Jan Bartovsky
email: j.bartovsky@esiee.fr

Dominik Schneider
email: d.schneider@esiee.fr

Eva Dokladalova
email: e.dokladalova@esiee.fr

Petr Dokládal
email: petr.dokladal@mines-paristech.fr

Vjaceslav Georgiev

Mohamed Akil
email: m.akil@esiee.fr

P Dokladal

Morphological Classification of Particles Recorded by the Timepix Detector

come   L'archive ouverte pluridisciplinaire

I. INTRODUCTION

The Timepix device is a new generation of CMOS pixel detectors -derived from the Medipix2 detector and designed by CERN -allowing three types of measurements: i) "time of arrival" (ToA), ii) "time over threshold" (ToT) and iii) and counting [START_REF] Llopart | Timepix, a 65k programmable pixel readout chip for arrival time, energy and/or photon counting measurements[END_REF]. In counting mode, the Timepix pixels increment the counter each time the deposited energy exceeds the threshold. In ToA mode the pixel records the timestamp of the hit. In ToT mode, the pixels value indicates the total deposited energy. Three operating modes supported by one chip enable a large scale of applications; from astronomical observations, X-ray fluorescence imaging to event reconstruction in physical numerous experiments (i.e., analyse radioactive fluxes from unknown radioactive sources). The device allows a high sampling rate; it can record up to 3000 frames per second (fps).

Behind the CMOS sensor, there is a threshold allowing to suppress the noise, retaining only the energy of the particles [START_REF] Jakubek | Precise energy calibration of pixel detector working in time-over-threshold mode[END_REF]. This eases the image processing, since those pixels that do not receive a sufficient energy deposit (above threshold) from a particle contain a zero value. Consequently, the obtained images are considered as noise-free.

The principle of the event reconstruction is based on the charged particle recognition and its class identification (e.g., α, γ, electrons, etc.), followed by some statistical measurements (i.e., major particles and their angle of incidence) [START_REF] Bouchami | Measurement of pattern recognition efficiency of tracks generated by ionizing radiation in a medipix2 device[END_REF]. The particles recognition requires to identify and analyse the trace, representing the particle's "signature", left by the particle whenever it strikes the Timepix detector. The different particles leave differently shaped traces in dependence on the type of the particle, its energy and incidence angle. Consequently, the shape and the energy deposited alongside every track can be used for identification of the particle [START_REF] Bouchami | Measurement of pattern recognition efficiency of tracks generated by ionizing radiation in a medipix2 device[END_REF].

In this paper, we concentrate on the application of the Mathematical Morphology (MM) tools to the particle classification. The MM has been introduced in late sixties and the particle classification is a standard issue addressed by the MM from its beginning [START_REF] Klein | The texture analyser[END_REF], [START_REF] Serra | Image Analysis and Mathematical Morphology[END_REF]. In addition, the attention paid to realtime implementations [START_REF] Ch | A system on chip dedicated to pipeline neighborhood processing for mathematical morphology[END_REF], [START_REF] Bartovsky | Pipeline architecture for compound morphological operators[END_REF] results in efficient and modular solutions on various kind of hardware platforms, such as CPU, GPU or FPGA.

The organization of the paper is as follows: Section II introduces a notion of classification and Section III outlines main principles of our method. The proposed hardware implementation is detailed in Section VI.

II. CLASSIFICATION USING MORPHOLOGICAL CHARACTERISTICS

The Timepix device records a sequence of grey-valued images I: D × t → V . The support D ⊂ Z 2 is a rectangular 256×256 raster. The images are scalar-valued with the set of values V coded in 14 bits, with positive integer values from [0, 16383].

In the following, one cluster denotes a connected component of non-zero pixels. One cluster corresponds to the trace left by one particle (or more particles, if they overlap). In this work, though, we suppose that one cluster is left by only one particle.

The set of all traces observed at time t is defined as CC{(x, y) | I(x, y, t) > 0}, where CC denotes the connected components in a set, obtained with the 8-connectivity.

Each connected component can be associated with descriptors allowing to classify the particles into different classes. The most frequently used are morphological descriptors (based on the shape analysis), i.e. the area, the projected and the unrolled length, the skeleton, the geodesic diameter, the circularity, the tortuosity, etc. see [START_REF] Soille | Morphological Image Analysis: Principles and Applications[END_REF].

The descriptor-based classification methods are very efficient; their drawback though is the computing complexity. They require the computation of connected components, labeling, skeletonization and reconstruction, even before the descriptors can be computed. Even if optimized [START_REF] Matas | Parallel algorithm for concurrent computation of connected component tree[END_REF], the skeletonization and reconstruction are iterative, with datadependent computational intensity. Such properties infer high memory requirements, undefined latency, and slow computation inapplicable in high-frame-rate applications.

It is clear that the efficiency of the image processing bounds the sampling frequency of the image acquisition. At the same time, a high sampling frequency, limits the probability of overlapping traces.

This work presents a fast classification method based only on two descriptors, the thickness and the projected length. It uses only the morphological dilation and erosion, and simple arithmetic operators, and avoids all iterative, costly algorithms.

Implemented in a dedicated hardware, it takes advantage of recently proposed fast implementation of dilation and erosion. Thanks to the pipelining, the input image is classified in a single image scan at very high frame rate, reaching 738 fps. Furthermore, the proposed architecture is extensible in terms of the number of trace types to classify.

III. METHOD DESCRIPTION

In this study, we consider three main classes of traces called blobs, dots and tracks, see Fig. 1. These names correspond to the nuclear physics terminology used in [START_REF] Bouchami | Measurement of pattern recognition efficiency of tracks generated by ionizing radiation in a medipix2 device[END_REF] and [START_REF] Jakubek | Precise energy calibration of pixel detector working in time-over-threshold mode[END_REF]. The dots are generated by, e.g., low-energy electrons or photons. The blobs are left by α or heavy ions. And the linear or curly tracks are produced by minimum ionizing particles or electrons.

A. Mathematical background

At first, let us to introduce the basic MM operators [START_REF] Serra | Image Analysis and Mathematical Morphology[END_REF]. Let f : Z 2 → R denote a digital image. Then δ B (f ) denotes a dilation of f by a structuring element B, whereas ε B denotes the erosion of f by B. In this paper, the structuring element B ⊂ Z 2 is assumed rectangular and translation-invariant. The dilation and the erosion operations are defined by

δ B (f ) = b∈B f b and ε B (f ) = b∈ B f b (1)
where f b denotes the translation of f by some vector b. The B is the transposition of the structuring element (SE), equal to the set of reflection B = {x|x ∈ B}.

The concatenation of erosion and dilation forms a morphological opening

γ B (f ) = δ B ε B (f ) (2)

B. Residual approach for particle classification

The particle extraction based on the shape features and measurements is a classical problem of Mathematical Morphology [START_REF] Devaux | Particle size analysis of bulk powders using mathematical morphology[END_REF], [START_REF] Lee | A mathematical morphology approach to image based 3d particle shape analysis[END_REF].

Consider a family of shapes Ξ and an image I Ξ containing objects from Ξ. The shape ξ i ∈ Ξ can be extracted from I Ξ by opening γ ξi

I Ξ ′ = γ ξi I Ξ (3)
where Ξ ′ = Ξ \ {ξ i }, and I Ξ ′ = I Ξ -I ξ i . This type of opening is commonly considered as algebraic opening. If Ξ is ordered, the shapes {ξ i } can be extracted one by one. This approach proceeds in a few steps each of which recognizes and extracts one type of particles retaining the other particles intact in the residual image. The following step extracts another particle and so on.

The algebraic opening γ ξi from Eq. 3 can be constructed by morphological opening by reconstruction using the following steps:

1) Marker selection. It selects particles according to some criterion. A marker image m : Z 2 → R is commonly an image containing non-zero values intersecting the marked objects, and zero elsewhere. In the following, m ξi will be used to mark objects of the shape ξ i . 2) Object reconstruction (e.g. [START_REF] Serra | An overview of morphological filtering[END_REF], [START_REF] Schmitt | Morphologie mathématique[END_REF]), recovers from the marker m the original values and shape from f . It is based, in general, on the geodesic dilation of m under

f , m < f , δ f (m) = δ(m) ∧ f (4)
hence from, by iteration

(δ f ) n (.) = δ f [(δ f ) n-1 (.)] (5)
we obtain the reconstruction

R f (m) = lim n→∞ (δ f ) n (m) (6)
Here we have a family of shapes Ξ = {α, γ, ǫ}. The process of separation based on a cascade of openings is a binary, decision tree classifier, see Fig. 2. First, we extract the thick dots (the α particles), second, the thin tracks (the ε particles). Finally, the last residual image will contain the dots (γ particles) only. The reconstruction is an iterative process based on the geodesic dilation Eq. 4 with unitary geodesic ball as structuring element (omitted for brevity). We will show that these stages can be approximated by a concatenation of basic morphological operators, erosion/dilation, and simple arithmetical operations. It can be computed only in one scan of the input image and "on the fly" without intermediate memory.

In the following section we describe in detail the proposed filter-based method of the morphological classification of particle traces.

IV. IMPLEMENTATION

As indicated above, the extraction of a shape ξ i is done by algebraic opening γ ξi , constructed by morphological opening by reconstruction.

Recall that the reconstruction is iterative process, iterated until idempotence. Given the restricted, and known family of shapes, we can approximate the reconstruction by only one geodesic dilation.

Hence, the stages consist of the following steps. 1) extraction of marker of the shape ξ by a morphological opening

m ξ = γ B ξ I (7)
2) geodesic dilation (approximating the reconstruction) of the marker under the image

I m ′ = δ I B (m ξ ) (8)
3) extraction of the image I ξ containing the ξ-shaped objects

I ξ = I if m ′ > 0 0 elsewhere (9)
Based on this scheme, Eqs. 7-9, the particle classification is done in the following order. (Refer to Tab. I for parameters of the structuring elements. The reconstruction step uses alike structuring element B for both shapes α and ε.)

1) blobs -First we obtain I α from the initial image I {α,ε,γ} . The residual image is I {ε,γ} = I {α,ε,γ} -I α .

2) tracks -Second, we obtain I ε . The usual morphological approach to detect curvilinear objects is to use the supremum of openings γ B ϕ by a rotating linear segment B ϕ , oriented in ϕ. It is well known that a supremum of openings is itself an opening.

γ = ϕ∈Φ γ Bϕ (10)
The tracks are thin, curvilinear, oriented in arbitrary angle. This reguires a fine angular sampling of Φ, resulting in a high computational cost.

Here, to limit the number of discrete angles ϕ ∈ Φ, we thicken the tracks by a dilation perpendicular to the opening. This allows to obtain satisfactory results with only two discrete angles, horizontal and vertical Φ = {H, V }. Hence, using Eq. 10 for γ B ξ in 7, with ξ = ε, we obtain

m ε = ϕ=H,V γ B ε ϕ δ B ′ ϕ I {ε,γ} (11)
where B V = rot(B H ), the copy of H rotated by 90 o , for both B ε and B ′ .

3) dots -Finally, the residuum image I γ = I {ε,γ} -I ε contains the dots, i.e. the gamma particles.

V. EXPERIMENTAL RESULTS

To evaluate the proposed classification method, we have performed a statistical measuring of the traces' dimensions on randomly selected images of the Timepix database. The results suggests that the diameter of blob traces is at least 4 px. Therefore, the thickness criterion R equal to 4 (accords to B α = [START_REF] Klein | The texture analyser[END_REF][START_REF] Klein | The texture analyser[END_REF]) identifies the blobs.

On the other hand, the dot traces fit inside 2×2 bounding box. So the length parameter L equal to 3 (see

B H =[1, 3])
separates tracks from dots. The approximated reconstruction uses in both cases the SE of the marker's erosion plus one pixel in all directions. Such SE has the minimal surface necessary for the proper recovery of the original shape (cf. Table I).

The computed confusion matrix, see Table II, allows to appreciate the performance. The resulting errors are mainly due to: i) the border effects: particles touching the image border are sometimes misclassified, ii) the limit cases: the proposed method only approximates (with rectangular SE) the measurements of the particle trace thickness and projected length. The result misclassification of the method is below 7% of particles (each type of particles considered separately). Extensions: Notice that the proposed method can be used to further analyse the three main classes by splitting them into sub-classes. The sub-classes definition is defined by the purpose of the particular physical measurement. We can illustrate this idea on the example of sorting the blobs with respect to their thickness. It requires to apply several consecutive blobs classification procedure with varying R.

Another example could be rough sorting of the track impact angles. The principle is to refine the angular sampling of Φ in Eq. 10.

VI. HARDWARE ARCHITECTURE

We present the hardware implementation of the proposed particle classification in this section.

The overall architecture is displayed in Fig. 3. It consists of a several Recognition Units (RU), Control Unit, and optional Visualization Memory if results are to be displayed. The classification of a given type of particles is carried out in one RU block. The RU performs three tasks as described in the previous section: (i) the marker creation, (ii) the reconstruction, and (iii) the residual image. The RU outputs two images, I ξ containing classified particles, and the residual image I Ξ ′ containing other particles.

In applications that need more types of particles to be recognized multiple RUs are instantiated in a pipeline (Fig. 3). It allows us to classify all types of particles concurrently on time-shifted data. The residual image of an RU is taken as an input by the following RU.

The control unit provides both controls and programmable parameters for each RU through ctrl ru x signal (which is a set of {ctrl mmb i, ctrl alb j}; i ∈ {1 : 5}; j ∈ {1 : 2}). The classified particles I ξi of any RU can be either read by a further block (RU, output, image compression, etc.) or stored in the global visualization memory.

A. Recognition Unit

The internal structure of the RU is shown in Fig. 4. First, the marker image m ξ is to be created. It is made by processing the image according to 7. Both ϕ = H and V in the supremum in [START_REF] Lee | A mathematical morphology approach to image based 3d particle shape analysis[END_REF] are independent and therefore separated in two parallel branches. Each branch computes one erosion and one dilation using two Mathematical Morphology Blocks (MMB1-4). The marker is completed from the parallel branches in Arithmetic Logic Block 1 (ALB1) that performs the .

In the second step, the marker m ξ is used in the approximated particle reconstruction. It consists of the marker dilation (MMB5) followed by threshold operation defined in eq. ( 9) with the input image. The result image I ξ containing only the desired particles is obtained through comparison with the RU input image, see [START_REF] Matas | Parallel algorithm for concurrent computation of connected component tree[END_REF]. Both previous operations are evaluated in ALB2.

Finally, the RU input image is split into two output images; I ξ with classified particles, and the residual image I Ξ ′ . This step is carried out in ALB2 as well. The FIFO memory connected between the input image and ALB2 must be sized properly to compensate the delay of the branch containing MMB{1:5}. For instance, let us consider that MMB{1:5} infer total delay of 5 image lines due to δ, ε intrinsic latency. The intrinsic latency is inavoidable and defined by dimensions of B. Hence, the FIFO must be capable of storing at least 5 image lines as well.

B. Morphological and Arithmetic Blocks

Both MMB and ALB are the basic elements of each RU. They have a few common properties. Both units are designed to work with the streamed data. Because the shortterm processing rate of MMB may vary with data [START_REF] Bartovsky | Pipeline architecture for compound morphological operators[END_REF], each block integrates a front-end FIFO to balance currently different processing rates.

The units are fully run-time programmable, i.e., the parameters modifying the behavior can be changed between two frames without any overhead, as well as they can be entirely bypassed. The bypass input parameter is commonly used by marker m ξ which needs only one MMB. When selected, a unit appears as a FIFO memory only. The ctrl contains the start and reset signals. The MMB performs either morphological dilation or erosion (it decides upon the funct select signal) on an input image by the structuring element B. The precedent version of the MMB was published at [START_REF] Bartovsky | Pipeline architecture for compound morphological operators[END_REF]. The funct, dimensions and origin position of B (W × H, note definition of B in Section III), and bypass are programmable parameters.

The ALB is intended to perform several arithmetic operations. Besides the reconstruction and the residue process described previously, basic arithmetic operations as min(), max(), <, >, >0, <0, addition, or subtraction is selected via funct parameter.

C. Application Demonstration

The application of particle traces classification into three types was implemented, see Fig.

Fig. 1 .

 1 Fig. 1. Examples of traces deposited by different particles.

Fig. 2 .

 2 Fig.2. Flowchart of residual approach. I {α,ǫ,γ} denotes the input image, and I α , I ǫ and I γ the result images.

Fig. 3 .

 3 Fig. 3. Overview of the proposed hardware implementation.

FIFOFig. 4 .

 4 Fig. 4. Internal structure of the RU. I ξ contains classified particles, I Ξ ′ is the residual image.

Fig. 5 .

 5 Fig. 5. Morphological and Arithmetic blocks

6 .

 6 It instantiates two RUs; the first I α classifies blobs using the m α marker image outputting dots and tracks in the residual image. The residual image of RU1 is read by the second RU2 that uses the marker m ε to classify tracks I ε . Hence, the residual image of RU2 I Ξ ′ = I γ contains dots only. All three outputs are stored in on-chip Visualization Memory and displayed on a screen.

Fig. 6 .

 6 Fig.6. Overview of application that classifies dot, blob, and track particle traces, see Section III.

TABLE III TIMING

 III RESULTS OF THE CLASSIFICATION.

	Image type	Time [ms]	Latency [µs]	Rate [fps]
	Best case	1.352	3.154	739
	Worst case	1.678	39.4	594
	Average Timepix	1.356	31.6	738

http://www.utef.cvut.cz

ACKNOWLEDGEMENT

The authors thank Ing. S. Pospíšil, DrSc. and Ing. J. Jakůbek, PhD. from IEAP 1 , Czech Republic, for the initial discussion and the motivation of this work, and to Ing. Z. Vykydal for preparing the images. The authors are grateful for their permission to use the Timepix images (property of IEAP) in this publication.

D. Implementation Results

The proposed demonstration application has been targeted to Xilinx Virtex-5 FPGA (XC5VLX50T-1). Although the maximal synthesis frequency is about 160 MHz, the design is clocked by 100 MHz. The design (without the optional visualization) occupies the following hardware resources: 1405 registers, 4495 of 6-input look-up tables, and 9 36-kbit on-chip block RAMs.

The time benchmarks of the proposed design were performed on a set of Timepix images, each containing a mixture of all three kinds of particles. The results are outlined in Table III. All Timepix images were processed in almost the same time with minimal differences, so we use the average value. The worst case presents the lowest granted stream performance obtained on the most unpleasent gray-level image (artificial image containing monotonous gradient) whereas the best case conforms to the constant image. One can see that processing of Timepix image is very close to the best case since the Timepix image contains many zero-valued areas.

VII. CONCLUSIONS

In this paper, we presented the method of particle traces classification using the filter-based morphological markers instead of descriptors based on connected components, which are very computation intensive. The classification recognizes three main types of traces: dots, blobs, and tracks; and can be naturally extended. We proposed the dedicated FPGA hardware architecture of the method. It processes the input image in a stream inferring the minimal latency. We achieved very high performance rate of 738 frames per second thanks the streaming pipeline structure. The high frame rate allows the Timepix detector to acquire images with a high sampling frequency, reducing thus the appearence of overlapping particles that can not be classified.


Nadine Lahoud

Jérôme Faucher

David Malec

Pascal Maussion
email: pascal.maussion@laplace.univ-tlse.fr

Electrical Ageing Modeling of the Insulation of Low Voltage Rotating Machines Fed by Inverters with the Design of Experiments (DoE) Method

Keywords: insulating and magnetic materials, remaining life models, ageing tests, design of experiments; ageing model

In the context of more electric aircrafts, the reliability of the low voltage insulation systems in rotating machines is an important issue. But, modeling and understanding their electrical ageing is a complex phenomenon especially when they are fed by PWM inverter. They involve a large amount of parameters related to both operating conditions and material design, which act together. Accelerated ageing tests are usually run in order to describe the electrical ageing process and to determine the lifetime of these materials. Nevertheless, full ageing tests with all the various parameters for different samples become rapidly time consuming. Moreover, there is not any complete model for insulation lifetime prediction under accelerated ageing tests. In this paper work, we propose a method based on the design of experiments (DoE) method, which is a useful statistical approach that would lead to a reliable and significant interpretation of the different ordering parameters of the insulation ageing process. Moreover, this method will help to reduce the number of required experimental or numerical trials and will, take into account the possible failure mechanisms and the various synergetic effects between them. Using the (DoE) method, a preliminary model of the insulation "lifetime" is presented with respect to the most important parameters at play and interactions between them.

INTRODUCTION

Over the last decades, several models have been proposed for the electrical insulation life-end modeling [START_REF] Mazanti | Electrical ageing and life models: The role of space charge[END_REF][START_REF] Crine | On the interpretation of some electrical aging and relaxation phenomena in solid dielectrics[END_REF][START_REF] Lewis | Ageing -A perspective[END_REF][START_REF] Lahoud | A multi-dimensional model to describe the ageing process of polymers used for electrical insulation[END_REF] with respect to the physical, thermal and electro-mechanical aspects of the electrical ageing process. Despite these studies, this phenomenon remains complex and difficult to understand, forecast and at least model. Particularly, the rate of insulation degradation in rotating machines fed by inverters could be affected by many operating factors such as voltage, frequency, temperature, pressure… and these stresses could have many synergetic effects between them [START_REF] Lahoud | A multi-dimensional model to describe the ageing process of polymers used for electrical insulation[END_REF].

Accelerated ageing tests are usually undertaken in order to predict the insulation lifetime. These tests are used to obtain the failure statistics and determine a functional relationship between an applied stress (electrical, thermal, mechanical…) and the characteristic insulation lifetime. However, the choice of the applied stress and the lifetime forms remains critical. In this article, the "Design of Experiments" (DoE) method is used in order to compare and to validate two theoretical lifetime models presenting the same parameters, but with different forms. The first model presents the insulation lifetime variation with respect to a linear form of different external applied stresses. The second model takes into account logarithmic and exponential forms of the different parameters. These forms are chosen with respect to previous theoretical studies and some experimental results. In this study, the DoE method is briefly presented followed by the way this statistical method is applied on accelerated ageing test results in order to obtain and compare two mathematical lifetime models. For each one, an additional experimental test allows validating the theoretical result.

II. THE DESIGN OF EXPERIMENTS (DOE) METHOD

The history of design of experiments started in the 1930s in England with M. Fisher [START_REF] Fisher | The Design of Experiments[END_REF], but it knew an accelerating development since the publication of some predefined tables by Taguchi [START_REF] Taguchi | Orthogonal arrays and linear graph[END_REF]. The principle of this methodology is to carry out a schedule of experiments designed to obtain the most accurate information for a specific problem with a minimum number of experiments [START_REF] Atkinson | Optimum Experimental Designs[END_REF][START_REF] Montgomery | Design and Analysis of Experiments[END_REF]. Its advantages were proved in different areas of application, especially in chemistry and mechanics, where a large number of parameters have to be optimized simultaneously. This method has been used in electronics, circuits and devices, components and packaging, for the design optimization in some industrial electronics applications [START_REF] Teck-Seng | Robust torque optimization for BLDC spindle motors[END_REF] and for powerful non linear control of power converters [START_REF] Faucher | On-line electrical quality improvement of a single-phase boost rectifier with fuzzy controller and experimental designs[END_REF]. Different designs exist in order to go with a large number of applications, but the "Full factorial design" is chosen in this study.

A. Full factorial designs

Full factorial designs involve designing a set of experiments, in which all relevant parameters, called factors, are varied systematically. Thus, two levels, a high and a low, are chosen for each factor. The desired criterion, called the response, is measured for each combination of the different factor levels.

The main purpose of these designs is to gain information on the effects of the selected parameters. The idea is to modify the level of each factor in each experiment according to a specific procedure. This allows a drastic reduction of the number of required experiments, the possibility of taking into account much more parameters and the detection of interactions between factors. A very simple example with only two levels is presented in Table I. Centered reduced variables are used, i.e. (-1) for the low level and (+1) for the high level of each factor. Each line represents an experiment and each column is indexed to a factor. For each experiment (i), the selected criterion value (y i ) is measured. Criterion Yi

1 1 -1 -1 +1 y1 2 1 +1 -1 -1 y2 3 1 -1 +1 -1 y3 4 1 +1 +1 +1 y4

M

According to the design of experiments methodology [START_REF] Weibull | A statistical distribution function of wide applicability[END_REF], the effect of a factor is obtained through [START_REF] Mazanti | Electrical ageing and life models: The role of space charge[END_REF]. For example, E 1 = 0.12 means that the factor 1 at high level has an effect of +0.12 on the criterion with respect to the average value of the criterion, named M.

4 4 3 2 1 1 y y y y E (1)
Moreover, one keypoint of the DoE method is that the effect of interactions between factors 1 and 2 can also be determined. Equation [START_REF] Crine | On the interpretation of some electrical aging and relaxation phenomena in solid dielectrics[END_REF] presents the average effect of interaction E 12 between factor 1 and 2, on the desired criterion. Consequently, the mathematical model relating the response Y to the different factors has the form of (3) :

Y ~M + E F1 .F 1 + E F2 .F 2 + E F1F2 .I F1F2 ( 3
)
where Y is the response which represents the insulation lifetime in this case, M is the mean value for all ageing test responses, F i are the factor levels affecting the ageing process, I FiFj are the interactions between factors Fi and Fj, and E i are the effects of the factors or the effects of their interactions on the global response. It is also easy to verify that the effect vector (Ê) can be calculated trough the following matricidal relationship:

Ê = X -1 .Y i (4) with 2 . 1 2 1 ˆF F F F E E E M E ( 5
)
where Ê is the vector of the different factor effects on the criterion and their corresponding interactions, X is the matrix obtained from the experience plan as shown in the light grey part of Table I and Y i is the vector of the experimental result values presented in the last column of Table I.

B. Application of the DoE for lifetime modeling

In the domain of electrical insulation degradation, the DoE method has already been used for tracking the influent operating parameters on the insulation lifetime of kapton films [START_REF] Khelil | Experimental designs for tracking the influent operating parameters on insulation reliability[END_REF] and for the degradation analysis in terms of a better understanding of a reliable water-treeing test [START_REF] Crine | When Taguchi meets water treeing[END_REF]. In this paper, the DoE method is used to analyze the ageing process of organic rotating machines insulation. The input variables are, in this case, the parameters affecting the insulation degradation and the process output is the insulation lifetime.

These designs include all combinations of every factor level. The number of experimental runs depends on the number of levels of each factor [START_REF] Tanco | Experimental design selection: guidelines for practitioners[END_REF]. These designs are usually noted X k , i.e. that the corresponding experiment table is composed of k factors, with X levels each.

As mentioned in the introduction, two mathematical models having the same parameters but with different forms, are defined by using this method. The first one presents a linear relationship between the response and the parameters. For the second model, the choice of the appropriate response and factor forms is explained in section IV-A-2.

III. ACCELERATED AGEING TESTS

Once the experimental design is chosen and the corresponding table is defined, accelerated ageing tests are performed in order to relate the applied external stresses (factors) to the insulation lifetime (response).

A. Materials

Rotating machines insulation is often made of polyesterimide (PEI) which is an organic material. Steel plates coated with PEI (thermal class: 180°C) with a coating thickness of about 90 µm, as shown in Fig. 1, are subjected to an accelerated ageing test under different external stress conditions. Coated steel plates having an insulator thickness well controlled have been prefered to twisted pairs. Moreover, these kinds of samples have also been used to perform complementary measurements such as conduction current and dielectric strenght measurements which need to have a known insulator thickness as well. For each test condition, the sample lifetime (i.e. when insulation properties fail or exceed the design limits) was measured. When a sample is broken down, the over-current is immediately detected by the HV-switch and the sample is switched off while the other ones remain supplied. Eight samples were simultaneously tested under each experimental condition. All lifetime data in this paper are presented either in terms of average values or using a Weibull's statistical treatment [START_REF] Weibull | A statistical distribution function of wide applicability[END_REF], which is commonly used for breakdown data treatment.

B. Applied stresses

Many different stresses can affect the insulation degradation phenomenon in rotating machines during normal service conditions, especially when fed by inverters. The failure process is driven by several stresses acting together such as electrical, thermal, mechanical and ambient (e.g. moisture, aggressive chemicals, dirt, radiation…). In rotating machines fed by inverters, over-voltages occur at the motor terminals and the voltage distribution in the winding is not homogeneous just after the voltage application. These over-voltages can lead to partial discharges occurring between phases, between turns or between turns and ground. In this study we consider the ageing of the insulation system due to a partial activity and not an intrinsic ageing. The experimental conditions of ageing have therefore been chosen in order to be sure that the insulation degradation is mainly due to the partial discharges. However, for the simplicity reasons, only three major parameters are studied for their corresponding ageing influence, which are:

The applied voltage (V) The frequency of the applied voltage (F) The temperature (T)

C. Experimental setup

The samples are tested in our experimental setup, shown in Fig. 2. Under electrical stress, the steel plate behaves as one electrode whereas a spherical stainless steel electrode (diameter: 1 mm) has been used as a second. The only pressure applied by the spherical electrodes on the sample is due to their mass (0.8g). No additional springs have been used. At the same time, samples are placed in a climatic chamber where the applied temperature is fully controlled.

This study is a part of a research project whose aim is focused on the electric motors & electronics for aeronautical applications in more electrical aircrafts. Two levels, a minimum and a maximum value, were defined for each stress with respect to this specific application. The traditional methodology for an experimental design consists on 4 steps: first the study preparation including the choice of the response and factor form, which is the main scope of this paper and the determination of factor levels, then the choice of the experimental design in the second step, the experiment itself and finally, the result analysis.

A. Step 1: The study preparation 1) Choice of the response and factors form

This paper presents two different ways for the insulation lifetime modeling. The first and simplest method is based on a linear relationship between the factors and the logarithm of the lifetime log(L). This approach was previously used for lifetime modeling of kapton films in [START_REF] Khelil | Experimental designs for tracking the influent operating parameters on insulation reliability[END_REF], with a model described by [START_REF] Taguchi | Orthogonal arrays and linear graph[END_REF]:

Log(L) ~M + E V .(V) + E F .(F) + E T .(T) + E VF .(V).(F) + E VT .(V).(T) + E FT .(F).(T) + E VFT .(V).(F).(T) (6)
The second approach is based on previous knowledge from the domain. It will be shown that it leads to a more reliable model but requires specific factor levels. In this approach, the description of the insulation degradation in a partial discharge regime is taken into consideration. In this specific case, the effect of the electrical stress level on the insulation lifetime is most often represented by the inverse power model [START_REF] Stone | Electrical insulation for rotating machines[END_REF], such as in [START_REF] Atkinson | Optimum Experimental Designs[END_REF]:

L = c.E -n ( 7
)
where L is the insulation lifetime, E is the electrical field, c is a material constant and n is called the power law constant. Our experimental results have shown that the lifetime evolution of our samples (for a given temperature and frequency) obeys well this relationship [START_REF] Lahoud | Using the Design of Experiments (DoE) to Elaborate an Electrical Ageing Model for the Insulation of Low Voltage Rotating Machines Fed by Inverters[END_REF]. An inverse power relationship has also been found (for a given temperature and voltage) when the lifetime has been estimated versus frequency.

Moreover, under electro-thermal stress, our experimental results [START_REF] Lahoud | Using the Design of Experiments (DoE) to Elaborate an Electrical Ageing Model for the Insulation of Low Voltage Rotating Machines Fed by Inverters[END_REF] and the state of the art showed that the variation of the insulation lifetime with temperature, at a fixed voltage and frequency, may follow (8):

Log(L) = a.exp(-b.T) ( 8
)
where L is the insulation lifetime, T is the applied temperature and a and b are material constants. Constant b is calculated from lifetime experimental results under electro-thermal stress. It is obtained by drawing the variation of the logarithm of the insulation lifetime with respect to the temperature (for a fixed V and F values). Its exact value is calculated from ( 8) on these experimental results as shown in [START_REF] Lahoud | Using the Design of Experiments (DoE) to Elaborate an Electrical Ageing Model for the Insulation of Low Voltage Rotating Machines Fed by Inverters[END_REF]. This assumption will be used in our insulation lifetime model.

For the second model, we have chosen, according to ( 7) and ( 8), to study the variation of the logarithm of the lifetime with respect to a logarithm form of the electrical stress (i.e. the logarithm of the voltage and the frequency) and an exponential form of the temperature. Consequently, the corresponding model has the following form:

Log(L) ~M + E V .log(V) + E F .log(F) + E T .exp(-bT) + E FV .log(V).log(F) + E VT .log(V).exp(-bT) + E FT .log(F).exp(-bT) + E VFT .log(V).log(F).exp(-bT) (9)

2) Determination of factor levels

As already stated, three factors are chosen for this study: the applied voltage, the frequency and the temperature. The corresponding levels were chosen as follows:

The extreme values of the applied voltage (square wave bipolar with 50% duty cycle) are ±1 kV and ±3 kV for its lower and higher value respectively. The lower value corresponds to a possible overvoltage in normal service conditions. Indeed, by considering a 500 Vdc bus voltage and a complete impedance mismatch between the motor and its feeding cable, depending on the distance between the first turn of different phases and the last one, the voltage stress between them can rise up to 1 kV. The higher one is chosen to accelerate the ageing tests.

The frequency extreme values are 5 kHz and 15 kHz for the lower and higher ones respectively that could be considered as normal PWM frequencies in these applications.

The temperature extreme values are -55°C for the lower one (aeronautic service conditions) and 180 °C for the higher (= thermal class of the insulating material) and also chosen in a way to accelerate the ageing tests.

Table II and III present the chosen factors with their corresponding form for models 1 and 2 respectively.

B. Step 2 and 3: Choice of the experimental design and experimentation

As already mentioned a "Full factorial design" is used for the accelerated ageing results analysis. The number of experiments to be done is 2 3 (3 factors, 2 levels each). Table IV gives all the possible combinations between the different factor levels. Factors are (V), (F) and (T) for model 1 and log(V), log(F) and exp(-bT) for model 2. The corresponding experiment plan was carried out and the sample lifetime values are represented in Table IV (in the light grey columns). These columns present the Weibull treatment and the average values of eight samples simultaneously tested under each experimental condition. These values are very close and the Weibull statistical treatment results, which are commonly used for breakdown analysis, have been chosen for this study.

Model 1 V F T V.F V.

T F.T V.F.T Log(L) Model 2 Log(V) Log(F) exp(-bT) Log(V).Log(F) Log(V).exp(-bT) Log(F).exp(-bT) Log(V).Log(F).e (-bT) Test n°M

F1 F2 F3 I(V.F) I(V.T) I(F.T) I(V.F.T)

Weibull Average It should be noticed that tests n°9 and 10 represent the experiments at the center of the study domain for models 1 and 2 respectively, as shown in Table II and Table III. These tests are run for the model validation, in order to compare the predicted lifetime and the experimental one at the center of the experimental domain.

1 1 -1 -1 -1 1 1 1 -1 2,822 2,769 2 1 -1 -1 1 1 -1 -1 1 1,452 1,431 3 1 -1 1 -1 -1 1 -1 1 2,457 2,396 4 1 -1 1 1 -1 -1 1 -1 1,165 1,154 5 1 1 -1 -1 -1 -1 1 1 1,485 1,461 6 1 1 -1 1 -1 1 -1 -1 0,805 0,793 7 1 1 1 -1 1 -1 -1 -1 1,187 1,172 8 1 1 1 1 1 1 1 1 0,2 0

C. Step 4: Results Analysis

As mentioned before, the application of (4) to our experimental design matrix and lifetime responses allows calculating the effects of the different factors and interactions on the sample lifetime. These effects are calculated for models 1 and 2.

In order to verify the exactitude of the obtained mathematical models, an experimental test at the center of the level domain is undertaken. It is a point where factor and interaction levels are nil, which means the absence of any influence from factors and interactions with respect to the average value of the response (M). In this case, according to the theoretical models, as shown in ( 6) and ( 9), the response should be equal to the mean (M) of the ageing test values for each condition. In the following, the factors and interaction effect values, the mathematical form and verification will be presented for both models.

1) Factors and interaction effect values

The different effects are calculated by applying equation ( 4) on the experimental and the response matrices presented in Table IV Results of Table V may be presented in a diagram form as in Fig. 3. This diagram clearly shows the effect of each factor on the average value (M) and the following conclusions could be deduced:

The three factors (i.e. voltage, frequency and temperature) have a decreasing effect on the insulation lifetime.

The voltage and the temperature effects are more important than the frequency effect. Bars of the bar-graph for each model in Figure 3, are shown in the order in Table V, ie for the first M, V for the second in model 1 and log(V) in model 2…

2) The mathematical models

In order to obtain a mathematical form for model 1, we should replace the different effect of ( 6) by their corresponding values in Table V. Thus, a mathematical model is obtained for the insulation lifetime with respect to the linear forms of the different parameters as in [START_REF] Faucher | On-line electrical quality improvement of a single-phase boost rectifier with fuzzy controller and experimental designs[END_REF].

In the same way, the mathematical form of model 2 could be obtained using results from equation ( 9) and Table V. This model presents the variation of the logarithm of the lifetime with respect to a logarithmic form of the electrical stress and an exponential form of the temperature, as shown in [START_REF] Khelil | Experimental designs for tracking the influent operating parameters on insulation reliability[END_REF].

Log(L) ~ 1.45 -0.53.log(V) -0.19.log(F) -0.54.exp(-bT) -0.03.log(V).log(F) + 0.12.log(V).exp(-bT) -0.03.log(F).exp(bT) -0.05.log(V).log(F).exp(-bT) (11)

3) Models verification

An experimental test at the center of the level domain has been undertaken in order to verify the exactitude of each mathematical model.

For model 1, the center of the domain corresponds to V = 2 kV, F = 10 kHz and T = 117.5 °C (cf. Table II). Lifetime results show that Log(L) = 1.06. The theoretical value is 1.45, which means that the error level between experiments and the model is of 26.9 %.

For model 2, this test is run for V = 1.73 kV, F = 8.7 kHz, and T = 26.7 °C (cf. Table III). Results show that Log(L)=1.43 at the center of the domain, which is very close to the theoretical value, i.e. 1.45 with only 1.4 % of error.

V. CONCLUSION

It has been shown, in a previous work of our research team, that the use of the DoE methodology is very useful for tracking the influent operating parameters on insulation reliability and for the lifetime modeling. In this study, two different lifetime models are defined and compared by using this method. Both models present a relationship between the insulation lifetime and the same external parameters, which are: voltage, frequency and temperature. The difference between these models comes from the form of these parameters.

The first model, which is the basic one, displays the lifetime variation with respect to a linear form of the different parameters. The second model takes into account a logarithm form of the electrical applied stress and an exponential form of the temperature. The definition of the parameter forms is based on previous knowledge in this domain and on experimental results.

Results of both models show that, in a partial discharge regime, the applied voltage and the temperature have a higher decreasing effect on the insulation lifetime than the frequency. Besides, these most influent factors have the highest interaction.

However, a significant disparity between the models arises from their correlation with experiments at the center of the study domain. Results show that model 1 presents a significant divergence, 26.9 % of error, between theory and experiments. Model 2 shows only 1.4 % of error between the theoretical and the experimental lifetime value at the center of the domain. Thus, the use of a linear form of the parameters to describe the variation of the insulation lifetime is not sufficient. A logarithm form of the electrical stress and an exponential form of the temperature should be integrated for a reliable description of the insulation lifetime.

Fig. 1 .

 1 Fig. 1. Coated steel plate (15cm x 9cm)

Fig. 2 .

 2 Fig. 2. Experimental steup for accelerated ageing tests

  The most influent factors (i.e. voltage and temperature) have the highest interaction.

Fig. 3 .

 3 Fig. 3. The diagram effects for models 1 and 2

  Log(L) ~ 1.45 -0.53.(V) -0.19.(F) -0.54.(T) -0.03.(V).(F) + 0.12.(V).(T) -0.03.(F).(T) -0.05.(V).(F).(T)

TABLE I :

 I EXAMPLE OF AN EXPERIMENTAL TABLE

	Experiment	Factor	Factor	Interaction
	number	1	2	12

TABLE II .

 II FACTOR LEVELS FOR MODEL 1

	Factors	Level (-1)	Level (+1)	Level (0)
	Voltage (kV)	1	3	2
	Frequency (kHz))	5	15	10
	Temperature (°C)	-55	180	117,5

TABLE III

 III

		. FACTOR LEVELS FOR MODEL 2
	Factors	Level (-1)	Level (+1)	Level (0)
	Log (Voltage (kV))	Log(1)	Log(3)	Log(1.73)
	Log((Frequency (kHz))	Log(5)	Log(15)	Log(8.7)
	Exp(-b.Temperature (°C))*	Exp(55b)	Exp(-180b)	Exp(26.7b)

*b is a constant calculated experimentally (b=5.64 x 10 -3 )

TABLE IV .

 IV FULL FACTORIAL DESIGN MATRIX FOR THREE FACTORS WITH 2 LEVELS EACH

  . The different effect values are presented in Table V for both model 1 and 2.

TABLE V .

 V ACTION EFFECT VALUES FOR MODELS 1 AND 2.

	Model 1	Model 2	Effect
	M	M	1.45
	V	Log(V)	-0.53
	F	Log(F)	-0.19
	T	Exp(-bT)	-0.54
	I V.F	I Log(V).Log(F)	-0.03
	I V.T	I Log(V).exp(-bT)	0.12
	I F.T	I Log(F). exp(-bT)	-0.03
	I V.F.T	I Log(F).Log(F). exp(-bT)	-0.05

ACKNOWLEDGMENT

This work makes part of the PREMEP project. PREMEP is a national collaborative research project, approved by the Aerospace Valley pole and focused on the electric motors & electronics for aeronautical applications. The objective of PREMEP is to prepare new equipments for the new power supply network (230 Vac and 540 HV DC ). The partners are Technofan, Liebherr Aerospace Toulouse, LAPLACE, CIRTEM, Ateliers de Navarre and DELTY.


Radosław Dębek

Maria Elena Galvez

Franck Launay

Monika Motak

Teresa Grzybek

Patrick Da Costa
email: patric.da_costa@upmc.fr

Low temperature dry methane reforming over Ce, Zr and CeZr promoted Ni-Mg-Al hydrotalcite-derived catalysts

Keywords: Hydrotalcite materials, nickel catalysts, methane dry reforming, syngas, hydrogen

Hydrotalcite derived catalysts promoted with Ce, Zr and CeZr showed considerable activity in dry methane reforming (DMR) at low temperatures (550°C). Direct methane decomposition resulting in the extensive formation of fishbone-type carbon nanofibers was substantially inhibited in the presence of Zr. Physicochemical characterization by means of N 2 adsorption, XRD, TPR and CO 2 -TPD evidenced narrower porosity and higher surface areas for the Zrcontaining catalysts, together with the presence of smaller Ni particles (around 4 nm) and CO 2 preferential adsorption in weak basic sites. Such small Ni particles are inactive towards the direct methane decomposition reaction. The ability of the Zr-containing catalysts to adsorb CO 2 on weak basic sites results in the formation of active carbonate species that are able to react with methane through the DMR route. The reverse Boudouard reaction occurs simultaneously to a certain extent in the presence of Zr-promoted catalyst, since carbon nanotube formations were visible on the catalyst surface upon its utilization.

Introduction

Dry methane reforming (DMR) has attracted considerable attention in the last decades as a perspective method for CO 2 valorization, yielding an equimolar mixture of H 2 and CO.

Such a syngas can be directly used for liquid fuel synthesis through the Fischer-Tropsch process, or for the production of valuable oxygenated compounds [START_REF] Al-Fatesh | CO 2 Reforming of Methane to Produce Syngas over gamma-Al 2 O 3 -Supported Ni-Sr Catalysts[END_REF][START_REF] Bradford | Catalytic reforming of methane with carbon dioxide over nickel catalysts. 1. Catalyst characterization and activity[END_REF]. However, the DMR process presents still important drawbacks towards its practical application, mainly related to the simultaneous occurrence of carbon-forming reactions, such as direct methane decomposition, and, to a lesser extent, the Boudouard reaction [START_REF] Barroso-Quiroga | Catalytic activity and effect of modifiers on Ni-based catalysts for the dry reforming of methane[END_REF][START_REF] Bradford | Catalytic reforming of methane with carbon dioxide over nickel catalysts. 2. Reaction[END_REF][START_REF] Hu | Catalytic Conversion of Methane to Synthesis Gas by Partial Oxidation and CO 2 Reforming[END_REF].

Nickel-containing catalysts have been recently presented as a promising alternative to noble metal based ones [START_REF] Hu | Catalytic Conversion of Methane to Synthesis Gas by Partial Oxidation and CO 2 Reforming[END_REF][START_REF] Albarazi | Hydrogen and syngas production by methane dry reforming on SBA-15 supported nickel catalysts: On the effect of promotion[END_REF][START_REF] Alipour | Effects of support modifiers on the catalytic performance of Ni/Al 2 O 3 catalyst in CO 2 reforming of methane[END_REF][START_REF] Meshkani | Nanocrystalline MgO supported nickel-based bimetallic catalysts for carbon dioxide reforming of methane[END_REF][START_REF] Nimwattanakul | Potential of Ni supported on clinoptilolite catalysts for carbon dioxide reforming of methane[END_REF][START_REF] Daza | Co-precipitated Ni-Mg-Al catalysts containing Ce for CO 2 reforming of methane[END_REF][START_REF] Tsyganok | Dry reforming of methane over catalysts derived from nickel-containing Mg-Al layered double hydroxides[END_REF]. Among these materials, the catalysts obtained through the thermal decomposition of layered double hydroxides, i.e. hydrotalcites, have been recently reported to show interesting catalytic performance over long-run catalytic tests [START_REF] Daza | Co-precipitated Ni-Mg-Al catalysts containing Ce for CO 2 reforming of methane[END_REF][START_REF] Tsyganok | Dry reforming of methane over catalysts derived from nickel-containing Mg-Al layered double hydroxides[END_REF][START_REF] Gonzalez | Dry reforming of methane on Ni-Mg-Al nano-spheroid oxide catalysts prepared by the sol-gel method from hydrotalcitelike precursors[END_REF][START_REF] Perez-Lopez | Effect of composition and thermal pretreatment on properties of Ni-Mg-Al catalysts for CO 2 reforming of methane[END_REF][START_REF] Hou | Meso-porous Ni/Mg/Al catalysts for methane reforming with CO 2[END_REF][START_REF] Shishido | CO 2 reforming of CH 4 over Ni/Mg-Al oxide catalysts prepared by solid phase crystallization method from Mg-Al hydrotalcite-like precursors[END_REF][START_REF] Djaidja | Characterization and activity in dry reforming of methane on NiMg/Al and Ni/MgO catalysts[END_REF] and at relatively low temperatures [START_REF] Debek | Effect of nickel incorporation into hydrotalcite-based catalyst systems for dry reforming of methane[END_REF][START_REF] Debek | Nicontaining Ce-promoted hydrotalcite derived materials as catalysts for methane reforming with carbon dioxide at low temperature -On the effect of basicity[END_REF]. Calcination results in an homogeneous mixture of finely dispersed M II and M III oxides, having high thermal stability among other very interesting physico-chemical features. Moreover, varying the molar ratio allows the tailoring of these properties, i.e. their intrinsic basicity and redox properties. Gonzalez et al. [START_REF] Gonzalez | Dry reforming of methane on Ni-Mg-Al nano-spheroid oxide catalysts prepared by the sol-gel method from hydrotalcitelike precursors[END_REF] studied Ni-Mg-Al hydrotalcite derived oxides obtained by sol-gel method with different nickel content -4, 15 and 19 wt.%. The prepared catalysts showed high activity and stability at 800°C. Perez-Lopez et al. [START_REF] Perez-Lopez | Effect of composition and thermal pretreatment on properties of Ni-Mg-Al catalysts for CO 2 reforming of methane[END_REF] synthesized Ni-Mg-Al hydrotalcites with different Ni/Mg and M 2+ /M 3+ molar ratios by a co-precipitation method at constant pH. The composition of the catalyst precursor had a large influence on catalyst performance, i.e. catalytic activity was mainly affected by the M 2+ /M 3+ molar ratio. More recently, several hydrotalcite-like materials were prepared and tested in DMR, using different Ni/Mg molar ratios for a fixed value of M 2+ /M 3+ = 3, typical of the naturally occurring Mg-Al hydrotalcite [START_REF] Debek | Effect of nickel incorporation into hydrotalcite-based catalyst systems for dry reforming of methane[END_REF][START_REF] Debek | Nicontaining Ce-promoted hydrotalcite derived materials as catalysts for methane reforming with carbon dioxide at low temperature -On the effect of basicity[END_REF]. Catalytic activity and thermal stability of Ni-based catalysts can be improved by means of using promoters such as CeO 2 and/or ZrO 2 . The addition of Ce-species into the catalytic hydrotalcite-based structure was found to promote the reducibility of the nickel species and resulted in the introduction of new strong (low coordinated) oxygen species and intermediate (Lewis acid-base pairs) strength basic sites, which increased the CO 2 adsorption capacity of the catalysts [START_REF] Debek | Nicontaining Ce-promoted hydrotalcite derived materials as catalysts for methane reforming with carbon dioxide at low temperature -On the effect of basicity[END_REF]. Moreover, ZrO 2 may increase the content in oxygen vacancies on the catalyst surface, which are of key importance for the dissociative adsorption of CO 2 [START_REF] Koubaissy | CO 2 reforming of methane over Ce-Zr-Ni-Me mixed oxides[END_REF][START_REF] Sharifi | Syngas production via dry reforming of CH 4 over Co-and Cu-promoted Ni/Al 2 O 3 -ZrO 2 nanocrystals synthesized via sequential impregnation and sol-gel methods[END_REF].

In the present paper Ni-Mg-Al hydrotalcite-derived catalysts were prepared, promoted either with Ce, Zr and CeZr. In all cases, the Ni/Mg and M 2+ /M 3+ molar ratios were kept respectively around 0.3 and 3, corresponding to a Ni-content of approximately 20 wt.%. Their activity and selectivity towards DMR was tested at low temperatures, i.e. 550°C, with special attention on the carbon formation reactions leading to catalyst deactivation. The textural, structural and chemical features of the promoted catalysts were carefully studied in order to identify the key mechanisms leading to the suppresion of extensive carbon deposition.

Experimental

Catalysts preparation

The hydrotalcite catalyst precursors were obtained by co-precipitation from an aqueous solution of Mg, Ni and Al nitrates (POCH), using a 0.05 M sodium carbonate (Acros Organics) solution and 1 M NaOH (POCH), corresponding to a nominal Ni content of 25 wt.%. The nitrate solution with M 2+ /M 3+ molar ratio equal to 3 and 1 M NaOH were added drop-wise into the sodium carbonate solution at 60°C and at fixed pH of 10 ± 0.2. The obtained suspension was kept under vigorous stirring for 1 h, then filtered and dried overnight at 80°C. In case of zirconia promoted samples, the zirconium species were introduced into hydrotalcite structure at the co-precipitation stage. The zirconium oxynitrate was used as Zr 4+ precursor. The molar ratio of Al 3+ /Zr 4+ was equal to 9/1. In order to introduce Ce-species into the hydrotalcite precursors, these materials were kept in contact with a 3% wt. aqueous solution of [Ce(EDTA)]-complexes for 24 h at room temperature. The hydrotalcite materials were subsequently calcined at 550°C for 4 h. Four different catalysts were prepared: HT-25Ni, prepared without either Ce or Zr, HTNi-Ce, promoted with Ce, HTNi-Zr, promoted with Zr, and HTNi-CeZr, promoted with both Ce and Zr.

Catalysts characterization

The elemental analysis of the hydrotalcite-derived catalysts was performed by means of XRF using an energy dispersive XEPOS spectrometer (Spectro Ametek). The sample was analyzed in its powder form. Quantitative data were determined using the MicroPowder method. XRD patterns were acquired in an Empyrean diffractometer from PANalytical, equipped with CuK α anode (λ = 0.154059 nm). Temperature programmed reduction (H 2 -TPR) profiles were acquired in a BELCAT-M device from BEL Japan, equipped with a thermal conductivity detector (TCD). The materials (50 mg) were firstly outgassed at 100°C for 2 h and then reduced using 5%H 2 /Ar at a heating rate of 7.5°C/min. The basicity of these catalysts was evaluated by means of CO 2 -temperature programmed desorption in the BELCAT-M apparatus. 60 mg of material were first degassed for 2 h at 500°C, then cooled down to 80°C. A mixture of 10%CO 2 /He was then fed for 1 h during the adsorption step. A flow of He was subsequently fed for 15 minutes in order to desorb the physically adsorbed CO 2 . The material was then heated up under He at 10°C/min, while the evolution of CO 2 was measured with the aid of the TC detector. Textural parameters of the different materials were calculated from their corresponding N 2 adsorption isotherms obtained at -196°C in a Belsorp Mini II apparatus from BEL Japan. Thermogravimetric measurements were carried out with a SDT Q600 apparatus (TA Instruments), under air flow (100 mL/min) heating from ambient temperature to 900°C at a rate of 10 °C/min.

Dry methane reforming (DMR) experiments

The activity and selectivity of the different HT-derived catalysts was assayed in a tubular quartz reactor of 1.2 cm diameter, heated by a cylindrical resistive electric furnace.

Temperature was measured inside the catalytic bed, with the aid of a quartz-shielded K-type thermocouple. A total flow of reactant gas mixture of 100 mL/min consisting of CH 4 /CO 2 /Ar = 1/1/8 was fed using several mass flow controllers (BROOKS 5850E). Under such conditions, the gas hourly space velocity (GHSV) corresponded to 20,000 h -1 , i.e. approximately 200 mg of catalyst, 0.2 mm particle size, non inert-diluted. The catalysts were reduced in situ at 900°C during 1 h, using a 3%H 2 /Ar mixture. After reduction, the catalysts were cooled down to 550°C and the reactant gas mixture was supplied to the reactor. The analysis of the products was carried out on-line in a Varian GC490 micro chromatograph equipped with a thermal conductivity detector (TCD). The Ce-containing catalyst, HTNi-Ce, behaves similarly to the catalyst containing only Ni, HT-25Ni. Both methane and CO 2 conversion reach comparable values, both around 40%, with methane conversion being slightly higher in the case of HT-25Ni. The lower methane conversion measured for HTNi-Ce, together with the higher values of H 2 /CO ratio, close to the desired value of 1, point to a slightly positive effect of Ce, which may avoid to a certain point the occurrence of the simultaneous direct methane decomposition reaction [START_REF] Debek | Nicontaining Ce-promoted hydrotalcite derived materials as catalysts for methane reforming with carbon dioxide at low temperature -On the effect of basicity[END_REF].

Results and discussion

Activity and selectivity in DMR

The promoting effect of Ce is widely known and has been ascribed to its large oxygen storage capacity, which might be favoring the oxidation of the carbon deposits formed upon direct methane decomposition [START_REF] Debek | Nicontaining Ce-promoted hydrotalcite derived materials as catalysts for methane reforming with carbon dioxide at low temperature -On the effect of basicity[END_REF][START_REF] Koubaissy | CO 2 reforming of methane over Ce-Zr-Ni-Me mixed oxides[END_REF]. Note here that the thermodynamic analysis of the DMR reaction set (performed with the aid HSC 5.0 Outokumpu software) predicts a CO 2 conversion around 43%, and around 83% for methane, resulting in high H 2 /CO ratios around 4.

When Zr is present in the catalyst formulation, both methane and CO 2 conversions are considerably lower, i.e. 25% CH 4 conversion and 30% CO 2 conversion after 300 min timeon-stream for HTNi-CeZr. In fact, the values of CO 2 conversion are all the time relatively higher than the values of methane conversion for these Zr-containing catalysts, opposite to the thermodynamically forecasted trends. This is directly reflected in the H 2 /CO ratios measured during the DMR experiments, which are considerably lower than for HT-25Ni and HTNi-Ce, especially for the catalyst that does not contain Ce, i.e. HTNi-Zr. Zirconia thus modifies the selectivity of the catalysts resulting in an excess of CO in the syngas mixture. Direct methane decomposition is substantially inhibited, as well as the water gas shift reaction, since no excess of H 2 is detected. Other reactions, such as either the direct or the reverse Boudouard reaction, 2CO = CO 2 + C, might be significantly favored [START_REF] Sharifi | Syngas production via dry reforming of CH 4 over Co-and Cu-promoted Ni/Al 2 O 3 -ZrO 2 nanocrystals synthesized via sequential impregnation and sol-gel methods[END_REF][START_REF] Zhang | Effects of metal content on activity and stability of Ni-Co bimetallic catalysts for CO 2 reforming of CH 4[END_REF].

Influence of Ce, Zr and CeZr on catalyst stability: Carbon formation

From the activity plots shown in Figure 1, it becomes clear that competitive reactions, such as methane direct decomposition and the Boudouard reaction may be happening to a certain extent in the presence of the different HT-derived catalysts. The study and quantification of the carbon deposits formed can be very helpful in determining the role of the presence of Ce and Zr in the formulation of these catalysts. Transition electron microscopy images are shown in Figure 2, for the HT-derived catalysts after 300 min of DMR reaction at 500°C. The spent HT-25Ni and HTNi-Ce catalysts contain plenty of carbon deposits. The original particles of both catalysts appear almost completely covered by these carbon formations. Ni particles are still visible, most of them detached from the HT-derived mixed oxide structure and at the end of well-developed fishbone carbon nanofibers. These fibers contain several graphite planes, with thicknesses varying from 5 to 20 nm. In the case of the Ce containing catalyst, the fiber structures contain more defects and appear frequently broken or damaged, but still covering an important part of the active surface.

Such fiber structures are completely absent in the case of the spent catalyst containing Zr, HTNi-Zr and HTNi-CeZr. Carbon formations resembling multi and even single wall carbon nanotubes are present on the surface and growing out of the catalyst surface. These carbon filaments are composed of only 1 to 4 graphite planar layers, sometimes forming bamboo-like structures, and all the time much thinner than the fishbone fibers observed for HT-25Ni and HTNi-Ce. For the Ce-containing catalyst, HTNi-CeZr, some fishbone structures can be found, but their presence is minimal in comparison to HTNi-Ce. The presence of Zr has therefore a definitive influence on the type of carbon deposits formed. According to the TEM images acquired for the spent HT-derived catalysts, it seems that Zr substantially inhibits the formation of carbon fibers through the direct methane decomposition. reaction and might promote other routes for carbon formation, i.e. the Boudouard reaction.

The thermogravimetric oxidation of the carbon deposits formed on the surface of the catalysts upon reaction yields further information on their amount and thermal stability. A wide DTGA peak starting at temperatures around 300°C and extending up to maximally 525°C appears for both HTNi-Zr and HTNi-CeZr. Since the area of these peaks is much smaller, one can definitively conclude from this plots that carbon formation upon DMR reaction is minimal, in any case substantially reduced, when Zr is present in the catalyst formulation vis-à-vis the other catalysts in this series that do not contain Zr. In agreement with the TEM observation of the spent catalysts, Zr seems to be able to modify the selectivity of the catalyst, activating the DMR route and to some extent the Boudouard reaction but almost completely inhibiting the direct methane decomposition reaction. The use of Zr as a promoter in these HT-derived catalysts seems to be therefore a warranty for high catalyst stability.

Physicochemical features of the Ce, Zr and CeZr doped HT-derived catalysts: the role of

Zr in the DMR reaction.

The textural, structural and chemical properties of the different HT-derived materials promoted with either Ce, Zr or CeZr were determined, in order to clarify their influence on the activity and selectivity of these catalysts, and to elucidate the role of the different promoting species. Table 1 shows the composition of the different catalysts, as determined by XRF. A Ni content between 17.3 and 19.6 wt.% was measured for all the catalysts. Ni/Mg ratios are all the time close to 0.3, corresponding to a ratio M 2+/ M 3+ around 3, the typical value in naturally existing hydrotalcites. Let us note here that the values of this molar ratio presented in Table 1 slightly differ from the nominal value of 3, i.e. 3.51 for HTNi-CeZr. This may come from the co-precipitation procedure leading to the raw hydrotalcite structure, and to the possible influence of the presence of Zr cations on pH modification resulting in such slightly higher M 2+/ M 3+ ratios. Ce content in both HTNi-Ce and HTNi-CeZr was found to be 3.7 and 4.7 wt.%, respectively. Zr contents of 2.5 to 2.7 wt.% was measured for both HTNi-Zr and HTNi-CeZr.

The values of surface area, S BET , total pore volume, V p , and mean pore size, derived from the N 2 adsorption isotherms acquired for the different HT-derived catalysts are presented as well in Table 1. The catalyst HT-25Ni shows values of surface area, total pore volume and mean pore size typical of mesoporous hydrotacite-derived Mg-Al-Ni mixed oxides [START_REF] Cavani | Hydrotalcite-Type Anionic Clays: Preparation, Properties and Applications[END_REF][START_REF] Pavel | Acido-basic and catalytic properties of transitionmetal containing Mg-Al hydrotalcites and their corresponding mixed oxides[END_REF]. Zr-doping results in HT-derived mixed oxides of higher surface area, i.e. S BET increases from 115 to 229 m 2 /g, due to the creation of smaller pores of mean diameter around 2 nm. The simultaneous presence of Ce results in a material, HTNi-CeZr, having still higher surface area, S BET = 158 m 2 /g, and intermediate pore sizes, i.e. 4.7 nm. This increase in surface area and the favored presence of narrower pores should explain a higher resistance towards deactivation due to impeded growth of carbon fibers, but does not provide itself an explanation to the lower activity, or to the substantially hindered direct methane decomposition reaction in the presence of the Zr-containing catalysts.

The XRD patterns acquired for the fresh hydrotalcite materials and the calcined HTderived catalysts are shown in Figure 4 a and b. Before calcination, Figure 4 a, all the materials show the typical layered structure of hydrotalcite [START_REF] Cavani | Hydrotalcite-Type Anionic Clays: Preparation, Properties and Applications[END_REF][START_REF] Pavel | Acido-basic and catalytic properties of transitionmetal containing Mg-Al hydrotalcites and their corresponding mixed oxides[END_REF]. The absence of any other additional crystalline phase in the diffractograms points to successful incorporation of nickel cations into the brucite-like layers. The XRD patterns for the calcined HT-derived catalysts, Figure 1 b, evidence two main reflections at 43.5 and 63°, which can be assigned to the periclase-like structure of mixed Ni-Mg oxides generated upon the thermal decomposition of hydrotalcite materials [START_REF] Pavel | Acido-basic and catalytic properties of transitionmetal containing Mg-Al hydrotalcites and their corresponding mixed oxides[END_REF].

The intensity of the (111) reflection, appearing around 35°, decreases in the presence of Zr. It becomes wider, and seems to be directly related to the size of Ni-crystallites, being thus smaller for the Zr-containing catalysts. TEM observation, together with the histograms plotted for the micrographs corresponding to each HT-derived catalyst, further confirm this fact. Mean particle size from these histograms was found to decrease from around 10-12 nm in HTNi-25 and HTNi-Ce to 3-5 nm in HTNi-Zr and HTNi-CeZr. There is thus a considerable effect of the presence of Zr in the Ni particle size that can explain, up to a certain point, the differences in the selectivity observed for the HT-derived catalysts towards the different reactions involved. It has been previously reported [START_REF] Hu | Catalytic Conversion of Methane to Synthesis Gas by Partial Oxidation and CO 2 Reforming[END_REF] that bigger Ni particles enhance the direct methane decomposition reaction, favoring its deactivation through the extensive formation of carbon deposits. This reaction should be thus substantially inhibited when smaller Ni particles are present, i.e. as it was observed for the Zr-containing catalysts. Moreover, CO 2 adsorption is enhanced on small metal particles [START_REF] Zhang | Effects of metal content on activity and stability of Ni-Co bimetallic catalysts for CO 2 reforming of CH 4[END_REF], what will favor the reverse Boudouard reaction, resulting in increased CO formation (see the low H 2 /CO ratios registered for the Zr-containing catalysts). Note that the presence of a separate CeO 2 phase in Ce-promoted catalyst, fluorite-type structure, has been previously reported [START_REF] Debek | Nicontaining Ce-promoted hydrotalcite derived materials as catalysts for methane reforming with carbon dioxide at low temperature -On the effect of basicity[END_REF].

Temperature programmed reduction yields further information on the reducibility and dispersion of the different active species contained in this series of HT-derived catalysts. TPR curves are shown in Figure 5 a. As previously observed, the presence of Ce favors the reducibility of Ni species, as pointed out by the shift of the main peak appearing on the TPR profile to lower reaction temperatures. The peak for HTNi-Zr appears centered at relatively higher temperatures, i.e. 25°C higher than for HT-25Ni, corresponding to the more difficult reduction of smaller Ni particles, in complete agreement with TEM observation and XRD. Hydrotalcite-derived materials exhibit three CO 2 desorption peaks in temperature range 100-500°C [START_REF] Di Cosimo | Structure and surface and catalytic properties of Mg-Al basic oxides[END_REF][START_REF] Di Cosimo | Structural requirements and reaction pathways in condensation reactions of alcohols on Mg y AlO x catalysts[END_REF][START_REF] Zhao | The NiAl mixed oxides: The relation between basicity and SO 2 removal capacity[END_REF]. The first desorption peak observed at 100-150°C is attributed to the desorption of CO 2 from weak Brønsted OH groups, the peak observed at ca.190°C can be assigned to the formation of bidentate carbonates formed on metal-oxygen pairs, and finally the CO 2 adsorbed on strong basic sites is desorbed at temperatures higher than 280°C [START_REF] Di Cosimo | Structure and surface and catalytic properties of Mg-Al basic oxides[END_REF][START_REF] Di Cosimo | Structural requirements and reaction pathways in condensation reactions of alcohols on Mg y AlO x catalysts[END_REF]. The presence of Zr substantially hinders the adsorption of CO 2 in these last strong basic sites, normally CO 2 bonded on low-coordination oxygen anions, since no peak is detected in the TPD profile for HTNi-Zr. On the contrary, the presence of Ce seems to favor this kind of strong basicity. The CO 2 adsorbed on strong basic sites reacts more difficultly with methane and direct methane decomposition is therefore enhanced, above all in the presence of relatively big Ni particles. Though it is still to early to state anything about the reaction mechanism in the presence of Zr, it is clear that its presence affects the CO 2 -adsorption pattern that in turn can modify the reaction pathway. Further tests and characterization need to be performed in order to clarify this fact, maybe also through the evaluation of the influence of the molar Ce/Zr ration on the catalytic behavior.

Conclusions

Ni-Mg-Al hydrotalcite-derived materials were synthesized in the presence of either Ce, Zr or CeZr, and used as catalysts for syngas production through dry methane reforming (DMR) at low temperatures. The presence of Zr was found to strongly determine both the activity and the selectivity of these catalysts. Zr considerably inhibited the direct methane decomposition reaction, favoring the interaction of methane with CO 2 (DMR reaction) together with other important parallel reactions such as the reverse Boudouard reaction.

Though lower conversions of both methane and CO 2 were measured, almost no carbon was deposited on the catalyst surface upon 5 h of DMR reaction at 550°C. Carbon nanotubes were formed instead of the typical fishbone fibers formed upon direct methane decomposition on Ni-catalysts.

The physicochemical characterization of the catalysts evidenced the formation of narrower porosity, resulting in higher surface areas, for the Zr-containing catalysts. XRD together with TEM observation of the catalysts pointed to the presence of smaller particles, around 4 nm, in these catalysts, in comparison to the almost 12 nm measured for the catalysts prepared in the absence of Zr. Smaller Ni-particles are no longer active towards direct methane decomposition and are thought to favor other side reactions such as the reverse Boudouard reaction. Moreover, the presence of Zr was found to promote the adsorption of CO 2 on weak basic sites, resulting in favored interaction of the adsorbed bidentate carbonates with methane. Figure 2. TEM images for a) HT-25Ni catalyst, at x 80,000, x 80,000 and x 400,000 augments, b) HTNi-Ce catalyst, at x 80,000, x 30,000 and x 400,000 augments, c) HTNi-Zr catalyst at x 80,000, x 300,000 and x 400,000 augments, and d) HTNi-CeZr catalyst, at x 80,000, x 120,000 and x 500,000 augments, all after 300 min DRM at 550°C. Figure 2. TEM images for a) HT-25Ni catalyst, at x 80,000, x 80,000 and x 400,000 augments, b) HTNi-Ce catalyst, at x 80,000, x 30,000 and x 400,000 augments, c) HTNi-Zr catalyst at x 80,000, x 300,000 and x 400,000 augments, and d) HTNi-CeZr catalyst, at x 80,000, x 120,000 and x 500,000 augments, all after 300 min DRM at 550°C.

Figures

Figure 1 a

 1 Figure 1 a, b and c show the methane and CO 2 conversions, together with the H 2 /CO ratio, measured during the DMR experiments at 550°C, in the presence of the different HTderived catalysts. Even at this low reaction temperature, the HT-derived catalysts are notably active towards methane dry reforming. Upon 5 h time-on-stream, the catalysts present no evidences of deactivation.

Figure 3

 3 Figure 3 contains the thermogravimetric curves, i.e. the derivative of the weight-loss registered as a function of temperature, for the different HT-derived spent catalysts. It can be clearly observed that, in the presence of the catalysts HT-25Ni and HTNi-Ce, greater amounts of carbon deposits are formed upon 300 min DMR reaction at 550°C, as indicated by each corresponding peak in the DTGA signal appearing at temperatures between 450 and 650°C. These carbon deposits (the fishbone fibers observed in Figure 2 a and b) are oxidized at lower temperatures in the presence of Ce, i.e. the DTGA peak appears at lower temperatures, the difference between the two maxima being approximately 25°C.

  The temperature programmed desorption curves acquired upon CO 2 adsorption for the Ce, Zr and CeZr containing catalysts after reduction at 900°C for 2 h are shown in Figure5 b.CO 2 desorption at different temperatures allows the determination of the basicity of each catalyst, which is substantially modified by the presence of the Ce and Zr promoters.

Figure 1 .

 1 Figure 1. DMR runs at 550°C, in the presence of the different catalysts: a) CH 4 conversion, b)

  Figure 1. DMR runs at 550°C, in the presence of the different catalysts: a) CH 4 conversion, b) CO 2 conversion, and c) ratio H 2 /CO 2 .

Figure 3 .

 3 Figure 3. Thermogravimetric oxidation of the carbon deposits in the spent HT-derived catalyst: Derivative of weight-loss as a function of temperature.

Figure 4 .

 4 Figure 4. XRD patterns for a) the hydrotalcite materials before calcination, and b) the materials upon calcination, i.e. the different HT-derived catalysts.

Figure 5 .Figure 1 .

 51 Figure 5. a) Temperature programmed reduction (TPR) profiles and b) CO 2 temperature programmed desorption (TPD) for the Ce, Zr and CeZr promoted catalysts.

Figure 3 .Figure 4 .Figure 5

 345 Figure 3. Thermogravimetric oxidation of the carbon deposits in the spent HT-derived catalyst: Derivative of weight-loss as a function of temperature.

Table 1 .

 1 Composition and textural properties of the different HT-derived catalysts.

	Tables
	Catalyst	Ni (wt.%)	Mg (wt.%)	Al (wt.%)	Ce (wt.%)	Zr (wt.%)	Ni/Mg M 2+/ M 3+ S BET (m 2 /g)	V p (cm 3 /g)	Mean d p (nm)
	HT-25Ni	19.6	23.9	11.8	-	-	0.34	3.02	115	0.41	14
	HTNi-Ce	17.9	21.5	10.8	3.7	-	0.34	2.96	102	0.33	13
	HTNi-Zr	17.3	24	9.6	-	2.5	0.30	3.60	229	0.62	2.3
	HTNi-CeZr	19.3	28.4	11.5	4.7	2.7	0.28	3.51	158	0.56	7.4

Acknowledgements R. Debek acknowledges the International Group of Research (GDRI) "Catalysis for polluting emissions after treatment and production of renewable energies" and the French Embassy in Poland for the financial support. The present work was also founded within NCiBR strategic research project 'Technologies supporting development of safe nuclear energy', research task no. 1 'Development of high temperature reactors for industrial applications', agreement no. SP/J/1/166183/12, step task no. 15 'Preparation and physicochemical characterization of catalysts for dry reforming of methane'. We kindly thank Dr. P. Beaunier at the UPMC for her guidance through the acquisition of TEM images.