Sughosh Deshpande

Abdallah Bouzid

Pierre Lagarrigue

Yann Landon

Anna Carla Araujo
email: araujo@insa-toulouse.fr

Material identification in helical milling for smart drilling applications

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Industry 4.0 is the need of the hour in current global market scenario and all the processes are moving towards automation and smart manufacturing. The data exchange between different systems in the factory is of primary importance in order to correct and adapt to real time circumstances by decision making. The use of OPC UA (Open Platform Communication Unified Architecture) and MT connect based platforms to exchange data between machine tools and clients is demonstrated by Liu et al [START_REF] Liu | A Cyber-Physical Machine Tools Platform using OPC UA and MTConnect[END_REF]. The IoT based predictive maintenance of CNC machines by real time condition monitoring is demonstrated by Al-Naggar et al [START_REF] Mohammed Al-Naggar | Condition monitoring based on IoT for predictive maintenance of CNC machines[END_REF].

The hardware and techniques required for data monitoring and acquisition should be feasible enough for easy implementation on the shop floor without expensive investments and disturbance to current processes [START_REF] Axinte | Assessment of the effectiveness of a spindle power signal for tool condition monitoring in machining processes[END_REF]. The machine data from the modern day CNC machines can have significant value and are also easy to acquire without any additional accessories or hardware setup [START_REF] Lauro | Monitoring and processing signal applied in machining processes -a review[END_REF]. The internal sensors in the machine tool capture variety of data which can be useful for the operator to improve productivity and tool life for a particular machining process. Cutting tool condition monitoring using machine internal sensors is demonstrated by Demko et al [START_REF] Demko | Cutting tool monitoring while drilling using internal CNC data[END_REF].

Modern day airplanes are made of multiple light weight high performance materials to achieve better fuel efficiency and reliability [START_REF] Boyer | Materials considerations for aerospace applications[END_REF]. This also includes using stacked layers of Aluminium, Titanium and CFRP especially in the wings and air frames where thousands of holes have to be drilled before final assembly.

Aerospace stack hole making is an application where lot of research is being carried out in order to enhance the process productivity and hole quality [START_REF] Zhaoju | Investigation on performance characteristics and metallographic transformation on drilling aluminium/titanium sandwich[END_REF][START_REF] Vijayan | Comprehensive Review on Drilling of Multimaterials Stacks[END_REF].

Each of the material layer in a stack has different machinability and using one common tool for holemaking in both the layers is a challenge which results in poor hole quality and lower productivity. Also, changing the tool geometry suitable for each layer during the drilling process is not practically advisable. The idea of adapting right cutting conditions for each material layer in real time by a single tool can be feasible by implementation of smart machining strategies involving data acquisition, monitoring and feedback [START_REF] Araujo | Smart drilling for Aerospace Industry: state of art in research and education[END_REF].

Orbital drilling is a helical milling process where in the tool moves simultaneously in X,Y and Z positions resulting in material removal at bottom and peripheral cutting edges of the end mill. Numerous articles have compared different quality aspects of holes produced during helical milling and axial drilling [START_REF] Ge | Investigating hole making performance of Al 2024-T3/Ti-6Al-4V alloy stacks: A comparative study of conventional drilling, peck drilling and helical milling[END_REF][START_REF] Keys | Hole-making processes and their impacts on the microstructure and fatigue response of aircraft alloys[END_REF][START_REF] Iyer | Helical milling: An enabling technology for hard machining precision holes in AISI D2 tool steel[END_REF]. Some of the quality aspects include burr height, surface finish and fatigue life of the produced holes which are crucial for aerospace applications. Better chip evacuation, lesser forces result in better tool life and hole quality in helical milling. Implementation of helical milling for producing holes in aerospace stacks is also widely researched topic and considerable work is being done in this area [START_REF] Wang | Experimental research in CFRP/Ti stack through different helical milling strategies[END_REF][START_REF] Denkena | Helical milling of CFRP-titanium layer compounds[END_REF].

Precise real time material identification along with instantaneous correction in cutting condition if required is crucial for successful implementation of smart machining strategies. Fang et al [START_REF] Fang | A Force Sensorless Method for CFRP/Ti Stack Interface Detection during Robotic Orbital Drilling Operations[END_REF] developed force sensor less method to detect stack interface in robotic orbital drilling operations which can be helpful to adapt proper cutting conditions. The identification of process incidences during stack drilling by assessing different decision making algorithms is demonstrated by Pardo et al [START_REF] Pardo | Assessment of decisionmaking algorithms for adaptive drilling of aerospace stacks[END_REF]. Monitoring of signals from AE sensors for tool position identification in CFRP/Aluminium stacks is shown by Neugebauer et al [START_REF] Neugebauer | Acoustic emission as a tool for identifying drill position in fiber-reinforced plastic and aluminum stacks[END_REF]. Our recent work demonstrated material identification during circular milling by development of data maps of specific cutting coefficients in Aluminium and Titanium alloys by online monitoring of cutting forces [START_REF] Deshpande | Experimental analysis of circular milling for material identification in aerospace industry[END_REF].

The goal of this paper is to analyse and verify the applicability of data maps in helical milling of stacked Aluminium and Titanium alloys for real time material identification. This is achieved by monitoring machine spindle power and calculating specific cutting coefficients to distinguish the materials in the stack. Our work also proposes and verifies the possibility of utilizing CNC machine internal sensors for online data monitoring which can be advantageous compared to using external expensive sensors like force dynamometers.

In the following sections, the machining force model is presented and identification of the cutting coefficients methodology in helical milling is reviewed, followed by experimental set-up used in this research. The cutting forces and power results are presented and discussed, and lastly, the identification map with cutting coefficients derived by monitoring spindle power are presented.

Helical milling 2.1 Process kinematics

In orbital drilling, the milling tool follows a helical trajectory as shown in Fig. 1(a). The combination of tool movement in XY plane and Z plane simultaneously results in gradual removal of material for every orbital rotation of the tool (Eq. 1). The depth of material removed per orbital rotation is designated as pitch P (mm/rev) and it is a function of the feed and the radius of the trajectory R tt , calculated based on the tool diameter D t and the machined diameter D (Eq. 2). The resulting ramp angle is indicated as α (Eq. 3), a function of the axial feed and the circular feed [START_REF] Wang | Prediction of cutting forces in helical milling process[END_REF].

⃗ f z = ⃗ f xy (xy plane)+ ⃗ f a (axial) (1)
P = fa 2πRtt fxy = f a π(D -D t ) f xy (2)

Analysis of uncut chip geometry for force modelling

The uncut chip geometry and prediction of cutting forces in helical milling is discussed by recent articles [START_REF] Rey | Modelling of cutting forces in orbital drilling of titanium alloy Ti-6Al-4V[END_REF][START_REF] Wang | Experimental research in CFRP/Ti stack through different helical milling strategies[END_REF]. In case of end milling, there are two zones of chip generation: at the peripheral edge, that it is represented by the index 'p' in this article, and the bottom edge of the tool, represented by 'b' index.

In the periphery, the chip width b p is a function of θ 2 and the axial position of the tool in the orbital rotation [START_REF] Shang | Modelling of cutting forces and researching calibration method in helical milling[END_REF] and the chip thickness h p is described by Martellotti equation [START_REF] Martellotti | An analysis of the milling process[END_REF]:

b p (θ 2 ) = P - P π arccos R tt -R t cos(θ 2 ) R 2 tt + R 2 t -2R t R tt cos(θ 2 ) (5)
h p (θ 2 ) = f z sin(θ 2 ) (6) b b = Dt 2 (7) h b = f z P π(D -D t ) (8)
In the bottom edge, the chip length b b can be approximated to tool radius (Eq. 7) and the chip thickness is described by Eq. 8. The bottom uncut chip thickness can be assumed constant and independent of cutting velocity. The secondary cutting edge can be assumed to have zero position angle. The specific force coefficients can be identified for the bottom edge and peripheral edge of the tool based on the local uncut chip load. Figure 2

Cutting forces and specific force coefficients

The mechanistic force models predict the cutting forces based on uncut chip load at the cutting edge. The cutting force predictions has become more and more closer to the experimental values by including various factors like tool geometry, operation type, tool vibrations etc in the force models [START_REF] Altintas | Generalized Modeling of Mechanics and Dynamics of Milling Cutters[END_REF][START_REF] Wu | Cutting force prediction for circular end milling process[END_REF]. The forces for a general orthogonal cutting can be described by a mechanistic force model considering only cutting action of the cutting edge neglecting plowing and chisel edge effects. The machining force ⃗ F m is calculated considering the small finite elements of the cutting flute in the cutting edge referential frame decomposed: tangential (dF t ), radial (dF r ) and axial (dF z ) components for flute j is given by below equations:

⃗ dF m =   dF t dF r dF z   (9)
Figure 2(b) illustrates the cutting forces exerted by the peripheral and bottom edges of the tool on the work piece during helical milling. The tangential, radial and axial force components are depicted at peripheral (F tp ,F rp ,F ap ) and bottom cutting edges (F tb , F rb , F ab ) respectively. However, the tangential (F tb ) and radial (F rb ) force components at the bottom edge is significantly small and can be neglected. The force components can be expressed as a function of uncut chip cross section and flute rotation angle θ 2 as:

F tp,j = K tp .h p (θ 2 ) j b p (θ 2 ) j (10) F rp,j = K rp .h p (θ 2 ) j b p (θ 2 ) j (11) F ap,j = K ap .h p (θ 2 ) j b p (θ 2 ) j (12) F ab,j = K ab .h b R t ( 13
)
where K tp ,K rp ,K ap are the specific force coefficients for tangential, radial and axial force components obtained at peripheral cutting edge j and K ab is the specific force coefficient from axial force component obtained at bottom cutting edge j. Hence the total force due to peripheral and bottom edges considering Z flutes in a tool can be expressed as below:

F t = Z j=1 K tp .h p (θ 2 ) j b p (θ 2 ) j (14)
F r = Z j=1 K rp .h p (θ 2 ) j b p (θ 2 ) j (15)
F a = Z j=1 K ap .h p (θ 2 ) j b p (θ 2 ) j + Z.K ab .h b R t (16)
However, during experiments, the cutting forces recorded are in work piece referential (F xm , F ym , F zm ) and can be transferred to one of the reference cutting edges. The reference flute position (θ 2 ) being known, the angular position of remaining flutes for a particular tool can be calculated:

(θ 2 ) j = (θ 2 ) + (j -1)λ (17)
where λ=2π/Z is the tool pitch angle The axial components (F ap +F ab ) can be approximated to cutting force (F zm ) obtained in Z direction during experiments. The rotation matrix for transformation of forces is given by Eq.18:

  F r (θ 2 ) j -F t (θ 2 ) j F a   =   cos(-θ 2 ) j -sin(-θ 2 ) j 0 sin(-θ 2 ) j cos(-θ 2 ) j 0 0 0 1   .   F X F Y F Z   (18)

Cutting power model

In case of end milling, the cutting power is summation of power consumed by all the flutes (j = 1..Z) in active contact with the work piece at any instant of time. P ower p and P ower b denotes cutting power because of peripheral and bottom cutting edges respectively which are in active contact with the work piece :

P ower cut = Z j=1 [P ower p (j) + P ower b (j)] (19)
Depending upon the cutter pitch angle, the number of peripheral flutes simultaneously in contact with the work piece can be determined considering peripheral angle of immersion between ϕ= 0 to 180 o for helical milling. It is important to note that the bottom edges of all the flutes are always in contact with the work piece during helical milling. Tangential force component F tp at the peripheral cutting edge is the major component of cutting force in magnitude and can be considered for the calculation of cutting power P ower p at peripheral edge. Similarly, axial force component F ab is the major cutting force at the bottom edge and can be used to express cutting power P ower b at bottom edge of the tool. Hence cutting power can be expressed approximately as a function of cutting force and cutting velocity V c . The cutting velocity at a point on the bottom edge varies along the edge based on its distance from the tool center. Hence the cutting power is expressed as a function of average cutting velocity V c for the bottom cutting edges as shown below:

P ower cut = Z j=1 1 60 g(θ 2 ) j • (F tp ) j • V c + (F ab ) j • V c ( 20
)
where g(θ 2 )=0 or 1 is a contact function based on position of the peripheral flute in or out of immersion angle zone. Tangential F tp and axial F ab force components can be further expressed as a function of specific force coefficients (K tp ,K ab ) and uncut chip load (h p , b p , h b , b b ) as follows:

P ower cut = Z j=1 1 60 g(θ 2 ) j • [h p (θ 2 ) • b p (θ 2 )] j • K tp • V c + [h b • b b ] j • K ab • V c (21)

Identification of specific force parameters using power

Machine spindle power can be monitored during machining and can have significant information for decision making process. The total spindle power monitored has components of cutting, non cutting or idle power because of spindle inertia and power because of tool feed motion as shown in the Fig. 3. The total spindle power can be expressed as:

P ower total = P ower idle + P ower cut + P ower f eed

The idle power component for a particular machine spindle can be determined during experiments by recording non cutting spindle power. The power because of tool feed motion is assumed to be relatively less in helical milling. During experiments, power total can be recorded for different known values of θ 2 at pre defined cutting conditions.The modelled cutting power Eq. 21 can be re-written to determine values of K tp and K ab as a function of cutting power and chip dimensions.

Materials and methods

The aim of the experiment is to monitor spindle power for material identification during hole making of stacked aerospace materials. Cutting forces are also recorded using a dynamometer to compare with the power signal especially at material interface to verify changes in gradient of signals. However, the main goal is to utilize CNC machine internal sensors for material identification considering the advantages of easier implementation on industrial shop floor. Helical milling experiments were carried out on most commonly used aerospace stacks made of Aluminium (2017A) and Titanium (Ti6Al4V) alloy at different cutting conditions. The experimental setup is described in the following subsections.

Experimental setup

Experiments were carried out on a CNC milling center DMU85-DMG mono block machine under wet condition. A carbide end mill from Fraisa with 4 flutes and 8 mm diameter was used for all the helical milling

Design of Experiments

Experimental results

The following subsections present the cutting power, cutting forces monitored during helical milling of stacks and estimated specific force coefficients data map using cutting power. The data maps of specific coefficients show distinct data points indicating different materials and can be advantageous for material identification especially at interface layers of different material [START_REF] Deshpande | Specific force map for smart machining applications with rotating tools[END_REF]. Cutting power is monitored by utilizing machine internal sensors while cutting forces is monitored by external sensor (Dynamometer) simultaneously, However, specific coefficients are estimated from cutting power signal and this is to verify the possibility of utilising spindle power for material identification. Cutting forces are presented to compare with the power signal especially at material interface to verify material transition at a specific hole length in both the signals.

Cutting power

Figure 7 shows cutting power as a function of hole depth at various feed per tooth and stack sequences. The material layers can be approximately identified by the distinct steps observed in the power signal at the stack interface approximately at 4mm where tool transition occurs from one layer to another. It can be seen from the Fig. 7 (c) and (d) that the tool transition from Titanium to Aluminium shows distinct peaks especially at the layer interface. Figure 7 (d) shows further disturbances in the signal during machining of Aluminium and its difficult to approximate two different material layers. This can be mostly attributed to sticky chips of Titanium sticking to the cutting edge which is re-machined while machining Aluminium. This phenomenon is also reaffirmed in the cutting force signals observed during tool transition from Titanium to Aluminium layers which is shown in the next subsection. It is important to note that these signal disturbances were not consistent for all Ti→ Al stack sequence experiments but was observed frequently.

Conclusions

Our work validates the possibility of material identification by data maps during orbital drilling of stacked Aluminium and Titanium alloys. These data maps are developed by online data monitoring utilizing machine internal sensor to monitor spindle power and an external photoelectric sensor to detect flute position. The data map of axial cutting force coefficient (K ab ) has distinct data points distinguishing two separate regions in the map indicating two separate material layers. However, it is difficult to identify two different material layers by observing data map of tangential cutting force coefficient (K tp ) as the data points are unevenly distributed without any specific regions for different material layers. The stack sequence also plays a crucial role in terms of generated cutting forces and required cutter power for machining. Especially, the transition of tool from Titanium to Aluminium layer is accompanied by disturbances in monitored signal of cutting force and power. This may lead to improper value of data points which in turn result in erroneous material identification. However, if there is a small delay in identification of Aluminium while the tool is transiting from Titanium, it does not result in any catastrophic loss of the tool. The consequences of stack sequence on data maps needs further studies. Our work also demonstrates utilization of machine internal sensors for online data monitoring as a substitute to external expensive sensors and can be explored further for industrial applications on shop floor. The map of cutting force coefficients can be used to train machine learning models in the future for smart machining applications including adapting proper cutting parameter suitable for a particular layer.

Figure 1 Figure 1 :

 11 Figure 1(b) shows tool trajectory with reference to work piece (X m , Y m ) and tool (X t ,Y t ) referential frames. The tool rotates around its own axis at N (rpm) spindle speed (or θ2 rad/s) and around hole center O at N orb rpm (or θ1 rad/s) to machine the hole. The offset distance between tool center C and hole center O is designated as R tt .

  (a) shows chip generation during orbital milling.

Figure 2 :

 2 Figure 2: Chip generation and cutting forces during helical milling

Figure 3 :

 3 Figure 3: Spindle power components

Figure 4 :

 4 Figure 4: Experimental setup

  (a) Spindle position (SP) (b) Reference cutting edge position θ 2

Figure 5 :

 5 Figure 5: Identification of reference flute position The identification of δ is possible by the photoelectric sensor which gives a voltage high as it encounters the reflective tape placed directly above the reference cutting flute as shown in the Fig. 5(b). The machine spindle position values (0 -360 o ) are also simultaneously recorded during this time interval. The clock on the CNC machine and the sensor connected to Labview is set identical before recording the values of spindle position and flute position. The set of data points having common time stamps from both the systems is then super imposed as shown in the Fig. 6 to identify angular difference between the reference cutting flute and spindle encoder reference position. The sensor signal peak (voltage high) in the graph denotes reference cutting flute detection and the corresponding value of the spindle position is found to be around 297 o . This

Figure 6 :

 6 Figure 6: Identification of δ

  Al→ Ti: fa=0.002 mm/th, fz=0.044 mm/th Al→ Ti :fa=0.003 mm/th, fz=0.059 mm/th Ti→ Al :fa=0.002 mm/th, fz=0.044 mm/th Ti→ Al :fa=0.003 mm/th, fz=0.059 mm/th

Figure 7 :Figure 9 :Figure 10 :

 7910 Figure 7: Spindle power as a function of hole depth at different cutting conditions.

Table 1 :

 1 Cutting conditions Stackf a (mm/th) f z (mm/th) V c (m/min) N orb (rev/min) P (mm/rev) value is offset from the recorded machine spindle position values in order to get real time reference cutting flute position (θ 2 ) by real time data monitoring. This method involves integrating data from two different platforms and the determined δ value is just an approximation for establishing θ 2 .The cutting coefficients calculated by approximating θ 2 values in both the cases, (i.e reference flute aligned with machine spindle reference and unaligned reference flute where sensor is used to approximate flute position) has identical values and similar data maps.

	Ti-→ Al	0.002	0.044		30
	Ti-→Al Al-→Ti Al-→Ti	0.003 0.002 0.003	0.059 0.044 0.059	40	40 30 40	0.5
	Ti-→Al Ti-→Al	0.001 0.002	0.044 0.059		30 40	0.3
	0 50 100 150 200 250 300 δ 09:56:32 Angle (deg) 350	09:56:33	09:56:34 Time stamp	09:56:35 Sensor signal Machine trace:Spindle position

Table 1

 1 summarizes the cutting conditions adopted for helical milling experiments and the stack sequence of Aluminium and Titanium alloy for each test. The cutting velocity (V c ) is 40 m/min for all the experiments and a range of feed per tooth in axial (f a ) and trajectory (f z ) is defined resulting in different N orb and pitch. A 11 mm diameter hole (through hole) is produced in the stacks by helical milling. The cutting velocity is opted considering machining of two different materials layers and 11mm diameter hole being one of the most commonly produced hole diameters in aerospace industry.

Cutting forces

 c) and (d) at the layer interface (at length 4mm) while the tool is moving from one material layer to the other layer. However, it can be observed from Fig. 8 (d) that the axial force F a at the Aluminium region is higher compared to Titanium region accompanied by signal disturbances which was also seen previously in the cutting power results for tool transition from Titanium layer to Aluminium layer.

Cutting force coefficients

Cutting force coefficients K tp (at tool periphery) and K ab (at tool bottom edge) are estimated from cutting power signal as described in subsection 2.5. The coefficients are calculated by taking maximum power values for every half orbital rotation of the tool and corresponding chip dimensions at that instant. K tp and K ab are represented as a function of hole depth for different stack sequence as shown in the Fig. 9 and 10. The values of K ab for both the material layers can be seen in the Fig. 9 (a) and 10 (a) and these data points indicate stacked materials of different machinability. The data points observed in Fig. 10 (a) has some unpredictable values when the tool moves from Titanium to Aluminium layer. This may be attributed to sticky Titanium chips at the cutting edge being re-machined at the Aluminium layer. However, we can still distinguish two different material layers from the data map of K ab . Figure 9 (b) and 10 (b) shows the tangential cutting force coefficient K tp for both the material layers at f a =0.002 mm/th and f z =0.044 mm/th. It is difficult


Kévin Planolles

Senior Member, IEEE Marc Chaumont ⋆ †

Frédéric Comby

A STUDY ON THE INVARIANCE IN SECURITY WHATEVER THE DIMENSION OF IMAGES FOR THE STEGANALYSIS BY DEEP-LEARNING

Keywords: Steganalysis, Images of arbitrary size, Invariance in security, NNID dataset, Deep Learning

In this paper, we study the performance invariance of convolutional neural networks when confronted with variable image sizes in the context of a more "wild steganalysis". First, we propose two algorithms and definitions for a fine experimental protocol with datasets owning "similar difficulty" and "similar security". The "smart crop 2" algorithm allows the introduction of the Nearly Nested Image Datasets (NNID) that ensure "a similar difficulty" between various datasets, and a dichotomous research algorithm allows a "similar security". Second, we show that invariance does not exist in state-ofthe-art architectures. We also exhibit a difference in behavior depending on whether we test on images larger or smaller than the training images. Finally, based on the experiments, we propose to use the dilated convolution which leads to an improvement of a state-of-the-art architecture.

INTRODUCTION

Steganalysis is the subject of many academic publications but its use in real-world conditions ("in the wild") is often far from the laboratory protocols [START_REF] Ker | Moving Steganography and Steganalysis from the Laboratory into the Real World[END_REF] [START_REF] Cogranne | The ALASKA Steganalysis Challenge: A First Step Towards Steganalysis[END_REF]. In laboratory conditions, the worst-case attack is used, meaning that: payload size, image development (demosaicing, gamma correction, blur, color balance, compression parameters, use of color, etc.), are known by the steganalyst.

This paper, therefore, fits in the spirit of works on a more "wild/realistic" steganalysis. We are specifically focusing on the case where the dimension 1 of the images is not known by the steganalyst. Said differently, we would like to keep detection performances constant whatever the dimension of the considered image.

Since the advent of deep-learning in steganalysis in 2015 [START_REF] Chaumont | Deep Learning in steganography and steganalysis[END_REF], a few architectures have the intrinsic capability to accept input images of variable size [START_REF] Yedroudj | Yedrouj-Net: An Efficient CNN for Spatial Steganalysis[END_REF], [START_REF] Zhang | Depth-Wise Separable Convolutions and Multi-Level Pooling for an Efficient Spatial CNN-Based Steganalysis[END_REF], [START_REF] Reinel | GBRAS-Net: A Convolutional Neural Network Architecture for Spatial Image Steganalysis[END_REF], [START_REF] Fu | CCNet: CNN Model with Channel Attention and Convolutional Pooling Mechanism for Spatial Image Steganalysis[END_REF], [START_REF] Su | Arbitrary-Sized JPEG Steganalysis Based on Fully Convolutional Network[END_REF], [START_REF] Luo | Image Steganalysis with Convolutional Vision Transformer[END_REF], [START_REF] Clément | Steganalyzing Images of Arbitrary Size with CNNs[END_REF], [START_REF] You | A Siamese CNN for Image Steganalysis[END_REF], etc. Nevertheless, it is reasonable to ask ourselves if those architectures are efficient in detection whatever the dimension. More precisely we would like to know if the used architectures and/or the tricks ensure an invariance in security. This notion of invariance in security will be formally defined in the section 2.

The contributions of that paper are: 1) a well thought experimental setting (dataset building, payload size tuning, and learning protocol) leading to the definition of difficulty and to the Near-Nested Image Datasets (NNID), 2) the definition of the invariance in security, 3) the reported experimental observations and finally, 4) the proposition of an update of the architectures in order to be closer to invariance.

In Section 2 we briefly discuss the payload size with a recall of the Square Root Law [START_REF] Ker | The Square Root Law of Steganographic Capacity[END_REF], and we present the stateof-the-art architectures able to process variable dimension images. In Section 3, we describe the way the NNID are built; this comes with the definitions of "same" difficulty of the datasets, and "same" security due to the embedding in each of those datasets. We also propose an upgrade to the deeplearning architectures. Then, in Section 4 we give the experimental protocol, and the experimental results, and discussed the invariance notion.

TOOLS USED FOR OUR STUDY

Few words on the square root law

It is well known that the size of a cover object is a major factor in its capacity to hide information, but the relationship between secure steganographic capacity and cover size is still a discussed subject. In Ker et al.'s paper [START_REF] Ker | The Square Root Law of Steganographic Capacity[END_REF], it is shown that payload size should be proportional to the square root of the cover size. From the Square Root Law we can derive, given a positive constant k ∈ R + , that the relative payload size, α, for an adaptive embedding, ensuring the same security whatever the dimension w × h of an image, should be (in bit per pixel):

α = k wh × √ wh × log(wh). (1)
But in practice, the statistical properties of the cover has to be taken into account, and it appears that the square root law is not usable as it is. For example, a homogeneous cover will be much less secure than a cover with a lot of textures.

In our study, we propose another solution to choose the relative payload ensuring a similar security considering the dimension of images. It is based on careful datasets building and the use of a detector i.e. a deep-learning network (see Section 3).

State-of-the-art deep learning architectures

There are roughly two families of deep learning architecture that have the property to accept images of various dimensions, those only using the average, and those using more than only one statistical moment.

For the family based on the average, we can mention the following networks. The Yedroudj-Net [START_REF] Yedroudj | Yedrouj-Net: An Efficient CNN for Spatial Steganalysis[END_REF] architecture is based on the Global Average Pooling (GAP) technique to aggregate the values of the feature maps just before feeding the classification block. The Zhu-Net [START_REF] Zhang | Depth-Wise Separable Convolutions and Multi-Level Pooling for an Efficient Spatial CNN-Based Steganalysis[END_REF] architecture is inspired by Yedroudj-Net. Its main characteristic is the use of a Pyramidal Global Average pooling to retrieve features at multiple scales. A few other "small" architectures such as GBRAS-Net [START_REF] Reinel | GBRAS-Net: A Convolutional Neural Network Architecture for Spatial Image Steganalysis[END_REF], CC-Net [START_REF] Fu | CCNet: CNN Model with Channel Attention and Convolutional Pooling Mechanism for Spatial Image Steganalysis[END_REF], etc, dealing with spatial image steganalysis have then improved the Yedroudj-Net and the Zhu-Net, and are also integrating a GAP. We should also mention a very recent proposition integrating a transformer [START_REF] Luo | Image Steganalysis with Convolutional Vision Transformer[END_REF] with a GAP. Finally, EWNet [START_REF] Su | Arbitrary-Sized JPEG Steganalysis Based on Fully Convolutional Network[END_REF] is an original approach that uses a coder-decoder, and proposes to compute the average of the image of scores for the cover (resp. the stego).

For the family based on more than only one statistical moment, we can mention the following networks. The SID [START_REF] Clément | Steganalyzing Images of Arbitrary Size with CNNs[END_REF] architecture is based on a modified version of the Ye-Net network [START_REF] Ye | Deep Learning Hierarchical Representations for Image Steganalysis[END_REF]. The main idea of the SID architecture is to extract four statistical moments (minimum, maximum, average, and variance) from the last feature maps and use those moments for classification. The SiaSteg [START_REF] You | A Siamese CNN for Image Steganalysis[END_REF] architecture is also based on the extraction of statistical moments (the same as SID), and uses a siamese network in order to add a contrastive loss in conjunction with the classification loss.

In some of those papers, there are experiments on the "robustness" to the variation in dimension, and for a subset of those papers, the notion of secure steganographic capacity is mentioned, but in none of them the results agreed with this secure steganographic capacity notion. Additionally, none of them has set a common difficulty (see definition in section 3.1) between the dimensions, which ensures that the variation between datasets is only due to the relative payload size. In this paper, our experimental protocol ensures the same empirical security (thanks to adapted payloads) between the dimensions and works with datasets of various dimensions and similar difficulty.

PROPOSITION

Nearly-Nested Image Datasets (NNID) ensuring the same difficulty

For mastered experiments, we need to build what we name Nearly-Nested Image Datasets (NNID) such that each dataset owns images of the same dimension, and each dataset is issued from a cropped version of the images belonging to the dataset with the biggest dimensions. This last dataset is named mother dataset and the images are named mother images.

By using NNID we ensure that the development is the same in all of the datasets. We also impose, as an additional constraint, that the difficulty of each dataset is the same. By same difficulty we mean that the distribution of costs is the same whatever the dataset. This additional constraint implies a specific way to crop the images, and most importantly, ensure that the experimental results obtained between the various dimension will be comparable since the source cost distribution of each dataset is the same. With the NNID we are able to avoid any impact of the development or the difficulty, on the experimental results; All the datasets are very similar except for the dimension.

We use, as a mother dataset, the LSSD dataset [START_REF] Ruiz | LSSD: a Controlled Large JPEG Image Database for Deep-Learning-based Steganalysis "into the Wild[END_REF]. LSSD is a mix of RAW images from ALASKA#2, BOSS, StegoApp DB, Wesaturate, RAISE, and Dresden datasets and uses a modified development script issued from the Alaska competition 2 .

For a given image from the mother dataset, we define the smart crop 2 as the crop (i.e the area of the mother image) that keeps the same distribution of costs between the mother image and the cropped one. To compare the distribution, we used symmetrized Kullback-Leibler distance:

D KL (P, Q) := i P (i) log P (i) Q(i) + i Q(i) log Q(i) P (i) , (2)
for given discrete probability distributions P and Q. Note that in this paper, we consider the cost obtained with the S-UNIWARD algorithm [START_REF] Holub | Universal Distortion Function for Steganography in an Arbitrary Domain[END_REF], which is one of the most efficient and generic embedding algorithm [START_REF] Sedighi | Toss that BOSSbase, Alice![END_REF]. Note that a brute force approach has to be done to test all the areas and find the one with the minimal Kullback-Leibler symmetrized distance3 . To avoid redundant computation and reduce the computational cost, we use the histogram integral approach [START_REF] Murat | Integral Histogram: A Fast Way To Extract Histograms in Cartesian Spaces[END_REF] which is an extension of the well-known integral image approach, defined in the paper of Viola and Jones [START_REF] Viola | Rapid Object Detection using a Boosted Cascade of Simple Features[END_REF]. Given a mother image of size n × m, and a crop area of size w × w, the complexity for computing all the histograms for all the positions in the mother image is O(n × m × w 2 ) whereas it is a much smaller complexity of O(n × m) with the histogram integral approach.

Figure 1 shows a mother image of size 2594 × 3898 with its costs histogram, and a near-nested image of size 256×256, issued from the smart crop 2 of the mother image, with its costs histogram.

Relative payload in each dataset ensuring the same security

Given the NNID and an embedding algorithm, we need to find the number of bits to embed in each dataset. In this paper, we only need to focus on the average accuracy obtained by a classifier for each dataset. Using the square root law in order to find the correct payload size to embed in each dataset (such that the security is the same for all) does not ensure, in practice, the same accuracy for all the datasets.

In order to obtain the relative payload size to embed for each dimension, we thus go by a dichotomous method, by running, for each dimension, multiple detections until finding the desired accuracy. Note that we use the Square Root Law as an initialization of this empirical research, for finding the relative payload size for each dimension (see Equation 1). This protocol is the one that was used to set the payload sizes in the experiments of this article.

Invariance in security

We give here the definition of the invariance in security. Let's suppose an NNID that ensures similar pixel distributions, similar contents, the same development, and the same difficulty for all the datasets, plus a payload size for the embedding (described in Section 3.2) that ensures the same empirical security. We define a deep learning network invariant in security with respect to the dimension when its obtained average accuracy is the same whatever the dimensions. This definition, even if very simple, allows a much finer analysis of the invariance property than done previously.

Use of dilated convolution

Some authors have proposed to introduce invariance to the dimension by performing multiple convolutions in parallel on resized versions of the input image [START_REF] Van Noord | Learning Scale-Variant and Scale-Invariant Features for Deep Image Classification[END_REF] [START_REF] Marcos | Scale Equivariance in CNNs with Vector Fields[END_REF]. Nevertheless, we cannot perform resampling without losing information on the steganographic noise. We, therefore, propose to use the principle of dilated convolution [START_REF] Yu | Multi-Scale Context Aggregation by Dilated Convolutions[END_REF], which consists in spacing the elements of the convolution kernel, as an approximation of the resizing. There is then no more subsampling of the input image.

The dilated convolution operator is defined, for an image, z : Z 2 → R, a kernel, k : Z 2 → R, and a scalar, d ∈ N, standing for the dilation factor, by [START_REF] Yu | Multi-Scale Context Aggregation by Dilated Convolutions[END_REF]:

(z * k)(x, y) = i j z(x -d • i, y -d • j)k(i, j).
Lots of the networks designed for steganalysis have their first convolution block that serves to remove the influence of the image content [START_REF] Chaumont | Deep Learning in steganography and steganalysis[END_REF]. Additionally, most of them have their second convolution block that outputs feature maps whose height and width are equal to these of the image fed to the network.

One thus can modify most of the networks by substituting the second convolution block with an inception block [START_REF] Szegedy | Going Deeper with Convolutions[END_REF] made of dilated convolutions of various dilation factors. This can be easily done without changing neither the number of parameters of the network, either the depth, width, or height of the feature maps.

Applied to the Yedroudj-Net architecture (see Figure 2), the second convolution block still inputs and outputs 30 features maps of size 256 × 256, but the 30 convolution filters of size 5 × 5 are replaced by 10 standard convolutions (without dilatation), 10 convolutions with dilation of 2 (i.e. the kernel elements are spaced by one pixel), and 10 convolutions with dilation 4 (i.e. the elements of the kernel are spaced by three pixels), all of them of size 5 × 5.

EXPERIMENTS

Experimental protocol

In the NNID 4 , each dataset contains images whose dimensions are all equal. Each of them is named UNI w, with w ∈ {256, 512, 1024, or 2048}, the size w × w of the images of the dataset. UNI stands for unidimensional.

For each UNI dataset, the train part is made of 12000 cover/stego pairs (24000 images in total) with 19200 images dedicated to the train, and 4800 images to the validation. For each UNI dataset, the test dataset is made of 3000 cover/stego pairs (6000 images in total).

An additional dataset, named MULTI, is derived from the datasets UNI w, with w ∈ {256, 512, 1024} such that 4000 cover/stego pairs of each UNI dataset are randomly selected, in order to obtain 12000 cover/stego pairs, and thus a total of 24000 images, with 19200 images dedicated to the train, and 4800 images to the validation.

We used S-UNIWARD [START_REF] Holub | Universal Distortion Function for Steganography in an Arbitrary Domain[END_REF] for the embedding in the spatial domain with its MATLAB implementation 5 .

We trained the SID network 6 and the Yedroudj-Net network 7 using the hyper-parameters from the GitHubs, with a batch of 32. We trained the "Dilated" Yedroudj-Net8 with the same parameters as Yedroudj-Net, except that the batch size is set to 16. For all networks, the learning rate is divided by two if the validation's accuracy does not improve for ten consecutive epochs. We set the maximum number of epochs to 400 for all networks, but if the validation's accuracy does not improve for fifty consecutive epochs, the learning is stopped. After the training, we saved the weights which gave the best validation accuracy and use them for the test on the test dataset (The standard deviation of networks is extremely low; As an example, for a SID trained on 256 × 256 images it is below 0.02% when testing the top-5 trained networks).

Probably due to unadapted hyper-parameters, SiaSteg9 , and Zhu-Net10 networks did not converge. We thus restricted our study to SID and Yedroudj-Net which are two representatives of each family of approaches.

Relative payload for the UNI datasets

As a preliminary experiment, we embedded at a relative payload size of 0.4 bpp (bits per pixels) in the 256 × 256 images, and deduced with the Square Root Law mentioned previously, a relative payload of 0.225 (resp. 0.125, and 0.06875) for 512 × 512 (resp. 1024 × 1024, and 2048 × 2048) images. We then trained and tested a SID on 256 × 256 images, and another one on 512 × 512 images. Accuracies were not at all equal with respectively 69% and 62%, indicating that some hypotheses (asymptotic hypothesis + independencies assumption) of the Square Root Law were not met and that this law could not be used given our experimental conditions.

We thus updated the relative payload size used for each dimension as explained in section 3.2 such that after a manual dichotomous approach the accuracy for each UNI dataset for the Yedroudj-Net model is 76%. Note that this accuracy is The table 1 gives the adjusted payload for each dimension and the corresponding accuracy.

Learn on a UNI dataset

Our first case study consists to learn a network on a UNI dataset (i.e. images have the same dimensions) and evaluating its invariance in security on the other UNI dataset. We note as ARCHI-DIM, where ARCHI denotes the name of the architecture, DIM denotes the dimension on which the network was trained.

The results for SID, Yedroudj-Net, noted Y, and Dilated-Yedroudj-Net, noted DY, are reported in Table 2. The diagonals correspond to the clairvoyant scenario without any mismatch in dimension. The accuracy for the diagonal values for SID (resp. DY) are close. It confirms that the security by accuracy defined in Section 3.2 is a fine grain definition of the security since given a detector, for each UNI dataset it gave close accuracy (close to 69.9% for SID and close to 77.5% for DY). Looking at the non-diagonal results it appears that the performance systematically decrease compared to the diagonal. The biggest performance loss is for the learning at 1024 when evaluated on smaller dimensions, with a loss from 8% (SID) to 5% (Yedroudj-Net and Dilated-Yedroudj-Net).

SID and Yedroudj-Net are two representatives of the two families of networks accepting images of various dimensions and are also well-established networks. The above results let us guess that current networks from the literature are not intrinsically invariant to the change in dimension since their accuracies, when confronted with dimension never seen during the learning, are not constant.

Going deeper into the observation of the variance in security phenomenon, considering for example the DY-512, (see table 2), it appears that the accuracies are very similar (around 76%) for a test on the lower dimension 256 × 256 or on the higher dimension 1024 × 1024, but the behavior varies greatly with image size. Indeed, as observed in Table 3, when tested on a lower dimension, the model tends to over-classify in stego, while when tested on a higher dimension, it overclassifies images as covers. We checked if this variance in security was due to a wrong decision threshold that should be updated when facing a dimension not seen during the learning. It appears in experiments with Y-512 and SID-512 that updating the threshold does not change the accuracy for the unseen dimensions.

We also checked if there was a difference in the noise pattern depending on the dimension which could explain the variance in performance. Using the activation map (using integrated gradient [START_REF] Sundararajan | Axiomatic Attribution for Deep Networks[END_REF]) for a few stego images of size 512 × 512, and the associated nearly nested images 256 × 256, such that the first group is well classified and the second group is wrongly classified, it appears that the activation maps are very close. Thus the latent space may be very sensitive to small differences indicating that the feature maps are not sufficiently robust (i.e varies) to the change in dimension.

Finally, we should mention that the introduction of the dilated convolution to the Yedroudj-Net (see Table 2) increases the accuracy by 1% (see diagonal results) and slightly improves the results on unseen dimensions (non-diagonal results), so probably encouraging the invariance to the dimension.

Learn on the MULTI dataset

Our second case study consists of learning a network on the MULTI dataset (i.e. images have various dimensions) and evaluating its invariance in performance on the UNI datasets. We refer as ARCHI-MULTI, the networks trained on multiple dimensions, where ARCHI denotes the name of the architecture.

The results for SID, Yedroudj-Net, and Dilated-Yedroudj-Net are reported in Table 4. While those models are not invariant with respect to dimension, the variations in accuracies are less important compared to learning on a UNI dataset, particularly for 512×512 and 1024×1024 images. This confirms that training on multiple dimensions improves the invariance, which was a trick already used in past publications, as a measure for improving the robustness to various dimensions.

Nevertheless, as we can see in Table 4, the invariance is not reached since the accuracy for the dimension 256 × 256 is lower by 1.6% to 3.7% than those obtained at dimension 512 × 512 or 1024 × 1024. This phenomenon is also observed with the Dilated-Yedroudj-Net-MULTI which highlights the fact that future work has to be done to ensure invariance. We should also note that the Dilated-Yedroudj-Net-MULTI allows obtaining the best results which is a piece of interesting practical information for the topic of invariance in dimension.

CONCLUSIONS

In this paper, we explain how to build the Near Nested Image Datasets (NNID) thanks to a smart crop 2 applied to an initial dataset. Those NNI Datasets, all each containing images of the same dimension, have similar pixel distribution, similar semantic content, same development, and the same distribution of costs such that we talk about same difficulty for all of the datasets. We also propose to dichotomously find a relative payload size for each dataset such that a pre-chosen neural network exhibit the same accuracies, leading to the notion of same security for all the cover/stego datasets. During the building of the NNI Datasets, we thus exhibit that the theoretical results of the square root law might not apply in a real-world context. Then, using the resulting cover/stego datasets allows us to observe that even in the case of learning with images of various dimensions, there is not any property of invariance in security for the current state-of-the approaches. We also remarked a difference in behavior depending on whether the network was tested on a larger or smaller dimension than the one on which it was trained. In the case of a lower dimension, there is an overestimation of the number of stegos while in the case of a higher dimension, there is an overestimation of the number of covers. Finally, we proposed a new architecture, Dilated-Yedroudj-Net, which gave better results than the other networks. 11

Fig. 1 .

 1 Fig. 1. A mother image of size 2594 × 3898 with its costs histogram, and a near-nested image of size 256 × 256, issued from the smart crop 2 of the mother image, with its costs histogram.

Fig. 2 .

 2 Fig. 2. The Yedroudj-Net architecture with the block where dilated convolutions are applied is highlighted.

Table 1 .

 1 Relative payload for each dimension.

	Dimension Relative payload Accuracy (Yedroudj-Net)
	256	0.4	76.97%
	512	0.3204	76.38%
	1024	0.28895	76.78%
	a meaningful accuracy that lets a sufficient margin for future
	experiments.

Table 2 .

 2 Accuracies for the SID, the Yedroudj-Net (noted Y), and the Dilated-Yedroudj-Net (noted DY), models.

	Dim	SID-256 SID-512 SID-1024
	256 × 256	69.48%	67.05%	60,9%
	512 × 512	69.30%	70.7%	66.93%
	1024 × 1024	66.73%	66.93%	69.62%
	Dim	Y-256	Y-512	Y-1024
	256 × 256	76.97%	73.48%	71.76%
	512 × 512	74.55%	76.38%	74.97%
	1024 × 1024	72.83%	73.57%	76.78%
	Dim	DY-256	DY-512	DY-1024
	256 × 256	77.7%	76.25%	71.92%
	512 × 512	75.21%	77.3%	76.2%
	1024 × 1024	72.03%	76.88%	77.53%

Table 3 .

 3 Confusion matrices of DY-512. DY-512 tested on 256 × 256 DY-512 tested on 1024 × 1024

	Pred.			Pred.
	Truth	Cover	Stego	Truth	Cover	Stego
	Cover	2140	860	Cover	2530	470
	Stego	565	2435	Stego	917	2083
	Percentage	45%	55%	Percentage	56%	43%

Table 4 .

 4 SID-MULTI, Y-MULTI and DY-MULTI accuracies.

	Dim	SID-MULTI Y-MULTI DY-MULTI
	256 × 256	66.93%	73.93%	75.63%
	512 × 512	69.46%	75.5%	78.1%
	1024 × 1024	70.6%	75%	78.06%

See https://www.lirmm.fr/ ∼ chaumont/LSSD.html.

For the NNID, the search space is square areas of dimensions 256x256, 512x512, 1024x1024, and 2048x2048.

Send an email to marc.chaumont@lirmm.fr to get a private copy. https: //www.lirmm.fr/ ∼ chaumont/NNID.html

See http://dde.binghamton.edu/download/stego algorithms/.

SID is from the Github of SiaSteg: https://github.com/SiaStg/SiaStegNet

Yedrouj-Net: https://github.com/yedmed/steganalysis with...

Dilated Yedroudj-Net: https://github.com/Kevin-Planolles/steg...

SiaSteg: https://github.com/SiaStg/SiaStegNet

Zhu-Net: https://github.com/1204BUPT/Zhu-Net-image-steganalysis

FAQ can be found there https://www.lirmm.fr/ ∼ chaumont/publications/ QA-ICASSP2023.pdf

The authors would like to thank the French Defense Procurement Agency (DGA) for its support through the ANR Alaska project (ANR-18-ASTR-0009). We also thank Douglas Benhamou and Mohamed Benkhettou for their technical help.


Ludovic Farines
email: ludovic.farines@mahytec.com

Frédéric Thiebaud

Dominique Perreux

Compressed hydrogen form-fitted tank

Keywords: Hydrogen storage, form-fitted tank, composite, filament winding

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Nowadays, several car makers try to replace the energy source of their vehicles. The main objectives are to give an alternative for oil as the world reserves are decreasing, and to produce low CO 2 emission vehicles. So, Hydrogen could be considered as the best energy vector to achieve these objectives.

Hydrogen storage

Actually, classical gas engines or fuel cells can use hydrogen to produce energy, the main problem is still the storage. The technologies for storage are gas compressed, metal hydride and liquid hydrogen tanks. The liquid hydrogen technology means to use an extremely low temperature (20K) for the storage. Therefore, the energetic cost to reach this temperature has to be taken into account [START_REF] Aceves | Analytical and experimental evaluation of insulated pressure vessels for cryogenic hydrogen storage[END_REF] as the cost of tank's insulation [START_REF] Peschka | Hydrogen: The future cryofuel in internal combustion engines[END_REF]. As a consequence, the liquid technology seems to be too expensive due to insulation management. The solid storage state uses the absorption / desorption cycle of metal hydride [START_REF] Bentzen | Screening of hydrogen storage media applying high pressure thermogravimetry[END_REF]. Depending on the hydride, it is a low pressure storage which requires a careful management of heat exchange. Metal hydride's density gives an access to low volume tanks at the cost of high weight and complex heat management. The compressed gas storage actually uses well known structures:  Type I, a load bearing metal bottle, mainly a tube closed by hemispherical parts  Type II, type I reinforced by a resin impregnated continuous filament on a cylindrical part,  Type III, a non-load bearing metal liner fully wrapped and reinforced by a composite  Type IV, a non-load bearing polymer liner fully wrapped and reinforced by a composite Type III and type IV tanks are lighter than metal hydride ones, they store more hydrogen per weight unit around 5 % (some authors provide up to 13% [START_REF] Zuttel | Materials for Hydrogen Storage[END_REF]) in mass versus 2%The main backwards are pressure and volume, the tank works at high pressure (between 35 MPa and 80 MPa), at 70 MPa the internal volume of the tank is 125 L to store about 5kg of hydrogen.

Major constraints for automotive industry

This study is a part of the French program HYPE. This project investigates the improvement of compressed gas hydrogen storage, and is intended for automotive industry. In order to decrease the development cost, the tank has to use the remaining space in a car, moreover to be as light as possible to decrease the energy consumption. This study presents a way to change the overall shape of types III and IV, in order to adapt the tank to the free space on a vehicle, the theoretical and experimental basis for the application, and then the manufacturing and testing of a form-fitted tank.

2 From type III or IV gas tank to a form fitted one Actually, types III and IV represent a known structure with associated international standards for natural gas [START_REF]ISO 11439, Gas cylinders --High pressure cylinders for the on-board storage of natural gas as a fuel for automotive vehicles[END_REF] or hydrogen [START_REF]ISO 15869, Gaseous hydrogen and hydrogen blends --Land vehicle fuel tanks[END_REF] storage. The shape used is presented on figure 1, it consists in a cylinder closed by a spherical or ellipsoidal dome. This geometry has a revolution axis therefore it's easy to reinforce the liner by filament winding and achieve all the design requirements. On a second thought, this shape complicates the integration on a vehicle, in most cases the tank reduces the available space for the trunk. To save space, the shape has to be more complex in order to use another site on a vehicle. For instance in figure 2, this geometry could use the space under the floor of the vehicle. A finite elements analysis shows that this structure could not bear the pressure. Indeed at the same burst pressure with a similar thickness of composite, the displacement on the center is about 172 mm, with a maximum strain along fibers of about 16% (which is way above the limit of classical fibers).

In fact, the loss of the revolution axis creates a need of reinforcements parallel to the pressure fields. Therefore, in order to use this design, we have to introduce reinforcement through the thickness of the geometry presented in figure 2.

Shape reinforcement 3.1 Type of reinforcement

To reinforce this type of flat surface on a tank without making liner too complex, we decide to insert some rods through the thickness. This choice leads to the following problems: the fixation of the reinforcement and the hydrogen tightness. The chosen reinforcements are T700 carbon fiber / epoxy resin rods made by Soficar, table 1 gives the mechanical characteristics. The manufacturing process of the rod is pultrusion, this process could made large quantities at a moderate cost. These rods are used for several applications, civil engineering, offshore exploration… The main way to make an assembly is to use adhesive joints, so an intermediate part has to be designed, the rods would be sticked to this part. This one could be weld or stick to the liner. Figure 3 presents the rods, the attaching parts and an assembly ready to be tested in tension. To design exactly the fixation, we need to know the characteristics of the adhesive joints, length and thickness.

Fixation parts : numerical study

The shear stress inside the adhesive joint is determined by equation 1.

(

) 1
where is the shear stress, the tensile strength, the diameter of rod, the length of adhesive joint. If we consider that the adhesive joint mustn't fail before the rod, F is determined by equation 2.

(2) where is the ultimate strength of the rod The equations 1 and 2 define a design rule as equation 3 [START_REF] Bentzen | Screening of hydrogen storage media applying high pressure thermogravimetry[END_REF] where is the ultimate shear strength of the adhesive joint For the rest of the study, the diameter of rods is 6 mm and the design of the fixation part is presented on figure 4 The fixation parts consist in a cylinder for welding or sticking on the liner, and a cone to increase the length of the adhesive joint. To determine the cone angle, we made some finite elements analysis. Figure 5 presents the evolution of the shear stress along the adhesive joint, there is one curve by calculation step. Table 2 gives the maximum shear stress for a given angle. As the figure 5 and Table 2 show, the shear stress is maximum at the beginning of the adhesive joint and increase with the cone angle. As a consequence, the chosen cone angle is 2°. The optimum thickness of the joint would be determined experimentally for a given adhesive length of 90 mm

Fixation parts : experimental study

In order to realize a complete mock-up of form fitted tank, we have tested different adhesives, protocols and different thicknesses. For every case, at least 10 tests were realized. Two protocols for bind fixation parts and rods were used :

 Protocol 1: The contact surface on the fixation part and the rod was coated with an adhesive and then the rod is inserted in the fixation part  Protocol 2: Only the rod is coated with glue and then inserted in the fixation part

The protocol 1 hasn't be used for adhesive B because the pot life was too short for applying it. When all the samples were prepared, the tensile tests have been realized, strength and displacement were recorded and measured, the loading rate was 100 N/s for all tests. Figure 6 presents the typical observed behavior. The behavior presents a linear increase of shear stress until debonding and then sliding of the rod out of the fixation part. Figure 7 presents for each adhesive, each thickness and each protocol the average of maximum measured shear stress. According to figure 7, the adhesive C has the best performances, the shear stress increases with thickness until 0.4 mm and then decreases with it. This result was also confirmed by Arenas et al. [START_REF] Arenas | Optimum adhesive thickness in structural adhesive joints using statistical techniques based on Weibull distribution[END_REF]. So, adhesive C with a thickness of 0.4 mm was used to realize a prototype of a form-fitted tank.

First mock-up 4.1 Materials and process

Figure 8 shows a tank with two flat surfaces which were realized in order to test the reinforcement, the inner volume is about 6L, 18 rods reinforce the liner. In order to wrap the resulting liner by filament winding, aluminium alloys parts were made to soften sharp edges. Total outside dimensions are 300 mm x 205 mm x190 mm. To create a reference, a second prototype was made with the same shape but without the rod.

Internal pressure testing

We made two types of tests on the prototypes, air tightness they were loaded at 10 bar of air pressure during 24 hours and a burst test under hydraulic pressure. Figure 10 shows the crack responsible of the leak, it is located on a welded joint. The burst limit of the prototype was not observed, but the leakage appears at a 24% higher pressure on the reinforced one.

Conclusion and acknowledgement

This paper introduces a way to reinforce form fitted tanks by using composite rods and the developments of some theoretical and experimental points to achieve the reinforcement and design. Finally, two prototypes were tested and even the first results are encouraging. Further developments have to be done for completing this study

This study is a part of the HYPE project which was supported by the french ANR and performed by MAHYTEC and University of Franche-Comté in collaboration with PSA, CEA and Soficar. The authors want to thank all the participants of the project for their supports.

Crack

Figure 1 .

 1 Figure 1. Typical liner cross-section of type III and IV

Figure 2 .

 2 Figure 2. Example of a form fitted improvement -Pressure field on a cross section

Figure 3 .

 3 Figure 3. Carbon/epoxy rods, attaching parts, and testing systems

Figure 4 .

 4 Figure 4. General design of a fixation part

Figure 5 .

 5 Figure 5. Numerical study of the shear stress in the adhesive joint -Cone angle 5°

Figure 6 .

 6 Figure 6. Shear stress versus displacement

Figure 7 .

 7 Figure 7. Maximum shear stress in the glue joint

Figure 8 .

 8 Figure 8. Form fitted liner made of stainless steelaluminium shape adapter

Figure 9 .

 9 Figure 9. Filament winding of the form-fitted tank

Figure 10 .

 10 Figure 10. Crack on the welded joint -source of the leakage

Table 1 .

 1 Mechanical characteristic of composite rods

	Young modulus [MPa]	160000
	Ultimate tensile strength [MPa]	3000
	Ultimate Strain	2%
	Shear modulus [MPa]	3200
	Shear strength [MPa]	88
	Density	1,59

Table 2 .

 2 Maximum shear stress for different cone angles

  Table 3 presents the three different adhesives used and their properties

	Adhesive° Shear Stress [MPa]	Curing Cycle
	A	23	1h at room temperature (RT)
	B	25	6 min at RT
	C	13,6	1h at RT

Table 3 .

 3 List of used adhesives

Table 3 .

 3 Table 3 presents the results of the test tank 1 is the reinforced one Maximum pressure test

	Tank n°	Air tightness	Pressure [MPa]	Type of Failure
	1	OK	51,1	leakage
	2	OK	38,5	leakage