D Ballivet-Tkatchenko

Séverine Camy

Jean-Stéphane S Condoret

Carbon Dioxide, a Solvent and Synthon for Green Chemistry

Keywords: carbon dioxide fixation, supercritical carbon dioxide, catalysis, dialkyl carbonate, dimethyl carbonate, phase equilibria, fractionation

come

Introduction

The development of environmentally-improved routes and the design of green chemicals are two facets of Green Chemistry devoted to reducing the impact of chemical processes and compounds on the environment [START_REF] Anastas | The role of catalysis in the design, development, and implementation of green chemistry[END_REF]. To reach the ultimate goals of cleaner production and sustainable development, new and improved syntheses of chemicals have to meet economics, ecological and social criteria [START_REF] Vollenbroek | Sustainable development and the challenge of innovation[END_REF]. The design of chemical reactions minimising waste, air emission, and hazardous reactants is on the way to environmentally benign technologies. For the academic chemist, minimisation of waste and emission relies on chemical yield, selectivity, and atom utilisation [START_REF] Sheldon | Consider the environmental quotient[END_REF]. Therefore, catalytic processes likely to provide rapid and selective chemical transformations as well as effective recovery of both catalyst and product, without creating environmental problems, do have a significant impact in the chemical industry. In most cases catalyst recovery and recycling is of paramount importance for the economics of the process due to multistage, sophisticated, and costly recycling operations. The alternative of leaving-in the catalyst is acceptable in few cases. For example, the latest generations of Ziegler-Natta and metallocenebased catalysts are so productive that the catalyst present in concentration at the ppm level is left in the polyolefin product [START_REF] Mülhaupt | Novel polyolefin materials and processes: overview and prospects[END_REF].

Carbon Dioxide as a Solvent

In organic synthesis, most reactions are performed in the liquid state by the addition of a solvent with several beneficial purposes: (i) bringing the reactants to a single phase for rate enhancement, (ii) decreasing the viscosity of the reacting mixture for better diffusion of the reactive species, and (iii) providing easier mastering of heat effects. It should be pointed out that when one of the reactants is in the gaseous state (dihydrogen, carbon monoxide, dioxygen, …), the gas-liquid mass transfer is often rate determining. The use of toxic solvents contributes to air emission of volatile organic compounds (VOCs) and of chloro hydrocarbons; they are now considered as environmentally unacceptable [START_REF] Eckert | Tuning fluid solvents for chemical reactions[END_REF]. In the field of soluble metal-based catalysts, a considerable progress has been achieved through the concept of diphasic liquid-liquid catalysis: here the catalyst is recovered in one liquid phase and the product in the other one. This has led to drastic technological improvements but it has only reached single cases of industrialisation (Keim 1984;[START_REF] Cornils | Introducing TPPTS and related ligands for industrial biphasic processes[END_REF][START_REF] Driessen-Hölscher | Multiphase homogeneous catalysis[END_REF]. Further possibilities deserve attention with promising results in the use of fluorous solvents [START_REF] Horvath | Fluorous biphase chemistry[END_REF], non-aqueous ionic liquids [START_REF] Wasserscheid | Ionic liquids-New solutions for transition metal catalysis[END_REF], and supercritical media (Jessop and Leitner 1999). These systems are potentially cost-effective by combining reaction and separation into a single reactor [START_REF] Freemantle | Eyes on ionic liquids[END_REF].

The ideal supercritical fluid (SCF) should be non-toxic for man and the environment, non-carcinogen, non-flammable, and its intrinsic chemical reactivity should not be the source of runaway reactions. Concerning carbon dioxide, its impact in the global warming may be a handicap, but, when CO 2 applications are implemented, carbon dioxide is never released to the environment. While commercial developments of supercritical carbon dioxide (scCO 2 ) technology are successful for separation and extraction, its application as a reaction medium and as a reactant are still in its infancy (Jessop and Leitner 1999;[START_REF] Noyori | Supercritical fluids[END_REF]. The wide range of miscibility of gaseous reactants, e.g. dihydrogen and dioxygen, in supercritical fluids simplifies greatly the design of reactors in comparison with conventional ones which operate under di-or triphasic conditions. Furthermore the good transport properties of these fluids (viscosity, diffusivities) allow to design small and efficient reactors, where catalysts may have longer lifetime. The post-reacting separation is likely to be easy. Small temperature or pressure variations lead to solvent-free products. Fractionation of the effluent is also possible without involving any further separating agent. The greatest safety concern of supercritical fluids is the use of high pressure components in the process equipment.

Carbon Dioxide as a C1-Building Block for Chemicals

Carbon dioxide, one of the major man-made greenhouse gases, is a renewable resource of carbon when we consider the reuse of existing CO 2 as a carbon source for producing chemicals. The industrial syntheses of urea, cyclic carbonates, salicylic acid, and methanol already involve carbon dioxide as a reactant. Nowadays, the development of new applications is of major interest from the point of view of carbon dioxide sequestration and within the scope of green chemistry [START_REF] Dinjus | Carbon dioxide as a C1-building block[END_REF]. Using CO 2 instead of CO or COCl 2 constitutes an attractive alternative avoiding hazardous and toxic components [START_REF] Aresta | Carbon dioxide: a substitute for phosgene[END_REF]. However, it has the lowest chemical reactivity which is a serious drawback for its transformation/incorporation to organic molecules. Several ways of activation are currently under investigation; among them catalysis offers a number of options, but it still is a challenge to find activities of practical interest.

We focused our research on new syntheses for open chain organic carbonates because their production is historically dominated by phosgene chemistry (Fig. 49.1, route A). The unfavourable opinion on the phosgene industry concerns the environmental impact, transport, safety and waste elimination. The lethal concentration threshold for a 30 min exposure is 10 ppm, as compared to 870, 4 000, and 30 000 ppm for dichlorine, carbon monoxide, and ammonia, respectively. In addition, the wastes contain hydrogen chloride as well as chlorinated solvents, and they have to be treated prior to disposal. These environmental and safety handicaps motivate the development of new technologies for commodity chemicals (>10 000 t yr -1 ). Its industrial use is likely to be confined to small groups of experts who are properly equipped [START_REF] Senet | Phosgene chemistry and environment, recent advances clear the way to clean processes: a review[END_REF]. For the production of dimethyl carbonate (DMC), catalytic alternatives via the oxidative carbonylation of methanol (Fig. 49.1, route B) have provided an answer [START_REF] Rivetti | The role of dimethyl carbonate in the replacement of hazardous chemicals[END_REF]. However, the use of carbon monoxide imposes safety constraints and the use of dioxygen requires a strict control of the kinetics.

Dimethyl carbonate (DMC) is an alternative to phosgene in carbonylation reactions, and a substitute for methyl halides and dimethyl sulfate in methylation reactions [START_REF] Tundo | New developments in dimethyl carbonate chemistry[END_REF]. Its current production is estimated to be around 80 000 t yr -1 worldwide, with a growing demand for captive use by polycarbonate firms. DMC has a low toxicity, is not corrosive, and will not produce environmentally damaging byproducts (no organics or salts). If the economics of the current technologies were more favourable, the market potential could be an order of magnitude higher because DMC is a good candidate for the replacement of methyl tert-butyl ether (MTBE) as a fuel additive [START_REF] Pacheco | Review of dimethyl carbonate manufacture and its characteristics as a fuel additive[END_REF]. As a consequence, alternative reactions are under investigation. Among them, reacting methanol (or dimethyl acetals) and CO 2 Three reaction routes to open chain carbonates from alcohol and C1-building blocks in the presence of a catalyst (Fig. 49.1, route C) leads to DMC under supercritical conditions [START_REF] Isaacs | High pressure routes to dimethyl carbonate from supercritical carbon dioxide[END_REF][START_REF] Ballivet-Tkatchenko | Reactivity of carbon dioxide with butyl(phenoxy)-, (alkoxy)-and (oxo)stannanes: insight into dimethyl carbonate synthesis[END_REF]; a drastic increase in activity is found if the experiments are conducted at ca. 2 000 bar and 180 °C [START_REF] Sakakura | Metal-catalyzed carbonate synthesis from carbon dioxide and acetals[END_REF]. There is a real challenge from these very first results to commercial application, because on one hand the activity is low and on the other hand the most active systems are tin(IV) compounds which are not environmentally friendly. An important task is the knowledge of the reaction mechanisms involved to get structure-activity relationships. This paper addresses some issues on the chemistry and emphasises the reactor design under supercritical conditions for route C (Fig. 49.1). It also gives an insight to the complete process, including the post-reacting fractionation using potentialities of supercritical state.

Experimental General

All reactions were carried out under dry argon using Schlenk tube techniques. The solvents were purified by standard methods. The organotin compounds n-Bu 3 SnCl, n-Bu 2 SnCl 2 , n-BuSnCl 3 , (n-Bu 3 SnO) 2 , and (n-Bu 2 SnO) n were used as received from Aldrich and Acros Chimica for the syntheses of the alkoxystannanes derivatives according to already published procedures [START_REF] Ballivet-Tkatchenko | Reactivity of carbon dioxide with butyl(phenoxy)-, (alkoxy)-and (oxo)stannanes: insight into dimethyl carbonate synthesis[END_REF]. CO 2 N45 was purchased from Air Liquide. The 1 H, 13 C, and 119 Sn nuclear magnetic resonance (NMR) spectra were measured at 500.132, 125.770, and 186.501 MHz, respectively, on a Bruker DRX 500 spectrometer. For a detailed description and assignment of the experimental spectra see [START_REF] Ballivet-Tkatchenko | Reactivity of carbon dioxide with butyl(phenoxy)-, (alkoxy)-and (oxo)stannanes: insight into dimethyl carbonate synthesis[END_REF]. Infrared spectra were obtained with a FT-IR Bruker Vector 22 spectrometer, the sample being placed between NaCl windows either as neat or dispersed in Nujol. Elemental analysis was performed at the Laboratoire de Synthèse et Electrosynthèse Organométalliques, Université de Bourgogne, Dijon.

Volumetry

A Schlenk tube containing 1 mmol of the tin compound in 1 ml of toluene was connected to a pressure transducer and to a CO 2 reservoir of known pressure and volume, maintained at 19 °C. The amount of CO 2 gas absorbed by tin compound was calibrated by reference experiments. The calculated CO 2 :Sn molar ratio was at ±0.05.

Reaction under CO 2 Pressure

In a 100-ml stainless steel batch reactor, a solution (10-30 ml) of the tin compound (4 mmol Sn) was introduced. The reactor was pressurised with CO 2 , heated to 145 °C, then the CO 2 pressure was adjusted to the desired value, typically between 90 and 220 bar. After the run, the reactor was cooled to 0 °C, depressurised, and the liquid phase was analysed by gas chromatography (Fisons 8000, FID detector, J&W Scientific DB-WAX 15 m megabore column) and gas chromatography-mass spectrometry for identification (Fisons MD 800, EI 70 eV, J&W Scientific DB-1 60 m capillary column). Evaporation of the volatiles under vacuum at room temperature allowed to characterise the residue by NMR.

Experimental Set-up for the Fractionation Study

For the fractionation study, we have used an experimental process schematically shown on Fig. 49.2, comprising a 200 ml contacting vessel C (the reactor) followed by three cyclonic separators S1, S2, and S3 (ca. 20 ml each). As an efficient immobilised catalyst has not yet been found, the reaction could not be operated experimentally. We therefore worked with a mimicked reacting mixture in the contacting vessel where an intimate contact between a methanol-dimethyl carbonate-water mixture and CO 2 entering the process takes place. A constant feed flow rate of CO 2 of ca. 4 kg h -1 is kept. The outgoing fluid from the contactor C composed of a CO 2 -methanol-dimethyl carbonate-water quaternary mixture undergoes a three successive depressurisation stages S1, S2, and S3, in order to recover the targeted components (DMC and water), and to recycle CO 2 and methanol.

Liquid phase analyses were done by gas chromatography with a Hewlett-Packard 5890 series II chromatograph equipped with a Supel-QTM Plot capillary column (30 m, 0.53 mm ID) from Supelco (USA) and a thermal conductivity detector (TCD). Synthetic mixtures were prepared from distilled water, dimethyl carbonate (Aldrich, 99%, D15,292-7), and methanol (Prolabo Chromanorm, min. 99.8%, 20834.291).

Numerical Methods for Thermodynamic Calculations

In this study, phase equilibria are calculated using the cubic equation of state proposed by Redlich and Kwong [START_REF] Redlich | On the thermodynamics of solution. V: An equation of state. Fugacities of gazeous solutions[END_REF], modified by Soave [START_REF] Soave | Equilibrium constants from a modified Redlich-Kwong equation of state[END_REF], and named SRK equation. To account for interaction taking place between components in the mixture, the "MHV-2" mixing rules, developed by Huron and Vidal [START_REF] Huron | New mixing rules in simple equations of state for representing vapourliquid equilibria of strongly non-ideal mixtures[END_REF] and modified by Michelsen [START_REF] Dahl | High-pressure vapor-liquid equilibrium with a UNIFAC-based equation of state[END_REF], are used. This type of modelling is now commonly recognised as a good choice for high pressure phase equilibrium calculations involving polar compounds, as it is the case in this study. Equations of state such as SRK equation give satisfying results at high pressure but have to be used only when dealing with apolar or poorly polar compounds. Conversely, activity coefficient models (differently named γ-φ approach) cannot be used at high pressure but are particularly appropriate for thermodynamic calculations involving polar compounds. The MHV-2 approach conciliates these two application domains, involving an activity coefficient model into mixing rules of an equation of state. The UNIQUAC activity coefficient model [START_REF] Abrams | Statistical thermodynamics of liquid mixtures: a new expression for the excess Gibbs energy of partly or complete miscible systems[END_REF] has been chosen to determine the value of the free excess Gibbs energy needed in the calculation of the mixture parameters.

Thermodynamic models have proved to be of great help in predicting thermodynamic behaviour of mixtures. However, these models need specific mixture parameters, reflecting interactions between the components in the mixture, that are obtained by fitting a limited set of experimental equilibrium data. The data used to determine mixture parameters can be equilibrium data from the binary or ternary sub-systems constituting the quaternary methanol-CO 2 -water-DMC mixture. In our case, some binary or ternary data can be found in the existing literature. For DMC-water and DMC-CO 2 mixtures, no experimental work is available, and experiments have been necessary. Such new results are now available from our recent publication [START_REF] Camy | Fluid phase equilibria of the reacting mixture in the dimethyl carbonate synthesis from supercritical CO 2 . J of Supercritical Fluids[END_REF]. Binary interaction parameters are calculated using the commercial software ProReg™ (PROSIM S.A., France). This model fed by adequate binary interaction coefficients allows us to describe the thermodynamic behaviour of the reacting mixture in the reactor itself and in the separation system.

Results and Discussion

Mechanistic Approach for Dimethyl Carbonate Formation

Our interest in the reaction of carbon dioxide with alcohols to afford dialkyl carbonates led us to focus on the mechanistic approach with tin compounds. These compounds were chosen because 119 Sn NMR spectrocopy provides useful information on the number of tin species and their coordination [START_REF] Hani | 119 Sn NMR in coordination chemistry[END_REF] in addition to 1 H and 13 C spectra. IR spectroscopy was also used to monitor the presence of absorption bands of the carbonate moieties. It is not intended to report here in details the synthesis and characterisation of the compounds as preliminary results have already been published [START_REF] Ballivet-Tkatchenko | Reactivity of carbon dioxide with butyl(phenoxy)-, (alkoxy)-and (oxo)stannanes: insight into dimethyl carbonate synthesis[END_REF]. It is more important to summarise and emphasise some elementary reaction steps for the purpose of reactor design.

Several tin(IV) compounds were studied, n-Bu 3 SnCl (Bu = butyl), (n-Bu 3 SnO) 2 , n-Bu 3 SnOR (R = phenyl, methyl), n-Bu 2 SnCl 2 , (n-Bu 2 SnO) n , n-Bu 2 Sn(OR) 2 (R = phenyl, methyl, isopropyl, tert-butyl), n-BuSn(OCH 3 ) 3 , Ph 3 SnOCH 3 (Ph = phenyl), and Ph 2 Sn(OCH 3 ) 2 . The fixation of carbon dioxide was effective for compounds containing OR groups, preferably methoxy and isopropoxy. The new species formed is the result of carbon dioxide insertion in the Sn-OR bond, leading to the carbonate fragment Sn-OC(O)OR. At room temperature and atmospheric pressure, the reaction is reversible leading back to Sn-OR. Volumetric experiments showed that reaction stoichiometry is CO 2 :Sn = 1, whatever the initial number of alkoxy fragments. Therefore, only one OR group is reacting. This result has been assigned to the dimeric structure of the polyalkoxystannes as shown in Fig. 49.3 for n-Bu 2 Sn(OCH 3 ) 2 . A recent X-ray single crystal structure determination of (CH 3 ) 2 Sn(OCH 3 ) 2 and its carbonated form strengthens this assignment [START_REF] Choi | Reaction of dialkyltin methoxide with carbon dioxide relevant to the mechanism of catalytic carbonate synthesis[END_REF].

The formation of dialkyl carbonates was only found for the polyalkoxybutylstannanes. For example, starting from n-Bu 2 Sn(OCH 3 ) 2 dimethyl carbonate is quantitatively produced (DMC:Sn = 1) upon heating a methanolic solution at 150 °C under 200 bar of carbon dioxide. Further experiments conducted in toluene instead of methanol point out that methanol is not directly involved in DMC formation [START_REF] Ballivet-Tkatchenko | CO 2 as a C 1 -building block for dialkyl carbonate synthesis[END_REF]). An intra-molecular rearrangement of the tin coordination sphere is taking place, but, in the overall reaction, methanol and carbon dioxide should be the reactants for the catalytic cycle (Fig. 49.1, route C). Under these experimental conditions, CO 2 reaches the supercritical state (P c = 73.8 bar, T c = 31 °C). Supercritical CO 2 as a solvent and a reactant has a great potential for optimising chemical reactions (Jessop and Leitner 1999); however, in our case the origin of the enhanced chemical reactivity is not clear as the phase behaviour under reaction conditions have a great influence. It can also be expected that CO 2 pressure has a beneficial effect on the carbonation reaction, which was found to be reversible at room temperature and atmospheric pressure.

Dimethyl Carbonate Synthesis Using Supercritical CO 2

Operation of chemical reactions in supercritical media is regularly emphasised by experts in the domain as a very promising field of research. Nevertheless, conception of reactors, as well as optimum choice of operating conditions, are still to be developed.

It is now well admitted in chemical engineering strategy, that conception of the post-reacting separation as early as the conception of the reactor, leads to more effi-Dimeric arrangements for n-Bu 2 Sn(OCH 3 ) 2 and its carbonated form cient processes. It is particularly true for supercritical media, because their adjustable solvation power is a very convenient way to operate the purification of products. In the case of the carbonation reaction of methanol (Fig. 49.1, route C), there is an additional reason, because one product of the reaction, water, has a detrimental effect on a possible reversal of carbonation reaction, as well as on the good operation of the catalyst. This implies that it would be preferable to eliminate reaction products as the reaction proceeds, in order to shift the equilibrium of the reaction. As a consequence the study of the entire process could be of a great help for optimising the reaction, and investigation of the fractionation process implemented at the output of the reactor has to be undertaken.

One first compulsory initial stage is to study the thermodynamic behaviour of the reacting mixture, i.e. the quaternary methanol-CO 2 -water-DMC mixture. This knowledge is essential to characterize the possible coexisting phases in the reactor and define the optimum reaction conditions, as well as to design the post-reacting fractionation device.

Study of Operating Conditions in the Reactor

The main information needed is the description of phase equilibria existing in the reactor as a function of pressure and temperature. For this, a hypothetical perfectly mixed continuous reactor, fed with a methanol-CO 2 mixture, is considered. The DMC synthesis takes place with an arbitrarily chosen conversion, i.e. the concentrations inside the reactor are accordingly. Then the physical state of the mixture in this hypothetical reactor is calculated thanks to the thermodynamic model described above.

Figure 49.4 presents, for two different mixtures in the reactor, the coexistence zones of monophasic and diphasic states. In each diagram, qualitative information about the state of the mixture is marked for each domain. The letter L refers to a liquid phase, whose density is high (ca. 800-900 kg m -3 ). Conversely, the vapour state, marked with the letter V, refers to a low-density phase (<100 kg m -3 ). Finally, the letter F designates a fluid state whose density lies between that of a liquid and a gas. Because the critical line of this quaternary mixture was not calculated here, these denominations remain qualitative. Figure 49.4 shows that for a methanol rich mixture (diagram a), no fluid phase is present and there is a large diphasic liquid-liquid (L1-L2) zone, where a first liquid phase, mainly composed of water and methanol, is in equilibrium with a second liquid phase containing a large proportion of CO 2 and DMC. This equilibrium zone exists for low temperatures, at a pressure greater than about 80 bar. A second diphasic liquid-vapour zone (L-V) is present at low pressures, consisting in the equilibrium between a liquid phase and a CO 2 rich vapour phase. The main monophasic zone is a liquid (L); however, at high temperatures and low pressures, a restricted monophasic vapour phase zone (V) is evidenced. For a CO 2 rich feed (diagram b), the phase diagram undergoes perceptible modifications. Indeed, the diphasic zone is here further reduced and no liquid-liquid equilibrium is now observed. In this case, there is no longer liquid-liquid diphasic zone and a liquid-vapour zone (L-V) transforming into a liquid-fluid zone (L-F) is now present. At higher pressure and temperature we now observe a plain fluid phase.

Study on dimethyl carbonate synthesis mechanism has shown that, for the moment, the most interesting results are obtained using polyalkoxybutylstannane catalysts, being active at about 150 °C. Moreover, to avoid mass transfer limitations which are likely to occur with the low-pressure diphasic system liquid mixture-gaseous CO 2 (Kizlink andPastucha 1994, 1995), the reaction will advantageously be operated in a monophasic reacting mixture, and preferably in a "fluid" state, or vapour state. By comparison with the vapour state, the "fluid" state, that corresponds to higher pressures, is more interesting because (i) the volume of the reactor will be smaller (ii) the effect of pressure has been proved to be positive on the kinetics of the reaction, and (iii) the separation of the reaction products can be made easier by using the tunable solvent power of supercritical fluids. From Fig. 49.4 it can be concluded that, to be sure of running the reaction in a homogeneous fluid medium, a large excess of CO 2 is needed. Moreover, for such mixtures, a drop of pressure and temperature after the reactor would easily allow a return to a diphasic state, with a view to obtaining an efficient mixture fractionation. This last topic is the aim of the next part.

Study of the Mixture Fractionation

As previously mentioned, it is worthwhile to investigate the feasibility of the fractionation of the effluent methanol-DMC-water mixture, and to test a convenient and quite Coexisting zones of monophasic and diphasic mixtures at 60% conversion for: a methanol rich feed, b CO 2 rich feed simple process, generally used to run post-extraction fractionation in supercritical technology (Fig. 49.2). Due to the great number of parameters, this study of the postreacting fractionation cannot only lean on an experimental approach. Modelling of the process must be developed in order to represent the dynamic behaviour of the whole experimental process. Indeed, even if this kind of pilot is often used to operate extraction operations, the literature proposes very few results dealing with its dynamic modelling.

Our description of the process is based on the conventional chemical engineering concept of theoretical stage of equilibrium. A simplified numerical approach used to solve dynamic mass balances has been proposed and validated in comparison with a rigorous resolution of the algebro-differential system of equations [START_REF] Camy | Dynamic modelling of a fractionation process for a liquid mixture using supercritical carbon dioxide[END_REF]. The results of the modelling were compared to experiments and gave good results for the contactor, while it was not very satisfactory for the description of the separation. Even if discrepancies between experimental and calculated results may probably originate from experimental procedure, and because we think that thermodynamic modelling is correct, hydrodynamic description of the separators is here likely to be oversimplified. The cyclonic separators cannot be regarded as simple theoretical stages as it is often done in the literature [START_REF] Camy | Fluid phase equilibria of the reacting mixture in the dimethyl carbonate synthesis from supercritical CO 2 . J of Supercritical Fluids[END_REF]). We proposed an other description [START_REF] Camy | Dynamic modelling of a fractionation process for a liquid mixture using supercritical carbon dioxide[END_REF], that, although more suitable, needs still to be improved by taking into account, for instance, the imperfect collection of droplets.

Our work has shown that is not realistic to envisage the separation of the resulting methanol-dimethyl carbonate-water mixture with such a simple device because components have too strong affinities. The use of simple separators in order to separate a liquid mixture when volatility of components, as well as their solubility into CO 2 , are comparable, is not enough efficient. Under progress is now the use of modelling to investigate the feasibility of this separation, either using a greater number of separators, or by implementing a more complex strategy of separation. For instance a suitable way would be to consider the operation of one or several counter current columns of separation. Together with advances in the conception of an efficient catalyst, these approaches will be a useful contribution to the success of a viable process from CO 2 .

Conclusion

Supercritical CO 2 as a reaction medium offers the opportunity to replace conventional organic solvents due to its adjustable solvation property as regards to both temperature and pressure, either pure or through the addition of solubilizers. The relatively mild critical point of CO 2 , its benign nature, easy handling, availability, non volatile emitting are particularly attractive for catalytic applications in chemical synthesis, over a wide range of temperatures and pressures. The benefits of coupling catalysis and supercritical fluids are both environmental and commercial: less waste and VOCs emission, improved separation and recycling, and enhanced productivity and selectivity.

The case study described in this paper is of significant interest because the carbonation of alcohols to dialkyl carbonates replaces phosgene by carbon dioxide. Of course, carbon dioxide is much less reactive than phosgene, which means more energy input.

However, Life Cycle Analysis applied to the assessment of the environmental impact of the phosgene and carbon dioxide routes is greatly in favour of CO 2 [START_REF] Aresta | Life cycle analysis applied to the assessment of the environmental impact of alternative synthetic processes. The dimethyl carbonate case[END_REF]. The future of this molecule in green chemistry, including supercritical applications, is highly linked to the development of basic knowledge, know-how, and tools for the design of catalyst precursors as well as the technological conception of reactors and fractionation devices. The multi-component nature of a catalytic reaction (catalyst precursor, reactants, products), its changes upon time, and the pressure-temperature conditions make difficult the experimental approach. Synthetic chemistry, analytical chemistry, and chemical engineering are mandatory to cope with the abovementioned requirements. Indeed, chemical engineering can bring better knowledge of the rather uncommon thermodynamics in the reactor, and has demonstrated the interest of studying the coupling of the reaction and the separation.

  Pilot SF200. C: contactor; D1, D2, D3: depressurizarion valves; P: pressure pump; PI: pressure indicators; R: back pressure regulator; S1, S2, S3: separators; V1, V2, V3, V4: sampling valves

Acknowledgements

We are grateful for financial support of this work from the Centre National de la Recherche Scientifique under the programme "Catalyse et catalyseurs pour l'industrie et l'environnement".


Cédric Perez
email: cedric.perez@ensiacet.fr

Christine Lors

Benjamin Erable

Implication of Biofilm on the Biodeterioration of Cementitious Materials under Anaerobic Digestion Conditions

Keywords: Biodeterioration, Cementitious Material, Biofouling, Biofilm, Bacteria, Anaerobic Digestion

Introduction

Anaerobic digestion is a process where organic matter is degraded while producing two products of interest: the biogas and the digestate. The digestate can be used as a fertilizer for agriculture and the biogas has an energetic interest as it can either be burned to produce heat and/or electricity or be processed into natural gas or biofuel. Usually anaerobic digestion tanks are made in concrete. Furthermore, it is known that some chemical components, produced by the microorganisms during the anaerobic digestion process, are aggressive towards cementitious materials. Those components are the volatile fatty acids, the ammonium and the carbon dioxide [START_REF] Voegel | Mechanisms of cementitious material deterioration in biogas digester[END_REF]. It is also suspected that the occurrence of microorganisms forming a biofilm attached to the concrete is responsible of increasing the deterioration kinetics.

Even if the mechanisms behind this catalytic effect are not well known, it is expected that the biofilm activity is locally increasing the concentrations of aggressive components [START_REF] Bertron | Understanding interactions between cementitious materials and microorganisms: a key to sustainable and safe concrete structures in various contexts[END_REF][START_REF] Magniont | A new test method to assess the bacterial deterioration of cementitious materials[END_REF]. Our goal is then to understand and evaluate the specific role of biofilms in the biodeterioration of cementitious materials during an anaerobic digestion process. More precisely, we wanted to give more insights in the spatial and temporal heterogeneity of the biofilm, and link it with the biodeterioration observed.

For that, CEM I Portland cement paste pellets were immerged in cultures mimicking industrial anaerobic digestion conditions during 2, 3, 4 and 5 weeks. Those cultures were made of synthetical biowaste inoculated with activated sludge. The pellets were then taken out and both the paste and the biofilm were analysed (Fig. 1). The spatial heterogeneity of the biofilms is evaluated through successive chemical removal of the biofilm layer. The microbial population of each layer was determined through 16S RNA sequencing. The concentration of the aggressive components (ammonium ions, total inorganic carbon and volatile fatty acids) at 2, 3, 4 and 5 weeks was measured. The biodeterioration of cementitious pellets was evaluated using SEM/EDS observations.

The deterioration profile of the cement paste immerged for 2, 3, 4 and 5 weeks was roughly the same: 4 deteriorated zones and the sound paste. Only the thickness of the deteriorated zones was changing from one duration of exposition to another while their composition was similar from one exposition time to another. The first zone had a thickness of about 100 µm and was Cédric Perez, Christine Lors, and Benjamin Erable devoid of calcium with as well higher proportions of silicon aluminum and phosphor than the sound paste. The second zone was very thin, about 25 µm, and enriched in calcium while impoverished in silicon. Finally, the thickness of third and fourth zones was very heterogeneous, from 100 µm to 400 µm, while having a composition close to that of the sound paste. It seems that the global thickness of the biodeteriorated zone is increasing over time, but observations on pellets immerged in longer time are necessary to confirm that tendency.

Microbial analyses showed that the liquid media had higher concentrations of microorganisms involved in the methanogenesis, mainly the archaea genus methanosarcina, which represent about 18% of the detected species in the media. Concerning the biofilm populations, about 50% of the detected species in the most deepest layer of the biofilm were acidogens, such as the genus Clostridium. This heterogeneity between sessile and planktonic biomass could be a lead to explain the biofouling effect of the biofilm since, as suspected, the higher proportion of acidogens in the biofilm could locally increase the concentrations of volatile fatty acids inside the biofilm.

ORCID

Cédric Perez: https://orcid.org/0000-0002-2057-5958 Christine Lors: https://orcid.org/0000-0002-2222-5556 Benjamin Erable: https://orcid.org/0000-0002-5332-9622

Analytical techniques

Cementitious matrix


Astronomy and colonialism in Hawai'i by Pascal Marichalar version: 2 February 2023

One of the largest social movements in recent Hawaiian history took place in the summer of 2019 at the foot of a mountain on the Big Island. This was not just any mountain: beautiful Mauna Kea, a dormant volcano, the highest point of the Pacific Ocean towering at 13,803 feet (4,207 meters) above sea level.

Thousands of people who called themselves kia'i or "protectors" of the mountain braved the cool, windy climate, camping for months on the winding road to the summit. Though the main figures of the movement were Kānaka Maoli (Native Hawaiian), it included descendants of the migrant workers from Portugal, Japan, the Philippines and Mexico, who had come to work in the sugarcane plantations and giant cattle ranches in generations past, and who now called Hawai'i Island (the other name for the Big Island) home ; members of native and indigenous peoples from the Pacific and mainland United States and Canada, who joined in solidarity ; and some residents who had only recently arrived on the island, who demonstrated thus their attachment to the community and the environment.

The kia'i opposed the construction of a new astronomical facility on the summit of Mauna Kea, a cutting-edge instrument called the « Thirty Meter Telescope », or TMT, in reference to the diameter of its primary mirror. Many onlookers, including some of the scientists who used the existing observatories, expressed their disbelief and bewilderment at the protests. Why would one be against astronomy, of all things? Wasn't it a non-polluting activity carried out solely for the benefit of humankind? The kia'i must be antiscience, ignorant, irrational. Social media were blamed for making it easy for them to spread their untruths. The protesters were also certainly opportunistic: or why else would they fight astronomy now, even though many observatories had been built on the mountain during the past five decades with no memorable opposition? Each of the previous allegations is disproved by historical inquiry. Since 2019, I have been working in the archives of the institutions that develop and manage observatories at the summit of Mauna Kea. My research confirms what many old-timers, on both sides of the conflict, told me during oral history interviews: astronomy's foothold on the mountain is intimately linked to the legacy of colonialism; opposition to summit development started early, when the first large telescope project was announced in the 1970s; and many of the reasons for which the kia'i wish to protect Mauna Kea from further desecration (in their own words) are founded in a long, painful history.

"Discovery"

The first foreign astronomer to set foot on the Big Island of Hawai'i was none other than Captain James Cook himself, during his third voyage in the Pacific. At the time, astronomy was closely linked to the colonial enterprises: sailors observed the night sky mainly to determine the geographic coordinates of the land which they had "discovered". As HMS Resolution and Discovery sailed into Kealakekua Bay at the beginning of December, 1778, thousands of Native Hawaiians paddled and swam out to meet them. Two nights later, the captain observed a lunar eclipse from the coast. Measuring the distance between the moon's limbs and two stars, he established the precise coordinates of this addition to the archipelago he had named the "Sandwich Islands". However, Cook met his demise a few weeks later in the same bay, killed in a fight with Native Hawaiians after he attempted to abduct their leader in reprisal for the theft of a small boat.

Fast-forward to 1959, when the Territory of Hawai'i became the 50 th state of the United States. That same year, the first non-stop jet engine connection with the mainland was established. From a businessman's perspective, the islands were full of economic promise, in large part because of the impending touristic explosion.

Yet on the Big Island, prospects were not so rosy. The profits of sugarcane plantations were dwindling. In 1960, a tsunami destroyed part of the business district of Hilo, the most populous town. A member of the Chamber of Commerce named Mitsuo Akiyama looked up at the snowcapped mountains and wondered: Would there not be a way to put them to some economic use? By building a rocket launching facility, or a factory transforming lava into construction material, or even an astronomical observatory?

The famous Dutch-American astronomer Gerard Kuiper was precisely on the lookout for a high altitude site on which to develop a new generation of infrared telescopes. Invited by Akiyama, Kuiper came with his assistant Alika Herring, a master mirror-maker and observer who happened to be from the island, the descendant of missionaries. Mauna Kea's summit, which often rose over a sea of clouds, was enticing, but unfortunately it lacked an access road. Hawai'i's second governor, John A. Burns, did not need much convincing: barely a month later, a dirt road had been bulldozed through the lava.

In the spring of 1964, Herring spent many weeks alone in the windswept, polar conditions of the summit with what he considered to be his finest mirror of all. He was baffled by what he saw. Craters of the Moon and storm formations on Jupiter appeared to him in unprecedented detail. At an inauguration ceremony for the test telescope, Kuiper enthusiastically announced the news to the scientific community: "This mountaintop is probably the best site in the world -I repeat -in the world, from which to study the Moon, the planets, the stars (...) To use the words of Mr. Alika Herring, our first observer, 'This mountain is it'. It is a jewel! This is the place where the most advanced and powerful observations from this Earth can be made."

Conquest

Though it counted very few astronomers, the University of Hawai'i (UH) was interested. As UH astronomer John Jefferies later recalled, the mountain "could reasonably have been regarded as under Hawai'i's jurisdiction", therefore there was no reason to leave it to outside institutions such as the University of Arizona, which employed Kuiper. The University of Hawai'i managed to convince NASA to grant it -and not Kuiper's team -the funding to build a full-size telescope on the mountain. In 1967, Jefferies became the founding director of a new semi-autonomous entity within the university named the Institute for Astronomy. Its main mission was to manage Mauna Kea's summit in order to develop astronomical facilities.

Telescopes look upward yet they are built on land (with the exception of a handful of space telescopes). Land is a touchy subject in Hawai'i, a sovereign state which was unilaterally annexed by the United States in 1898, in spite of the petitions signed then by tens of thousands of Native Hawaiians. Adding to the potential complexity, some of the lands on Mauna Kea's summit and alongside the access road were historically part of the "Crown lands", which Hawaiian monarchs had previously set aside to benefit their subjects. At the end of the 1960s, though, none of this seemed problematic to the burgeoning State government. The Institute for Astronomy was entrusted with the care of the summit lands via a $1 per annum lease running over 65 years. Jefferies in turn offered similarly priced sub-leases to the astronomical organizations from various countries and universities who were interested in building a telescope on the mountain.

One unresolved issue was the road. In order to attract large projects, the Institute for Astronomy wanted to improve the crude dirt trail by widening and paving it. However, Governor Burns opposed this. He considered a good road would make it too easy for non-scientists to access the summit, and this risked jeopardizing the site's quality for astronomy. In his words to a local journalist, the problem was that "a public road cannot be closed to anyone". At the beginning of the 1970s, Burns even suggested building a cable-car which would make it possible to filter access to the summit; but the project proved too expensive. A compromise unsatisfactory to all parties was eventually reached, which consisted in keeping the road in a permanently semi-hazardous state -to the present day...

Protecting the mountain

The consensus among the first proponents of astronomy was that Mauna Kea was a terra nullius. Others users of the mountain did not agree. Environmentalists identified many species of flora and fauna, some of them endemic, which they considered endangered by the construction and operation of telescopes: the māmane and naio trees, the silversword bush, the palila bird, the wēkiu bug. Hunters and skiers were also upset at the idea of loosing access to a recreational area that was important to them. In 1974, these different constituencies expressed their discontent prior to the groundbreaking ceremony of the first major project, the Canada-France-Hawai'i Telescope.

In the following years, new environmental regulations at the federal level gave opponents leverage to at least slow down new observatory projects. However, astronomers always prevailed, especially during a construction boom in the 1980s and 1990s, when many facilities saw first light, including workhorses of contemporary astronomy such as the Keck, Subaru and Gemini North telescopes.

Mauna Kea has always been an important place for residents of the island with Native Hawaiian ancestry, though this was not usually identified by journalists and politicians before the 1990s. In oral history interviews, some kūpuna (eleders) describe for example the long-standing tradition of burying a newborn baby's umbilical cord on Mauna Kea. With the cultural renaissance and renewed historical awareness that marked the last quarter of the twentieth century, Native Hawaiian voices progressively joined the chorus of opponents to further development of the summit.

In 2006, a group lead by Hawaiian cultural practioner and former telescope employee Kealoha Pisciotta convinced NASA to cancel funding for an extension to the twin Keck telescopes. In October 2014, a new generation of kia'i interrupted the groundbreaking ceremony for the Thirty Meter Telescope, planting the seeds for the movement that would successfully stave off any attempt to build it until now.

The kia'i I have met are neither irrational nor antiscience. They explain that astronomy is their target only insofar as it mimics the stance of the US military and other capitalist ventures (touristic exploitation, agroindustry...) regarding land use and custody. They also wonder why these multimillion dollar facilities bring so few economic and cultural benefits to the inhabitants of the island. Because of its beauty and its exceptional qualities (upon which astronomers, in their way, agree), Mauna Kea has become the focal point for mobilizations against the colonial theft of land and mindless environmental harm.

The embodied historical knowledge of Native Hawaiians brings them to question the conditions in which, one day, foreign scientists felt entitled to claim an extraordinary mountain as their own, and their own only. Today, many astronomers identify such attitudes as problematic and strive not to reproduce them in their everyday practices. However, the inequalities and injustice borne from two centuries of colonial history will not be easily repaired.


Naji Najari
email: naji.najari@orange.com

Samuel Berlemont
email: samuel.berlemont@orange.com

Grégoire Lefebvre
email: gregoire.lefebvre@orange.com

Stefan Duffner
email: stefan.duffner@liris.cnrs.fr

Christophe Garcia
email: christophe.garcia@liris.cnrs.fr

RESIST: Robust Transformer for Unsupervised Time Series Anomaly Detection

Keywords: Unsupervised anomaly detection, Robust Transformers, Self and Co-attention, Network traffic anomaly detection

In the last decades, Internet of Things objects have been increasingly integrated into smart environments. Nevertheless, new issues emerge due to numerous reasons such as fraudulent attacks, inconsistent sensor behaviours, and network congestion. These anomalies can have a drastic impact on the global Quality of Service in the Local Area Network. Consequently, contextual anomaly detection using network traffic metadata has received a growing interest among the scientific community. The detection of temporal anomalies helps network administrators anticipate and prevent such failures. In this paper, we propose RESIST, a Robust transformEr developed for unSupervised tIme Series anomaly deTection. We introduce a robust learning strategy that trains a Transformer to model the nominal behaviour of the network activity. Unlike competing methods, our approach does not require the availability of an anomalyfree training subset. Relying on a contrastive learning-based robust loss function, RESIST automatically downweights atypical corrupted training data, to reduce their impact on the training optimization. Experiments on the CICIDS17 public benchmark dataset show an improved accuracy of our proposal in comparison to recent state-of-the-art methods.

Introduction

With the substantial increase of network anomalies in modern communication networks, anomaly detection has gained considerable interest over the last few years. The classical detectors, i.e., signature-based detectors, identify anomalies based on a predefined set of rules that models known attack signatures. These signatures must repeatedly be updated to integrate new attacks. Despite their effectiveness in identifying known threats, these systems fail to detect new emerging anomalies, e.g., zero-day attacks and non-malicious faults. To address these limitations, all the more present with the development of the Internet of Things (IoT), contextual anomaly detection becomes of big interest in the network analysis landscape.

Anomaly Detection (AD) in time series is a broad research field affecting numerous application domains such as network and object monitoring, medical data analysis, fraud detection, and network intrusion detection [START_REF] Choi | Deep Learning for Anomaly Detection in Time-Series Data: Review[END_REF]. In such fields, detecting outliers mainly relies on the temporal continuity assumption, defined by Aggrawal [START_REF] Aggarwal | Outlier Analysis[END_REF] as "the fact that the patterns in the data are not expected to change abruptly unless there are abnormal processes at work." As such, a temporal outlier is an abrupt change in the data pattern, which results in a discontinuity of the data with its local context. This assumption makes temporal AD more challenging than the classical unsupervised punctual AD, since considering the ordinal causality between observations is of paramount importance.

Numerous extensive studies have been carried out in the field of temporal AD. Contributions have shifted their focus towards semi-supervision, a.k.a., One-Class Classification. Here, an algorithm is first trained to model the nominal patterns of the anomaly-free training data. Then, any deviation from the trained model is flagged as an outlier. Despite yielding encouraging results in some specific applications, these classical anomaly detectors generally assume the availability of anomaly-free training data, and their performance drastically declines in the presence of corrupted observations. Unfortunately, in real-world applications, the data collection process is prone to contamination, as the training data may be corrupted with an unknown fraction of outliers. For example, in network intrusion detection, diverse anomalies may occur during the collection of the training network trace, due to faulty sensors, traffic congestions, and security attacks. The manual filtering of training anomalies is laborious, because of increasing data volumes and the diversity of emergent anomalies. This motivates the development of robust unsupervised temporal anomaly detectors, insensitive to training contamination.

In this paper, we propose RESIST, a Robust transformEr designed for unSupervised tIme Series anomaly deTection. We introduce a novel training strategy that identifies and downweights the impact of contaminants. RESIST is trained to mine the common temporal correlations that link successive sliding windows. Only common patterns are modelled and instance-specific rare patterns are ignored, since they may be caused by training corrupted data. RESIST training optimizes the robust Geman-Mcclure loss function, to reduce the impact of training outliers.

This paper is organized as follows: Section II introduces related work in temporal AD, and focuses particularly on Transformers for robust AD. Section III presents our contribution: RESIST. Section IV depicts the datasets used in our experiments, the training protocols, and the experimental results. Finally, conclusions and perspectives are drawn.

Related Work

Time series AD is an active research field that has drawn increasing attention in the data mining and machine learning community [START_REF] Blázquez-García | A review on outlier/anomaly detection in time series data[END_REF][START_REF] Choi | Deep Learning for Anomaly Detection in Time-Series Data: Review[END_REF]. Time series AD mainly include four main families: density-based, clusteringbased, prediction-based, and reconstruction-based methods. Density-based methods rely on a local density criterion to identify outliers. Observations that have few adjacent neighbours are considered anomalous. Density-based methods, such as Local Outlier Factor (LOF) [START_REF] Breunig | LOF: Identifying Density-Based Local Outliers[END_REF] and Deep Autoencoding Gaussian Mixture Model (DAGMM) [START_REF] Zong | Deep autoencoding gaussian mixture model for unsupervised anomaly detection[END_REF], are extensively used in non-temporal anomaly detection. Many works extend these classical methods to time series anomaly detection, by restricting the local density criterion to local sliding windows [START_REF] Angiulli | Distance-based outlier queries in data streams: the novel task and algorithms[END_REF]. Cluster-based methods firstly determine the optimal set of clusters that model the nominal data. Then, these clusters are used as a reference for normality: the anomaly score is defined as the distance to the closest cluster centre. The most common cluster-based anomaly detectors include Support Vector Data Description (SVDD) [START_REF] Tax | Support Vector Data Description[END_REF], and Deep-SVDD [START_REF] Ruff | Deep one-class classification[END_REF]. Similarly, numerous studies have been carried out to adapt such methods to temporal AD [START_REF] Angiulli | Distance-based outlier queries in data streams: the novel task and algorithms[END_REF]. Prediction-based methods train a model to forecast a posterior observation using only past data. Anomalies are points that are different from their predictions. Various models were developed within this category, ranging from AutoRegressive Integrated Moving Average (ARIMA) [START_REF] Zhang | Statistics-based outlier detection for wireless sensor networks[END_REF], to Long Short-Term Memory recurrent neural networks [START_REF] Hundman | Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding[END_REF]. Finally, reconstruction-based methods learn to compress the nominal data points into a low-dimensional representation and reconstruct the original data based on these compressed encodings. In other words, these methods learn to extract the most important information of the norm by mapping the data into a subspace of lower dimensionality, with the least reconstruction error. Since anomalies generally comprise non-representative features, it is harder to project them in this subspace without loss of information, which results in a larger reconstruction error. The most common reconstruction-based anomaly detectors are AutoEncoders. They are extensively used to identify non-temporal anomalies [START_REF] Malhotra | LSTM-based Encoder-Decoder for Multi-sensor Anomaly Detection[END_REF][START_REF] Najari | RADON: Robust Autoencoder for Unsupervised Anomaly Detection[END_REF][START_REF] Najari | Robust Variational Autoencoders and Normalizing Flows for Unsupervised Network Anomaly Detection[END_REF][START_REF] Su | Robust Anomaly Detection for Multivariate Time Series through Stochastic Recurrent Neural Network[END_REF]. To extend this approach to time series data, Su et al. [START_REF] Su | Robust Anomaly Detection for Multivariate Time Series through Stochastic Recurrent Neural Network[END_REF] propose a hybrid method that combines a Variational AutoEncoder (VAE) and a Gated Recurrent Unit (GRU). While the GRU learns the temporal correlations of the input sequences, the VAE is trained to map the observations into a latent stochastic space. Similarly, Malhotra et al. [START_REF] Malhotra | LSTM-based Encoder-Decoder for Multi-sensor Anomaly Detection[END_REF] propose an LSTM-AE, tailored for time series AD.

Within the reconstruction-based category, a series of recent studies has shown the advantage of using Transformers over classical methods [START_REF] Chaudhari | An Attentive Survey of Attention Models[END_REF]. Benefiting from the self-attention mechanism and parallel computations, Transformer-based anomaly detectors show a higher detection performance and a more efficient training process [START_REF] Wen | Transformers in Time Series: A Survey[END_REF]. Some recent studies, e.g., TranAD [START_REF] Tuli | TranAD: Deep Transformer Networks for Anomaly Detection in Multivariate Time Series Data[END_REF] and MT-RVAE [START_REF] Wang | Variational transformer-based anomaly detection approach for multivariate time series[END_REF], propose combining the Transformer-based architecture with common generative models, Generative Adversarial Networks (GANs) and VAEs, to further improve the model performance and robustness to training contaminations. Alternatively, Xu et al. [START_REF] Xu | Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy[END_REF] renovate the self-attention mechanism by introducing a new AnomalyAttention module, specifically tailored for unsupervised time series anomaly detection. Their method, called AnomalyTransformer, is based on the intuition that, due to the rarity of anomalies, it is harder to find an association spread over the whole sequence. The authors remark that the self-attentions of anomalous points generally tend to be located in their adjacent data points. Consequently, AnomalyTransformer leverages this adjacent concentration bias to make anomalous points more distinguishable. The authors formalize the adjacent concentration bias by defining the Association Discrepancy (AssDis) criterion. For each data point, the Association Discrepancy quantifies the disparity between the local attention relative to the adjacent points and the global attention with the whole series. As it is difficult to find a global mapping that links anomalous points with the whole sequence, both local and global self-attentions are mostly localized in the surrounding. As such, anomalies have smaller Association Discrepancy than nominal points. After training, AnomalyTransformer is used to assess the anomalousness of new samples. For a test data matrix X ∈ R T ×d , containing T consecutive data points of dimension d, and its reconstruction X ∈ R T ×d , the anomaly score is computed as follows:

AnomalyScore(X) = Softmax(-AssDis) X -X 2 2
.

(

) 1
The classical reconstruction error is amplified with a term inversely proportional to the AssDis. Since anomalies have smaller AssDis than inliers, their reconstruction error is amplified, which improves anomaly detection performance. AnomalyTransformer shows that encouraging global attention spread over the entire sequence improves Transformer anomaly detection performance. Despite being more robust than vanilla Transformers, AnomalyTransformer attention is still restricted to the input sequence and lacks longer-term dependencies extracted from historical sequences. In fact, time-series data are usually split into fixedlength consecutive segments using a sliding window. The reference of normality in AnomalyTransformer is bounded to a single segment and ignores all previous windows. Even though anomalies are rare, the same anomaly may occur twice in the same window. In this case, the adjacent concentration bias becomes invalid, as anomalous observation self-attention is no longer limited to its surroundings. This is why we propose RESIST, which addresses this limitation, by extending the adjacent concentration prior to accounting for historical long-range properties.

Method

Unlike AnomalyTransformer, we propose to extend the Transformer attention to cover the historical data, in order to reject unusual observations. We hypothesize that rejecting training contaminants requires building pairwise associations not only between data points of the same sequence but also with instances of previous segments. The main intuition is that nominal instances present a regular behaviour shared across multiple segments. That is, reconstructing nominal sequences using either self-information extracted from the current input (i.e., self-reconstruction) or using relevant information extracted from the history (i.e., cross-reconstruction) would lead to similar results. In contrast, since anomalies are rare and different, building inter-sequence associations (or similarities) is more difficult and less informative. Building on this insight, we propose RESIST, a Robust transformEr for unSupervISed Time-series anomaly detection. RESIST is trained to reconstruct input sequences using a hybrid representation that combines local intra-sequence information as well as global properties, shared between multiple segments. Firstly, we introduce a Siamese training strategy that ensures that the model pays equal attention to the input sequence as well as to the previous ones. Secondly, we train RESIST with a robust loss function to reduce the impact of large reconstruction errors caused by training outliers. In the following, we detail our contributions and the hypotheses that we will analyze in the experimental part. First, we depict a global architecture overview of RESIST to present its main building blocks. Then, we present each component separately. Finally, we present our hypotheses, the corresponding experimental protocols and results.

RESIST Architecture

RESIST presents an encoder-decoder architecture, comprised of four main components: a positional encoding and embedding layer, a siamese encoder, a fusion layer, and a decoder (cf. Figure 1). Similar to vanilla Transformers [START_REF] Vaswani | Attention is all you need[END_REF], the original data is firstly encoded using the linear embedding and the positional encoding units. Both encoder and decoder are composed of stacked identical blocks, where each block contains a multi-head attention unit followed by a Feed-Forward Network (FFN) layer.

RESIST takes as input K non-overlapping sequences X w t = (x w t-K+1 , ..., x w t ): an input sequence x w t and its K -1 previous sequences. Here, each sequence is composed of w consecutive data points x w t = (x t-w+1 , ..., x t ), where x t ∈ R d is an observation of dimension d, recorded at the timestamp t. In Figure 1, we illustrate our method for K = 2. Firstly, the linear embedding and the positional encoding units encode the input sequences (x w t-K+1 , ..., x w t ) and output the K embedded sequences (e w t-K+1 , ..., e w t ). Secondly, the encoder extracts from each embedded sequence e w t a low-dimensional latent encoding z w t . Then, the fusion layer aggregates these encodings into a single representation. The decoder maps the fusion encoding to the input space in order to reconstruct the original sequence x t . Finally, RESIST minimizes the Geman-McClure robust function between the reconstructed sequence x w t and the original one x w t . After presenting the global architecture of our method, we will thoroughly review each component in the following Sections.

Siamese Encoder RESIST encoder, illustrated in Figure 1, learns to project K consecutive sequences into K low-dimensional embeddings. The encoder receives a sequence x w t and its associated history, which contains the K -1 sequences preceding x w t . It models the point-wise correlations between x w t and the history. Then, it learns to project these data into a common reduced space of dimension d enc ∈ N * , where common data points share similar representations. This task is notoriously hard for anomalies, since they present non-representative uncommon patterns. For this reason, we propose an encoder with a Siamese architecture, with K identical sub-networks that share the same parameters. Input sequences Unlike classical Siamese Neural Networks, our encoder is not trained to learn a similarity metric between input sequences. Its objective is to reduce the data dimensionality to only keep the most important information. Each siamese encoder sub-network is composed of a stack of N = 2 identical blocks. Each block comprises two sub-modules: a multi-head attention unit followed by a FFN layer (cf. Figures 2 and3). While the attention mines the temporal correlations in the data, the FFN layers are used for dimensionality reduction.

The Siamese encoder is a hybrid composition of both Self-Attention (SA) and Co-Attention (CA) units. While the SA units are used to extract the contextual properties of the current sequence, the CA unit is destined to extract inter-segment properties and only keep common relationships.

Self-attention and Co-attention Module Attention modules are intended to mine pairwise interactions between data points. We propose to leverage the SA and CA layers, initially in multimodal Visual Question Answering (VQA) [START_REF] Yu | Deep Modular Co-Attention Networks for Visual Question Answering[END_REF], to our task of unsupervised AD.

VQA is a visual reasoning task where we train a model to answer a question concerning an image. Identifying joint visual-linguistic representations is crucial in VQA. In [START_REF] Yu | Deep Modular Co-Attention Networks for Visual Question Answering[END_REF], Yu et al. propose a Transformer-based VQA model where they introduce a co-attention layer, a.k.a., guided attention layer (see Figure 3). This layer is mainly designed to model multimodal interactions between a sentence and an image. The architecture of co-attention is the same as the self-attention layer. The main difference is that co-attention receives two different input sequences, a sentence and an image. It extracts the Query from the image and the pair (Key, Value) from the sentence. Recent studies [START_REF] Tan | LXMERT: Learning Cross-Modality Encoder Representations from Transformers[END_REF] show the potential of coattention to learn contextual representations and to improve model generalization performance.

We propose to extend CA to our task of unsupervised anomaly detection. CA can be seen as a module that filters similar data points between a sequence and the history. Then, it weights the current sequence observations with the relative normalized similarities. The aim is to guide the reconstruction with intersequence common information and to filter out sequence-specific rare patterns. This encourages the model to ignore unusual patterns that are only relevant for a single sequence. Different compositions of CA and SA may result in different configurations of RESIST. In Section 4.3, we will present these configurations and we will experimentally evaluate their impact on the AD performance.

Fusion Layer

We propose to leverage multiple data views for robust reconstruction. The fusion layer combines the multiple encodings extracted by RESIST encoder into a single vector representation. In this work, we propose an additionbased fusion. This module comprises a fusion layer, followed by a FFN layer. The RESIST additive fusion strategy is inspired from the well-known manifold mixup method [START_REF] Zhang | Mixup: Beyond Empirical Risk Minimization[END_REF]. The original mixup method was initially proposed for data augmentation in supervised learning. For two training inputs x i and x j , having two labels y i and y j , respectively, mixup generates a new training instance, x, using a linear interpolation:

x = βx i + (1 -β)x j and ŷ = βy i + (1 -β)y j . (2)
ŷ is the corresponding label of x. The interpolation term β ∈ [0, 1] is an hyperparameter. In other words, mixup trains supervised classifiers to adapt a linear behaviour in the boundaries between training classes. Mixup reduces classifier regularization error and makes classifiers more robust to corrupted labels [START_REF] Zhang | Mixup: Beyond Empirical Risk Minimization[END_REF].

We extend the mixup method to robust unsupervised anomaly detection. Similar to the original mixup strategy, mixup fusion merges K instances into a single vector through linear interpolation. The merged representation of K encodings (z w t-K+1 , ..., z w t ) is defined as follow:

z w t = 1 K t i=t-K+1 z w i (3)
We propose a uniform contribution of all encodings. For K = 2, we have z w t = 0.5z w t-1 +0.5z w t . When the input sequence x w t presents common properties relative to its history, represented by x w t-1 , we expect that the siamese encoder extracts close latent representations z w t and z w t-1 . In this case, the fusion representation would be similar to the encoding of a vanilla Transformer, i.e., z w t ≈ z w t-1 . In contrast, when the current sequence comprises an uncommon pattern, the encoder self-attention and co-attention modules potentially extract different encodings. Therefore, the linear interpolation may generate an inconsistent sample and the reconstruction task become more difficult.

Finally, this compact representation z w t is forwarded to the FFN of the fusion module and the final output is:

F w t (z w t-K+1 , ..., z w t ) = ReLU ( z w t W f + b f ), (4)
where W f ∈ R denc×d f refers to the linear layer weights and b f ∈ R d f to the bias vector. d enc is the dimension of the fusion module inputs and d f is the dimension of the outputs. In all experiments, we use

d f = d enc = 16.
RESIST Decoder Finally, the RESIST decoder learns to reconstruct the last sequence of the input using the compact representation that is the output of the fusion module. It is composed of a stack of N = 2 identical blocks. Each block comprises two sub-modules: a multi-head self-attention unit followed by a FFN layer. While Rectified Linear Unit (ReLU) activation function is used in the first block, the last block is followed by a Sigmoid function to ensure that the output has the same range as the input [0, 1].

Robust Training Loss

To hedge against training contaminants, we train RESIST using a robust loss function. Indeed, the commonly used Mean Squared Error (MSE) is sensitive to outliers, since squaring large deviations results in the dominance of anomalies during the training. In contrast, a robust loss can resist noise and anomalies by reducing the influence of their large reconstruction errors. There have been numerous studies to explore robust leaning in the presence of outliers. The robust function list includes Charbonnier loss, Cauchy loss, Geman-McClure loss, and Welsch loss. Recently, Barron [4] generalizes these common losses in a single parametric function, ρ(x, α, c), parameterized by the scale c and the robustness parameter α.

ρ(x, α, c) =          1 2 ( x c ) 2 if α = 2 log( 1 2 ( x c ) 2 + 1) if α = 0 1 -exp(-1 2 ( x c ) 2 ) if α = -∞ |α-2|
α ((

( x c ) 2 |α-2| + 1) α 2 -1) otherwise (5)
Particular values of α define common robust losses: L2 loss (α = 2), Charbonnier loss (α = 1), Cauchy loss (α = 0), Geman-McClure loss (α = -2), and Welsch loss (α = These cases are visualized in Figure 4, extracted from [START_REF] Barron | A General and Adaptive Robust Loss Function[END_REF]. We refer the reader to [START_REF] Barron | A General and Adaptive Robust Loss Function[END_REF] for a detailed description of these losses.

L(x) = ρ(x, α = -2, c) = 2 ( x c ) 2 4 + ( x c ) 2 (6)
where c is a scale parameter that modulates the loss robustness range. In all our experiments, we set x = λIQR, where IQR is the interquartile range and λ = 0.1.

Hypotheses

We synthesize our contributions into the following hypotheses:

-Hypothesis 1 (H1) We conjecture that guiding the Transformer reconstruction with both intra-sequence properties, extracted using SA units, and inter-sequence pairwise interactions with the history, extracted with CA units, results in a more robust anomaly detector. -Hypothesis 2 (H2) We hypothesize that training RESIST with a robust loss function, and particularly the Geman-McClure loss, reduces the impact of training noise and anomalies;

Experiments and Results

In this section, we explore the validity of the assumed hypotheses on the benchmark dataset: the Canadian Institute of Cybersecurity Intrusion Detection System (CICIDS17) evaluation dataset [START_REF] Sharafaldin | Intrusion Detection Evaluation Dataset (CICIDS2017)[END_REF]. In addition, we extensively compare our contribution against common unsupervised anomaly detectors. First, we provide an overview of the dataset. Then, we develop the training and testing protocols. Finally, we present and analyze the empirical results.

Dataset Description

CICIDS17 [START_REF] Sharafaldin | Intrusion Detection Evaluation Dataset (CICIDS2017)[END_REF] is a recent public dataset developed by the Canadian Institute of Cybersecurity (CIC) for IDS evaluation. Overall, this dataset comprises about 3 million labelled network flows collected over 5 days, starting from July 3, 2017, and ending on Friday, July 7, 2017. 83% of this traffic is benign and the remaining 17% is anomalous. To collect the traffic, Sharafaldin et al. developed a testbed containing two networks: an Attack-Network and a Victim-Network. The Victim-Network comprises three servers, one firewall, two switches and ten interconnected PCs. One switch was configured to mirror all the traffic passing through the network. The Attack-Network is a separate network that runs network attacks on the Victim-Network.

CICIDS17 provides full packet capture of the collected data in pcap files. In addition, the raw data are processed using CICFlowMeter, a flow-based feature extractor, to extract metadata from the packet traces. Each flow record is represented by 85 features: a flow ID, 83 flow metadata features, and a class label. A detailed description of the 83 flow-based features is presented in [START_REF] Kurniabudi | CICIDS-2017 Dataset Feature Analysis With Information Gain for Anomaly Detection[END_REF]. CICIDS2017 comprises 15 classes: a nominal class and 14 attack types, including DoS, Distributed DoS (DDoS), Web attacks, and Infiltration attacks. This dataset was extensively used in many recent publications [START_REF] Kurniabudi | CICIDS-2017 Dataset Feature Analysis With Information Gain for Anomaly Detection[END_REF], since it covers various recent attacks and it comprises both punctual and collective anomalies.

Data Preprocessing

We follow the same preprocessing steps proposed in [START_REF] Lai | Revisiting Time Series Outlier Detection: Definitions and Benchmarks[END_REF]. Since the original dataset is voluminous, we focus on the data subset that is collected during one day: Thursday, July 6 2017. This subset contains 170231 network flow and represents around 6% of the whole dataset. 98.7% of this traffic is benign and the remaining 1.3% is anomalous. We rescale numerical features to be in the range [0, 1], using the min-max normalization method. Then, we randomly split the benign data into 40% for the training and 60% for testing.

Training and Testing Protocols

Protocol 1 (P1): Modular Composition of Co-attention and Selfattention Modules RESIST encoder is composed of two attention-based components: the self-attention and the co-attention modules. Different combinations of these modules result in different variants. In this section, we study the performance of RESIST with three modular compositions of these units.

For ease of illustration, we only visualize the RESIST encoder part for the three configuration. The first variant, RESIST-SS (cf. Figure 5), is the baseline. This first configuration does not consider the history for data reconstruction. In this case, only the input sequence flows through self-attention units to gradually extract the intra-properties of each sequence Then, RESIST-SS decoder is trained to reconstruct the sequence based only on this self-encoded representation. The second configuration, RESIST-SC (cf. 6), considers inter-sequence similarities between the input and the history. Indeed, both sequences are processed using a first self-attention unit to model intra-sequence relationships. Then, the encoded representation of the current sequence is processed using a self-attention unit, while the historical representations are fed into a co-attention unit to introduce pairwise similarities between consecutive sequences. Finally, the third variant is RESIST-CC (cf. Figure 7). Here, the input sequence is encoded through cascaded self-attention units and adjacent sequences are encoded using co-attention units. The main difference between RESIST-SC and RESIST-CC is that the former encodes the history with a hybrid encoder that alternates CA and SA, while in the latter, only CA units are used to encode the previous segments. Protocol 3 (P3): Comparison with Competing Methods Finally, we globally compare our contribution against common unsupervised time series anomaly detectors. In this experiment, we select the best performing configuration of RESIST: a siamese encoder that comprises a hybrid composition of self and co-attention units, and trained with the Geman-McClure loss. The baselines selected in our experiments belong to the different categories of unsupervised anomaly detection presented in Section 2. These baselines include one-class classifiers: IF [START_REF] Liu | Isolation forest[END_REF], OSVM [START_REF] Tax | Support Vector Data Description[END_REF]; density-based methods: LOF [START_REF] Breunig | LOF: Identifying Density-Based Local Outliers[END_REF]; reconstructionbased algorithms: OmniAnomaly [START_REF] Su | Robust Anomaly Detection for Multivariate Time Series through Stochastic Recurrent Neural Network[END_REF], LSTM-AE [START_REF] Malhotra | LSTM-based Encoder-Decoder for Multi-sensor Anomaly Detection[END_REF], MSCRED [START_REF] Zhang | A Deep Neural Network for Unsupervised Anomaly Detection and Diagnosis in Multivariate Time Series Data[END_REF], USAD [START_REF] Audibert | USAD: UnSupervised Anomaly Detection on Multivariate Time Series[END_REF], and vanilla Transformer [START_REF] Vaswani | Attention is all you need[END_REF]. In addition, we assess the performance of robust Transformers including TranAD [START_REF] Tuli | TranAD: Deep Transformer Networks for Anomaly Detection in Multivariate Time Series Data[END_REF] and AnomalyTransformer [START_REF] Xu | Anomaly Transformer: Time Series Anomaly Detection with Association Discrepancy[END_REF].

Training Parameter Settings and Evaluation Criteria

We follow the well-established protocol used by many recent papers [START_REF] Shen | Timeseries Anomaly Detection using Temporal Hierarchical One-Class Network[END_REF]. We transform the input time series into consecutive sub-sequences using nonoverlapped sliding windows of length w = 100. After preliminary tests, we use the same architecture for all autoencoder-based models. The autoencoders are a 5-layer MLP with 78-32-16-32-78 units. All latent layers are followed by ReLU activation function. The last layer is followed by a sigmoid function. We use the Adam optimizer to train all the neural networks, with an initial learning rate of 0.001, and a step-scheduler with a step of 0.5. All models are trained for 100 epochs, with a batch size of 64 in all experiments, and random parameter initialization. To limit the impact of random parameter initialization, we repeat each experiment five times and average the results over these five runs. Regarding Transformerbased anomaly detectors, we set the dimension of the embedding to 128 and we use 2-head attention units. In all our experiment, RESIST hyperparameter c is set as c = 0.1IQR (cf. Equation 6). Similar to the validation protocol adapted by Ruff et al. [START_REF] Ruff | Deep semi-supervised anomaly detection[END_REF], the competing methods hyperparameters are tuned on the predefined validation subset. To minimize hyperparameter selection problems, we select the optimal hyperparameters that maximize their validation Area Under the Curve of the Receiver Operating Characteristics (AUROC). This deliberately grants competing methods an advantage over RESIST. Lastly, all the experiments were run on a laptop equipped with a 12-core Intel i7-9850H CPU clocked at 2.6GHz and with NVIDIA Quadro P2000 GPU.

Results

Protocol 1 (P1) : Modular Composition of Co-attention and Selfattention Modules For a fair comparison, the three variants have the same architecture and configuration. The three variants use the mixup fusion strategy and are trained with the same robust loss: Geman-McClure loss. The only difference between the three variants, is the modular composition of co-attention and self-attention units. The experimental results of these 3 variants are shown in Figure 8. These first results highlight that the structure of RESIST encoder has a significant impact on the global performance, since varying the encoder composition of self and co-attention units is clearly reflected in the results.

Firstly, RESIST-SS, whose encoder is purely composed of a cascade of selfattention units, performs poorly compared to the other variants. Indeed, RESIST-SS is similar to a vanilla Transformer trained to reconstruct the input, using the robust Geman-McClure loss, and without considering the historical data. This variant shows the lowest AUROCs in this first set of experiments, with a mean equal to 76.6%, and with a large standard variation of 5%. The other two variants, which integrate intra and inter-sequence properties with co-attention units, globally show better results with reduced standard variations. This confirms our first hypothesis (H1), the sense that guiding the Transformer reconstruction with both intra-sequence properties and inter-sequence pairwise interactions with the history results in a more robust anomaly detector.

Furthermore, we note that the hybrid RESIST-SC reports higher AUROC, 80.5% ± 0.9, compared to RESIST-SS, 78.8% ± 0.3. This advantage is statistically significant, according to Welch's test with p-value = 0.05. This observation reveals that encoding the history with both self-attention and co-attention units is better than using only co-attention units. In RESIST-SC, the self-attention unit firstly extracts the intra-dependencies of the history. Then this first representation, which considers the history local context, is combined with the intermediate representation of the input. In contrast, RESIST-CC neglects history intrasequence context and focuses only on inter-sequence properties. This result is consistent with other works in VQA [START_REF] Yu | Deep Modular Co-Attention Networks for Visual Question Answering[END_REF]. In the following, we will use RESIST-SC encoder architecture as the basis for all next RESIST variants.

Protocol 2 (P2) : Robust Loss Function Similar to the protocol followed previously, all the variants share the same configuration, except the training loss function. The three variants have a hybrid siamese encoder, similar to RESIST-SC encoder. The results are reported in Figure 9. From this figure, we can see that the training loss function has a significant influence on the performance. We note that the results steadily improve when decreasing the robustness parameter α of the loss function ρ(x, α, c), defined in Section 3.2. Firstly, RESIST-MSE, trained with the common Euclidean distance, i.e., α = 2, show the worst performance, with an AUROC around 74%. This result is in line with previous studies, which state that the mean-squared error is considerably influenced by outliers. Secondly, the Charbonnier loss, a.k.a, the pseudo-Huber loss, with α = 1, does not improve the performance (cf. Figure 9). As shown in Figure 4 (left), even though the gradients of large error are reduced compared to the L2 loss, these gradients saturate to a non-zero value. That is, even though their contribution is slightly reduced, training contaminants still contribute to parameter optimization during the training. Nevertheless, when α ≤ 0, the gradient magnitude decreases and converges to 0, when the error is higher than the scale parameter c. As such, large errors are completely ignored and do not impact the training. The speed of converging to 0 clearly depends on the parameter α. The lower α, the higher the decreasing speed of large error gradients. Our results confirm this interpretation, in the sense that RESIST-GM, trained with Geman-McClure loss (α = -2), exceeds RESIST-Cauchy, trained with Cauchy loss (α = 0), by 2.6% on average. We can conclude that the second hypothesis (H2) is validated. Training RESIST with the Geman-McClure loss significantly reduces the impact of anomalies. of RESIST-SC, the mixup fusion layer, and the robust Geman-McClure loss, with c = 0.1IQR. The experiment results are reported in Figure 10. Globally, RESIST achieves superior results compared to all the baselines, on the CICIDS17 dataset, with an average AUROC of 80.6% ± 1.3. First, we note that RESIST is substantially more robust than vanilla Transformers. RESIST improves vanilla Transformer average AUROC by 10%. Second, the lowest results are reported with a density-based anomaly detector: LOF. Indeed, detecting contextual and collective outliers based on the local density of high-dimensional data is challenging. Surprisingly, Transformer-based anomaly detectors show poor performance on this dataset, even with a careful tuning of these architectures. TranAD and AnomalyTranformer report AUROCs of 50.7% ± 1.0 and 52.4% ± 2.1. This implies that these methods are significantly sensitive to training outliers, on this network traffic dataset. It is however difficult to explain such poor results, despite the careful fine-tuning of the hyperparameter on the dedicated validation subset. Third, classical anomaly detectors, i.e., IF and OSVM, give better results than deep neural network-based anomaly including OmniAnomaly, MS-CRED, Vanilla Transformer, and LSTM-AE. This observation ties well with the previous study conducted by Lai et al. [11]. We speculate that this might be due to the fact that the latter are developed for semi-supervised AD. Indeed, they assume that the training data are anomaly free. In the case of data pollution with anomalies, this assumption is not respected and consequently, these methods fail to distinguish both classes. Fourth, RESIST exceeds IF AUROC by 4% and OSVM AUROC by 3%, on average. These results demonstrate that RESIST is more robust than these competing anomaly detectors on the CICIDS17 dataset.

Conclusion and Perspectives

In this paper, we introduced RESIST, a Robust transformEr designed for unSupervised tIme Series anomaly detection. Thanks to the modular composition of self and co-attention units, RESIST learns to reconstruct each input sequence using a hybrid representation that aggregates both the local information that is specific to the current input and the global information shared with the history. Moreover, we proposed a robust training strategy that minimizes the Geman-McClure function, to reduce the impact of training contaminants. We extensively studied the contributions of RESIST components in the global performance, and the experimental evaluation on the CICIDS17 benchmark dataset confirmed that RESIST outperforms existing unsupervised anomaly detection.

Fig. 1 .Fig. 2 .Fig. 3 .

 123 Fig. 1. RESIST architecture.

Fig. 4 .

 4 Fig. 4. The general robust loss function proposed in [4].

  Fig. 5. RESIST-SS

Fig. 7 .

 7 Fig. 7. RESIST-CC

Protocol 3 (Fig. 8 .Fig. 9 .Fig. 10 .

 38910 Fig. 8. Comparison between RESIST three variants: RESIST-SS, RESIST-SC, and RESIST-CC, on the CICIDS17.