Jawad H Al
email: murielle.rabiller-baudry@univ-rennes1.fr

How microwaves can help to study membrane ageing

Keywords: PES/PVP membrane, ageing, microwaves irradiation, ATR-FTIR, contact-angles, SEM-EDX, SEC-HPLC, UF

This paper studies original protocols of rapid PES/PVP membrane NaOCl degradation allowing at reaching ageing states that are representative of industrial ageing. The long term objective is to propose basis for further fundamental studies aiming at the improvement of the impact of membrane ageing on behavior in UF (fouling and cleaning mastering). The key of several protocols is the use of ageing acceleration thanks to microwave irradiation, either continuous or pulsed ones, that can be further associated (or not) with short ageing time in UF conditions. To evaluate the representativeness of obtained aged membranes, comparisons are achieved between pristine, voluntary laboratory aged membranes and an industrial membrane at the end of its service-life. Several physico-chemical analyses were used (ATR-FTIR, SEM-EDX, contact angle, SEC-HPLC). Evaluation of UF performances were made in UF of a model protein (Lysozyme, 14,300 g.mol -1 ). Finally, the proof of concept is done that conditions using MW exist to reach ageing state representative of industrial ageing.

Introduction

At industrial scale, increasing difficulties in fouling and cleaning are often encountered in the second part of the membrane life. Disruptions occur at unpredictable times and membranes have sometimes to be changed in emergency. To avoid such stress, several factories use to renew membranes at a preselected service life duration before disruption. None of these two strategies is really a sustainable one, but can be justified by the lack of fundamental understanding of membrane ageing at industrial scale. To go ahead we have started ten years ago, a systematic study of the impact of the membrane ageing on disruptions, knowing that itis probably the consequence of the combination of both chemical and mechanical impacts, as explained by Pellegrin et al., [START_REF] Pellegrin | Multi-scale analysis of hypochlorite induced PES/PVP ultrafiltration membranes degradation[END_REF][START_REF] Pellegrin | Mechano-chemical ageing of PES/PVP ultrafiltration membranes used in drinking water production[END_REF] .

In dairy, polyethersulfone/polyvinylpyrrolidone (PES/PVP) membranes are commonly used in ultrafiltration (UF) of skim milk for the standardization of the protein content before the cheese making process or for the filtration of acid and rennet whey. For these applications, membranes are twice daily cleaned with cascades of formulated detergents. Classically an alkaline cleaning step and an acid one, often with nitric acid, are achieved. After the cleaning in place (CIP) by these two solutions, a final disinfection step and a water rinsing are added, before the production start again. The main difference between the3different cases of the dairy industry is the nature of the alkaline and acid cleaning solutions. However, their order and real effect in the cascade are also questioned. Several studies have reported that the chemical ageing of PES/PVP UF membranes is not related to the alkaline formulated detergent the pH of which is in the range 11.5-12.0. Similarly, the nitric acid step, for which the pH is close to 1.6 is not responsible of the membrane chemical ageing. For instance, we have previously shown that the nitric acid step is harmlessness towards these membranes even after soaking in more concentrated HNO 3 solution and up to 1 mol.L -1 owing a null pH [START_REF] Bégoin | Autopsie de membranes spirales de l"industrie laitière-Physico-chimie du nettoyage de membranes PES d"ultrafiltration de lait écrémé (Autopsy of spiral membranes of dairy industry. Physico-chemistry of the cleaning of PES membranes used in skim milk ultrafiltration)[END_REF][START_REF] Bégoin | Methodology of analysis of a spiral wound module. Application to PES membrane of ultrafiltration of skimmed milk[END_REF][START_REF] Bégoin | Ageing of PES industrial spiral wound membrane of acid whey ultrafiltration[END_REF][START_REF] Delaunay | Nettoyage éco-efficace de membranes planes et spirales d"ultrafiltration de lait écrémé. Approches physico-chimiques et hydrodynamiques concertées (Eco-efficient cleaning of flat and spiral membranes used in skim milk ultrafiltration. Dual approach based on physico-chemistry and hydrodynamic)[END_REF]. Moreover a PES/PVP nanofiltration membrane has been reported to be stable over a year after immersion in 5.9 mol.L -1 phosphoric acid that is a very concentrated solution with a "negative" pH [START_REF] Diallo | Transfert de complexes métalliques en milieu acide phosphorique concentré ou dilué par membrane de nanofiltration. Application à la production de l'acide phosphorique[END_REF]. Nowadays, it is well-known that the disinfection step is the main responsible of the PES/PVP membrane ageing, especially when it is achieved in oxidant conditions obtained by chlorine based disinfectants (see for instance [START_REF] Wienk | Chemical treatment of membranes of a polymer blend: mechanism of the reaction of hypochloride with poly(vinylpyrrolidone)[END_REF][START_REF] Arkhangelsky | Impact of chemical cleaning on properties and functioning of polyethersulfone membranes[END_REF][START_REF] Yadav | Effects of hypochlorite exposure on flux through polyethersulphone ultrafiltration membranes[END_REF][START_REF] Prulho | Analyse multi-échelle de la dégradation de membranes polymères d'ultrafiltration au contact de l'hypochlorite de sodium (Multi-scale analysis of ultrafiltration polymer membrane degradation by contact with sodium hypochlorite)[END_REF][START_REF] Prulho | Ageing of polyethersulfone/ polyvinylpyrrolidone blends in contact with bleach water[END_REF] . Classically in dairy NaOCl (bleach) solutions are set at 150-200 ppm in total free chlorine (TFC) and pH close to 11.0-11.5 and used at 50°C. However, NaOCl induces more or less degradation of the two polymers constituting the membrane (Figure 1).

Insert Figure 1 about here PVP, the minor but "hydrophilic" constituent of the membrane, has been shown to lead to intermediate degradation products after contact with NaOCl at pH= 7.0 -8.0. After a long time contact, that is not clearly evaluated, PVP totally disappears. It can be underlined that such pH range is the more favorable one to induce degradation according to a radical mechanism. . These intermediates have not been evidenced after contact with NaOCl at pH= 11.5 [START_REF] Prulho | Analyse multi-échelle de la dégradation de membranes polymères d'ultrafiltration au contact de l'hypochlorite de sodium (Multi-scale analysis of ultrafiltration polymer membrane degradation by contact with sodium hypochlorite)[END_REF]. Nevertheless, the full disappearance of PVP after long term NaOCl treatments at pH= 11.0-11.5 achieved at industrial scale has been confirmed by autopsy of membranes at the end of their service life [START_REF] Bégoin | Autopsie de membranes spirales de l"industrie laitière-Physico-chimie du nettoyage de membranes PES d"ultrafiltration de lait écrémé (Autopsy of spiral membranes of dairy industry. Physico-chemistry of the cleaning of PES membranes used in skim milk ultrafiltration)[END_REF][START_REF] Bégoin | Methodology of analysis of a spiral wound module. Application to PES membrane of ultrafiltration of skimmed milk[END_REF][START_REF] Bégoin | Ageing of PES industrial spiral wound membrane of acid whey ultrafiltration[END_REF] . Regardless of the NaOCl pH the removal of PVP might induce an increase in the membrane hydrophobicity. PES is simultaneously the main polymer and the more hydrophobic one of the membrane. Different evolutions due to oxidizing treatments are reported in literature. It goes from simple hydroxylation of the phenyl groups, a slight modification that is compatible with an increase in hydrophilicity of the membrane, to the cleavage of a C-S covalent bond of the PES backbone leading to formation of sulfonate (~SO 3 -) fixed groups attached to the aged membrane. This last modification is in good agreement with an increase in the overall membrane hydrophilicity with respect to the presence of charges. The conditions of the occurrence of the two modes of PES degradation are still controversial, probably with respect to the NaOCl ageing duration used in the studies that are always achieved in different conditions, for instance with respect to the concentration. On one hand, Yadav and Morison [START_REF] Yadav | Effects of hypochlorite exposure on flux through polyethersulphone ultrafiltration membranes[END_REF] have proposed the cleavage of C-S covalent bond of the backbone at high alkaline pH. On the other hand, Hanafi et al. [START_REF] Hanafi | Degradation of poly(ethersulfone)/polyvinylpyrrolidone membranes by sodium hypochlorite: insight from advanced electrokinetic characterizations[END_REF][START_REF] Hanafi | Electrokinetic analysis of PES/PVP membranes aged by sodium hypochlorite solutions at different pH[END_REF] have found, from streaming potential (SP) measurements, that the backbone cleavage occurs at pH= 60.-8.0 but not at pH= 11.5. Moreover their SP measurements for PES/PVP membranes aged in NaOCl agreed with the hydroxylation of the phenyl group at pH 6.0-8.0 and pH= 11.5. The same authors have also proved that the two evolutions of PES can co-exist at pH= 6.0. It can be noticed that direct ATR-FTIR analysis on membranes (a technique that will be used in the present study) is not able to distinguish between the two mechanisms as the two PES possible evolutions lead to a new band located exactly at the same wavenumber close to 1030 cm -1 . A difficulty to study the impact of membrane ageing at lab. scale is the availability of aged membranes at different steps of their service life without any other variations. To collect industrial membranes is generally difficult for economic reasons. Moreover it is not sufficient because such membranes are generally fouled by proteins (even when having carefully be cleaned) and it becomes quite complicated to discriminate if the changes in the membrane performances are due to either residual fouling or membrane ageing or a combination of the two. That is why, in the present study, we have chosen to voluntary aged membranes by immersion in NaOCl solutions using different protocols aiming at finding one that can be rapid and able to lead to ageing representative of ageing state reached at industrial scale. Among several assays reported in this paper, the most original approach is based on the use of ageing acceleration thanks to micro-waves (MW) irradiation. MW activation of reactions is now commonly used for synthesis in organic chemistry [START_REF]Microwaves in Organic Synthesis[END_REF]. For a better understanding of the reasons having conduced us to select MW irradiation, the next paragraph gives some generalities on MW activation.

Micro-wave activation of reactions

Microwaves in chemistry

Microwave (MW) irradiation is nowadays a well-established technology in organic chemistry laboratories [START_REF]Microwaves in Organic Synthesis[END_REF][START_REF] De La Hoz | [END_REF]. Microwave assisted chemistry is based on the use of intensive directed irradiation and its purposeful application can have several advantages such as short heating times, wide usable temperature and pressure range, accumulation of energy added to the system, inversion of heating flux in the reactor, higher energy efficiency, sophisticated measurement and safety technology, modular systems that allow changes from the milligram up to the kilogram scale [START_REF] De La Hoz | [END_REF]. Essential to chemical synthesis are reaction equilibrium conditions and how rapidly they can be reached. MW reaction rates are several times faster than conventional heating, because the energy efficiency is higher due to the fact that the solvent is rapidly/directly heated, thus eliminating the energy required to raise the temperature of the containing vessels [START_REF] Wharton | Microwave Chemistry-Out of the lab and into production[END_REF]. MW electromagnetic energy has gained significant attention in domestic, medical, pharmaceutical and industrial applications such as for domestic microwave oven applications, for pasteurization, sterilization [START_REF] Chatterjee | Microwave driven convection in a rotating cylindrical cavity, a numerical study[END_REF] or at lab scale to prepare product of high quality [START_REF] Cha-Um | Experimental and Numerical Analysis of Microwave Heating of Water and Oil Using a Rectangular Waveguide: Influence of Sample Sizes, Positions and Microwave Power[END_REF]. Similarities and differences between the conventional and MW heating mechanisms in terms of yield and purity of products have been reviewed by Nuchter et al. [START_REF] Nuchter | Review: microwave-assisted chemical reactions[END_REF]. However, significant technological problems arise in attempting to scale up to production scales, particularly due to the restricted penetration depth of microwave irradiation in absorbing materials. Nevertheless, industrial oven already exists and are used for various applications (Figure 2). The possible scale-up is an important aspect for us because it means that our methodological approach could also be developed on membrane of industrial size and not only on small flat membrane as it will be shown in this paper.

Insert Figure 2 about here 2.2. micro-wave effects

Microwaves are a part of the electromagnetic spectrum occurring in the frequency range of 300 MHz to 300 000 MHz (Figure 3). Generally domestic as well as laboratory ovens deliver MW at 2,450 MHz with a wavelength of 12.2 cm corresponding to a quantum of energy of about 1 J.mol -1 (0.23 cal.mol -1 ). For a given power P= 680 W, the delivered energy is 680 J.s -1 . Considering a classical chemical reaction requiring an energy of activation of 209 kJ.mol -1 (50 kcal.mol -1 ), it takes about 5 min.mol -1 (time = 209,000/680= 307 s) to deliver such energy that is a high value with respect to the small quantities generally placed in the MW oven cavity.

Insert Figure 3 about here MW effects can be classified into thermal and non-thermal ones. The thermal effects result from microwave heating and are due to rapid heating, volumetric heating, superheating, hotspots and selective heating while the non-thermal effects are associated with surface polarization [START_REF] Remya | Current Status of microwave application in wastewater treatment -A review[END_REF]. The principal heating mechanisms of MW are due to dipolar polarisation, conduction mechanism and interfacial polarisation. The dipolar polarisation is responsible for most of the heating observed in solvent systems while the conduction mechanism occurs when an electrical conductor is irradiated with MW leading to the movement of charge carriers under the influence of an electric field resulting in polarisation. The combination of both processes produces interfacial polarisation in systems comprising both conducting and non-conducting materials [START_REF] Remya | Current Status of microwave application in wastewater treatment -A review[END_REF].

Media on which MWs are applied

The success of the MW irradiation in chemical reactions largely depends on the electromagnetic field distribution in the volume of the solvent/reactants mixture inserted in the oven cavity. The MW penetration depth (ET) depends on materials and particularly on their dielectric constant (equation 1).

ET = (  / 2  ). ( " r 1/2 /" r ) (1)
With : ET : the penetration depth of MW (cm)  the wavelength of the MW (cm) " r : the dielectric constant of the medium (measure of the ability of the molecules to become polarised by an external electric field) " r : the dielectric loss of the molecule (measure of the efficiency with which electromagnetic energy can be converted into heat, it usually goes through a maximum as the dielectric constant is decreased)  = 12.2 cm at 2,450 MHz

Microwave absorption via dielectric heating depends on the imaginary part of the material permittivity. The higher is the imaginary part of the permittivity, the higher is the absorbance.

The ratio of the dielectric loss to the dielectric constant is defined as the dielectric loss tangent, tan δ, which is an important number for characterising microwave heating [START_REF] Hayes | Microwave Synthesis, Chemistry at the speed of Light[END_REF]. Several authors considered that tan δ is representative of the absorption because it reveals the compromise between the two parameters mentioned just above.

Table 1 shows some typical values of penetration depths. Whereas metals and graphite are fully reflective, water that owns a high dielectric constant is a strong microwaves absorbent. This property can be used to accelerate chemical reactions in water solution but it induces a difficult temperature control during MW irradiation and a sudden increase in temperature can easily be observed that might favor the formation of undesirable side-products. Organic polymers such as PVC appear as intermediate absorbents of MW and probably it is also the case for PES and PVP, but unfortunately no information has been found dealing with these two polymers constituting the membrane studied in the present paper.

On the contrary quartz is quasi fully transparent and appears as a nice material to use for reactor fabrication when reaction is achieved in a liquid medium. Porous glass is less interesting with respect to the energy efficiency. Nevertheless, taking into account the cost and practical aspects, as well the possible scale-up, glass reactors have been used in the following.

Insert Table 1

about here

The MW penetration depth (ET) depends also on the temperature and for instance in water ET increase from 1.4 cm to 5.7 cm at 25°C and 95°C, respectively. Finally, it must also be said that the boiling points of polar solvents are higher under MW (Nucleation Limited Boiling Temperature, NLBT) than without MW as shown for a selection of solvents in Table 2. This possible local increase of temperature allows acceleration of reactions with MW irradiation compared to a reactor classically heated (Figure 4).

Insert Table 2 about here

Insert Figure 4 about here

The power transferred to a reaction mixture by MW is of course of great importance and is given by the following equation:

P d = ( + 2 π ν ε" r ) │E│ 2 (2)
With P d : the power transferred per unit volume of material : the medium conductivity ε' r : the dielectric constant of the medium E : the local electric field intensity of MW ν : the MW frequency (often set at 2450 MHz)

To reach and maintain a temperature corresponding to the actual industrial one applied during membrane disinfection by bleach (50°C) we have experimentally checked that the required power was close to 60 W. Although, increasing the power level was a good way to increase membrane degradation but much more attention had to be paid to reach an acceptable temperature.

Application mode of MW

Two different types of ovens exist: the most sophisticated are single-mode ovens running in continuous mode whereas the simpler ovens are multi-mode ones acting in a discontinuous mode. These two oven types allow more or less subtle assays and will be quickly described in the following because both of them have been used in the present study.

2.3.1.

Continuous MW / single-mode oven. Figure 5 shows a single mode oven and the principle of wave-guidance up to the sample located in a small cavity. The use of such oven allows the definition of precise positions within the oven, exactly where the electric field intensity is maximum. Remember that the positions of the maximum electric field intensities change from the maximum to zero in a distance of one-quarter of the operating wavelength (E typically follows a half sinus-wave pattern, Figure 3, called the "standing wave effect"). The effect linked to the well-chosen position of the sample in the electric field is observed immediately after applying the MW power and therefore it only needs few minutes for the solution to reach a uniform heating state (Figure 5). Accordingly, both temperature and power fine controls are possible (Figure 6). The only disadvantage of such oven for the present study is that only small membrane coupons can be studied because the solution must be contained in 10 ml vessels up to 100 ml round-bottomed borosilicate glass flasks (chosen here), preventing from further filtration tests, but the magnetic stirring is possible to enhance the solution homogeneity.

Insert Figure 5 about here Insert Figure 6 about here 2.3.2. Pulsed (discontinuous) MW and multi-mode oven. Figure 7 shows multi-mode ovens delivering pulsed MW. Contrary to the previous one, the power is applied discontinuously, meaning that its regulation is far from be nicely controlled. Another consequence is the absence of mastering of the temperature. To avoid too high increase in temperature, the experimenter has to manually choose to apply power for a given time that has to be experimentally determined according to the objectives dealing with temperature limitation. For instance, Figure 8 depicts that the size and form of the reactor as well as the number of reactors simultaneously presents in the oven can significantly modify the water evaporation rate and consequently the concentration of reactants and thus the results with a given power and oven. The size to volume ratio of membrane to solution as well as the overall matter present in the oven must be controlled for study optimisation.

Insert Figure 7 about here

Insert Figure 8 about here 2.3.3. Optimisation depend on the MW oven. More or less, all ovens, either laboratory or domestic ones, have the same magnetron, but even at constant frequency (generally 2,450 MHz) and same applied power, optimised reaction conditions are oven-dependent. This is due to the difference in the statistical distribution of the waves inside the oven, that depends on several parameters such as: the different systems to guide (waveguide) and disperse the waves (wave brewer) toward the sample inside the oven, the power supply unit, the cavity size of the oven and of course the overall volume and chemical nature of the samples in the cavity. That is why in the present study we have systematically performed experiments with constant membrane to solution ratio and constant number of glass reactors (always the same series) in the multi-mode oven (see experimental part). The question is less sensitive with the singlemode oven because only one sample can enter the very small cavity but similar precautions have been taken.

conclusion on MW

To sum up, chemical reactions under MW irradiation are affected by overheating, hot spot formation, polarization, dielectric properties, solvent sensitivity to microwaves, spin alignment and nuclear spin rotations. Considering the large use of MW for synthesis purpose and knowing that degradation involved similar chemical mechanisms as synthesis, we have decided ten years ago to systematically study "How micro-waves can help to study membrane ageing and consequences on fouling and cleaning". This paper is the first one giving the overall trends that underpin and validate the approach.

Materials and Methods

Water and solutions

Water used for membrane rinsing and preparation of all solutions was demineralised and 1 µm filtered. In standard conditions (except other comments) sodium hypochlorite (NaOCl) concentration, was set at 400 ppm TFC and used either at pH = 11.5 ± 0.1 or pH= 8.0 ± 0.1 by addition of NaOH or HCl of analytical grade (Acros), respectively. It was obtained by appropriate water dilution of concentrated commercial bleach (MIC, bleach at 96,000 ppm TFC). A formulated alkaline detergent (Ultrasil 10, powder, pH 12.0 at 4 g.L -1 ) provided by Ecolab (Issy Les Moulineaux, France) was used for membrane cleaning. This detergent is known to be efficient for the protein removal from pristine PES/PVP membrane [START_REF] Diagne | On the actual cleanability of polyethersulfone membrane fouled by proteins at critical or limiting flux[END_REF]. Lysozyme from hen egg white (MW= 14,300 g.mol -1 , isoelectric point pI= 10.7, Stokes radius Rs= 1.8 nm) in hydrochloride form was provided by Ovonor (Tregueux, France). This protein has been chosen because its size is close to that of -lactalbumin, the smallest soluble protein of milk, but lysozme was less expensive. Solutions set at 1 g.L -1 were filtered at natural pH (pH = 4.5). In such physico-chemical environnement, Lysozyme was highly positively charged. Occurrence of charge on the filtered protein induce occurrence of similar charges on the fouled membrane. Accordingly, repulsive electrostatic interactions were efficient between lysozyme free in solution and the fouled membrane. The consequnce is the enhancement of the protein rejection by the membrane when compare to pure size exclusion [START_REF] Rabiller-Baudry | Application of a convection-diffusion-electrophoretic migration model to ultrafiltration of lysozyme at different pH values and ionic strengths[END_REF]. Addition of salt at sufficient concentration allowed to screen these electrostatic interactions. This allowed to reach transfer mechanism mainly based on steric exclusion and not on the combination of steric and electrostatic repulsions. This filtration conditions were better to appreciate the impact of membrane ageing on protein rejection. Consequently, NaCl solution at 500 mmol.L - 1 were prepared from powder of analytical grade (Acros) and sometimes added to ultrafiltered lysozyme solutions..

Membranes and UF conditions

3.2.1. Membranes. The UF membrane (HFK 131, 5-10 kg.mol -1 ) was provided by Koch (USA). This membrane is worldwide commonly used at industrial scale for UF in dairy industry. HFK-131 is mainly made of PES but contains also some PVP [START_REF] Rabiller-Baudry | Evidencing the chemical degradation of a hydrophilised PES ultrafiltration membrane despite protein fouling[END_REF]. One spiral membrane (6.7 m 2 , 4333 K131 VYV module) was used in which flat coupons of 127 cm 2 filtering area were sampled.

Filtration with flat membranes.

Prior any other use, the preservative (glycerol) was removed by soaking the flat membrane in demineralised water (removal was checked by ATR-FTIR analysis). Then the membrane was inserted in a plate and frame cell (Rayflow X100, Orelis, France). Each flat membrane was compacted by filtering water at 3 bar, 25°C, during 4 h in cross-flow mode (velocity close to 2 m.s -1 ) until a plateau value of permeance (Lp 0 = J 0,water /TMP) was reached. Several virgin membranes were used in lysozyme UF. The following UF standard conditions were: 50°C, 2 m.s -1 , transmembrane pressure TMP= 2 bar and VRR=1 (full recycling of permeate and retentate in the feed tank). Others membranes were voluntary aged in NaOCl according to various protocols tested (see below). After the ageing treatment, hey were re-compacted at 3 bar in water and finally used in lysozyme UF in standard conditions. The careful rinsing as well as the re-compaction together with the temperature control during water flux measurement were required because this membrane is both pH and temperature responsive. Precision on fluxes was better than 5%. Regardless of the membrane, either virgin or NaOCl aged, after lysozyme UF, each membrane was carefully rinsed by water. Then the membrane was demounted for analysis.

Protocols for flat membrane ageing

Regardless of the protocol, the treatment duration varied. It is commonly expressed as a cumulative dose of NaOCl received by the membrane and generally given in ppm.d total free chlorine (TFC). According to the provider the HFK-131 membrane was guaranteed up to a cumulative NaOCl dose equal to 5,000 ppm.d TFC. For a "D" ppm TFC NaOCl solution, the received dose was expressed according to: NaOCl dose (ppm.d) = D (ppm) x number of days (3)

Ageing by soaking in NaOCl.

Small membrane coupons of about 10 cm 2 and 127 cm 2 filtering area flat membranes were soaked in NaOCl solutions at given concentration in the 0 to 96,000 ppm TFC range up to 200 days. Moreover the pH was fixed either at pH= 8.0 (ideal for PES/PVP degradation, and corresponding to a pH commonly used in water applications at room temperature) or pH= 11.5 (less favourable to prone PES/PVP membrane degradation but corresponding to pH commonly used in dairy applications at 50°C). The temperature was maintained at 50°C all day long and decreased slowly during the night down to room temperature. Solutions were replaced every week. Regardless of the other conditions, the NaOCl solution volume to membrane area ratio was always 14.6 L.m -2 . This ratio was more or less arbitrary chosen but it was the same that was used in UF with respect to the pilot dead volume.

Ageing in UF conditions at 2 bar.

Flat membranes of 127 cm 2 filtering area were continuously immersed in 400 ppm TFC NaOCl solution at pH 8.0 (14.6 L.m -2 ) on a UF pilot filtering all day long at 50°C. However the filtration was stopped during the night but the membrane remained immersed in the NaOCl solution. The temperature was able to slowly decrease during the night down to room temperature. Finally it was estimated that UF ageing was only one third of the time performed in the standard hydrodynamic conditions described above.

Accelerated ageing by immersion under continuous microwaves (60-70 W).

Small membrane coupons (14.6 L.m -2 ) were immersed in NaOCl solution set at 400 ppm TFC at either pH= 8.0 or pH= 11.5. Simultaneouslys they were submitted to continuous micro-waves irradiations at 60 W that were applied during few hours in a CEM Explorer® 24 single-mode oven (Labmate, 2,450 MHz, Figure 5). The microwave irradiation parameters (power and temperature) were monitored by the ChemDriver software. The limitation of the power allowed to control the temperature that was kept constant at 50 ± 1 °C (Figure 6).. The membrane coupons were exposed to MW irradiation for either 120 min (33.3 ppm.d TFC dose) or 240 min (66.7 ppm.d TFC dose). However, this oven had a too small cavity to insert 127 cm 2 membrane preventing thus from possibility of further UF tests.

Accelerated ageing by immersion under pulsed microwaves (680 W).

Small membrane coupons of 10 cm 2 area (always the same numbers simultaneously in the oven) or 127 cm 2 filtering area flat membrane (only one in the oven) (14.6 L.m -2 ) were immersed in NaOCl solution set at 400 ppm TFC either at pH= 8.0 or pH= 11.5. They were submitted to pulsed microwaves at 680 W in a discontinuous mode that was applied few minutes in a multi-mode domestic oven (Moulinex, 31 L, 2,450 MHz, Figure 9). In order to limit the temperature increase, and to try to be as close as possible to conditions of the single-mode oven described above, each 3 min the warm NaOCl solution was changed for a similar volume of a fresh one initially at room temperature. The membranes were exposed to micro-waves irradiation for a maximum duration of 45 min (12.5 ppm.d TFC dose).

Insert Figure 9 about here 3.3.5. Combination of ageing in UF conditions then pulsed micro-waves (170 W). Several flat membranes of 127 cm 2 filtering area had continuously filtered a 400 ppm TFC solution at pH= 8.0 until a 500 ppm.d TFC dose exposition (14.6 L.m -2 , in standard UF conditions, 50°C). After this first ageing step, the membranes were demounted and immersed in 400 ppm TFC solution at pH 8.0 (14.6 L.m -2 ) under pulsed microwaves (170 W, Moulinex) for a given duration that was maximum 12 h (corresponding to a 700 ppm.d TFC maximum cumulative dose). Finally the membranes were carefully rinsed by water, compacted once again and finally used in UF.

Physico-chemical characterisation of membrane by ATR-FTIR

Membrane degradation by NaOCl as well as protein amount on membrane was followed by ATR-FTIR. Prior to measurements membranes were carrefully dried in a dessiccator under dynamic vacuum during several days in order to get rid of water. The dryingefficiency was checked on all spectra via the absence of the OH band in the 3000 cm -1 region allowing to estimate that the OH band harmonic, much lower than the previous one and located close to 1660 cm -1 was null. Spectra were aquired with a spectrum 1000 spectrometer (Perkin Elmer, spectrum for windows software) equipped with an ATR accessory (ZnSe Crystal, 12 reflexion, incidence angle of 45°, 20 scans, resolution: 2 cm -1 ). Membrane samples were carefully pressed on the crystal (maximum pressure using a flat tip) for a nice signal to noise ratio. Figure 10 shows typical spectra of new membranes. All bands can be assigned to PES except the band located at 1661 cm -1 that was the single one assigned to PVP (C=O).

Insert Figure 10 : the average height of the baseline measured in the 2060-2240 cm -1 range of wavenumbers. Value equal to 0.0165. The quantification was possible in a wide range of fouling from 1 to 350 µg of proteins per square centimetre of membrane (geometric area) with a precision of 1 µg.cm -2 . 19 samples of fouled pristine membranes have been used to establish the calibration, allowing to reach r 2 = 0.997.

Membrane characterisation by ATR-FTIR.

In the following, the membrane "age" was estimated with respect to two main markers: PVP disappearance and PES backbone modification according to a procedure explained in [START_REF] Rabiller-Baudry | Evidencing the chemical degradation of a hydrophilised PES ultrafiltration membrane despite protein fouling[END_REF] and briefly explained in the following for sake of clarity. The PES degradation was easily evidenced by the increase of a band located at 1030 cm -1 (Figure 10). This band was common to C-OH due to hydroxylation in ortho position of phenyl group of PES and to sulfonate groups due to PES backbone cleavage (Figure 1). The degradation level was expressed as the H PES-backbone 1030 /H PES 1240 ratio in the following because no modification of the height of the PES band located at 1240 cm -1 was observed due to the membrane ageing. The progressive disappearance of PVP was easy to highlight with un-fouled membranes, either virgin or aged. Following the decrease of the 1661 cm -1 band on spectra (Figure 10), the degradation level was expressed as the H 1661 PVP /H 1240 PES ratio in the following.

Atomic composition by SEM-EDX

Micro-analysis coupled with scanning electron microscopy (SEM-EDX) allowed to evidence variation in atomic composition of the membranes. They were previously dried and metallised with Au-Pd during a controlled time. Aiming at developing a quantitative or semiquantitative method, the penetration depth of the electron beam must be controlled as much as possible. This depth depends on several parameters among which is the accelerating voltage that was always chosen equal to20 kV. Membranes active layer could be heterogeneous. In order to have an average value that can be considered as representative and not a particular composition related to a specific location that could be non-representative, the EDX analysis was performed during 50 s on a wide surface of the sample and not at a specific point. For this purpose a 400 magnification of the sample was arbitrary chosen corresponding to a 198 µm x 198 µm area and the whole picture was analysed. The precision was better than 5 % for each element. The main elements existing on the pristine membranes are C and N, but there was an overlapping of the two signals, and consequently it was not possible to distinguish unambiguously the PVP presence from that of PES. O and S were clearly evidenced as single atoms.

PES cleavage by SEC-HPLC

Size exclusion chromatography was used to analyse PES molecular weight evolution with respect to ageing. The stationary phase was made of a styrene/divinyl benzene copolymer (PL-gel 5 µm, MIXED-GEL, 7.5 cm x 30 cm, Polymer Laboratories). A pre-column of same reference was added (PLgel, 5µm, 5 cm). The CHCl 3 eluent (chloroform of HPLC grade, Acros) flow rate was set at 1 mL.min -1 . 10 µL of samples dissolved in chloroform were injected thanks to a VALCO valve. The UV detection was achieved at 254 nm allowing the PES detection (with respect to its phenyl groups) but not the PVP one (Spectromonitor 3000 L.D.C.). Peaks surface were integrated with a Hewlett Packard 3396.A integrator. The column linearity was checked to be in the 1,447,000 g.mol -1 -104 g.mol -1 molecular weight range with respect to polystyrene (PS) standards. With this calibration, the apparent molecular weight of the PES constituting the membrane was close to 22,000 g.mol -1 . Prior analysis, PES/PVP small membrane coupons of a given constant area of 10 cm 2 were soaked in 250 mL CHCl 3 allowing to separate the membrane support from the other parts of the membrane (intermediate and active layers). But, the dissolution of both the intermediate and active layers was not total in such conditions. Nevertheless, for sake of chloroform minimal consumption (and because it was not possible for us to change the nature of the eluent of the HPLC apparatus for practical aspects), the supernatant was injected after a classical 45 µm filtration. The degradation of the membrane was then followed with respect to 2 complementary datas: (1) the evolution of the amount of the soluble fraction highlighted by the overall peak intensity and (2) the average molecular masses in number and weight (apparent Mn and Mw) and the polydispersity index (apparent PI = Mw/Mn).

Contact angles and polar/apolar balance evolution

Contact angle (Ɵ) measurements were measured by the sessile drop technique with a GBX-DS Digidrop apparatus with an accuracy better than 3°. For sake of reproductibility, the membranes were very carefully dried in an oven at 100 °C during 2 days. It was previously checked that this dying method was equivalent to a drying achieved in a dessiccator under vacuum for a much longer time. For the characterisation of a given membrane, 3 different solvents of known characteristics were used, namely water, diiodomethane and formamide. By applying the Young-Dupré-Van Oss equation [START_REF] Van-Oss | Forces Interfaciales en Milieux Aqueux Masson[END_REF] it was possible to determine the global superficial tension of the membrane ( S ) and its decomposition in apolar/hydrophobic ( S LW ), acid ( S A ) and base ( S B ) components:

(1 + cos Ɵ)  L = 2 [ ( S LW +  L LW ) 1/2 + ( S A +  L B ) 1/2 + ( S B +  L A ) 1/2 ] ( 5
)
Where S and L indexes referred to membrane and liquid respectively.

Results and discussion

At industrial scale NaOCl is generally used at 150-200 ppm, 50°C and pH 11.5 for the disinfection step in dairy. To study membrane degradation at laboratory scale, other conditions have to be found to shorten studies. However, they must be representative of the ageing state that can be reached at industrial scale during the service life of the membrane. Up to naow, the classical trend was to increase the NaOCl concentration assuming the supposition that the overall dose calculated thanks to equation 3 was a good parameter. Even if often used in literature, such assumption has never been proved and is probably partially false, especially with too high concentrations.

Preliminary experiments to determine acceptable conditions for acceleration of ageing

The first set of experiments aimed at the identification of acceptable conditions for accelerating the membrane ageing. These conditions have been mainly determined from SEM-EDX analysis before conducting an in-depth study using several analytical tools for an overall convincing demonstration.

4.1.1.

Ageing by soaking at pH= 11.5, 50°C, and various NaOCl doses. As already said, this pH is the one used for disinfection at industrial scale in dairy at 50°C. Membrane ageing was firstly achieved by immersion in various with NaOCl doses ranging from 50 to 200 ppm and during up to 90 days. Together with C+N, S and O, additional Cl was evidenced by SEM-EDX on aged membranes. It must be underlined that no additional cations were evidenced on the aged membranes, meaning that Cl was not in its chloride anion form. This result was in good agreement with the PES backbone cleavage of the C-S bond that is associated with the Cl fixation on the degraded PES backbone appearing simultaneously with the sulfonate groups" appearance (Figure 1). It can be underlined here, that the S amount cannot be modified by the sulfonate group appearance when the aged membrane is compared to the pristine one because it is only an oxidation of the initial sulfone group. For a semi-quantitative estimation of the degradation level of the membrane, the Cl to S atomic ratio was calculated assuming that S atom only belong to the membrane regardless of its oxidation state. SEM-EDX analyses highlighted clearly (1) the Cl uptake by the membrane and (2) an acceleration of the ageing by increasing the NaOCl concentration (Figure 11). A particular attention can be paid to significant variations between 150 and 200 ppm confirming the interest of new trends in disinfection at industrial scale by slightly lowering NaOCl concentration to 150 ppm.

Insert Figure 11 about here 4.1.2. Acceleration of membrane ageing by increase of the NaOCl dose. At high alkaline pH, naturally obtained by increasing the NaOCl concentration, when soaking the membrane at room temperature in 96,000 ppm TFC solution, the active layer was attacked in few minutes. Several cracks appeared, highlighting that a too high increase in NaOCl concentration cannot be a nice alternative to accelerate the ageing in a representative way of industrial ageing. Similar behaviour have been found with lower, but quite high doses. Based on a trial and error approach, we have estimated that concentrations up to 800 ppm TFC could probably be used, but to take into account possible concentration during MW further irradiation, with respect to possible water evaporation, we have voluntary limited the initial concentration to 400 ppm TFC aiming also at limiting side-reactions if any.

Acceleration of membrane ageing due to pH decrease at 400 ppm TFC dose.

Decreasing the pH from 11.5 to 8.0 allowed to accelerate the Cl uptake (Table 3). Comparable Cl uptake were reached with either a 40,000 ppm.d dose at pH 11.5 or a 8,000 ppm.d dose at pH 8.0. In both cases this Cl uptake was close to that reached for the industrial membrane at the end of it service life (knowing from its autopsy that only a very small percentage of this value is due to salt precipitation on the industrial membrane [START_REF] Bégoin | Autopsie de membranes spirales de l"industrie laitière-Physico-chimie du nettoyage de membranes PES d"ultrafiltration de lait écrémé (Autopsy of spiral membranes of dairy industry. Physico-chemistry of the cleaning of PES membranes used in skim milk ultrafiltration)[END_REF][START_REF] Bégoin | Methodology of analysis of a spiral wound module. Application to PES membrane of ultrafiltration of skimmed milk[END_REF]).

Evidencing of ageing acceleration by MW irradiation at pH=8

.0 and NaOCl 400 ppm TFC dose. When membrane coupons were immersed in solution at pH= 8.0 under pulsed MW at 680 W during 45 min (66.7 ppm.d) the Cl uptake was the same as that reached either with the industrial ageing or the membrane aged up to 8,000 ppm.d without any MW irradiation (Table 3). This result confirmed the acceleration thanks to micro-waves that was reached as expected.

Evidencing of the combination of chemical and mechanical ageing?

From SEM-EDX analysis it was evidenced that ageing at pH= 8.0 and 400 ppm.d TFC in UF conditions allowed to increase the Cl uptake by the membrane (Table 3). At this moment, it remained unclear if the ageing level was due to a better diffusion of NaOCl in the membrane structure or if a mechanical ageing was added to the chemical one. This point will be discussed in the following part. The main problem with this approach was related to the UF equipment made of stainless steel. NaOCl at such "low" pH and moreover at this concentration was very corrosive. Some holes have appeared in the pipes of our pilot preventing from the systematic use of such experimental approach.

Insert Table 3 about here

Systematic investigation of ageing at NaOCl 400 ppm TFC

With respect to the preliminary results detailed above, NaOCl concentration set at 400 ppm has been chosen for the following. Nevertheless, aiming at taking into account potential differences in the degradation mechanisms at pH= 11.5 and pH= 8.0, these two values have been used in parallel for several trials and characterisations. Once the NaOCl concentration has been chosen, Figure 12 shows the overall approach experimentally followed to both accelerate ageing and avoid degradations that could be non-representative on a physicochemical point of view but also on a mechanical point of view (detachment of the active layer avoiding UF tests for instance). In the following, results are given following the characterisation technique used in order to better highlight comparison between the different ageing protocols.

Insert Figure 12 about here 4.2.1. ATR-FTIR characterisation. First of all, it has been checked that the overall characteristics of the ATR-FTIR spectra of aged membranes were not changed by increasing the NaOCl concentration from 200 ppm TFC to 400 ppm TFC, either at pH= 11.5 or pH= 8.0. This remark was true either with or without MW irradiation. Similar variations were evidenced, namely disappearance of the PVP 1661 cm -1 band and appearance of the 1030 cm -1 band. Only the band intensities were able to vary. No other band appearance or disappearance was evidenced on all the registered spectra. Table 4 shows the evolution of the PVP disappearance according to the ageing protocols. At 400 ppm, moving from pH 11.5 to pH 8.0 confirmed the ageing acceleration in static immersion. At pH 8.0, the same disappearance was reached with a 4,000 ppm.d dose without MW and a 12.5 ppm.d dose with MW irradiation, thus confirming the acceleration due to microwaves. All tested durations were insufficient to reach the PVP level of the membrane aged at industrial scale but the trend of the PVP disappearance was significant. After a 2,050 ppm.d TFC dose the degradation in UF conditions allowed to reach the level observed on the industrial aged membrane. Table 5 shows the evolution of the PES backbone degradation with respect to the ageing protocols. Results confirmed that the PES backbone was much more stable than the PVP and consequently quite difficult to degrade. UF conditions allowed to evidence the PES degradation. Nevertheless trends suggested that it could also be possible, for longer and/or optimised MW treatments. These results suggested that it could be possible to select MW degradation conditions that could be related only to PVP disappearance or to both PVP and PES degradation. This is an interesting result that could be used in the future aiming at studying the respective impact of the evolution of the two polymers on UF performances.

Insert Table 4 about here

Insert Table 5 about here 4.2.2. Contact angle and polar/apolar balance evolution. The evolution of the polar/apolar balance is given by the  S AB / s LW ratio. A decrease in this ratio means a decrease in the hydrophilic overall character of the membrane. Figure 13a depicts that the aged membranes became less polar than the new one when NaOCl dose increased up to 10,000 ppm.d, regardless of the pH in static immersion. Then the hydrophilic character increased but remained lower than that of the virgin membrane. Attempt of correlation between the  S AB / s LW ratio and the PVP content in the membrane deduced from ATR-FTIR is shown Figure 13b.Obviously the polar/apolar character decrease can be related to the PVP departure evidenced from ATR-FTIR spectra. Roughly, experimental data obtained at pH= 11.5 and pH= 8.0 followed the same global trends. Nevertheless, some outlier data were observed at pH= 11.5 suggesting that this cannot be the single explanation.

Insert Figure 13 about here

Remembering that the PES backbone modification can increase the hydrophilic character of the aged membrane, the evolution in two times of the  S AB / s LW ratio could be in good accordance with a first rapid removal of PVP and a PES degradation starting after a sufficient NaOCl dose. Table 6 shows the evolution of the polar/apolar character of some aged membranes. These results cannot be discussed without the understanding of the previous comment.

Insert Table 6 about here 4.2.3. SEC-HPLC. Membranes aged for a long time in static immersion either at pH=11.5 or pH= 8.0, were dissolved in CHCl 3 before SEC-HPLC injection. Figure 14 shows that the soluble fraction increased with the NaOCl dose received by the membrane, regardless of the pH. This results is in good agreement with the PES backbone evolution. Mn, Mw and PI are shown Figure 15 for different ageing protocols. Obviously, simultaneously with the increasing amount of the soluble fraction, the characteristics of the soluble fraction evolved. Clearly, SEC-HPLC was in good agreement with the PES C-S bond cleavage, as it has been already suggested by the Cl uptake (see above, SEM-EDX).

Insert Figure 14

Permeance to water of membranes aged by static immersion or under MW.

The membrane permeance to water was measured with respect to the membrane ageing (Table 7). The Lp aged /Lp new ratio variation evidenced the permeance decrease with ageing down to 40%-30% of the initial value. The permeance was close for membranes aged (1) close to 80,000 ppm.d at both pH 11.5 and pH 8.0 and (2) under pulsed micro-waves at 12.5 ppm.d at both pHs. The decrease was in good accordance with the PVP removal already mentioned above. The increase in the membrane hydrophobic character is in agreement with an increase of the overall membrane resistance to water transfer. Nevertheless no simple relationship was found between H PVP 1661 band of ATR-FTIR spectra and membrane permeance.

None of the tested conditions allowed to observe an increase in permeance as it was the case for the membrane aged at industrial scale. Was it due to a too short MW irradiation time or to absence of mechanical degradation in absence of UF conditions? The answer remained unclear at this moment.

Insert Table 7 about here 4.2.2. Permeance to water of membranes aged in UF conditions. The membrane permeance to water (L p ) was measured for 8 flat membranes aged up to various NaOCl doses (Figure 16). Lp increased linearly up to a 2,500 ppm.d TFC dose with an excellent reproducibility.

Then the dispersion increased a little. However, the Lp aged /Lp new ratio remained roughly linear up to a 4,000 ppm.d dose (Figure 17). The permeance increase for this final dose was in good agreement with that estimated for the membrane aged at industrial scale from few measurements achieved on several flat coupons of 127 cm 2 aleatory sampled in the industrial spiral membrane (Figure 17). These results were in agreement with the assumption claiming that ageing in UF conditions could be a real requirement to superimpose mechanical ageing to chemical one.

Insert Figure 16 about here Insert Figure 17 about here

Permeance to water of membranes aged by combination of UF and MW conditions.

To minimise the UF duration in NaOCl (with respect to the integrity of the UF pilot) combination of short UF up to 500 ppm.d dose (1.25 day) and immersion under pulsed microwaves has been tested. Simultaneously the power applied has been strongly decreased when compared to that used in the trials described above with the multi-mode oven. A power equal to 60 W has been previously shown to be efficient with the single-mode oven but this power cannot be selected with the multi-mode oven used in the present study. Finally, 170 W has been arbitrary selected because it was the lowest possible value with the multi-mode oven.

Figure 17 depicts that no permeance increase was observed after the short UF ageing. But adding short MW irradiation times (up to 20 h, 833 ppm.d dose) allowed, as expected, to increase the permeance. The degradation of both PVP and PES have been checked by ATR-FTIR for a membrane aged by a combination of short UF + 12h MW (Figure 18).

Insert Figure 18 about here 4.2.4. Rejection of lysozyme and fouling. UF of lysozyme was achieved in standard conditions at 50°C on pristine and flat membranes aged either in UF (Figure 19a) or in static immersion with or without MW irradiation (Figure 19b). Whereas the protein rejection was full with the new membrane, ageing protocols by static immersion with or without MW induced a more or less pronounced decrease. This impact of membrane ageing on rejection was in good accordance with industrial observations. It is well known in dairy that -lactalbumin initially retained by the pristine membrane is able to transfer in the permeate with an aged one (generally the transmission can be increased up to 10-15% before the membrane being changed). Of course, with respect to this criterion, time under MW irradiation had to be optimised to adjust the treatment duration to the expected degradation level.

Insert Figure 19 about here

Conclusions

The present study highlights potentiality of microwaves irradiation to accelerate PES/PVP membrane ageing by NaOCl aiming at proposing a rapid ageing protocol useful at laboratory scale for further fundamental studies to improve filtration performances of aged membranes at industrial scale. Immersion of the UF membrane under pulsed MW (650 W) in deionised water have no impact on the membrane chemical degradation as checked by ATR-FTIR. On the contrary, irradiation by continuous MW (60 W, at a controlled temperature of 50°C) or by pulsed MW (650 W, with less temperature control) accelerate the degradation by NaOCl, highlighting a MW impact that cannot be only related to thermal effects of MW. The chemical degradation was followed by SEM-EDX, ATR-FTIR, SEC-HPLC and contact angle measurements with a nice agreement between all results. Nevertheless, these physicochemical characterisations were not sufficient to conclude on the degradation representativeness when compared to ageing at industrial scale. UF performances had also to be checked and water flux as well as behaviour during UF of a model protein were determined for this purpose. Aiming at contributing to the understanding of the relative impact of chemical and mechanical degradation, combination of a short UF step and short treatment under pulsed MW (170 W) has been studied. The combination was demonstrated to be similarly efficient as a single long UF step performed without any MW irradiation. These results suggest that mechanical degradation cannot be reached by only MW irradiation. However this assumption is in contradiction with our own more recent study highlighting that MW conditions can be found to reach the expected ageing state [START_REF] Rabiller-Baudry | Simulation of membrane ageing to go ahead in fouling and cleaning understanding during skim milk ultrafiltration[END_REF]. Regardless of this last remark, conditions using MW exist to reach ageing state representative of progressive membrane degradation at industrial scale. Of course, adjustments of at least the applied power, the irradiation duration of (pulsed) MW are required together with the control of the overall matter present in the (given) oven.

To date, we have already transposed the present study using a quite NaOCl resistant PES/PVP membrane to a less resistant one made of aromatic polyamide (RO) in order to evaluate the harmlessness of non-oxidant biocides when compared to NaOCl. Adapation of MW irradiation conditions were required, but the general trends confirmed the interest of MW irradiation to study the ageing or stability of other polymer membranes [START_REF] Petit | Methodology for the demonstration of harmlessness of a detergent on a polyamide reverse osmosis membrane[END_REF].

So the proof of concept is done and it seems that characterisation thanks to ATR-FTIR combined to simple UF performances (water flux and rejection of a model solute) could be sufficient to go ahead.

Nomenclature section

Microwaves : MW : micro-waves ET : the penetration depth of MW (cm)  the wavelength of the MW (cm) " r : the dielectric constant of the medium " r : the dielectric loss of the molecule P d : the power of MW transferred per unit volume of material : the medium conductivity E : the local electric field intensity of MW ν : the MW frequency (Hz) tan δ: dielectric loss tangent P: power delivered by the MW oven (W) Membrane separation : Lp 0 : permeance of pristine membrane to water (L.h -1 .m -2 .bar -1 ) Lp aged : permeance of aged membrane to water (L.h -1 .m -2 .bar -1 ) J 0,water : pristine membrane flux to water (L.h -1 .m -2 ) TMP: transmembrane pressure (bar) VRR : volume reduction ratio = V feed initial / V feed final (dimensionless) UF : ultrafiltration Ageing in oxidant conditions : TFC : total free chlorine (ppm) D : dose in TFC (ppm) NaOCl dose : cumulative TFC dose (ppm.d) ATR-FTIR characterisation : [P]: the protein concentration on membrane (µg.cm -2 ) H 1240 PES : the height of the band at 1240 cm -1 attributed to PES (absorbance unit) H 1539 protein amide II : the height of the band at 1539 cm -1 attributed to protein amide II band (absorbance unit) SEC-HPLC : Mn: apparent average molecular masses in number (g.mol -1 ) Mw: apparent average molecular masses in weight (g.mol -1 ) PI: apparent polydispersity index, PI = Mw/Mn (dimensionless) Contact angle measurements : Ɵ: contact angle between the dried membrane and a given solvent(°)  S : global superficial tension of the membrane (mJ.m -2 )  S LW : apolar/hydrophobic contribution to  S (mJ.m -2 )  S A : acid contribution to  S (mJ.m -2 )  S B: base contribution to  S (mJ.m -2 ) and of the membrane aged at industrial scale at the end of its service life (dashed line). The band located at 1661 cm -1 was assigned to PVP, that at 1030 cm -1 to PES backbone degradation and all others to PES. The degradation level will be expressed as the H PVP 1661 /H PES 1240 and H PES-backbone 1030 /H PES 1240 ratios in the following. • Pristine membrane:

Tables

List and captions of Figures

• PES :

• PVP :

• NaOCl little aged membrane:

• PES • PVP

• degradation products of PVP identified at pH 7.0-8.0  not evidenced at pH= 11.5

• NaOCl highly aged membrane:

• PES • no more PVP • degradation products of PVP at pH= 7.0-8.0 ? none at pH= 11.5

• degradation products of PES 

  about here Insert Figure 15 about here 4.2. UF performances according to ageing protocols

Figure 1 :

 1 Figure 1: PES and PVP and theirs degradation products after NaOCl exposure at pH= 7.0-8.0 or pH= 11.5 according to available literature data.

Figure 2 :Figure 3 :Figure 4 :Figure 5 .Figure 6 :Figure 7 .

 234567 Figure 2: Industrial micro-waves ovens

Figure 8 :

 8 Figure 8:Evaporation of aqueous solutions depending on the power and form of the reactor as well as on the number of reactors simultaneously presents in the oven. MW cycle: 30 min MW + 5 min without any MW applied and so on. (Samsung oven, 23 L, black oven of Figure7).

Figure 9 :Figure 10 :

 910 Figure 9: Picture of the oven and scheme of the entire 127 cm 2 flat membrane in the glass reactor

Figure 11 :

 11 Figure 11: SEM-EDX analyses (Cl to S atomic ratio) of membranes immersed in NaOCl at pH 11.5 and 50°C and various concentrations up to 200 ppm TFC.

Figure 12 :

 12 Figure 12: Scheme of the overall experimental approach

Figure 13 :Figure14:

 13 Figure 13: Evolution of the polar/apolar balance of membranes aged in static immersion in 400 ppm TFC solution at 50°C, at pH 11.5 (•) and pH = 8.0 (♦).

Figure15:

  Figure15: SEC-HPLC of the soluble fraction of the membrane aged in 400 ppm TFC NaOCl solution at 50°C in static immersion or under pulsed MW either at pH= 11.5 or pH= 8.0. (a)Apparent average molecular masses, (b) Polydispersity index

Figure 16 :

 16 Figure 16: Permeance to water (at 50°C) of 8 flat membranes aged in UF conditions in 400 ppm NaOCl pH= 8.0. Each colour correspond to 2 membranes aged up to a same final dose in ppm.d (green: 1,300 -blue: 2,050 -violet: 2,900 -orange: 4,100).

Figure 17 :Figure 18 :Figure 19 :Figure 1 :

 1718191 Figure 17: Permeance to water (at 50°C) of membranes aged in 400 ppm NaOCl pH= 8.0. (■) in UF conditions up to 4,100 ppm.d. (•) by combination of UF (500 ppm.d) and pulsed MW (170 W) up to a maximum of 833 ppm.d NaOCl dose -straight lines equations: UF: y = 0.0006 x + 0.7179with r 2 = 0.996 UF+MW: y = 0.0064 x -1.8348 with r 2 = 0.98

Figure 2 :

 2 Figure 2: Industrial micro-waves ovens

Figure 3 :Figure 4 :Figure 5 .Figure 6 :Step 1 :Figure 7 .Figure 8 :

 3456178 Figure 3: Microwaves in the electromagnetic spectrum

Figure 9 :

 9 Figure 9: Picture of the oven and scheme of the entire 127 cm 2 flat membrane in the glass reactor

Figure 10 :

 10 Figure 10: ATR-FTIR spectra of the virgin membrane PES/PVP membrane (straight line)and of the membrane aged at industrial scale at the end of its service life (dashed line). The band located at 1661 cm -1 was assigned to PVP, that at 1030 cm -1 to PES backbone degradation and all others to PES. The degradation level will be expressed as the H PVP 1661 /H PES 1240 and H PES-backbone 1030 /H PES 1240 ratios in the following.

Figure 11 :Figure 12 :Figure 13 :

 111213 Figure 11: SEM-EDX analyses (Cl to S atomic ratio) of membranes immersed in NaOCl at pH 11.5 and 50°C and various concentrations up to 200 ppm TFC.

Figure14:

  Figure14: Peak height of the soluble fraction of the membrane in SEC-HPLC for membranes aged in static immersion in 400 ppm TFC solution at 50°C, at pH 11.5 (•) and pH = 8.0 (♦).

Figure15:

  Figure15: SEC-HPLC of the soluble fraction of the membrane aged in 400 ppm TFC NaOCl solution at 50°C in static immersion or under pulsed MW either at pH= 11.5 or pH= 8.0. (a) Apparent average molecular masses, (b) Polydispersity index

Figure 16 :Figure 18 :Figure 19 :

 161819 Figure 16: Permeance to water (at 50°C) of 8 flat membranes aged in UF conditions in 400 ppm NaOCl pH= 8.0. Each colour correspond to 2 membranes aged up to a same final dose in ppm.d (green: 1,300 -blue: 2,050 -violet: 2,900 -orange: 4,100).

  about here 3.4.1. Protein amount on membrane. The calibration used has been established in our team few years ago and reported in[START_REF] Delaunay | Mapping of protein fouling by FTIR-ATR as experimental tool to study membrane fouling and fluid velocity profile in various geometries and validation by CFD simulation[END_REF][START_REF] Rabiller-Baudry | A dual approach of membrane cleaning based on physico-chemistry and hydrodynamics: Application to PES membrane of dairy industry[END_REF]:

	With: [P]: the protein concentration on membrane in µg.cm -2 H 1240 PES : the height (absorbance) of the band at 1240 cm -1 attributed to PES H 1539 protein amide II : the height of the band at 1539 cm -1 attributed to protein amide II band
	(CN+NH) H 2060-2240 baseline
	H 1539	protein amide II / H 1240	PES -H 2060-2240	baseline = 0.0034 [P]	(4)

Table 1 :

 1 penetration depth (ET) of MW in different solvent or materials for  = 12.2 cm at 2450 MHz

	Solvents / materials	T(°C)	ET (cm)
	Water	25	1.4
	Rubber	25	15 to 350
	PVC	20	210
	Epoxy resin (araldite CN-501)	25	4 100
	Teflon	25	9 200
	Porous glass	25	35
	quartz	25	16 000

Table 2 :

 2 Evolution of the boiling point (bp) and of the Nucleation Limited Boiling Temperature, (NLBT, under MW irradiation at 2450 MHz) of a selection of polar solvents

	Solvent	bp (°C)	NLBT (°C)	T (°C)
	H 2 O	100	104	4
	EtOH	79	103	24
	MeOH	65	84	19
	CH 2 Cl 2	40	55	15
	CH 3 CN	81	107	26
	Propan-2-ol	82	100	18
	(CH 3 ) 2 CO	56	81	25
	BuOH	118	132	14
	AcOEt	78	95	17

Table 3 :

 3 SEM-EDX analyses of virgin and aged flat membranes and comparison to industrial aged spiral membrane.

	Ageing pH	NaOCl dose (ppm.d)	Cl/S atomic ratio	Reference
		Aged membrane at industrial level
	pH 11.5	unknown	0.033 ± 0.005	[4, 25]
		Flat membranes in 400 ppm NaOCl, 50°C
			Static immersion
	pH 11.5 pH 8.0	8,000 40,000 4,000 8,000	0.028 0.033 0.024 0.033	This study
		under pulsed microwaves -multi-mode oven 680 W
	pH 8.0	33.3 66.7	0.024 0.033	This study
		UF in 400 ppm NaOCl, 50°C, 2 bar
	pH 8.0	1,300	0.067	This study

Table 4 :

 4 ATR-FTIR analyses of virgin and aged flat membranes and comparison to industrial aged spiral membrane.

	Ageing pH	NaOCl dose (ppm.d)	H PVP 1661 /H PES 1240	Reference
			New membrane
	None (7 membranes)	0	0.15 ± 0.05
		Aged spiral membrane at industrial level
	pH 11.5	unknown	0.06	[4, 25]
		Flat membranes in 400 ppm NaOCl, 50°C
			Static immersion
	pH 11.5 pH 8.0	4,000 8,000 4,000 8,000	0.14 0.13 0.09 0.08	This study
		under continuous microwaves (60 W) -single mode-oven
	pH 8.0	33.3	0.10	This study
		under pulsed microwaves (680 W) -multi-mode oven
	pH 8.0	12.5	0.09	This study
		UF in 400 ppm NaOCl, 50°C, 2 bar
	pH 8.0	2,050	0.06	This study

Table 5 :

 5 ATR-FTIR analyses of virgin and aged flat membranes and comparison to industrial aged spiral membrane.

	Ageing pH	NaOCl dose (ppm.d)	H PES-backbone 1030 /H PES 1240	Reference
			New membrane
	None (7 membranes)	0	0.04 ± 0.01	This study
		Aged membrane at industrial level
	pH 11.5	unknown	0.29	[4, 25]
		Flat membranes in 400 ppm NaOCl, 50°C
			Static immersion
	pH 11.5 pH 8.0	4,000 8,000 2,000 8,000 to 40,000	0.05 0.07 0.05 0.07	This study
	under continuous microwaves (60-70 W) -single-mode oven
	pH 8.0	66.7	0.05	This study
	under pulsed microwaves (680 W) -multi-mode oven
	pH 8.0	12.5	0.04	This study
		UF in 400 ppm NaOCl, 50°C, 2 bar
	pH 8.0	4,100	0.13	This study

Table 6 :

 6 Polar

	/apolar balance ( S	AB /  S	LW ) of the membranes deduced from contact angle
		measurements.
	Ageing pH	NaOCl dose (ppm.d)	 S AB /  S LW
		New membrane
	None		0	0.25
	Flat membranes in 400 ppm NaOCl, 50°C
		static immersion
	pH 11.5	2,000-4,000 8,000	0.08 0.01
	pH 8.0	4,000 8,000	0.16 0.04
		under pulsed MW (680 W) -multi-mode oven
	pH 11.5	12.5	0.08
	pH 8.0	12.5	0.16

Table 7 :

 7 Evolution of the water permeance (Lp aged /Lp new ) of aged flat membranes and comparison to industrial aged spiral membrane.

	Ageing pH	NaOCl dose (ppm.d)	Lp aged /Lp new	Reference
			New membrane
	None	0	1.00	This study
		Aged membrane at industrial level
	pH 11.5	unknown	3.5 (estimation)	[4, 25]
		Flat membranes in 400 ppm NaOCl, 50°C
			Static immersion
		40,000	0.88
	H 11.5	52,800	0.30
		81,200 40,000	0.30 0.88	This study
	pH 8.0	48,800	0.54
		70,800	0.54
		under pulsed microwaves (680 W) -multi-mode oven
	pH 11.5 pH 8.0	4.2 12.5 4.2 12.5	0.69 0.43 0.54 0.43	This study

Acknowledgements.

The authors thanks the French National Agency for Research (ANR) for the financial support during the Meduse Project (ANR-09-BLAN-0055-02) and especially to prof. Christel Causserand, coordinator of the project, for discussions. The authors acknowledge Francis Gouttefangeas, from the CMEBA microscopy platform of the ScanMAT UMS of "Université de Rennes 1" (https://scanmat.univ-rennes1.fr/la-plateforme-cmeba) for SEM pictures for SEM-EDX analysis of all membranes. HAJ acknowledges the Lebanese Association for Scientific Research « LASER », the AZM association (Lebanon), Université de Rennes 1 (ISCR-CIP, ISCR and SDLM doctoral school), Lebanese University / Université Libanaise for the grants having financially supported her PhD.


Omar Cherrak
email: omar.cherrak@iga.ac.ma

Hicham Ghennioui

Nadège Thirion Moreau

El Hossein Abarkan

Blind separation of complex-valued satellite-AIS data for marine surveillance: a spatial quadratic time-frequency domain approach

Keywords:

In this paper, the problem of the blind separation of complex-valued Satellite-AIS data for marine surveillance is addressed. Due to the specific properties of the sources under consideration: they are cyclo-stationary signals with two close cyclic frequencies, we opt for spatial quadratic time-frequency domain methods. The use of an additional diversity, the time delay, is aimed at making it possible to undo the mixing of signals at the multi-sensor receiver. The suggested method involves three main stages. First, the spatial generalized mean Ambiguity function of the observations across the array is constructed. Second, in the Ambiguity plane, Delay-Doppler regions of high magnitude are determined and Delay-Doppler points of peaky values are selected. Third, the mixing matrix is estimated from these Delay-Doppler regions using our proposed non-unitary joint zero-(block) diagonalization algorithms as to perform separation.

INTRODUCTION

This paper concerns the spatial automatic identification system (S-AIS) dedicated to marine surveillance by satellite. It covers a larger area than the terrestrial automatic identification system [START_REF] Tetreault | Use of the automatic identification system (ais) for maritime domain awareness (mda)[END_REF], [START_REF]International Association of Maritime Aids to Navigation and Lighthouse Authorities (IALA), IALA guidelines on the universal automatic identification system (AIS)[END_REF]. The idea of switching to satellite monitoring was introduced because of the fast and dynamic development of the marine traffic [START_REF] Høye | Space-Based AIS Reception for Ship Identification[END_REF][START_REF] Wahl | New possible roles of small satellites in maritime surveillance[END_REF][START_REF] Eriksen | Maritime traffic monitoring using a space-based ais receiver[END_REF]. It was an emergency to adopt a method that operates a global monitoring with reliability, efficiency and robustness. However, this generalization to space involves several phenomena. Among these phenomena, we found:

1. The speed of the satellite movement generates the Doppler effect which creates frequency offsets at the S-AIS signals [START_REF] Burzigotti | Advanced receiver design for satellite-based ais signal detection[END_REF],

2. The propagation delay of the signals and their attenuation due to the satellite altitude [START_REF]Improved Satellite Detection of AIS[END_REF],

3. When a wide area is covered by the satellite, it certainly includes several traditional AIS cells. In fact, the time propagation of signals transmitted from vessels to the satellite vary according to the position of the Journal Homepage: http://www.iaescore.com/journals/index.php/IJECE IJECE ISSN: 2088-8708 1733 ships and the maximum coverage area of the satellite antenna. Due to these two problems, it mainly affects the organizational mechanism of S-AIS signals. It results a collision data, as illustrated in the Figure 1, issued by vessels located in different AIS cells but received at the antenna of the same satellite [START_REF] Tunaley | An analysis of ais signal collisions[END_REF], [START_REF] Yang | Collision and detection performance with three overlap signal collisions in space-based ais reception[END_REF].

For this reason, we present new approaches to address this problem where the Doppler effect and the propagation delay are also taken into consideration. In fact, to solve the collision problem, few works have focused on blind separation of sources (BSS) methods [START_REF] Prevost | Interference mitigation and error correction method for ais signals received by satellite[END_REF], [START_REF] Zhou | Multi-user leo-satellite receiver for robust space detection of ais messages[END_REF]. In [START_REF] Zhou | Multi-user leo-satellite receiver for robust space detection of ais messages[END_REF], Zhou et al. present a multi-user receiver equipped with an array of antennas embedded in Low Orbit Earth (LEO) satellite. The principle of this receiver is to exploit spatial multiplexing in a nonstationary asynchronous context. Indeed, the authors consider the equation below:

X = HG (S Φ) + N, (1)
where is the Schur-Hadamard operator, X = [x 1 , x 2 , . . . ,

x P N ] ∈ C M ×P N , x n = x(nT s ), 1 ≤ n ≤ P N , is the observation matrix, H = [h 1 , . . . , h d ] ∈ C M ×d is the matrix of antenna response, G = diag{g 1 , g 2 , . . . , g d } ∈ R d×d contains the power of the sources, S = [s H 1 , s H 2 , . . . , s H d ] H ∈ C d×P N
is the matrix of sources and

Φ =      1 ϕ 1 1 . . . ϕ P N -1 1 1 ϕ 1 2 . . . ϕ P N -1 2 . . . . . . . . . . . . 1 ϕ 1 d . . . ϕ P N -1 d     
, where ϕ k = e j2π∆f k Ts contains the Doppler frequencies of the sources.

The principle of this method is based on joint diagonalization (JD) of matrices in order to reconstruct the S-AIS sources from separation matrix estimation [START_REF] Van Der Veen | An analytical constant modulus algorithm[END_REF]. However, because of the very specific properties of the S-AIS signals (complex and cyclo-stationary with two close cyclic frequencies), we opt for spatial quadratic time-frequency domain methods. Our aim is reshaping the collision problem into BSS problem more simpler than (1). We will show how another type of decomposition matrix named joint zero-diagonalization (JZD) of matrices set resulting from spatial quadratic time-frequency distributions allows the restitution of S-AIS sources.

TRANSMISSION SCHEME 2.1. AIS Frame

The AIS frame is a length of 256 bits and occupies one minute. It is divided into 2250 time slots where one slot equals 26.67 ms [START_REF] Chang | Study of ais communication protocol in vts[END_REF]. Its structure as illustrated in Figure 2 contains a training sequence (TS) consisting zero and one which takes 24 bits. The start flag (SF) and the end flag (EF) for information takes 8 bits. A Frame ISSN: 2088-8708 Check Sequence (FCS) (or 16 bits Cyclic Redundancy Code (CRC)) is added to the data information (168 bits) in which a zero is inserted after every five continuous one. The binary sequence {a k } 0≤k≤K of the AIS frame takes the values {-1, +1} since the NRZI encoding is used. Moreover, the modulation specified by S-AIS standard is Gaussian Minimum Shift Keying (GMSK) [START_REF] Linz | Efficient implementation of an i-q gmsk modulator[END_REF]. The encoded message is modulated and transmitted at 9600 bps on 161.975 MHz and 162.025 MHz frequencies carrier.

GMSK modulation

The resulting sequence after the bit stuffing and NRZI coding procedure is modulated with GMSK which is a frequency-shift keying modulation producing constant-envelope and continuous-phase. Hence, the signal can be written as s g (t) = +∞ k=0 a k g(t -kT s ), where a k are the transmitted symboles, T s is the symbol period and g(t) = 2π log 2 B exp -2 log 2 (πBt) 2 represents the shaping Gaussian filter where B is the bandwidth of the Gaussian filter. The GMSK modulation is described by the bandwidth-time (BT) product where S-AIS uses BT= 0.4 and T s = 1 9600 s). Making the signal on one of the frequencies carrier f c , produces a signal of spectral characteristic which is adapted to the band-pass channel transmission. The GMSK signal is, thus, expressed as : s(t) = {e -j(2πfct+φ(t)) } = I(t) cos(2πf c t) -Q(t) sin(2πf c t), where {•} is the real part of a complex number, φ(t) = 2πh +∞ k=0 a k g(t -kT s ) is the instantaneous phase of s g (t) where, in the AIS system, the modulation index is theoretically equal to h = 0.5 [START_REF] Prevost | Joint phase-recovery and demodulation-decoding of ais signals received by satellite[END_REF], I(t) (resp. Q(t)) modulates the frequency carrier in phase (resp. in phase quadrature). All steps of the GMSK modulation can be presented in the Figure 3.

sin φ(t)

Gaussian filter

Integrator

cos φ(t) - × × a k s g(t) φ(t) sin(2πf c t) cos(2πf c t) I(t) Q(t) s(t)
Figure 3. GMSK modulator scheme.

PROBLEM STATEMENT: COLLISION & BSS IN INSTANTANEOUS CONTEXT 3.1. Mathematical model of collision problem

The collision problem can be simply expressed as follows:

x(t) = J j=1 h j s j (t -τ j ) e -i2π∆fj t + n(t), (2)
IJECE Vol. 9, No. where x(t) is the received signal by the satellite, s j is the transmitted signal by the j -th vessel, h j , τ j and ∆f j are respectively the coefficients of the channel, the delay and the Doppler shift corresponding to the j -th vessel with J is the number of vessels and n(t) is an additive stationary white Gaussian noise, mutually uncorrelated, independent from the s j , with the variance σ 2 n .

Reshape the collision problem into BSS problem

We show, here, that (2) can be written in BSS nomenclature in which the delay and the Doppler shift caused by the satellite speed are considered. However, before any reformulation, we notice that the mixing matrix considered for S-AIS application is an instantaneous mixture due to the absence of obstacles in the ocean. Thus, we set J = n, the collision problem can be easily modeled in a BSS problem as follows:

x(t) = Hs(t) + n(t), (3)
where

H is a (m × n) mixing matrix, s(t) = [s 1 (t), s 2 (t), . . . , s n (t)] T is a (n × 1) sources vector with s j (t) = s j (t-τ j ) exp{-i2π∆f j t}, ∀j = 1, . . . , n and x(t) = [x 1 (t), x 2 (t), . . . , x m (t)] T , n(t) = [n 1 (t), n 2 (t), . . . , n m (t)]
T are respectively the (m × 1) observations and noises vectors. The superscript (.) T denotes the transpose operator.

Our developments are based on the following assumptions: Assumption A: The noises n j (t) for all j = 1, . . . , m are stationary, white, zero-mean, mutually uncorrelated random signals and independent from the sources with variance σ 2 n . Assumption B: For each s j of the n sources, there Delay-Doppler points of only one source is present in the Ambiguity plane. Assumption C: The number of sensors m and the number of sources n are both known and m ≥ n to deal with an over-determined model (the under-determined case is outside of the scope in this paper).

PRINCIPLE OF THE PROPOSED METHODS BASED ON THE SPATIAL GENERALIZED MEAN AMBIGUITY FUNCTION

We show, here, how the algorithms proposed in [START_REF] Cherrak | Non-unitary joint zeroblock diagonalization of matrices using a conjugate gradient algorithm[END_REF], [START_REF] Cherrak | Nouvel algorithme de zéro-bloc diagonalisation conjointe par approche de levenberg-marquardt[END_REF] adresses the problem of the separation of instantaneous mixtures of S-AIS data. The principle of the proposed methods are based on three main steps: first, the SGMAF of the observations across the array is constructed. Second, in the Ambiguity plane, Delay-Doppler regions of high magnitude are determined and Delay-Doppler points of peaky values are selected. Third, the mixing matrix is estimated from these Delay-Doppler regions so as to perform separation and to undo the mixing of signals at the multi-sensor receiver.

The Spatial Generalized Mean Ambiguity Function

With regard to BSS, it has been shown that spatial time-frequency distributions are an effective tool when signature of the sources differ in certain points of the time-frequency plan [START_REF] Belouchrani | Blind source separation based on time-frequency signal representations[END_REF]. However, in the cyclo-stationary sources case, the Delay-Doppler frequency domain seems to be a more natural field for the re-estimation of sources than the time-frequency domain. As mentioned in [START_REF] Amin | Blind time-frequency analysis for source discrimination in multisensor array processing[END_REF], the approaches based on information derived from spatial Ambiguity function (SAF) or on SGMAF should be used. In fact, for any vectorial complex signal z(t), the SGMAF is expressed as [START_REF] Hlawatsch | Temps-fréquence et traitement statistique[END_REF][START_REF] Kozek | On the transfer function calculus for underspread ltv channels[END_REF][START_REF]Matched weyl-heisenberg expansions of nonstationary environments[END_REF]:

Āz (ν, τ ) = ∞ -∞ r z (t, τ )e -j2πνt dt = E { z, s τ,ν z } , (4)
where (s τ,ν z) is the operator of elementary Delay-Doppler translations of z defined by

(s τ,ν z)(t) = z (t -τ ) e j2π(t-τ )ν and r z (t, τ ) = R z t + τ 2 , t -τ 2 = E z t + τ 2 z H t -τ 2
, where R z (t, τ ) stands for the correlation matrix of z(t), E {.} stands for the mathematical expectation operator and superscript (.)

H denotes the conjugate transpose operator. Āz (ν, τ ) characterizes the average correlation of all pairs separated by τ in time and by ν in frequency [START_REF] Kozek | On the transfer function calculus for underspread ltv channels[END_REF], [START_REF]Matched weyl-heisenberg expansions of nonstationary environments[END_REF]. Notice that the diagonal terms of the matrix Āz (ν, τ ) are called auto-terms, while the other ones are called cross-terms.

ISSN: 2088-8708

Selection of peaky Delay-Doppler points

Under the linear data model in (3), the SGMAF of observations across the array at a given Delay-Doppler point is a (m × m) matrix admits the following decomposition:

Āx (ν, τ ) = H Ās (ν, τ )H H + Ān (ν, τ ), = H Ās (ν, τ )H H + R n (τ ), (5)
where Ās (ν, τ ) represents the (n × n) SGMAF of sources defined similarly to Āz (ν, τ ) in ( 4) and

R n (τ ) = σ 2 n α(τ )I m with α(ν) = ∞ -∞ e -j2πνt
dt and I m is the m × m identity matrix. It is known that the matrix Ās (ν, τ ) for any τ and ν has no special structure. However, there are some Delay-Doppler points where this matrix has a specific algebraic structure :

• Diagonal, for points where each of them corresponds to a single auto-source term for all source signals,

• Zero-diagonal for points where each of them correspond to all two by two cross-source term (this structure is exploited because the signature of the sources differ in certain points of the Delay-Doppler plan on the zero-diagonal part (as shown in section 5.).

Our aim is to take advantage of these properties of the Āx (t, ν) in ( 5) since the element of this is no more (zero) diagonal matrices due to the mixing effect in order to estimate the separation matrix B (the pseudo-inverse of matrix H) and restore the unknown sources. We use the detector suggested in [START_REF] Fadaili | Nonorthogonal joint diagonalization/zero diagonalization for source separation based on time-frequency distributions[END_REF] (denoted C Ins ) for the instantaneous mixture considered without pre-whitening of the observations. The idea is to find "useful" Delay-Doppler points which consists in keeping Delay-Doppler points with a sufficient energy, then using the rank-one property to detect single cross-source terms (we don't make any assumptions on the knowledge of cyclic frequencies) in the following way:

     Āx (t, ν) > 1 , λ max Āx (t, ν) Āx (t, ν) -1 > 2 , (6)
where 1 , 2 are (sufficiently) small positif values and λ max {.} is the largest eigenvalue of a matrix.

Non-unitary joint zero-(block) diagonalization algorithms (NU -JZ(B)D)

The matrices belonging to the set M (whose size is denoted by N m (N m ∈ N * )) all admit a particular structure since they can be decomposed into H Ās (ν, τ )H H with Ās (ν, τ ) a zero-diagonal matrix with only one non null term on its zero-diagonal. One possible way to recover the mixing matrix B is to directly joint zerodiagonalize the matrix set M. It has to be noticed that the recovered sources (after multiplying the observations vector by the estimated matrix B) are obtained up to a permutation (among the classical indetermination of the BSS). Hence, two BSS methods can be derived. The first called JZD CG DD algorithm based on conjugate gradient approach [START_REF] Cherrak | Non-unitary joint zeroblock diagonalization of matrices using a conjugate gradient algorithm[END_REF]. The second JZD LM DD algorithm based on Levenbreg-Marquardt scheme [START_REF] Cherrak | Nouvel algorithme de zéro-bloc diagonalisation conjointe par approche de levenberg-marquardt[END_REF].

To tackle that problem, we propose here, to consider the following cost function [START_REF] Cherrak | Non-unitary joint zeroblock diagonalization of matrices using a conjugate gradient algorithm[END_REF], [START_REF] Cherrak | Nouvel algorithme de zéro-bloc diagonalisation conjointe par approche de levenberg-marquardt[END_REF],

C ZBD (B) = Nm i=1 Bdiag (n) {BM i B H } 2 F
, where the matrix operator Bdiag (n) {.} is defined as follows:

Bdiag (n) {M} =     M 11 0 12 . . . 0 1r 0 21 M 22 . . . 0 2r . . . . . . . . . . . . 0 r1 0 r2 . . . M rr     ,
where M is a N × N (N = n(L + L ) where L is the order of the FIR filter and L is the number of delays considered when the convolutif mixture is considered) square matrix whose block components M ij for all i, j = 1, . . . , r are n i × n j matrices (and n 1 + . . . + n r = N ) denoting by n = (n 1 , n 2 , . . . , n r ). Note that when L = 0, L = 1 we find the instantaneous model since Āx are no more matrices but scalars. Thus, it leads to the minimization of the following cost function: IJECE ISSN: 2088-8708 1737

C ZD (B) = Nm i=1 Diag{BM i B H } 2 F , (7)
where M i = Āx i is the i -th of the N m matrices belonging to M. We suggest to use conjugate gradient and Levenberg-Marquardt algorithms [START_REF] Cherrak | Non-unitary joint zeroblock diagonalization of matrices using a conjugate gradient algorithm[END_REF], [START_REF] Cherrak | Nouvel algorithme de zéro-bloc diagonalisation conjointe par approche de levenberg-marquardt[END_REF] to minimize the cost function given by Equation . [START_REF]Improved Satellite Detection of AIS[END_REF] in order to estimate the matrix B ∈ C n×m . It means that B is re-estimated at each iteration m (denoted B (m) or b (m) when the vector b (m) = vec B (m) is considered). The matrix B (or the vector b) is updated according to the following adaptation rule for all m = 1, 2, . . .

Conjugate gradient approach

b (m+1) = b (m) -µ (m) d (m) B , d (m+1) B = -g (m+1) + β (m) d (m) B , ( 8
)
where µ is a positive small factor called the step-size, d B is the direction of search, β is an exact line search and [START_REF] Cherrak | Non-unitary joint zeroblock diagonalization of matrices using a conjugate gradient algorithm[END_REF] how the optimal step-size µ opt , ∇ a C ZD (B)

g = vec (∇ a C ZD (B)) is the vectorization of the complex gradient matrix G = ∇ a C ZD (B) = 2 Nm i=1 [Diag{BM i B H }BM H i + Diag{BM i B H } H BM i (see the proof provided in
and β are calculated at each iteration).

Levenberg-Marquardt approach b (m) = b (m-1) -H (m-1) e + λI m 2 -1 g (m-1) , (9)
where [.] -1 denotes the inverse of a matrix, λ is positive a small damping factor,

I m 2 is the m 2 × m 2 identity matrix, H e = H eB,B * = A00+A T 11 2 H eB * ,B * = A01+A T 01 2 H eB,B = A10+A T 10 2 H eB * ,B = H eB,B * T
is the Hessian matrix of C ZD (B) composed of four complex matrices with:

A 00 = M T i B T ⊗ I N T T Boff (B * M * i ⊗ I N ) + M * i B T ⊗ I N T T Boff B * M T i ⊗ I N + M * i ⊗ OffBdiag (n) {BM i B H } +M T i ⊗ OffBdiag (n) {BM H i B H } = A * 11 , (10)
A 10 =K T N,M I N ⊗ M i B H T T Boff (B * M * i ⊗ I N ) + K T N,M I N ⊗ M H i B H T T Boff B * M T i ⊗ I N = A * 01 , (11)
where the operator ⊗ denotes the Kronecker product, K N,M is a square commutation matrix of size N M × N M and T Boff = I N 2 -T Diag , is the N 2 × N 2 "transformation" matrix, with T Diag = diag{vec(BDiag{1 N })}, 1 N is the N × N matrix whose components are all ones, diag{a} is a square diagonal matrix whose diagonal elements are the elements of the vector a, I N 2 = Diag{1 N 2 } is the N 2 × N 2 identity matrix, and Diag{A} is the square diagonal matrix with the same diagonal elements as A.

Summary of the proposed methods

The proposed methods JZD CG DD and JZD LM DD combine the NU -JZD algorithms which are JZD CG and JZD LM together with the detector C Ins . Its principles are summarized below: Data: Consider the Nm matrices of set M : { Āx 1 , Āx 2 , . . . , Āx Nm }, stopping criterion , step-size µ (for conjugate gradient), max. number of iterations Mmax Result: Estimation of joint zero diagonalizer B initialize: B (0) ; λ (0) ; m = 0; D (0) (for conjugate gradient);

COMPUTER SIMULATIONS

Computer simulations are performed to illustrate the good behavior of the suggested methods and to compare them with the same kind of existing approach denoted by JZD Chabriel DD proposed in [START_REF] Chabriel | Algebraic joint zero-diagonalization and blind sources separation[END_REF] with the Delay-Doppler point C Ins detector. We consider m = 3 mixtures of n = 2 frames of 256 bits correspond to two vessels with different characteristics. The frames are generated according to the S-AIS recommendation as mentioned in the Figure 2 (see also [START_REF] Zhou | Multi-user leo-satellite receiver for robust space detection of ais messages[END_REF], [START_REF] Prevost | Interference mitigation and error correction method for ais signals received by satellite[END_REF]). These frames are encoded with NRZI and modulated in GMSK with a

The real part and the imaginary part of their SGMAF is given on the left and on the right of the Figure 4 respectively. Then, the SGMAF of the observations x is then calculated by ( 5) and finally the 100 resulting SGMAF are averaged. We have chosen 1 = 0.07 and 2 = 0.08 for the detector C Ins in order to construct the set M to be joint zero-diagonalized. The signal-to-noise ratio SNR is defined by SNR = 10 log( 1

σ 2 N
) of mean 0 and variance σ 2 n . The selected Delay-Doppler points using the proposed detector are represented in the Figure 5 for SNR = 10 dB and 100 dB. To measure the quality of the estimation, the ensuing error index is used [START_REF] Moreau | A generalization of joint-diagonalization criteria for source separation[END_REF] :

The SGMAF of the source 1

I(T) = 1 n(n -1)   n i=1   n j=1 T i,j 2 F max T i, 2 F -1   + n j=1   n i=1 T i,j 2 F max T ,j 2 F -1     , (13)
where (T ) i,j for all i, j ∈ 1, . . . , n is the (i, j)-th element of T = BH. The separation is perfect when the error index I(•) is close to 0 in a linear scale (-∞ in a logarithmic scale). All the displayed results have been averaged over 30 Monte-Carlo trials. We plot, in the Figure 6, the evolution of the error index versus the SNR in order to emphasize the influence of this in the quality of the estimation. All algorithms are initialized using the same initialization suggested in [START_REF] Chabriel | Algebraic joint zero-diagonalization and blind sources separation[END_REF]. First, we can deduce from the Figure 4 that the diversity in the Delay-Doppler regions is obtained on the zero-diagonal part which supports the use of zero diagonalization algorithms. Then, our analysis are examined on the Figure 6 according to noiseless and noisy contexts . For the noiseless context (when SNR=100 dB), the JZD CG DD and JZD LM DD reach approximately -64 dB and -60 comparing with JZD Chabriel DD method which reaches -20 dB. From this comparison, we have checked the validity of the good behavior of JZD CG DD and JZD LM DD compared to the JZD Chabriel DD approach. Moreover, we observe that the JZD LM DD based on the computation of exact Hessian matrices is more efficient than the JZD CG DD approach. Even in a difficult (noisy) context (for example SNR=15 dB), we note that the best results are generally obtained using the JZD LM DD (-36 dB) then JZD CG DD (-33 dB) especially the JZD LM DD algorithm based on the computation of exact Hessian matrices. It may be concluded that the approaches exploiting the Delay-Doppler diversity of S-AIS signals seem rather promising. Due to its robustness to the noise, it seems to be able to solve the problem of BSS (i.e the collision problem) in a marine surveillance context.

Figure 1 .

 1 Figure 1. Collision problem: The AIS signals from two different SO-TDMA cells received to the satellite antenna at the same time.

Figure 2 .

 2 Figure 2. AIS Frame.

4. 3 .

 3 Construction of M (set of Delay-Doppler matrices of the observations across the array at the chosen Delay-Doppler points)

ISSN 10 ,

 10 B (m+1) -B (m) 2 F ≤ ) ou (m ≥ Mmax)); Levenberg-Marquardt repeat Calculate g (m)Calculate the diagonal of He Calculate b (m+1) Calculate the error e(m) = 1 Nm C ZD (B (m+1) ) m = m + 1; if e (m) ≥ e (m-1) then λ (m) = λ (m-1) e (m) = e (m-1) else λ (m) = 10λ (m-1) end until (( B (m+1) -B (m) 2 F ≤ ) ou (m ≥ Mmax));bandwidth-bit-time product parameter BT= 0.4. The transmission bit rate is = 9600 bps and the order gaussian filter is OF= 21. The frequency carrier of the first source (resp. the second source) is 161.975 MHz (resp. 162.025 MHz), taking into account a delay of 10 ms and a Doppler shift of 4 kHz (resp. a delay of 0 ms and the Doppler shift of 0 Hz). These sources correspond to 1400 time samples which are mixed according to a mixture matrix H whose components stands for:

Figure 4 .

 4 Figure 4. Left : The SGMAF real part of the S-AIS sources. Right : The SGMAF imaginary part of the S-AIS sources.

Figure 5 .

 5 Figure 5. Delay-Doppler points selected with the detector C Ins . left : SNR=100 dB. right : SNR=10 dB.

Figure 6 .

 6 Figure 6. Comparison of the different methods: evolution of the error index I(T) in dB versus SNR.

ISSN: 2088-8708

CONCLUSION

In this paper, we have shown that the blind source separation based on SGMAF can be performed. We have considered complex-valued S-AIS data for marine surveillance which can be received at the same time-slot in where the collision of these data is caused. In addition, it is presented that the collision problem can be reshaped into BSS problem. Moreover, it is shown that proposed BSS methods are established thanks to an automatic single cross-term selection procedure combined with two NU -JZD algorithms denoted Conjugate Gradient and Levenberg-Marquardt which are based on the minimization of a least-mean-square criterion. Finally, we deduced that the JZD LM DD and JZD CG DD offer the best performances even in noisy contexts. As perspective, a question needing analysis is to study more realistic and complex cases in which the number of S-AIS messages received at the antenna embedded in the satellite would be much higher and mixing models could also be considered.