Héloïse Delpouve

Gérald Camus

Bruno Humez

Hervé Plaisantin

Claudie Josse

Jacques Sylvain
email: jacques@lcts.u-bordeaux.fr

Relationship between both thickness and degree of crystallisation of BN interphases and the mechanical behaviour of SiC/SiC composites

Keywords: ceramic matrix composite, interphase, fibre push-out, FIB-SEM, TEM, In-plane shear tests

SiC/BN/SiC-Si single-ply composites with Hi-Nicalon S TM fibres were synthesised by chemical vapour infiltration followed by the liquid route. These are model composites representing the behaviour of industrial composites intended to be used as structural parts in the hot sections of aeronautical engines. Four interphases with two different degrees of crystallisation and, in each case, two different thicknesses were tested. The interfacial shear stress measured by fibre push-out test is significantly higher when the crystallisation degree of the BN interphase is low. Yet, in this case, it decreases with the thickness of the interphase. This higher interfacial bonding is also associated, albeit less significantly, with better macromechanical properties as measured by tensile and shear tests. The cracks observed in the composite with different microscopy techniques are also less long and open.

Depending on the interphases, the debonds are more or less pronounced and occur preferentially at different locations in the interfacial system.

Introduction

The ceramic matrix composites (CMCs) consisting of a SiC-based matrix reinforced with SiC-based fibres are replacing the traditional superalloys used in the hot sections of aeronautical engines [START_REF] Kellner | Space age ceramics are aviation's new cup of tea[END_REF][START_REF] Bouillon | SiC-based ceramic matrix composite behavior enhancement for gas turbines hot sections[END_REF].

All the CMCs are the subject of intense research aimed at improving the methods for their manufacture and their thermomechanical behaviour [START_REF] Dicarlo | Advances in SiC/SiC composites for aero-propulsion[END_REF][START_REF] Liu | Application requirements and challenges of CMC-SiC composites on aero-engine[END_REF][START_REF] Wang | Advances in modifications and hightemperature applications of silicon carbide ceramic matrix composites in aerospace: A focused review[END_REF]. Nowadays, matrix manufacturing is not limited to the traditional CVI (chemical vapour infiltration), a batch process derived from CVD (chemical vapour deposition). It is complemented by slurry cast of SiC particles and then infiltration of molten silicon (MI) to reduce the residual porosity of the composite. Furthermore, the mechanical behaviour of CMCs is made non-brittle by the presence of an interface coating placed between the fibres and the matrix called "interphase" [START_REF] Naslain | Single-and multilayered interphases in SiC/SiC composites exposed to severe environmental conditions: an overview[END_REF]. Pyrocarbon is the common interphase material but because of its sensitivity to oxidation it may be replaced by turbostratic boron nitride which has a sp 2 -hybridized form and a layered structure similar to pyrocarbon [START_REF] Chen | Boron nitride (BN) and BN based multiple-layer interphase for SiC f /SiC composites: A review[END_REF]. Contrary to pyrocarbon, BN is poorly wetted by Si and presents an increased resistance to its chemical attack [START_REF] Mukai | Wettability of ceramics with molten silicon at temperatures ranging from 1693 to 1773[END_REF][START_REF] Yuan | Wettability and reactivity of molten silicon with various substrates[END_REF]. It has been demonstrated in the development of MI SiC composites that BN fibre coatings can survive the silicon melt infiltration process [START_REF] Corman | General Electric Company: Selected Applications of Ceramics and Composite Materials[END_REF][START_REF] Borom | Fiber containing composite[END_REF].

It has been known for several decades that the structure of the interfacial system, particularly the thickness and microstructural organisation of the interphase, has an effect on the micro-and macromechanical properties of CMCs [START_REF] Naslain | Single-and multilayered interphases in SiC/SiC composites exposed to severe environmental conditions: an overview[END_REF][START_REF] Chawla | Interface mechanics and toughness[END_REF][START_REF] Miller | Fiber coatings and the fracture behavior of a continuous fiber ceramic composite[END_REF][START_REF] Sauder | Influence of interface characteristics on the mechanical properties of Hi-Nicalon type-S or Tyranno-SA3 fiber-reinforced SiC/SiC minicomposites[END_REF][START_REF] Karakoc | Fiber/matrix debonding evaluation of SiC f /SiC composites using micropillar compression technique[END_REF][START_REF] Buet | Influence of texture and thickness of pyrocarbon coatings as interphase on the mechanical behavior of specific 2.5D SiC/SiC composites reinforced with Hi-Nicalon S fibers[END_REF]. In the particular case of BN interphases, work on this effect has been carried out with the first generations of fibres from the Nippon Carbon company (Tokyo, Japan), namely Nicalon TM [START_REF] Prouhet | Mechanical characterization of Si-C(O) fiber/SiC (CVI) matrix composites with a BN-Interphase[END_REF] and Hi-Nicalon TM [START_REF] Gallet | Influence of a multilayered matrix on the lifetime of SiC/BN/SiC minicomposites[END_REF]. However, the thermal instability of the fibres, the sizing residues or unexpected effects during thermochemical treatments leading to the formation of undesired phases at the interfaces (free carbon and silica) often prevented a clear conclusion on the influence of the interphase itself on the mechanical properties of the CMC. In the case of the latest generation of fibres, De Meyere et al. have also shown that the thickness of the BN interphase influences the interfacial properties measured from micro-mechanical push-out tests [START_REF] De Meyere | Optimizing the fiber push-out method to evaluate interfacial failure in SiC/BN/SiC ceramic matrix composites[END_REF]. Fibre pushout tests provide a direct measure of the local fibre-matrix interfacial bond strength [START_REF] Rebillat | Interfacial bond strength in SiC/C/SiC composite materials, as studied by single-fiber push-out tests[END_REF][START_REF] Lv | Tunable strength of SiC f /β-Yb 2 Si 2 O 7 interface for different requirements in SiC f /SiC CMC: Inspiration from model composite investigation[END_REF][START_REF] Lu | Microstructure and mechanical performance of SiC f /BN/SiC mini-composites oxidized at elevated temperature from ambient temperature to 1500 °C in air[END_REF]. They are very useful and can be repeated on a large number of fibres in the same specimen for statistical purpose yet, they are only complementary to macro-scale tests which are the only ones able to determine the global mechanical behaviour of the composite.

In an industrial composite made by CVI, there are usually variations in interphase thickness due to gas infiltration gradients in the depth of the fibrous preform [START_REF] Naslain | Design, preparation and properties of non-oxide CMCs for application in engines and nuclear reactors: an overview[END_REF]. Furthermore, in woven preforms, the fibres in contact one with each other may locally prevent the growth of the interphase during its synthesis because of lack of space. To minimise these infiltration gradients, BN interphases are obtained by CVI using low manufacturing temperatures [START_REF] Cholet | Chemical vapor infiltration of boron nitride interphase in ceramic fiber preforms: discussion of some aspects of the fundamentals of the isothermal chemical vapor infiltration process[END_REF][START_REF] Leparoux | Influence of isothermal chemical vapor deposition and chemical vapor infiltration conditions on the deposition kinetics and structure of boron nitride[END_REF]. The degree of crystallisation and structural organisation of a BN coating depends largely on the synthesis temperature [START_REF] Carminati | Low pressure chemical vapour deposition of BN: Relationship between gas phase chemistry and coating microstructure[END_REF][START_REF] Dai | Effect of temperature on the growth of boron nitride interfacial coatings on SiC fibers by chemical vapor infiltration[END_REF][START_REF] Plaisantin | TEM characterization of turbostratic and rhombohedral BN interphases synthesized by chemical vapour infiltration in SiC/SiC-Si composites[END_REF]. This leads to an interphase consisting of turbostratic BN (t-BN) with a quasi-isotropic structure and a low degree of crystallisation. BN is then not very stable and is particularly sensitive to moisture, which can affect the mechanical properties of the CMC [START_REF] Udayakumar | Effect of intermediate heat treatment on mechanical properties of SiC f /SiC composites with BN interphase prepared by ICVI[END_REF][START_REF] De Meyere | Micromechanical properties of vapour-exposed SiC f /BN/SiC ceramic-matrix composites[END_REF]. The mechanical behaviour of CMCs with a wellcrystallised BN interphase made by CVI remains poorly studied, whereas better stability with respect to the ambient environment should be expected.

In the present study, we are interested in the effect of the average interphase thickness for which the differences were obtained intentionally by varying the synthesis time. The effect of the degree of crystallisation on the mechanical properties of CMCs was studied by modifying the CVI temperature.

Minicomposites consisting of a single straight fibre tow are often used as model composites to study mechanical properties and associated damage mechanisms because they are easier to produce than industrial parts and are idealized units of CMC [START_REF] Naslain | Micro/minicomposites: a useful approach to the design and development of non-oxide CMCs[END_REF][START_REF] Swaminathan | Microscale characterization of damage accumulation in CMCs[END_REF]. Yet, these minicomposites suffer from a major drawback: the morphology of the fibre bundles (in terms of shape, volume content of the various constituents and undulation) is somewhat distant from their reality inside a structure. Besides, it is only possible to perform an on-axis tensile test. That is why another type of model composite has been preferred in the present work. It consists of a single 2D woven SiC fibre ply [START_REF] Plaisantin | TEM characterization of turbostratic and rhombohedral BN interphases synthesized by chemical vapour infiltration in SiC/SiC-Si composites[END_REF]. The "single-ply" model composite thus allows a good compromise between rapid and easy laboratory preparation, homogeneity of infiltration and representativeness of the industrial composite. Fibre push-out tests were used to assess the micromechanical behaviour, while tensile and shear tests were used for the macro-mechanical behaviour. The damage morphologies (matrix cracking, debonding and crack deflection) were observed by microscopy to investigate the links between the behaviours at different scales.

The aim of this study was to establish, through the use of single-ply model composites, the relationships between a BN interphase in terms of thickness and microstructure, and both micro-and macro-mechanical properties of SiC/SiC composites.

Experimental procedure

Synthesis

The single-ply SiC/BN/SiC-Si composites used in this study were synthesised in the same way as those used in the study carried out by Plaisantin et al. [START_REF] Plaisantin | TEM characterization of turbostratic and rhombohedral BN interphases synthesized by chemical vapour infiltration in SiC/SiC-Si composites[END_REF]. They were composed of a single 2D 8-harness satin-weave SiC fibre cloth (Hi-Nicalon S from NGS Advanced Fibers Co., Ltd., total thickness ≈ 0.5 mm), a BN interphase and a matrix comprising both SiC obtained by the gaseous route as well as Si obtained by the liquid route. The fibres were desized during a process made of an oxidation step followed by a treatment step with an acid to remove the silica layer formed during the oxidation step [START_REF] Loison | Silicon carbide fiber treatment method[END_REF]. The BN and SiC coatings were infiltrated in a hot-wall CVI reactor working at low pressure. The fibrous cloth was maintained compressed in a graphite tooling. The BN interphases were infiltrated at two temperatures, 900 °C and 1200 °C, respectively, from NH 3 and BCl 3 , with H 2 as diluent gas. Infiltration times were adjusted to achieve either "thin" or "thick" interphases, i.e. with target thicknesses of 200 nm and 500 nm respectively. The SiC matrix was then infiltrated at low pressure in the same CVD/CVI apparatus from a mixture of hydrogen and methyltrichlorosilane at a temperature of about 1000 °C. It is worth mentioning that the samples were not exposed to the ambient air between the infiltration of the BN interphase and the infiltration of the SiC matrix. The samples were then removed from the graphite tooling and liquid silicon was infiltrated into the remaining matrix porosity using a special apparatus at a temperature slightly above the melting point of silicon for 30 minutes.

In what follows, four interphases are named 9/t, 9/T, 12/t and 12/T for thin and thick interphases synthesised at 900 °C and thin and thick interphases synthesised at 1200 °C, respectively. The thicknesses of the interphases were measured at tow edges from scanning electron microscope observations of cross-sections obtained after laser cutting, epoxy resin embedding and mechanical polishing. These measurements were carried out at the centre and at the two opposite edges of the useful area from which the homogeneous mechanical test specimens were obtained. They are given in Table 1. It should be noted that, while the variability of the measured thicknesses is reasonable for CMC interphases, it appears particularly high in the case of interphase 12/T. This may reflect a more difficult infiltration of the BN interphase into the fibre cloth at high temperatures. The microstructures of these BN interphases have been characterised in terms of structural anisotropy and degree of crystallisation in a previous study by Plaisantin et al. [START_REF] Plaisantin | TEM characterization of turbostratic and rhombohedral BN interphases synthesized by chemical vapour infiltration in SiC/SiC-Si composites[END_REF]. The cross-sectional areas of the specimens as well as the proportions of the respective components were obtained from image analysis of the observations made with an optical microscope also after laser cutting, embedding in resin and mechanical polishing. For information and taking into account all the measurements, the average value of the cross-sectional areas is 2.9 mm 2 with a standard deviation of 0.4 mm 2 . The average volume fractions are 40%, 47% and 13% for the fibres, CVI silicon carbide and MI silicon (with standard deviations of 4%, 7% and 5%) respectively.

Fibre push-out tests

The test specimens were prepared using metallographic techniques with anhydrous cutting and polishing lubricants. Pieces of a few millimeters in length were cut from the single-ply composites and sandwiched between a silicon wafer and a glass slide, then embedded in epoxy resin. Sections of this sandwich with a thickness of approximately 800 µm were cut out with a diamond wire saw (ESCIL Well 3032) and then thinned by mechanical polishing using a diamond size down to 0.5 µm (Buehler, MINIMET™ 1000) to reach a total specimen thickness of about 100 µm. This low thickness allows achieving complete debonding and fibre sliding during the push-out test [START_REF] Rebillat | Properties of multilayered interphases in SiC/SiC chemical-vapor-infiltrated composites with "weak" and "strong" interfaces[END_REF] as it avoids both excessive wear effects, exaggerated shear stresses at the interface and the risk of fibre misalignment [START_REF] De Meyere | Optimizing the fiber push-out method to evaluate interfacial failure in SiC/BN/SiC ceramic matrix composites[END_REF]. The push-out tests were carried out with a nanoindenter (Micro Materials Ltd, NanoTest NTX) equipped with a flattened conical diamond tip of 5.5 µm diameter. This fulfils the optimal ratio of 1:2 for the tip:fibre diameter found by De Meyere et al. to properly perform push-out tests independently on each fibre without cracking it [START_REF] De Meyere | Optimizing the fiber push-out method to evaluate interfacial failure in SiC/BN/SiC ceramic matrix composites[END_REF]. The tests were performed under controlled force with a constant loading rate of 1 mN/s. The stress-displacement curves were obtained by dividing the measured force during displacement by the section of the fibre being pushed. For each single-fibre push-out test, the stress σ d corresponds to the initiation of the fibre-matrix debonding on the surface of the sample, taken from the end of the linear domain of the elastic deformation of the fibre. For each test, the interfacial shear stress (ISS), , was determined using the following equation [START_REF] Rebillat | Interfacial bond strength in SiC/C/SiC composite materials, as studied by single-fiber push-out tests[END_REF]:

 = F p D f L f
where F p is the plateau force at which the fibre is pushed out of the matrix after total debonding, D f is the diameter of the tested fibre and L f is its length (i.e. the specimen thickness).

Macro-mechanical tests

The macro-mechanical test specimens were laser cut (Trotec Speedy 400 Flexx -CO 2 Laser) from the as processed single-ply SiC/BN/SiC-Si composites. They were 30 mm long and 12 mm wide orientated within the fibre axis, and were about 0.5 mm thick. These samples, with four specimens for each plate, were cut perpendicularly to the major length for two reasons: (i) more specimens are available and (ii)

unexpected bending is avoided. The tests were performed with an Instron 4505 electromechanical machine equipped with a 5 kN load cell, the crosshead speed being 0.05 mm/min.

On-axis tensile tests

Given the small dimensions of the specimens, aluminium extensions tabs of 14 mm × 40 mm were glued (3M Scotch-Weld EC-9323-2 B/A) to each end of the tensile specimens. Besides, it helped to fairly distribute the forces imposed by the jaws, the hydraulic pressure for jaw clamping being 20 bar. The strain was measured by two extensometers mounted on each opposite face of the specimen. The gauge length was 10 mm. From these tests, some sound values have been measured such as the initial Young's modulus within the fibre direction, E 1 o , the pseudo elastic threshold Rt 0.005 and the maximum values of strain and stress reached during the test,  1 max and  1 max .

A pseudo-elastic threshold has been selected in place of the real damage threshold for the following reason: similarly to metallic alloy, the real threshold may be difficult to set up, especially when some damage (i.e. at least debonding) is present in the as-processed material. Different and quite numerous experiments at both Safran Ceramics and LCTS have led to choose the stress at a strain of 0.005 % (thus denominated Rt 0.005 ).

Besides, in order to remain in the homogeneous domain, i.e. before strain localization and the concomitant plateau or even the softening behaviour, maximum strain and stress values have been considered instead of the rupture values.

In-plane shear tests

A Iosipescu-type fixture was used for the in-plane shear tests. Because of the same small size of the specimens, aluminium extension tabs were added in two parts (14 × 40 mm 2 and 50 × 27 mm 2 ) to fit the Iosipescu testing device, using the same glue.

The specimen strain fields between the end-tabs were monitored by digital image correlation (GOM-ARAMIS software) thanks to a speckle deposit.

Similarly to the tensile tests, values measured and reported elsewhere are the initial shear modulus

G 12 o
, the pseudo-elastic threshold Rs 0.005 and the maximum values of angular shear strain ( 6 max ) and shear stress (𝜎 6 max ) reached during the test.

Microscopy

Optical microscopy and scanning electron microscopy

A first field emission gun scanning electron microscope (FEG-SEM, Hitachi S4500 FEG) was used in the LCTS laboratory not only to measure the BN interphase thicknesses, but also to observe the fracture surface and the fibre pull-out of the composite specimens after the mechanical tests.

Cross-sections obtained from the mechanical specimens were also analysed. They were roughly 12 mm long and were located away from the fracture zone and from the end-tabs. After embedding in epoxy resin, the specimens were mirror polished (Buehler, MINIMET™ 1000). These sections were observed by optical microscopy (OM, Nikon ME600L) to obtain images which were analysed to calculate the proportions of the components and the area of the mechanically loaded section in each specimen. The matrix cracks were observed at the "Centre de Microcaractérisation Raimond Castaing" using a FIB FEG-SEM coupled with energy-dispersive spectroscopy (EDS). The apparatus used was a FEI Helios NanoLab 600i coupled to an Aztec Oxford EDS system (SDD detector, WD 4 mm). Cross sections of specific representative locations were obtained by focused ion beam (FIB) milling (Ga + ions). By alternating sequences of in situ FIB milling and SEM observation in a same sample area, matrix crack paths could be followed in all 3 spatial dimensions from the outside to the inside of selected tows.

Transmission electron microscopy

In a first step, small parts were taken from the samples of the composites after macro-mechanical testing. These epoxy-coated pieces were sandwiched between a silicon wafer and a glass slide and mechanically thinned to a thickness of 120 µm. The electronic transparency was obtained in a second step by ion milling using two different methods. The first method was carried out at LCTS, based on the milling of the sample by a low-energy Ar + ion beam (JEOL, Ion Slicer, EM-09100IS). The second method was carried out at the "Centre de Microcaractérisation Raimond Castaing" by FIB milling.

The thin foils thus prepared were then observed by transmission electron microscopy (TEM, Philips, CM30ST, the LaB 6 source operating at 300 kV). Direct images in both bright field (BF) and dark field (DF) modes were recorded. The DF images were formed from electron beams scattered by sp 2 -BN basal atomic layers of 0.33 nm spacing. High-resolution transmission electron microscopy (HRTEM) images were obtained in the thinnest areas of the thin foils. Selected area electron diffraction (SAED) patterns were recorded from areas of 400 nm in diameter within thick interphases.

Results

Fibre push-out behaviour

In Fig. 1 are displayed typical push-out test curves obtained from single-fibres selected from the singleply SiC/BN/SiC-Si composites with the different BN interphases. The values of the interfacial micromechanical characteristics deduced from all these push-out curves are reported in Table 2.

On-axis tensile behaviour

Regarding the mechanical behaviour of the model composites at the macro-scale, Fig. 2

On-axis in-plane shear behaviour

The matrix fracture surfaces observed after the on-axis in-plane shear tests are oriented at 45° to the fibres (Fig. 3). This feature is typical for tests involving shear loading in CMCs possessing a stiff matrix [START_REF] Lynch | Effects of off-axis loading on the tensile behavior of a ceramic-matrix composite[END_REF][START_REF] Camus | Modelling of the mechanical behavior and damage processes of fibrous ceramic matrix composites: application to a 2-D SiC/SiC[END_REF]. The fibre pull-outs show that the BN interphases do act as a mechanical fuse. The average curves of in-plane shear stress versus angular shear strain are presented in Fig. 4. As in the tensile tests, the shape of the curves is typical of the behaviour of CMCs, with a nonlinear domain linked to both microcracking and fibre-matrix debonding following the initial linear elastic region. Each curve is based on 4 tests for each type of interphase, except for the 12/t samples for which only half of the tests were fully valid. However, all initial plane shear moduli deduced from the linear domains appear to be well representative of the materials and were therefore accounted for. The average values of G 12 o , Rs 0.005 ,  6 max and 𝜎 6 max deduced from the tests are reported in Table 2. The conclusions that can be drawn from these in-plane shear tests are roughly similar to those derived from tensile tests. The average mechanical properties obtained with the interphases synthesised at 900 °C are better than those obtained with the interphases synthesised at 1200 °C. In particular, the composites are stiffer (G

12/t

For a given temperature of interphase processing, their thickness influences the in-plane shear maximum properties of the CMCs. For the interphases synthesised at 900 °C, the thickness of 500 nm results in maximum angular strains of ~ 0.5%. However, the best mechanical shear strength is obtained with the thickness of 200 nm (𝜎 6 max = 145 ± 31 MPa). For the interphases processed at 1200 °C, the average mechanical shear strength is better with the 500 nm thick interphase than with the 200 nm thick interphase (𝜎 6 max = 120 ± 13 MPa and 𝜎 6 max = 85 ± 2 MPa, respectively), almost at the level of the 9/t interphases if scattering is considered.

Crack morphologies after in-plane shear tests

Although the mechanical behaviour of a CMC cannot be quantified from its crack morphology alone, multiple observations of CMCs after mechanical tests allow comparisons and identifications of trends.

That is what motivates the search for results obtained from these observations. As sound results were better obtained with in-plane shear tests, observations of crack morphologies were focused on samples obtained from these tests.

Meso-scale

Regarding the poorly crystallised interphases prepared at 900 °C, different morphologies of matrix cracks are evidenced depending on their thickness. When this thickness is about 200 nm, the crack is open, with an opening of a few micrometres (Fig. 5a). It splits and propagates over long distances inside the tows. When the interphase thickness is 500 nm, the matrix cracks are thinner (less than one micron of opening), do not split, and propagate over short distances within a tow (Fig. 5b).

When considering the highly crystallised interphases prepared at 1200 °C, it appears that the matrix crack morphologies are similar. For both the 200 nm and 500 nm thicknesses, the cracks are few in number, wide open (approaching ten microns) and tend to split. They propagate both between and within the tows over very long distances. An example of this feature is given in Fig. 5c for the 12/t interphase.

Micro-scale

In the case of the interphase synthesised at 900 °C with a thickness of 200 nm, the main crack observed by SEM on the FIB cross-sections has a large opening of about 0.3 µm (Fig. 6a). EDS analyses revealed the presence of carbon and oxygen in the crack on the sample surface, certainly due to the infiltration of the resin used to prepare the section. The vertical straight stripes visible on the milled surfaces in the micrographs are artefacts resulting from a curtaining effect of the ion mill. As the FIB milling proceeded, the main crack was accompanied by small, thin secondary cracks with an opening of less than twenty nm. Eventually, only the secondary cracks remained.

Tracking of a secondary crack is possible due to the resin leading to the formation of small bulges, pores and edgings that are visible by SEM. For example, Fig. 6b shows the deflection of a secondary matrix crack in a rare case where a thin fibre-matrix debonding occurred in the interphase on the matrix side (unmeasurable opening). However, with the 9/t interphase, the majority of debonds have a large opening (up to ~ 150 nm) and occur on the fibre side (Fig. 7) according to the mechanism termed "inside debonding" by Morscher et al. [START_REF] Morscher | Effect of a boron nitride interphase that debonds between the interphase and the matrix in SiC/SiC composites[END_REF]. However, inside debonding (i.e. along the surface of the fibre) is most often observed (Fig. 8a). HR-artefact

nm

MET observation shows that a few basal atomic planes of sp 2 -BN remain attached to the fibre (Fig. 8b).

While at a larger scale of observation the interphase failure may appear adhesive, at this very small scale it can be called to be in fact "cohesive near the interface". It can be assumed that these atomic planes, which are locally better organised than in the rest of the interphase [START_REF] Plaisantin | TEM characterization of turbostratic and rhombohedral BN interphases synthesized by chemical vapour infiltration in SiC/SiC-Si composites[END_REF], remain a weak link in the interphase.

Fig. 8 HR-TEM observation of debonding in a 9/t interphase after in-plane shear test, (b) is a detail of (a)

In the case of an interphase also synthesised at 900 °C but with a thickness of 500 nm, the matrix cracks found on the surface are thin and remain thin without undergoing splitting into secondary cracks in the section after FIB milling. Although the opening width could not be measured, crack tracking was facilitated by an edge brightness effect. The deflection from mode I to mode II occurs gradually in the interphase from the matrix side to the fibre side where the crack seems to stop its propagation (Fig. 9a). Deeper into the FIB milling section, deflections of the same matrix crack can be observed in the interphases of two adjacent fibres (the crack branches in the interphases as it deflects) (Fig. 9b).

The debonds between fibres and matrix are not clearly visible. Yet, since the crack seems to reach the surface of the fibres through the interphase without causing their failure, it can be assumed that the debonds are very thin and take place on the surface of the fibres. Cracks and debonds with a 9/T interphase could only be observed by TEM in a thin specimen prepared by FIB at the "Centre de Microcaractérisation Raimond Castaing". One of these observable debonds is presented in Fig. 10. It is thin and does take place on the fibre side. debonding occurs either at the fibre-interphase interface or at the interphase-matrix interface. Figure 12 shows an example of a crack deflection with debonding on the matrix side. A summary of all these micro-scale observations describing crack morphologies and debonds is presented in Table 3.

Discussion

The scattering observed with the macro-mechanical tests is typical of CMCs and is of the same level for each type of interphase. Taking this scattering into account, it appears that the thinnest interphase synthesised at 1200 °C leads to significantly poorer macro-mechanical properties than for the other three interphases. It should be noted that for these three other interphases, the differences that may appear between the average macro-mechanical characteristics are in agreement with the results of the micromechanical tests. However, these differences are quite tenuous, which hardly allows discerning the roles of these interphases on the behaviour of the single-ply composites. On the other hand, the effects of the microstructure for all the interphases and of the thickness for the weakly organised one are clearly visible in push-out and in terms of crack morphology.

Push-out ISS values show that the thickness of the interphases synthesised at 1200 °C has little effect.

Yet, scattering of the results is proportionally higher for 12/T than with the other interphases. This scattering may be related to the high deposition rate of BN at high temperature which, even in a singleply composite a priori simpler to infiltrate than an industrial composite, leads to infiltration issues, i.e.

strong interphase thickness gradients and therefore heterogeneity as shown in TEM (Fig. 13).

Compared to 12/t, increasing the thickness of this interphase by increasing the processing duration allows more time for the gaseous precursors to infiltrate the tows and thus leads to fewer fibres being poorly coated. In addition, it creates r-BN crystallites which increase the surface roughness of the interphase [START_REF] Plaisantin | TEM characterization of turbostratic and rhombohedral BN interphases synthesized by chemical vapour infiltration in SiC/SiC-Si composites[END_REF], and can then promote interlocking of the matrix with the interphase. Although these effects are not evidenced in micromechanics, it however results in better macro-mechanical properties. It seems that obtaining a BN interphase with a high degree of crystallisation while having a homogeneous thickness throughout the fibre preform would further improve the behaviour of these SiC/BN/SiC-Si composites. One way to achieve this is to use a continuous CVD process [START_REF] Jacques | Multilayered BN coatings processed by a continuous LPCVD-treatment onto Hi-Nicalon fibers[END_REF][START_REF] Suzuki | Uniformization of boron nitride coating thickness by continuous chemical vapor deposition process for interphase of SiC/SiC composites[END_REF]. Such a process in which a single tow is treated separately reduces the infiltration gradients and coats the fibres homogeneously. The tow thus prepared must then be shaped (braiding, weaving...) to elaborate the preform and manufacture the final CMC, as in the case of the "prepreg" process developed for gas turbine applications [START_REF] Luthra | Melt infiltrated (MI) SiC/SiC composites for gas turbine applications[END_REF].

Whatever the interphase thickness, (9/(t and T)) is greater than (12/(t and T)). This was anticipated by Gavalda-Diaz et al. [START_REF] Gavalda-Diaz | Mode I and Mode II interfacial fracture energy of SiC/BN/SiC CMCs[END_REF]. A low degree of crystallisation of isotropic t-BN classically infiltrated at low temperature is related to local atomic stacking defects which increase the bonding between the sp 2 -BN basal planes. Conversely, in the case of a 12/(t and T) interphase deposited at high temperature, the sp 2 hybridisation nature of t-BN is more pronounced with basal planes preferentially aligned parallel to the fibre. Because of the weak bonding between these planes, the ratio of the critical energy release rate in the deflection direction towards the one in the propagation direction G c d /G c p is likely reduced.

The cohesive character of the failure is consequently reinforced as revealed by microscopic observations: the preferential place of debonding shifts away from the surface of the fibre.

By contrast, in the case of 9/(t and T) interphases synthesised at 900 °C, the observed decrease in ISS with the decrease of the interphase thickness is counterintuitive and has no obvious explanation. It interphases our ISS values are globally higher, probably due to the initial fibre surface treatment. The resulting strengthening of the interfacial bonding could be the reason for a different effect of the interphase thickness.

The crack morphologies are in good agreement with the macro-mechanical and, moreover, the micromechanical properties: a stronger fibre-matrix bond (higher σ d and ) means higher tensile and shear strengths, as well as shorter and thinner cracks. Compared to micro-and minicomposites, the use of single-ply composites as model specimens to study interphases is particularly relevant here, and their synthesis remains sufficiently easy at the laboratory scale.

The openings and lengths of damage cracks, which can occur for example in an accidental situation with a CMC, are important characteristics to control. Indeed, even if they seem to have little influence on the overall macro-mechanical behaviour, strong bonds reduce these cracks, thus confining the gap left for corrosive species which could enter them. Beyond the organisation of BN and the exact location of preferential debonding in the interphase, it is mostly the confinement and the synergy between BN and SiC that allow the easy formation of borosilicate seals protecting the BN interphase from corrosion [START_REF] Yang | Microstructure and damage evolution of SiC f /PyC/SiC and SiC f /BN/SiC mini-composites: A synchrotron X-ray computed microtomography study[END_REF][START_REF] Carminati | Oxidation/corrosion of BN-based coatings as prospective interphases for SiC/SiC composites[END_REF]. Thus, for the synthesis of a BN interphase using the CVI batch process, it is advantageous to favour conditions that give a sufficiently thick but yet submicron coating with a low degree of crystallisation to obtain a strong fibre-matrix bond. It may then be necessary to carry out a post-heat treatment judiciously chosen to further crystallise and stabilise the BN interphase with respect to the ambient environment, without increasing significantly its structural organisation [START_REF] Cheng | BN coatings prepared by low pressure chemical vapor deposition using boron trichloride-ammonia-hydrogen-argon mixture gases[END_REF][START_REF] Ma | Effect of heat treatment on the mechanical properties of SiC f /BN/SiC fabricated by CVI[END_REF].

There is still room for improving the behaviour of SiC/SiC composites with CVI-processed BN interphases. The presence of small defects or pores at the BN-fibre interface was not observed as in the work of Gavalda-Diaz et al. carried out with untreated Hi-Nicalon fibres [START_REF] Gavalda-Diaz | Mode I and Mode II interfacial fracture energy of SiC/BN/SiC CMCs[END_REF]. In the present work, the failures are nevertheless close to the interface with the fibre but they are cohesive at the nanoscale, and ISS values above 100 MPa could be obtained. While inside debonding is not a priori a concern, it appears to be due to the preferential alignment of the first sp 2 -BN atomic planes.

Preventing this local organisation through a better control of the deposition transient would further increase the bonding to the fibre.

Conclusion

A hierarchy of fibre-matrix bonding strengths as a function of the thickness and degree of crystallisation of the BN interphase could be established using single-ply model SiC/BN/SiC-Si composites. The observations made at different scales are consistent with each other and, besides, also with microscopic and macroscopic behaviours. Depending on the interphases, the main matrix cracks are more or less long and open, leading or not to secondary cracking. Besides, debonds are more or less pronounced and occur preferentially at different locations in the interfacial system.

The low crystallisation degree of a BN interphase synthesised at 900 °C always leads to a stronger fibrematrix bond and a better mechanical behaviour of the resulting CMC than a high degree of crystallisation of the BN interphase synthesised at 1200 °C. Besides, for the interphase synthesised at 900 °C, a thickness of 500 nm is preferable to a thickness of 200 nm.

It would now be worth studying the macroscopic mechanical behaviour under high temperature oxidising environments of these single-ply composites to verify that the BN interphase 9/T, which is considered to be the most interesting, will still be interesting under the conditions of the aimed application.

Fig. 1

 1 Fig. 1 Typical single-fibre push-out curves for the single-ply composites with the 4 different BN interphases

Fig. 3 Fig. 4

 34 Fig. 3 Rupture surfaces obtained from SEM observations on samples tested in shear with an interphase (a) 9/t and (b) 12/T

Fig. 5

 5 Fig. 5 SEM observations of cracks induced by a shear loading on single-ply 2D SiC/SiC-Si composites with various interphases, (a) 9/t, (b) 9/T and (c) 12/t

Fig. 6 Fig. 7

 67 Fig. 6 FIB-SEM images of a crack in a single-ply composite with a 9/t interphase of a sample tested in shear. (b) is a magnification of (a)

Fig. 9

 9 Fig. 9 FIB-SEM images of a crack (yellow arrows) in a single-ply sample with a 9/T interphase. (b) is further in the cutting than (a)

Fig. 10

 10 Fig. 10 BF-TEM observation of a debond (purple arrows) in a 9/T interphase after an in-plane shear test

Fig. 11 FIBFig. 12 FIB

 1112 Fig. 11 FIB-SEM image of cracks in a SiC/BN/SiC-Si single-ply sample with a 12/t interphase

Fig. 13

 13 Fig. 13 TEM observations of debonds (purple arrows) (a) in BF mode in an interphase 12/t, and (b) and (c) in DF mode in interphases 12/T after in-plane shear test

Table 1

 1 Interphase thicknesses measured by SEM at tow edges in the useful area of SiC/BN/SiC-

Si composites BN interphase 9/t 9/T 12/t 12/T synthesis temperature (°C)

			900	900	1200	1200
		target thickness (nm)	200	500	200	500
	edge 1 of	mean (nm)	186	443	197	665
	useful area	standard deviation (nm)	91	170	52	472
	centre of	mean (nm)	195	485	151	517
	useful area	standard deviation (nm)	56	213	66	354
	edge 2 of	mean (nm)	204	398	196	572
	useful area	standard deviation (nm)	74	175	51	297

Table 2

 2 Mechanical results

				interphase	9/t	9/T	12/t	12/T
	micromechanics	(push-out)	σ d 	mean (MPa) standard deviation (MPa) number of tests mean (MPa) standard deviation (MPa) number of tests	2101 300 17 74 14 19	3996 456 16 124 9 15		1223 368 12 34 12 15
				mean (GPa)	261	250		229
			E 1 o	standard deviation (GPa)	34	33		27
				number of specimens	7	8		6
	macro-mechanical properties	on-axis tensile tests in-plane shear tests	Rt 0.005  1 max  1 max G 12 o Rs 0.005  6 max  	mean (MPa) standard deviation (MPa) number of specimens mean (%) standard deviation (%) number of specimens mean (MPa) standard deviation (MPa) number of specimens mean (GPa) standard deviation (GPa) number of specimens mean (MPa) standard deviation (MPa) number of specimens mean  standard deviation (%) number of specimens	194 28 7 0.33 0.08 7 336 34 7 86 23 4 78 29 4 0.32 0.07 4	161 41 7 0.46 0.09 7 350 39 7 76 12 4 78 16 4 0.5 0.15 4	0.28 0.1 0.33 0.01	137 24 7 0.28 0.05 7 306 43 7 60 9 4 61 10 4 0.3 0.05 4
				mean (MPa)	145	123		120
			𝝈 6 max	standard deviation (MPa)	31	11		13
				number of specimens	4	4		4

Table 2 .

 2 The lowest tensile mechanical properties are obtained for 12/t whereas the best maximum properties are obtained with the 9/T interphase. However, if the average maximum strain is clearly higher with this interphase, the mechanical strength is, on the other hand, close to those obtained with the other two interphases: 9/t

	and 12/T.

shows examples of tensile stress-strain curves obtained with the four composites possessing different BN interphases. The nonlinear curves are typical of CMCs with non-brittle behaviours involving multicracking of the matrix as well as concomitant fibre-matrix debonding. The values of E 1 o , Rt 0.005 ,  1 max , and 𝜎 1 max deduced from all the tensile curves are presented in Fig. 2 Examples of monotonic stress/strain curves obtained from on-axis tensile tests performed on the 4 different SiC/BN/SiC-Si composites

Table 3

 3 Summary table of the morphological observations performed on the 4 different single-ply SiC/BN/SiC-Si

	composites regarding cracks and debonds
		interphase	9/t	9/T	12/t and 12/T
		opening	▐	│	█
		splitting	+	∅	+
	OM	length	▬	•	▬
		inter-tow	∅	∅	+
		intra-tow	+	+	+
		opening	▐	│	█
	FIB-SEM	splitting BN/M F/BN	+ ~ ∅ ++	∅ ∅ ++	+ + +
		BN	∅	∅	+
		opening	▐	│	▐ and │
	TEM	BN/M F/BN	+ ++	∅ +	+ +
		BN	+	∅	+
	crack opening: █: very wide, ▐: wide, │: small
	crack length: ▬: long, •: short
	++: very frequent, +: frequent, ~ ∅: rare, ∅: absent
	BN/M, F/BN, BN: location of debonding on the fibre side, on the matrix side or in the middle of the interphase
	respectively.

  contradicts, for example, the fibre push-out results obtained by De Meyere et al. with their HNS/BN/SiC

CMCs

[START_REF] De Meyere | Optimizing the fiber push-out method to evaluate interfacial failure in SiC/BN/SiC ceramic matrix composites[END_REF]

. The number of tests performed is much smaller and therefore the statistical study is far from being as sound as that of De Meyer et al. It should be noted, however, that with 9/(t and T)

Ethics declarations

Conflict of interest

Author H. Delpouve has received a PhD grant from SAFRAN CERAMICS.


Nina Manomba-Mbadinga

Simona Niculescu A-B

Narimane Zaabar

Jean-Bernard Mombo

Guanyao Xie

Grand Libreville (Gabon) coastline using machine learning and convolutional neural network detection and automatic extraction of the methods

Keywords: Remote sensing, machine learning, deep learning, Grand Libreville, coastal erosion, OBIA_PBIA, RF, SVM, CNN

Coastal erosion is a major problem that has been worsened by climate change, along with other natural occurrences like droughts and marine flooding. Countries situated along coastlines are facing significant challenges when it comes to preserving their land and protecting their people and assets. To mitigate the damage caused by the encroachment of the sea on land, effective monitoring tools and methods are required. Several remote sensing techniques and methods have been developed to address these issues, including machine learning and deep learning methods. In this study, objectoriented analysis (OBIA), pixel-oriented analysis (PBIA), and convolutional neural network (CNN) methods are used to automatically detect and extract the Greater Libreville coastline, based on Pléiades very high-resolution satellite image dating from 2022. Three test areas were chosen there and then extracted. The first zone is located in the north of the municipality of Akanda (marked by the presence of small coastal cliffs). The second zone is located in the commune of Libreville (sandy beach). The third zone is located in the municipality of Owendo (artificialized beach, mostly muddy).

The images of the three zones were the subject of a classification based on the methods mentioned above. Results of proposed methodologies showed competitive Overall accuracy (OA) values obtained with OBIA method and the CNN model. However, the OBIA method using Random Forest algorithm (RF) achieved the highest accuracy rates, which reached 95%, 90%, and 80% for the 3 test areas respectively.

INTRODUCTION

Artificial intelligence (AI) is an essential tool of the current era. It is present everywhere, both in our homes and outside. Although AI is somewhat controversial because it is seen as an adversary to humans, it is proving to be a revolution for humanity in several areas. Machine learning (ML) and deep learning (DL) are subfields of AI that offer many algorithms that are widely used in various professional fields on different topics. Geomatics deals with various related subjects, such as human activities, agricultural plots, drought and coastal erosion monitoring, and various other human pursuits. It has been able to integrate ML and DL using robust and reliable algorithms. The ML algorithms include decision trees (DT), the k-nearest neighbors (K-NN) algorithm, linear regression, the Naïve Bayes algorithm, logistic regression, gradient boosting, forests (RF), and the support vector machine (SVM). On the other hand, DL integrates several algorithms such as, convolutional neural networks (CNN), recurrent neural networks (RNN), radial basis function networks (RBFN), long-term and short-term memory networks (LSTM), iterative adversarial networks (GANs) and restrictive Boltzmann machines (RBM).

Coastal erosion is a topical issue that has been the focus of renewed attention for several decades. "Coastal areas will see continued sea level rise throughout the 21st century, contributing to more frequent and severe coastal flooding in low-lying areas and coastal erosion. Extreme sea level events that previously occurred once in 100 years could happen every year by the end of this century". Given this reality, several developed countries have conducted decades of research to find solutions to this problem. While several developing coastal countries are struggling to assess the evolution of their coast. In this study, which deals with the detection and extraction of the Greater Libreville coastline, machine, and deep learning methods were used, including random forest (RF) and support vector machine (SVM) for machine learning and CNN for deep learning. These are considered to be among the most effective classification methods. Nevertheless, opinions differ on their accuracy, even though their reliability is undisputed. Some studies confirm the similarity of classification accuracy between random forest and support vector machine ( [START_REF] Dalponte | Tree species classification in boreal forests with hyperspectral data[END_REF], [START_REF] Adam | Land-use/cover classification in a heterogeneous coastal landscape using RapidEye imagery: Evaluating the performance of random forest and support vector machines classifiers[END_REF]). However, studies ( [START_REF] Maxwell | Assessing machine-learning algorithms and image-and lidar-derived variables for GEOBIA classification of mining and mine reclamation[END_REF], [START_REF] Raczko | Comparison of support vector machine, random forest and neural network classifiers for tree species classification on airborne hyperspectral APEX images[END_REF], [START_REF] Bengoufa | Machine learning and shoreline monitoring using optical satellite images: case study of the mostaganem shoreline, algeria[END_REF]) believe that SVM outperforms RF. Conversely, other studies ( [START_REF] Abdel-Rahman | Detecting Sirex noctilio grey-attacked and lightning-struck pine trees using airborne hyperspectral data, random forest and support vector machines classifiers[END_REF], [START_REF] Shang | Classification of Australian native forest species using hyperspectral remote sensing and machinelearning classification algorithms[END_REF], [START_REF] Lawrence | The AmericaView classification methods accuracy comparison project: A rigorous approach for model selection[END_REF]) tend to believe that RF performs better than SVM. As for CNN, according some studies [START_REF] Yoo | Comparison between convolutional neural networks and random forest for local climate zone classification in mega urban areas using landsat images[END_REF], [START_REF] Xie | Mapping and Monitoring of Land Cover/Land Use (LCLU) Changes in the Crozon Peninsula (Brittany, France) from 2007 to 2018 by Machine Learning Algorithms (Support Vector Machine, Random Forest, and Convolutional Neural Network) and by Post-classification Comparison (PCC)[END_REF] give more satisfactory results than RF and SVM. In this paper, we evaluated the performance of these different approaches for the detection and extraction of the Greater Libreville coastline using Pléiades very high-resolution image from 2022. For this comparison, we selected the models whose relevance was based on the parameterization of the number of trees (Ntree) and the number of variables (Mtry) for the RF, the cost value (C), and the gamma (γ) penalty function for the SVM, the scale and homogeneity for the CNN.

Study area

The Grand Libreville town is composed of four municipalities (Figure 1), namely Libreville, Ntoum, Owendo, and Akanda. The area is situated within the coastal sedimentary basin of Gabon, which is characterized by low altitudes.

Three study areas were selected in the coastal municipalities of Greater Libreville to apply the proposed methodology.

The first area is located in the municipality of Akanda and covers an area of about 5 km. It is covered with shrubby vegetation and characterized by small discontinuous coastal cliffs. In addition, the beach is essentially characterized by an extension of the reef flat towards the sea and covered with a thin layer of sand. The second one, located in Libreville, is more urbanized and extends over approximately 4 km. Its projecting sandy beaches leave rocky outcrops in some places. This sector is part of the heart of the capital and boasts many infrastructures, including roads, schools, hotels, restaurants, and residences located along its sandy beaches. The third area, located in Owendo, is an urbanized area that stretches for about 13 km.

Methodology

To address the assigned purpose of this study, the proposed methodology includes the following steps: the choice of the baseline of the coastline, the choice of data, the processing tools, and the processing methods.

There are about 45 coastline indicators [START_REF] Boak | Shoreline definition and detection: A review[END_REF] depending on the type of coast around the world. The vegetation limit, the outer limit of coastal construction, the run-up limit, and the limit between the dry sand and the wet sand are the references used for the characterization of the coastline of our three test zones.

Materials

Both open-source and paid software were used, these are QGIS, Orfeo tool box (OTB), ArcGis, and eCognition.

QGis (version 3.28.4) was used for image preprocessing, image segmentation, and cartographic presentation of our input data (images and samples). OTB (version 8.1.1) was useful for the generation and prediction of RF and SVM classification models for both PBIA and OBIA approaches. ArcGis (version 10.8.1) on the other hand was used to generate the training and verification points selected according to the characteristics of the images randomly. These data are very important for the application of the different methods. Also, ArcGis was used for the extraction of the coastlines of our different areas of interest as well as the layout of the final cartographic results. To carry out the image classification through CNN, we used eCognition software version 10.0.

Machine learning approaches

Two machine-learning algorithms were established and compared: RF and SVM. The objective was to define the most efficient one for the accurate detection and extraction of the coastline. These algorithms were applied in two image levels according to PBIA approach based on pixels and the OBIA approach based on image segmentation.

The pixel-based image analysis approach is a process that consists of classifying each pixel of an image directly according to its spectral similarity. It was tested using OTB software for shoreline detection. Five steps were followed: identification of thematic classes, model training, classification, accuracy assessment, and shoreline extraction (Figure 2). In this context, we decided to classify our image into five classes as previously defined. For each class, at least, 200 samples were created using ArcGIS software. Of the samples, 80% were used in the training phase, and the remaining 20% were used for the crucial validation phase. It was imperative to use the input data, which is the very high-resolution Pléiades image and the training and validation samples, to test the robustness of the random forest (RF) and the support vector machine (SVM) for the classification pixel by pixel (figure 2). Object-based image analysis (OBIA), on the other hand, is based on the fundamental principle that an image is not made up of pixels but of several objects. Objects are created based on similarity criteria built on the spectral response, texture, and neighbourhood. The eCognition software was the main tool used to perform this analysis. This approach is almost identical to the previous one, with one difference: the segmentation phase. Segmentation is a crucial step that strongly influences the classification quality. The scale parameter in multiresolution segmentation is key to controlling the size of the segmented objects, and should be optimized for improving OBIA classification [START_REF] Zaabar | Application of convolutional neural networks with objectbased Image Analysis for Land Cover and Land Use Mapping in Coastal areas: a case study in ain témouchent, Algeria[END_REF]. There are a variety of segmentation algorithms. For this study, multi-resolution [START_REF] Baatz | Multiresolution segmentation: an optimization approach for high quality multiscale image segmentation[END_REF] segmentation algorithm was selected, making it possible to extract some relevant information (figure 3).

Random Forest is an algorithm built into the OTB software. Build multiple decision trees using a randomly selected subset of samples and learning variables. It is one of the most successful classifiers in machine learning. It has many advantages, such as high-precision output [START_REF] Rodriguez-Galiano | Predictive modelong of gold potential with the integration based on random forest: a case study on the Rodalquilar area, Southern Spain[END_REF]. Despite the robustness of radio frequency, it also has some obvious disadvantages, such as tree visualization, due to the use of multiple trees for prediction [START_REF] Breiman | Random forests[END_REF]. Its classification division rules are ambiguous, so it is considered a black-box classifier [START_REF] Rodriguez-Galiano | Predictive modelong of gold potential with the integration based on random forest: a case study on the Rodalquilar area, Southern Spain[END_REF]. The Ntree and Mtry are the two parameters that strongly influence the RF. They are user defined. The influence of these parameters on the different precision and the Mtry parameter is more significant than the Ntree parameter [START_REF] Ghosh | Ramework for mapping tree species combining hyperspectral and lidar data: role of oelected classifiers and sensor across three spatial scales[END_REF]. Nevertheless, the use of the optimal values for the two parameters is essential to obtain a better precision. Belgiu and Drǎguţ [START_REF] Belgiu | Random forest in remote sensing: a review of applications and future directions[END_REF], proposed 500 as the default number for Ntree. Along the same lines, Guan and al [START_REF] Guan | Integration of orthoimagery and lidar data for objectbased urban thematic mapping using random forests[END_REF] advise as many Ntree values as possible, indicating that the RF classifier is efficient/robust and resistant to overfitting. Regarding the Mtry parameter, it is usually defined as the square root (sqrt) of the number of input variables unlike other researchers who intend it to be equal to the total number of available variables [START_REF] Ghosh | Ramework for mapping tree species combining hyperspectral and lidar data: role of oelected classifiers and sensor across three spatial scales[END_REF]. The opinion of Belgiu and Drǎguţ [START_REF] Belgiu | Random forest in remote sensing: a review of applications and future directions[END_REF] is completely opposite and asserted that setting such a value can however affect the speed of the algorithm because the method has to calculate the information obtained from all the parameters expressed to split the nodes.

In this work, we assigned the values of 15 and 100 respectively to Ntree and Mtry after several tests. This setting was maintained for each of the study areas. After training the model and passing it through the classification phase, we tested its reliability, and for this, 20% of the samples were used to produce the matrix and calculate the Kappa coefficient and the overall accuracy (Overall Accuracy) on OTB (Figure 3). Then the image, which was in the raster file, was converted to a vector file. The last step was the extraction of the coastline. The basic principle of SVM is to reduce a classification or discrimination problem to a hyperplane (feature space) in which the samples are separated into several classes whose boundary is as far as possible from the data points (maximum margin) [START_REF] Devadas | Support vector machine classification of objectbased data for crop mapping, using multi-temporal Landsat imagery[END_REF].

Several kernels, such as linear, polynomial, Gaussian radial basis function, and sigmoid kernels can be used in SVM models.. The cost parameter C and the gamma parameter are the two main parameters that can significantly affect the performance of the SVM. RBF is the most popular used in support vector machines. In this work, the linear kernel was applied and the default values of two parameters were maintained, namely 1 for each of the parameters.

Convolutional neural network (CNN)

The CNN architecture was created in Trimble eCognition Developer (v.10). The CNN Training process consists of three main steps: 1) creating patch samples, 2) generating and training the model, and 3) applying the model. To this process is added that of classification based on the Object-Based Image Analysis (OBIA) (Figure 4). First, it would like to point out that the convolutional neural network is a deep learning (DL) model inspired by the architectures of biological neural networks. This model is inspired by the ability of the human brain to detect and process text, images, and videos. CNN is composed of neurons with learnable weights and biases [START_REF] Noshad | Fault Detection in Wireless Sensor Networks through the Random Forest Classifier[END_REF].

As input, convolutional layers use patches of image samples containing all the features by scanning the entire image. The first convolution layer detects image features such as edges, shapes, and textures. Subsequent layers then detect more complex features based on the features detected by the previous layer. A fully connected layer that combines the features detected by the convolution layers and uses them to classify the image usually follows the last convolution layer.

Several parameters are crucial for CNN optimization. Tuning the sample patch size, hidden layers and learning rate are essential steps to obtain a performing model. Thus, in order to choose a relevant sample patch size, we took into consideration the dimensions of our five target classes (Water, wet sand, dry sand, vegetation, and urban). Since the patch sample size is considered one of the most critical parameters in the optimal CNN architecture [START_REF] Ghorbanzadeh | Optimizing Sample Patches Selection of CNN to Improve the mIOU on Landslide Detection[END_REF], several sample sizes were tested: 8×8, 10×10, 16×16, 20×20, and 32×32 pixels. After having followed a cross-validation process, the CNN models of our three test images (Akanda, Libreville, Owendo) were fed with the 20×20 sample patch size; 8×8 and 20×20 pixels respectively. In total, the global number of labeled sample patches for training the models of the images Akanda, Libreville, and Owendo are respectively: 5000, 10000, and 10000.

Once the sample patches have been created, the next step is to create the CNN model. In this process, all spectral bands of the input data have been solicited. Two hidden layers were constructed for each CNN model after running cross-validation and evaluating the CNN output accuracy results. The maximum pooling was applied. Then following a cross-validation method, a convolution was implemented. The models of the images of the Akanda and Owendo areas were parameterized so that the kernel size value of the first layer is 5 × 5 and 7 × 7 for that of the second layer. While the second model, the one generated from the Libreville area image has a kernel size of 3x3 for the first and second layer.

In training step of CNN model of Akanda area, the following parameters were retained: patch size of 50 and 5000 training steps. From a cross-validation process revealed that the optimal learning rate to be set at 0.0006. This made it possible to achieve a good performance. The same configuration was assigned in the case of CNN architecture of the two other areas. Moreover, after several cross-validation processes (with rates set at 0.0008, 0.0006, 0.0005, 0.0003 and 0.0001), their optimal learning rate retained was 0.0001 each. Note that if the learning rate is insufficient, it can either increase the time of the learning process (at low rate), this could block the network in the local minima, or reduce it (at a high rate), but it is could then, in this case, that the network does not reach the minima. In both cases, it would be impossible to obtain correct weights.

The application of the CNN generated from the three images allowed to obtain three thermal maps were generated based on fully connected layers. The layers correspond to the occupation of the ground according to the five predefined classes. These heatmaps have a unit for each class predicted by CNN where two possibilities were considered: a value close to 1 or a value close to 0. The first case would indicate a higher probability of the category, while the second case would indicate a probability weaker.

The results of the training of the built models of the three zones images served as input datasets for the OBIA classification. The latter is dedicated to the development of automated methods for the segmentation of geospatial imagery into image objects. Since the CNN is carried out at the pixel level, the OBIA approach will be applied to it so that the entirety of this image is transformed into a segmented object image from the multi-resolution algorithm [START_REF] Baatz | Multiresolution Segmentation: an Optimization Approach for High Quality Multi-Scale Image Segmentation[END_REF].This last is a widely used segmentation algorithm for very high spatial resolution data applications. It is based on the evolution of the fractal network and aggregating individual pixels into objects of increasing size at several levels in an iterative process. Critical MRS issues are parameter optimization and segmentation quality assessment. This segmentation process is based on three parameters whose adjustment is submitted to the user. Mainly: 1) the scale, (defined as the maximum allowed heterogeneity within the objects); 2) the shape (weight between the spectral and a shape factor); and 3) compactness (regularization factor). After cross-validation, the scale, Shape and compactness parameters were set to: 20, 0.9 and 0.1 respectively for the images of our three areas of interest. The resulting objects were trained and classified based on a combination of neighborhood, spatial properties, and similarity in CNN probability. After final classification, the polygon vector images obtained were converted to polyline format in order to detect and extract the target shoreline on each of the images. The selected coastlines are the limit of the run-up, the limit between dry sand and wet sand, the limit of vegetation on the sea side as well as the limit on the land side of protection works. In fact, the extraction is done by selecting the class identifier of interest in the attribute table and eliminating all other class polylines (figure 4). "Edit function" (ArcGis). This approach is applied based on the "ComputeConfusionMatrix" process on OTBv8.1.0.

Data

Pleiades

The methodology followed in this study was applied to three Pléiades satellite images acquired on 21 and 27 August 2022, and provided by Airbus DS. The images available with high spatial, multispectral, and panchromatic resolution have four bands: red, green, blue, and near-infra-red. The precision of this image is 2 meters (Table 1). The projection system of the study areas is (WGS 84 32 N).

Images Acquisition day Precision (m) Resolution (m)

Pléiades Previously, these images went through a pre-processing phase to improve their visual quality (figure5). First, the images collected were georeferenced using the "georeferencing" tool. Georeferencing allows the user to define the location of rasters to be georeferenced in their spatial location based on geographic coordinates. In our case, a satellite image of Greater Libreville dating from 2013 was used as a base. Then; the images were mosaicked using the "mosaic" algorithm. Tiling allows multiple rasters or images from the same sensor to be merged into a single overview image. At another time, this mosaic underwent an orthorectification. An ortho-rectification is a process allowing correct the geometry of the images in order to make them superimposable with other rasters. Finally, our three different areas of interest were extracted from this mosaic from the Polygon Shapefiles representing the companies in the areas. The "raster" tool was used for this purpose. As with the type of algorithm chosen, the quality and number of classified samples has a significant impact on the accuracy of the expected result (land cover map). The selection of samples is therefore a crucial step. Controversy over the size of these samples exists in the scientific community. For some, to obtain good classification accuracy, the training data must represent 0.25% of the total study area [START_REF] Thanh Noi | Comparison of Random Forest, k-Nearest Neighbor, and Support Vector Machine Classifiers for Land Cover Classification Using Sentinel-2 Imagery[END_REF]. In contrast, others argue that training samples should not be less than 10 times the number of features in the classification model [START_REF] Jensen | Traitement d'image numérique d'introduction : Une perspective de télédétection[END_REF]. Never mind, you have to choose a large number of samples to improve the results.

Two hundred (200) train samples were created for each class in the three test zones. We took care to ensure that these points did not overlap. We then converted these points into polygons (squares) to form the various models. Each sample was labelled according to the class it belongs to.

Results and discussion

The results presented within the framework of this study come from the application of three approaches, which are the PBIA, the OBIA and the CNN. The first two approaches were designed from models based on two algorithms: RF and SVM. As for the CNN, it was combined with the OBIA approach. Given the diversity of the results obtained, the analysis will be based on the results of the approach that demonstrated the best performance rates for the classification of the three test areas located respectively in the municipalities of Akanda, Libreville and Owendo. 15 classified images from the three different approaches were obtained. Each algorithm was tested on the three test areas. As well as with the PBIA and OBIA approaches, the RF recorded the best classification performance rates but those obtained from the RF-OBIA are the most relevant (Table 2).

. Table 2: comparison of the performance of ML and DL algorithms OA and kappa values of the image classifications of the three zones are respectively: 95% and 94% for the Akanda zone; 90% and 88% for the Libreville area and 80% and 75% for the Owendo area. Overall, SVM-OBIA was also achieved satisfactory results. It showed OA index and kappa index rates of 92% and 90 for the Akanda area; 82% and 77% for the Libreville area and 67% and 58% for the Owendo area. The approach having been the least efficient for the classification of the coastline of the three images of the test areas is the CNN. The OA and the recorded kappa indices are respectively: 91% and 90%, 68% and 75 and 79% and 74%.

Of the 15 images resulting from the tests of the different approaches, only three images will be presented zone (1, 2 and

3). These are the resulting classification images from the RF-OBIA. The figures below (figures 7, 11 and 13) present in each case the image of the study area and then the result of its classification and "urban". This confusion may arise from the fact that certain pixels of the sand have spectral information similar to certain pixels belonging to the "wet sand". The slight confusion between the two other classes can also be explained by a similarity of spectral signature between dry sand and bare soils included in the "urban" class. Furthermore, it would like to point out that in the majority of cases, the class "wet sand" actually represents the rocky flat which is covered with a thin layer of wet sand. The indicators by class (precision, recall and f-score) are also correct since they are above 90% in most cases.

From these excellent results, the coastline was extracted by converting the polygon vector image into polyline vectors. This made it possible to extract the coastline (Figure 8) by selecting the vegetation and urban classes in the attribute table. The coastline extracted is that defined by the limit of the vegetation at the top of the cliffs. The top of the cliffs are not always covered with vegetation. In the rare cases where the vegetation is hindered by built-up areas, the limit on the sea side of the building (barrier) was considered for In addition, the coastal line is also a broken aspect linked to the confusion of classification between vegetation and buildings. It can be seen that there are linear sectors belonging to the "urban" class which encroach on the vegetation in urbane zone. In this case, we consider this linear as a coastline because it reflects the limit of vegetation at the top of the cliffs (Figure 9). As a whole, the coastline does not suffer from any gap (discontinuity) thanks to the fusion of the linear obtained from the "urban" class. In other cases of class confusion between the vegetation and the urban, the limit of the latter has been considered as the coastline (figure 10). 11). The "urban" class has the lowest classification accuracy rate, at 78%. This rate comes from a confusion between this class and all the other classes. However, the vegetation class causes the most confusion. This confusion may be related to the shade. Because the class "urban" includes buildings and these buildings often generate shade, as well as vegetation (tree). The conversion of the polygon vector image into polyline vectors allowed extracting two coastlines. The first is instantaneous water line and the second is wet/dry line or runup maxima (Figure 12). These indicators turned out to be very relevant because the sandy beach makes it visible almost over the entire area of interest. It should be reported that compared the two extracted coastlines, it is the second, which is interrupted, unlike the first, which is a continuous line. According to the results of the learning rates obtained for the classification of the image of the third test area located in the municipality of Owendo, the 5 classes of were not correctly extracted (Figure 13). Consequently, the learning rates by class rarely reach the 80% mark, for instance "vegetation" class and "Water" class, which exceed the 80% threshold.

The "dry sand" and "urban" classes are my well-ranked classes. Many pixels belonging to the "dry sand" class have been classified as flat to the "wet sand" and "urban" classes.

Figure 13: Zone 3 classification by RF-OBIA May be confusion with the "urban" class comes from the fact that this class also takes into account bare soils whose spectral characteristics would seem similar to those of the "dry sand" class. Moreover, the "urban" class, for its part, merges with almost all the other classes except the "dry sand" class. The "wet sand" and "water" classes have the most biased rates. Indeed, this confusion with the aforementioned first class is linked to the fact that wet bare soils have spectral signatures similar to that of wet mud or sand. It should be noted that the Owendo area has a mostly muddy coast due to the supply of continental sediments to the beaches via the Komo River. It is not entirely fortuitous to recall that the "urban" class includes sub-classes such as: built-up areas, bare soils and all kinds of anthropogenic marks. Thus, note that the quay of Owendo has been "erased" to the detriment of the "water" class.

The reason for this may lie in the fact that the quay in Owendo's port is most likely coated with a thin layer of wet sand at the outset. Additionally, the tide coefficient was at a low point during image acquisition, which could emphasize the turbidity of the seawater and in turn, affect classification by introducing spectral features akin to the dock, ultimately causing confusion between categories.

Considering previous classification results, the extraction stage of the coastal zone was important. Similarly, the polygon vector image was converted to a polyline vector (Figure 14). The coastline used here is derived from a combination of several other reference points: inflow maxima or wet/dry lines, landward edges of coastal structures, and vegetation Limit. The extraction of coastlines heavily relies on their accurate classification, as a flawed categorization renders the extraction process unfeasible. To overcome the challenges posed by the discontinuity of each frame of reference, multiple frames of reference were utilized. Although significant efforts were made to obtain a complete coastal line encompassing the entirety of the study area, errors in classification still resulted in a fragmented appearance.

The primary objective of the classification process is to extract the coastline using various indicators such as the boundary between dry and wet sand, the limit of the run-up, the limit of vegetation or buildings like barriers, riprap, arrows, and the foot of the cliff. To achieve this, the conversion of the image into a polygon vector format had to be transformed into polyline vectors, aligning it with the aforementioned reference lines. The unsmoothed coastline after the conversion from polygon to polyline format is exhibited in figure 14-a. This is merely a rough drawing made to provide a general overview of the coastline. A visual inspection was then performed, confirming that the reference line was clearly recognizable and matched reasonably well with the coastline in the imagery.

Comparing the three classification approaches, we found that ML with RF was more relevant than DL for classifying the three test domains. These areas have same spatial resolutions and topographic features.

The application of RF-OBIA method in test area 1, our objective was achieved very satisfactorily. The classification and extraction of coastlines was facilitated by the fact that there were not many signs of enthronization marks. However, this stretch of coastline has more noise than other areas because it is based on treetop routing. Manual digitization of vegetation (shrubs) requires more time and attention to detail. Being able to do this thanks to the classifications in Rescore is quite a feat. However, a smoothing process is needed to better reflect the actual situation. Cliff areas are often difficult to access, so this approach provides an excellent relief for field data collection, although it is also important for better coastal surveillance.

Furthermore, the second area classification results show that the classification of sandy coastlines can simultaneously extract three coastlines, despite the necessity of a judicious choice of identified classes. As well, the coastlines in question are : the instantaneous limit of the run-up; the boundary between dry sand and wet sand; and, the vegetation line. The coastline defined by the limit of the run-up is the best executed but the least relevant because of its very changing nature over time. The last two, although often discontinuous due to classification errors, are to be preferred for extraction. Visual inspection efforts and adjustments (manual scanning) are still required. As for urbanized areas and muddy foreshore like those of the third zone, their classifications are not satisfactory because the RF model struggles to clearly identify the different objects such as dry sand, wet sand and built-up areas. We can see that only the vegetation class was successfully classified, reaching an accuracy rate of 96%.

Badly classified pixels hinder the recognition of the coastal line in the sense that they do not reflect the reality on the ground but also do not allow the recognition of the coastline. Moreover, if the discontinuous character of the anthropogenic indicators (limit of riprap, residential barriers, retaining walls, etc.) and geomorphological (dry sand, wet sand, foot of cliff) cannot by themselves serve as a definition on several kilometers, they nevertheless serve as a connection in certain places where the vegetation or the limit of the run-up shows these limits, etc. It is difficult to define a coastline in its entirety with only one indicator, unless it is a very small study area. In our three test areas, the vegetation limit seems more suitable for the delimitation of the geomorphological coastline [START_REF] Leberre | Cartographie synthétique de l'environnement littoral du Finistère, exploitation de SPOT pour la cartographie de l'estran, du trait de côte et de l'occupation du littoral, Rapport final[END_REF] as well as the limit of the run-up are the most represented indicators because of their continuity in space.

Conclusion

This study entitled "Automatic detection and extraction of the coastline of Greater Libreville (Gabon) using machine learning methods and convolutional neural networks" aimed to find a relevant automation method for the extraction of the feature coast of Greater Libreville. It was used as a spatial data a Pléiades very high resolution (VHR) satellite image acquired on 2022. Three areas of interest were extracted for the satellite images. To reach the primary objective of this study, different Machine and Deep Learning approaches have been tested. For this purpose, PBIA and OBIA approaches based on ML algorithms were performed and compared to the CNN integrated with OBIA approach.

As well, three algorithms (RF, SVM and CNN) were examined in three areas located respectively in the municipalities of Akanda, Libreville and Owendo. For the implementation of the different approaches, sampling points (training and validation) as well as the three extracted satellite images were requested. The selected algorithms allowed to assess the performance of the proposed approaches by creating models that could be used for image classification and validation.

Five classes were distinguished for each classified image: 'water', 'wet sand', 'dry sand', 'vegetation' and 'urban'.

Fifteen classified images were obtained but only three of them were presented. It is from them that the coastlines were extracted and they were obtained thanks to the OBIA approach driven by the RF. Indeed, the RF-OBIA approach was the most efficient for the detection and the extraction of the coastline. It reached OA and kappa index rates equal to 95% and 94% of the Akanda area; 90% and 88% for the Libreville area and 80% and 75% for the Owendo area. In second position, the SVM then the CNN. Although the classification results were generally satisfactory, after visual inspection and consulting the information provided by the confusion matrix, there is a great confusion of classes coming mainly from the 'urban' and 'dry sand' classes in the municipality of 'Owendo. These confusions of classes have repercussions on the extraction of the coastline, thus preventing the recognition and extraction of certain indicators in certain sectors where the error is large. Moreover, certain anthropogenic and geomorphological indicators present more limits related to their discontinuities in time, which calls into question their relevance as coastline indicators. Additionally, on the coast, the vegetation limit and the run-up are the most appropriate indicators because of their continuities in space, making the detection, extraction and choice of the latter as reference points less complex. This study showed the relevance of machine learning for the automatic detection and extraction of varied coastlines. Although the latter are very affected by noise due to the fact that the algorithm that generates them processes data in great detail. If, the automation of the coastline proves to be a perfect alternative for the extraction of the coastline in on small scale linear like that of Akanda or Libreville, manual adjustments will be required to improve results.

Figure 1 :

 1 Figure 1: Geographic situation of the study area

Figure 2 :

 2 Figure 2: Shoreline extraction by PBIA approach

Figure 3 :

 3 Figure 3: Shoreline extraction by OBIA approach Another algorithm was tested, it's the support vector machine (SVM). It is a supervised machine learning classification algorithm [19]. It is a linear classifier. It is part of the most powerful machine learning (ML) algorithms.

Figure 4 :

 4 Figure 4: Shoreline extraction from CNN integrated with OBIA

Figure 5 :

 5 Figure 5: Pre-processing of images

Figure 6 :

 6 Figure 6: Creation of samples

Figure 7 :

 7 Figure 7: Zone 1 classification by RF-OBIA

Figure 8 :

 8 Figure 8: Shoreline extraction by RF-OBIA in zone 1

Figure 9 :

 9 Figure 9: Coastline fragmented

Figure 10 :

 10 Figure 10: Case of class confusion

Figure 11 :

 11 Figure 11: Zone 2 classification by RF-OBIA

FFigure 12 :

 12 Figure 12: Shoreline extraction by RF-OBIA in zone 2

Figure 14 :

 14 Figure 14: Shorelines extraction by RF-OBIA in zone 3

Table 1 :

 1 Pleiades characteristic

				4 spectral bands: visible Red,
	_PHR1A	2022-08-27	2	Green, Blue and Near infrared
	Akanda			(RGB and NIR)
				4 spectral bands: visible Red,
	Pléiades_PHR1A	2022-08-21	2	Green, Blue and Near infrared
	Libreville			(RGB and NIR)
				4 spectral bands: visible Red,
	Pléiades_PHR1A	2022-08-27	2	Green, Blue and Near infrared
	Owendo			(RGB and NIR)

Acknowledgments

The authors would like to thank CNES (Centre national d'études Spatiales) for the Pléiades image « Pléiades © CNES 2022, Distribution Airbus DS. ICR_FC_378341. This research was funded by the the project CNES (Centre national d'études Spatiales) / TOSCA 7618 / 2022.

Conflicts of interest

The authors declare no conflicts of interest.