Romain Kervarc

Ariane Piel

Stéphanie Lala

Jean Bourrely

Assessing component impairing at mission level

Keywords: Space systems, System of systems, Performance assessment, Vulnerability assessment, Simulation exploitation

Whilst the amount of debris around the Earth steadily increases, the danger of collisions between debris and operating man-made space systems becomes a major issue. Whilst on the one hand fine physical simulation allows predicting accurately failure occurrences or manoeuvre consequences, and on the other hand fine behavioural models allow apprehending the services expected from a given system as an organisation of functions performed by various agents, it is difficult to have both approaches work together. This paper proposes a bridge between both approaches by developing a model describing in a unified way dependencies, redundancies, and interactions between physical components concurring to ensure elementary functions of a system, and shows how this approach was applied to the assessment of remedial measures to space debris issues for space assets.

Introduction

Space debris, i.e. non-operating man-made objects found in orbit around the Earth, have increased since the beginning of space exploitation to a critical point where the space environment has become unstable and debris population grows by itself as the result of debris collision [START_REF] Liou | Instability of the present LEO satellite populations[END_REF]. Figure 1 shows a monthly average number of objects seen in Earth orbit, sorted by object type: active spacecrafts are in blue, mission or launching related debris in green and orange, and on top of that the purple curve shows fragmentation debris. The figure evidences the phenomenon of exponential growth Figure 1: Space debris: monthy number by type [START_REF][END_REF] (left) and density (right) of fragmentation debris, which make up the most part of objects in orbit. Since two catastrophic events in the late 2000s, awareness has increased about this major threat for operating man-made space systems, and several remedial measures to be enforced are been considered by major space actors so as to reduce space mission risk and ensure sustainable space activities. These measures rely on models of long-term debris environment evolution [START_REF] Walker | Analysis of the effectiveness of space debris mitigation measures using the DELTA model[END_REF] coupled together with risk assessment tools.

Projections using software MASTER [START_REF] Flegel | The MASTER-2009 Space Debris Environment Model[END_REF], a debris flux simulation tool developed on behalf of ESA 1 and experimentally checked using data from ISS 2 maintenance, show that the steady growth of space debris in the past years is a tendency that will be kept in the future. Figure 1 shows the monthly number of objects in orbit around Earth, with calculated previsions until 2030 (the total curve is particularly relevent here). The situation is particularly dire in orbits closest to Earth, where debris population has been increasing for more than 50 years of space activity. Recent simulations indicate that the in-orbit population, wracked by the Kessler syndrome, is instable and will grow for the next centuries [START_REF] Liou | Instability of the present LEO satellite populations[END_REF]. Even with a 90 % implementation of the commonly adopted mitigation measures, based on the initial population of 2009 provided by ESA, the debris population in orbits closest to the Earth is expected to increase by an average of 30 % in the next 200 years [START_REF] Liou | Stability of the Future Leo Environment, Inter-Agency space Debris Coordination committee (IADC) report[END_REF].

The physics of the phenomenon is well-understood and allows producing fine sim- 1 European Space Agency 2 International Space Station 2 ulations and credible projections confirmed by feedback information coming from servicing missions on existing space systems (e.g. returned parts of Hubble's solar panels after space repair [START_REF] Kearsley | Impacts on Hubble space telescope solar arrays: discrimination between natural and man-Made particles[END_REF]) or from observed effects on the satellite or on its trajectorye.g. impact on Jason-1 deduced from attitude and electrical current disturbances [21] -or, for larger debris, from Earth observation and debris cataloguing. This leads to fine simulations such as MASTER 2009, which provide detailed information on debris fluxes (and is the source for the data on Figure 1), which can in turn be used as an input to physical simulations assessing the effects of debris.

However, this evaluation is to be performed at several levels, with differents methods each implementing a different physics and extremely varied effect models. Hence, obviously, the exploitation of this knowledge is not easy at all, especially with the purpose of providing recommendations about the future effects of the various remedial measures that can be considered. In order to address this issue, an important aspect to be taken into account is the mission of the system, i.e. more specifically the services provided by the system to its users or customers on the ground. Indeed, the availability of these services throughout time is the only criterion that can be used to compare objectively the effects of various debris issues and various remedies.

Such methods have been discussed in previous works [START_REF] Kervarc | A generic logical-temporal performance analysis method for complex systems[END_REF][START_REF] Kervarc | Performance evaluation based on temporal logic[END_REF][START_REF] Kervarc | Evaluation of space mission vulnerability to space debris[END_REF][START_REF] Bertrand | Space system vulnerability assessment to space debris: a methodology and a program[END_REF], where the ATLAS 3 approach is presented. It relies on a modelling of the behaviour of the system leading to the service being provided to the ground by a temporal logic of the interval family [START_REF] Zhou | A calculus of durations[END_REF][START_REF] Hansen | Semantics and completeness of the duration calculus[END_REF][START_REF] Hansen | Duration calculus: logical foundations[END_REF] based on Allen's operators [START_REF] Allen | An interval-based representation of temporal knowledge[END_REF][START_REF] Allen | Maintaining knowledge about temporal intervals[END_REF], leading to a logic tree describing the organisation of the different elementary functions of the system, over which an availability metric is computed, allowing the computation of a vulnerability index [START_REF] Jolly | Satellite protection: a system's approach through the 3R concept[END_REF][START_REF] Bertrand | A temporal logical methodology for probabilistic vulnerability analysis of space missions: Application to vulnerability analysis of an Earth observation mission due to catalogued space debris[END_REF], which defines a risk of mission performance degradation due to effects of both trackable and untrackable space debris on a complex space system. The purpose of this research is to connect these two different fields of expertise: on the one hand, there exist fine physical simulations providing a good knowledge of the way components evolve in their environment and information such as life expectancy (i.e. component time-evolved failure rates); on the other hand, there also exist evolved 3 Analysis by Temporal Logic of Architectures of Systems 3 multi-agent representation that allow expressing mission fulfilment as a combination of elementary function fulfilment and reason in terms of fulfilling user needs. Indeed, physical simulation relies on concrete physical components of the system, whilst multiagent mission assessment rely on functions. Each representation is pertinent for its own field and inadequate for the other, and a bridge is needed between both.

This paper provides a theoretical framework which may be used as a common representation for spacecraft design knowledge and where it is possible to compute inputs for the ATLAS method from fine physical simulations results. It is organised as follows. Section 2 presents the physical knowledge about debris that we want to exploit, as well as the ATLAS approach that will be used as an integration framework. Section 3 presents the theoretical notions which are used to transfer information from physical simulation to ATLAS mission assessment. Section 4 shows a case study. Section 5 gives some conclusions and perspectives about this work.

The issue of debris effect integration

Space debris effect knowledge

As pointed out in the introduction, there exist fine simulations such as MASTER 2009 by ESA, which provide detailed information on debris fluxes. This statistical information can in turn be used as an input to simulations implementing debris effect models. These simulations are of two different types, since the debris population may be separated in two distinct populations.

"Large" debris are objects trackable from the ground (i.e. roughly of a size larger than a certain size (ranging from 10 cm in LEO 4 to 50-100 cm in GEO 4 . with intermediate sizes in MEO 4 . which may be listed in a catalogue (about 16,000 such objects are known today). Collisions with such objects are always catastrophic for the spacecraft, but are predictable, which allows manoeuvring to avoid them. However, collision avoidance manoeuvres have several damageful consequences, among which that some functionalities of the spacecraft (such as its payload) are generally unavailable during manoeuvre; thus, each manoeuvre temporarily prevents the system to fulfil its mission; and that manoeuvres consume propellant, which is also required for station keeping; thus, more frequent manoeuvres reduce the lifetime expectancy of the spacecraft.

"Small" debris are untrackable objects (the number of which is evaluated to range in billions) for which the only available knowledge on the ground is a statistical repartition model. Collision with such object is not predictable, but may be less severe if the spacecraft is suitably protected and the size of the object is small enough (typically less than 1 cm). Still, too frequent impacts also have dire consequences for the spacecraft: impacts may accelerate the ageing of spacecraft components and increase their failure rate, reducing their performance as time goes by; and, if the impacting object is large enough, or if the impacted component is vital enough, may cause the loss of the complete system or at least of one important subfunction.

An intermediate category of untrackable debris which are large enough to cause a catastrophic collision is sometimes distinguished as a specific subcategory. Hence, there are two possible studies:

• The study of untrackable debris relies on penetration probabilities base on balistic models, assuming that a penetrated component fails [START_REF] Putzar | Vulnerability of spacecraft harnesses to hypervelocity impacts[END_REF]. This leads to average lifetimes for spacecraft components, but these studies are limited to a physical failure of the system, which does not necessarily imply the unability of the system to perform at least partially its mission, and hence tends to overestimate the effect of small debris, especially in densely populated orbits.

• The study of trackable debris relies on collision prediction and avoidance manoeuvre computation. This allows two differents computations: a probability to be manoeuvring at a given time to address short-term effects, as well as an expectation of the remaining amount of propellant to address long-term effects.

The issue that arises here is the following: how is it possible to integrate all these effects into a same performance model?

F G G F F G F G F G F G F G F G F G F G F G F G Table 1: ATLAS operators

The ATLAS approach

The ATLAS approach is documented in various previous publications [START_REF] Kervarc | A generic logical-temporal performance analysis method for complex systems[END_REF][START_REF] Kervarc | Performance evaluation based on temporal logic[END_REF], as well as its application to space system performance assessment [START_REF] Kervarc | Evaluation of space mission vulnerability to space debris[END_REF][START_REF] Bertrand | Space system vulnerability assessment to space debris: a methodology and a program[END_REF], and the notion of vulnerability index that can be added to it to compare space debris scenarios [START_REF] Jolly | Satellite protection: a system's approach through the 3R concept[END_REF][START_REF] Bertrand | A temporal logical methodology for probabilistic vulnerability analysis of space missions: Application to vulnerability analysis of an Earth observation mission due to catalogued space debris[END_REF].

Let us just recall that the method relies on a decomposition of the mission into elementary functions that can be linked to system components, according to the operators described on Table 1 Once this decomposition has been performed, a performance measure is computed over the tree. This measure is an availability notion, defined as follows: π F (s, t) is the (conditional) probability that a function F succeeds at time t provided it was requested at time s. Availability π is provided as an input for elementary functions, and computed recursively for higher level functions according to the semantics associated to the various operators, as shown on Figure 2.

Once this availability notion has been computed for the root function (which represents the mission of the system), it is possible to compare it for various configurations of the system and therefore assess a loss or gain of service which may be compared to user needs. For further detail, the reader may refer e.g. to [START_REF] Bertrand | Space system vulnerability assessment to space debris: a methodology and a program[END_REF].

The gap between physical and logical models

The issue is to provide input for elementary functions described above. Consider the workflow for space system performance assessment on Figure 2: the "debris knowledge" level represents physical simulation. The "vulnerability data" level represents the information needed to integrate the various effects of space debris, thanks to the "mission architecture" level: these two levels represent the ATLAS approach.

Here, we see that trackable debris effect may directly be integrated into mission availability measures, since the computed effects (probability for the payload to be unavailable, or probability that the propellant reaches a level where the spacecraft must cease to be operated) are directly interpretable in terms of mission.

However, untrackable debris effect is more difficult to integrate: it may be translated in term of physical component liveness, but this requires an additional level of knowledge (called "spacecraft design" here) in order to express these effects in terms of system mission, which will be done in the next section.

An important point to take into consideration is the fact that the form of this spacecraft design knowledge is something which may vary considerably in form in industry: each company, if not each team, will have its own way to represent this knowledge.

Therefore, it is particularly important, since the issue address here is not limited to a specific spacecraft platform, to have a common way to describe this knowledge so as to allow the use of a consistent methodology over very varied space assets.

The CRIOS model

In order to address the issue above, a model is developed, which is called an architecture association, and aims at making the link between components and functions.

Moreover, this model includes a notion of resource, which allows taking into account transversal infrastructures upon which the system relies without having dependency issues on functions, since the ATLAS computations rely on an independency hypothesis.

Resource

Resource modelling allows tackling dependency issues in the functional model:

whilst it is clear that most components will e.g. require that electrical supply components work, it is not possible to link these components to all functions. Indeed, the elementary functions would then be associated to dependent probabilities, which would make probability computation throughout the tree extremely problematic.

In this modelling, each component, or group of components, is associated to one or several resources. A resource defines a physical quantity that is produced by a component, or required by it to work properly. For a given instant, if the availability in a given resource drops below the need, defined by the quantity required by the active physical components, then the system cannot fulfill its mission anymore. The probability of success of the mission shall drop to zero.

This notion may be illustrated on two different examples, both pertaining to space system study: electrical power, which is essential to most components and is locally produced by solar arrays, and propellant, for which a given amount is available at the beginning and is consumed without replacement throughout the life of the spacecraft.

Two measures are associated to each resource R i :

1) the needed amount of resource is associated to each function F: r F i (s, t) is the amount of resource R i needed by F when it is requested at time s and succeeds at time t.

2) the available amount of resource is defined at the level of the whole system: M R i (s) is the amount of resource R i available at time s.

The first measure, r is very similar to π, and is also computed recursively throughout the functional tree according to a semantics given in terms of operators. On the other hand, tjhe second measure, M, strongly depends on the kind of resource and on the information available in the scenario.

Resource measures are used to correct availability π. Indeed, π is computed assuming infinite resource availability to avoid dependency issues. It is therefore postprocessed to take resource into account:

πF (s, t) =          π F (s, t) if ∀i r F i (s, t) M R i (s) 0 otherwise
The computation of π and r for elementary functions will be addressed by CRIOS together , whilst that of M will be addressed separately.

Architecture association

As stated above, it is necessary to describe a link between the elementary functions of the functional tree and the physical architecture, taking into account interactions and redundancies between components, i.e. the fact that several physical solutions may satisfy the generic elementary functions of the tree. In order to do this, information from spacecraft design knowledge is used to write a mapping between elementary functions and components. This mapping is called an architecture association. Figure 3 represents an example of architecture association (functional -physical). The physical architecture is described by the means of classical logic that define all the possible configurations of the system to fulfill the function. To satisfy the "Determine Attitude" function of a spacecraft, two types of alive gyroscopes and at least one among three set of alive star trackers are required. In nominal mode, regardless the debris threat, the performance of each function is given by the ability of the system in each configuration to satisfy the function.

The idea here is to be able to assess thanks to fine physical simulation the way in which components degrade over time, thus providing probabilities to be in each configuration, so as to be able to assess the effects of this degradation on elementary function performance, and, through the logical model, its consequences on overall performance.

The architecture association includes the notion of resource by defining, for each component and each element, how much resource is needed for the fulfilment of the element and, for each element, how much resource it produces.

More precisely, an architecture association contains the following information:

1) for each function, a list of elements pertaining to the function (the fact that E pertains to F is denoted by E ∈ F), each containing: a list of n components; a number k of alive components needed among these n to ensure the element; an order of priority for the use of components; for each component C and each resource i, an amount r C i (s, t) of this resource needed by C to contribute to ensure the element between s and t;the element; note that the fact that a component C contributes to ensure an element E is denoted by C ∈ E;

2) for each function, a list of configurations, where each configuration X contains: a list of ensured elements for the function; an elementary temporal performance table on sample S , i.e. a function π X (s, t) defined for each configuration X and each pair (s, t) ∈ S ;

3) for each resource R i , a list CL(R i ) of components producing this resource, as well as a production table for each component C, i.e. an instantaneous amount m R i C (t) of produced resource; Note that elementary measures π, r, and m are the outcome of industrial know-how about spacecraft design.

The CRIOS model

CRIOS 5 is able to use the information above to convert component liveness into the three kinds of input needed by ATLAS, namely, for each elementary function, its 5 Component Redundancy and Interaction in Operational Systems 10 availability and resource need throughout time, and, for the overall system, available resource. These three features are respectively called the π-converter, the r-converter, and the M-converter. The following notation is introduced to represent the combinatorics underlying these converters: for each element E of the function, a partial permutation is a vector A ∈ {0, 1} n stating, for each of the n components contributing to ensure the Assuming the existence of the following elements:

1) a time sample S , made of instant pairs (s, t), which is not explicited;

2) for each component C of the system, a probability F C (t) that the component has failed at time t -this probability is the output of physical simulation: it must be assessed homogeneously over all components of the system and, if it is associated to an uncertainty, this information may be used to compute several cases from best to worst and determine sensitivities;

3) an architecture association linking the physical system to the elementary functions of a functional tree; it is possible to compute the various inputs needed by the ATLAS method. Indeed, it is possible to compute the probability that a given partial permutation A occurs:

p A (t) = A such that A(C)=1 (1 -F C (t)) × A such that A(C)=0 F C (t)
and, therefore, the probability that element E is ensured:

p E (t) = A such that A k p A (t)
. and from this, the probability to be at a given instant t in configuration X:

p X (t) = E X (1 -p E (t)) × E∈X p E (t).
and this allows computing the overall availability of the function by:

π F (s, t) = X p X (t)π X (s, t).
The resource need may also be computed for each partial permutation where E is ensured, i.e. each partial permutation A with A k:

r A i (s, t) = k first components C such that A(C)=1 r C i (s, t)
where "first components" is to be understood in the sens of the priority order available in the input. Moreover, for each partial permutation A where E is not ensured, the associated need in any resource i is: r A i (s, t) = 0. With this notion, also using the probability p A (t) to be in a given partial permutation at a given instant t defined above, it is possible to compute the expectation of the resource needed to ensure element E:

r E i (s, t) = A p A (t)r A i (s, t)
and, consequently, the resource need for each function F, defined by:

r F i (s, t) = E∈F r E i (s, t)
It is worth noting that the notion of configuration defined for the π-converter is not used here: this is due to the fact that the probability associated to each partial permutation is rather included in the expectation for the element.

Finally, the available amount of resource may be computed. It depends however on the type of resource considered:

• for a cumulable resource:

M R i (t) = C∈CL(R i ) F C (t)m R i C (t)
• for a concurrent resource: We choose to compare the following different possibilities: (i) the choice of the launcher between Vega and Soyuz; (ii) the choice of the chaser (Fig. 4): with two nets or a robotic arm; (iii) the choice of the deorbitation technique: with a deorbitation kit (propulsive element appended to the debris) or by dragging the debris.

M R i (t) = max C∈CL(R i ) F C (t)m R i C (t) 4

Functionality description

The first step is to detail each elementary functionality of the mission and specify temporal constraints between these elementary functionalities, success probabilities associated to them, links to system components, and evolution throughout time of these components. As described above, the task is decomposed in five elementary functionalities: Launching, Reaching ENVISAT orbit, Placing, Capturing ENVISAT, Initiating deorbitation. These functionalities have to exactly follow each other, so the appropriate operator to be used between all functionalities is operator "meets" detailed in Table 1. Each elementary functionality must now be precisely detailed and linked to components to assess its associated success probabilities throug CRIOS. Functionality 1 The launcher launches the chaser in the orbital plane of the debris. The launching may not be operated all the time and is only possible during a 2h period each day of the first trimester of 2020. These time slots are considered as system components from the CRIOS point of view. If the task manager decides anyhow to launch out of such a time slot, the launch is operated at the beginning of the next slot. If the order is initiated inside a nominal slot, the chaser is immediately launched. Weather and other external conditions are not considered here since they would have the same impact on the task for all studied configurations. For similar reasons, it is considered that, if the launch vehicle takes off, the probability of success of this functionality is 1.

Functionality 2

The goal of this functionality is to manoeuvre the chaser to phase it with the debris. Placing the chaser in the right orbit (ENVISAT's orbit) depends on the choice of the launcher. Vega places it on an orbit of around 300km in about 800s [START_REF] Perez | Vega user's manual[END_REF].

One must wait several minutes to a few hours to compensate the possible phasing difference between ENVISAT and the chaser. It is assumed that the launching slots have been judiciously chosen so that the phase difference be minimised. To simplify this example that has a strictly illustrative vocation, the 2h time slot component is divided into three overlapping time slot elements (0 to 40 min, 40 to 80 min, and 80 to 120 min), that are considered sucessively alive in the sense of CRIOS, and that are associated to three different configurations, where the time necessary to reach the orbit is respectively of 10 min, 20 min, and 30 min. The success probability of this function is 90% (respectively 40%, 30%, and 20% according to launching time). The situation is simpler for the Soyuz launcher since it places the chaser directly in the correct orbit (790km) in about 60 min [START_REF] Perez | Soyuz from the Guiana space centre user's manual[END_REF].

Functionality 3 This functionality varies depending on the equipment of the chaser. In the case of a chaser equipped with nets:

F3.1 This corresponds to the observation and debris evaluation phase and may take more or less time to succeed. A delay of one or two minutes is considered.

F3.2 The chaser manoeuvres to move closer to the debris (to reach a distance of about 100m) and positions itself so as to be able to observe the debris with a dedicated sensor. Depending also on time slots above, several elements are considered, associated to configurations where the duration of this functionality is either 5 min, 7 min or 10 min.

In the case of a chaser equipped with a robotic arm:

F3.1 Greater precision is required for the operation. If necessary three attempts may be made, attempts being also modelled in CRIOS as elements, with one out of three having to success and a priority given according to attempt order. They are asociated to configurationswith delays respectively of 5 min, 10 min, and 15 min, and each with a success probability of 50%.

F3.2 The chaser manoeuvres to reach a distance of about 1m close to the debris and positions itself. In link with the above elements, It is assumed that the duration of this functionality is either 30 min, 40 min or 50 min.

Functionality 4

This functionality aims at establishing the mechanical contact with the debris. It also varies depending on the equipment used.

In the case of nets, it is considered that two nets are on-board. If the first net fails, a second net is launched 5 min later. It is assumed that both nets have the same success probability which is estimated at 60%. The capture time is constant (about 1 min).

These two nets are also modelled in CRIOS as different elements for which one at least must be ensured.

In the case of a robotic arm, the functionality has three chances to succeed in hitching the debris, after 5 min, 6 min, and 7 min, each of which has a probability of success or 30%. These attempts are also modelled as CRIOS elements concurring to a hitching component, and another component is taken into account to represent the de-tumbling that must be operated by the robotic arm and takes about 30min and has a high success probability of 95%, invariant over the mission.

Functionality 5 Two options are considered here. If a deorbitation kit is chosen, it has to be attached to the debris so as to change its trajectory. It is assumed that this functionality would take about 1 min and would have a success probability of 80%. If the debris is dragged, the success probability is evaluated to 90%. For practical reasons, the deorbitation kit is only considered when using a robotic arm since the latter would be necessary to append it to the debris.

ATLAS results

The results presented here do not have the vocation to provide an actual answer to the studied issue since the data used is approximative. The aim is to give an idea of the types of result the CRIOS-ATLAS method may offer. If M is the whole task, the CRIOS-ATLAS chain provides the probability Π M (s, t) that the deorbitation be successful depending on the chosen configuration, at a given instant t, knowing the task has started at instant s. Different post-treatments may then be applied to the resulting data to interpret it.

For instance, since the launching 2h time-slot has been divided into three with the Vega launcher (cf. Functionality 2), it may be interesting to consider the overall success probability in each time-slot, i.e. for the first slot:

t 0≤s≤40 Π M (s, t). These results are presented in Table 2. If the duration of the task is crucial, it is also possible to take into account a time limit. For instance, if the duration should be limited to 100min because of a limited quantity of propellant (so that the chaser doesn't become a debris to be deorbitised), the success probabilities are t,t-s≤100 0≤s≤40 Π M (s, t) presented in the last column of Table 2.

It may also be interesting to consider the success probability of the task with regard to the task duration, i.e. for the first time-slot 0≤s≤40 Π M (s, s + d) where d is the task's length. These results are presented as graphs in Fig. 5 Beyond the straightforward conclusion that the Soyuz launcher with a robotic arm and the dragging option is the best configuration, ATLAS details the precise delays linked to the successful realisation of the overall task. Post-treatments such as presented here may thus be applied to the result data to bring to light different aspects. In addition, changes in configuration may easily be compared, which allows to study the sensitivity of the system.

Conclusions and perspectives

CRIOS is a generic representation allowing to make a correspondance between high-level system functions and mission logical architectures on the one hand, and system components and physical architectures on the other hand. It allows incorporating industrial knowledge using a common representation in order to be able to translate information about component evolution in terms of functional consequences. It is hence a useful common language that can be shared between various industrial, physical simulation specialists, and system performance experts. It allowed general result integration in project P 2 ROTECT in a highly innovative multifold approach:

1) The tool works at mission level (i.e. the services offered to Users) instead of spacecraft level only, thus allowing the analysis and meaningful comparison of different architecture solutions (spacecraft redundancy, spacecraft factorization. . . ), as well as the evaluation of global trade-off between different remedial measures (e.g. comparison between Spacecraft Protection, Space Surveillance Tracking, Active Debris Removal).

2) At space segment level, it takes into account threats coming from both trackable (i.e.

inducing avoidance maneuvers) and untrackable debris (i.e. inducing collisions with the spacecraft from catastrophic to minor levels) in a commeasurable way.

3) This allows showing effects (or sensitivities) of multi-scale protection solutions (i.e.

at mission level, at space segment level,a at component level) as well as combined external solutions (i.e. Space Surveillance, Mitigation, and Active Removal).

Further work will focus on several axes. Firstly, resource limitations are taken into account in a rather simplistic way. Indeed, lack of resource availability is considered in a binary way in the update of π. We plan to develop a finer model in order to account for smoother degradations of performance, thus leading potentially to less conservative results. Secondly, the architecture association could also be improved: indeed, redundancies are treated using a priority list, whilst more elaborate reconfiguration strategies could be taken into account. We plan to extend this model in this direction, thus allowing FDIR (Fault Detection, Identification, and Reconfiguration) strategies to be implemented so as to compare their efficiencies under various debris conditions.

Figure 2 :

 2 Figure 2: ATLAS method overview (left) and Space system performance assessment workflow (right)

Figure 3 :

 3 Figure 3: Association of a physical architecture to function "Determine Attitude"

  225element, whether it is alive[START_REF] Allen | An interval-based representation of temporal knowledge[END_REF] or not (0); the cardinal of each such partial permutation is the number of alive components, i.e.: A = C∈E A(C) where A(C) denotes the value (1/0) indicating whether component C is alive or not.

. Case study 4 . 1 .

 41 Deorbitation of retired satellite ENVISAT The case study presented here serves as an illustration of the ATLAS performance analysis method and has no purpose of realism concerning the data used. It shows what could be achieved with the intervention of technical experts to determine the data associated to each elementary functionality. Let us consider the task of completing the deorbitation of retired satellite EN-VISAT [5]. ENVISAT ("Environmental Satellite") is an inoperative Earth-observing satellite still in orbit. It was launched in 2002, into a Sun synchronous polar orbit at an altitude of 790 km, and the task ended in 2012. It is now considered as large debris: 26 m × 10 m × 5 m and 8,200 kg. For this reason it a candidate for a space debris removal task. The aim is to study different possible ways of removing ENVISAT with a chaser. The general task may be decomposed as follows: 1) launching the chaser; 2) reaching ENVISAT's orbit; 3) placing the chaser; 4) capturing ENVISAT; 5) initiating deorbitation.

Figure 4 :

 4 Figure 4: Different possible equipments for the chaser [6]: ROGER net system (left) and Canadarm-2 ISS operating arm principle (right)

Figure 5 :

 5 Figure 5: Graphical representation of the ATLAS results

Table 2 :

 2 Success probabilities and task length of ENVISAT deorbitation

				S M	Duration d	Success	Success
					(min)		with d≤100
				0-40	30-43	29.0%	29.0%
		Net	Drag	40-80	40-53	21.8%	21.8%
				80-120	50-63	14.6%	14.6%
				0-120	30-63	65.4%	65.4%
				0-40	93-125	26.9%	7.7%
	Vega		Drag	40-80	103-135	20.2%	0%
				80-120	113-145	13.5%	0%
				0-120	93-145	60.6%	7.7%
		Robotic Arm
				0-40	94-126	23.9%	6.1%
			Kit	40-80	104-136	18.0%	0%
				80-120	114-146	12.0%	0%
				0-120	94-146	53.9%	6.1%
		Net	Drag 0-120	67-80	72.6%	72.6%
	Soyuz	Robotic Arm	Drag 0-120	130-162	60.6%	0%
			Kit	0-120	131-163	53.9%	0%

LEO: Low Earth Orbit, GEO: Geostationary Earth Orbit, MEO: Medium Earth Orbit


Pauline Debanes

Modes of Insertion into Global Value Chains as a Source of Firms' Heterogeneity? Evidence from a Panel of Korean Manufacturing Firms 1990-2015

Keywords: Global Value Chains, Heterogeneity, Investment Behaviour, Korea, Firm-Level Evidence

While the slowdown of accumulation has been at the center of the financialization literature since the 2000s, not much has been written on the investment behavior of firms beyond the US and Europe neither in the case of non-leading firms. This article addresses this gap by testing if the "low growth, low investment" track of the Korean economy since the Asian crisis can be explained by the modalities of firms' insertion into global value chains (GVCs), defined according to the activity of firms, the governance of the chain they are part of, and their possibility of upgrading. Empirical evidence derived from a cluster analysis using micro and sectoral data of manufacturing firms, confirm that modalities of insertion into GVCs are a source of heterogeneity of firms' investment behavior. The original methodology developed in this paper enriches the understanding of the complexity and heterogeneity of governance intra-value chains and intra-firms.

ABOUT THE INCAS PROJECT

INCAS is a Marie Skłodowska-Curie Actions R.I.S.E funded project under the European Commission's H2020 Programme.

The project INCAS aims at creating a top-level research and advanced training network on institutional change in Asia, in comparative perspective with Europe. The coordinator, Ecole des Hautes Etudes en Sciences Sociales (France), promotes this network together with Oxford University (UK), Freie Universität Berlin (Germany), and in collaboration with Waseda University (Japan). The aim of the proposed mobility scheme is to give birth to a European consortium and network of faculties and advanced graduate students specialized in the comparative analysis of institutional change in Asia and Europe. The partners have chosen Japan as a reference point because of its comparability with Europe as shown by previous studies, its historical influence on development and further institutional changes in Asia, and the expertise accumulated within our research team.

Analyzing current economic dynamics in Japan and later expanding this analysis to other Asian countries promises to generate insights that might be help to better understand challenges for Europe and to prepare relevant policy proposals. Our purpose is to compare the results obtained in the case of Japan and few other Asian countries (South Korea, Taiwan, China, and possibly Thailand, after having checked the data availability), not only to previous results on Europe but also to original results we will get on European countries (primarily France -which will be our reference country in Europe -and then the UK, Germany, and Italy) in mobilizing new historical data and applying our theoretical framework.

Biography

Pauline Debanes is an advanced Ph.D. candidate at EHESS, Paris. Before starting her research on the transformation of the role of the state in South Korea, she worked as an economic attaché at the French Embassy in Korea for one year. For her Doctoral research, she did an intensive fieldwork in Seoul's startup ecosystem during the first semester of 2016. Interested in comparing institutional change in Asia, she has edited a special issue entitled "Towards a Renewal of the Developmental State in Asia?" with Sébastien Lechevalier (Critique Internationale, 2014) and has co-authored, with Sébastien Lechevalier and Wonkyu Shin, an article comparing the financialisation of industrial policy in Japan and Korea (Structural Change and Economic Dynamics, 2017).

Introduction

The structural decreasing trend of investment rate in advanced economies has been one of the major stylized facts of the post-Fordist era. In the case of the United States (US), a large body of literature has pointed out the increasing financialization of non-financial corporations since the 1980s that would explain the slowdown of fixed assets accumulation. This macroscopic trend is also associated to the globalization of production, which has given incentives to large firms in core countries for cutting costs by outsourcing part of their activities [START_REF] Gereffi | International trade and industrial upgrading in the apparel commodity chain[END_REF][START_REF] Milberg | Shifting sources and uses of profits: Sustaining US financialization with global value chains[END_REF][START_REF] Milberg | Outsourcing economics: global value chains in capitalist development[END_REF]. The spatial restructurings of trade and production were concomitant with the financial liberalization and the global expansion of financial markets. Indeed, the outsourcing strategy of firms has been encouraged by shareholders lurking on the higher rate of returns yield by financial transactions rather than productive ones [START_REF] Krippner | The financialization of the American economy[END_REF][START_REF] Crotty | The neoliberal paradox: the impact of destructive product market competition and 'modern'financial markets on nonfinancial corporation performance in the neoliberal era[END_REF].

More attention has recently been given to the interrelation of the processes of financialization and globalization of production. The findings show a significant correlation between outsourcing behavior and financialization in the case of leading global firms, mainly from the US and Europe (Baud & Durand, 2011;Froud. et al., 2012;[START_REF] Milberg | Outsourcing economics: global value chains in capitalist development[END_REF][START_REF] Soener | Why do firms financialize? Meso-level evidence from the US apparel and footwear industry, 1991--2005[END_REF]. However, less has been written on the investment behavior of firms beyond the US and Europe, nor in the case of non-leading firms. Scholars looking at developing and emerging economies stress the important heterogeneity of firms behavior depending on their transnational linkages and their local institutional embeddedness [START_REF] Ashman | The crisis in South Africa: Neoliberalism, financialization and uneven and combined development[END_REF][START_REF] Powell | Subordinate financialisation: a study of Mexico and its non-financial corporations[END_REF][START_REF] Akkemik | Macroeconomic and institutional determinants of financialisation of non-financial firms: Case study of Turkey[END_REF][START_REF] Bonizzi | International financialisation, developing countries and the contradictions of privatised Keynesianism[END_REF]. This article addresses this gap by focusing only on the impact of global trade restructuring on firms' investment behavior in the case of Korean manufacturing firms since the 1990s 1 . The Korean economy has experienced a slowdown of accumulation following the Asian crisis of the late 1990s and has been ever since in a "low growth, low investment" trajectory (see Park & Doucette, 2016). This domestic economic environment has been mitigated by the active participation of Korean firms in regional and global networks of production. Following a fast upgrading during the industrialization period, they have now become pivotal stakeholders of several production networks by governing their regional supply chains [START_REF] Frederick | Korea in Global Value Chains: Pathways for Industrial Transformation[END_REF]. It is proposed here to investigate the modalities of insertion into GVCs, taken as a source of heterogeneity of investment behavior. The modalities of insertion into GVCs are defined according to the activity of firms, the governance of the chain they are part of, and their possibility of upgrading. This dynamic concept of modes of insertion intends to grasp the localized features of the firms within value chains as well as their mobility, given the overall hierarchical structure of value chains.

The contribution of this article is twofold. A theoretical effort is made to conceptualize the modalities of insertion into GVCs. This concept accounts for the recent development of the GVC literature and incorporates a more dynamic perspective on firms' engagement in GVCs. It is argued that the modalities of firm insertion into GVCs are a source of heterogeneity, especially regarding investment behavior. The second contribution is empirical. The original taxonomy of five modes of insertion into GVC is provided based on a cluster analysis using micro and sectoral data. The use of micro-data for GVC analysis is rare, and the methodology developed in this paper enrich the understanding of the complexity and heterogeneity of governance intra-value chains and intra-firms.

The article proceeds as follows. The first section discusses at greater length the various features that characterize the modes of insertion into global value chains (the activity of firms, governance of supply chains and upgrading opportunities). The second section implements a cluster analysis to determine the mode of insertion at the firm-level based on firms' financial data completed by sectoral data from input-output tables.

Mode of insertion into GVC and heterogeneity of firms' investment behavior.

Facing a heighten competition from developing and emerged economies and under pressure for profitability from the capital market, non-financial corporations have resorted to different strategies to maintain their activity and sustain their profitability. It is argued here that their mode of insertion into GVCs is a key determinant of their investment behavior. This subsection defines a mode of insertion as a dynamic apprehension of firms' activity in the value chain combined with their coordination capabilities of intra-and inter-value chains. As such, the concept of mode of insertion echoes two concepts at the core of the GVC framework; those of governance of the value chains (power relations and the coordination between firms), and upgrading opportunities. Existing taxonomies of governance, individual empirical cases, and firm-level studies are surveyed in this section to delineate the contours of modes of insertion

Mode of insertion: intra and inter-chains coordination at the firm-level

The existing taxonomies of global value chains are related to the concept of governance, which embodies the organizational consequences of the power of leading firms over the supply chain. The analysis of coordination of the chains by leading firms, or their governance, refines transaction cost theories by conceptualizing a spectrum of relationships between leading firms and suppliers (see [START_REF] Humphrey | How does insertion in global value chains affect upgrading in industrial clusters?[END_REF][START_REF] Gereffi | The governance of global value chains[END_REF].

A basic dichotomy has initially been proposed by [START_REF] Gereffi | Commodity chains and regional divisions of labor in East Asia[END_REF][START_REF] Gereffi | International trade and industrial upgrading in the apparel commodity chain[END_REF] between two types of chains: producer-driven and buyer-driven supply chains, which are two types of control of leading firms over their backward linkages (see contribution in Gereffi and Korzeniewicz [eds], 1994;[START_REF] Gereffi | International trade and industrial upgrading in the apparel commodity chain[END_REF][START_REF] Gereffi | The global apparel value chain: What prospects for upgrading by developing countries[END_REF]. The producer-driven supply chains are to be found in the more technical manufacturing sectors (electronics, automobile, aircraft, and semiconductors) where the manufacturer leads the production process, while buyer-driven chains reflect the weight of global buyers, focused on branding, marketing or retailing, in charge of the coordination of the production process. Types of chains are associated with organizational features, mainly the degree of vertical integration. Producer-driven chains tend to be dominated by few vertically integrated firms, in close coordination with their subcontractors, exercising strong market power over the distribution channels. On the contrary, buyer-driven chains are more competitive and deconcentrated; only the higher-end of the chain is concentrated into a few global buyers, shaping their sourcing strategies to optimize their revenues.

Building upon this buyer/producer-driven distinction, the concept of governance has emerged to take into consideration organizational features of the value chain. Essentially, the type of governance determines how the value added is shared across firms, the more the governance is hierarchical, the more the value added is concentrated at the higher-end of the chain. In-between completely decentralized relationships ('Markets') and vertical integration ('Hierarchy'), [START_REF] Gereffi | The governance of global value chains[END_REF] proposed three intermediate categories that reflect the distribution of power and the dependence between lead firms and suppliers which can be 'Modular' , 'Relational' or 'Captive' . It is largely consistent with [START_REF] Humphrey | How does insertion in global value chains affect upgrading in industrial clusters?[END_REF] who define two intermediate categories of 'Networks' and 'Quasi-hierarchy' .

The governance of the value chain is closely linked to the array of relationship possible between firms at the micro-level. Thus, in each type of governance, the position of firms involves coordination intra and inter-chain, with downstream and upstream industries. Indeed, GVC scholars have documented on the contingency of the activity of suppliers, themselves embedded in supply chains they do not govern, on not only the linkages they have with leading firms but also on their local network. For instance, the emergence of core (or top-tier) suppliers mentioned in the previous section is a good example of how some suppliers have gained power over the rest of the value chain by becoming the only interlocutor of leading firms (see Palpacuer et al., 2004). Then, while first-tier suppliers need to sustain their capabilities to keep their preferred position which necessitates investment spending, component suppliers are more focused on price competition in markets of highly demanded standardized goods [START_REF] Blažek | Towards a typology of repositioning strategies of GVC/GPN suppliers: the case of functional upgrading and downgrading[END_REF]. The coordination of non-leading firms, from the lower-end of the chains, can also create nodes of productivity, as described by [START_REF] Newman | Financialization and changes in the social relations along commodity chains: The case of coffee[END_REF] who shows that farmer's cooperatives proved to be related to higher capital accumulation than individual farmers.

Beyond the established typologies of governance or the success stories of localized strategies of industrial upgrading, scholars have recently argued for a more dynamic and granular approach of modes of governance (Sturgeon & Ponte, 2013). As convincingly defended by [START_REF] Blažek | Towards a typology of repositioning strategies of GVC/GPN suppliers: the case of functional upgrading and downgrading[END_REF] based on a thorough account of the literature, typologies of modes of governance should preferably be used to understand the localized part of GVCs in order to account for the evolution of modes of governance over time, but also for their coexistence within the same value chain and even within the same firm (see also Haakonsson, 2009).

The analytical concept of mode of insertion intends to contribute to this line of research by putting the firm at the center of the analysis. The insertion of firms at the micro-level hinges not only on their business activity but also on their dynamic capabilities to engage with upstream and downstream industries, as well as across value chains. GVCs are then apprehended as dynamically interconnected, which involves that they overlap and have an evolutive design. Such a dynamic approach fits the aim of this paper to grasp the heterogeneity of the investment behavior of firms across value chains by considering the combination of different levels of embeddedness and change. In particular, the governance of value chains will impact the investment behavior of firms, whether it is for non-leading firms to maintain an established type of coordination or to challenge it, or for leading firms to sustain their extraction of value added.

Mode of insertion: industrial upgrading and the possibility of change

Industrial upgrading is one of the core concerns of the GVC framework which has been providing the analytical tools to analyze the successful -or not-experience of firms in climbing the value-added ladder of the supply chains. In a more modular and dynamic approach, industrial upgrading can be defined as a significant improvement of firms' capabilities that impact the intra or inter-chains involvement of the firm 2 . This definition allows moving beyond an approach of industrial performance to consider the gain of capabilities, in terms of innovation but also welfare or sustainability. Except for the intrinsic features of firms that determine their capabilities to grow and develop, external factors can foster upgrading such as the institutional environment [START_REF] Yeung | Governing the market in a globalizing era: developmental states, global production networks and inter-firm dynamics in East Asia[END_REF] but also the spatial localization of firms.

Studies of upgrading opportunities have highlighted the importance of the spatial proximity of firms and their geographical localization. Concerned with the linkages of firms within their regional and global networks, GVC scholars have analyzed the knowledge and capabilities in cases of spatial agglomeration such as industrial clusters [START_REF] Humphrey | Governance and upgrading: linking industrial cluster and global value chain research[END_REF][START_REF] Giuliani | Upgrading in global value chains: lessons from Latin American clusters[END_REF][START_REF] Sturgeon | Value chains, networks and clusters: reframing the global automotive industry[END_REF]. [START_REF] Bair | Local clusters in global chains: the causes and consequences of export dynamism in Torreon's blue jeans industry[END_REF] observe the advantage of large firms in the Torreon blue jean cluster in Mexico, able to take advantage of the entry of foreign buyers to upgrade their process while small firms remained trap in the maquiladoras model. To the size factor, [START_REF] Giuliani | Upgrading in global value chains: lessons from Latin American clusters[END_REF] add that the benefits from spatial agglomeration are strongly dependent upon the industrial sector. [START_REF] Gereffi | Development models and industrial upgrading in China and Mexico[END_REF] stresses the local specificities, such as the 'supply-chain cities' , reflecting the spatial concentration and specialization of some segment of the production process at the core of China's model of upgrading.

Moreover, the geographical localization of production increasingly matters when considering the opportunities for firms to improve their mode of insertion into GVCs (see [START_REF] Gibbon | Trading down: Africa, value chains, and the global economy[END_REF] on the different upgrading trajectories in Africa; [START_REF] Hernández | Global value chains and world trade: Prospects and challenges for Latin America[END_REF] for Latin America). The North-East Asia experience of industrialization is often taken as a successful case of upgrading. Indeed, it has involved the upgrading of Japan followed by the NIEs (Hong-Kong, Taiwan, Singapore, South Korea) which have sustained their power in the value chains by extending their reach into South-East Asia [START_REF] Gereffi | International trade and industrial upgrading in the apparel commodity chain[END_REF][START_REF] Kishimoto | Clustering and upgrading in global value chains: the Taiwanese personal computer industry[END_REF]Escaith & Inomata, 2013). In particular, East Asian firms have managed to upgrade from supplier to leading positions in low productivity sectors, such as the apparel industry, and then upgrade to medium and high-tech industries (Table 1). The external linkages of the NIEs with US firms have also played a role as highlighted by Feenstra and Hamilton (2006: p212) who reenacted the supply-side story of the developmental state in the industrial upgrading of Korea. Given the time and space specificities of the Japan and NIEs' experiences, the possibilities of industrial upgrading of China is highly debated nowadays; Chinese manufacturers seem to have fewer opportunities to climb the ladders of the supply chain as exemplified by the business strategy of Foxconn International Holdings (Froud et al., 2012;Lüthje & Butollo, 2016). The localized understanding of value chains dynamics is, in this case, crucial to understanding the potential lock-in effects that prevent firms down the value chains to build their capabilities. Moreover, the limited upgrading opportunities of suppliers shed light on the dialectic of the spatial restructuring of trade. Indeed, the GVC framework has focused on the inclusiveness, often neglecting the corresponding 'disarticulation' forces [START_REF] Bair | Commodity chains and the uneven geographies of global capitalism: a disarticulations perspective[END_REF].

It is expected that the relationship between the upgrading dimension and the mode of insertion will depend on the activities undertaken by the firm. Indeed, investment in fixed assets, in the case of manufacturing, is only needed to expand the production process (tangible activities), while intangible investment corresponds to the higher-end of value chains activities such as ante-production (R&D) or post-production (Marketing and branding) (see the distribution of value in manufacturing GVC in Frederick et al. [2017: 5-12]). Hence, upgrading opportunities for third-tier suppliers will be positively correlated with investment in fixed assets while upgrading opportunities for top-tier suppliers might involve a trade-off between investment in fixed assets and intangible investment.

The three outlined dimensions of the mode of insertion into GVCs resonate with existing qualitative studies on Korean firms. If Korea has attracted so much attention in the 1990s, it is due to its label of NIE gained at this period given the rapid and successful industrial upgrading of Korean firms from the textile industry to the electronics and automotive industries (Lee & Lim, 2001). The outsourcing drive kicked-off in the late 1980s and accelerated after the Asian crisis (Figure 1). When looking into the mode of insertion of firms into GVCs, the contemporary Korean case is fascinating because Korean firms are involved in global leadership positions as well as global suppliers, in both producer-driven 2. The upgrading possibilities, and their spatial component, are a key feature of the dynamism of the mode of insertion into GVCs. In reference to the evolutionist theory of the firms [START_REF] Teece | The dynamic capabilities of firms: an introduction[END_REF][START_REF] Dosi | Introduction[END_REF][START_REF] Winter | Understanding dynamic capabilities[END_REF], firms are always adapting to new constraints and new prospects, through which they dynamically use and build their capabilities. Hence, if firms are constantly evolving, so is the design of GVCs, despite some structural features of stability. At the theoretical level, this paper argues that the concept of mode of insertion, articulating the dimensions of activity, governance and upgrading at the firm-level, allows a dynamic analysis of how firms are engaging into GVCs, without presupposing a unimodal and linear path of evolution possible from supplier to leading firms. chains (Samsung, LG, Hyundai, Kia, Asiana, Korean air) and buyer-driven chains with large retailing firms (Gmarket, Lotte). Moreover, in a context of growing importance of the Asian region in global trade patterns and global production network [START_REF] Azmeh | Asian firms and the restructuring of global value chains[END_REF], Korean firms are at the forefront of GVC restructuring. In particular, their mode of insertion is likely to be impacted by the deep embeddedness of Korean firms with Chinese firms, which is at the same time a major feature of the highly vertically integrated type of governance of Korean global manufacturers, and a likely source of limitation of upgrading opportunities of firms across several value chains considering the rise of the Chinese manufacturers [START_REF] Mu | Knowledge diffusion, market segmentation and technological catch-up: The case of the telecommunication industry in China[END_REF]. This section has described the three dimensions of the mode of insertion into GVCs: activity, governance, and upgrading, which aim at capturing the engagement of firms into GVCs dynamically. The next section determines the data at the firm-level that will be used to implement a cluster analysis of the mode of insertion into GVCs.

Table 1 Share of Medium and High-Tech exports in total manufacturing exports by country (%Total exports)

Source: CHELEM database (Total export is the sum of non-manufacturing and manufacturing exports)

Figure 1 Evolution of trade integration in Korea

Source: World Development Indicators

Estimation of modes of insertion into GVC at the firm-level, a cluster analysis approach

This section aims at delineating the kind of variables at the firm-level needed to infer the mode of insertion into GVCs, in order to implement a cluster analysis of firms according to their mode of insertion. The definition of the mode of insertion in the previous section emphasized three components: the vertical integration of firms, the composition of outputs, and the linkages across firms. Two components of sectoral linkages and growth are added after reviewing the literature making use of sectoral and firm-level data. From these components, concrete variables are constructed from a dataset of financial statements of Korean manufacturing firms extracted from the Korea Information Service database. Then, the number of dimensions is reduced with a principal component analysis that is used to implement a cluster analysis.

Data

The data used in this paper come from the Korea Information Service (KIS-value) database that provides financial statements and non-financial data of firms with assets above ₩7bn 3 . This dataset contains exhaustive information across all the sectors of the economy on surviving firms. The study focuses here on non-financial corporations in the manufacturing sector (the C section according to the Korean industrial sector classification with December as a fiscal month) from 1990 to 2015. Two samples are drawn from the raw dataset.

A first sample is constituted to investigate the decomposition of the balance sheet of Korean manufacturing firms. Because the median of each variable is looked individually, the top and bottom 1% for each regression variables (except the dependent variable) are trimmed. The sample is then reduced to 163 804 observations with 9898 firms in 2015. The cluster analysis is performed on a stratified random sample on size and age of 500 firms drawn from the trimmed dataset of Korean manufacturing firms. Only firms with more at least three consecutive years of observations after cleaning the missing values for regression variables are included in the sample.

These firm-level data are complemented by input-output tables published by the Bank of Korea since 1990. A table of correspondence is established by the author between sectors of the tables and the Korean classification of industry into twenty-four manufacturing sectors.

3. Data are compiled by the National Information & Credit Evaluation Inc. This database is widely used in empirical studies.

Variables

The components of modes of insertion are grouped into four categories of vertical integration, the composition of outputs, spatial and sectoral linkages and growth. These four components are largely consistent with the few studies determining the type of GVC governance or supply chain strategies at the firm level [START_REF] Palpacuer | Changing governance patterns in European food chains: the rise of a new divide between global players and regional producers[END_REF][START_REF] Brancati | Global value chains, innovation and performance: firm-level evidence from the Great Recession[END_REF].

Firm-level studies mainly make use of data obtained from qualitative surveys. [START_REF] Brancati | Global value chains, innovation and performance: firm-level evidence from the Great Recession[END_REF] exploit a qualitative survey to determine the mode of participation to GVCs at the firm-level, defined in a similar way as by [START_REF] Humphrey | How does insertion in global value chains affect upgrading in industrial clusters?[END_REF] and [START_REF] Gereffi | The governance of global value chains[END_REF], that vary according to three dimensions: the formal vertical integration, the linkages with other firms and the company's value added. [START_REF] Palpacuer | Changing governance patterns in European food chains: the rise of a new divide between global players and regional producers[END_REF] propose a typology, based on quantitative and qualitative data, of the main governance patterns across the largest agrifood producers in Europe. They add variables of ownership control and the type of industrial strategy. [START_REF] Saliola | Multinational firms, global value chains and the organization of knowledge transfer[END_REF] use the criterion of knowledge transfer to distinguish three different types of value chain governance. With a panel data of Thai firms (PICS survey), they test the variables determining the type of governance, including the presence of multinational firms, their local embeddedness and the capabilities of local suppliers measured by qualitative data and the number of patents filed. Usual control variables of age, size, and industry are added in studies at the firm level.

Inspired by existing literature but given the limitation of our study to quantitative data from financial statements, proxies of components are chosen as follows. The vertical integration of firms is proxied by three variables: the capitalintensity ratio, the affiliation to a group and the size of the firm. One of the main reasons for a vertical integration strategy is lowering costs of transactions and maximizing the firm's share in the value chain. Hence, highly vertically integrated firms are more likely to have a dominant position in the value chain, either governing the value chains or being a top-supplier of leading firms. The capital intensity ratio is expected to be positively correlated with vertical integration because less prone to outsourcing. Belonging to a group and the size are associated with higher integration. Indeed, firms belonging to a group are de facto integrated, and large firms are more likely to be vertically integrated. The size and the affiliation to a group are two dummy variables, with the former representing large firms (fourth quartile of asset distribution in the total dataset).

The composition of outputs exposes the organization of firms' production. The variables used are value-added to sales and the intangible assets intensity (taken as a proxy of technological intensity). The ratio of value-added to sales discloses the number of production stages undertaken by the firms, as well as their respective contribution to the value chains. It is therefore expected that high-value-added to sales be correlated with a leading position in the value chain, but because the financialization of firms has a negative impact on value added [START_REF] Tomaskovic-Devey | Did financialization reduce economic growth?[END_REF], leading global firms might have a lower ratio than other firms. The intangible intensity, which increases the probability of a leading position, is an important variable to identify the upgrading potential of firms. The technological intensity is also related to vertical integration, positively for downstream industries and negatively for upstream industries [START_REF] Acemoglu | Vertical integration and technology: theory and evidence[END_REF].

The third component are the linkages across firms, divided into sectoral and spatial linkages. Following Hirshman (1958), backward and forward linkages derived from input-output matrixes have widely been used to inform of the relative importance of sectors and their linkages [START_REF] Gereffi | The global apparel value chain: What prospects for upgrading by developing countries[END_REF][START_REF] Giuliani | Upgrading in global value chains: lessons from Latin American clusters[END_REF][START_REF] De Backer | Mapping global value chains[END_REF][START_REF] Alfaro | Internalizing global value chains: A firm-level analysis[END_REF]. While backward linkages measure the number of production stages from other sectors incorporated into a given output, and therefore the length of suppliers, forward linkages estimate the linkages of firms with downstream industries [START_REF] Jones | The measurement of Hirschmanian linkages[END_REF]. Backward and forward linkages of each industry are computed yearly from the national input-output tables. The sectoral linkages are combined with a spatial linkage at the firm-level. Following [START_REF] Scholl | Detecting spatial clustering using a firm-level cluster index[END_REF] a spatial clustering index is computed with the address of firms' headquarters:

A high value of indicates a strong spatial proximity of firm with other firms. In the literature on cluster industries and regional innovation systems, it has been shown that the agglomeration of firms has a positive impact on growth and productivity [START_REF] Sturgeon | Value chains, networks and clusters: reframing the global automotive industry[END_REF]. Hence, a higher clustering index should be associated with a higher position in global value chains.

Finally, the growth component reflects the yearly dynamic as well as the sectoral dynamic at the firm level. It is proxied by two variables: the growth of sales and the return on assets, which are two indicators of performance and efficiency. Growth is expected to be correlated positively with the linkages of firms and the vertical integration. The correlation between growth variables and the variables serving as proxies of the composition of output is expected to be rather low because it highly depends on the sector and the activity undertaken by the firms.

Cluster analysis

Before implementing a cluster analysis, a principal component analysis is run on a set of variables reflecting the four components of the mode of insertion described in the precedent sub-sections (Table 2). This first step aims at reducing the number of variables into a limited number of factors, linear combinations of the chosen variables of interest. The analysis is based on the distribution of variables in deciles, which have the advantage of dealing with outliers as well as take into account categorical variables such as affiliation and size. In the first step, the polychoric matrix is computed and then serves as an input for a principal component analysis (see the mathematics of polychoric matrix in Müthen [1983]). Four factors which represent 60% of total inertia (criterion of eigenvalue above one) are retained. Based on the factor loadings of each variable, the four axes can be interpreted as follows: vertical integration, profitability, the capture of value-added, modularity of the supply chain.

Table 2 Summary statistics of the variables used in the PCA (before discretization)

Source: KIS-data, stratified random sample of 500 hundred manufacturing firms, Author's calculation

The participation modes of Korean manufacturing firms to GVCs is determined by cluster analysis with no initial hypothesis on the clusters. This method has the advantage to take into account the multidimensional aspect of participation in GVCs and its dynamics. Indeed, the principal component analysis is constructed with yearly firms' data, and cluster assignment can vary from year to year for a given firm. Therefore, this methodology can grasp the industrial upgrading (or downgrading) of firms. With the PCA, each observation can be characterized by its factor coordinates. The number of clusters and the initial centers of clusters is determined by the Ward method, a hierarchical clustering method minimizing the within-cluster variance. Five clusters are chosen, and modes of insertion are identified based on the score of individuals across factors.

The modes of insertion are determined based on the score of factors for each cluster but also by the mean and median value of the nominal variables of vertical integration, the composition of output, linkages, and growth (Figure 2). Five modes of insertion are described based on the factors according to the three dimensions of activity, governance and upgrading opportunities (Table 3). To describe these modes of insertion further, we estimate a probit model for each modality where the panel structure of the data is taken into consideration (Generalized Estimating Equations). The continuous variables used in the cluster analysis are used supplemented with sectoral dummies and size dummy. The profile of each mode of insertion reveals that firms' engagement to GVCs cannot be reduced to sectoral specificities. For instance, firms from the automotive sector are likely to have a stable or an established mode of insertion. The petroleum, chemical and metal industries are more represented in the restrained, adaptive or established modes of insertion. The disruptive mode of insertion has a more distinctive sectoral pattern in coherence with its definition.

Table 3 Description of modes of insertion inferred from the cluster analysis

Source: Author Table 4 Determinants of mode of insertion -GEE Probit **: pvalue<0.01; * pvalue<0.05. Note: The models test the probability of being in one cluster across years. Hence, a given firm can belong to different cluster depending on its upgrading trajectory. The reference of the sectoral dummies is the value 0 (do not operate in the given sector). The reference for the size dummy is the medium size, defined as the second and third quartile of the distribution). Source: KIS-data, stratified random sample of 500 hundred manufacturing firms, Author's calculation.

Heterogeneity of investment behavior by mode of insertion

Given the five modalities of insertion into GVCs identified at the firm-level, this sub-section now turns to the investment behavior of firms over time. The median level of investment is plotted by mode of insertion, for the period 1991-2015 with a smooth filter (Figure 3) and unfiltered data are plotted for the 2009-2015 period (Figure 4).

The plot of the median level of investment by mode of insertion yields interesting results. In the long run (Figure 4), there are distinct levels of investment by mode of insertion. Firms inserted into GVCs according to the restrained modalities, essentially component suppliers, have a lower and steadily declining level of investment. The global manufacturers, inserted according to the established modality, have the lowest level of investment after the restrained firms, though with a rebound after the Asian crisis. The trajectory of firms belonging to the adaptive modality is closer to the overall median, which reveals a larger sensitivity to the national context and better faculty to adjust their investment level. The stable and disrupting modalities of insertion are associated with a higher level of investment over the period studied. While the stable modality, corresponding to top-tier suppliers, has a rising trend of investment level from 1991 to the mid-2000s followed by a declining trend, the level of investment of the disrupting cluster was significantly higher before the mid-2000s but dropped sharply afterward. After the post 2008-crisis rebound (Figure 5), the investment level of firms with a stable, disruptive and adaptive mode of insertion has stabilized around 0.2. During this period, firms in the established modality experienced the sharpest drop of investment rate and the restrained modality bottomed out at 0.12. These findings confirm our initial hypothesis that the investment behavior of firms is correlated to their mode of insertion into GVCs. Moreover, the heterogeneity of investment rate between the modes of insertion is coherent to the literature. Indeed, the trajectory in the established modality fits the empirical evidence that large global manufacturers tend to decrease their investment in fixed assets to focus on other types of investment. The low and declining trend of investment rate of low-rank suppliers inserted into GVCs in a restrained way corroborates the global trend of rationalization of the supply chain with some suppliers limited to low-value-added activity and no prospect to upgrade. Although some suppliers, especially those in a dominant position enjoying a stable insertion into GVCs, have kept a higher level of investment in fixed assets, given that they are ensuring the larger bunk of the production process.

The contribution of this second section is threefold. First, based on a thorough review of the literature, the modes of insertion are conceptualized. This analytical concept is then operationalized with firm-level data of Korean manufacturing firms using non-hierarchical cluster analysis. Finally, this research method provides conclusive results on the importance of the GVC channel to explain the heterogeneity of investment behavior of firms.

Conclusion

This paper has investigated the heterogeneity of firms' investment behavior by focusing on the participation to GVCs. This research engages, on the one hand, with the literature on the heterogeneity of firms that is mainly concerned with the size of firms, the export capabilities and, in the case of Korea, the affiliation to chaebols. On the other hand, it participates to the renewed research program apprehending financialization and globalization as interrelated processes [START_REF] Milberg | Shifting sources and uses of profits: Sustaining US financialization with global value chains[END_REF] that account for the engagement of firms into GVCs only by considering their outsourcing strategies.

The empirical results have shed light on a fruitful typology of modalities of insertion into GVCs that grasp an original source of heterogeneity across firms and an econometric estimation of the determinant of investment taking into account both the financialization and the GVC channels. The restructuring of production process along global value chains has led firms to coordinate their activities intra and inter value chains. Hence, modes of insertion are characterized by three dimensions of activity, governance, and upgrading opportunities. A cluster analysis based on key variables of vertical integration, the composition of output, linkages across firms and growth has yielded five distinct modes of insertion-Restrained, Adaptive, Stable, Disruptive, and Established that correspond to distinct investment behavior. While firms belonging to the Restrained modality have the lowest investment rate during this period, a high rate is sustained by the firms in the Stable modality, a high but more volatile rate is a feature of the Adaptive and Disruptive modalities, and the Established firms have steadily decreased their rate of investment after a post-2008 rebound.

The contributions of the chapter are as follows. First, an original methodology is developed to infer the insertion into GVCs at the firm-level from microeconometrics data. There is a technical difficulty of quantitative work mobilizing the GVC framework when no survey data on this topic are available. In this chapter, only financial statements and industry-level are used, and an extra effort of featured engineering has provided essential indicators of firms' linkages with global production network at the domestic level. Second, the empirical analysis provides evidence on other sources of heterogeneity of firms' behavior besides for the size or the affiliation to a group, the two usual sources found in the literature on Korean firms. Finally, the definition of modalities of insertion at the firm-level constitutes a theoretical step in considering the GVC channel within financialization framework. This paper takes part in a broader research program on financialization in Korea. Building upon these results, the typology of modes of insertion are then introduced to a post-Keynesian specification of an investment function to test the different hypotheses on the impact of the GVC channel on investment behavior and its relationship with the financialization channels of crowding-out and financial burden for a panel of Korean manufacturing firms.

The main limit of this paper is technical. The database used has too many missing values for the information on export, and no qualitative information about their activity beyond the national space, nor about their relationship with upstream and downstream firms 4 . One avenue for future research is, therefore, to consolidate different database, qualitative and quantitative, in order to derive more informed results on the modalities of insertion into GVCs. To the author's knowledge, few isolated attempts by independent research groups and international organizations exist to build such a database incorporating. There is a gap between the increasing use of the GVC framework by scholars and practitioners and the lack of comprehensive datasets; more research is needed in this direction.

Moreover, future research should further explain the determinants of the modalities of insertion into GVCs and explore the trajectories of firms over time. In the sample studied, some firms remain in the same modality for the whole period while others change from one modality to another. Put aside the technical considerations on the limits of cluster analysis, firms engage in GVCs in a dynamic fashion, and several case studies document the upgrading trajectory of firms from low-rank manufacturers to global leaders. The determinants of trajectories can be tackled by several aspects, either by management approaches of firms' agility navigating production networks, quantitatively by exploring larger dataset or by sociologically grounded analysis.

4. There exist databases based on survey of firms in relation to exports and sourcing behavior such as the survey of business activities by Korea National Statistics Office but with a restricted access.

Figure 2

 2 Figure 2 Profile of mode of insertion (standardized median values by cluster)

Figure 3

 3 Figure 3 Investment rate by type of value chains 1991-2015 (smoothed median level)

Figure 4

 4 Figure 4 Investment rate by type of value chains after 2008 (median level)

Acknowledgment

This work was funded as part of a 3-year EHESS full Ph.D. scholarship and benefited from the RISE Marie Skłodowska-Curie program "INCAS". I am grateful to the German Institute for Japanese Studies (DIJ) in Tokyo, and its director Franz Waldenberger, for the very stimulating intellectual environment during the writing. I also benefited from fruitful discussions with participants to the Inaugural Conference on Global Production at National University of Singapore (December 6-8 2017). Besides, I want to thank Robert Boyer and Gregory Jackson for their useful comments at the 2017 annual workshops of the INCAS research program.