognition on a mobile robot[END_REF]. In the first case, bottom-up saliency maps [START_REF] Itti | model of saliencybased visual attention for rapid scene analysis[END_REF], [START_REF] Zhang | Saliency detection: a boolean map approach[END_REF] highlight stimuli in the input image that are intrinsically salient in their context. However, interesting elements are 1 U2IS, ENSTA ParisTech, Inria FLOWERS team, Université Paris-Saclay, 828 bd des Maréchaux, 91762 Palaiseau cedex France celine.craye@ensta-paritech.fr 2 Thales -SIX -Theresis -Vision & Sensing 1, avenue Augustin Fresnel, 91767 Palaiseau, France celine.craye@thalesgroup.com not always intrinsically salient, some approaches suggest to add a top-down modulation to further enhance elements related to a given task [START_REF] Frintrop | VOCUS: A visual attention system for object detection and goal-directed search[END_REF]. In the second case, indoor object segmentation based on depth information usually rely on finding planar surfaces and objects lying on it. Those methods can accurately detect objects on tables or floor, but are limited by the sensor quality, the physical properties of the objects, or the geometrical constraints (size or distance to the objects). In recent years, other approaches have proposed to directly generate bounding boxes around potential objects of interest [START_REF] Alexe | Measuring the objectness of image windows[END_REF], [START_REF] Zitnick | Edge boxes: Locating object proposals from edges[END_REF], thus avoiding the traditional sliding window approach for object recognition. Nevertheless, the measure used to generate boxes (such as objectness) is often tightly bounded to the concept of saliency. So far, saliency maps are mostly used as a black box and are not learned (although sometimes refined) directly during the exploration of a particular environment. We present here a method that incrementally learns saliency as the robot observes the environment.The produced saliency maps are therefore dedicated to the environment that was explored, but remain flexible to novelty. The model that is learned here is a top-down type of saliency, dedicated for generic robotics tasks (i.e. a saliency that detects objects the robot can interact with). The term saliency in this article is therefore more related to the concept of objectness, and the model that is learned is used to produce object-oriented saliency maps. We further show that these saliency maps can be used to refine object boxes proposals.

Active exploration by robots can be done in many different ways depending on the task and available hardware. On mobile robots aiming at making a semantic cartography of the environment, predefined path plans [START_REF] Meger | Curious george: An attentive semantic robot[END_REF], navigation graphs [START_REF] Kragic | Object search and localization for an indoor mobile robot[END_REF], or frontier-based explorations [START_REF] Jebari | Combined vision and frontier-based exploration strategies for semantic mapping[END_REF] can drive the robot's displacement. In the context of learning an optimal action policy given visual inputs (typically learning eye saccades to identify objects), reinforcement learning approaches have been proposed [START_REF] Borji | Online learning of task-driven object-based visual attention control[END_REF], [START_REF] Paletta | Q-learning of sequential attention for visual object recognition from informative local descriptors[END_REF]. The use of intrinsic motivation (i.e. using a reward system that is not related to an external goal, but to the acquisition of competences or knowledge) has also been largely investigated. Oudeyer et al. proposed to drive exploration using learning or competence progress [START_REF] Baranès | R-iac: Robust intrinsically motivated exploration and active learning. Autonomous Mental Development[END_REF], [START_REF] Oudeyer | Intrinsic motivation systems for autonomous mental development[END_REF], while [START_REF] Chentanez | Intrinsically motivated reinforcement learning[END_REF] have used the error of prediction of salient event to speed up a classical reinforcement learning approach, and [START_REF] Luciw | Artificial curiosity with planning for autonomous perceptual and cognitive development[END_REF] have integrated artificial curiosity to deal with high dimensional visual observation in the context of reinforcement learning. Our main contribution is to propose a method, called RL-IAC (for Reinforcement Learning Intelligent Adaptive Curiosity, that provides an exploration strategy Fig. 1. General architecture of our system based on the ideas of the IAC algorithm [START_REF] Oudeyer | Intrinsic motivation systems for autonomous mental development[END_REF]. One of the challenges for applying such a method to the task of saliency learning is that the cost for actions (displacement of the robot in our case) is not considered in IAC, while it is critical in our framework. We therefore add a reinforcement-learning module that is retrained after each displacement to determine the action that is the best compromise between learning and displacement. Note that RL here is not used as a final goal (we intend to learn saliency, not displacement), but as a mean to decide at each step the best actions to follow in order to learn saliency.

In a previous work [START_REF] Craye | Environment exploration for object-based visual saliency learning[END_REF], we described the core mechanism of the online learning of saliency based on depth segmentation and demonstrated its efficiency compared to state-of-the-art techniques. We here propose a way to use the generated saliency maps to produce boxes proposals for objects in the environment. Second, we presented in [START_REF] Craye | Environment exploration for object-based visual saliency learning[END_REF] some preliminary results of our exploration mechanism based on the Intelligent Adaptive Curiosity (IAC) [START_REF] Oudeyer | Intrinsic motivation systems for autonomous mental development[END_REF], adapted to the problem of saliency learning. At that time, we successfully applied IAC in a semi-simulated setup so that an accurate saliency model could be learned with a limited number of relevant visual samples. However, the time spent by the robot in displacements was not taken into account, so that the time really spent during exploration was not considered. We here propose RL-IAC (for Reinforcement Learning-IAC) that provides a way to get a trade-off between the time lost in displacements across the environment, and the acquisition of relevant visual samples allowing a faster and better learning.

II. SALIENCY LEARNING AND OBJECT PROPOSAL

Figure 1 presents the general architecture of our system along with the corresponding section for each block. In a learning stage, the system extracts RGB features (see Section II-A.1) and learns the visual (RGB) aspect of salient elements within their context using a depth-based object segmentation as a supervision signal (see Section II-A.2). Based on the supervision signal and the estimated saliency, we use a metalearner to obtain an estimation of the local learning progress (see Section III-C). Then, based on the progress estimation in different portions of the environment we evaluate with an RL approach the best action to take between moving to a region that has a higher learning progress, and keep learning around the current position (Section III-D). Once exploration and learning are finished, we exploit the model to generate environment specific saliency maps using the RGB image (Section II-A.4), and use these saliency maps to generate boxes that isolate objects of interest (Section II-B).

A. Saliency learning

We here recall the key elements of our saliency learning approach. Please refer to [START_REF] Craye | Exploration strategies for incremental learning of object-based visual saliency[END_REF], [START_REF] Craye | Environment exploration for object-based visual saliency learning[END_REF] for further explanations.

1) Feature extraction : A feature extractor is applied to the RGB image in order to encode the color of each pixel and its neighborhood at different scales, averaged using superpixels. The feature extractor is applied on the whole input frame, and returns a 39 dimensions feature vector for each pixel. Unlike depth segmentation, features are available everywhere in the image. Refer to [START_REF] Craye | Exploration strategies for incremental learning of object-based visual saliency[END_REF] for more details.

2) Depth-based object segmentation : The object segmenter is based on the depth map and detects objects lying on planar surfaces (typically tables or floor), with a size between 10 and 150 centimeters. We use an adapted version of the method proposed by [START_REF] Caron | Neural network fusion of color, depth and location for object instance recognition on a mobile robot[END_REF]. The segmentation is based on detecting the floor plane in the depth map, removing walls, and creating clusters with points that neither belong to the floor nor to the walls to create object candidates. Those clusters of points are also used in Section II-B to generate SegBoxes. Then, the segmentation mask is constructed as follows (See Fig. 4, last row for illustrations): Grey areas of the segmentation mask are pixels where depth value is unavailable (dark gray), pixels that either belong to the floor or walls are labelled not salient (black). To avoid false positives as much as possible, we categorize as undetermined (light gray) the clusters that are either too small, too large, or having a contact with the border of the frame (a lot of false detection are due to portions of walls at the border of the image that match all the geometrical features of an object). Other clusters are considered as salient object, labelled salient (white).

3) Online learning: The classifier is continuously updated based on the saliency labels provided by the segmentation mask and the corresponding RGB features. Each pixel of the input image is associated with a feature vector from the feature extractor and a label from the segmentation. We train our classifier with the feature-label samples (we only keep those that were labelled salient or not salient) in order to predict the saliency of a given pixel. The classifier used in our implementation is a modified random forest, designed to re-train a model on-the-fly as new samples arrive (See more details in [START_REF] Craye | Environment exploration for object-based visual saliency learning[END_REF]). After each update, the classifier is able to estimate the saliency of an input based on the model trained with the previous observations, and the RGB image only.

4) Saliency estimation: The saliency maps are constructed by applying the classifier to RGB images. For each pixel, the classifier outputs a score between 0 and 1 that is used as its associated saliency (see Fig. 4, fourth row for examples). Although less accurate than depth segmentation, saliency maps provide a more complete estimation of the saliency, for each pixel of the image.

B. Object bounding boxes proposal

This section presents a new contribution that is a practical application to the saliency learning. The saliency map provides an indication of the interestingness of a given pixel. In order to localize objects in an image, an additional step is necessary to group salient pixels into object candidates. To this end, we use two types of bounding box proposals, and we select or reject each of them based on a score related to saliency. The first bounding boxes are obtained by the EdgeBoxes [START_REF] Zitnick | Edge boxes: Locating object proposals from edges[END_REF] algorithm: we compute for a given RGB input the 100 most likely EdgeBoxes, and their associated edge score (h in b in [START_REF] Zitnick | Edge boxes: Locating object proposals from edges[END_REF]). The second type of bounding boxes are obtained with the segmentation result (called SegBoxes here for simplicity): during segmentation, pixels of the depth map are clustered in order to create object candidates (See Section II-A.2). Among object candidates, some are labelled salient, some should be salient objects but are labelled undetermined because they touch a border or are poorly segmented, and some are just artifacts. We define Segboxes as the bounding boxes around all objects candidates (labelled salient or undetermined) of the segmentation mask.

For both EdgeBoxes and SegBoxes, we associate each box B with a score related to saliency (called here the saliency consistency score, or SCscore), representing the ratio of salient pixels in the box:

SCscore(B) = 1 w B × h B i,j∈B S(i, j) (1)
where S(i, j) is the saliency of the pixel at (i, j) , obtained from the saliency map and w B and h B are the width and height of B. The highest the score is for a given box, the most likely it is to contain a salient object. For the EdgeBoxes, the SCscore is multiplied by h in b . This way, small boxes found within a salient object might be rejected if the h in b score is low enough. Last we filter out Segboxes and Edgeboxes with a final score below a certain threshold and keep the remaining ones. In our dataset, we found SCscore = 0.2 for SegBoxes and SCscore × h in b = 0.01 to be good trade-off thresholds between false alarms and false rejections.

III. RL-IAC

In the scope of an autonomous, life-long exploration and learning, the robot must be equipped with an exploration strategy able to drive the robot's actions. This one should allow the robot to collect interesting examples, while avoiding problems such as catastrophic forgetting. Exploration should be such that the robot focuses on areas where learning is neither trivial nor impossible. This avoids decreasing in the learning quality because of irrelevant samples, and speeds up learning by focusing on appropriate areas first.

Our exploration strategy, that we call Reinforcement Learning-IAC (or RL-IAC), uses learning progress as an intrinsic reward as suggested by the IAC (Intelligent Adaptive Curiosity) algorithm [START_REF] Oudeyer | Intrinsic motivation systems for autonomous mental development[END_REF]. In this section, we recall the main components of IAC, explain the major challenges of applying such an algorithm to our problem, and describe the proposed solution to this end.

A. IAC

IAC is originally designed to learn a sensorimotor mapping. The robot takes actions and learns to predict their consequences through sensor feedbacks. In IAC, the robot is learning this mapping by taking actions that maximize the learning progress, so that focus is put on cases that are neither too easy nor too hard, thus avoiding unlearnable situations. The key components of the algorithm are:

• a learner that learns a mapping X → Y between motor commands X and sensor inputs Y . • a separation of the motor space into regions. This separation is essential as it allows a local estimation of the learning evolution. • a meta-learner that monitors the learning evolution in each region and estimates progresses. Progresses are estimated based on the evolution of the error between the learner estimate and the actual sensor input. To apply the algorithm, the following procedure is used: The robot takes an action (for example, moving its arm with the input motor command X) in a given region R i . It receives a sensor feedback about the consequence of the action (for example, the 2D position Y of the hand of the robot in the frame of a camera), while the learner tries to predict the sensor feedback Y based on the X input and previously seen samples. The learner is then updated based on the (X, Y ) sample, whereas the prediction error Y -Y is added to the error history of the meta-learner region R i . Last, the progress in region R i is re-evaluated based on the error history over the last few samples. The next action to be taken from the robot is then randomly chosen in the region that has the highest learning progress.

B. Application to saliency learning on a mobile robot 1) Role of the motor commands: The mapping learned in IAC is between motor command and sensor input. Our saliency algorithm learns a mapping between sensor inputs X (the RGB-features) and other sensor inputs Y (the depthbased segmentation). Motor commands are here used to move the robot across the environment to a new position and orientation. They are not used directly as new samples for our learner, but as a way to receive new incoming samples (from the RGB-D input), by showing a different point of view of the environment. Once learning is finished, the model is then completely independent from any motor command.

2) Regions definition: In IAC, the regions are obtained by incrementally splitting the input (X) space of the mapping which is also the motor space. In our case, the X space of the mapping is the 39 dimensions space of the RGBfeatures which is not well-suited to define regions: first, the dimensionality is much higher than spaces where IAC has been used. Second, examples are not directly accessible. In IAC, examples are accessible by sending a motor command X and receiving the sensor feedback Y . In our case, to get a specific feature vector X and associated label Y , the robot has to reach a point of view that contains X. To plan displacements with this method, the robot should know the available features at each point of view. To avoid it, we define regions in the space of positions (x, y) and orientations(θ) accessible by the robot. This space only has 3 dimensions and can be targeted by the robot without prior knowledge of the environment.

3) Cost for actions: In IAC, the cost for taking actions is not considered, and a greedy policy that chooses the regions with highest learning progress is enough. For a mobile robot moving in a large environment (e.g. a building), the displacements between two regions can be extremely time consuming, making the greedy policy inefficient. We then extend the IAC policy with a RL module that estimates the best trade-off between progresses and displacement. At each step, the robot chooses between moving to a region with higher progress, or stay nearby and keep learning.

C. Progress estimation

In our approach, the learner is the classifier that learns saliency from RGB features and depth-based segmentation (see Section II-A.3). The space that is separated into regions is the space of position/orientations accessible by the robot. A regions is a subset of positions (x, y, θ) that the robot can reach. Thus, the robot is in region R i at time t if its current position (x(t), y(t), θ(t)) ∈ R i . An action in this is a displacement of the robot to a given position (x , y , θ ). In our current implementation, the geometry of the robot's environment is supposed to be known, and the regions are defined arbitrarily prior to the experiment.

As in IAC, the meta-learner stores for each region a history of the learning error based on the differences between estimated saliency (from the learner estimation) and observed saliency (from the segmentation algorithm). Each time a new frame is acquired in region R i , saliency map is estimated and segmentation mask is computed. By keeping only salient and not salient pixels from the segmentation, we generate the observation set O, and by taking the associated saliency response for each of these pixels, we obtain the estimation set E. Thus, error evaluation Err i (t i ) is obtained after a new frame is acquired in region R i after t i observations in the region by the following formula:

Err i (t i ) = 1 -F 1 (O ti , E ti ) (2)
where F 1 (., .) is the F 1 score 1 . An estimation of the learning progress in region i, is obtained by a linear regression of the error rate history Err i over the last τ samples (τ = 10 in our case):

   Err i (t -τ ) . . . Err i (t)    = β i (t) ×    t -τ . . . t    +    (t -τ ) . . . (t)    (3)
1 F 1 = 2tp 2tp+f p+f n , where tp, f p and f n are the true positives, false positives and false negatives. We use the F 1 score as our error metrics for Err i , because not salient pixels are representing more than 80% of the samples, making accuracy inappropriate for error estimation. with (t) the residual error. The learning progress LP i in region i is defined as the derivative of the learning curve (or the opposite of the error rate) in that region:

LP i (t) = -β i (t) (4)

D. Exploration policy

Because of the displacement time, the exploration strategy that only follows the highest learning progress is not wellsuited as is. Therefore, we propose to use Q-learning [START_REF] Christopher | Q-learning[END_REF] to constantly re-estimate the best policy to find a good tradeoff between moving and learning, given the progress in each region. The idea is to simulate future displacements of the robot, and to determine the policy that optimizes progress (or reward). The next displacement is taken by following this policy, the progress in regions is updated, and a new policy is re-estimated.

The problem is modelled as a navigation graph where states are the regions in which progress is evaluated. Adjacent regions are connected by edges in the graph, and the cost for moving to an adjacent region is defined by the time a robot would take to move between the centroids of the two regions. See Figure 2 for an example of navigation graph. The robot can move to adjacent regions or stay within the current region by taking a displacement action in M = {up, down, lef t, right, stay}, or learn in the current region. If the action learn is selected, the robot grabs an RGB-D input, process it and updates the saliency learner as well as the meta-learners. If the action is in M , the robot moves to the corresponding adjacent region, randomly selects a new position (x , y , θ ) in it and stops at this position.

Suppose that at time t the robot is in region R i . Each region R j of the environment is then associated with an estimated learning progress LP j (t). To decide the next action to take, we simulate 1000 episodes for an horizon of time N = 3600s (i.e. from t to t + N ) in which the robot takes action in the environment and collects reward based on learning progress. The time spent for displacement depends on the distance between centroids of two regions, whereas the time spent for learning is set as 1s (See Section IV-B for more details about those values). For each episode, the initial state is always R i . The learning progress is considered as constant during the whole episode, and the reward received when taking an action a in region R j is as follows:

r(R j , a) = LP j (t) if a = learn 0 otherwise (5)
Based on the simulated episodes, we determine an optimal policy by updating a Q-matrix according to the following rule

Q(s k , a k ) = r(s k , a k ) + γ Max a ∈M ∪{learn} Q(s k+1 , a ) (6)
with γ the discount factor (0.1 in our implementation), s k the region where the robot is after k actions, a k the action to take next, and s k+1 the region after taking action a k . Once all the episodes have been simulated, we select the next action a t taken by the robot such that

a t = Argmax a ∈M ∪{learn} (Q(R i , a )) (7)
After this action is taken, learning progress is re-estimated and a new batch of episodes is simulated to train a new Q matrix and decide the next action to take. Note that each Q-learning policy is obtained by considering the reward as constant in time. This assumption is wrong in practice, as each new learn action influences the learning progress (and therefore, the reward) that would eventually decrease to 0 when the learner cannot be any better. However, the assumption is accurate enough to estimate the next action to take. As the Q matrix is re-estimated before each new action, this approximation does not introduce a significant bias. Moreover, to force the robot to quickly get a first estimation of the progress in each region, we forced the progress in a given region to be very high as long as less than three samples were collected in that region. This additional constraint has the same effect as the R-MAX [START_REF] Brafman | R-max-a general polynomial time algorithm for near-optimal reinforcement learning[END_REF] exploration policy. Last, we used an epsilon-greedy strategy to move to a random region 10% of the time.

IV. EXPERIMENTAL RESULTS

For experimental results, we used two different Kinect datasets composed of RGB-D data with associated camera positions (x, y, θ) obtained by a SLAM algorithm. The saliency and associated object proposal were evaluated on the images of the dataset without considering the position of the camera (see Section IV-A). The exploration strategy was evaluated by simulating the displacement of the robot to one of the position/orientation available in the dataset and getting the associated RGB-D data(see Section IV-B).

The first dataset was collected from a pioneer 3DX robot, with a Kinect RGB-D camera mounted at 1 meter from the ground and tilted slightly downward. We manually controlled the robot in an office building in order to visit corridors, laboratory, hall and offices. We recorded a 15 minutes length video sequence at 20Hz with the robot moving at a 0.3m/s average speed, in which a large variety of views were captured (See Figure 2). The second one is a publicly available dataset called RGB-D scenes dataset [START_REF] Lai | A largescale hierarchical multi-view rgb-d object dataset[END_REF]. The dataset consists of 8 video sequences of indoor scenes of everydaylife objects lying on tables. For both datasets, we manually labelled 100 frames to obtain ground truth bounding boxes and masks to create an evaluation set. Those frames were removed from the dataset and used for evaluation only.

A. Object proposal

Before presenting the saliency learning progression, we analyze the performance reached when enough samples are used to train the classifier. The evaluation in this section is done with a saliency model that was learned from the entire training sequences and evaluated on the testing datasets. In [START_REF] Craye | Environment exploration for object-based visual saliency learning[END_REF], we demonstrated that our saliency model outperformed several state-of-the-art saliency techniques when trained and evaluated on a similar environment. We now demonstrate that these saliency maps can be used to improve the relevance of the EdgeBoxes [START_REF] Zitnick | Edge boxes: Locating object proposals from edges[END_REF] and SegBoxes (See Section II-B). To this end, we ran the EdgeBoxes algorithm for each frame of the evaluation set, we collected the 100 best ranked bounding boxes along with their h in b score. We calculated the SCscore for each box based on Eq. 1 and used it to produce a new ranking for the bounding boxes. We also generated the SegBoxes and filtered out the one with an SCscore above 0.2. When combined with the EdgeBoxes proposal, the SegBoxes bounding boxes were ranked before the EdgeBoxes, as they are much more likely to actually contain objects.

The evaluation metric is the detection rate versus the number of proposal, based on the intersection over union measure (IoU=0.7 in our case) to count the number of detections. This measure is used by [START_REF] Zitnick | Edge boxes: Locating object proposals from edges[END_REF] to evaluate their performance over state of the art approaches. Results are displayed in Figure 3 for the two datasets. The curves represent the performance for :

• EdgeBoxes alone (EdgeBoxes),

• EdgeBoxes re-ranked by the SCscore (Edge-Boxes+SCscore), • EdgeBoxes re-ranked by the SCscore produced by a bottom-up saliency map method called BMS [START_REF] Zhang | Saliency detection: a boolean map approach[END_REF](EB+BMS SCscore), • SegBoxes filtered by the SCscore (SegBoxes+SCscore)

• the combination of re-ranked EdgeBoxes and SegBoxes (EB+SegBoxes+SCscore). As expected, the use of the SCscore on EdgeBoxes allows a much better detection rate on both datasets. Moreover, using a bottom-up saliency map such as BMS instead of our saliency slightly improves the performance on the RGB-D scenes dataset, but performs worse on the other one. The SegBoxes are often very relevant, but the number of proposals is low (less that 8 in any cases), and they do not cover the entire image (reflective objects are poorly detected, objects more than 4 meters away from the Kinect are not processed). For that reason, the SegBoxes alone have a limited detection rate, but they provide a set of boxes that is complementary to the EdgeBoxes. When SegBoxes proposal are combined with EdgeBoxes, the detection is significantly improved. Figure 4 shows sample results to compare the ground truth (first row), the top 5 EdgeBoxes proposals (second row), the top 5 EdgeBoxes+SCscore proposals (third row, blue) as well as the SegBoxes proposals (third row, yellow). The SegBoxes almost always provides relevant boxes, but it also misses a lot of objects, either because they are too far to be segmented (sample 5, 7), or because segmentation failed (sample 4). In this case, the remaining objects locations are recovered by the EdgeBoxes. Moreover, the use of the SCscore to modify the ranking of the EdgeBoxes allows to favor boxes that surround salient elements while removing distractors such as windows or cables (sample 2, 7, 8). Last, it is possible to cope with frames that does not contain any salient object (sample 6) by filtering boxes with an SCscore above a certain threshold (0.01 in our case).

B. Exploration strategy

We now look at the evolution of the saliency quality during incremental learning. We use again the two datasets, and associate a navigation graph to both of them. The navigation graph of the sequence recorded in our building (displayed on Figure 2) has been manually designed based on the robot path during the sequence. The centroids were chosen to be roughly equally spaced. For the RGB-D dataset, the navigation graph represents a building in which each room contains a sequence (8 in total) of the dataset. Each room is divided into 6 regions, and some regions are connected to other rooms (as if there was doors between rooms). To simulate the displacement of the robot and the acquisition of new frames, we associate a set of frames to each region of the navigation graph, based on their recorded (x, y, θ) positions. When the exploration policy sends a command to move the robot to a region R i , we randomly select a frame that belongs to R i , and calculate the time the robot would take to move to this position based on the euclidean distance at a 0.3m/speed. The action learn consists in grabbing an RGB-D input and launching the saliency learning procedure that contains the following steps and execution time2 :

• feature extraction: 60ms • depth segmentation: 20 to 1000ms based on the geometrical complexity of the input • saliency estimation: 30ms • meta-learner update: 10ms • learner update: 10 to 5000s based on the number of samples from the beginning of the experiments. The learner is trained in a separate process that keeps running while the robot is moving.

• calculate a new RL policy: 100ms

To demonstrate the benefits of exploring the environment using RL-IAC, we compare the evolution of the saliency when exploring the environment with different strategies. Each exploration strategy was tested 10 times on each dataset and considers the average and variance over those experiments. The performance of the system was evaluated using the evolution of the overall error rate of the system: based on the reference frames on which a ground truth is available, we compare the estimated saliency map for all of these frames with the available ground truth. We then use the formula provided by Equation 2 on each frame and take the average error. Note that the overall error rate is an extrinsic metrics used to evaluate the performance of the system. It then differs from the region error rate, the intrinsic metrics (based on segmentation rather than ground truth) used to get an estimate of the error in each region in Section III-C. Figure 5 shows the evolution of the overall error rate in time on both environments, for 4 exploration strategies:

• RND: Random selection of a region and a position in it. Find the fastest path in the navigation graph to reach this position. Move to that position. Once arrived, take action learn that updates the saliency learner and metalearner. After learning, select a new position to reach. • IAC: Same as RND, except that the region selected is the one with highest learning progress. • RND+learn: Same as RND, except that during displacement, the action learn is taken once in each visited region, rather than just in the region of destination. • RL-IAC, as described in Section III.

On both datasets, RL-IAC is the one with the fastest decreasing error. IAC is, with RND, the slowest approach. Note that RND and IAC were both evaluated in [START_REF] Craye | Environment exploration for object-based visual saliency learning[END_REF], but the evaluation was done by drawing the error rate vs the number of observations. Here, we simulate the time the robot would actually take to move in the environment and learn, thus making the experiment more realistic. The RND+learn experiment provides a more realistic exploration scenario where the robot keeps learning while moving, the error rate then decreases much faster, but still slower than RL-IAC.

To get a better insight of the way exploration is done by the robot, we divide the building in 4 main areas, namely lab, office, corridor and hall (See Figure 2). In these areas the difficulty to learn saliency is not the same. For example, the corridor does not contain any salient element (Fig 4 ,sample 6), whereas the hall is a very large room with many salient items and many distractors (Fig 4 ,sample 8,9). We compare in Figure 6 the average percentage of time spent in each area when using RL-IAC and when using random (RND+learn) exploration strategies. The graphs have been constructed by using a sliding widow of 500s over the whole experiment, and measuring for each window the number of frames obtained in each area. For random exploration, the time spent in each area is roughly the same all along the sequence. 40% to 50% of the time is spent in the corridor, whereas 10% is spent in the office. With RL-IAC, the time spent in the corridor (the less 'interesting' area) oscillates between 30% and 20%, except at the beginning, and almost 20% is spent in the office. Moreover, the time spent in exploring each area is evolving in time: the time spent in the office finally decreases to 0%, because no progresses are made in there anymore. In the middle of the sequence, most of the time is spent exploring the lab, while most of the time

V. CONCLUSION AND FUTURE WORK

In this paper, we have presented an approach to incrementally learn visual saliency, using an exploration strategy based on learning progress and reinforcement learning. We show that this method could be used to produce relevant bounding boxes around objects of interest that could be further used for recognition. To allow the robot to autonomously discover and learn about its environment, we proposed a method called RL-IAC, that finds the best compromise between spending time moving to an area with higher progress, or keep learning in a less progressing area nearby. We show that this type of exploration strategy makes learning faster and better than it would be with random exploration.

In a future work, we would like to investigate the use of other types of intrinsic motivation (such as novelty or uncertainty) to drive the robot's actions. The use of navigation graphs is also pretty restrictive as it forces an operator to manually determine regions and the robot's trajectories. An exploration that would incrementally generate regions and transitions would be more appropriate. We could also apply this framework with other definitions of saliency. Instead of a generic object segmentation, we could for example use objects detectors and specialize our saliency to find those objects within their environments.

Fig. 2 .

 2 Fig. 2. Navigation graph used for displacing the robot. The path followed by the robot to record the sequence is represented by a purple line. Nodes of the navigation graph are represented by the region centroids, and available actions to move to adjacent regions are represented by arrows.

Fig. 5 .Fig. 6 .

 56 Fig. 5. Overall error rate and variance evolution versus simulated time for a few exploration strategies. Results are obtained both on (a) RGB-D scenes artificial building and (b) our building

Our implementation was tested on Ubuntu 14.4 with an Intel Core i3-3240, CPU at

3.4GHz quadcore processor


Olivier Herbinet

Baptiste Sirjean

Roda Bounaceur

René Fournet

Frédérique Battin-Leclerc

Gérard Scacchi

Paul-Marie Marquaire
email: marie.marquaire@ensic.inpl-nancy.fr

PRIMARY MECHANISM OF THE THERMAL DECOMPOSITION OF TRICYCLODECANE

In order to better understand the thermal decomposition of polycyclanes, the pyrolysis of tricyclodecane has been studied in a jet-stirred reactor at temperatures from 848 to 933 K, for residence times between 0.5 and 6 s and at atmospheric pressure, in order to obtain a conversion between 0.01 and 25 %. The main products of the reaction are hydrogen, methane, ethylene, ethane, propene, 1,3-cyclopentadiene, cyclopentene, benzene, 1,5-hexadiene, toluene and 3-cyclopentyl-cyclopentene. A primary mechanism containing all the possible initiation steps, including those involving diradicals, as well as propagation reactions has been developed and allows experimental results to be satisfactorily modeled. The main reaction pathways of consumption of tricyclodecane and of formation of the main products have been derived from flow rate and sensitivity analyses.

INTRODUCTION

The study of the thermal decomposition of cyclanes and, still more, of polycyclanes presents several kinetic difficulties which have received little attention. The unimolecular decomposition of cyclic hydrocarbons involves either the breaking of a C-H bond, which has a large bond energy (99 kcal.mol -1 ) or the opening of the ring and the formation of a diradical.

Studies about gas phase reactions of polycyclanes have been the subject of several papers, but the present understanding is far from complete. The thermal decomposition and the oxidation of exo-tricyclo[5.2.1.0 2,6 ]decane (the structure of which is presented in Figure 1a and which is called tricyclodecane further in this paper) have been examined because it is the main component of synthetic fuels (e.g. RJ-6, JP-9 and JP-10) that are used in aircraft due to their high volumetric energy content. Its thermal decomposition have experimentally been studied in plug flow reactors with gas chromatography analyses, at temperatures up to 873 K, by Striebich and Lawrence (1) and between 903 to 968 K, by Rao and Kunzru (2), in a micro-flow tube with mass spectroscopy analysis, at temperatures up to 1700 K, by Nakra et al. (3) and, in a shock tube with analysis by UV absorption, at temperatures between 1100 to 1700 K, by Davidson et al. [START_REF] Horning | AIAA-01-3707 37th Joint Propulsion Conference 2001[END_REF]. A global mechanism has been proposed by Li et al. [START_REF] Li | [END_REF] for the oxidation of tricyclodecane and has been validated by modeling ignition delay times obtained in shock tubes (6,7). This model has also been tested by Nakra et al. (3) in order to reproduce their experimental data, but simulations did not predict the formation of several important products. That is due to the fact that the model of Li et al. [START_REF] Li | [END_REF] includes globalized reactions leading directly from the reactant to cyclopentene (8,9) and small species, such as ethylene, acetylene, propargyl and allyl radicals, without considering the formation of intermediate species.

O'Neal and Benson studied the diradical mechanism of pyrolysis of some three-and four-membered ring compounds and of some polycyclic molecules (10,11). For most species, Arrhenius parameters estimated by these authors were consistent with available experimental data. Recently Tsang (8,9) proposed reaction channels to account for the fate of diradicals in the case of cyclohexane and cyclopentane and Billaud (12) et al. and Ondruschka et al. (13) in the case of decaline, but no previous publication gives any clues about the fate of diradicals obtained from tricyclic species. Concerning propagation reactions, the rate constants of the decomposition by β-scission involving the opening of a ring or of the isomerization involving polycyclic transition states are still very uncertain.

The first purpose of this paper is to present new experimental results for the thermal decomposition of tricyclodecane performed in a jet-stirred reactor, a type of reactor different from the flow tube and shock tube used in the most part of previous studies. In order to capture the first steps of the reaction, this reactor has been operated at temperatures between 848 and 933 K corresponding to a conversion between 0.01 and 25 %. The second objective is to describe the development of an exhaustive primary mechanism including all the possible initiation channels, written by following a diradical approach as proposed by Tsang for the cyclohexane and the cyclopentane, as well as the propagation reactions deriving from the H-abstraction from tricyclodecane and 3-cyclopentyl-cyclopentene (Fig. 1b). It will be shown later in this paper that 3-cyclopentyl-cyclopentene is an important product from a kinetic point of view.

EXPERIMENTAL STUDY OF THE THERMAL DECOMPOSITION OF TRICYCLODECANE

As the experimental apparatus used in this study has been described in details in a previous paper concerning the thermal decomposition of n-dodecane (14). The main features and the specificities of the present analyses are discussed below.

Experimental procedure

Experiments were carried out in a continuous jet stirred reactor (internal volume about 90 cm 3 ) (15) made of quartz and operated at a constant temperature and pressure. The heating of the reactor was achieved by means of electrically insulated resistors directly coiled around the vessel. Temperature was measured by using a thermocouple located inside the reactor in a glass finger. In order to obtain a spatially homogeneous temperature inside the reactor, reactants were preheated at a temperature close to the reaction temperature. Corresponding residence time in the preheating section was approximately 1% of the total residence time. Experiments were performed at a pressure slightly above atmospheric pressure (106 kPa). The pressure was manually controlled by a control valve placed upstream the products analysis zone.

The liquid tricyclodecane (96.6 wt% exo form, 2.5 wt% endo form) was contained in a glass vessel pressurized with nitrogen. After each load of the vessel, nitrogen bubbling and vacuum pumping were performed in order to remove oxygen traces dissolved in the liquid hydrocarbon fuel. The liquid reactant flow rate was controlled by using a liquid mass flow controller, mixed to the carrier gas (helium, 99.995% pure) and then evaporated by passing through a single pass heat exchanger whose temperature is set above the boiling point of the mixture. Carrier gas flow rate was controlled by a gas mass flow controller located before the mixing chamber.

The analyses of the products leaving the reactor were performed in two steps due to the formation of compounds, which were either gaseous or liquid at room temperature. For the analysis of heavy species, i.e. the liquid ones at room temperature, the outlet flow was directed towards a trap maintained at liquid nitrogen temperature during a determined period of time to concentrate the sample. At the end of this period (typically between 5 and 15 min), the trap was removed and, after the addition of acetone and of an internal standard (n-octane), progressively heated up. When the temperature of the trap was close to 273 K the mixture was poured into a small bottle and then injected by an auto-sampler in a gas chromatograph with flame ionization detection (FID) for quantification. The column used for the separation was an HP-1 capillary column with helium as carrier gas (oven temperature profile was: 313 K held 30 min, 5 K.min -1 , 453 K held 62 min). In the conditions of this study, the column provided a good separation for the following products (retention time in min), cyclopentene (3.6), 1,3cyclopentadiene (3.7), benzene (4.9), 1,5-hexadiene (4.5), toluene (7.9), exo-tricyclodecane (41,2), 3-cyclopentylcyclopentene (41.6) and endo-tricyclodecane (42.7). Identification of heavy species was performed by a gas chromatography-mass spectroscopy system working in the same conditions as the chromatograph used for the quantification. Calibrations were performed by analyzing a range of solutions containing known amounts of n-octane and of the compound quantified.

For the analysis of light species, like hydrogen and hydrocarbons containing less than five atoms of carbon, analysis was performed on-line using two gas chromatographs in parallel. The first chromatograph was fitted with both thermal conductivity detector (TCD) for hydrogen detection and FID for methane and C 2 hydrocarbons detection and used a carbosphere packed column. Hydrocarbons analysis was performed with an oven temperature of 473 K. In these conditions the column provided a good separation for: methane (2.4), acetylene (5.3), ethylene (7.3), ethane (9.6) and propene (40.7). The separation of the hydrogen peak from the helium peak (experimental carrier gas) was obtained with a oven temperature of 303 K. Argon was used as column carrier gas and also as reference gas for the TCD in order to have the better sensibility for hydrogen detection. The second gas chromatograph, which was used for C 3 and C 4 hydrocarbons analysis, was fitted with FID and a Haysep D packed column with nitrogen as carrier gas (oven temperature profile: 313 K held 30 min, rate 1K.min -1 , 473 K held 30 min).

Analyzed species and their relative retention times were: methane (2.6), ethane (15.5), propene (61.2) and cyclopentadiene (147.8). Light species identification and calibration were realized by injection of gaseous standard mixtures provided by Air Liquide. Data obtained using the three different chromatographs were compared through mole fractions of products which were detected by two chromatographs, i.e., mole fractions of cyclopentadiene obtained using Haysep-D column were compared to those obtained using HP-1 column. The variation between the mole fractions obtained with the different chromatographs were less than 5%. A study of the reproducibility of the experimental results was carried out for both kinds of products analyses.

Calculated maximum uncertainties on the experimental results were ± 5% with the online analysis (light species analysis) and ± 8% for the discontinuous process of analysis (heavy hydrocarbons analysis).

Experimental results

The thermal decomposition of tricyclodecane has been studied in the above-described reactor operated at atmospheric pressure, temperatures between 848 and 933 K, residence times from 0.5 to 5 s and initial hydrocarbon mole fractions from 0.7 to 4 % with dilution in helium. In all the figures presented in this part, the points refer to experimental observations and the curves come from simulations.

Figure 2 presents the evolution of the conversion of tricyclodecane with residence time at several temperatures (873, 893, 913 and 933 K) for an initial hydrocarbon mole fraction of 4 % (Figure 2a) and with temperature at a residence time of 1s and for several initial hydrocarbon mole fractions (0.7, 2, 4%) (Figure 2b). Conversions (0.01-25%) have been deduced from the sum of the concentrations of reaction products, because the values deriving from the difference between the amounts of reactant entering and leaving the reactor were not accurate enough (relative uncertainty on conversion is better than 10%).

Figure 2b shows that the conversion is a function of reactant concentration, as then that the current order of reaction is different from 1. Figure 2c displays results obtained in the same conditions for ndodecane with an initial concentration of 2 % (14). This results shows that the linear alkane is much more reactive than the tricyclane, despite the fact that the later is a strained molecule.

FIGURE 2

For experiments performed at temperatures between 873 and 933 K and residence times between 0.5 and 6 s, 11 main products of the reaction have been analyzed : hydrogen, methane, ethylene, ethane, propene, 1,3-cyclopentadiene, cyclopentene, benzene, 1,5-hexadiene, toluene and 3-cyclopentyl-cyclopentene. Figures 3 and4 present the evolution of the mole fractions of these products with residence time at several temperatures (873, 893, 913 and 933 K) for an initial hydrocarbon mole fraction of 4 %.

FIGURES 3-4

These figures show that the major products of the thermal decomposition of tricyclodecane are hydrogen, ethylene, propene and 1,3-cyclopentadiene, which have selectivities always higher than 10 % and that the formation of cyclopentene is lower than that of cyclopentadiene and close to those of benzene and toluene.

As the differences between the masses of reactant entering and leaving the reactor were not accurately enough determined for such low conversions (lower than 25%), the mass balance could not be directly checked. Nevertheless, the ratio between the numbers of C-atoms and H-atoms present in the molecules of reaction products (reactant excluded) can be calculated whatever the conversion and be compared to the theoretical value which corresponds to the same ratio in the initial hydrocarbon (tricyclodecane) molecule. This ratio has been calculated for every experiment performed in this study and an average value of 0.61±0.03 (close to the theoretical value of 0.625) was obtained.

Primary products have been determined from an analysis of the selectivities (the selectivity of a product is the ratio between the mole fraction of this product and the sum of the mole fractions of all products -non converted reactant excluded-). A species is probably a primary product if the extrapolation to origin of its selectivity versus residence time gives a value different from zero.

Selectivities of products versus residence time have been calculated for the experiments performed at 873 K (Figures 34), for which conversion is lower than 2%. Figure 5a displays the selectivities of 1,3-cyclopentadiene, cyclopentene, 1,5-hexadiene and 3-cyclopentyl-cyclopentene and shows that these products seem to be primary products. 1,3-cyclopentadiene is often a secondary product deriving from cyclopentene, but here it probably has a primary source. Ethylene, which is not shown in Figure 5, seems also to be a primary product. At this temperature, benzene and toluene present trends of primary products but their initial selectivities are very close from zero. We have then performed experiments at 848 K in order to plot the selectivities of benzene and toluene vs. residence time at a conversion lower than 0.5% as shown in figure 5b. That allows us to conclude to a probable primary character of these aromatic compounds.

DESCRIPTION OF THE MODEL

The detailed kinetic model has been constructed by using the same systematic way as EXGAS software, which performs an automatic generation of mechanisms, but cannot be directly applied to polycyclic compounds. EXGAS has been mainly developed and tested to model the oxidation of alkanes (16,17),

but it has been recently used to produce a mechanism for the pyrolysis of n-dodecane (18). Except for diradicals for which the calculations are detailed further in the text, specific heats, standard enthalpies of formation and entropies of all the considered molecules or free radicals have been calculated using THERGAS software (19) based on the group and bond additivity methods and on statistical thermodynamics approach proposed by Benson (20). According to the CHEMKIN II formalism, the thermochemical data are stored as 14 polynomial coefficients [START_REF] Kee | Sandia Laboratories Report[END_REF].

General structure of the mechanism

The mechanism presented here includes two parts:

A C 0 -C 6 reaction base
This reaction base includes all the reactions involving radicals or molecules containing less than six carbon atoms (C 0 -C 2 reaction base [START_REF] Barbé | [END_REF]), the reactions of C 3 -C 4 unsaturated hydrocarbons (23), such as propene and the reactions of C 5 to C 6 hydrocarbons (24). The kinetic data used in these reaction bases were taken from the literature. This C 0 -C 6 reaction base has been used here after removing all the species or reactions involving the presence of oxygen atoms.

A comprehensive primary mechanism Since, as it will be shown further in the text, under the studied conditions, 3-cyclopentyl-cyclopentene is the quasi exclusive initiation product from tricyclodecane, the two only molecular reactants considered in this part of the mechanism are tricyclodecane and 3-cyclopentyl-cyclopentene. The primary mechanism includes the following elementary steps:

• Unimolecular initiations by bond fission,

• Propagations by metathesis, or hydrogen abstraction, from the two reactants,

• Propagations by β-scission decomposition,

• Propagations by isomerization involving cyclic transition state,

• Terminations by combination of two free radicals; radicals involved in combination are C 0 -C 4 radicals, radicals deriving directly from tricyclodecane by metatheses and stabilized free radicals that cannot break through β-scission of a Csp 3 -Csp 3 or Csp 3 -H bond.

The following parts of this paragraph describe which initiations and propagations have been written

for tricyclodecane and 3-cyclopentyl-cyclopentene and how the related rate constants have been estimated.

Unimolecular initiations by bond fission from tricyclodecane and 3-cyclopentyl-cyclopentene

The unimolecular initiations by breaking of a C-H bond have been considered through their corresponding reverse reactions, the combinations of the two radicals with a rate constant taken from Allara and Shaw (25).

In the case of linear or ramified alkanes, the unimolecular initiations by breaking of a C-C bond lead to the formation of two free radicals, while diradicals are obtained in the case of cyclic and polycyclic hydrocarbons, as shown in Figure 6 for tricyclodecane and in Figure 7 for 3-cyclopentyl-cyclopentene. THERGAS and corrections due to the second radical center were estimated assuming that there was no interaction between the two radical centers. The enthalpy of formation of •R• (Δ f H°( 298K) (•R•)) was then obtained according to equation {1}:

Δ f H°( 298K) (•R•) = E(R-H)+ Δ f H°( 298K) (HR•) -Δ f H°( 298K) (H•) {1}
with: E(R-H) : energy of the bond broken in HR• to give •R•,

Δ f H°( 298K) (HR•) : enthalpy of formation of HR•, Δ f H°( 298K) (H•) : enthalpy of formation of H• (52,1 kcal.mol -1 (20)).
The entropy of a species S (S°( 298K) (S)) can be estimated from the entropy of a model compound M (S°( 298K) (M)) according to equation {2} established by Benson (20):

S°( 298K) (S) = S°( 298K) (M) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + S M σ σ Rln ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + M S n n Rln +Rln(2s+1)+C {2}
with: σ M and σ S : the total symmetry numbers of M and S, respectively.

n M and n S : the number of optical isomers of M and S, respectively.

Rln(2s+1): the electronic correction. The spin s is equal to 0 in the case of a molecule or a diradical in the singlet state, to 1/2 for a free radical and to 1 for a diradical in the triplet state. For a diradical (mixture of 75% in the triplet state and 25% in the singlet state [START_REF] Benson | Thermochemical Kinetics[END_REF])

the electronic contribution is equal to 2Rln(2). R is the gas constant.

C is the sum of the other corrections due to the differences of structure between S and M (free internal rotations, barrier corrections, vibrations of H atoms, translations and external rotations).

Applying equations {2} to the case of •R•, •RH, HR• and HRH, we obtain equation {3}:

S°( 298K) (•R•) = S°( 298K) (HR•) -(S°( 298K) (HRH)-S°( 298K) (•RH)) ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - • • • • HR RH R HRH σ σ σ σ Rln ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ - • • • • R HRH HR RH n n n n Rln {3}
In the case of diradical formed by the initiation (1) of Figure 6,

σ RH =2, σ •RH =1, σ ΗR• =1 and σ •R• =1, the symmetry correction is equal to -Rln(2); n RH =1, n •RH =1, n ΗR• =1 and n •R• =1, the optical isomers correction is equal to 0.
According to Benson (20), the specific heat of •R• (Cp T (•R•)) was deduced from equation {4}:

Cp T (•R•) = Cp T (HR•) -( Cp T (HRH)-Cp T (•RH)) {4}
Table 1 presents the thermodynamic data of the 7 diradicals directly obtained from tricyclodecane and for the 2 radicals and the 5 diradicals deriving from 3-cyclopentyl-cyclopentene. In the case of 3-cyclopentyl-cyclopentene only breakings of alkylic and allylic C-C bonds were taken into account because activation energies of these reactions are much lower than the activation energy of the breakings of vinylic C-C bonds. This table shows that a good agreement is obtained between the estimations above explained and much time consuming quantum calculations in the example of diradical BR1. Thermodynamic data have been calculated from geometric parameters and vibrationnal frequencies obtained at the UB3LYP/cbsb7 level of theory (26). The diradical BR1 was computed as a singlet state within the broken symmetry spin-unrestricted approach using the GUESS=MIX option of Gaussian 03 [START_REF] Frisch | Gaussian03, revision B05[END_REF]. This method has been shown to provide reliable energies and geometries [START_REF] Lahiti | [END_REF](29).

Computations were performed using the Gaussian 03 suite of programs. Isodesmic reaction analysis is used to further improve accuracy on enthalpy of formation. Isodesmic reactions are actual or hypothetical reactions in which the types of bonds that are made in forming the products are the same as those which are broken in the reactant. To obtain more accurate enthalpies of formation it is better to use isogyric reactions (reactions that conserve the spin) and to choose species which own structures as similar as possible (Examples of isodesmic reactions used to estimate the enthalpy of reaction of diradical BR1 are given in Figure 8).

TABLE 1 FIGURE 8 b/ Estimation of the kinetic parameters of the unimolecular initiations

Kinetic parameters of the unimolecular initiations have been deduced from data from the literature (10,11). An average value of 5.0×10 15 cm 3 .mol -1 .s -1 has been used for the A factor, which is close to what is used by EXGAS software for acyclic alkanes (17). This value is close to A factors of numerous reactions of thermal decomposition of cycloalkanes and polycycloalkanes [START_REF] Benson | Thermochemical Kinetics[END_REF]. According to O'Neal and Benson (10,11), activation energy of the opening of a (poly)cyclane is given by {5} :

E 1 =DH(C-C)-ΔE TC +E -1 {5}
With E 1 the activation energy of the reaction of the opening of the cycle.

DH(C-C) the bond energy of the broken C-C bond.

ΔE TC the difference of ring strain energy occurring through the reaction. Benson [START_REF] Benson | Thermochemical Kinetics[END_REF]. The ring stain energy of 3-cyclopentyl-cyclopentene (12 kcal.mol -1 ) is assumed as twice that of cyclopentane. The breaking of vinylic C-C bonds in 3-cyclopentyl-cyclopentene has not been taken in account because activation energy of such reaction is much higher (102 kcal.mol -1 ) than the ones of breakings of alkylic and allylic C-C bonds. Table 2 summarizes the values taken for the energies of activation of the reactions of unimolecular initiation by breaking of a C-C bond from tricyclodecane and 3-cyclopentyl-cyclopentene.

TABLE 2

Fate of the diradicals obtained through the unimolecular initiations of tricyclodecane and

3-cyclopentyl-cyclopentene

The fate of cyclic and polycyclic diradicals has not yet been much studied. Tsang (8,9) has proposed some channels in the case of diradicals deriving from cyclohexane and cyclopentane. Figure 9a

FIGURE 9

We have then systematically written all the β-scission decompositions and internal isomerizations for the 12 diradicals directly obtained from tricyclodecane and from 3-cyclopentyl-cyclopentene and for those deriving from them by β-scission decompositions. Only the β-scission decompositions involving the breaking of a Csp 3 -Csp 3 bond have been considered, except when the only possible decomposition was the breaking of a Csp 3 -Csp 2 bond (activation energy 6.8 kcal.mol -1 higher than the one of the breaking of a Csp 3 -Csp 3 bond). Tables 3 and4 show the products obtained by β-scissions and isomerizations for the diradicals formed by the initiation (1) of Figure 6 and by the initiation (2) of The rate constants used for the β-scission decompositions of diradicals are the same as those used for free radicals, the estimation of which will be detailed further in the text, but for the breaking of a Csp 3 -Csp 3 bond in β-position of two radical centers, as shown in Figure 10. The activation energy of the β-scission of Figure 10a, which leads to the formation of two alkenes, is low and has been estimated to 2.8 kcal.mol -1 by CBS-QB3 method (32) performed with Gaussian03 software [START_REF] Frisch | Gaussian03, revision B05[END_REF]. The use of CBS-QB3 method on diradical species in a broken symmetry approach involves a modification of the empirical correction included in CBS-QB3, this correction has been described elsewhere and was shown to provide reliable energies (33). In all the quantum estimations of rate parameters presented in this paper, Intrinsic Reaction Coordinate calculations have been performed to insure that the transition states connect correctly the reactants and the products. The same value was used for the activation energy of the β-scission in the case of cyclic diradicals in which a single cycle bears two radical centers (such as 1,4-cyclohexadiyl diradical) except for the particular case of 1,3-cyclopentadiyl diradical for which Ea is higher (22 kcal.mol -1 ) because of steric inhibition of π bonding (20).

2.8 kcal.mol -1 22 kcal.mol -1 ;

The activation energy of the β-scission of Figure 10b was estimated as that of the model reaction displayed in Figure 10c assuming that, for acyclic compounds, the activation energy of a β-scission decomposition Ea (acyclic β-scission) is a linear function of its enthalpy of reaction Δ r H (1000K) . As shown in Figure 11, this has been proved correct for 12 reactions with the following Evans-Polanyi relationship (in kcal.mol -1 ):

Ea (acyclic β-scission) = 18.9 + 0.53 × Δ r H (1000K) {6}
The enthalpy of the reaction of Figure 10c 5) is the actual strain energy of the new polycycle created (34-36).

The strain energy due to the presence of side rings have been neglected.

The structures of the transition states assumed in the case of the isomerisations of Table 3

Propagation reactions

Propagation reactions include metatheses from the reactant, β-scission decompositions and isomerizations.

a/ Propagations by metathesis from the reactant Species which have been considered for the reactions of metathesis with the tricyclodecane and the 3-cyclopentyl-cyclopentene are small free radicals (hydrogen radicals, methyl radicals and ethyl radicals) and stabilized free radicals that cannot break through β-scission of a Csp 3 -Csp 3 or Csp 3 -H bond (allyl radicals for example). The abstractions of vinylic H-atoms have been neglected. Reactions of metatheses with tricyclodecane lead to the formation of the 6 tricyclic radicals presented in Figure 13a and with 3-cyclopentyl-cyclopentene to the 6 radicals shown in Figure 13 b. The correlations used for the estimation of the rate constants have been deduced from those used by EXGAS software (16,37,38) and are given in Table 6. As the energy of the Csp 3 -H bond is about 13 kcal.mol -1 higher than that of the Csp 3 -Csp 3 bond, β-scission decompositions by Csp 3 -Csp 3 bond fission have been considered preferentially to β-scissions by Csp 3 -H bond fission, except when only Csp 3 -H bond fission was possible. Table 7 displays examples of β-scission decompositions in the case of the tricyclic free radical (6) obtained by metathesis from the tricyclodecane. In the case of cyclic and polycyclic free radicals, β-scission decompositions lead to new species which carry both a radical center and a double bond. The reverse reaction of addition of the radical center to the double bond can give back the same cyclic radical, but in some cases, also a different one as shown in figure 14 in the case of the cyclohexyl radical. These reactions were also taken in account and written as their reverse decomposition.

FIGURE 13
The rate constants of β-scission decompositions involving acyclic species or the breaking of a C-H bond are given in Table 6 and are deduced from the values used by EXGAS software (16,37,38). The activation energies of Table 6 are not valid for β-scission decompositions leading to the opening of cyclic and polycyclic free radicals. As shown in Tables 8 and9, the activation energies of β-scission decompositions of cyclohexyl and cyclopentyl radicals are equal to 29.3 and 34.4 kcal.mol -1 , respectively, whereas the value of Table 6 in the case of the β-scission decomposition of a secondary free radical would be of 27.7 kcal.mol -1 . That has led us to perform density function theory calculations using CBS-QB3 method (32) with Gaussian03 software [START_REF] Frisch | Gaussian03, revision B05[END_REF] to estimate activation energies of 22 model β-scission decompositions involving five-and six-membered ring compounds. As illustrated in Table 7 in the case of the β-scission decompositions of two radicals deriving from metatheses on tricyclodecane, the activation energy of all the β-scission decompositions involving the opening of a cycle have been estimated as being equal to that of one of these model reactions. The values of A factor used in the case of cyclic compounds are the same than the values used by EXGAS for the corresponding reactions; i.e.

2x10 13 s -1 for each identical alkylic bond which can be broken and 3.3x10 13 s -1 for an allylic bond.

TABLES 8-9 c/ Propagation by isomerization

Only isomerizations giving directly a resonance stabilized radical have been considered. As shown in Table 7, no isomerization is then considered for the radical formed by the reaction of metathesis (6) of Figure 13a and only the transfer of the H-atom (x) is taken into account in the case of the deriving radical. As for diradicals, A-factors are mainly based on the changes in the number of internal rotations as the reactant moves to the transition state (17). Activation energies are set equal to the sum of the activation energy for H-abstraction from the substrate by analogous radicals and the strain energy of the cyclic transition state (16,17). Activation energies for the abstraction of H by •R are taken to equal 6.5

kcal.mol -1 (secondary allylic H-atom) and 5.5 kcal.mol -1 (tertiary allylic H-atom). Strain energies of the monocyclic transition states are taken to equal 26.0 kcal.mol -1 (for a four-membered ring), 6.3 kcal.mol -1 (for a five members ring), 1 kcal.mol -1 (for a six-membered ring) according to Benson [START_REF] Benson | Thermochemical Kinetics[END_REF].

For an isomerization through a polycyclic transition state strain energy used for the estimation of the activation energy of the reaction is the one of the corresponding hydrocarbon (Table 5) (34-36).

DISCUSSION

Simulations have been performed using the software PSR of CHEMKIN II (20) and the mechanism above described which involves 898 species and includes 2623 reactions. The agreement between computed and experimental mole fractions vs. residence time is globally satisfactory for conversion of tricyclodecane (Figure 2a) and for products such as ethylene, 1,3-cyclopentadiene, cyclopentene, 1,5-hexadiene, toluene and 3-cyclopentyl-cyclopentene (Figures 3 and4). Computed mole fractions of benzene and hydrogen are slightly under-predicted for the longest residence times. Light products such as methane, ethane and propene are more strongly under-predicted (a factor around 2 for methane and propene, a factor up to 4 for ethane).

Figure 2b displays a comparison between computed and experimental conversions of tricyclodecane as a function of temperature for several initial hydrocarbon mole fractions (0.7, 2 and 4%) and for a residence time of 1 s. Simulations show that computed conversions depend on the initial hydrocarbon mole fraction as it is the case experimentally. Nevertheless computed conversions are over-predicted by a factor lower than 2 for initial hydrocarbon mole fractions of 0.7 and 2%.

Figures 15 and16 present flow rate analysis performed at 933 K and at a residence time of 1 s corresponding to a conversion of 5.25%. The arrows and the percentages represent the flow of consumption of a species through a given channel. Flow rate analysis shows that 88.4% of the reactant is consumed through metathesis reactions (paths 1-4 in figure 15 and 6-7 in figure 16) with small radicals (hydrogen, methyl and allyl radicals). It underlines also the importance of reactions of unimolecular initiation (path 5 in figure 16) in the consumption of tricyclodecane (11.6%).

Unimolecular initiation step leads to the formation of one diradical (path 5) which is quasi-exclusively consumed (99.7%) by a reaction of isomerization (Figure 12c) to form 3-cyclopentyl-cyclopentene. This last species is then consumed by reaction of unimolecular initiation (95.6%) to form a new diradical species which leads to C 5 and allyl radicals through successive β-scission decompositions.

The fact that tricyclodecane mainly leads to 3-cyclopentyl-cyclopentene through diradical BR1 (path 1 in Fig. 7) may be surprising because the activation energy of this reaction of unimolecular initiation (77 kcal.mol -1 ) is 6 kcal.mol -1 higher than the activation energy of the reaction of unimolecular initiation

(2) of Figure 6 as shown in Table 2. If quasi stationary state is assumed for diradicals, the global kinetic constant (k g ) of the reaction of formation of a product generated from a diradical can be expressed by the following equation:

k g =(k 1 ×k 2 )/(k -1 +k 2 ) {8}
with :

k 1 , k -1 and k 2 the rate constants of the unimolecular initiation leading to the given diradical, of the reverse reaction of recombination and of the reaction of β-scission decomposition or of isomerization consuming the diradical, respectively (Figure 9a).

Diradical BR1 reacts mainly by isomerization to form 3-cyclopentyl-cyclopentene. At 1000 K, k 1 is equal to 9.5×10 -2 s -1 according to Table 2, k -1 is equal to 1.3×10 9 s -1 according to Table 2 and k 2 is equal to 3.8×10 11 s -1 according to Table 3. This leads to a global rate constant k g(BR1) of about 9.5×10 -2 s -1 .

Diradical BR2 is less stable than diradical BR1 as shown in Table 1 and the activation energy of its main isomerization is much larger. At 1000 K, the values of k 1 , k -1 and k 2 are respectively equal to 1.9 s -1 (Table2), 3.8×10 13 s -1 (Table 1) and 1.3×10 9 s -1 (A 2 = 9.7×10 9 xT s -1 and Ea 2 = 17.5 kcal.mol -1 ), leading to a global rate constant k g(BR2) of 6.5×10 -5 s -1 which is lower than the previous value of a factor 1500.

FIGURES 15-16

As explained in the description of the mechanism six radicals are obtained through reactions of metathesis on the reactant. Radicals obtained through path 1 are mainly consumed to form ethylene and a C 8 radical species which leads to the formation of toluene and methyl radicals (45.6%) and to the formation of benzene and hydrogen radical (45.6%). Radicals obtained through path 2 lead to cyclopentadiene and methyl radical (16.0%), cyclopenten-3-yl radical (precursor of cyclopentadiene) and 1,4-pentadiene (8.7%) and 3-ethenyl-cyclopentene through two ways (66.5 and 8.7%). The formation of 3-ethenyl-cyclopentene has not been detected experimentally. This species should react through secondary reactions to produce toluene. Radicals of path 3 are mainly consumed through β-scission decompositions to form ethylene and a new C 8 radical that leads to the formation of cyclopentadiene and allyl radical through several isomerizations and β-scission decompositions.

Radicals of path 4 lead mainly to cyclopentene and cyclopenten-4-yl radical (precursor of cyclopentadiene). Discussion on path 5 (unimolecular initiation) has been previously presented.

Radicals formed through path 6 mainly produce allyl radicals and norbornene. Norbornene reacts easily through retro Diels-Alder reaction (concerted mechanism) to form ethylene and cyclopentadiene (39).

Radicals obtained through path 7 are consumed through two ways, 62.3 % of them give cyclopentadiene and cyclopenten-3-yl and 37.4% ethylene and benzene through several isomerizations and β-scission decompositions.

As there are too many ways of formation of light products such as hydrogen, propene (mainly formed through metatheses of hydrogen radical or of allyl radical on the reactant) and ethylene, Table 10 displays only the main ways of production of cyclopentadiene, cyclopentene, benzene and toluene.

Cyclopentadiene comes from path 3 of Figure 15 (28.6%) and from the concerted decomposition of norbornene formed through paths 2 and 6 (28.1%). It is also formed from cyclopenten-4-yl radical (21.6%), cyclopenten-3-yl radical (4.6%) and 3-methyl-cyclopenten-5-yl radical (3.9%). Another source of cyclopentadiene is the molecular decomposition of cyclopentene (10.8%). Cyclopentene is mainly obtained from path 4 (44.4%). It is also formed through path 7 (17.9%) and through the metathesis of the cyclopenten-3-yl radical on the reactant (31.2%). Benzene is mainly obtained though the paths 1 and 7 (respectively 65.6 and 25.2 %). Another source of formation is the reaction of allyl radicals with propargyl radicals (8.3%). The formation of toluene mainly occurs through path 2 (98.9%). Path 5 (unimolecular initiation step) is the only source of formation of 3-cyclopentyl-cyclopentene and 1,5-hexadiene is obtained from the combination of two allyl radicals.

TABLE 10

Figure 17 displays sensitivity analyses related to the mole fractions of tricyclodecane, 3-cyclopentyl-cyclopentene, cyclopentadiene and benzene. They were performed at a temperature of 933 K and at a residence time of 1 s. Sensitivity analysis on tricyclodecane shows that the conversion of the reactant is controlled by three types of reactions: the reaction of unimolecular initiation of tricyclodecane leading to the formation of diradical BR1, the reactions of metathesis of allyl radicals on tricyclodecane and the reaction of unimolecular initiation of 3-cyclopentyl-cyclopentene which leads to the formation of the diradical BR60. The formation of 3-cyclopentyl-cyclopentene is mainly ruled by the reaction of unimolecular initiation of tricyclodecane to BR1. Two reactions have an influence on its consumption: the unimolecular initiation leading to diradical BR60 and to a lesser extent the unimolecular initiation producing radicals R175 and R69. Like the conversion of tricyclodecane, the formation of products, such as cyclopentadiene and benzene, is mainly ruled by the unimolecular initiations of tricyclodecane and 3-cyclopentyl-cyclopentene giving diradicals BR1 and BR60, respectively, and by reactions of metathesis of hydrogen, methyl and allyl radicals on tricyclodecane.

The formation of benzene is also influenced by reactions (1.5), (1.6), (6.1) and (6.2) of figures 15-16.

Indeed reactions (1.5) and (1.6) are competitive: reaction (1.5) leads to the formation of toluene and methyl radical whereas reaction (1.6) leads to the formation of benzene, ethylene and hydrogen radical. This is the same explanation for reaction (7.1) and ( 7.2): reaction (7.2) is a way of formation of benzene whereas path (7.1) produces C 5 species.

FIGURE 17

According to flow rate and sensitivity analyses some simplifications of the mechanism can be done.

As previously explained reactions of unimolecular initiation of the tricyclodecane exclusively lead to the formation of 3-cyclopentyl-cyclopentene and it is possible to consider the only reactions of unimolecular initiation and of isomerization which form this species. It was shown that 3-cyclopentyl-cyclopentene mainly reacts by unimolecular reactions. Reactions of metathesis of radicals on this species (bimolecular reactions) can be neglected because in the conditions of the study presented here its concentration remains low (the rate of consumption of this species is of the same magnitude than its rate of formation). On the contrary reactions of metathesis of radicals on the initial reactant appeared to be very important and can't be simplified. It seems to be difficult to simplify the part of the mechanism related to the reactions of propagation of the radicals obtained from metatheses on the reactant (β-scission and isomerization) because kinetic parameters of these two kinds of reactions are of the same magnitude.

The conversion of tricyclodecane is greatly influenced by unimolecular initiations, that was also true in the case of the thermal decomposition of n-dodecane (18). While an unimolecular initiation of a linear alkane leads directly to the formation two free radicals which can react by metathesis with the reactant and promote chain reactions, the unimolecular initiation step of tricyclodecane leads to a stable molecule, which only at its turn decomposes to give two active radicals. Therefore, despite the fact that unimolecular initiations are easier for strained polycyclic compounds than in linear hydrocarbons, the reactivity of tricyclodecane is much lower than that of n-dodecane as shown in Figure 2c.

The under-estimation observed for light products, such as hydrogen, methane, ethane and propene, is mainly due to the fact that secondary reactions of middle weight primary products have not been comprehensively taken in account at this step of the study. Light hydrocarbons are primarily obtained from the reactant through numerous channels (see fig. 15 and16), but also from intermediate middle weight products through secondary reactions which are not included in the model presented in this paper (excepted for the primary products which are taken in account in the C 0 -C 6 reaction base). Future work will involve the writing of an n-airy mechanism in which the reactions of primary products (such as 3-ethenyl-cyclopentene for example, whose formation is predicted by the model, but which is not detected experimentally) will be detailed.

CONCLUSION

The thermal decomposition of tricyclodecane has been studied in a jet-stirred reactor over a range of temperature from 848 K to 933 K and for residence times between 0.5 and 6s. Conversion of the initial hydrocarbon varied between 0.01 and 25%. Eleven products of the reaction were identified. Major products are hydrogen, ethylene, propene and cyclopentadiene. Products such as cyclopentadiene, benzene and toluene which are often secondary products seem to have here primary sources.

A comprehensive detailed kinetic model has been written using a systematic method and by following a diradical approach for the unimolecular initiation step of tricyclodecane. Kinetic parameters were taken from literature when available or deduced from estimation performed by theoretical density function theory calculations in the case of reactions involving cyclic compounds and diradicals.

Agreement between experimental and computed mole fractions is satisfactorily for both the conversion of the reactant and most products of the reaction. The under-estimation observed for some light products underlines the need to write a n-airy mechanism in which the reactions of primary products will be more comprehensively detailed.

Flow rate and sensitivity analyses were performed at a temperature of 633 K and at a residence time of 1 s. The results of these analyses underlined the importance of the reactions of unimolecular initiation of tricyclodecane and of 3-cyclopentyl-cyclopentene for conversion of the initial hydrocarbon. Another future work would be a reduction of this comprehensive, but certainly in some ways uselessly detailed mechanism, by using the results of flow rate and sensitivity analyses.

TABLE 1 : Thermodynamic data of the 7 diradicals directly obtained from tricyclodecane (see Figure 6) and for the 2 radicals and the 5 diradicals deriving from 3-cyclopentyl-cyclopentene (see Figure 7).

Values in bold have been determined by quantum calculations. (units: kcal.mol -1 for ΔHf°, cal.mol -1 .K -1

for S° and Cp°).

Cp° Species

ΔHf° a Ring strain energy taken equal to twice that of cyclopentane according to Benson [START_REF] Benson | Thermochemical Kinetics[END_REF].

(298 K) S° (298 K) (300 K) (400 K) (500 K) (600 K) (800 K) (1000 K) (1500 K)
b Ring strain energy taken equal to the sum of those of cyclopentane and cyclohexane according to Benson [START_REF] Benson | Thermochemical Kinetics[END_REF].

c Ring strain energy taken equal to that of norbornane according to Benson [START_REF] Benson | Thermochemical Kinetics[END_REF].

d Formation of two cyclic radical species.

e Ring strain energy taken equal to the one of cyclopentane or of the one of cyclopentene according to Benson [START_REF] Benson | Thermochemical Kinetics[END_REF].

f Activation energy for a broken bond in position β of a Csp 2 -Csp 2 bond taken equal to that of the decomposition of 1-pentene to give allyl and ethyl radicals (8). a Activation energy taken equal to that of model reaction 7 in Table 8.

b Activation energy taken equal to that of model reaction 4 in Table 8.

c Activation energy taken equal to that of model reaction 8 in Table 8.

d Activation energy taken equal to that of model reaction 9 in Table 8.

e Activation energy taken equal to that of model reaction 10 in Table 8. written for the radical formed by the reaction of metathesis (6) of Figure 13 and their rate constants.

Activation energies are given in kcal.mol -1 and A-factors in s -1 . b Activation energy of model reaction 6 and 7 deduced from model reaction 5 and from the correlations used in the Exgas software (16).

Product

Table 10 : Formation flow analysis for cyclopentadiene, cyclopentene, benzene and toluene (see Figure 15 and Figure 16). enthalpy of reaction Δ r H (1000 K) (17).

Species

FIGURES 6- 7 a

 7

E - 1

 1 the activation energy of the reaction of the closure of the diradical. It was observed that the sum DH(C-C)+E -1 is almost constant (it fluctuates around 87 kcal.mol -1 ) for numerous cycloalkanes such as cyclohexane, cyclopentane, cyclobutane and cyclopropane. For tricyclodecane activation energy E 1 was obtained by substracting the difference of ring strain energy ΔE TC to 87 kcal.mol -1 . When the broken bond was in β position of a double bond the activation energy was estimated in the same way by assuming that the sum DH(C-C)+E -1 was close to the activation energy of the breaking of the allylic bond in 1-pentene (Ea=71.2 kcal.mol -1 (8)). The ring stain energy of tricyclodecane (22 kcal.mol -1 ) has been deduced from the enthalpy of formation experimentally measured by Boyd et al. (31) by subtracting the sum of the contributions of groups as proposed by

  shows how the diradical deriving from cyclohexane can either give back the initial hydrocarbon by cyclisation (reverse reaction of unimolecular initiation) or react by β-scission decompositions to give molecules and/or smaller diradicals and by isomerization to form 1-hexene. This isomerization, which involves the internal transfer of a H-atom in β-position of a radical center, transforms a diradical in a stable molecule and acts then as an internal disproportionnation. Billaud et al.(12) have proposed similar types of reactions in the case of decaline. The energy diagram of Figure9bshows the energy levels associated to the reactions involved in cyclohexane unimolecular initiation step. Energy of the transition state appears clearly smaller in the case of the isomerization of the biradical obtained from unimolecular initiation of cyclohexane than in the case of its reaction of decomposition through β-scission.

Figure 7 .

 7 Figure 7. We have thus obtained 250 reactions involving 48 diradicals, 6 radicals and 127 molecules for

are shown in Figure 12 .

 12 FIGURE 12

a

  Breaking of a bond in β position of two radical points as shown in Figure 10b (Ea=22.5 kcal.mol -1 ).b 10 kcal.mol -1 were added to the activation energy because of initial resonance stabilized radical.

Figure 1 :Figure 2 :

 12 Figure 1: Structure of (a) exo-tricyclo[5.2.1.0 2,6 ]decane, also called exo-tetrahydrodicyclopentadiene or

Figure 3 :Figure 4 :Figure 5 :

 345 Figure 3: Mole fractions of light products vs. residence time at several temperatures for an initial

Figure 7 :Figure 9 :

 79 Figure 7: The 2 radicals and the 5 diradicals which can be obtained from 3-cyclopentyl-cyclopentene by unimolecular decomposition involving the breaking of a C-C bond.

Figure 10 :

 10 Figure 10: Scheme of β-scission decompositions involving the breaking of a Csp 3 -Csp 3 bond in β-position of two radical centers (a, b) and model reaction used for the determination of the activation

Figure 11 :

 11 Figure 11: Activation energy of β-scission decomposition of acyclic compounds Ea (acyclic β-scission) vs.

Figure 14 :

 14 Figure 14: β-scission decomposition of the cyclohexyl radical and the two reverse reactions of

Figure 15 :

 15 Figure 15: Major flows of consumption of tricyclodecane at a temperature of 933 K, a residence time of 1 s and a initial hydrocarbon mole fraction

Figure 16 :

 16 Figure 16: Minor flows of consumption of tricyclodecane at a temperature of 933 K, a residence time of 1 s and a initial hydrocarbon mole fraction

Figure 17 :

 17 Figure 17: Sensitivity analyses for (a) tricyclodecane, (b) 3-cyclopentyl-cyclopentene, (c) cyclopentadiene and (d) benzene (T=933 K, τ=1 s).

TABLE 6 16

 6

b/ Propagations by β-scission

TABLE 2 :

 2 Activation energies of the unimolecular initiations by breaking of C-C bonds from tricyclodecane (ring strain energy of 22 kcal.mol -1 ) and 3-cyclopentyl-cyclopentene (ring strain energy of 12 kcal.mol -1 ). The reactions in bold are those with the higher flow rate under the conditions of our study.

	Unimolecular initiation (see figures 6 and 7)	Diradical ring strain energy (kcal.mol -1 )	Lost ring strain energy (kcal.mol -1 )	Activation energy (kcal.mol -1 )
		from tricyclodecane (see figure 6)
	1	12 a	10	77
	2	6 b	16	71
	3	12 a	10	77
	4	12 a	10	77
	5	16 c	6	81
	6	16 c	6	81
	7	16 c	6	81
		from 3-cyclopentyl-cyclopentene (see figure 7)
	(1) d	-	-	71.2 f
	2	6 e	6	65.2 f
	3	6 e	6	65.2 f
	4	6 e	6	81
	5	6 e	6	81
	6	6 e	6	81

TABLE 3 :

 3 Products and rate constants of the β-scissions and isomerizations written for the diradical formed by the initiation (1) of Figure6. Activation energies are given in kcal.mol -1 and A-factors in s -1 .

	Product	Reaction pathway	A		b	Ea
		Diradical obtained from tricyclodecane
		y
		4		z
		1	x	3
		w	2
		5
	+	Breaking of bond 1	2.0×10 13	0	30.4 a
		Breaking of bond 2	2.0×10 13	0	35.9 b
		Breaking of bond 3	2.0×10 13	0	37.5 c
		Breaking of bond 4	2.0×10 13	0	34.8 d
		Breaking of bond 5	2.0×10 13	0	37.7 e
		Isomerization by transfer
		of H-atom w through a 6 members ring for	1.9×10 10	1	19.85
		the transition state
		Isomerization by transfer
		of H-atom x through a 5 members ring for	9.7×10 9	1	17.75
		the transition state
		Isomerization by transfer	y 1.9×10 10	1	7.75
		of H-atoms y or z
		through a 5 or a 7 members ring for the transition state	z 1.9×10 10	1	27.75

TABLE 4 :

 4 Products and rate constants of the β-scissions and isomerizations written for the diradical formed by the initiation (2) of Figure7. Activation energies are given in kcal.mol -1 and A factors in s -1 .

	Product	Reaction pathway	A	b	Ea
		Diradical BR60 obtained from 3-cyclopentyl-cyclopentene
		x	1	x	1
	+	Breaking of bond 1	3.3×10 13	0	22.5 a
		Isomerization by transfer
		of H-atom x through a 5 members ring for	2.9×10 8	1	17.75 b
		the transition state
		Isomerization by transfer
		of H-atom x through a 3 members ring for	1.7×10 9	1	19.50 b
		the transition state
		Isomerization by transfer
		of H-atom x
		through a 3 members ring for
		the transition state

Table 5 :

 5 Ring strain energies for some cyclic and polycyclic hydrocarbons.

	Name of the (poly)cyclic species	Ring strain energy (kcal.mol -1 )
	cyclobutane	26 a
	cyclopentane	6 a
	cyclohexane	0 a
	bicyclo[2.2.1]heptane (norbornane)	16 a
	bicyclo[3.2.1]octane	16 b
	bicyclo[4.2.1]nonene	26 b
	tricyclodecane	22 c
	a Ring strain energy according to Benson (20).

b Ring strain energy calculated by Maier and Schleyer Von Rague (36).

c Ring strain energy calculated by Boyd et al.

(31)

.

TABLE 6 :

 6 Quantitative Structure-Reactivity Relationships. Rate constants are expressed in the form k = A×T b ×exp(-E/RT) (with the units cm 3 , mol, s, kcal) by H atoms which can be abstracted or by bonds which can be broken. R p, R s and R res. stab. are primary, secondary and resonance stabilized free radicals, respectively.

	H-abstraction reactions
		Secondary alkylic H Tertiary alkylic H Secondary allylic H Tertiary allylic H
		lg A	b	E	lg A	b	E	lg A	b	E	lg A	b	E
	H	6.65	2	5.0	6.62	2	2.4	4.43	2.5	-1.9	4.40	2.5	-2.79
	CH 3	11	0	9.6	11	0	7.9	10.7	0	7.3	10.7	0	5.6
	C 2 H 5	11	0	11.0	11	0	9.2	0.34	3.5	4.14	0.34	3.5	2.34
	R res. stab. 1.6	3.3	18.17	1.6	3.3	17.17	1.6	3.3	18.17	1.6	3.3	17.17
	Beta-scission reactions which do not involve a ring
								lg A		b		E
	Beta-scission of a free radical to
		CH 3 + alcene						13.3		0		31.0
		R p + alcene						13.3		0		28.7
		R s + alcene						13.3		0		27.7
		R res. stab. + alcene					13.5		0		22.5
		CH 3 + diene						13.1		0		38.2
		H(secondary) from an alkyl radical			13.2		0		34.8
		H(tertiary) from an alkyl radical			13.2		0		34.3
		H(primary) from an allylic radical			13.2		0		51.5
		H(allylic) from an allylic radical			13.2		0		40.7
		H(vinylic) from an allylic radical			13.1		0		60.0

TABLE 7 :

 7 List of the first reactions of propagation (β-scission decompositions and isomerization)

  Activation energy taken equal to that of model reaction 6 in Table 8 with 6.2 kcal.mol -1 subtracted because of the formation of an allylic radical.

	Reaction pathway		A	b	Ea
	Radical directly obtained from metatheses on tricyclodecane
		1
	Breaking of bond 1		4.0×10 13 a	0	34.80 b
	Radical obtained from β-scission of the previous radical
	4
	3
	2	1	x
	Breaking of bond 1		3.3×10 13	0	25.20 c
	Breaking of bond 2		2.0×10 13	0	35.90 d
	Breaking of bond 3		2.0×10 13	0	35.90 d
	Breaking of bond 4		2.0×10 13	0	35.90 d
	Isomerization by transfer of
	H-atom x through a 4 members ring for the		3.3×10 9	1	32.50 e
	transition state

a Two identical bonds can be broken .

b Activation energy taken equal to that of model reaction 9 in Table

8

. c d Activation energy taken equal to that of model reaction 4 in Table

8

.

e Presence of side rings neglected.

TABLE 8 :

 8 Activation energies of model β-scission decompositions by fission of a C-C bond of five-membered ring species calculated by quantum methods. Values in bold are from the literature.

		Reaction		Activation energy (kcal.mol -1 )
	1			33.5 34.4 a
	2			24.1
	3			37.8
	4			35.9
	5		+ CH 3	33.7
	6	R	+ R P	31.4 b
	7	R	+ R S	30.4 b
	8			37.5
	9			34.8
	10			37.7
	11		+ CH 3	34.3
	12		+ C 2 H 4	26.3 27.7 c
	a Activation energy from (8)
	b Activation energy of model reaction 6 and 7 deduced from model reaction 5 and from the correlations used in the Exgas
	software (16,17).
	c Activation energy used in the Exgas software (17)

TABLE 9 :

 9 Activation energies of model β-scission decompositions by fission of a C-C bond of six-membered ring species calculated by quantum methods. Values in bold are from the literature.

		Reaction		Activation energy (kcal.mol -1 )
				31.0
	1			29.3 a
	2			19.2
	3			35.3
	4			33.4
	5		+ CH 3	31.2
	6	R	+ R P	28.9 b
	7	R	+ R S	27.9 b
	8			35.0
	9			32.3
	10			35.2

a Value deduced from the activation energy of the reverse reaction

(40)

.

  nC 3 H 7 =C 2 H 4 +CH 3 1-C 5 H 9 =CH 3 +1,3-C 4 H 6 1-C 6 H 11 =C 2 H 5 +1,3-C 4 H 6 5-CH 3 -1-C 6 H 10 =sC 3 H 7 +1,3-C 4 H 6 4-CH 3 -1-C 5 H 8 =CH 3 +1,3-C 5 H 8 nC 4 H 9 =C 2 H 5 +C 2 H 4 3-CH 3 -nC 4 H 8 =s-C 3 H 7 +C 2 H 4 vC 5 H 9 =C 2 H 5 +aC 3 H 4 1-C 5 H 9 =C 2 H 4 +aC 3 H 5 1-C 6 H 11 =aC 3 H 6 +aC 3 H 5 3,3-(CH 3 ) 2 -nC 4 H 7 =C 2 H 4 +tC 4 H 9 4-CH 3 -vC 5 H 8 =sC 3 H 7 +aC 3 H 4 5,5-(CH 3 ) 2 -1-C 6 H 9 =1,3-C 4 H 6 +tC 4 H 9 vC 4 H 7 =CH 3 +aC 3 H 4 3,3-(CH 3 ) 2 -nC 4 H 7 =C 2 H 4 +tC 4 H 9 C 4 H 9 =aC 3 H 6 +CH 3 2-CH 3 -C 4 H 8 =tC 4 H 8 +CH 3

ACKNOWLEDGMENTS

This work was supported by MBDA-France and the CNRS. The authors are very grateful to E. Daniau, M. Bouchez and F. Falempin for helpful discussions.

Figure 12: Structures assumed for the transition states of the isomerizations of Table 3.

(a)

metatheses with R (b)

Figure 13: The 6 tricyclic free radicals obtained from metatheses with tricyclodecane (a) and the 6 bicyclic free radicals obtained from metatheses with 3-cyclopentyl-cyclopentene (b). 50