V D'ambrosi
email: veronica.d'ambrosi@cea.fr

C Destouches

S Breaud

DEN, Cea

G Ricciardi

F Lebon

E Sarrouy

J M Gatt

J Julien

were with DEN/ D Parrat

Experimental characterization of PCI impact on vibrating fuel rod under axial turbulent flow representative of JHR irradiation device ADELINE:

Set-up conception and measurement method Experimental characterization of PCI impact on vibrating fuel rod under axial turbulent flow representative of JHR irradiation device ADELINE:

Set-up conception and measurement method Veronica D'Ambrosi, Stephane Breaud, Christophe Destouches, Guillaume Ricciardi, Frederic Lebon, Emmanuelle Sarrouy, Jean-Marie Gatt, Jerome Julien and Daniel Parrat

Abstract-Mechanical loading originating due to Pellet-Cladding Interaction (PCI) in PWR nuclear fuel rod constitutes a first order importance phenomenon when attempting at increasing the flexibility of nuclear reactors operation to follow grid demand. The need to improve the understanding of such complex multi-physics phenomena motivates the realization of particular irradiation sequences carried out in highly instrumented devices located in Material Testing Reactors. Among this kind, ADELINE irradiation device is being developed and will be installed in the future Jules Horowitz Reactor. In the perspective of designing the adapted measurement methodology to detect and characterize PCI phenomenology during irradiation, we present in this paper the experimental bench and its associated measurement program, designed to investigate eventual effects of PCI on the non-linear, flow induced vibrations of nuclear fuel rod. Analytical and numerical models cannot predictively describe the system due to the complexity of phenomena thus the IMPIGRITIA experimental set-up has been developed to reproduce the mechanical interaction between the pellet and the clad at low pressure, room temperature and out of neutron flux. The designed test bench presents a clamped free single short rod, centred in the test section by mean of four centring elements. Different rod configurations are implemented and localized closure of the gap is remotely realized by means of a dilatation system. Laser Doppler Vibrometry is used to measure the transversal displacement of the sample rod in three different conditions: in air, in stagnant water and under turbulent axial flow rate. The experimental program and expected results are presented and discussed. Index Terms-Nuclear, Instrumentation, Measurement, Bench, fuel rod, PCI, dynamics, vibrations, LDV

I. INTRODUCTION: BACKGROUND AND OBJECTIVES

T HROUGH the past years, Pellet-Cladding Interaction (PCI) has constituted an issue in the definition of technical specifications for the operation of nuclear power plants and for the identification of associated safety margins. Consequently, research has attempted to improve the knowledge of this complex phenomenon by numerical simulations, developing multi-physics models, and by experiments in Material Testing Reactors (MTR) [START_REF] Michel | Simulation of Pellet-Cladding Interaction with the PLEIADES Fuel Performance Software Environment[END_REF]. In the latter, environmental constraints have strongly limited the possibility to obtain real time measurements and thus to allow characterisation of the kinetics of the phenomenology. At present days, a need for highly instrumented experiences in MTRs and for on-line measurements to gain real time data during irradiation has been expressed. In the next future JHR, ADELINE is a specific irradiation device where PWR temperature and pressure conditions are reproduced and which will be partially dedicated at studying this phenomenology.

In this frame we have identified relevant and measurable parameters associated to PCI during normal irradiation and incidental conditions. We also proposed a model to characterize fuel material behaviour undergoing initiating central melting in the attempt at evaluating its macroscopic impact on PCI [START_REF] D'ambrosi | Proceedings of MECAMAT 2018[END_REF]. We are working to propose innovative and efficient measurement methods for detecting and characterizing this complex multi-physics phenomenology. Among the identified relevant parameters, vibration distinguished as a possible application case. Flow Induced Vibrations (FIV) of nuclear fuel rods in axial turbulent flow rate have been concerned by a large variety of scientific studies. According to Païdoussis [START_REF] Païdoussis | Fluid-Structure Interactions, Slender Structures and Axial Flow[END_REF] [4] and Axisa [START_REF] Axisa | Modélisation des systèmes mécaniques : Vibrations sous écoulements[END_REF] flow induced vibrations come from two mechanisms: the drag force in the turbulent boundary layer near the structure (nearfield component) and from the wall pressure fluctuations and far field noise. They generally induce transversal vibrations of small amplitudes, typically the vibration amplitude y/D c does not exceed 10 -3 , y being the r.m.s. amplitude of vibration and D c the cylinder diameter. In the nuclear field, works are mainly motivated by fretting concern, phenomenon appearing at the grid-rod interface. Few researches have instead been carried out on the effects of non linear mechanisms arising from the presence of pellets within the fuel rod. It is generally argued that modeling those effects is rather difficult [START_REF] Ferrari | Non-linear vibrations of nuclear fuel rods[END_REF]. Benhamadouche in [START_REF] Benhamadouche | CFD estimation of the flow induced vibrations of fuel rod downstream a mixing grid[END_REF] proposed to evaluate an equivalent mass density for the rod which accounts for the presence of pellets. This density is then used in the evaluation of the dynamic behaviour of the fuel rod taken as a linear Euler Bernoulli beam. Park et al. in [START_REF] Park | Indirect estimation method of the turbulence induced fluid force spectrum acting on a fuel rod[END_REF] make the point on the fact that since a gap exists between pellets and gap, the contribution of the pellet mass to the density for dynamic evaluation cannot be clearly determined. They propose to compare the natural frequencies of empty and fulfilled rods to estimate an appropriate density. The fuel rod vibration is then evaluated, still assuming a linear behaviour. The non linear vibration of fuel rod has been recently studied by Ferrari et al. [START_REF] Ferrari | Non-linear vibrations of nuclear fuel rods[END_REF]: his study concerned a 900 mm zircaloy clad, clamped at both extremities, eventually fulfilled with cylindrical tungsten carbide pellets modelling uranium fuel pellets in terms of dimensions and density. By comparing the dynamics of empty rod, fulfilled rod freely moving (no spring at one bottom of the fuel column) and fulfilled rod axially constrained in air and in quiescent water, they observed that pellets decrease natural frequencies of the rod and that axial constriction increases natural frequencies and reduced damping with respect to freely moving configuration, both in air and in water. Moreover, they stated that non linear mechanisms were experimentally observed during tests. No studies have been retrieved discussing the effect on the dynamics of the fuel rod of local pellet-clad contact due to gap closure. The impossibility to predictively model the non-linear system justified the design of the experimental set up IMPIGRITIA 1 to state the feasibility of measuring such impact. This paper is structured as follows: we briefly proceed in section II with the numerical approach of the system, highlighting the empirical parameters to be measured to then present in section III the measurement principles.

Section IV is devoted to the design criteria of the experimental set-up, the definition of rod configurations and associated instrumentation. Section V then briefly describes the experimental program and expected results. Section VI proceeds to conclusions and future work.

II. THE NUMERICAL APPROACH A. Definition of the model

Figure 1 shows a schematic view of the proposed model. The sample holder and the empty clad are modelled as a cantilevered Euler-Bernoulli beam by a 2D finite element model. Each node of the clad can move along the radial (u x ) and the axial direction (u y ) and can rotate (θ z ). Pellets are considered as discrete masses m p interacting along the radial direction with corresponding clad nodes through the non linear mechanism of dissipative shock and with each other through Coulomb friction. The equation of motion to be solved is [START_REF] Gradin | Mechanical Vibrations, Theory and Application to Structural Dynamics[END_REF]:

[M ]{ẍ} + [C]{ ẋ} + [K]{x} + {f nl} = {F e } (1)
Where [M ] N,N is the total mass matrix, [C] N,N the total damping matrix, [K] N,N the total stiffness one. They are obtained as follows:

[M ] =   [M c ] 0 0 [M p ]   [C] =   [C c ] 0 0 [C p ]  
1 Acronym form "Interaction Mécanique PastIlle Gaine :RéalIsation du Test vIbrAtoire", from latin impigritia, impigritiae; means "zeal, dedication"

[K] =   [K c ] 0 0 [K p ]   (2)
where [M c ] n,n is the tridiagonal mass matrix for the clad and [M p ] m,m is the diagonal mass matrix for the pellets, with N = m + n. In the same way the total stiffness matrix and the total damping one depends on clad and pellets ones.

Rayleigh damping is used to model the damping matrix [C]:

[C] = α[M ] + β[K] (3)
Assuming proportional damping, the dissipation in the structure can be described by two parameters α and β. Those parameters, which are not a priori known, are experimentally determined measuring the first two eigen-frequencies of the system in air. Indeed it can be shown that [START_REF] Alarcon | Code aster: Modeling of damping in dynamics linear[END_REF]:

ζ = 1 2 α ω i + βω i ( 4
)
where ζ is the modal damping, which can be recovered by logarithmic decrement from free damped vibrations of the system and ω i are the eigen-frequencies. The non-linear forces acting on the system are expressed by the {fnl} term in equation [START_REF] Michel | Simulation of Pellet-Cladding Interaction with the PLEIADES Fuel Performance Software Environment[END_REF]. Those forces are the dry friction between discretized pellet nodes and the shock interaction between pellet nodes and clad ones. Gap size is a parameter in the formulation of pellet-clad shock interaction. The presence of external water plays a role in the external solicitation {F e } but it also induces an additional viscous damping to the structure: according to De Pauw in [START_REF] De Pauw | Operational modal analysis of flow-induced vibration of nuclear fuel rods in a turbulent axial flow[END_REF] the effects of flowing fluid on the spectral response of the structure is described by an added mass m a , corresponding to the mass of displaced fluid, and a dynamic amplification factor C m such that:

f = 1 2π K M + C m m a (5)
where K and M are the structural stiffness and mass of the system. The dynamics amplification factor is equal to 1 for quiescent water thus the two parameters can be experimentally obtained by comparing the oscillation frequencies of the system in air, in quiescent water and in fluid flow. {F e } corresponds to the excitation mechanisms acting on the system, notably the flow solicitation. We decided to apply a statistical approach and model {F e } by taking the envelop PSD defined by Axisa [START_REF] Axisa | Modélisation des systèmes mécaniques : Vibrations sous écoulements[END_REF] and applying an arbitrary stochastic phasing.

To solve the equation, explicit Newmark scheme has been implemented. As reported in [START_REF] Gradin | Mechanical Vibrations, Theory and Application to Structural Dynamics[END_REF] direct time integration is necessary when the problem is non linear in order to avoid strong dependencies of results on integration time step.

B. Investigation of parameters: an empirical model

The displacement {x} of the structure, obtained when solving motion equation ( 1) by mean of explicit Newmark integration scheme, can be expressed as a function of the set of parameters P, resulting from the previous discussion:

{x} = f {P} = f M p , M c , m a , C m , K p , K c , α, β, K c , C c , µ, j, c 2 (6)
where M i , K i , α and β have already been defined, m a and C m are the added mass and the dynamic amplification factor due to the fluid presence and fluid flow. K c and C c are the parameters characterising the pellet-clad shock interaction, modelled through a contact stiffness K c and a viscous dissipation C c [START_REF] Wriggers | Computational Contact Mechanics[END_REF]; µ is the friction coefficient to model the pellet-pellet interaction. j is the width of the gap and c is the fluid velocity. While some of those parameters are completely defined by the geometry of the structure (i.e. the mass matrix of pellets M p and sample holder M c , the stiffness matrix of the sample holder), the others have to be experimentally determined. Identification of model parameters adapted to fit at best experimental data allows calibration of the model. They are resumed in table I.

III. THE MEASUREMENT PRINCIPLE

The presence of pellets inside the clad induces the appearance of non linear mechanical dissipations [START_REF] Ferrari | Non-linear vibrations of nuclear fuel rods[END_REF]. Internal attachment between pellets and clad as a consequence of gap closure limits those effects and impacts mode and frequencies of the system. We expect local and progressive mechanical contact between pellets and clad to reduce structural damping as a consequence of reduced dissipative mechanisms and to decrease its eigen-frequencies. Those variations can be retrieved by measuring the displacement of the system x(t). Experimental identification of the frequencies and of modal properties, as the modal damping, can be carried out both in the time domain or in the frequency one through direct or inverse Fourier transform. Indeed:

x(t) ↔ X(ω)
where X(ω) is the Fourier transform of the time signal of the displacement x(t) of the point characterized by the highest transversal displacement. X(ω) and x(t) are linked by the relations:

X(ω) = P[x(t)] = ∞ -∞ x(t)e -iωt dt (7)
x(t) = P -1 [X(ω)] = 1 2π ∞ -∞ X(ω)e iωt dω (8)
In both time and frequency domains, system identification shall be carried out on the basis of the model presented in this section, adapting its parameters to fit at best the experimental data. Several methods are available in literature [START_REF] Gradin | Mechanical Vibrations, Theory and Application to Structural Dynamics[END_REF] and [START_REF] De Pauw | Operational modal analysis of flow-induced vibration of nuclear fuel rods in a turbulent axial flow[END_REF].

The impact of pellet-clad interaction on the transversal vibration x(t) can be experimentally obtained by comparing specifically designed rod configurations under the same excitation conditions. Calibration of parameters previously discussed allows validation of the model capability to simulate the dynamic response of the structure.

IV. DESIGN CRITERIA A. Objectives

We have manufactured the experimental test bench to state the capability to measure whether gap closure impacts fuel rod dynamics. We want to identify if a minimum number of pellets has to interact with the clad to have a measurable effects and to define if FIV are sufficient to have a passive measurement and to study the influence of this axial flow excitation on the feasibility of this measure. Application domain is the ADELINE device.

B. The representativeness issue

ADELINE [START_REF] Gonnier | Proceedings of IGORR 2017[END_REF] is designed to be a 4m high irradiation device and constitutes the evolution of ISABELLE 1 system as it was in OSIRIS reactor [START_REF] Alberman | Technique for power ramp tests in the isabelle 1 loop of osiris reactor[END_REF]. As its predecessor, it presents a single rod test section where temperature and pressure conditions characteristics of a PWR are reproduced (155 bar and 275 • C inlet water temperature). The tested rod has geometrical characteristics of FABRICE type fuel-rod [START_REF] Alberman | Technique for power ramp tests in the isabelle 1 loop of osiris reactor[END_REF]: a short element (about 60 cm in length) obtained cutting a previously irradiated 4m fuel rod and adapted to MTR geometry. The rod is cooled by an up-streaming turbulent flow rate. It is maintained in the section by a sample holder and centred by four centring elements. In order to be representative of ADELINE configuration, we accounted for the real environmental conditions, for the geometrical design, material characteristics and hydraulic solicitation.

1) The environment: Thermal and mechanical properties are obviously impacted by the environmental conditions but, through the years, several correlations have been developed to account for these phenomena. Those correlations will be used during post treatment of results to establish the attended behaviour in PWR conditions [START_REF] Fink | Thermophysical properties of uranium dioxide[END_REF]. The pressurization of the circuit has no impact on the vibration of the component, thus leading to design a law pressure system.

2) The geometry: Mechanical similarity and scale reduction cannot simply be applied and a 1:1 scale system implied non negligible conception, exploitation and cost issues. Still, geometry and fixation conditions strictly impact the dynamics of a structure thus the clamped free conditions of ADELINE sample is maintained in the experimental set-up. Moreover, ADELINE sample holder is made of an upper part and a lower part, the sample rod a centring elements being located in this last one. The two parts are coupled by a mechanical system. The specific configuration and material properties of the real system lead us to decide to limit our study to the lower sample holder part. It results an experimental system of about 1.5 m. This choice is expected to strengthen the impact of a local pellet-clad interaction on the global dynamics of the structure.

3) The hydraulic similarity for FIV: Fuel rod to be installed in the ADELINE device will be submitted to a turbulent flow rate of approximately 1 m/s at about 275 • C and 155 bar along the axial direction, from the bottom to the top. Such kind of turbulent flow rate induces the appearance of FIV of the sample rod. Hydraulics is dimensioned in order to reproduce the external solicitation in terms of the axial turbulent flow and pressure fluctuation in the flow. We identified a range of representativeness first by imposing the conservation of wall pressure fluctuations and secondly applying the Burgreen principle. The conservation of wall pressure fluctuation p r.m.s was imposed according to the definition proposed by Axisa in [START_REF] Axisa | Modélisation des systèmes mécaniques : Vibrations sous écoulements[END_REF] on the basis of the envelop PSD derived from Clinch data [START_REF] Clinch | Measurements of the wall pressure field at the surface of a smooth-walled pipe containing turbolent water flow[END_REF] and reported in equation [START_REF] Gradin | Mechanical Vibrations, Theory and Application to Structural Dynamics[END_REF]. The simulation criterion established by Burgreen [START_REF] Prakash | Experimental qualification of subassembly design for prototype fast breeder reactor[END_REF] instead has been recently used by De Paw et al. in [START_REF] De Pauw | Operational modal analysis of flow-induced vibration of nuclear fuel rods in a turbulent axial flow[END_REF] to study flow induced vibrations in a prototype representative of the MHYRRA system and it is reported in equation [START_REF] Alarcon | Code aster: Modeling of damping in dynamics linear[END_REF]. c exp = c ρ 0.5 µ -0.33 E -0.33 M 0.165 ρ 0.5 exp µ -0.33 exp E -0.33 exp M 0.165 exp [START_REF] Alarcon | Code aster: Modeling of damping in dynamics linear[END_REF] Subscript 'exp' stands for prototype, µ the fluid dynamic viscosity, E elastic modulus and M the mass of the sample rod at operating temperature.

Applying the described criteria in our test conditions we found a range of representative flow rate varying between 0.9 to 2.6 the fluid velocity at the sample rod in ADELINE.

c exp c ∈ [0.9 : 2.6] (11)
V. THE EXPERIMENTAL SET-UP AND PROGRAM

For the experience several representative hollow zircaloy clad were supplied. As previously mentioned, the geometrical configuration of sample rods was defined on the basis of FABRICE type fuel rods used in ADELINE: the zirconium alloy clad has an external diameter of 9.5 mm, its material properties are reported in table II. We defined a length coherent with FABRICE characteristics thus 550 mm long. Each side is welded to a plug which is screwed on a prolongation tube in stainless steel.

The prolongation tube constitutes the sample holder and it is fixed at the top of the experimental section. The other side is instead free to move. A simplified scheme of the sample holder is presented in figure 2.

Due to environmental and realisation issues, the UO 2 constituting the real fuel material was replaced by cylindrical Molybdenum pellets, which is one of the most representative materials according to internal researches carried out at CEA. A comparison of room temperature material properties of UO 2 and Mo are resumed in table II. Pellets diameter was defined according to standard radial dimension of UO 2 fuel pellets, the height instead was deduced by mass conservation of UO 2 fuel pellets.

In order to fulfil the fabrication gap existing between pellets and clad and thus remotely control PCI, a dilatation system capable of local expansion is used. The tool, showed in figure 3, is used in the medical domain for stent implantation: it is made of a balloon which can be externally inflated and a connection tube (the shaft) allowing positioning and inflation of the system.

The component is introduced from the top of the sample holder, through centrally drilled pellets and the balloon is placed in the region where gap closure wants to be induced. There, pellets are replaced by two shells which are displaced by the dilatation of the system, leading to pellet-clad contact. We decided to test different rod configurations taking advantage of different length of balloons in order to identify the minimum number of contacting pellets leading to a measurable effects. Rod configurations are resumed in table V. To calibrate the model and characterize system dynamics response, three other rod configurations were manufactured: an empty rod C0 to characterize modal parameters governing the linear dynamic response of the sample rod; C1 which corresponds to the fuel rod being fulfilled with Mo pellets, allowing to highlight possible bias due to the presence of dilatation system; and C6, where Mo pellets and clad are designed to stick together. This last configuration allows to measure to effect on sample rod dynamics due to complete closure of the gap. As previously mentioned, the sample rod is maintained by a sample holder, centered in the experimental section by mean of four elements. In order to collect vibration data of the sample rod from Laser Doppler Vibrometer (LDV) system, the experimental section is completely designed in optical quality plexiglass. This type of non-contact measuring system is capable of collecting the vibration of structures even in the presence of surrounding water.

Specifically designed holders allow axial translation of sensible heads. This allows for reconstruction of mode shapes of the rod and experimental modal analysis. The measurement system is showed in figure 4.

To produce and control flow conditions in the experimental section we have designed a dedicated independent water loop. as shown in figures 5 and 6. All conditioning components are located on a separate frame to limit noise effect on LDV measures. To monitor conditions in the circuit we have installed a flow meter at the experimental section inlet, three thermocouples located at different positions to verify temperature evolution in the loop and three pressure gauges to check pressure drops. A summary of instrumentation characteristics and accuracy is reported in table IV.

Measures during the experience are carried out in three different conditions: in air, in quiescent water and under axial, turbulent flow rate. When the system is in air and in stagnant water, the excitation technique is constituted by a magnetic solicitation system attracting the final section of the sample holder, especially made of ferromagnetic material. Logarithmic decrement applied on the collected signal of the underdamped system is used to obtain its damping ratio. Test of the different rod configurations in air and in stagnant water leads VI. CONCLUSIONS AND FURTHER WORK The IMPIGRITIA test bench was designed to investigate PCI and innovative measurement methods. The experiment is conceived to verify the capability of measuring the modification of modal properties and dynamic response as a function of the partial closure of internal pellet-clad gap under turbulent flow excitation representative of PWR environment. Open literature supports the fact that the non linear mechanisms acting on the dynamics of the fuel rod structure Fig. 6. View of designed water loop conditioning the experimental section induce measurable variations: the closure of the gap causes a global increase in the isotropy of the dynamic response and a reduction in damping and frequencies of the structure. The system has been designed though material, mechanical and hydraulic similarity, to reproduce mechanical PCI at room temperature, at low pressure and being representative of the geometry of ADELINE device. Some modifications in the geometry have been carried out which enhance the possibility of measuring the investigated effects. Due to environmental issues, UO 2 cannot be used in such experiments: the identified representative material is Molybdenum. According to literature, transversal vibrations in axial turbulent fluid flow are due to pressure fluctuations in the fluid pressure field: hydraulic similarity has been applied and a range of flow velocities varying between [0.9:2.6] ADELINE's one has been identified, using the conservation of pressure fluctuation and the Burgreen principle. An expansion system has been chosen to locally induce gap closure. To understand and simulate the physics of the dynamic response of the structure, a model has been developed. It cannot be predictive for the phenomenon under analysis as a large set of parameters has to be first experimentally calibrated. The experimental program has thus been defined to cope with calibration issues, testing in different experimental conditions (air, stagnant water and turbulent axial flow) several rod configurations, notably an empty rod, a fulfilled rod without dilatation system, four rods having PCI axial extension progressively increasing and a full rod with pellets stuck to the clad. We will characterize vibration mode in terms of damping ratio and eigen-frequencies by measuring the transversal displacement of the system under active controlled solicitation and under passive flow induced vibration. We expect that a correlation could exists, coupling the axial extension of gap closure with the damping modification of the structure. Whether a measurable modification is clearly identified, we shall proceed to a study to evaluate an adapted instrumentation methodology to cope with ADELINE configuration and nuclear environment, where it would lead to a better understanding of the PCI mechanism under irradiation.

V

  . d'Ambrosi, S. Breaud, C. Destouches, G. Ricciardi, Frédéric Lebon, E. Sarrouy, J.-M. Gatt, J. Julien, Daniel Parrat To cite this version: V. d'Ambrosi, S. Breaud, C. Destouches, G. Ricciardi, Frédéric Lebon, et al.. Experimental characterization of PCI impact on vibrating fuel rod under axial turbulent flow representative of JHR irradiation device ADELINE: Set-up conception and measurement method. ANIMMA 2019 -International conference on Advancements in Nuclear Instrumentation Measurements Methods ans their Applications, Jun 2019, Portoroz, Slovenia. cea-02339454

Fig. 1 .

 1 Fig. 1. Numerical model of IMPIGRITIA: schematic view of the configuration

  p r.m.s = 0.003(ρc 2 ) (9)where p r.m.s is the root mean square of pressure fluctuations, ρ is fluid density and c is average flow velocity.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Sample holder scheme

Fig. 4 .Fig. 5 .

 45 Fig. 4. View of measurement system by LDV: the clad, highlighted in orange, is visible through the plexiglass experimental section; two metallic rods helps supporting the two red structures holding laser heads. The two laser heads located at 90 • lead to verify axisymmetric vibrations of the rod


Onur Tasar

Yuliya Tarabalka

Pierre Alliez

Incremental Learning for Semantic Segmentation of Large-Scale Remote Sensing Data

  L'archive ouverte pluridisciplinaire

Incremental Learning for Semantic Segmentation of Large-Scale Remote Sensing Data Onur Tasar, Student member, IEEE, Yuliya Tarabalka, Senior member, IEEE, Pierre Alliez

Abstract-In spite of remarkable success of the convolutional neural networks on semantic segmentation, they suffer from catastrophic forgetting: a significant performance drop for the already learned classes when new classes are added on the data having no annotations for the old classes. We propose an incremental learning methodology, enabling to learn segmenting new classes without hindering dense labeling abilities for the previous classes, although the entire previous data are not accessible. The key points of the proposed approach are adapting the network to learn new as well as old classes on the new training data, and allowing it to remember the previously learned information for the old classes. For adaptation, we keep a frozen copy of the previously trained network, which is used as a memory for the updated network in absence of annotations for the former classes. The updated network minimizes a loss function, which balances the discrepancy between outputs for the previous classes from the memory and updated networks, and the mis-classification rate between outputs for the new classes from the updated network and the new ground-truth. For remembering, we either regularly feed samples from the stored, little fraction of the previous data or use the memory network, depending on whether the new data are collected from completely different geographic areas or from the same city.

Our experimental results prove that it is possible to add new classes to the network, while maintaining its performance for the previous classes, despite the whole previous training data are not available.

Index Terms-Incremental learning, catastrophic forgetting, semantic segmentation, convolutional neural networks

I. INTRODUCTION

R ECENT improvements in satellite sensors have enabled us to capture massive amounts of remote sensing data with high spatial resolution, as well as rich spectral information. Generation of maps from such huge amounts of satellite images and updating them automatically have been long standing problems, as they are crucial for a wide range of applications in domains such as agriculture, navigation, environmental management, urban monitoring, and mapping. In this context, having a strong classification system, which performs a high-quality, pixel-wise, large-scale classification is the most essential step.

In the last decade, with the great advances in deep neural networks, notably convolutional neural networks (CNNs), it has been possible to obtain accurate segmentations [START_REF] Maggiori | High-resolution semantic labeling with convolutional neural networks[END_REF]- [START_REF] Audebert | Semantic segmentation of earth observation data using multimodal and multi-scale deep networks[END_REF]. Among the CNN-based approaches, U-net architecture [START_REF] Ronneberger | U-net: Convolutional networks for biomedical image segmentation[END_REF] has O. Tasar, and P. Alliez are with Université Côte d'Azur and also with Inria, TITANE team, 06902 Sophia Antipolis, France. E-mail: onur.tasar@inria.fr Y. Tarabalka is with LuxCarta Technology, Parc d'Activité l'Argile, Lot 119b, Mouans Sartoux 06370, France. gained a particular attention due to its success in various segmentation problems in different domains (e.g., medical imaging and remote sensing). This network architecture consists of a contracting path that captures the context and a symmetric expanding path, enabling accurate localization. In addition to traditional encoder-decoder layers, U-net architecture uses skip connections, which combine low level features with the high level ones in the expanding path to increase precision of localization. Variants of this network [START_REF] Huang | Large-scale semantic classification: outcome of the first year of inria aerial image labeling benchmark[END_REF]- [START_REF] Iglovikov | Ternausnetv2: Fully convolutional network for instance segmentation[END_REF], (e.g., U-net, including VGG-11 [START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF] encoder and corresponding decoder) have been applied to remote sensing images and have shown a remarkable performance.

The major drawback of the recently proposed methodologies is their assumption that the whole training data are available in the beginning, which is not the case in real world remote sensing applications, as new images are collected from all over the world everyday. Besides, having large amounts of standard and unique label maps is almost impossible, because the label maps retrieved from different sources usually have distinct classes. In addition, it is not always possible to store enormous volume of training data. For the reasons described above, designing an incremental learning methodology, which can learn from the new training data while retaining performance for the old classes without accessing to the entire previous training data is crucial. Although a good solution for this problem is necessary to generate high-quality maps from satellite images that cover a large geographic extent, yet it has remained unexplored in remote sensing community.

Rather than assuming that we have all the training data initially, we aim to design an incremental learning methodology. Let us explain with an example of a real-world problem (see Fig. 1) where, in the beginning, we are provided with images from several cities in Austria with correspondent label maps for building and high vegetation classes. Later on, we are given other training data, having label maps for water class, collected from different areas in Germany. Finally, we receive new satellite images and their annotations for road and railway classes from certain cities in France. Every time when new data arrive, we assume that only a small portion of the previous data is stored. In such a scenario, our goal is to add segmentation capabilities for the new classes to the previously trained network without forgetting the already learned information so that maps for all the learned classes could be generated by the network. In addition to the described problem, because labeling satellite images covering a large geographic area requires a lot of manual work, it is quite common that annotations of different classes for the same images are provided sequentially in time. In this kind of situation, it is not feasible to train a new classifier from scratch every time new label maps are obtained. The limitations pointed out in this section motivated us to design an incremental learning methodology.

A. Related Work

The biggest challenge in incremental learning problem is that when new tasks are intended to be added to a classification system, performance of the system for the previously learned tasks degrades abruptly, which is referred as "catastrophic forgetting" in the literature [START_REF] French | Catastrophic forgetting in connectionist networks[END_REF], [START_REF] Goodfellow | An empirical investigation of catastrophic forgetting in gradient-based neural networks[END_REF]. Incremental learning has been a historically important problem. Even before neural networks have become popular, researches had been studying this issue [START_REF] Thrun | Is learning the n-th thing any easier than learning the first?[END_REF]- [START_REF] Bruzzone | An incremental-learning neural network for the classification of remote-sensing images[END_REF]. More recently, various convolutional neural network based methodologies have been proposed. There have been attempts, which change architecture of the neural network as new classes are added. In [START_REF] Sarwar | Incremental learning in deep convolutional neural networks using partial network sharing[END_REF], the network is trained incrementally by sharing early layers and splitting later ones by adding new convolutional kernels. In [START_REF] Xiao | Error-driven incremental learning in deep convolutional neural network for large-scale image classification[END_REF], a tree-structured model, which grows hierarchically, is proposed. In [START_REF] Rusu | Progressive neural networks[END_REF] and [START_REF] Yoon | Lifelong learning with dynamically expandable networks[END_REF], described approaches grow the network horizontally. The methodology described in [START_REF] Xu | Reinforced continual learning[END_REF] tries to solve the problem of determining the number of filters to be added to each layer by reinforcement learning. The major weakness of these approaches is that since the network grows during training, the number of parameters increases drastically as new tasks are added to the network. The methodologies proposed in [START_REF] Rebuffi | iCaRL: Incremental classifier and representation learning[END_REF]- [START_REF] Hou | Lifelong learning via progressive distillation and retrospection[END_REF] use not only the new training data but also a small portion of the old data. To determine the most important samples for the previous classes, the approach in [START_REF] Li | Supportnet: solving catastrophic forgetting in class incremental learning with support data[END_REF] trains a Support Vector Machine (SVM) from the previous training data. The support vectors of the SVM correspond to the samples to be used for the former classes, while the network is adapted to the new training data. In [START_REF] Wu | Incremental classifier learning with generative adversarial networks[END_REF], [START_REF] Shin | Continual learning with deep generative replay[END_REF], instead of using the old data directly, fake previous data are generated by generative adversarial networks (GAN). It has been proven that many configurations of the network parameters may produce the same result [START_REF] Sussmann | Uniqueness of the weights for minimal feedforward nets with a given input-output map[END_REF]. Inspired by this idea, several works, which try to find a configuration of the network parameters that represents both the previous and the new training data well, have been published. The key idea behind these approaches is to find the important neurons for the old tasks and prevent these neurons from changing greatly or completely when the new tasks are added to the network. The proposed methodology explained in [START_REF] Kirkpatrick | Overcoming catastrophic forgetting in neural networks[END_REF] is one of the approaches that falls into this category. In the loss function defined in the paper, there is an elastic weight consolidation (EWC) term, which is a multiplication of the importance value of parameters for the old tasks and quadratic penalty on difference between parameters of the previous and the updated networks. The importance value of the parameters is measured by the estimated diagonal Fisher information matrix. The same work has been extended in [START_REF] Liu | Rotate your networks: Better weight consolidation and less catastrophic forgetting[END_REF] by rotating the Fisher matrix. [START_REF] Zenke | Continual learning through synaptic intelligence[END_REF] is also quite similar to [START_REF] Kirkpatrick | Overcoming catastrophic forgetting in neural networks[END_REF], but the elastic weight consolidation is performed in online fashion. In [START_REF] Aljundi | Memory aware synapses: Learning what (not) to forget[END_REF], importance of each neuron is determined by averaging gradients of the network output with respect to parameters of the neuron. In [START_REF] Triki | Encoder based lifelong learning[END_REF], in the training stage, features from the previous data are reconstructed in unsupervised manner using autoencoders. The features are then used to preserve information, which the old tasks rely on when the new tasks are added. [START_REF] Lee | Overcoming catastrophic forgetting by incremental moment matching[END_REF] is another extension of [START_REF] Kirkpatrick | Overcoming catastrophic forgetting in neural networks[END_REF], where trained models for all the tasks are combined via incremental moment matching (IMM). The proposed approaches in [START_REF] Mallya | Packnet: Adding multiple tasks to a single network by iterative pruning[END_REF] and [START_REF]Piggyback: Adding multiple tasks to a single, fixed network by learning to mask[END_REF] try to learn a mask, which marks important neurons for the old tasks. When the new tasks need to be added, only the masked out neurons are updated. In [START_REF] Fernando | Pathnet: Evolution channels gradient descent in super neural networks[END_REF], paths through the network, which represent a subset of parameters are determined by using tournament selection genetic algorithm. During the training stage, only the neurons that are located along the paths are updated. When the data come sequentially, the works explained in [START_REF] Zeno | Bayesian gradient descent: Online variational bayes learning with increased robustness to catastrophic forgetting and weight pruning[END_REF]- [START_REF] Nguyen | Variational continual learning[END_REF] optimize the parameters of the network by updating the posterior approximation by the Bayesian inference based methods. Distilling the knowledge approach proposed in [START_REF] Hinton | Distilling the knowledge in a neural network[END_REF], which enables to transfer the knowledge from a network or an assembly of several networks to a smaller network has inspired several works on incremental learning. The proposed methods in [START_REF] Li | Learning without forgetting[END_REF], [START_REF] Furlanello | Active long term memory networks[END_REF] facilitate a similar distillation loss described in [START_REF] Hinton | Distilling the knowledge in a neural network[END_REF] to maintain performance on the previous tasks. The proposed approach in [START_REF] Castro | End-to-end incremental learning[END_REF] uses a distillation loss function, which also uses samples for the previous classes in addition to samples for the new classes. Another knowledge distillation Fig. 2. The network structure. The number below each layer corresponds to number of filters. We refer the last layer, shown by yellow color as the classification, and the rest as the shared layers.

based approach has been proposed in [START_REF] Shmelkov | Incremental learning of object detectors without catastrophic forgetting[END_REF]. They deal with incremental object detection and classification tasks at the same time. Although the incremental learning problem has been explored in depth in the literature, none of the works described in this section studies incremental learning for dense labeling.

B. Contributions

We propose a novel incremental learning methodology for semantic segmentation problem, where the network learns segmenting new classes without deteriorating performance for the previously learned classes, even when the entire previous training data are not stored 1 .

We deal with two common real-world problems, in which the former is the situation of retrieving stream of training data, where at each time step, the data contain satellite images collected from different locations in the world and annotations for separate classes, the latter is the case, where label maps for the same geographic area are provided sequentially. To investigate how our methodology performs on the first problem, we test our approach on the Luxcarta dataset, consisting of the satellite images captured over different cities in France and Austria. For the second problem, we conduct experiments on the Vaihingen and the Potsdam benchmark datasets provided by the ISPRS [START_REF]ISPRS. 2d semantic labeling contest[END_REF]. The first problem is much more challenging, as the satellite images have high color variations and visual feature differences. Besides, for the first problem, by following a similar strategy described in [START_REF] Maggiori | Can semantic labeling methods generalize to any city? the inria aerial image labeling benchmark[END_REF], we test the trained models on the data collected from completely different geographic areas than the ones we use during training.

We provide rich experimental results for both problems by comparing our methodology with static learning, multiple learning, fixed representation, and fine-tuning (see Sec. III-A). Our experimental results prove that by training only one network, it is possible to learn new classes without catastrophically forgetting the previous classes. To the best of our knowledge, this is the first work, which proposes a solution for the incremental semantic segmentation problem.

II. METHODOLOGY

A. Network Architecture

Our network (see Fig. 2) is a variant of U-net, which consists of an encoder that is architecturally the same as the first 13 convolutional layers of VGG16 [START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF], a corresponding decoder, mapping low resolution encoder feature maps to original input image size of outputs, and two center convolutional layers. We prefer to use VGG16 as the encoder, because it provides a good compromise between complexity and performance, as it is not as deep as e.g., VGG19 but still it is one of the best performers on famous benchmark challenges (e.g., ImageNet [START_REF] Russakovsky | Imagenet large scale visual recognition challenge[END_REF]).

The output of each pooling layer in the encoder is concatenated with the output of the symmetric deconvolutinal layer in the decoder through skip connections to combine higher level features with the lower ones. Kernel size and stride in all the convolutional layers are 3 and 1 respectively. Padding parameter in the convolutional layers is set to 1 so as to keep height and width of output the same as output of the previous layer. The max-pooling layers, having 2 × 2 window with stride 2 are used to halve width and height of the previous layer. In order to upsample output of the previous layer by factor of 2, both kernel size and stride parameters are set to 2 in deconvolutional layers. Except the last convolutional layer, all the convolution and deconvolution operations are followed by a ReLU. Since batch normalization uses the memory inefficiently, we prefer not to use it to add more patches in a batch.

Multi-task learning is the learning strategy which solves multiple problems at the same time by learning all the tasks jointly. In deep neural networks, bottom layers enable to share information for all the tasks, whereas the last layers are dedicated to provide a solution for each task [START_REF] Caruana | Multitask learning[END_REF], [START_REF] Ruder | An overview of multi-task learning in deep neural networks[END_REF]. In incremental semantic segmentation problem, since the label maps of a remote sensing image for a class or several classes come sequentially, we consider the segmentation tasks as a multi-task learning problem, where performing a binary classification for each class corresponds to a different task. The output of our network is a 3D matrix that is a stack of binary predicted maps for all the classes. In the test stage, to generate a binary segmentation for each class, we first convert outputs of the final convolutional layers to probability maps using sigmoid; then, we threshold the probabilities at 0.5.

B. Adapting the Network to the New Training Data

To explain the adaptation phase, let us assume that the current training data are indicated by D curr . We denote sets of the previously learned classes and the classes in D curr by L prev and L curr , where L prev ∩ L curr = ∅. The main goals we try to achieve during adaptation are to update the formerly trained network so that segmentation capabilities for L curr are added, and to fine-tune the network on D curr for L prev , although annotations for L prev are not available in D curr . The output of the updated network is the matrix consisting of binary segmentations for L updated = L prev ∪ L curr .

We use the knowledge distillation from the previously trained network, which we refer to as memory network, as a proxy in absence of the ground-truth for L prev in D curr . We create an updated network, having exactly the same structure except the last classification layer, which has |L updated | filters instead of |L prev |. During creation of the updated network, additional |L curr | filters in the last classification layer are initialized using Xavier initialization [START_REF] Glorot | Understanding the difficulty of training deep feedforward neural networks[END_REF], and the rest of the parameters are loaded from the memory network. When D curr arrive, the incoming label map is first converted to a 3D matrix, consisting of binary ground-truth for L curr . The probability maps generated by the memory network are concatenated with this 3D matrix to provide information about L prev to the updated network. The final 3D matrix as well as the input image in D curr are fed to the network as the new training data. While concatenating output of the memory network with the new ground-truth, we prefer to use soft probability maps generated by the memory network rather than hard classification maps in order to reduce the propagated error rate, caused by imprecision in output of the memory network, at each time step of incremental learning.

Let us denote the binary target label vectors for n training samples i = 1 . . . n in a batch from D curr by y (i) curr and the predicted probabilities for L prev from the memory network by ŷ(i) mem . We denote by ŷ(i) up curr and ŷ(i) up prev , the predicted probabilities for L curr and L prev from the updated network. The classification loss L class quantifies mismatch between y (i) curr and ŷ(i) up curr . In order to compute L class , since we deal with generation of a binary segmentation for each class as a separate task, we use sigmoid cross entropy loss defined as:

L class = - 1 n|L curr | n i=1 |Lcurr| k=1 y (i) curr(k) log ŷ(i) up curr(k) + 1 -y (i) curr(k) log 1 - ŷ(i) up curr(k)
.

(

) 1
In order for the updated network to learn L prev on D curr , we try to keep discrepancy between ŷ(i) up prev and ŷ(i) mem as small as possible. The distillation loss L distil , which measures this disparity is defined as:

L distil = - 1 n|L prev | n i=1 |Lprev| k=1 ŷ(i) mem(k) log ŷ(i) up prev(k) + 1 - ŷ(i) mem(k) log 1 - ŷ(i) up prev(k)
.

( The overall adaptation loss L adapt that is optimized during adaptation is computed by adding these two terms:

) 2
L adapt = L class + L distil . (3)
Fig. 3 depicts how the network is adapted to the new data.

C. Remembering From the Previous Training Data

We denote the previous training data by

D prev = D (1) prev ∪ D (2) prev ∪. . .∪D (m)
prev , where D

w c = median(f c |c ∈ L (j) prev ) f c , (4)
where f c denotes frequency of the pixels that are labeled as class c. We then assign an importance value I (l) to the l th training patch in D (j)

prev as:

I (l) = c∈L (j) prev w c f (l) c , (5)
where

f (l) c
denotes the number of pixels, belonging to c in the patch. We store certain number of patches that have the highest I value, which we denote by D (j) prev imp . In order to diversify the patches that are fed to the network, we randomly select a small fraction of the remaining patches. We denote the randomly chosen patches by D prev random . The number of patches that is selected randomly and using the importance value needs to be determined by the end user.

Let us denote the target vector for the i th sample among n samples in a batch from D (j) prev rem by y (j)(i) prev . We denote by ŷ(j)(i) up prev the predicted vector from the updated network for the same sample. The remembering loss L rem is calculated as:

L rem = - 1 n|L (j) prev | n i=1 |L (j) prev | k=1 y (j)(i) prev(k) log ŷ(j)(i) up prev(k) + 1 -y (j)(i) prev(k) log 1 - ŷ(j)(i) up prev(k) . (6)
During remembering from D (j)

prev , we freeze the classification layers that are responsible for c ∈ L (j) prev and optimize the rest of the network. The user needs to determine how often and on which data L rem is optimized. An example optimization sequence is depicted in Fig. 4.

III. EXPERIMENTS A. Methods Used for Comparison

Table I compares our methodology with the following approaches:

Static learning: This is the traditional learning approach, where we assume that all the training images and annotations for the same classes are available at the time of training. In real-world segmentation problems, this condition is extremely hard to meet. This method does not support learning new classes continually.

Multiple learning: In this learning strategy, we train an additional classifier whenever the new training data are obtained. The number of classifiers that needs to be stored increases linearly. In addition, because the test images have to be segmented using all the trained classifiers to generate a map for each class, the test stage might be extremely long. Therefore, this approach is extremely expensive in terms of storage and segmentation efficiency.

Fixed representation: To learn new classes, we remove the classification layers, which were optimized for the previous classes, and plug in new classification layers dedicated for the new classes. The newly added classification layers are initialized with Xavier method [START_REF] Glorot | Understanding the difficulty of training deep feedforward neural networks[END_REF]. When new training data arrive, we optimize only the newly added classification layers and freeze the rest of the network. Hence, training is very fast. During testing, we append the formerly trained classification layers back to the network to generate label maps for all the classes. The major issue is that although performance for the initial classes is preserved, the network struggles in learning new classes, because the previously extracted features are not optimized to represent the new classes. Fine-tuning: We use a similar strategy that we follow in fixed representation. The only difference is that while training the network, instead of only the classification layers, we optimize the whole network using only the new training data. In this methodology, although the network performs a remarkable performance for the new classes, it suffers from catastrophic forgetting. Example network structures for fixed representation and fine-tuning, for both training and test phases, are illustrated in Fig. 5.

For incremental learning, it is required for the memory network to generate probability maps from the training patches to optimize L distil . Therefore, training time for our approach is slightly longer than the others. This can be considered as the only disadvantage of the proposed methodology.

B. Datasets and Evaluation Metrics

The first data we use are the Luxcarta dataset, containing 8 bit satellite images collected from 22 different cities in Europe. 11 of these cities are located in France and the other 11 are in Austria. The cities cover the total area of approximately 1367 km 2 . The images were collected from the following cities: Amstetten, Enns, Leibnitz, Salzburg, Villach, Bad Ischl, Innsbruck, Klagenfurt, Osttirol, Sankt Pölten, Voitsberg in Austria, and Albi, Angers, Bayonne-Biarritz, Béziers, Bourges, Douai, Draguignan, Lille, Lyon, Nîmes, Roanne in France.

The spectral bands of the images are composed of Red (R), Green (G), and Blue (B) channels. The spatial resolution is 1 m. Since the images were captured over different geographic locations, they have different color distributions and visual features. The annotations for building, road, high vegetation, water, and railway classes are provided.

The other two datasets, on which we conduct our experiments are the Vaihingen and the Potsdam benchmarks provided by the ISPRS [START_REF]ISPRS. 2d semantic labeling contest[END_REF]. Both datasets contain 8 bit aerial images. The Vaihingen dataset consists of 33 image tiles (of average size 2494 × 2064), where 16 of them are provided as training and the rest as test. The images comprise 3 spectral bands: Near Infrared (NIR), R, and G. The spatial resolution is 9 cm. The Potsdam dataset includes 38 tiles (of size 6000 × 6000), out of which 24 are dedicated for training and the remaining for test. The images contain 5 channels: NIR, R, G, B, and the normalized DSM (nDSM) data. The resolution of the images in this benchmark is 5 cm. Both datasets contain full annotations for 6 classes: impervious surfaces, building, low vegetation, high vegetation, car, and clutter. However, since only 0.78% of the pixels in the Vaihingen dataset is labeled as clutter, we ignore this class in the experiments on this benchmark. As of 2018 summer, the competition for these benchmarks is over, and all the reference data are publicly available. Hence, we use all the training tiles for training, and test tiles for validation. To account for the labeling mistakes while the datasets are annotated, the eroded groundtruth is also provided. We use this ground-truth to assess the performance on the benchmarks.

To quantitatively assess the performance for each class, we compare the binary predicted map and the binary groundtruth using two evaluation metrics: intersection over union (IoU) [START_REF] Csurka | What is a good evaluation measure for semantic segmentation?[END_REF] and F1-score [START_REF] Audebert | Semantic segmentation of earth observation data using multimodal and multi-scale deep networks[END_REF].

C. Experiments on the Luxcarta Dataset

In this experimental setup, we suppose that the training data are obtained sequentially in time, and every snapshot of the streaming training data contains the satellite images from different cities and label maps for separate classes. As the training data, we use 18 cities, out of which 9 are located in Austria and the other 9 are in France. We use 2 cities from each country for validation. We split the training cities into three sets as reported in Table II by paying attention that the cities in each set are the ones, which contain a reasonable amount of samples for the given annotations, and whose color distributions are as diverse as possible. We assume that the training cities are streamed in this order: Train1, Train2, Train3. For multiple learning, fixed representation, and finetuning we assume that the previous data are not accessible. For incremental learning, we store only 30% of the training patches in the previous data, out of which 15% are selected using the importance value and 15% are chosen randomly, as explained in section II-C. We also test our approach without accessing to the previous data (i.e., without optimizing L rem ), which we refer as incremental learning w/o L rem . Since static learning does not support adding new classes continually, for this approach, we use all the training images from 18 different cities and label maps of all 5 classes for each image when training a network. For this reason, we expect it to be an obvious upper bound of the other methods.

During the pre-processing step, we split all the training images into 384 × 384 patches with an overlap of 32 × 32 pixels between the neighboring patches. The validation images are divided into 2240 × 2240 patches with 64 × 64 pixels of overlap. After all the validation patches are classified, they are combined back to get the original size classification maps. Because the satellite images arrive sequentially (except for static learning), it is not possible to compute mean values for the image channels. Hence, for the normalization, we subtract 127 from all the pixels, as the images are 8 bit.

We train a single model for static learning using the whole training data for 500 epochs, in which each epoch has 100 iterations. For multiple learning, we train 3 separate models from scratch on Train1, Train2, and Train3 with the same hyper-parameters. For fixed representation, fine-tuning, and the proposed incremental learning methodologies, every time when the new classes are added from the new data, we optimize the network for the same number of epochs and iterations as for static learning and multiple learning. In every 5 training iterations of the network for incremental learning approach on Train2, we optimize L rem on Train1 for 1 iteration and L adapt for the next consecutive 4 iterations. During the training on Train3, since the network has already learned information from both Train1 and Train2, we prefer to remind the network the previously learned information more often. On Train3, the optimization sequence as follows: L rem on Train1 for 1 iteration, L adapt for 2 iterations, L rem on Train2 for 1 iteration, and L adapt for 2 iterations again.

To update parameters of the network, we use Adam optimizer, where the learning rate is 0.0001, exponential decay rate for the first and the second moment estimates are 0.9 and 0.999, respectively. In every training iteration, a mini-batch of 12 patches is used for the optimization. When sampling a patch, we first select a random country (i.e., Austria or France). We then sample a random patch belonging to the city, which is also randomly chosen from the selected country.

While training the network we apply online data augmentation to enrich the training data. The patches are augmented

x curr = (x prev -µ) * k + µ, (7)
where x prev and µ are the pixel value and mean of all the pixels before the change, x curr is the pixel value after the change, and k is the distortion a random value between 0.75 and 1.5. Gamma correction is formulated as:

x curr = x prev γ , (8)
where γ is the correction factor, which is drawn uniformly between 0.75 and 1.25. In Eqs. ( 7) and ( 8), we assume that the pixel values range between [0-1]. Fig. 6 illustrates the effect of gamma correction and the contrast change.

The overall F1-scores of all the classes on the Luxcarta dataset for each method are reported in Table III. The method, which achieves the most similar performance with static learning is highlighted. Fig. 7 depicts the change of IoU values on the validation cities as the training progresses. Visual closeup results for static learning, multiple learning, incremental learning w/o rem and incremental learning generated by the final models are shown in Fig. 8. Although our network generates a binary label map for each class, for the sake of compact and better visualization, we provide multi-class predicted maps obtained by assigning each pixel to the class, for which the highest probability is produced. In the figure, the pixels, having no probability higher than or equal to 0.5 are labeled as background.

As expected, static learning outperforms the other approaches on the Luxcarta dataset (see Table III), because in the training stage, we feed much more and diverse training data to the model compared to the other approaches. Although static learning is superior to the other approaches on the Luxcarta dataset, it is applicable only if the data are static and the annotations are unique, which is almost never the case in realworld applications. In multiple learning, even if the previous data are not accessible, predicted maps for all the presented classes can be generated. However, because of the growing number of classifiers, this approach is inefficient in terms of test efficiency and storage. In addition, for each individual classifier, learning is limited to the data, on which the classifier was initially trained. For instance, building -high vegetation classifier trained on Train1 can not be fine-tuned on Train2, as annotations for these classes are not available on Train2.

In fixed representation methodology, the exact performance for the initially introduced classes is retained as neither the shared nor the classification layers for these classes change. On the other hand, the network performs extremely poorly for the new classes as shown in Fig. 7c and reported in Table III. All in all, we conclude that shared layers of the network have to be adapted to the new training data. When we apply fine-tuning, since instead of initializing all the parameters randomly, the extracted features for the previous classes are used, performance for the new classes is remarkable, especially when there is only one class to be added. For instance, it is the best performer for water class. However, the results justify that the network catastrophically forgets the previously learned information.

As reported in Table III, incremental learning exhibits the closest performance to static learning. Since our approach enables the network to learn the old classes on the new data and remember them from the previous data, performance for the previous classes gets better over time. If the previous data are never shown, performance for the old classes may decrease as a result of adapting the network to the new data completely and imprecision of output of the memory network on the new data for the previous classes. Fig. 9 compares incremental learning and incremental learning w/o L rem for high vegetation before and after adding road and railway classes on Train2 (i.e., before and after the 500 th epoch) to the building & high vegetation classifier trained on Train1. The close-ups from Roanne in Fig. 8 show that incremental learning w/o L rem fails in detecting a lot of high vegetation, whereas incremental learning exhibits a good performance. We also observe that incremental learning significantly outperforms multiple learning for building class. The reason is that the network in multiple learning learns building only on Train1, while incremental learning facilitates learning the same class from all the training data sequentially. Although when buildings are small and regular shaped as in Leibnitz and Roanne, both approaches generate similar outputs, multiple learning is not able to delineate the borders very well when buildings cover a large area as in Amstetten. Road and Railway classes turn out to be the most difficult classes, as the numeric results for them are much lower than the others. As can be seen in the close-up from Lille, they visually look quite similar, which makes the classifiers confuse between them in some cases.

Incremental learning seems detecting the roads and railways that are mis-classified by incremental learning w/o L rem .

D. Experiments on the Benchmark Datasets

In the experiments on the benchmarks, we assume that we have access to the whole training tiles, but we are provided the annotations sequentially. We suppose that every time a new set of annotations are retrieved, the previous one is not accessible. On the Vaihingen dataset, we consider that we retrieve label maps for building and high vegetation classes in the beginning. We are then given the ground-truth for impervious surfaces and low vegetation. Finally, we receive the annotations for car class. On the Potsdam dataset, since there is an additional clutter class, we assume that the label map for this class is also available in the initial training data. For our approach, since we always use the same training images, we remind the network the old classes using output of the memory network (i.e., we only optimize L adapt ). On contrary the other approaches, for static learning, we use all training tiles as well as annotations for all the classes at once in the training stage.

Because the images in the benchmarks are of much higher resolution than the satellite images in the Luxcarta dataset, the patches need to be larger to cover a reasonable area. Therefore, we divide the training tiles into 512 × 512 patches. The validation tiles are split into 2000 × 2000 patches. The training and validation tiles have 64 × 64 and 120 × 120 pixels of overlap, respectively. We compute a global mean for each channel from the training tiles and subtract it from all the pixels.

For each approach, we train the same number of models for the same number of epochs and iterations using the same optimizer with the same parameters as in the experiments on the Luxcarta dataset. As size of the training patches is larger than in the previous experiments, we randomly sample 8 patches instead of 12. Another difference is that since both training and validation patches are from the same city, we augment the patches by only random flips and rotations.

We present the qualitative and quantitative experimental results on the benchmarks in a similar way described in Sec. III-C. We report F1-score for each class in Tables IV and V, illustrate the plots of IoU vs. number of epochs on the Vaihingen benchmark in Fig. 10, and show close-ups from both benchmarks in Fig. 11. As we use all the annotations at once for static learning, we again choose this approach as the reference method.

From the plots in Figs. 7 and 10, our first observation is that IoU values for each model, as the training iterations continue, fluctuate much more on the Luxcarta dataset than on the Vaihingen benchmark. We also observe that models, trained from the Vaihingen dataset converge faster. The reason for these two conclusions is that in the Vahingen dataset, a single aerial image was split into smaller tiles, while images in the Luxcarta dataset were taken from different cities at different dates; therefore, they have distinct color variations and visual features. Furthermore, the Luxcarta images are of much lower resolution, and the validation set consists of the cities that are not seen by the network during training. Because of all these reasons, accuracies for the same classes (i.e., building and high vegetation) are significantly lower in the experiments on the Luxcarta dataset than on the benchmarks.

Our observation for fixed representation and fine-tuning is similar to the experiments on the Luxcarta dataset. As can be seen in Fig. 10c, for fixed representation, although some classes such as impervious surface and low vegetation can be learned relatively well, the network performs poorly if the newly added class represents small objects like car.

Since training as well as test tiles are from the same city, output of the memory network becomes almost the groundtruth for the previous classes. As a result, even if annotations for the previous classes are not accessible, new classes can be learned while exhibiting a similar performance for the former classes. We justify this claim in Fig. 10e, in which it is demonstrated that IoU plots for the previously learned classes remain quite flat over time. The predicted maps of the close-ups from Vaihingen in Fig. 11 for 3 approaches look very similar. The advantage of our approach is that with the help of the features for the previous classes, the network converges very fast for the new classes. For instance, as illustrated in Fig. 10a, it takes roughly 50 epochs in order for the network to converge for low vegetation class when static learning is applied, whereas with the proposed approach, a similar accuracy for the same class can be achieved in only a few epochs, as depicted in Fig. 10e.

In this experimental setup, if the classes have distinct visual appearance and features like in the Vaihingen benchmark, as the classification tasks are shared between several classifiers, multiple learning performs better especially when the class has a low number of samples such as car. As training tiles of the Potsdam dataset contain the nDSM data, detecting car class is easier on this dataset than on the Vaihingen benchmark. As reported in Table V, the gap between multiple learning and the other approaches is smaller for this class. On the contrary, as can be seen in the last row in Fig. 11, clutter class has high visual similarities with some pixels labeled as impervious surfaces or low vegetation. Hence, a single classifier that is trained jointly for all the classes, performs better in distinguishing these classes. Unlike multiple learning, where several isolated classifiers are trained, our approach allows joint training via the memory network. Therefore, our approach performs better for these classes, as confirmed by Table V. The last row in Fig. 11 exemplifies some misclassified clutter pixels by multiple learning but correctly detected by our approach.

E. Running Times

We have implemented all the approaches in Tensorflow2 , and conducted all the experiments on an Nvidia Geforce GTX1080 Ti GPU with 11 GB of RAM. fine-tuning, multiple learning, and static learning is almost the same; therefore, we refer to these approaches as the others and report the average of their training time in the table. Since we optimize only the classification layer for fixed representation, its training is extremely fast. For incremental learning, the current training patch needs to be segmented by the memory network for the knowledge transfer. Hence, the training time in each iteration for incremental learning is about 0.3 seconds longer than for fine-tuning, multiple learning, and static learning.

IV. CONCLUDING REMARKS

We proposed a novel incremental learning methodology, which enables the neural network to learn segmentation capabilities for the new classes while retaining dense labeling abilities for the formerly trained classes without using the entire previous training data.

In our experiments, we first showed that the common learning approaches are extremely inefficient or inapplicable to learn from streaming data. We then demonstrated why using only the features extracted for the previous classes is inefficient to learn new classes. We also provided the results, showing that when the network is trained using only the new data without having any regularization, the learned information for the previous classes is catastrophically forgotten. Finally, on three different datasets we proved that the proposed approach achieves a high performance for the new classes without forgetting the old classes.

As the future work, we plan to explore how to incorporate domain adaptation techniques to our incremental learning methodology so that the trained network could better generalize to the data collected from new geographic locations.

Fig. 1 .

 1 Fig. 1. An example incremental learning scenario. Firstly, satellite images as well as their label maps for building and high vegetation classes are fed to the network. Then, from the second training data, the network learns water class without forgetting building and high vegetation classes. Finally, road and railway classes are taught to the network. Whenever new training data are obtained, we store only a small part of the previous ones for the network to remember. When a new test image comes, the network is able to detect all the classes.

Fig. 3 .

 3 Fig. 3. Adapting the network to the new training data. Although annotations for only 2 classes are provided, the updated network is still able to learn current classes as well as the previously learned 2 classes with the help of the memory network.

Fig. 4 .

 4 Fig. 4. An example optimization sequence. The new classes are added on Training data 3 to the network, which was already trained on Training data 1 and Training data 2. The optimization sequence is as follows: Lrem on Training data 1, L adapt on Training data 3, Lrem on Training data 2, and L adapt on Training data 3 again.

( 1 )

 1 prev corresponds to the first data, D(2)prev is the second data, and so forth. If the training data are captured sequentially from different geographic locations, in order for the network not to overfit on D curr for L prev , we remind the previously learned information by systematically showing patches from the stored, small portion of D prev . Since in most of the cases classes in the training data are highly imbalanced, when determining which training patches to store in D (j) prev , random selection may cause storing no samples for less frequent classes. For this reason, we take the class imbalance problem into account. We first compute weight w c of each class c ∈ L (j) prev in D (j) prev as:

  prev random . The data to be stored from D (j) prev for remembering are D (j) prev rem = D (j) prev imp ∪ D (j)

Fig. 5 .

 5 Fig. 5. Example network structures for fixed representation and fine-tuning. During the test stage, classification layers for the previous classes are appended to the network to generate label maps for all the classes.

4 Fig. 6 .

 46 Fig. 6. Illustration of the contrast change (a -b) and the gamma correction (d -e) for an example input image (c).

Fig. 7 .Fig. 8 .Fig. 9 .

 789 Fig. 7. Plots for the overall IoU values on the 4 validation cities of the Luxcarta dataset.

Fig. 10 .Fig. 11 .

 1011 Fig. 10. Plots for the overall IoU values on validation data of the Vaihingen benchmark dataset.

TABLE I ADVANTAGES

 I AND DISADVANTAGES OF OUR APPROACH WITH RESPECT TO THE COMPARED METHODS.

	Method	Training Time (1 iteration)	Test Time	Performance for the new classes	Performance for the old classes	Convergence time for the new classes	Number of Classifiers
	static learning	fast	fast	continual learning continual learning continual learning is not supported is not supported is not supported	1
	multiple learning	fast	very slow	good	good	medium	N
	fixed representation	very fast	fast	very bad	good	cannot learn	1
	fine-tuning	fast	fast	good	very bad	very fast	1
	incremental learning	medium	fast	good	good	very fast	1

TABLE II TRAINING

 II AND VALIDATION CITIES OF THE LUXCARTA DATASET.

		Data Type and
		Classes for
	mult. learning fixed rep. fine-tuning inc. learning	static learning	City (Country)	Area (km 2 )	Class Frequency (%) building high veg. road railway water
					Bad Ischl (Austria)	27.71	5.51	35.38	5.87	0.16	2.58
	Train1	building			Osttirol (Austria) Voitsberg (Austria) Bayonne-Biarritz (France) Bourges (France)	28.38 28.70 66.58 72.20	6.96 7.47 15.21 9.81	15.37 30.21 19.45 14.83	7.72 6.54 12.66 10.10	0.44 0.44 0.45 0.42	0.84 0.98 1.26 0.92
		high veg.		building	Draguignan (France)	25.54	9.64	34.99	10.24	0.00	0.08
					Nîmes (France)	26.62	21.78	19.65	14.10	1.30	0.04
			high veg.	Enns (Austria)	64.49	6.25	12.54	6.81	1.36	2.82
	Train2	road railway	Train	road railway	Innsbruck (Austria) Klagenfurt (Austria) Sankt Pölten (Austria) Béziers (France)	132.50 67.73 87.17 25.75	8.92 10.96 6.68 19.09	22.78 18.89 25.13 10.91	7.00 9.05 5.40 16.10	0.90 0.65 0.99 1.52	2.97 1.20 1.70 0.78
					Lyon (France)	187.14	18.48	16.82	12.59	1.41	2.83
				water	Albi (France)	25.76	17.20	15.19	13.93	0.55	1.65
	Train3	water			Villach (Austria) Salzburg (Austria) Angers (France)	43.59 134.71 74.16	9.26 9.44 15.78	19.91 23.88 15.97	9.61 7.90 10.40	1.02 0.79 0.63	2.69 2.41 1.39
					Douai (France)	58.10	13.31	14.62	8.63	0.93	2.09
	Validation		building high veg. road railway water		Amstetten (Austria) Leibnitz (Austria) Lille (France) Roanne (France)	14.26 32.72 117.58 25.84	11.11 6.96 18.36 18.44	15.61 16.84 15.40 8.33	9.67 6.99 11.39 14.00	1.85 0.34 1.32 0.78	1.72 3.30 1.02 0.95

TABLE III F1

 III SCORES ON THE LUXCARTA DATASET.

	Method	Epoch	Building	High veg.	Road	Railway	Water	Overall
	static learning	500	80.74 (Ref.) 71.26 (Ref.) 66.21 (Ref.) 61.72 (Ref.)	82.74 (Ref.)	72.54 (Ref.)
	multiple learning	500	71.25	68.88	59.28	55.65	79.83	66.98 (-5.56)
	fixed representation	1000 1500	71.25 71.25	68.88 68.88	2.71 2.71	0.00 0.00	-0.11	28.59 (-43.95)
	fine-tuning	1000 1500	28.91 27.90	0.17 7.71	59.30 0.14	60.06 0.01	-90.20	25.19 (-47.35)
	incremental learning	1000	74.19	66.32	56.57	50.87	-
	w/o Lrem	1500	74.91	66.87	58.14	51.70	82.32	66.79 (-5.75)
	incremental learning	1000 1500	75.98 76.78	72.38 72.06	57.29 59.58	50.18 53.07	-78.94	68.09 (-4.45)
			Training Set 1	Training Set 2	Training Set 3
	by random vertical/horizontal flips, 0/90/180/270 degrees of
	rotations, and distorting their radiometry by random contrast
	change and gamma correction. Contrast of each channel in the
	image is changed as:

TABLE IV F1

 IV SCORES ON THE VAIHINGEN BENCHMARK DATASET.

	Method	Epoch	Building	High veg.	Imper. surf.	Low veg.	Car	Overall
	static learning	500	93.61 (Ref.) 87.87 (Ref.)	91.55 (Ref.)	81.05 (Ref.)	82.83 (Ref.)	87.38 (Ref.)
	multiple learning	500	94.43	88.12	90.71	80.41	87.90	88.31 (+0.93)
	fixed representation	1000 1500	94.43 94.43	88.12 88.12	87.09 87.09	76.39 76.39	-13.37	71.88 (-15.5)
	fine-tuning	1000 1500	52.40 0.02	0.03 0.00	91.83 43.81	80.99 0.01	-86.18	26.00 (-61.38)
	incremental learning	1000	94.34	88.02	91.42	81.65	-
	w/o Lrem	1500	94.31	88.07	91.51	81.60	81.69	87.44 (+0.06)
			Training Set 1	Training Set 2	Training Set 3

TABLE V F1

 V SCORES ON THE POSTDAM BENCHMARK DATASET.

	Method	Epoch	Building	High veg.	Clutter	Imper. surf.	Low veg.	Car	Overall
	static learning	500	96.83 (Ref.) 85.04 (Ref.) 54.57 (Ref.)	92.62 (Ref.)	85.69 (Ref.)	94.84 (Ref.)	84.93 (Ref.)
	multiple learning	500	96.59	85.25	50.82	92.07	84.82	95.36	84.15 (-0.78)
	fixed representation	1000 1500	96.59 96.59	85.25 85.25	50.82 50.82	86.76 86.76	79.98 79.98	-72.14	78.59 (-6.34)
	fine-tuning	1000 1500	0.00 1.62	44.53 24.73	3.23 0.00	92.13 65.00	85.45 0.01	-94.60	30.99 (-54.94)
	incremental learning	1000	96.91	86.12	50.23	92.20	85.64	-
	w/o Lrem	1500	96.86	85.28	51.56	92.10	85.28	94.43	84.25 (-0.68)
				Training Set 1		Training Set 2	Training Set 3

  Table VI reports the training times for incremental learning, fixed representation, and the others. Let us remark that the training times for

		100									100
		80									80
	IoU	40 60					Impervious Surfaces Building	IoU	60 40				Impervious Surfaces Building
		20						Low vegetation High vegetation		20					Low vegetation High vegetation
								Car									Car
		0	0	100	200	300	400		500	0	0	100	200	300		400	500
					# of epochs							# of epochs
					(a) Static learning						(b) Multiple learning
		100
		80
	IoU	60 40		Impervious Surfaces Building
		20		Low vegetation High vegetation
					Car
		0	0	100	200	300	400	500	600	700	800	900	1,000	1,100	1,200	1,300	1,400	1,500
										# of epochs
								(c) Fixed representation
		100
		80
	IoU	60 40		Impervious Surfaces Building
		20		Low vegetation High vegetation
					Car
		0	0	100	200	300	400	500	600	700	800	900	1,000	1,100	1,200	1,300	1,400	1,500
										# of epochs
									(d) Fine-tuning
		0	0	100	200	300	400	500	600	700	800	900	1,000	1,100	1,200	1,300	1,400	1,500

TABLE VI TRAINING

 VI TIMES FOR EACH APPROACHMethodPatch Size Batch Size Time for 1 Iter. (seconds) Inc. learn.

		384	12	1.03
	Fixed. Rep.	384	12	0.31
	The Others	384	12	0.72
	Inc. learn.	512	8	1.21
	Fixed. Rep.	512	8	0.32
	The Others	512	8	0.87

Project page: https://project.inria.fr/epitome/inc learn

https://www.tensorflow.org

ACKNOWLEDGMENT

The authors thank ACRI-ST and CNES for initializing and funding this study.

Onur Tasar (S'18) received the B.S. degree from Hacettepe University, Ankara, Turkey, in 2014, and the M.S. degree from Bilkent University, Ankara,Turkey, in 2017, both in computer engineering. He is currently working toward the Ph.D. degree with the TITANE team of Inria Centre de Recherche Sophia Antipolis Méditerranée, Sophia Antipolis, France.

His research interests include computer vision, machine learning, and computational geometry with applications to remote sensing


R Henry

T Blay

I Zacharie-Aubrun

J M Gatt

C Langlois

S Meille

Fracture properties characterization of nuclear fuel using micro-cantilever bending

Notched micro-cantilever milled in irradiated nuclear fuel (UO 2 ) 16/10/2018 III. Results : Fracture properties of fresh and irradiated nuclear fuels UO 2 1. Fracture stress of nuclear fuels UO 2 2. Fracture toughness of nuclear

••

  PCI (Pellet-Cladding Interaction) Optical micrograph of a sample section of UO 2 fuel and its cladding Irradiated in PWR + power ramp test Power ramps Optical micrograph of a UO 2 fuel in the pellet's periphery Irradiated in PWR + RIA test Accidental situations  RIA (Reactivity Insertion Accident)  LOCA (Loss Of Coolant Accident) Optical micrograph of a sample section of UO 2 fuel and its cladding Irradiated in PWR To avoid cracks (and porosities)  To measure "intrinsic" properties Vickers indentation on irradiated fuel • Handy solution • Studied and used before • Sometimes difficult to make a proper measurement Indentation Notched µ-cantilever for fracture toughness measurement (ZrO 2 ) • Closer to bending test • Preparation with FIB/SEM(Ga beam) Crystallographic characteristics close • Mechanical properties similar (at the macroscopic scale) R. Henry 1 , T. Blay 2 , T. Douillard 1 , I. Zacharie-Aubrun 2 , J-M Gatt 2 , C. Langlois 1 , S. Meille 1 : To be published. 1 Université de Lyon, INSA-Lyon, MATEIS CNRS UMR 5510, 69621 Villeurbanne, France 2 CEA, DEN, DEC, Cadarache, 13108 St Paul Lez Durance, France Similar fracture toughness K IC ≈ 1.5 MPa.m 0.5  Good agreement with literature (macroscopic tests on single crystals) Higher fracture stress σ c ≈2 GPa (against ≈200 MPa for macro)  Scale effect : less defects in a µ-sample Movies of in situ bending tests No plasticity : brittle behavior (elastic up to fracture) Fracture load • Dimensions of the beam and notch FEM analysis (Cast3m® (CEA, France)) Calculation outputs : • K IC (fracture toughness) or • σ c (fracture stress) Numerical parameter study : • Optimization of the test  Dimensions, positioning, influence of different parameters • Study of the effect of anisotropic elasticity Coherent with numerical simulations at atomistic scale (MD and DFT) Scale effect on fracture stress  ≈3 GPa (micro) against ≈ 150 MPa (macro) Y. Zhang et al., "Crack tip plasticity in single crystal UO 2 : atomistic simulations, Journal of Nuclear Materials, 2012.

RESULTS

Fracture toughness of nuclear fuels UO 2

Context

Experimental approach