Franc ¸ois Pe

Jean-Christophe Grenouilleau

Spare parts supply modelling: application to a space station

Keywords: Spare parts, Space planning, Performance measurement, Logistics, Supply chain, Modelling

The work deals with the topic of spare parts management in a space system. The paper is divided into three parts. The first one is dedicated to the characterization of the system structure and presents the particularities related to the spare-elements procurement. Modelling is the object of the second part. After having exposed the bases of the problem to be solved, a macro-model is introduced. Each of the three elements of an orbital system, namely ground, flying and transport, is then described with a Petri net. Operation specificities of every element are then listed and integrated into the model. A concrete application of this modelling is given in the last part. It concerns the Columbus laboratory of the International Space Station. A representative function is selected and several supply strategies are evaluated.

Introduction

The ability of a system to be repaired plays an important role in the control of the performance and costs. The dependability methods usually take into account an ideal operational environment, i.e. the availability of maintenance resources is instantaneous and with unlimited capacity. Within the framework of operational and economical performance evaluation of the system during its useful life, these assumptions may not be acceptable. As they are integrated in the design process, the logistic support analyses (LSA) allow, in particular, the verification of the assumption of the ideal availability of maintenance resources and consequently to identify the cost-performance problems as early as possible to redirect the options already taken.

Among the resources that are necessary to achieve maintenance tasks by replacement or repair, the spare elements take a very specific place due to the potential impact of their unavailability. The teams that are involved in the preparation of the operational phase pay special attention to the management of their supply. Defined in accordance with the maintenance policy, the supply management strategy mainly determines the range of spare elements and their supply mode as well as their geographical dispatch.

The research works summarized in this article deal with the development and the use of decision-making tools in the context of an inhabited spatial system in the design phase. The work is divided in three parts.

We start with a presentation of the spare parts supply in a spatial context. After having briefly described the components of an orbital system we characterize the particularities of such a system, capable of influencing the supply management. We then develop an evaluation method of the spare parts supply during the operating phase. We show that the problem can be formulated in terms of looking for the best compromise between, on the one hand, the unavailability time of a function in the absence of a spare element and, on the other hand, the cost related to the selected strategy. We then develop a model for the spare parts supply based on the use of the Petri nets. Finally, we suggest an illustration of the method through the application of the spare parts supply strategy to a function of the Columbus laboratory of the International Space Station.

2. Spare element supply of an orbital station 2.1 Structure of a spatial system A spatial station system is generally defined by many interacting blocks called segments (see Figure 1):

. A flight segment (A), which includes the orbital infrastructure and crew as well as the communication means. as well as the infrastructure dedicated to users (preparation units of the elements to be launched and operated).

.

A transportation segment (C) which allows the transport between the station and the ground of the crew, the results of experiments, the necessary resources and other failing elements. It includes the launchers, the cargo vehicles, the infrastructures of launch preparation and eventually return preparation.

2.2 Specifics of spare parts supply of a spatial system 2.2.1 The need for spare parts. The feedback of previous experience concerning the maintenance of spatial systems (and consequently the supply of spare parts), is limited and the rare data collected constitute an estimation to be taken with precaution because the systems and equipments developed are most frequently unique. In the preliminary phases, then, one must frequently resort to analogies with past programs in order to evaluate the needs in terms of replacement. Several works have estimated the needs of an orbital station in this way. A conservative estimate based on experience indicates that the spareelements requirement represents annually 5 percent of the total mass of the system. However, this depends on the level of repair that is opted for. A rather low level of repair (i.e. repairing as many elements as possible, even down to the most basic) requires more tools and higher skills but, in return a lower mass at the time of restocking.

Stock.

They are organized in what we define as stock echelons which means that the place of storage can be either on the ground (in the launch area or at the manufacturer's) or in orbit. One must keep in mind that storage on board an orbital space station is very much constrained in terms of available space, which has been confirmed by the Russian experience. Even though volume is limited, this is not the only hindrance to storage in the station. Let us note that the Apollo missions gave up on storing elements on board lunar modules because of the lack of knowledge about effects of radiation and space environment on the material. Replacing a failing element with another whose condition could not be guaranteed was judged too risky and the adopted solution was then to specify early in the design phase the element with higher reliability. Concerning the ground stock, the geographic distribution may be very diverse: the elements could be stored at the user's base, could stay in a centralized depot at the manufacturer's, or again, be distributed between the two. The stock may concern goods at diverse levels of nomenclature (spare elements, repair items).

2.2.3 The elements to be supplied. Only a limited number of industrials are interested in contracts of a very small volume of parts. Very often, the development and manufacturing times are very long. Because of the manufacturing lead time constraints, the supply of elements needs to be performed at the same pace as the manufacturing in order for the spare elements to be available when the system is started. Moreover, the rapid evolution of the market associated with a considerable time required to design the system often implies that many elements will be obsolete by the end of the preliminary conception phase.

2.2.4 The repairs. As far as repairs in orbit are concerned, the main constraint is the astronaut's qualification. Often, one makes the hypothesis that the low-level repairs (e.g. a welding) are too complex and their quality too uncertain to be performed on board. Thus, the replacements are more generally performed by a total exchange of orbit replaceable units (ORU). When a failing element is brought back from orbit, it is generally restored into its original condition. Indeed, because returns for repair are rare, the elements are often totally dismantled and inspected to collect as much information as possible. According to [START_REF] Batteau | Probabilite ´s et De ´cisions dans l'Incertain[END_REF], the cost of a repaired element in the case of the Space Lab laboratory reaches between 70 and 75 percent of the cost of a new element, which means a gain of 25 to 30 percent compared to the cost of a new element. However, this gain could be greatly diminished by the cost of the shuttle return transport.

2.2.5 Transport. The frequency of transport (90 days for the International Space Station) is the fruit of a compromise between the fuel needs of the station and the load capacity of the space shuttle. It takes also into account a margin of security in case a restocking cannot be done. Shuttle launching data indicate that the major reason for postponement of a launch is of a meteorological nature. One complex transport problem in the context of space flight, is the existence of a lead time for loading. Because of the complexity of the evaluation process involved in the loading of space shuttles, the possibility of modifying the composition of the supply to be loaded is improbable. The continuous operations concept, such as the one envisaged for the International Space Station, poses serious difficulties when an urgent demand for supply is necessary. The potential impact on the planning of several flights, as well as the international aspect of the operations necessitates considering a mechanism of priorities [START_REF] Blagov | Orbital space stations mission control[END_REF]. Furthermore, because of the analyses of the required load, (among others the determination of the centre of gravity and moments of inertia), modifications are progressively impossible depending on the weight of elements to be added or withdrawn from the cargo.

2.2.6 Tests. The state of onboard systems of a space system is controlled almost permanently by means of telemetry and reports carried out by the astronauts. Consequently, failures are immediately communicated. The passive redundancies and the stored elements pose, nevertheless, some difficulties. Theoretically, the periodical test of elements increases the probability of failure. It is necessary, then, to arbitrate between the risk of keeping an element which is potentially out of order and the risk of causing its failure during the test.

Modelling the policies of spare parts supply 3.1 Formulation of the problem

Because of the uncertainties of demand and the capacity of the logistic chain, it is acceptable to think that the risks of seeing a deferred request are never negligible. We are, then, interested in seeing that the cost and availability objectives are reached. The search for an acceptable risk, in the economic sense of the term, necessitates the finding of a compromise between what the user is ready to invest a priori in order to reduce the risks of not attaining the objective, and what the user must spend a posteriori if the selected measures are not sufficient. One can envisage the construction of a curve showing the maintainability relevance (Figure 2). Let us consider the random variable X, representing the average time of unavailability of the function. We note PrðX . ObjectiveÞ, the probability that this average time exceeds the objective fixed by the user. It is accepted that there exists a zone where the variations around the objective are economically acceptable. We propose to construct this curve in order to proceed with the evaluation of the spare elements supply policies. Representing the influence of the decisions concerning the logistic chain requires taking into account the set of supply management parameters in the modelling that we propose:

. the storage echelons envisaged (in orbit, on the ground, at the manufacturers);

. the stock nomenclature (complete elements, sub-elements, parts);

. the supply possibilities (supply parts that were stored or parts that have been repaired or manufactured); and Because each selected combination is a potential solution, the problem may be difficult to resolve. The choice of a model and a resolution technique is the result of a compromise between the representation power, the handling power and the ease of implementation [START_REF] Pe ´re `s | Outils d'analyse de performance pour strate ´gies de maintenance dans les syste `mes de production[END_REF][START_REF] Noyes | Approches me ´thodologiques pour l'aide a `la conception et a `la conduite des syste `mes de production[END_REF]. The complexity of the analytical forms induced by the diversity and complexity of the phenomena that take place led us to choose the route of simulation. Among the available tools we selected the Petri nets because they are easy to use, they can adapt rapidly to structural or organizational modifications, and they integrate stochastic and determinist phenomena.

Little work, to our knowledge has been based on the Petri net for establishing models of logistic support [START_REF] Ereau | Re ´seaux de Petri pour l'e ´tude de la disponibilite ´ope ´rationnelle des syste `mes spatiaux en phases d'avant-projet[END_REF][START_REF] Ereau | Petri nets for the evaluation of redundant systems[END_REF]. In the majority of cases, the authors limit themselves to the evaluation of the number of operators to put in place in order to insure the availability of an installation. [START_REF] Ereau | Re ´seaux de Petri pour l'e ´tude de la disponibilite ´ope ´rationnelle des syste `mes spatiaux en phases d'avant-projet[END_REF] and [START_REF] Ereau | Petri nets for the evaluation of redundant systems[END_REF] propose, however, a simple description of logistic support of a constellation of satellites. [START_REF] Leroy | Le Risque Technologique, Que-Sais-Je?[END_REF] propose as well the concept of logistic mobilization for petroleum platforms. However, one can think that the representation of the supply chain could be much more complex. With this in mind, van der Aalst (1992) proposed models for logistic systems of distribution. We found it interesting to use the Petri net for modelling not only the orbital system, but also for the logistic support network. The models are developed and applied with the help of the Moca-RP tool [START_REF] Cordier | Integration of process simulations in availability studies[END_REF][START_REF] Signoret | Des diagrammes de fiabilite ´aux re ´seaux de Petri et aux calculs de productivite[END_REF]. We propose an interpretation of the Petri nets which permits the representation of the supply policies management and its impact on the system performance. We will show how to represent the orbital system as well as the spare parts logistic chain of supply.

Modelling

Figure 3 gives a sketched view of the modelling structure. In the following, we will successively describe the orbital system, the transportation system and the logistic chain. For more details on this modelling work, please refer to [START_REF] Ereau | Re ´seaux de Petri pour l'e ´tude de la disponibilite ´ope ´rationnelle des syste `mes spatiaux en phases d'avant-projet[END_REF] and [START_REF] Ereau | Petri nets for the evaluation of redundant systems[END_REF].

3.2.1 The orbital system 3.2.1.1 ORUs. Each replaceable element can be found in three states: Standby: this is the state when the element is not used. The transitions between the running state and the failure state are run by external promptings (start or stop impulsions). The start time can be immediate or tempered, eventually controlled by a usage function. This is the original state of the element.

(1) Running: this is the nominal state of the element that allows it to fully ensure its function. In this paper we do not take into consideration elements that would be in a deteriorated functioning state. The time before the transition towards a failure state can be represented by different distributions (Dirac, exponential, Weibull, etc.). ( 2) Failure: this is the state of the element that experienced a failure. Even though the successive damages can be contemplated, we assume that the transition is immediate. Return to the standby state happens after some replacement lead time that depends on the availability of the spare element. We consider this lead time for the replacement in orbit as negligible compared to other lead times taken into account.

Figure 4 shows a view of the related Petri nets.

The elements of an onboard system can be redundant [START_REF] Pages | La Fiabilite ´des Syste `mes[END_REF]Ushakov and Harrison, 1994). [START_REF] Ereau | Re ´seaux de Petri pour l'e ´tude de la disponibilite ´ope ´rationnelle des syste `mes spatiaux en phases d'avant-projet[END_REF] and [START_REF] Ereau | Petri nets for the evaluation of redundant systems[END_REF] suggested a modelling for redundant satellites. In this case several failures are necessary to put the element in the failure state. The following restrictions will be taken into consideration:

. the redundant systems are passive ones, meaning that they are in a waiting state, ready to fulfil their part;

. the commutation on the redundancy is totally reliable; and

. the failure of redundancies from the waiting state are not announced.

We give a representation of a material redundancy in Figure 5. The replacements of elements are determined by maintenance policies that have been selected by the designers (Figure 6):

. Corrective maintenance only: the replacement is performed at the nearest opportunity; the failures from the running state are reported by information released when the element goes through the related transitions; here the information related to the failures from the standby state are not taken into consideration.

. Preventive and corrective maintenance: the replacement is scheduled to be performed at a predetermined moment. Two cases can then occur: either this date is reached with no failure, or a failure occurs before. Let us now take the following scenario into consideration: the failure of an element occurs and there is no spare part available. If an identical element is present in the system, fulfilling a less important application, one can imagine exchanging elements between applications. It can then be represented by adding a transition between the waiting places of the similar elements. These transitions become valid if there is no stock. [START_REF] Sherbrooke | Optimal Inventory Modeling of Systems: Multi-echelon Techniques[END_REF] that the cannibalization can have a negative effect on the availability of the system if it is explicitly considered as an operation strategy and not used during the operation. We will then recommend that this strategy be avoided in the first place.

The phenomenon of cannibalization is sketched in Figure 7.

Functions fulfilled by the system.

Let us now consider all of the functions fulfilled by the orbital system. From the point of view of the function it is required for, the state of the element is binary (running, failure). In relation to the model which we have described for an element (see Figure 4), this means that the standby and failure states are to be considered equally. From our knowledge of the system operating conditions we can deduct the Petri net of the function. The transformation of these operating conditions described by reliability diagrams is possible. Based on this, [START_REF] Signoret | Des diagrammes de fiabilite ´aux re ´seaux de Petri et aux calculs de productivite[END_REF] recently proposed a method that allows the building of the Petri net of a system according to its production levels.

In Figure 8 we consider a function composed of two elements (1 and 2). We assign one place in the Petri net to each level of performance of the system. The entry conditions in the places are determined when transmitted messages are received at the time when a token passes through a transition.

3.2.2 Transport system 3.2.2.1 A basic model. The transport vehicle may be in two different states according to whether it is on the ground or in orbit. We consider the delay between the launch of the shuttle in orbit and its arrival at the station to be negligible (in reality this delay is two or three days). Consequently, when the shuttle is in orbit, we assume that it is docked. A place is assigned to each of the two preceding states. The vehicle is represented by a token. The evolution of the marked places of this network represents the state of the shuttle and therefore the movements of the vehicle between its orbit and the ground (see Figure 9).

Integration of loading constraints.

The loading and unloading activity is represented by transitions of varying lengths of time. We have chosen to consider these periods of loading as negligible compared to other constraints which cause delays of a much longer duration. In order to load an element, three conditions are necessary (see Figure 10): (1) the part must be available in sufficient quantities (marking of place number 12); (2) the shuttle must be on the ground and accept the load (marking of place number 14); and (3) intermediate storage in orbit must be possible (marking of place number 8).

It is possible to transport each element to the orbiting shuttle, but also from the orbit to the ground. It is then necessary to make a distinction between the ascending and descending elements. Consequently, the representation of an element must be modified to represent this (addition of a place standing for "descending stock"). A capacity constraint may be taken into consideration [START_REF] Proth | Les Re ´seaux de Petri pour la Conception et la Gestion des Syste `mes de Production[END_REF] by adding a place with limited capacity which would contain as many tokens as the number of marks in the storage places. The studies carried out at the ESA indicate that the part allocated to Europe for the restocking of maintenance supplies (400kg/year) is not restrictive [START_REF] Passaro | Colombus spares and support equipment provisioning documentation[END_REF]. Therefore, we will not verify this constraint further. If necessary, however, we would take a capacity limitation into account. On the other hand, there is a heavy constraint caused by the limited lead time after which it is no longer possible to carry out the loading. This lead time depends essentially on the mass of the element. One can consider a standard lead time by adding a place which corresponds to the state of "end of loading time" reached when going through a deterministic time transition. Note that the case of variable lead times according to mass has also been dealt with.

Let us note that other constraints such as the maximum number of round trip cycles by elements or the notion of priority element can be taken into account by Petri nets (coloured petri nets as far as the second constraint is concerned).

3.2.3

The ground segment. In order to represent the supply chain, we added, in the Petri nets, the flow of operations (supply, distribution, loading, manufacture, repair), the flow of information (regarding stock, failures, transport), as well as the flow of decisions (regulation actions, loading, unloading, purchase).

Operational level.

Our representation takes into account different stock echelons as well as their in and out flows. We consider the following construction bases (see Figure 11):

. a stock echelon is represented by one place; the number of tokens in that place corresponds to the stock level, that allows the introduction of a capacity constraint;

. the supply activities are represented by transitions of any time length; and . the weight given to the arcs gives information about the quantity supplied.

Representation of loading constraints

From then on, it is possible to model numerous structures. Let us remember that the need for supplies may be responded to in different manners: from a stock echelon, a manufacture on demand (transitions and conditions), or after the assembly of sub-elements (places and transitions). The supply of stock may be achieved by the dispatch of either newly manufactured or repaired elements. Supply by the manufacturer may have capacity or time restrictions (lifetime of aline of fabrication). The repair structure consists of a place standing for the operator, and a transition representing the repair time, no matter the type of distribution. The constraints of this structure, such as the number of operators available or the capacity of the repair centre are classic and easily integrated into the models.

Decision and information levels.

The management of the supply chain gives an answer to the questions we posed at the beginning of this section: Is it preferable to stock supplies? If so, where? Which elements must be supplied? When? In which quantity? And under what form? Should we repair?

The decisions concerning the supply of stock in orbit are linked with the system operational strategy. It is, then, principally the information regarding failures and deadlines which activate supply from the ground. We will show how to represent three standard policies (see Figure 12): (1) Static policy: most often concerns elements for which supply is later impossible.

(2) Calendar policy: this policy consists in supplying at a predetermined date, the fixed or variable quantity. (3) Threshold policy: contrary to the static policy, it permits the control of the quality of service because of its dynamic character -if the demand increases, so also does the frequency of supply. It is obvious that the number of possible combinations is not limited to what we propose here. However, the rules of construction for representing structures more complex remain similar and the modelling stays open to new structures.

Assembly of models.

In order to represent correctly the functioning of the space system and its support, it is first necessary to make their physical flows correspond. In the present case, the transportation plays exactly this part, by carrying the spare elements from the support system to the orbital system. The physical assembly of the models is performed through the transport network that enables the synchronization of the two other networks. The supply events have then to be coordinated with the events that happen in orbit.

To do that, one has to identify the data that flow in the system to activate the support actions. Finally, the choice of a policy determines both the physical

Application to the Columbus laboratory 4.1 Description of Columbus

The International Space Station recently became a reality with the successful launching and docking of its first two modules. Europe actively participates in this technological and scientific development by building many elements and in particular the orbital Columbus laboratory (see Figure 13). The laboratory is a pressurized habitable module designed to provide for ten years a multifunction laboratory able to welcome all the scientific disciplines related to micro gravity: technological and scientific research as well as industrial applications. The detailed design review of the laboratory is now under process and the launching of the laboratory is scheduled for October 2002.

The average availability objective for the laboratory functions can be different depending on whether it regards security functions (99.9 percent on 90 days during 10 years) or operating functions (94 percent on 90 days during 10 years). Reaching this objective requires the support of maintenance activities and in this perspective the laboratory carries about 300 replaceable elements representing 65 different types. Only 15 percent of these elements are subject to preventive maintenance, which consequently emphasizes the role of the logistic support system.

Evaluation of the supply policies of a selected function 4.2.1 Selection of a study function.

No scientific experiment can be run without electrical energy, this is the reason why the "payload power supply" function has been selected. This function is also interesting because of its relatively simple architecture that allows a rapid illustration of the model's implementation. The systems of the International Space Station provide the laboratory with direct current (120V DC) through two buses (see Figure 14).

Each bus feeds a Power Distribution Unit (PDU). The two elements receive electrical power and provide the connections, the distribution, as well as the protection of all the experiment racks. The power supply of the PDUs are also cross-strapped in order to compensate for the loss of a bus of the station. Each PDU is redundant and feeds two power supplies (nominal and auxiliary) which dispatch the power to the racks. This function, also belonging to the power distribution to the onboard systems, has to be available on average 99.9 percent on 90 days during 10 years because of its great impact on the laboratory security.

4.2.2 Modelling. The modelling of each of the PDUs is performed as described in paragraph 3. The replaceable elements have been integrated in the model by taking into account the possibility for the standby redundancy to fail. As far as the maintenance during the flight is concerned, the dimensions and the weight of the element make its orbital storage impossible. Because the cannibalisation is not considered, the astronauts will replace the element when it becomes available. This replacement will be performed either to restore the redundancy or after a complete failure. We consider the three following states for the power supply function:

(1) running on auxiliary power: from the PDU 1;

(2) running on auxiliary power: from the PDU 2; and

(3) not running: PDU 1 and PDU 2 failure.

As regards the subnet that represents the transport, the closure of the loading capacities happens 45 days before launching. The length of the orbital stay is set to 12 days (288 hours).

The first supply policy for the elements of the power supply function consists in supplying first the stock on the ground with one element and then to proceed with the return of failing elements in orbit for repair. The second policy is a static one where the first supply takes into account the number of expected failures during the lifetime.

4.2.3 Evaluation and discussion on the results. We can now deal with the analysis of the technico-economical performance of the supply policies. In order to do that, we first run a simulation (100,000 stories) which allows us to evaluate the selected indicators. The processing of the simulation results leads to the curve of the function average unavailability (see Figure 15).

We can directly visualize the probability of not meeting the average objective by plotting the related limit (99.9 percent on 90 days, i.e. approximately 2.2 hours of unavailability), still keeping in mind the extreme nature of the selected operation policy. It can be stated that the two policies are quasi identical as far as performance. Thanks to the simulation we can then proceed with the evaluation of the average costs of each of these policies. The results are as follows: One can see that the two policies are close in performance but not in cost. Let us note that this result does not confirm the intuition of the designers of the orbital laboratory. They thought that the repairs would not be economically worth the cost of transport.

Conclusion

The use of the Petri nets for the specification and analysis of logistic support systems seems to be a research perspective full of promise. With the help of coloured or uncoloured stochastic and deterministic Petri nets related to each support element, future works will lead to the development of a Logistic Support Analysis. The development of such a tool will allow the finding of a partial solution to the difficulty of implementation of this type of analysis. The work which has been presented in this paper goes in this direction. The modelling of the supply logistic chain and the evaluation of the technicoeconomical relevance of its structure and control became possible. A logical follow up of this work will consist in using formal tools and optimisation methods to analyse the Petri nets that represent the system and its logistic support. It will be then possible to detect, in the structure of the Petri nets, the potential problems of the support system in order to improve the relevance of the undertaken efforts. Eventually let us also mention that this work is currently being applied to the other functions of the Columbus laboratory where it is used as a guiding decision tool.

.

  A ground segment (B), which includes the infrastructure and the means necessary to monitor the flight segment (control and communication centres), the industrial structure that allows the support of the operation

  Figure 1. Components of a spatial system

.

  the management decisions (When to supply? Which elements and what quantity? Under which condition?).

Figure 2 .

 2 Figure 2. Relevance of the efforts of maintainability

Figure 3 .

 3 Figure 3. Architecture of the whole model

  Figure 4. Representation of a replaceable element

  Figure 5. Representation of a material redundancy

  Figure 7. Cannibalization between two elements

  Figure 8. Modelling of a function

  Figure 10. Representation of loading constraints

  Figure 11. Standard supply structure

Figure 12 .

 12 Figure 12. Different supply policies

  Figure 13. The International Space Station and the Columbus laboratory

Figure 14 .

 14 Figure 14. Simplified view of the "payload power supply" function

Figure 15 .

 15 Figure 15. Evolution of the power supply unavailability


Wafa Ben Hassen
email: wafa.benhassen@cea.fr

Fabrice Auzanneau #
email: fabrice.auzanneau@cea.fr

Luca Incarbone #
email: luca.incarbone@cea.fr

Ayeley P Tchangani
email: ayeley.tchangani@enit.fr

OMTDR using BER Estimation for Ambiguities Cancellation in Ramified Networks Diagnosis

Nowadays, increasing demands for on-line wire diagnosis using reflectometry have imposed serious challenges on signals processing, bandwidth control and interference mitigation. On-line diagnosis aims at detecting and locating faults accurately while the target system is running. In this work, a new reflectometry method, named "Orthogonal Multi-Tone Time Domain Reflectometry" (OMTDR), is proposed. OMTDR, based on Orthogonal Frequency Division Multiplexing (OFDM), is a suitable candidate for on-line diagnosis as it permits interference avoidance, bandwidth control and data rate increase thanks to the use of orthogonal tones and guard intervals. Over the diagnosis function, OMTDR adds communication between sensors to more accurately determine faults position in a multi-branch network using a distributed strategy. OMTDR was tested on a branched network consisting of three cables with different lengths, with sensors at each cable end. Here, the sensors signals are carefully constructed using a resource allocation scheme to use frequencies below and above the prohibited bandwidth, used by the target system, for communication and diagnosis. Simulation results

show that the proposed method performs well in a branched wiring network as it permits to detect and locate faults accurately even when the target system is operating.

I. INTRODUCTION

In aging aircraft, increasing demands for regular and thorough wire inspection have imposed serious challenges nowadays. A broken, chafing and corroded wire may lead to an in-flight fire or other disastrous accidents such as the crashes of TWA Flight 800 in July 1996 and Swissair Flight 111 in September 1998 [START_REF] Wheeler | Aging aircraft wiring fault detection survey[END_REF]. Several techniques have been proposed in order to detect and locate faults before problem appearance. Reflectometry is considered as the best method for wire diagnosis [START_REF] Parkey | A Method of Combining Intermittent Arc Fault Technologies[END_REF]. The sensor injects a test signal down the wire and then analyses the reflected one due to impedance discontinuities caused by likely existing faults [START_REF] Cataldo | Broadband Reflectometry for Diagnostics and Monitoring Applications[END_REF], [START_REF] Tengg | Reflectrometry based Fault Localization in Automotive Bus Systems[END_REF]. Nowadays, on-line diagnosis, aiming at detecting and locating faults continuously while wires in use are in-flight, is increasingly attractive. As the native signals presence on live wires may interfere with diagnosis, on-line diagnosis has imposed serious challenges on signal processing, bandwidth control and interference reduction. Recently, different reflectometry methods have been proposed to overcome these challenges. Among them let us mention: Spread Spectrum Time Domain Reflectometry (SSTDR) [START_REF] Wei | The Study of Spread Spectrum Time Domain Reflectometry for Cable Fault Detection and Location On-line[END_REF], Multi-Carrier Reflectometry (MCR) [START_REF] Amini | Filterbank Multicarrier Reflectometry for Cognitive Live Wire Testing[END_REF] and Multi-Carrier Time Domain Reflectometry (MCTDR) [START_REF] Lelong | On Line Wire Diagnosis using Multicarrier Time Domain Reflectometry for Fault Location[END_REF]. In SSTDR method, the sensor injects a sine wave modulated Pseudo Noise code as a test signal, permitting to diagnose live wires. Although SSTDR has been shown to be feasible for on-line diagnosis, it is still limited in terms of interference avoidance. This problem is partly solved by MCR and MCTDR methods. Both of them, based on multicarrier principle, employ a summation of harmonically related sine waves using Inverse Digital Fourier Transform. Here, each component magnitude in the frequency domain can be reduced or cancelled leading to bandwidth control. Although MCR and MCTDR are interesting methods for on-line diagnosis, they require a huge post-processing phase to reduce interference. In a complex wiring network, a distributed diagnosis strategy is crucial to locate faults accurately [START_REF] Ravot | Distributed Reflectometry-based Diagnosis for Complex Wired Networks[END_REF], [START_REF] Lelong | Distributed Reflectometry Method for Wire Fault Location Using Selective Average[END_REF]. The idea is to implement several sensors at different points of the network in order to maximise diagnosis coverage. However, as multiple sensors are making measurements simultaneously, specific signal processing methods are required to avoid interferences among concurrent modules. In [START_REF] Ravot | Distributed Reflectometry-based Diagnosis for Complex Wired Networks[END_REF], authors propose to use a modified SSTDR method where some constraints are imposed on the codes properties (primitive polynomial characteristics, code length and bit rates). Instead of working on the test signal, the proposed method in [START_REF] Lelong | Distributed Reflectometry Method for Wire Fault Location Using Selective Average[END_REF] uses well-chosen weighted average to remove location ambiguities and interference noise thanks to multiple measurements. However, it is important to know that the averaging process is based on the hypothesis that the network impulse responses do not change while the measurements are performed, otherwise, false alarms may be triggered. In practice, this hypothesis may not always be held when the target system is operating. Moreover, the efficiency of this method depends on several parameters such as measurements number, measurement time, noise, interference, etc.

In this paper, a new reflectometry method, named Orthogonal Multi-Tone Time Domain Reflectometry (OMTDR) is proposed. OMTDR, based on Orthogonal Frequency Division Multiplexing (OFDM) [START_REF] Rohling | OFDM: Concept for Future Communication Systems[END_REF], is a suitable candidate for on-line diagnosis as it permits interference avoidance and bandwidth control thanks to the use of orthogonal tones and guard intervals [START_REF] Chen | A Study of OFDM Synchronization Algorithm Based on Coaxial Cable Operating at Gigabit[END_REF]. Over the diagnosis function, OMTDR adds communication between sensors to more accurately discriminate ambiguous faults position in a multi-branch network using a distributed strategy. Sensors signals are carefully constructed using a resource allocation scheme to use frequencies below and above the prohibited bandwidth, used by the target network, for communication and diagnosis. Simulation results show that the proposed method performs well in a branched wiring network as it permits to detect and locate faults accurately even when the target system is operating. This paper is organized as follows. Section II derives a wave propagation model using ABCD matrix. Section III discusses the OMTDR methodology. Section IV proposes a resource allocation algorithm for the existing sensors. Simulation results of OMTDR are described in Section V. Section VI summarizes the paper and draws important conclusions.

II. ABCD MODEL FOR COMPLEX WIRING NETWORK

The wave propagation in a transmission line can be modelled by a RLCG circuit model [START_REF] Auzanneau | Defects detection and localization in complex topology wired networks[END_REF]. It is represented by Telegrapher's equations at time t as:

∂v(x, t) ∂x = -Ri(x, t) -L ∂i(x, t) ∂t . (1) ∂i
(x, t) ∂x = -Gv(x, t) -C ∂v(x, t) ∂t . (2)
where the quantities R (resistance), L (inductance), C (capacitance) and G (conductance) are the electrical per-unit-length parameters. In a lossless transmission line, the quantities R and G are equal to zero. Let v(x, t) and i(x, t) represent, respectively, voltage and current at time t and position x(0 ≤ x ≤ l) where l is the transmission line length. Considering a lossless transmission line, the propagation constant γ (radians/m), in the frequency domain, can be expressed by:

γ = -ω √ LC. ( 3
)
where ω is the angular frequency, ω = 2πf . Then, the characteristic impedance of the transmission line is obtained as follows [START_REF] Collin | Foundations for Microwave Engineering[END_REF]:

Z c = L C . (4)
Here, the ABCD matrix of wire W i is used to derive reflection and transmission coefficient formulas in a transmission line where:

A i B i C i D i = cosh γ i l i Z c sinh γ i l i sinh γili Zc cosh γ i l i (5)
Let's now consider a simple example: Y shaped network consisting of three transmission lines W 1 , W 2 and W 3 with the same characteristic impedance Z c and lengths l 1 , l 2 and l 3 respectively, as shown by Fig. 1. We assume that sensor

Y 2 = C 2 Z 2 + D 2 A 2 Z 2 + B 2 . ( 6
)
Y 3 = C 3 Z 3 + D 3 A 3 Z 3 + B 3 . (7)
In order to compute the equivalent reflection coefficient Γ 1 , ABCD matrix (5) of wires W 1 ,W 2 and W 3 are cascaded. Then, the equivalent impedance at the injection port is given as follows:

Z 1 = A 1 Z ′ 1 + B 1 C 1 Z ′ 1 + D 1 . ( 8
)
where the impedance of W 1 at the junction is expressed as

Z ′ 1 = 1/ (Y 2 + Y 3 ).
The equivalent reflection coefficient Γ 1 is given as:

Γ 1 = Z 1 -Z c Z 1 -Z c . (9)
The reflection coefficient enables to sensor S 1 to detect and locate faults in terms of distance relative to the sensor on the wiring network. However, as it is sometimes difficult to accurately locate faults in the case of symmetric network where transmission lines lengths l 2 and l 3 are almost the same, a communication between sensors is added to determine faulty wires. This function aims at solving diagnosis ambiguities in the case of complex symmetric wiring networks. Therefore, transmission coefficient needs to be computed in the studied network based on the S-parameters. Here, T 21 and T 31 denote the transmission coefficient from S 1 to S 2 and from S 1 to S 3 respectively and are obtained as:

T 21 = 2 (A 1 + Z c C 1 ) A 2 + B2 Zc + B1 Zc + D 1 ζ 21 . ( 10
)
T 31 = 2 (A 1 + Z c C 1 ) A 3 + B3 Zc + B1 Zc + D 1 ζ 31 . ( 11
)
where ζ 21 and ζ 31 are respectively expressed by:

ζ 21 = (C 2 Z c + D 2 ) + (C 3 Z c + D 3 ) • A 2 + B 2 /Z c A 3 + B 3 /Z c . ( 12
)
ζ 31 = (C 3 Z c + D 3 ) + (C 2 Z c + D 2 ) • A 3 + B 3 /Z c A 2 + B 2 /Z c . (13)
Using diagnosis and communication functions, the sensor S 1 is now able to locate faults in a branched wiring network. However, this is not possible with the interference due to live signals in the network. Then, OMTDR method is a suitable candidate for on-line diagnosis to avoid interference, bandwidth control and data rate increase as it is explained in the following sections.

III. OMTDR METHODOLOGY: DIAGNOSIS AND COMMUNICATION

In OMTDR reflectometry, the test signal injected down the wiring network by sensor S 1 is defined as:

x m (t) = N -1 n=0 X m,n g n (t -mT ) . ( 14
)
where m and n refer to the OFDM symbol number and the tone number in the considered OFDM symbol m. Each tone signal g n (t) is modulated independently by the complex valued modulation symbol X m,n and is expressed as:

g n (t) = e j2πn∆f t if t ∈ [-T G , T s ] . 0 if not. ( 15
)
where T s = 1 ∆f and T G represent respectively useful OFDM symbol duration and guard interval duration. ∆f is the frequency distance among two consecutive tones. As a numerical system is used, the test signal is sampled with the sample interval ∆t = 1/B = 1/N ∆f . Here, the samples of the transmit signal are denoted by x m,i where i ∈ {0, 1, • • • , N } and are expressed as follows:

x m,i = N -1 n=0 X m,n e j2πi n N . ( 16
)
A. Sensor Diagnosis Function using OMTDR Respecting the reflectometry principle, the sensor S 1 injects the test signal x m,i down the wiring network. During its propagation, a part of its energy reflects back to the sensor S 1 when it crosses impedance discontinuities such as a fault. Then, the received signal is expressed as:

y m,i = hr m,i * x m,i + n m,i . ( 17
)
where * is the convolution product and n m,i is the Additive White Gaussian Noise (AWGN) term. The channel impulse response hr m,i is expressed as:

hr m,i = 1 2π N -1 i=0 Γ 1 e jωi n N . ( 18
)
where Γ 1 is the equivalent reflection coefficient given by [START_REF] Lelong | Distributed Reflectometry Method for Wire Fault Location Using Selective Average[END_REF]. The block diagram of the diagnosis function is shown by

B. Sensor Communication Function using OMTDR

Thanks to the multi-carrier principle, OMTDR provides sensors communication in order to reduce diagnosis ambiguities due to multi-path propagation in complex wiring networks. The transmitted signal ht m,i for communication between S 1 and S 2 is expressed as follows:

ht m,i = 1 2π N -1 i=0 T 21 (ω)e jωi n N . (19)
The transmission coefficient T 21 is given by [START_REF] Rohling | OFDM: Concept for Future Communication Systems[END_REF]. The same formula is used for communication between S 1 and S 3 by replacing T 21 by T 31 (given by ( 11)). At the receiver side, the receiver sensor performs the inverse process of the transmitter [START_REF] Rohling | OFDM: Concept for Future Communication Systems[END_REF] (guard interval suppression, FFT, M-QAM Demodulation) as shown by Fig. 3.

In order to ensure both diagnosis and communication functions, a resource allocation scheme is required to control the available bandwidth and reduce interferences.

IV. A RESOURCE ALLOCATION SCHEME FOR SENSORS

In OMTDR reflectometry, the network bandwidth B is divided into N tones using OFDM modulation. Let's introduce the matrix H with dimension (K × N ) where K and N denote, respectively, the sensors number and available tones. H expresses resource allocation indicators where,

h k,n =    1 if tone n is allocated to sensor k. 0 if tone n is not allocated to sensor k. -1 if tone n is in a prohibited bandwith.
(20) Thanks to multi-tone reflectometry, the sensors signals are carefully constructed using a resource allocation scheme to choose frequencies below and above the prohibited bandwidth, used by the target system, for communication and diagnosis. Considering N p as the number of tones in the prohibited bandwidth, the authorized tones number N u is expressed as follows N u = N -N p . Let's assume that N diag and N com denote the tones number reserved for diagnose and communication respectively, where

N diag = ⌈αN u ⌉, N com = ⌈βN u ⌉ and α + β = 1.
Here, the proposed strategy imposes that sensor S 1 is responsible for network diagnosis and data communication by injecting periodically a test signal down the network. Then, sensors S 2 and S 3 ensure sensors communication. Therefore, N diag (S 1 ) = N diag and N com (S i ) = Ncom K tones should be allocated to each sensor i ∈ {1, 2, 3} for, respectively, diagnosis and communication where K = 3 in this work. Then, a resource allocation policy is needed for communication tones as shown by the pseudo code 1. The same pseudo code is applied for diagnosis tones al-

Algorithm 1 Communication Tones Allocation for k = 1 → K do j = 1; while N com (k) = 0 do if K k=1 H (k,j) = 0 then j = j + 1; else H k,j = 1; N com (k) = N com (k) -1 end if
end while end for location by replacing N com (k) by N diag (k) and matrix H is inherited from resource allocation phase. However, in this case, K = 1 as only the sensor S 1 is allowed to make diagnosis and the pseudo code is applied only by sensor S 1 aiming at avoiding the prohibited bandwidth.

V. SIMULATION RESULTS

OMTDR was tested on a Y shaped network (Fig. 1) consisting of three transmission lines with different lengths l 1 = 50m, l 2 = 60m and l 3 = 110m. The total bandwidth in the studied network is equal to 0 -256 MHz. For these simulations, the prohibited bandwidth is 64 -192 MHz. The characteristic impedance of all transmission lines Z c is equal to 100Ω. Considering additive white Gaussian noise, the SNR chosen here is equal to 10dB. Here, the allocation factors α and β are chosen as α=25% and β=75%. Simulation parameters are presented in Table I.

A. Hard Fault Detection: Open Circuit Fault

Let's now consider unmatched transmission lines (Z L = Z c ) on the network. Fig. 4 shows the reflectogram obtained by sensor S 1 using OMTDR method in a Y shaped network with Z L = +∞ at the end of lines W 2 and W 3 . Here, the proposed method detects and locates accurately the end of the lines W 2 and W 3 by sensor S 1 , referred by the positive obtained peaks at 110m and 160m. The first obtained negative peak at 50m represents the junction that connects the three lines.

B. Soft Fault Detection: Chafing Fault

In order to simulate a soft fault, a local variation of capacitance ∆C and inductance ∆L are simulated on the branch W 2 of the network where C d = (1 + ∆C) C and L d = (1 -∆L) L. C d and L d represent the fault capacitance and inductance. Fig. 5 shows a reflectogram at S 1 with a soft fault where ∆C = 50% and ∆L = 50%. Here, the fault portion is located at 70m from S 1 as shown by the very weak peak at that distance. The other weak peaks for example 130m, 150m, 180m, represent the same detected soft fault as the first peak but shifted in time due to round-trips in the network. Fig. 6 shows the soft fault peak variations in terms of fault

C. Sensors Communication

The Bit Error Rate (BER) is a key parameter used to characterise the communication channel quality. It represents the number of bit errors divided by the total number of transmitted bits during a given time interval. Fig. 7 shows the BER variation in terms of fault impedance (Z d ) variation relative to the characteristic impedance for different SNR values. Here, the BER increases when the fault severity increases. In our case (SN R = 10dB), the BER values for communication from S 1 to S 2 and S 1 to S 3 are given in Table II. Referring to Fig. 7, the BER(S 1 , S 2 ) corresponds to a healthy link between S 1 and S 2 (∆Z d = 0). However, when BER(S 1 , S 3 ) = 3.48%, ∆Z d is equal to 50%, indicating a soft fault on link S 1 to S 3 . Thus, sensors communication permits to give an additional information on the network quality and removes ambiguities caused by small faults.

D. Fault Localisation using Bayesian Networks

After network diagnosis and sensors communication, sensor S 1 is responsible for decision making about the network state and the position of likely detected faults. To determine the confidence level to be allocated in the results provided by this sensor, a probabilistic approach is used. It is based on the Bayesian Networks (BN) [START_REF] Godichaud | Disassembly Process Planning using Bayesian Networks[END_REF], [START_REF] Hassen | A Distributed Diagnosis Strategy using Bayesian Network for Complex Wiring Networks[END_REF]. Here, the variables of interest are defined in Table III. In this case, nodes of the BN are divided into two sets: ) .

(23) As expressed by equation (21), BER is not considered for fault localisation on branch W 1 . Here, the peak presence (PeakS1) and distance (DistS1) are sufficient because if DistS1="Inf50m", then there is no doubt about the fault presence on wire W 1 . The BN is modelled as shown by Fig. 8. For fault localisation, the BN is powered by the collected P (X 1 /Obs 1 , Obs 2 ='Healthy')=100% P (Obs 2 ='Sup50m')=100 % P (X 2 /χo -{Obs 4 } ='Faulty')=100% P (Obs 3 ='Sup1point6')=100% P (X 3 /χo-{Obs 3 } ='Healthy')=100% P (Obs 4 ='Inf1point6')=100%

BN results, the fault is present on branch W 2 with certainty (P r(X2/Obs 1 , Obs 2 , Obs 3 ) = 100%).

E. Discussion and Perspectives

Simulation results show that the proposed OMTDR method performs well in a branched wiring network. It permits not only to detect faults even with the presence of noise, but also to locate them with no ambiguities thanks to the communication between sensors. Here, only one sensor has to inject signal test for fault diagnosis, thus reducing the diagnosis process complexity. In this case, the BN seems to be not interesting as it provides a deterministic confidence level (equals to 100%).

However, it is more important considering other parameters ( sensor reliability, wires environment, etc.) which may increase the decision uncertainty. This is the purpose of future works.

VI. CONCLUSION

A new reflectometry method called OMTDR is proposed. Here, a test signal is constructed using OFDM principle. This test signal is sent down the wiring network and the received signal is examined to retrieve information regarding potential defects in the network while the target system is on-line. A communication function is introduced for sensors in order to reduce ambiguities caused by signals propagation and then improve location accuracy in complex networks. The proposed OMTDR was simulated in a branched wiring network and shown to work effectively. This work will be applied to more complicated network topologies, tested experimentally and then implemented in embedded systems as future works.

Fig. 1 .

 1 Fig. 1. Y Shaped Wiring Network S 1 injects at port 1 (line W 1 ) and the other lines W 2 and W 3 are loaded at their extremities by impedance Z 2 and Z 3 respectively. Y 2 and Y 3 , the admittance of lines W 2 and W 3 , respectively, are obtained as follows:

Fig. 2 .

 2 Fig. 2. Diagnosis Block Diagram using OMTDR Method.

Fig. 2 .

 2 Fig.2. The reflectogram is obtained using the inter-correlation function between the injected and reflected signals. Then, an averaging step is performed in order to reduce the undesirable signals and improve the Signal-to-Noise Ratio (SNR).

Fig. 3 .

 3 Fig. 3. The Block Diagram of Sensors Communication.

1 Fig. 4 .

 14 Fig. 4. End of Open Circuit Fault Location using OMTDR by Sensor S 1

Fig. 5 .Fig. 6 .

 56 Fig. 5. Soft Fault Detection using OMTDR by Sensor S 1

Fig. 7 .

 7 Fig. 7. Sensors Communication: BER performance

Fig. 8 .

 8 Fig. 8. The Bayesian Network Structure

  χ o is the set of nodes representing the observed symptoms of the studied system.Considering χ o = {Obs 1 , Obs 2 , Obs 3 , Obs 4 } and χ = {X 1 , X 2 , X 3 }, the conditional probability for faults on branch W 1 ,W 2 or W 3 is, respectively, given by:P (X 1 /Obs 1 , Obs 2 ) = P (X 1 ; Obs 1 , Obs 2 ) P (Obs 1 , Obs 2 ) .(21)P (X 2 /Obs 1 , Obs 2 , Obs 3 ) = P (X 2 ; Obs 1 , Obs 2 , Obs 3 ) P (Obs 1 , Obs 2 , Obs 3 ) .

	(22)
			TABLE III
			VARIABLES OF INTEREST
	Variable	Notation	Description	Modality
	Wire1	X 1	Wire W 1	Faulty/Healthy
	Wire2	X 2	Wire W 2	Faulty/Healthy
	Wire3	X 3	Wire W 3	Faulty/Healthy
	PeakS1	Obs 1	Peak Detection	Yes/No
	DistS1	Obs 2	Peak Distance to S 1	Inf50m/Sup50m
	BERS1toS2	Obs 3	BER (S 1 to S 2 )	Inf1point6/Sup1point6
	BERS1toS3	Obs 4	BER (S 1 to S 3 )	Inf1point6/Sup1point6
	• χ is the set of nodes representing the real state of the
	studied system.

• P (X 3 /Obs 1 , Obs 2 , Obs 4 ) = P (X 3 ; Obs 1 , Obs 2 , Obs 4 ) P (Obs 1 , Obs 2 , Obs 4


S Ferron

P Jehan

X Guillory

P Uriac

Intramolecular transesterification of depsides yields fluorescent 1Hisochromen-1-ones: application as a chemical probe for lichen determination

Keywords: Depsides, -keto esters, enolate, transesterification, fluorescent 1H-Isochromen-1-ones, chemical lichen determination, KUV probe Reagent K or K: 10% aq KOH solution; KUV probe:

Intramolecular transesterification of depsides yields fluorescent 1H-isochromen-1-ones: Application as a chemical probe for lichen determination

S Ferron, P Jéhan, X Guillory, P Uriac

Introduction

Lichens arise from a symbiotic relationship between a fungus and a photosynthetic partner (algae or cyanobacteria) and are considered a biological entity rather than a systematic one as their classification is based on the nature of the fungi.

Then, the analysis of the lichen specialized metabolites along with morphological and genetical data of fungi [START_REF] Asahina | Chemistry of Lichen Substances[END_REF][START_REF] Calcott | Secondary metabolism in the lichen symbiosis[END_REF][START_REF] Culberson | The Use of Chemistry in the Systematics of the Lichens[END_REF][START_REF] Elix | Recent Progress in the Chemistry of Lichen Substances[END_REF][START_REF] Huneck | Identification of Lichen Substances[END_REF] are widely used for the taxa and species determination, leading to the chemosyndrome concept. In this context, the study of the aromatic depsides, generated by the polyketide synthase (PKS) enzymatic complexe [START_REF] Armaleo | Insights from the first putative biosynthetic gene cluster for a lichen depside and depsidone[END_REF][START_REF] Herbst | The architectures of iterative type I PKS and FAS[END_REF][START_REF] Walsh | Natural Product Biosynthesis: Chemical Logic and Enzymatic Machinery, Chapter 2. Polyketide Natural Products. 597 598 Xanthoparmelia loxodes[END_REF], has been shown to resolve numerous taxonomic problems among lichens.

In a previous publication [START_REF] Hellou | A chemotaxonomic study of the Xanthoparmelia pulla group in Algeria[END_REF], we have shown that two depsides extracted from Xanthoparmelia delisei or X. loxodes, the glomelliferic acid 1 and the glomellic acid 2, exhibited a strong fluorescence at 365 nm when a solution of 10% aqueous KOH (the K spot reagent in lichenology) was added (Figure 1). This addition of K reagent is thereafter referenced as the KUV probe. An unusual structural feature of these two lichen specialized metabolites when compared to other depsides is that they are substituted on the C-6 of the A ring by a 2-oxoalkyl chain. This observation prompted us to explore their reactivity to rationalize the fluorescence observed and to broaden the use of the KUV probe onto other similar depsides from various lichens.

In this paper, the chemical behaviour of eight depsides treated with the KUV probe was explored and the fluorescent compounds isolated and fully characterized, leading to their identification as isochromen-1-ones (1H-2-benzopyran-1-ones). To explain their formation under basic conditions, a mechaninistic explanation, supported by DFT calculations, is presented. Finally, we highlight the interest of the KUV probe in the field of lichenology for lichen determination and exemplify its use, both out in the field by direct application on the medulla or in the laboratory on TLC, on a selection of European Porpidia species.

Results and discussion

Selection and purification of -keto ester-containing depsides

Using the literature data [START_REF] Huneck | Identification of Lichen Substances[END_REF], the depsides 1-7 and 4' reported in Figure 2 were selected and extracted from the corresponding lichens using acetone, followed by purification by column and/or thin layer chromatography using silica gel with the solvent system C (toluol/acetic acid, 85/15) as the mobile phase.

Reactivity of -keto containing lichen metabolites in basic conditions

The cleavage of the ester bond between A and B rings of the depsides (Figure 1) has been previously performed for structure elucidation purposes. Along with saponification (5% KOH or NaOH at 100°C) and alcoholysis (MeOH or t-BuOH) at high temperature, acidic hydrolysis (96% H 2 SO 4 , then H 2 O at 0°C) has been widely used [START_REF] Culberson | New Depsides from Lichens: Microchemical Methodologies Applied to the Study of new Natural Product Discovered in Herbarium Specimens[END_REF].

In this study, the selected depsides were allowed to react overnight with the reagent K at room temperature in order to mimic the conditions used for 1 and 2 (Figure 1). After neutralization with 10M aq. HCl, used to minimize the total water amount, two series of aromatic products (Figure 3) were obtained:

-tri-substituted 1H-Isochromen-1-ones: glomelline (8) [START_REF] Huneck | Struktur der glomellsäure[END_REF], 4-O-methylolivetonide (9) (Asai et al., 2017;[START_REF] Saeed | Synthesis of 8-hydroxy-6-methoxy-3-pentyl-1H-isochromen-1-one from Tessmannia densiflora[END_REF], insignine (10) [START_REF] Elix | Synthesis of Depsides Present in the Lichen Porpidia glaucophaea[END_REF] and olivetonide (11) [START_REF] Huneck | Mitteilung über Flechteninhaltsstoffe. Arthoniasaure, ein neues Depsid aus Arthonia impolita (Ehrh.)[END_REF][START_REF] Kaji | Synthesis of Antifungal Isocoumarins[END_REF][START_REF] Sanchez | Sur les résinoïdes de lichens fabriqués par un procédé en continu pour servir de matières premières en parfumerie[END_REF], fluorescent at 365nm (F) in basic conditions. These heterocycles were obtained by rearrangement of the -keto-ester moiety of the ring A.

-and various diphenolic acids (12-16) corresponding to the B ring after ester hydrolysis.

As demonstrated with the glomelliferic acid 1, the same complete reaction was observed if the neutralization was carefully performed using a saturated NH 4 Cl solution (pH: 4-5).

In the case of 4', bearing a second -keto-ester moiety on the B ring, three compounds were isolated by chromatography: along with 9 and 15 (previously obtained from 4), the fluorescent 2-O-methylolivetonide 17 [START_REF] Asahina | Lichen substances. XLVIII. Microphyllinic acid, a new depside from Cetraria collata f. microphyllina A[END_REF] was also obtained. This isomer of 9 is resulting of the rearrangement of the keto-ester moiety of the B ring (Figure 4).

At this stage, we wanted to investigate if identically substituted depsidones, linked by a supplementary ether bridge between C-2 and C-5', could also exhibit this specific reactivity. For this purpose, the same experimental conditions have then been applied to the -alectoronic acid 18 (Ochrolechia parella) [START_REF] Millot | Metabolites from the Lichen Ochrolechia parella Growing under Two Different Heliotropic Conditions[END_REF] and to the -collatolic acid 19 (Tephromela atra) [START_REF] Millot | Phytochemical investigation of Tephromela atra: NMR studies of collatolic acid derivatives[END_REF] (Figure 5A).

Their  -keto-ester moiety was not affected and neither the -alectoronic acid nor the -collatolic acid were obtained. In one last experiment, the importance of the keto function was demonstrated. Thus, the perlatolic acid 20 (2'-deoxoglomelliferic acid) (Elix, 1974) remained unchanged when treated with K in the same conditions.

Optical properties of the 1H-Isochromen-1-ones

The UV and fluorescence spectra (Figure 6) of the isochromen-1-ones 9 and 11 were recorded in methanol (blue curves). The addition of NaOH (red curves), induced a phenate formation in ortho of the C=O that results in a bathochromic (near 350 nm) and hypsochromic effect (near 240 nm) for compound 9. The effects were inversed for 11, due to the ionization of the second phenol in para of the C=O. The blue fluorescence emission is represented by the green curve.

Chemistry: Mechanism

Under basic condition, the observed isochromen-1-ones formation led us to propose, in accordance with the literature [START_REF] Duan | Synthesis of Naphthalenes through Three-Component Coupling of Alkynes, Fischer Carbene Complexes, and Benzaldehyde Hydrazones via Isoindole Intermediates[END_REF][START_REF] Sudarshan | Convenient Synthesis of 3-Glycosylated Isocoumarins[END_REF], the formation of an enolate anion (I) that reacts in an intramolecular transesterification to yield the isochromen-1-one derivatives (Figure 7A). The ketoenolate equilibrium was displaced by the cyclisation and the transformation was complete. Alternatively, the more usual ester saponification (II) followed by dehydration could be proposed, but this mechanism needs more drastic conditions and would lead to hydroxy-lactone intermediates which were never isolated during our numerous experiments. Interestingly, the same ester cleavage, but probably involving an ortho effect leading to ketene formation (III), was observed in the mass spectrometer (Figure 7B). DFT calculations were undertaken to assess differences in chemical reactivity between depsides and depsidones.Thus, under neutral conditions, an intramolecular hydrogen bond between the ester carbonyl and the OH-2 results in an energetically favoured planar conformation (Figure 8A), which is in accordance with the crystal structure of atranorine [START_REF] Brassy | Structure de l'atranorine[END_REF], a close structural analogue. Upon addition of K, deprotonation of the OH-2 disrupt the planar conformation and position the ester carbonyl group in a perpendicular conformation relative to the phenyl ring A that is suitable for a nucleophilic attack by the enolate (Figure 8B). Interestingly, the highest energy observed in the relaxed coordinate scans displays a geometry close to the transition state of the proposed mechanism.

On the contrary, in the case of the depsidones 18 and 19, the supplementary ether function between the A and B rings locks the compounds in a wide V-shaped conformation (118° angle, Figure 7C). The fixed geometry of the intra-cyclic ester of the depsidone core then prevents a nucleophilic attack by the enolate as the angle between the two isn't suitable (Figure 7D) and results in an electronical clash, explaining the absence of reactivity.

Interest in Lichenology

As previously reported [START_REF] Hellou | A chemotaxonomic study of the Xanthoparmelia pulla group in Algeria[END_REF], the KUV probe allows the easy distinction between Xanthoparmelia delisei (Duby) O. Blanco, A. Crespo, Elix, D. A.J. Schwab) [START_REF] Fryday | The genus Porpidia in northern and western Europe, with special emphasis on collections from the British Isles[END_REF].

-Most interestingly, lichenologists out in the field can use the KUV probe directly on the medulla of the lichen or using absorbant paper (without blanching agent), allowing quick determination of species with morphological similarities (Figure 10A). Of note, in the case of lichens containing atranorine (e.g. Furfuracea var. ceratea), which emits a strongly yellow fluorescence upon addition of reagent K, the TLC methods presented below should be used.

-This probe can also be used in the laboratory as a revelating agent for TLCs (Figure 10B). Deposition of one drop of the K reagent on the various spots of the TLC after elution of the acetonic extract of Co, I, C, S, T, M and R revealed a blue fluorescence at 365 nm with the exception of 16 and of the 2'-O-methylperlatolic acid.

Interestingly the methyl ester of 15 has the same behaviour as 4' and the KUV probe was positive. The spot 8 observed by Orange [START_REF] Orange | Porpidia irrigua, a new species related to P. contraponenda[END_REF] was corresponding to the oxo derivative of 5 (Figure 11). To the best of our knowledge such a keto function in position -1 of the alkyl chain was only observed in aliphatic acids such as dihydropertusaric, muronic and isomuronic acids. The presence of 9, 16 and of the methyl ester of 15 was probably due to the extraction and/or the TLC process.

Conclusion

This study illustrates the interest of both natural products and chemistry. The diversity resulting from the numerous pathways of the specialized metabolism offers interesting structural, mechanistic or synthetic challenges to chemists. Thus, the intramolecular transesterification occurring in some depsides bearing a 2-oxoalkyl chain in C-6 (ring A) has been elucidated. Reciprocally, the results of the chemical studies allow analysis and comprehension of biosynthetic processes and also provide useful tools to biologists. In our case the structure elucidation of some metabolites of European Porpidia species has been performed and a new easy to use chemical probe has been validated and proposed to lichenologists.

Experimental

Reagents

All reagents were of high quality and were purchased from commercial suppliers.

They were either used as received without further purification or were purified/dried according standard procedures.

Lichen material and identification

The lichen specimens used in this study were collected from different locations of France and UK (Table 1).

Morphological characters were examined with a Müller stereomicroscope (Gx10) and anatomical details of the samples were studied with an Olympus CX41 compound light microscope.

Extracts and sample preparation

Lichen thalli (often with mineral) were ground and extracted three times with warm acetone. After drying the solvent was evaporated under reduced pressure. (Process not optimized)

TLC analysis

Specialized metabolites were identified by thin-layer chromatography (TLC) using standards. The extracts and standards were loaded onto 10 × 20 cm aluminium sheets coated by Silica gel 60F254 (Merck). Thereafter the plates were developed with solvent C (toluene/acetic acid 85/15) and solvent G (toluene/ethylacetate/formic acid 139/83/8) for the Porpidia species study. All TLC plates were observed under UV at 254 and 365 nm (Fischer bioblock Scientific 12W, 6W-365nm, 6W-254nm).

Indicative Rf values in solvents C are given for each product. The Rf values of the classical references are: atranorine: 0.61; norstictic acid: 0.28; stictic acid: 0.12.

Purifications using Liquid-Chromatography

Silicagel 60 Merck and solvent system C (toluol/acetic acid, 85/15) were used for the purification of the different extracts. The combined fractions with the selected metabolite were washed once with water in order to elimine the acids, dried over MgSO 4 and evaporated under reduced pressue. Preparative TLC were also performed using the same solvents. (Process not optimized)

High Resolution Mass Spectrometry (HRMS) and Tandem Mass Spectrometry (MS-MS)

Mass spectra of standards were recorded at the CRMPO-Scanmat (Rennes, France) on an Orbitrap Thermo Fisher Scientific Q-Exactive instrument with an ESI (ElectroSpray Ionization) source in negative mode by direct introduction at 5-10 µg.mL -1 . Samples were prepared in methanol at 10 µg.mL -1 .

4.

DFT studies

All calculations were carried with Gaussian 16 program [START_REF] Frisch | Revision C.01[END_REF] basis and using PCM solvent models. The vibrational frequencies were computed at the same level to check whether each optimized structure is an energy minimum (no imaginary frequency) or a transition state (single imaginary frequency).

UV and Fluorescence studies

2 mg of the isochromen-1-ones 9 and 11 were dissolved in MeOH to obtain 10 -5 mol.L -1 solutions. Native UV spectra were recorded using a Jennway 7415 UV spectrometer (Cole-Parmer Instrument Company). Second spectra were recorded after addition of one drop of 1 mol.L -1 NaOH.

The emission fluorescence spectrum of these solutions was then measured between 360 and 600 nm using a Horiba Jobin-Yvon Fluorolog 3 spectrometer with an excitation at 240 nm.

4.10. Reactions with KOH: n x 5 mg of the metabolite were allowed to react under stirring with n x 100 L of aqueous 10% KOH at room temperature overnight.

After acidification with aqueous 10M HCl under cooling an extraction was performed using diethylether (2 x 5 mL). The organic layer was dried over MgSO 4 and the solvent was evaporated under vacuum. The conversion was checked by TLC and the purification was achieved either by preparative column chromatography or TLC.

Number of attempts > 3. Quantitative reactions for 1-7 and no reaction for 18-19.

Conversion study:

In order to confirm that the transesterification was complete the reaction was performed with a mixture (40 mg) of glomelliferic acid (89%) + perlatolic acid (11%) and K (0.8 mL). To avoid any eventual acidic deshydratation the reaction mixture was treated with a saturated aq NH 4 Cl solution (6 mL/pH 5-6) and extracted with ether (2 X 10 mL). The organic layer was dried over MgSO 4 and evaporated under reduced pressure giving 35mg of a colored oil (87%).

The TLC and 1 H NMR (see SI) of this crude reaction mixture showed that the glomelliferic acid 1 gave only the glomelline 8 and the phenolic compound 12 whereas the perlatolic acid remained unchanged (confirmed with pure perlatolic acid by TLC).

Remark: Along with the desired and purified compounds some minor specialized products as well as trace of starting material can be observed in very small amounts.

Then, the conversions can be always considered as > 90%. Considering the little amounts of starting material yields are not given.

Spectroscopic data

Glomelliferic 207.3, 174.4, 168.7, 166.6, 165.3, 165.0, 154.5, 150.0, 138.9, 116.2, 113.5, 109.7, 108.7, 104.2, 100.1, 55.6, 51.3, 44.6, 36.5, 31.9, 31.4, 22.5, 17.1, 14.0, 13.7. 168.6, 166.6, 164.9, 157.9, 151.5, 145.3, 138.9, 115.4, 113.4, 104.3, 103.1, 100.1, 56.4, 55.5, 51.3, 42.5, 33.9, 31.7, 31.3, 30.8, 23.3, 22.4, 14.0, 13.8 4, 168.9, 166.6, 165.0, 140.8, 138.8, 113.5, 105.1, 104.1, 100.1, 57.0, 55.6, 51.2, 42.5, 31.4, 31.3, 29.7, 23.4, 23.2, 22.5, 22.5, 13.9, 13.8. 6, 206.7, 169.3, 167.6, 166.7, 165.0, 158.5, 151.4, 139.0, 135.5, 121.8, 116.3, 113.5, 104.6, 104.4, 100.2, 56.4, 55.7, 52.5, 51.4, 47.7, 42.6, 42.3, 31.5, 31.4, 23.5, 23.4, 22.6, 14.1, 14.0 7, 207.3, 169.0, 166.7, 165.7, 165.2, 159.4, 152.5, 141.2, 139.0, 119.4, 119.4, 113.6, 105.2 104.2, 100.2,57.2, 55.7, 51.4, 49.2, 43.0, 42.7, 31.8, 29.3, 29.3, 29.3, 29.2, 23.9, 23.7, 22.8 22.7, 14.2, 14. 170.0, 166.6, 164.0, 149.5, 141.7, 116.1, 114.3, 109.1, 105.1, 102.7, 51.4, 42.7, 32.8, 32.5, 31.2, 24.0, 23.3, 23.2, 14.5, 14.3. 4, 170.2, 168.1, 166.7, 164.3, 158.8, 152.1, 141.5, 136.6, 123.3, 117.4, 114.4, 105.5, 104.9, 102.7, 56.7, 51.4, 47.7, 42.7, 42.5, 32.1, 32 163.6, 158.1, 139.5, 103.9, 101.0, 100.2, 55.7, 33.3, 31.1, 26.5, 22.4, 14.0 7, 103.9, 101.0, 100.1, 55.7, 33.3, 31.7, 29.0, 26.8, 22.6, 19.2, 14.0 7, 164.1, 163.3, 158.6, 140.2, 103.9, 102.2, 101.9, 33.4, 31.3, 26.9, 22.5, 14 166.3, 162.5, 149.0, 110.8, 103.4, 100.8, 36.3, 31.9, 31.6, 22.3, 13.4. 165.6, 160.8, 160.5, 142.3, 115.5, 108.3, 98.7, 56.8, 50.1, 43.0, 31.4, 23.2, 22.5, 14.0 166.3, 162.5, 149.0, 110.8, 103.4, 100.8, 36.3, 31.9, 31.6, 22.3, 13.4. 4, 207.6, 206.8, 169.0, 166.7, 165.5, 165.2, 159.4, 152.5, 141.0, 139.0, 119.4, 177.3, 113.6, 105.3, 104.3, 103.0, 57.2, 55.7, 51.4, 49.2, 43.7, 42.7, 42.4, 31.8, 30.1, 29.3, 29.2, 28.7, 23.9, 23.5, 23.2, 22.7, 14.2 1 [START_REF] Elix | Synthesis of the Lichen Depsides Glomelliferic Acid, Loxodellic Acid, Glomellic Acid, Their 4-Ortho-Demethyl Analogs and Oxostenosporic Acid[END_REF]; 2 [START_REF] Orange | Porpidia irrigua, a new species related to P. contraponenda[END_REF][START_REF] Elix | Synthesis of Depsides Present in the Lichen Porpidia glaucophaea[END_REF][START_REF] Elix | Synthesis of Further b-ketoalkyldepsides[END_REF]; 3 [START_REF] Culberson | Pseudevernia Furfuracea-Olivetorina Relationships: Chemistry and Ecology[END_REF][START_REF] Pérez | Actividad antioxidante de los polifenoles de HYPOGYMNIA TAVARESII D[END_REF]; 4: [START_REF] Huneck | Mitteilung über Flechteninhaltsstoffe. Arthoniasaure, ein neues Depsid aus Arthonia impolita (Ehrh.)[END_REF] 587 588

HRMS [M-H] -C

  Hawksw. & Lumbsch (KUV+) and X. pulla (Ach.) O. Blanco, A. Crespo, Elix, D. Hawksw. & Lumbsch (KUV-) as well as between X. loxodes (Nyl.) O. Blanco, A. Crespo, Elix, D. Hawksw. & Lumbsch (KUV +) and X. verruculifera (Nyl.) O. Blanco, A. Crespo, Elix, D. Hawksw. & Lumbsch (KUV-). Therefore this concept will be extended to other lichens using a selection of European Porpidia species (Friday, 2005). -A positive KUV probe was obtained with Porpidia cinereoatra (Ach.) Hertel and Knoph, P. tuberculosa (Sm.) Hertel and Knoph, P. speirea (Ach.) Kremp var speirea, P. melinodes (Körb.) Gowan & Ahti, P. contraponenda (Arnold) Knoph and Hertel, P. irrigua Orange and P. rugosa (Taylor) Coppins and Fryday whereas a negative KUV probe was obtained with the other Porpidia species containing stictic acid, norstictic acid (i.e. P. macrocarpa (DC.) Hertel and Schwab and P. platycarpoides (Bagl.) Hertel or without metabolites (i.e. P. hydrophila (Fr.) Hertel &

  and the results visualized in Maestro (Schrödinger, LLC, New York, NY, 2021). Simplified depsides and depsidones representative of their respective core scaffold were used to avoid unnecessary costly optimizations of the long aliphatic side chains. Structure optimizations of molecular structures in ground states and relaxed coordinate scans were carried out at the B3LYP-D3 level of theory in combination with the 6-31G(d,p)

Figure 1 .

 1 Figure 1. Molecular structures of glomelliferic acid 1 and glomellic acid 2 and their fluorescent behaviour upon addition of K. Key 2-oxoalkyl motif highlighted in blue.

Figure 2 .

 2 Figure 2. -keto ester-containing depsides considered in this study.

Figure 3 .

 3 Figure 3. Reactivity of depsides with K.

Figure 4 .

 4 Figure 4. Reactivity of the methyl, 2'-O-methylmicrophyllinate 4' with K.

Figure 5 .AB

 5 Figure 5. A Reactivity of the -alectoronic acid 18 and the -collatolic acid 19 with K. B Structure of the perlatolic acid 20.

Figure 6 .

 6 Figure 6. UV and fluorescence spectra of the isochromen-1-ones 9 and 11.

Figure 7 .

 7 Figure 7. A. Depsides rearrangement mechanisms with K; B. MS fragmentation.

Figure 8 .

 8 Figure 8. Relaxed coordinate scans of simplified despides under A. neutral and B. basic conditions; C. Energy minimized structure of simplified depsidone under basic conditions; D. Manually adjusted dihedral angle to position the enolate close to the ester carbonyl group.

Figure 9 .

 9 Figure 9. KUV probe on extracts of P. cinereoatra C, P. speirea var speirea S, P. irriguaI I, P. macrocarpa Ma and P. platycarpoides P. Extracts were spotted and K was added (right) or not (left).

Figure 10 .Figure 11 .

 1011 Figure 10. A. Direct application of the KUV probe on the medulla of P. cinereoatra; B. KUV probe on the eluted TLC (solvent G) of Porpidia cinereoatra C, P. tuberculosa T, P. speirea var speirea S, P. melinodes M, P. contraponenda Co, P. irrigua I and P. rugosa R

  Figure 3

  Figure 5.

  Figure 6.

  Figure 7.

  Figure 8.

  Figure 10.

Figure

  Figure 11.

7. 1 H and 13 C NMR

	Spectra were recorded at 300/75 MHz or 500/100 MHz (cryoprobe) respectively,
	using TMS as an internal standard. Shifts (δ values) are given in parts per million
	(ppm), coupling constants (J values) are given in Hertz (Hz), and multiplicity of

signals are reported as follows: s (singlet), d (doublet), t (triplet), q (quadruplet), quint (quintet), sext (sextet), m (multiplet), br. s (broad singlet), dt (doublet of triplet), td (triplet of doublet).

  C 12 H 15 O 4 calc. 223.09758 found. 223.0977; [B-H 2 O] -C 12 H 13 O 3 calc. 205.08702 found. 205.0872; [A-CO 2 ] - C 11 H 15 O 2 calc. 179.10775 found. 179.1080. Rf C: 0.42.

	Glomellic acid 2 [52589-14-7] C 25 H 28 O 9 MW: 472.47 g/mol
	2-Hydroxy-4-[[2-hydroxy-4-methoxy-6-(2-oxopentyl)benzoyl]oxy]-6-(2-oxopentyl)benzoic acid
	1 H NMR (300MHz, CDCl 3 ): 11.18 (s, 1H), 6.65 (d, J = 2 Hz, 1H), 6.50 ( d, 1H), 6.47
	(d, J = 2.5 Hz, 1H), 6.30 (d, J = 2.5 Hz, 1H), 4.04 (s, 2H), 3.84 (s, 3H), 3.22 *(s, 2H),
	2.39 (t, J = 7.5 Hz, 2H), 1.98* (m, 2H), 1.57 (m, J = 7.5 Hz 2H), 1.00 (t, J = 7.3 Hz,
	3H), 0.84 (t, J = 7.3 Hz, 3H). 1 H NMR (300MHz, CD 3 COCD 3 ): 11.04 (s, 1H), 6.70 (d,
	J = 2 Hz, 1H), 6.66 ( d, 1H), 6.49 (d, J = 2.5 Hz, 1H), 6.47 (d, J = 2.5 Hz, 1H), 4.19 (s,
	2H), 3.88 (s, 3H), 3.45 *(s, 2H), 2.47 (t, J = 7.5 Hz, 2H), 1.58* (m, 2H), 1.55 (m, J =
	7.5 Hz 2H), 0.97 (t, J = 7.3 Hz, 3H), 0.81 (t, J = 7.3 Hz, 3H). 13 C NMR (80MHz,
	CD 3 COCD 3 ): 207.1, 169.7, 166.7, 165.9, 164.0, 156.5, 141.6, 141.1, 114.0, 113.7,
	109.7, 106.5, 109.7, 100.6, 56.1, 51.2, 44.6, 43.5, 37.2, 17.6, 17.5, 14.3, 14.0. HRMS
	[M-H] -C 25 H 27 O 9 calc. 471.16606 found. 471.1657; [A] -C 12 H 13 O 5 calc. 237.07685
	found. 237.07690. Rf C: 0.33.
	Confluentic acid 3 [6009-12-7] C 28 H 36 O 8 MW: 500.23 g/mol
	2-Methoxy-4-[[2-hydroxy-4-methoxy-6-(2-oxoheptyl)benzoyl]oxy]-6-pentylbenzoic acid
	1 H NMR (300MHz, CDCl 3 ): 11.31 (s, 1H), 6.61 (d, J = 2 Hz, 1H), 6.55 ( d, J = 2 Hz,
	1H), 6.47 (d, J = 2 Hz, 1H), 6.30 (d, J = 2 Hz, 1H), 4.07 (s, 2H), 3.88 (s, 3H), 3.85 (s,
	3H), 2.74 (t, J = 8.1 Hz, 2H), 2.41 (t, J = 7.6 Hz, 2H), 1.62 (m, 2H), 1.53 (m, J = 7.5
	Hz, 2H), 1.34 (m, 4H), 1.21 (m, 4H), 0.89 (t, J = 7 Hz, 3H), 0.82 (t, J = 7 Hz, 3H). 13 C
	NMR (80MHz, CDCl 3 ): 207.3, 169.2,

HRMS [M-H] -C 25 H 29 O 8 calc. 457.18679 found. 457.1868; [B] -

  3H), 0.83 (t, J = 7 Hz, 3H), . 13 C NMR (80MHz, CDCl 3 ): 207.

	, HRMS [M-H] -C 28 H 35 O 8 calc. 499.23374 found. 499.2336 (0 ppm)
	[A] -C 13 H 17 O 4 calc. 237.11323 found. 237.1131 (1 ppm). Rf C: 0.40.
	2'-O-Methylmicrophyllinic acid 4 [79579-62-7] C 30 H 38 O 9 MW: 542.62 g/mol
	2-Methoxy-4-[[2-hydroxy-4-methoxy-6-(2-oxoheptyl)benzoyl]oxy]-6-(2-oxoheptyl)benzoic acid
	1 H NMR (300MHz, CDCl 3 ): 11.17 (s, 1H), 6.74 (d, J = 2.1 Hz, 1H), 6.63 ( d, J = 2.1

Hz, 1H), 6.47 (d, J = 2.5 Hz, 1H), 6.30 (d, J = 2.5 Hz, 1H), 4.07 (s, 2H), 4.03 (s, 2H), 4.00 (s, 3H), 3.85 (s, 3H), 2.59 (t, J = 7.5 Hz, 2H), 2.42 (t, J = 7.5 Hz, 2H, 1.61 quint, J = 7Hz 2H), 1.54 ( quint, J = 7Hz 2H), 1.30 (m, 4H), 1.22 (m, 4H), 0.89 (t, J = 6.7 Hz,

  HRMS [M-H] -C 30 H 38 O 9 calc. 541.24431 found. 541.2442 [A] -C 15 H 19 O 5 calc. 279.1238 found. 279.1235. Ortho effect: loss of CH 3 OH.

	Rf C: 0.33.
	Methyl, 2'-O-methylmicrophyllinate 4', Gustastatin [720698-33-9] C 31 H 40 O 9 MW:
	556.64
	Methyl, 2-Methoxy-4-[[2-hydroxy-4-methoxy-6-(2-oxoheptyl)benzoyl]oxy]-6-(2-
	oxoheptyl)benzoate
	1 H NMR (500MHz, CDCl 3 ): 11.29 (s, 1H), 6.58 (d, J = 1.9 Hz, 1H), 6.56 ( d, J = 1.9
	Hz, 1H), 6.46 (d, J = 2.3 Hz, 1H), 6.29 (d, J = 2.9 Hz, 1H), 4.06 (s, 2H), 3.87 (s, 3H),
	(s, 3.84, 3H), 3.82 (s, 3H) 3.70 (s, 2H), 2.43 (t, J = 7.2 Hz, 4H), 1.56 (m, 2H), 1.53 (m,
	2H), 1.28 (m, H), 1.24 (m, 2H), 1.22 (m, 2H), 1.19 (m, 2H), 0.87 (t, J = 7 Hz, 3H),

0.83 (t, J = 7 Hz, 3H). 13 C NMR (100MHz, CDCl 3 ): 207.

  . Attributions using 2D NMR experiments. HRMS [M+ Na] + C 31 H 40 O 9 Na calc. 579.25645 found.

	579.2563 (0 ppm) [AH + Na] + C 16 H 22 O 5 Na calc. 317.13594 found. 317. Rf C: 0.50.
	2'-O-methylsuperphyllinic acid 5 [108529-20-0] C 34 H 46 O 9 MW: 598.72 g/mole
	2-Methoxy-4-[[2-hydroxy-4-methoxy-6-(2-oxononyl)benzoyl]oxy]-6-(2-oxononyl)benzoic acid
	1 H NMR (300MHz, CDCl 3 ): 11.17 (s, 1H), 6.73 (d, J = 1.7, 1H), 6.63 ( d, J = 1.7 Hz,
	1H), 6.46 (d, J = 2.3 Hz, 1H), 6.29 (d, J = 2.3 Hz, 1H), 4.06 (s, 2H), 4.02 (s, 2H), 3.99
	(s, 3H), 3.84 (s, 3H), 2.59 (t, J = 7.5 Hz, 2H), 2.41 (m, 2H), 1.60 (m, 2H), 1.51 (m,
	2H), 1.28-1.20 (m, 16H), 0.87 (t, J = 7 Hz, 3H), 0.85 (t, J = 7 Hz, 3H), . 13 C NMR
	(100MHz, CDCl 3 ): 207.

  26 H 31 O 8 calc. 471.20244 found. 471.2026; [A] -C 12 H 15 O 4 calc.

	223.09758 found. 223.0977. Rf C: 0.22.
	Arthoniaic acid 7 [25556-24-5] C 29 H 36 O 9 MW: 528.59 g/mole
	2-Methoxy-4-[[2-hydroxy-4-hydroxy-6-(2-oxoheptyl)benzoyl]oxy]-6-(2-oxoheptyl)benzoic acid
	1 H NMR (300MHz, CDCl 3 ): 11.16 (s, 1H), 6.89 (d, J = 2 Hz, 1H), 6.68 (d, J = 2 Hz,
	1H), 6.38 (s, 1H), 4.15 (s, 2H), 3.88 (s, 3H), 3.86 (s, 2H), 2.50 (q, J = 7.7 Hz, 4H),
	1.52 (m, 4H), 1.4-1.1 (m, 8H), 1.25 (t, J = 7 Hz, 3H), 1.22 (t, J = 7 Hz, 3H). 13 C NMR
	(80MHz, CDCl 3 ): 207.

  . HRMS [M+H] + C 17 H 24 O 4 calc. 291.15908 found.

	291.1591 [M + H -H 2 O] + C 17 H 21 O 4 calc. 273.14852 found. 273.1486. Rf C: 0.60.
	Olivetonide 11 [3734-54-1]C 14 H 16 O 4 MW: 248.27 g/mol
	6,8-Dihydroxy-3-pentyl-1H-2-benzopyran-1-one
	1 H NMR (300MHz, CDCl 3 ): 11.15 (s, 1H), 6.38 (d, J = 2 Hz, 1H), 6.26 (d, J = 2 Hz,
	1H), 6.15 (s, 1H), 2.49 (t, J = 7 Hz, 2H), 1.66 (m, 2H), 1.36 (m, 4H), 0.91 (t, J = 7 Hz,
	3H). 13 C NMR (80MHz, CDCl 3 ): 166.

  .1. HRMS [M+H] + C 14 H 17 O 4 calc. 249.11213 found.

	249.1122. Rf C: 0.36.
	2,4-dihydroxy-6-pentylbenzoïc acid 12 [491-72-5] C 12 H 16 O 4 MW: 224.1 g/mol
	1 H NMR (300MHz, CDCl 3 ): 11.52 (s, 1H), 6.30 (d, J = 2.6 Hz, 1H), 6.28 (d, J = 2.6
	Hz, 1H), 5.16 (s, 1H), 2.92 (m, 2H), 1.59 (m, 2H), 1.35 (m, 4H), 0.90 (t, J = 7.1Hz,
	3H). 13 C NMR (80MHz, CD 3 COCD 3 ): 173.1,

  . HRMS [M-H] -C 15 H 18 O 4 calc. 237.11323 found. 237.1134. Rf C: 0.24.

	4-hydroxy-2-methoxy-6-(2-oxoheptyl) benzoic acid 15 [193617-80-0] C 15 H 20 O 5 MW:
	280.20 g/mol
	1 H NMR (300MHz, CDCl 3 ): 11.52 (s, 1H), 6.30 (d, J = 2.6 Hz, 1H), 6.28 (d, J = 2.6
	Hz, 1H), 5.16 (s, 1H), 2.92 (m, 2H), 1.59 (m, 2H), 1.35 (m, 4H), 0.90 (t, J = 7.1Hz,
	3H). 13 C NMR (80MHz, CD 3 COCD 3 ): 173.1,

  HRMS [M-H] -C 15 H 19 O 5 calc. 279.1238 found. 279.1235; [M-CO 2 -H] -C 14 H 19 O 3 calc. 235.13397 found. 235.1340. Rf C: 0.08.

	1 H NMR (300MHz, CDCl 3 ) :11.35 (s, 1H), 11.22, (s, 1H), 6.71 (d, J = 2.4 Hz, 1H),
	6.56 (d, J = 2.4 Hz, 1H), 6.46 (d, J = 2.4 Hz, 1H), 6.29 (d, J = 2.4 Hz, 1H). Mixture
	with 4' (See SI).
	Spot 7 Methyl, 4-hydroxy-2-methoxy-6-(2-oxoheptyl)benzoate
	[846606-93-7] C 16 H 22 O 5 MW: 294.34 g/mole (García-Fortanet et al., 2005)
	HRMS [M-H] -C 16 H 21 O 5 calc. 293.13945 found. 293.1394 [M-H-CH 3 ] -C 115 H 17 O 4 calc.
	261.11323 found. 261.1130.
	Spot 8 2'-O-methyl-8'''-oxosuperphyllinic acid C 34 H 44 O 10 MW: 612.30 g/mol
	2-Methoxy-4-[[2-hydroxy-4-methoxy-6-(2,8-dioxononyl)benzoyl]oxy]-6-(2-oxononyl)benzoic Methyl, 4-hydroxy-2-methoxy-6-(2-oxononyl) benzoate 16 [133362-68-2] C 17 H 24 O 5 acid
	MW: 308.37 g/mole
	1 H NMR (300MHz, CDCl 3 ): 11.16 (s, 1H), 6.73 (d, J = 1.6 Hz, 1H), 6.62 ( d, J = 1.6 HRMS [M-H] -C 17 H 23 O 5 calc. 307.1551 found. 307.1550. See Figure 6 Hz, 1H), 6.46 (d, J = 2.5 Hz, 1H), 6.30 (d, J = 2.5 Hz, 1H), 4.06 (s, 2H), 4.02 (s, 2H),
	2-O-methylolivetonide 17 [1195517-47-5] C 15 H 18 O 4 MW: 262.13 g/mol 3.99 (s, 3H), 3.85 (s, 3H), 2.59 (t, J =7.2 Hz, 2H), 2.43 (m, 2H), 2.41 (t, J = 7.2 Hz,
	6-hydroxy-8-methoxy-3-pentyl-1H-2-benzopyran-1-one 2H), 2.14 (s, 3H), 1.63 (m, 2H), 1.58 (m, 2H), 1.52 (m, 2H), 1.31 (m, 2H), 1.26 (m,
	1 H NMR (300MHz, CDCl 3 ): 6.43 (d, J = 2 Hz, 1H), 6.34 (d, J = 2 Hz, 1H), 6.06 (s, 2H), 1.2 (m, 2H), 1.2 (m, 2H), 1.2 (m, 2H), 0.85 (t, J = 7 Hz, 3H).
	1H), 3.90 (s, 3H), 2.44 (t, J = 7.5 Hz, 2H), 1.66 (m, J = 7.5 Hz, 2H), 1.33 (m, 4H),
	0.89 (t, J = 7 Hz, 3H). 13 C NMR (80MHz, CDCl 3 ): 163.9, 163.3, 160.9, 159.1, 142.6,
	103.2, 102.9, 102.2, 98.7 56.2, 33.4, 31.3, 26.6, 22.5, 14.1. HRMS [M-H] -C 15 H 17 O 4
	calc. 261.11323 found. 261.1131.
	-Alectoronic acid 18 [54226-87-8] C 28 H 32 O 9 ] MW: 512 .54 g/mol Rf C: 0.09. (Millot
	et al, 2007).
	-Collatolic acid 19 [522-52-1] C 29 H 34 O 9 MW: 526 .56 g/mol Rf C: 0.21. (Millot et al,
	2008).
	Perlatolic acid 20 [529-47-5] C 25 H 32 O 7 MW: 444.51 g/mol Rf C: 0.48. (Elix, 1974)
	UNKNOWN COMPOUNDS OF ORANGE (See Figure 6 and Table 2)
	Spot 2 Methyl, Microphyllinate CAS: [858027-82-4] C 30 H 39 O 9 MW: 542.60 g/mol,
	Methyl, 4-[[2-hydroxy-4-methoxy-6-(2-oxoheptyl)benzoyl]oxy]-6-(2-oxoheptyl)benzoate
	HRMS: [M-H ]-C 30 H 38 O 9 found. 541.2444 C 15 H 20 O 5 279.1238

13

C NMR (100MHz, CDCl 3 ): 209.

Table 1 .

 1 11. List of taxa with sampling and collecting details. 615

	

Acknowledgments

We are grateful to Dr Alan Orange of the National Museum of Wales and to the members of the Association Française de Lichénologie (AFL) for providing some of the studied lichens: J. Esnault, J. L. Farroux and J. Y. Monnat. The fluorescence study has been performed using the Spectroscopies-CDTP core facility (UMS Biosit, Univ Rennes, RENNES, FRANCE). We are also most grateful to the PRISM core facility (Rennes-Angers, France) for its technical support in NMR. XG is grateful to the 'Fondation ARC pour la recherche sur le cancer' for his post-doctoral fellowship (PDF20191209830).

Graphical Abstract

Correspondance * philippe.uriac@univ-rennes1.fr

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Associated content

Supporting Information: NMR spectra, UV fluorescence spectra of 9 and 11, examples of TLC, HRMS of spot 8.


G Grandjean

Y Thiery

C Hohmann

F Negulescu

Smai

Landslides risk mapping using the Vigirisks web-tool: application in Normandie (France)

Landslides threaten many parts of the world and cause many deaths and significant damage every year, and this should increase in the future due to climate change. To cope with this situation and prevent landslides impacts, a large variety of susceptibility and hazard mapping tools have been developed, either to assess current potential failure zones or to predict those that will appear in the near future. In the following, we present an application of the Vigirisks multirisks web-platform. This web-tools, developed by BRGM, propose computations allowing multi-risks mapping in a realistic manner, e.g., including cascading effects, vulnerability assessment and damages evaluation. The study site selected here is located in Diepe (Normandie, France); this is a typical case of complex flooding/landsliding processes. The Vigirisk web-tool was tested to evaluate risks when these two processes occur in the same time. We present here a simple "concomitant risks" workflow, implemented by using a weithing method.

Introduction

Landslides threaten many parts of the world and cause many deaths and significant damage every year, and this should increase in the future due to climate change. Landslides events are widely distributed throughout Europe, with a great concentration in mountainous areas. For example, between 1995-2014, 476 landslides caused 1370 deaths and 784 injuries. Annual economic loss in Europe is approximately estimated to 4.7 billion Euros [START_REF] Haque | Fatal landslides in Europe[END_REF].

To cope with this situation and prevent landslides impacts, a large variety of susceptibility and hazard mapping tools have been developed, either to assess current potential failure zones [START_REF] Rossi | Optimal landslide susceptibility zonation based on multiple forecasts[END_REF][START_REF] Reichenbach | A review of statistically-based landslide susceptibility models[END_REF] or to predict those that will appear in the near future (Bernardie et al., 2021). A broad review of commonly used approaches can be found in [START_REF] Corominas | Recommendations for the quantitative analysis of landslide risk[END_REF] or in [START_REF] Reichenbach | Geomorphological mapping to assess landslide risk: concepts, methods and applications in the Umbria Region of Central Italy[END_REF]. Depending on the available data and its quality, we can use indirect empirical or data driven and physically based methods [START_REF] Thiery | Improvement of landslide hazard assessments for regulatory zoning in France: STATE-OF-THE-ART perspectives and considerations[END_REF].

In the following, we present an application of the Vigirisks multirisks web-platform [START_REF] Tellez-Arenas | A web platform for storing, sharing and executing scientific workflows for Natural Risk Assessment: part 2 -description of an interoperable architecture based on opensource components[END_REF]. This web-tools (www.vigirisks.fr), developed by BRGM, has the ambition to propose a set of computations -implemented as workflows -allowing multi-risks mapping in a realistic manner, e.g., including cascading effects, vulnerability assessment and damages evaluation. The user can therefore realize several kinds of risks maps resulting from different kinds of hazard occurrence. In the present paper, we illustrate the case of a simple concomitant risks workflow occurring in the area of Dieppe (Normadie, France).

Data and method

The site selected in our study is located at the northern part of France, close to the city of Dieppe (Normandie, France); this is a typical case where complex flooding/landsliding processes can be observed, due to the particular geological settings and the occurrence of forcing rainfalls.

Different methods of analysis and mapping of the flooding or landslide hazard have been implemented in the Vigirisk plateform. The aim here is to show the possibilities offered by the original architecture of this web-tool in terms of single and multi-hazard analysis. Concerning landslides risks assessment, we already implemented and tested different algorithms, such as:  The hierarchical analytical process technique (AHP): an empirical indirect method [START_REF] Saaty | A scaling method for priorities in hierarchical structures[END_REF] used for about fifteen years for mapping landslide hazard (Castellanos Abella and van Westen, 2008).  The weight of evidence (WoE) method: a data-driven approach [START_REF] Bonham-Carter | Geographic Information System for Geoscientists: Modelling with GIS[END_REF]. It needs to get sufficient data available to estimate the relative importance of evidential rules via the log-linear form Bayesian formulation [START_REF] Spiegelhalter | A statistical view of uncertainty in expert systems[END_REF]. It defines unconditional prior probability and conditional posterior probability, where the prior probability is the probability of an event, similar to past known events, for a given time period. This probability can be revised from various sources of information, to define the posterior probability and so, it can be successively revised and updated with the addition of new evidence.  A damage indicator used to spatially evaluate risks caused by landslides and quantify potential multiscale consequences of elements at risk (EaR) when impacted by hazardous events. It extends the notion of Potential Damage Index (PDI) from [START_REF] Puissant | Landslide consequence analysis: a region-scale indicatorbased methodology[END_REF] and [START_REF] Graff | Characterization of elements at risk in the multirisk coastal context and at different spatial scales: Multi-database integration (Normandy, France)[END_REF] by taking into account the specific number and nature of criteria to be integrated in the consequences analysis and weight them based on their spatial location or importance. In this way, it adapts and improves the PDI method to the context of our study by integrating spatial scales of EaR, taking advantage of the different geographical databases available.

In this paper, we only show the results of risk map obtained by a workflow to assess concomitant risk maps obtained with pre-existing hazard maps coupled with the extended PDI risks assessment approach. The concomitant effects are based on a predefined procedure specifically implemented to guide end-users. The concomitant risk map (CRC) obtained is therefore a weighted sum of these two risk maps with the possibility of predominance of the intensity of one risk over the other (0.75 vs. 0.25) or no predominance of one risk over the other (0.5 vs. 0.5).

From a computing point of view, Vigirisks is designed with a frontend Java-web connected to a backend server. The GUI is implemented as developed from various open source tools [START_REF] Tellez-Arenas | A web platform for storing, sharing and executing scientific workflows for Natural Risk Assessment: part 2 -description of an interoperable architecture based on opensource components[END_REF]. The OpenLayers JavaScript library allows the display and manipulation of produced maps. The backend server produces WPS services and uses a Postgres database for data management, scenarios translated into workflows, input parameters and simulation results (Fig. 1). To operate such IT architecture a specific WebGIS interface was developed following the philosophy presented in [START_REF] Thiebes | A WebGIS decision-support system for slope stability based on limit-equilibrium modelling[END_REF].

Results and conclusion

Figure 2 shows the CRC obtained after the realization of the workflows that combine, using a weighing approach, a landslide susceptibility map computed with AHP (Fig. 2b) and a flooding map obtained by numerical modelling [START_REF] Graff | Contribution à la cartographie multirisques de territoires côtiers : approche quantitative des conséquences potentielles et des concomitances hydrologiques[END_REF]Fig.2a). For the combination, each of the risk values of these maps where taken into account with the same weight of 0.5.

The resulting multi-risk map (Fig. 2c) show the places where both of hazards could have an impact on assets located in the area. The level of risks appear to be generally medium over all the area with some places in low and high.

Even the combination of different kinds of risks can be interesting to have a global view of what could append in terms of damages in case of concomitance of several disasters, we see that some choice have to be made in the combination: we could have chosen to aggregate the two risks maps by taking the maximal value of each map's pixels, the result would have been different, increasing the areas impacted with the flooding.

The advantage of the Vigirisks platform lies in the different possibility to design the workflows, to adapt them for the particularities of scenarios, so that the user can produce a processing chain adapted to its field observations. Each if these workflows are stored and commented in the system so that they can be disseminated to all interested users.

In the following developments, we are considering integration of additional susceptibility/hazard assessment approaches as well as different strategies to combine them, depending on time/space concomitance or cascading affects are needed to be taken into account.

Figure 1 :

 1 Figure 1: Vigirisks architecture