Nicolas Faysse

Mohamed El Amrani

Soufiane El Aydi

Ahmed Lahlou

Soufiane El

The formulation and implementation of policies to deal with groundwater overuse in Morocco: which supporting coalitions?

Keywords: coalition, demand management, groundwater, Morocco, policy RÉSUMÉ coalition, gestion de la demande, eau souterraine, politique, Maroc

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

In Morocco, achieving sustainable use of groundwater has become one of the most pressing issues in water resource management as many of the major aquifers of the country are already overexploited (Moroccan Secretariat in Charge of Water and Environment, 2007). After decades of relative absence of the State in dealing with groundwater overexploitation, the administration is now showing increasing willingness to address this issue. New policies are being implemented that consider both supply and demand management. The Moroccan Secretariat in Charge of Water and Environment also perceives the need to form large coalitions of actors around a set of coordinated policies in large-scale overused aquifers. For that reason, it has asked the Catchment Management Agencies (CMA), who are in charge of water resource management, to set up aquifer management contracts in ten large-scale overexploited aquifers.

These contracts are intended to involve all major stakeholders.

The perceived need for coalition building corresponds to calls for considering the water sector as a complex system, where actions undertaken by a single actor are unlikely to have much effect on the sustainable use of water resources [START_REF] Mollinga | Politics, plurality and problemsheds: A strategic approach for reform of agricultural water resources management[END_REF]. Coalitions, which can be defined as groups of actors who coordinate their activities in order to achieve shared policy goals [START_REF] Schlager | Policy making and collective action: Defining coalitions within the advocacy coalition framework[END_REF], are increasingly seen as the key not only to ensuring the implementation of policies, but also in the policy choices made. This is especially the case of groundwater use, as the goals and degrees of implementation of policies to control overexploitation are particularly sensitive to the type of coalitions formed. Indeed, there is a general lack of successful experience and blueprints to tackle groundwater overexploitation, especially in developing countries [START_REF] Shah | Groundwater: a global assessment of scale and significance[END_REF]. As a result, there is no clearly-defined process to enable a shift from a situation of open access to one of sustainable use that would allow focusing on the creation of an appropriate coalition to ensure its successful implementation. Like surface water, the composition of the coalitions formed will influence the relative importance given to supply and demand management.

Concerning the management of demand, coalitions may attempt to apply direct management of groundwater uses. For instance, in India, upper caste farmers in Rajasthan agreed to the state-led policy to control groundwater use and deliver tradable rights, because they hoped that such a reform would prevent lower caste farmers from having access to groundwater [START_REF] Birkenholtz | Groundwater governmentality: hegemony and technologies of resistance in Rajasthan's (India) groundwater governance[END_REF]. Coalitions of actors may also favour more indirect approaches. Also in India, the government of Gujarat set up a dedicated electrical network for irrigation pumps, which made it possible to control the volume of water pumped and obtained the approval of the farmers as the energy supply became more reliable [START_REF] Shah | Taming the anarchy[END_REF]. However, the coalitions that are formed may not suffice to implement policies: the control of groundwater use that was planned to be implemented by groundwater user associations in Mexico was unsuccessful due to lack of support from both farmers and public organisations at federal level [START_REF] Wester | Assessment of the development of aquifer management councils (COTAS) for sustainable groundwater management in Guanajuato, Mexico[END_REF].

Coalitions may also oppose policies to control groundwater overdraft. In several states in India, farmers lobbied against attempts to stop the supply of free electricity for groundwater pumping systems, even though this policy had repeatedly been identified as a major cause of groundwater overuse [START_REF] Mukherji | Political ecology of groundwater: the contrasting case of water-abundant West Bengal and water-scarce Gujarat, India[END_REF].

A wide range of policies and supporting coalitions thus exist that address groundwater overuse, both between and within countries [START_REF] Mukherji | Groundwater socio-ecology and governance: a review of institutions and policies in selected countries[END_REF][START_REF] Shah | Taming the anarchy[END_REF]. Several authors attempted to explain this diversity by comparative studies using different analytical frameworks [START_REF] Faysse | Convergent readings of groundwater governance? Engaging exchanges between different research perspectives[END_REF]. Analyzing the attributes of users (as initially developed by [START_REF] Ostrom | Reformulating the commons[END_REF] and the behaviour of higher-level authorities made it possible to understand the differences observed in Spanish groundwater user associations [START_REF] Lopez-Gunn | Is self-regulation a myth? Case study on Spanish groundwater user associations and the role of higher-level authorities[END_REF]. [START_REF] Mukherji | Political ecology of groundwater: the contrasting case of water-abundant West Bengal and water-scarce Gujarat, India[END_REF] showed that the difference in the strength of farmers' organisations and the local political setting helped explain why strict demand management measures were implemented in groundwater abundant West Bengal, while policies to curb the use of fragile aquifers in Gujarat were limited. In the same way, because of farmers' different incentives for implementing groundwater recharge, hard rock aquifers that are generally considered to be vulnerable may actually prove to be more appropriate for sustainable groundwater use than large-scale alluvial aquifers in India [START_REF] Shah | Community Response to Aquifer Development: Distinct Patterns in India's Alluvial and Hard rock Aquifer Areas[END_REF].

Policies to address groundwater overexploitation in Morocco share constraints commonly found in developing countries, such as the limited means of public organisations in charge of groundwater resources and the high number of informal water users. The proposed goal to build coalitions gathering all stakeholders through aquifer management contracts is more original, since this approach is usually used in developed countries [START_REF] Petit | La politique de gestion des eaux souterraines en France. Une analyse en termes de gestion intégrée[END_REF]. This article analyses to what extent the actors involved in groundwater use and regulation come together around the definition and implementation of policies to deal with groundwater overuse in four Moroccan regions and provides some explanations for the differences in the involvement of actors and in the constitution of coalitions. These explanations may help reflect on how to support the creation of coalitions able to define and implement policies for sustainable agricultural use of groundwater, and which also take into account the diversity of existing types of agriculture.

METHOD

The analysis was based on four study areas: the Souss-Chtouka, Saiss, Berrchid and coastal Chaouia aquifers (see Figure 1 and Table I for basic data). Interviews with public organisations were conducted in all four study areas, in particular with the CMAs and the local offices of the Ministry of Agriculture and Marine Fishery (hereafter referred to as MoA). Surveys of 40 farms were undertaken in the Souss and Saiss regions. Both interviews and surveys investigated: i) actors' assessment of the current state of groundwater resources and, if they were aware of a drop in the groundwater table, the reasons for this; ii) actors' understanding of and support for existing public policies to deal with groundwater overdraft, and possible involvement in their implementation; iii) actors' own proposals on how to achieve sustainable use of groundwater. These surveys were complemented by similar work with 155 farmers in Berrchid [START_REF] Faysse | Learning to Voice? The evolving roles of family farmers in the coordination of large-scale irrigation schemes in Morocco[END_REF] and 39 farmers in the coastal Chaouia (Berrahmani et al., submitted). Although several of the study areas also face problems of groundwater pollution, our analysis was limited to quantitative aspects. In addition, groundwater is also used for drinking water and industry in our study areas, but only agricultural use was analysed here, since agriculture is by far the largest groundwater user (e.g., 95% in Souss).

Sebou

Saiss

RESULTS

Next we describe the policies that were planned and implemented to deal with groundwater overdraft in the four study areas, and then we describe the position of the main actors with regard to these policies, and the coalitions formed around these policies.

Policies specific to each area

The coastal Chaouia aquifer. In this area, groundwater overuse since the 1970s led to seawater intrusion in littoral land and decreasing groundwater levels further inland. The Souss and Chtouka aquifers. Here the neighbouring Souss and Chtouka aquifers are considered jointly, as is the case in most public policies, and the study area is hereafter referred to as the Souss region. These aquifers were the first in Morocco where the fall in the groundwater table became a subject of public concern [START_REF] Popp | Un 'man-made hazard': le surpompage de la vallée du Souss[END_REF]. In 2004, the Souss-Massa

Regional Council undertook a study to define a regional development strategy. This study ranked agriculture as a key component of the regional economy, with groundwater overdraft as its main Achilles heel. Indeed, in the El Guerdane area, groundwater overexploitation led to abandonment of the cultivation of 11,900 ha until a pipe was laid to bring water from an upstream dam. This project involved public subsidies and was the result of the active lobbying of large-scale farmers in the area concerned [START_REF] Houdret | The privatisation of irrigation water services: New partnerships and water conflicts in the El Guerdane project, Morocco[END_REF]. In 2005, the local CMA launched an initiative to control the drilling of boreholes and, in 2006, had stopped the drilling of 70 boreholes. In the same year, under the leadership of the Regional Council, a framework convention was negotiated and signed by the CMA, the Regional Council, the local offices of the MoA, the local Chamber of Agriculture, the regional federation of water user associations and three farmers' organisations involved in marketing citrus fruits and vegetables.

This convention outlined several actions to address the groundwater crisis. It had four components: 1) a decrease in water consumption and an increase in water productivity, mainly achieved by shifting from surface and sprinkler irrigation to drip irrigation and establishing a 'water police' force to control the drilling of boreholes; 2) more efficient irrigation practices and reuse of treated waste water; 3) use of deep groundwater resources; and 4) building of several small and medium-size dams. The funding required for these actions was estimated at around 3.5 million Euros per year and was to be provided by farmers who owned more than 15 ha. This category of farmers represents 20% of farms and 80% of pumped groundwater. After the signing of the convention, the coordination of its implementation was handed over to the Souss-Massa CMA.

The Souss-Massa CMA defined three scenarios and in particular a positive one of 'governance' where groundwater overdraft would be almost completely stopped by 2020.

However, this prospective exercise did not lead to a shared vision among stakeholders regarding the desirable forms of agriculture and territorial development in the future. As a result, the framework convention focused on the process of reducing overexploitation, without clearly explaining the expected end results of such actions.

Coordination between the Souss-Massa CMA and the local offices of the MoA and of the Ministry of the Interior permitted the seizure of borehole drilling machines that operated illegally. Those in charge of control often intervened after having been informed either by neighbouring farmers or local authorities that an illegal borehole was being drilled. From 2006 to 2009, 120 drilling machines were seized. In 2010, no drilling machine was seized, which was considered by the CMA as a sign that illegal borehole drilling had been drastically reduced.

However, borehole drilling continued in 2011 due to understaffing of the water police and, according to many farmers interviewed, because some farmers managed to obtain the informal consent of the staff of either the CMA or the Ministry of the Interior. Moreover, farmers are allowed to replace a dried up borehole by a deeper one. Other actions undertaken in the frame of the convention were changing all existing surface irrigation systems to drip irrigation, and the planned creation of a 10,000 ha irrigation scheme using desalinized water in the Chtouka area, which, according to plans discussed in 2011, would profit from public subsidies.

Policies common to the cases

The MoA provides farmers with subsidies to change from surface to drip irrigation. These subsidies cover between 90 and 100% of the total cost (with a funding limit for each component of the irrigation system). There is a wide consensus among public actors that this policy is an appropriate way to limit groundwater use and 'save' water. However, many studies have shown that farmers who use groundwater and who change from surface to drip irrigation often do not reduce their groundwater withdrawal (Pfeiffer and Lin, 2011), and that the change has limited impacts on the water balance at catchment or aquifer basin level [START_REF] Ward | Water conservation in irrigation can increase water use[END_REF].

The CMAs of the Berrchid, Saiss and Souss regions use a similar method to attempt to control groundwater use. First, a survey is undertaken to count existing wells and boreholes.

The farmers are then asked to come to the CMA to register their existing wells and boreholes. In 2011 this procedure was underway in the Souss, Saiss and Berrchid. The situation was scheduled to be 'frozen' by February 2012, and, from then on, the CMAS planned that all unregistered boreholes subsequently discovered would be closed down. Farmers who registered their boreholes may then be asked to pay a specific tax for water consumption. This method faces two main difficulties. First, only a few farmers have come forward. In the Souss, only farmers who wanted to legally drill a borehole (for instance because they owned one that had dried out) or to obtain subsidies for shifting to drip irrigation (for which formal registration of the borehole is required) accepted to follow this formal procedure. In 2010, legalised boreholes amounted to an irrigated area of 5,000 ha in the Souss. The second difficulty is obliging farmers to pay the planned groundwater use tax. In 2010, a nationwide decree was enacted that enables the CMAs to take legal action against farmers who do not pay.

Actors' positions

Efforts by CMAs and by the Souss-Massa Regional Council to enrol actors. In all three study areas, the CMAs have a limited presence in the field and a limited capacity to monitor groundwater use. For that reason, they need support from other public organisations to be able to control groundwater use. The Souss-Massa Regional Council succeeded in building a coalition of public organisations both to coordinate groundwater management policies and to launch the water police force. In the same way, the CMAs in the Saiss and Berrchid areas were able to involve the local offices of the Ministry of the Interior, which became the CMA 'organ'

for the implementation of the activities of the water police.

In the Saiss, the Sebou CMA was unable to obtain the support of other public organisations. This was particularly the case of the MoA, which supported further agricultural development. The MoA did not consider the situation to be critical, especially because of the expected transfer of water from the Mdez dam. The Sebou CMA took up the challenge and put forward a discourse of 'groundwater crisis'. While in the north-eastern part of the aquifer, the groundwater table is still at the same level as it was years ago, in its policy documents, the Sebou CMA systematically includes a graph of changes in the groundwater table in the area with the fastest decrease in the whole aquifer.

Using Gramsci's perspective (1971), the CMAs can be considered as simultaneously attempting to coerce the farmers and to obtain their consent for their policies. The CMAs' efforts to stop illegal drilling increased their power in their relation with the farmers. Indeed, after the first seizing of drilling machines in the Souss, farmers' organisations no longer considered that it was safer for them to remain outside the process of defining management policies. The CMAs also considered the aquifer management contracts as a tool to obtain the farmers' approval for the regulation of groundwater use.

Limited MoA and farmers' involvement. Apart from in the Souss, local MoA offices were not involved in the control of borehole drilling. The Souss MoA office manages irrigation schemes and has experience in dealing with water provision. In the three other areas, the local MoA offices do not manage water resources for irrigation and consider that groundwater resources are outside their mandate.

Farmers' organisations in the Souss who signed the convention either represent only a minority of large-scale farmers (the case of horticulture exporting associations) or have weak links with grassroots farmers (the case of the Chamber of Agriculture and the federation of water user associations). They do not represent all farmers; not even all farmers who own more than 15 ha. By contrast, a major dairy and citrus cooperative has 14,000 dairy farmer members and has strong links with them, but was not invited to sign the convention. In the three other areas, farmers' organisations are much weaker than in the Souss, and, in practice, have had very limited interactions with the CMAs.

Interviews with farmers revealed a wide range of assessments of the situation of groundwater resources and of possible actions to address their overexploitation. Farmers in the Souss, Saiss and Berrchid regions were generally aware of the links between intensive use of groundwater for irrigation and the drop in the water table (a result also found by [START_REF] Bekkar | On the difficulty of managing an invisible resource: the use of groundwater for irrigation[END_REF]. By contrast, many farmers in the coastal Chaouia area did not think that groundwater overuse was the main reason for seawater intrusion [START_REF] Bento | Farmers' relations to climate variability and changes: the case of groundwater users of coastal aquifers in France, Portugal and Morocco[END_REF]. Most farmers considered that the implementation of regulatory tools was above all the responsibility of the State (see also [START_REF] Bekkar | On the difficulty of managing an invisible resource: the use of groundwater for irrigation[END_REF]. Among the different options they proposed for sustainable groundwater use, only 9% of Berrchid farmers and no Chaouia farmer mentioned actions to control groundwater use, such as limiting the drilling of boreholes or installing water meters. By contrast, approximately half the farmers in Souss and Saiss mentioned at least one action to control groundwater use. Moreover, half the farmers interviewed in the Souss said that farmers helped the police stop illegal borehole drilling and agreed to the installation of water meters.

Considering each study area individually, there is a large coalition in the Souss, although the involvement of large-scale farmers is precarious. In the Saiss and Berrchid areas, the CMAs are in charge of setting up a large coalition, but are facing difficulties achieving this goal. While in the Souss, public institutions see the framework convention as a common construct, in the Saiss and Berrchid, the aquifer management contract is seen as a tool initiated and owned by the CMAs. In the Coastal Chaouia case, no actor is in charge of building a coalition.

DISCUSSION

In all the study areas, the CMAs are facing difficulties building coalitions because of the limited number of personnel and their lack of appropriate skills. CMA staff are mainly engineers and technicians trained in water resource sciences but not in agricultural or social sciences. They have limited experience with participatory processes and interactions with farmers. As a result, they find it difficult to coordinate multi-stakeholder processes and to deal with agricultural issues. In the Souss, the framework convention process slowed down when the coordination shifted from the Regional Council -which hired a consultant firm to support the process -to the CMA. Apart from this common constraint, the study areas display a wide range of public policies and supporting coalitions. Four factors explain this diversity.

Depth of the aquifer. The depth of the aquifer influences the speed with which the groundwater economy follows the pattern from growth to maturation and, in case of groundwater overuse, to possible decay [START_REF] Shah | Taming the anarchy[END_REF]. Such depth represents the 'buffering capacity' of the aquifer, i.e. the time available for coalitions to be built and policies to be set up.

In the Souss, public organisations and farmers have been aware of the groundwater problem for at least 30 years, and groundwater is still mostly available, so the actors have had time to find solutions to deal with the groundwater crisis. By contrast, in the Berrchid and Chaouia areas, which have shallow aquifers, less than 20 years passed between the start of intensive groundwater use and the appearance of an acute groundwater crisis: farmers and local public institutions have had much less time to acknowledge the importance and fragility of the groundwater economy, and to launch discussions over ways to avert the crisis. In that sense, the Chaouia and Berrchid cases are close to the 'exit' category of aquifers coined by [START_REF] Shah | Taming the anarchy[END_REF], which involves rapid overexploitation of fragile aquifers and farmers hastily moving away from the area. The Souss and Saiss regions, in their current situation, correspond more to the 'collusive opportunism' category defined by [START_REF] Shah | Taming the anarchy[END_REF], with ever decreasing levels of deep aquifers that may progressively drive smaller-scale farmers away from irrigated farming.

Although policies to obtain new water resources and to control groundwater use are implemented or planned in these two regions, they have not yet succeeded in halting the drop in the groundwater tables.

Recognition of irrigated farming as the main cause of a groundwater crisis in the local political arena. In the Souss, both farmers and public institutions have long understood the impacts of irrigation on the aquifer. As mentioned above, farmers in the coastal Chaouia area acknowledge only a limited link between groundwater overuse and seawater intrusion.

Moreover, in this region many farmers and some staff of the local MoA offices think that one major cause of the groundwater crisis is the building of a dam on the Oum Er-Rbia River in the 1990s, although this river in fact drains water from the aquifer.

The importance of the groundwater economy in the regional and national economy. The attention actors pay to the problem of groundwater overuse is influenced by its relative importance compared to non-agricultural activities or to rainfed agriculture. The Souss is a much drier area than the Saiss, where many crops can be rainfed. In addition, in the Souss, citrus and vegetables for export, which rank first in Morocco, have required major investments, and are grown on large-scale farms with strong lobbying capacities vis-à-vis the public administration. In comparison, the economic activities generated by the use of the Chaouia and Berrchid aquifers are only small components of the economy of the Doukkala Abda and Chaouia Ouaragha regions.

The motivation and capacities of actors to engage in policies for the sustainable use of groundwater. The motivation of public organisations to take an active stance in policies dealing with groundwater overdraft depends on the importance of the aquifer in the area they manage.

Addressing the groundwater crisis was at the top of the agenda of both the Souss-Massa Regional Council and the CMA. By contrast, the Saiss aquifer is shared between two regions, and neither of the Regional Councils took an active stance towards groundwater management.

Souss farmers are mostly land owners and are strongly integrated in local communities [START_REF] Faysse | Learning to Voice? The evolving roles of family farmers in the coordination of large-scale irrigation schemes in Morocco[END_REF]. By comparison, in the Berrchid region, many farmers rent land, and villages are scarce, hence the farmers are much less attached to either the land or the community. In the Souss, some farmers' organisations were sufficiently organised to play an active role in negotiations with public organisations. In the Chaouia and Berrchid there are far fewer farmers' organisations and those that exist are much weaker.

The three last factors are close to those identified by [START_REF] Ostrom | Reformulating the commons[END_REF] concerning the characteristics of appropriators enabling self-management of common-pool natural resources.

Indeed, among the factors that Ostrom identified: i) the common understanding of the resource relates to the second of the four above-mentioned factors; ii) the dependence of appropriators on the resource system for a major portion of their livelihood relates to the third one; and iii) the low discount rate for the future and prior organisational experience relate to the fourth.

However, assessing these factors should not lead to underrating the importance of the negotiation processes, with their due share of contingencies and path dependencies. In addition, these factors may change over time. Thus, these factors should not be considered as elements that could be used to separate situations in which large coalitions may reach sustainable groundwater use and others which are doomed to a tragedy of the commons. Rather, they should be considered as a guide to identifying which coalitions should be supported, which stumbling blocks need to be removed to reach relevant coalitions, and to identify the most appropriate policies that these coalitions may be able to design and implement. In the Souss and Saiss regions, collaboration with farmers' organisations could be reinforced, so as to tap the farmers' predisposition for the establishment of regulatory instruments, provided the latter are implemented in an equitable way. In the Chaouia and Berrchid regions, CMA staff could be specifically mandated to catalyze coalitions and to create a local dynamics to address the groundwater crisis.

CONCLUSION

In the recent past, several policies have been implemented to deal with the increasing groundwater crisis in Morocco, both in terms of demand and supply management. Many of these policies did not remain 'on paper', and, in particular, the activities of the water police have already had considerable impacts on the ground. The types of policies implemented differed widely between the study areas, mostly because of different supporting coalitions of actors.

However, despite the administration's stated objective of building large coalitions, existing coalitions are limited both in their number of members and in their objectives. Small- In the future, the CMAs will remain key actors in building large coalitions. However, they need to move from a posture of law enforcement, from which they derive their power and legitimacy, to one that places much more emphasis on coalition building, and this requires new skills. Moreover, as the water police become more present on the ground, the even-handedness with which this police force controls farmers will evolve into an increasingly contested issue.

Transparent monitoring of its functioning will be increasingly necessary. Finally, innovative ways to include small-scale farmers in coalitions should be supported, particularly by engaging with the many active farmers' organisations at local level [START_REF] Faysse | Learning to Voice? The evolving roles of family farmers in the coordination of large-scale irrigation schemes in Morocco[END_REF], even though these organisations may not be formally involved in water resource management.

Figure 1 .

 1 Figure 1. The aquifers studied in Morocco.

  Farmers had to adapt by changing cropping systems, by bringing fresh water to their farms, deepening boreholes or relocating to other regions. Groundwater stress was the main cause of the change in the region from intensive export-oriented agriculture to agricultural crisis. The Oum Er-Rbia CMA is responsible for the management of the western part of the aquifer and the Bouregreg-Chaouia CMA for the east. In practice, the CMAs only monitor piezometric levels and salinity rates. One reason is that, for both agencies, this aquifer is not of major importance compared to other larger aquifers and surface water issues. Thus the drilling and use of boreholes remains uncontrolled. Although around 90% of irrigation consists of drip irrigation (generally installed informally, without public subsidies), the groundwater balance still shows a deficit. In the 1990s, the local MoA office planned to set up a 2,500 ha irrigation scheme using water from the neighbouring Oum Er-Rbia River. In 2011, the project had not yet been implemented due to: i) lack of funding; ii) the absence of strong local farmers' organisations; iii) doubts over the availability of sufficient surface water and subsequent lack of support of the Oum Er-Rbia CMA.The Berrchid aquifer. The shallow Berrchid aquifer is the main groundwater resource in the area under the responsibility of the Bouregreg-Chaouia CMA. According to this CMA, the overall water volume stocked in the aquifer decreased from 1,500 million m 3 in 1980 to 800 million m 3 in 2009. Water is fully depleted at the outskirts of the aquifer so farmers located in these areas have attempted to move to the centre of the aquifer where water is still available.According to the survey, 52% of cropped area was farmed by tenants. Until 2010, most actions undertaken by the Bouregreg-Chaouia CMA focused on the supply side, with the construction of small weirs in river beds to increase groundwater recharge and of an irrigation scheme using treated waste water from the town of Berrchid. In 2011, the CMA held meetings to involve local public organisations, such as the local offices of the Ministry of the Interior and judiciary institutions, in the control of borehole drilling. This active stance resulted in the first seizure of a drilling machine in March 2011. The CMA planned to draw up an aquifer management contract, but had not yet started at the time of writing.The Saiss aquifer. This aquifer comprises a superficial layer and a deep layer, although there are many hydraulic connections between the two layers. The decrease in the groundwater table in some parts of the deep layer was the fastest in the whole country, with an average rate of decrease of 3 m/yr. The Sebou CMA decided to stop delivering authorisations for new boreholes, except for farms of less than 5 ha, for which authorisations are still delivered. The CMA started to control the drilling of boreholes and seized some drilling machines that were operating illegally. Despite this action, the MoA gave the concession of 7,250 ha formerly managed by two parastatals to private investors. It approved the investment plans of these investors including drilling boreholes for irrigation, for which the CMA eventually delivered authorisation. One reason behind the stance of the MoA is the planned transfer of water from the Mdez dam (under construction in 2011) that should supply 120 million m 3 , which is more than the groundwater deficit calculated by the Sebou CMA. While water levels have been declining, only a small percentage of small-scale farmers were limited in their production as they lacked investment capacities to pursue falling groundwater levels. In 2011, the CMA hired a consultancy firm to prepare the aquifer management contract and have it signed by stakeholders.

  scale farmers are not included in the already strong coalition between Souss large-scale farmers and the MoA for developing new water resources, nor are they part of the increasingly influential coalitions involving the CMAs and the Ministry of the Interior for implementing the water police. Moreover, groundwater governance has only made limited appearances in local public arenas. Aquifers have thus turned into a 'space of dependence' but have not yet become a 'space of engagement' (Venot et al., 2011).

Table I .

 I Basic data concerning the study areas.

	Rabat	Meknes	Fes
	Casablanca
	Agadir
			Souss-	Saiss	Berrchid	Coastal
			Chtouka			Chaouia
	Total area (km 2 )		5,090	2,200	1,500	1,200
	Average irrigated area using groundwater (ha)	122,100	38,000	18,000	*
	Number of wells and boreholes		20,000	8,000	1,700	*
	Maximum depth of the aquifer (m)		500	1,500	150	120
	Average decrease in the groundwater table in the	2.5	3	0.5	0.5
	area of maximum decrease (m/yr)
	Average deficit (million m 3 )		286	100	19	10
	Average groundwater withdrawal /average		180%	141%	140%	130%
	recharge (%)
	Source: interviews and CMA technical documents.* no recent data.

Souss- Massa Bouregreg & Chaouia Sebou Oum Er-Rbia

	Chaouia	Saiss
	Berrchid
	Souss		Undemarcated boundary
	Chtouka
	Areas under the management of the
	CMAs in charge of the studied aquifers
	Studied aquifers	N 0	100 km

Restricted and fragile coalitions

The coalitions considered here are limited to actors who are actively involved in the design and implementation of policies. Indeed, all actors agree about the usefulness of public subsidies to enable a shift to drip irrigation, but in practice only the MoA is involved in the implementation of this policy. The only large coalition is the one that was built during the design of the framework convention in the Souss, but large-scale farmers' involvement in this coalition was fragile, as they were critical of its limited effects in supporting agriculture. Two other more restricted coalitions exist concerning the development of the water resource and the regulation of groundwater use (Table II). In the Souss, large-scale farmers formed an alliance with the MoA to obtain state support for new resources, both for the pipeline bringing water to the El Guerdane sector and for the planned irrigated scheme using desalinized water in the Chtouka region. In the Saiss and Berrchid areas, farmers were much less actively engaged in supporting the mobilisation of new water resources. Coalition building for borehole drilling between the CMA and the Ministry of the Interior appeared to be particularly important for its implementation. Indeed, compared to India [START_REF] Shah | Taming the anarchy[END_REF], the control of borehole drilling (with a focus on the activities of drilling machines rather than on existing wells and boreholes) is not so much an economic issue, but rather of involving the Ministry of the Interior, due to the large presence of agents of this ministry in rural areas. In none of the cases were small-scale farmers part of a coalition.


Camille Raillon
email: camille.raillon@epfl.ch

Pierre Granjon
email: pierre.granjon@gipsa-lab.grenoble-inp.fr

Michael Graf
email: michel.graf@epfl.ch

Aleksandra Radenovic
email: aleksandra.radenovic@epfl.ch

Detection of RNAP-DNA complexes using solid state nanopores

come

I. INTRODUCTION

In this paper, we summarize recent findings on the power of nanopore-based sensing to detect and identify specific proteins or DNA-protein complexes based on the shape of its corresponding ionic current translocation traces [START_REF] Raillon | Nanopore detection of single molecule RNAP-DNA transcription complex[END_REF][START_REF] Raillon | Fast and automatic processing of multi-level events in nanopore translocation experiments[END_REF]. Nanopore-based analysis is an innovative technique used for a wide range of applications such as molecule length measurement, single-molecule dynamics or sequencing [START_REF] Kasianowicz | Characterization of individual polynucleotide molecules using a membrane channel[END_REF][START_REF] Akeson | Microsecond Time-Scale Discrimination Among Polycytidylic Acid, Polyadenylic Acid, and Polyuridylic Acid as Homopolymers or as Segments Within Single RNA Molecules[END_REF][START_REF] Meller | Rapid nanopore discrimination between single polynucleotide molecules[END_REF].

In the past decade, many single-molecule techniques have been used for a wide variety of biological systems: proteins, nucleic acids or complexes of the two. Most of what we know today about the transcription reaction was learnt from bulk studies, in which one measures the average signal issued from a very large number of molecules. In recent year, however, researchers have started measuring fundamental properties using single-molecule experiments. For example, by attaching a single molecular motor such as RNAP to a bead, researchers have been able to probe properties like step size, speed and force using optical tweezers [START_REF] Kim | Rapid fabrication of uniformly sized nanopores and nanopore arrays for parallel DNA analysis[END_REF][START_REF] Wang | Force and velocity measured for single molecules of RNA polymerase[END_REF][START_REF] Davenport | Single-molecule study of transcriptional pausing and arrest by E-coli RNA polymerase[END_REF][START_REF] Shaevitz | Backtracking by single RNA polymerase molecules observed at near-basepair resolution[END_REF]. Here, we For single-molecule applications such as nanopore sensing, the nanopore chip should satisfy several requirements. The membrane should contain one pore only, and the pore size should be comparable to the DNA diameter (2 nm for dsDNA) so that DNA passes through the pore in a linear fashion and the ion flux is significantly reduced when DNA molecule translocates.

The pore geometry needs to be well defined and reproducible. In addition, the pore surface should be hydrophilic to facilitate the microfluidic cell filling with solution and it should be neutral or positively charged to avoid DNA repulsion. The membrane has to be strong enough to withstand experiments for several hours but thin enough to make a nanopore in it. The chip should also tolerate salt concentrations ranging from 0.1 -2 M KCl and different pH conditions (2-9 pH). The starting substrate, for nanopore fabrication, is a double-sided polished silicon wafer with a triple stack of insulating layers, 20 nm of low-stress silicon nitride (Si x N y ), 100 nm of silicon dioxide (SiO 2 ) and 100 nm of Si x N y . The supporting silicon and insulating layers on the backside are dry and wet etched to form a 50x50 m 2 large, 220 nm thick membrane. Then electron beam lithography (EBL) is used to define a small square (500 x 500 nm 2 ) in the center of the Si x N y membrane. This region is then thinned to less than 20 nm using dry and wet etching.

Detection of RNAP-DNA complexes using solid state nanopores

C. Raillon, P. Granjon, M. Graf and A. Radenovic x 50 m 2 Si x N y . membrane (in green) in the center of the chip shown in a). This 220 nm thick membrane is composed of three stacked layers (20 nm low-stress Si x N y ., 100 nm SiO 2 and 100 nm low-stress Si x N y .) and is created by standard processes of photolithography, dry and wet etching. The small black dot in the center of the membrane corresponds to the thinned region c) TEM image of the thinned region; fabricated by electron beam lithography and etched down to a thickness of 20 nm. d) TEM images of several nanopore sizes. Taken from [START_REF] Raillon | Nanopore sensing of single molecules application to RNAP-DNA complexes, fabrication of graphene-nanopore devices and translocation algorithm analysis[END_REF].

35th Annual International Conference of the IEEE EMBS Osaka, Japan, 3 -7 July, 2013 978-1-4577-0216-7/13/$26.00 ©2013 IEEE This allows the creation of a very thin membrane, mechanically stable because made of Si x N y . That region is thin enough to drill a nanometer-sized hole with a highly focused electron beam. In this microfabrication process, we obtain 72 chips per wafer one such chip is shown in Figure 1. The tool used to drill nanoscale holes is typically a Transmission Electron Microscope (TEM). We use a Philips/FEI CM300 to make the nanopores. Nanopores form due to localized heating that fluidizes matter, and surface tension that creates geometry-dependent contraction or expansion [START_REF] Storm | Fabrication of solid-state nanopores with single-nanometre precision[END_REF]. The optimal parameters for nanopore drilling are following: an accelerating voltage of 200 kV and an extraction voltage of 4.2 kV using condenser lens 3 and spot size 5 (~10 nm) at a magnification of 220 000 X. In TEM mode, the beam is focused with the intensity knob for about 1 min. Sometimes it can take up to several minutes to obtain a nanopore; this mostly depends on the chip cleanliness. There are several ways to clean a nanopore chip from hydrocarbon contamination, we often use O 2 plasma.

The problem with this contamination is that it can migrate into the electron beam and be immobilized [START_REF] Radenovic | Fabrication of 10 nm diameter hydrocarbon nanopores[END_REF]. We were originally drilling nanopores at an accelerating voltage of 300 kV but, in order to limit hydrocarbon contamination we have lowered it to 200 kV and we have used the cold trap; which condenses all vapors and so limits contamination at the nanopore drilling site. It is also best to wait that drift stabilizes before starting the drilling process, and 30 min is usually enough. The use of TEM as a nanopore fabrication tool allows for the variation of nanopore sizes. Figure 1 d) shows four nanopores ranging from 2 to 20 nm. This is extremely important since it allows tuning of the pore size, one of the prerequisites for recognition of protein-DNA complexes [START_REF] Raillon | Nanopore sensing of single molecules application to RNAP-DNA complexes, fabrication of graphene-nanopore devices and translocation algorithm analysis[END_REF].

B. Measurement conditions and setup

Once the pore is fabricated, it is put into a microfluidic cell that is filled with an ionic solution Figure 2 a). To optimize translocation signal, the size of the pore is matched to the size of the protein, DNA or Protein DNA complex. In our case pores slightly bigger than RNAP-DNA (around 20 nm) complex gave best results.

To get an ionic flow, the pore needs to be hydrophilic, to do so we store the chips in degassed and filtered 1:1 ddH 2 O:EtOH solution until use. This straightforward step yields highly reproducible wettability of nanopores. Two other solutions are to use O 2 plasma or to deposit aluminum hydroxide (Al 2 O 3 ) on the chip after pore drilling [START_REF] Radenovic | Fabrication of 10 nm diameter hydrocarbon nanopores[END_REF]. ALD (Atomic Layer Deposition) can also be used to precisely control the nanopore diameter. In our hands, the first simple solution of storing nanopores in a mixture of water and ethanol worked better than the Al 2 O 3 deposition.

Transparent microfluidic cells allow for fast detection, hence removal, of large air bubbles. An Axopatch 200B (Molecular Devices, Inc. Sunnyvale, CA) is used to amplify the ionic current through the nanopore. The Axopatch is a low noise patch clamp amplifier widely used in nanopore setups. The Ag/AgCl electrodes are immersed in the buffer solution immersed in the reservoirs on each side of the nanopore and connected to the Axopatch preamplifier.

The microfluidic cell and the Axopatch preamplifier are mounted on a damping breadboard (Thorlabs, NJ) and closed in a Faraday cage.

The sample is introduced into the cis side of the nanopore, and a voltage is applied across the membrane In the absence of a flow, the DNA will face two different regimes, one regime that is diffusion limited (far away from the nanopore) and one regime that depends on the pore diameter, its length and the applied voltage (closer to the nanopore. Signals are filtered at 10 kHz using the low-pass Bessel filter built-in the Axopatch and sampled at 100 kHz using a National Instrument PXI-4461 DAQ card. This allows for low-noise measurement.

To allow for discrimination of events above the noise level, a custom made LabVIEW program only records data when the current signal peak depth is above 4 x IRMS and the event longer than 50 s, which makes files lighter and easier to analyze. The applied voltage can be controlled directly on this interface. This same voltage can be swept to establish the I-V characteristic of the nanopore before starting the experiment Figure 2 b) and c) [START_REF] Raillon | Fast and automatic processing of multi-level events in nanopore translocation experiments[END_REF][START_REF] Raillon | Nanopore sensing of single molecules application to RNAP-DNA complexes, fabrication of graphene-nanopore devices and translocation algorithm analysis[END_REF].

II. RESULTS

The higher the voltage, the bigger the capture radius [START_REF] Wanunu | Electrostatic focusing of unlabelled DNA into nanoscale pores using a salt gradient[END_REF].

In the experiments on bare RNAP and RNAP-DNA complexes, we tried to keep the applied voltage as low as possible (50 mV) in order to minimize the electrophoretic force and maximize the dwell times for each event. This proved to be successful in most experiments and allowed us to visualize orientation of bare RNA whether force or flow predominates as well as detect individual protein-DNA complexes [START_REF] Raillon | Fast and automatic processing of multi-level events in nanopore translocation experiments[END_REF][START_REF] Raillon | Nanopore sensing of single molecules application to RNAP-DNA complexes, fabrication of graphene-nanopore devices and translocation algorithm analysis[END_REF]. Typical ionic current events from experiment with RNAP-DNA complexes with RNAP halted at one end of the DNA template are shown in Figure 3.

In our recent publications [START_REF] Raillon | Fast and automatic processing of multi-level events in nanopore translocation experiments[END_REF][START_REF] Raillon | Nanopore sensing of single molecules application to RNAP-DNA complexes, fabrication of graphene-nanopore devices and translocation algorithm analysis[END_REF] we described the appropriate volume-based approach using previous knowledge on RNAP, its dipole, its charge and its atomic structure. For the first time, we have shown that at low bias voltage:

1) RNAP translocates in different measureable orientations whether it is the RNAP dipole or the drag force that predominates.

2) using a volume-based approach we have shown that we could distinguish between bare RNAP and single RNAP-DNA complexes using nanopore sensing.at higher voltages:

3) RNAP subunits could break off the core enzyme in measurable subunits

III. OPENNANOPORE SOFTWARE

The complexity of our nanopore signals tailored the needs for a level-detection software that we developed [START_REF] Raillon | Fast and automatic processing of multi-level events in nanopore translocation experiments[END_REF]. This software is based on the cumulative sum (CUSUM) algorithm that does fast and automated detection of events and their levels even when the signal to noise ratio is close to 1. A major advantage of this software is that events can be classified according to their number of levels and so it is easy to make statistics on sub-populations. This new method has demonstrated promising results on complex signals such as protein-DNA complexes. This new software was critical to demonstrate the small difference of levels depending on the orientation of the translocating molecule [START_REF] Raillon | Fast and automatic processing of multi-level events in nanopore translocation experiments[END_REF][START_REF] Raillon | Nanopore sensing of single molecules application to RNAP-DNA complexes, fabrication of graphene-nanopore devices and translocation algorithm analysis[END_REF].

As mentioned above, in a typical nanopore experiment a constant voltage is applied between the two sides of the pore and the current passing through the pore is measured. Thanks to the electrical potential, charged molecules are driven through the pore (if their size allows it). During this translocation process, the molecules provoke a current blockade in the pore, which gives a characteristic current drop motif. This current-drop motif, which is generated during molecule transition through the pore, is referred to as event.

The software uses two key concepts the CUSUM algorithm and a recursive lo pass filtering. With this software we can compute event dwell times and conductance drops for each level inside each event. All events are classified as one, two or multi-level event. Statistics can also be performed directly with the OpenNanopore Statistics. The GUI (Graphical User Interface) is extremely intuitive each point in the scatter plot can be selected, and the event is then displayed at the bottom. Dwell time and current blockage histograms are displayed on each side of the scatter plot. Both histograms are level histograms; this means each level corresponds to one count in the histogram. Such tools allow the user to select a sub-population of events based on the number of levels in each event and do statistical studies on each population separately. We have first validated OpenNanopore software on prototypical data of DNA molecules translocating a nanopore.

In the current blockage histogram displayed in Figure 5 from our recent publication [START_REF] Raillon | Fast and automatic processing of multi-level events in nanopore translocation experiments[END_REF], it is easy to distinguish two sub-populations of events, the one-level events (in green) and the two-level events (in blue and red). What stems out is that one-level events are centered around two different current blockages: 0.2 and 0.4 nA but the majority is around the 0.2 nA peak whereas, for two-level events, the quantity of 0.2 nA levels is equal to the quantity of 0.4 nA levels. This shows the statistical repartition of DNA molecules translocating a nanopore one-level events are mostly events where the DNA molecule translocates in a linear and unfolded fashion and two-level events are events where the DNA molecule translocates partially unfolded (0.2 nA) and partially folded (0.4 nA). Such a statistical study can be used further in experiments with proteins and biocomplexes where the aim is to distinguish between different sizes of molecules and their orientation while translocating the nanopore [START_REF] Raillon | Fast and automatic processing of multi-level events in nanopore translocation experiments[END_REF][START_REF] Raillon | Nanopore sensing of single molecules application to RNAP-DNA complexes, fabrication of graphene-nanopore devices and translocation algorithm analysis[END_REF].

OpenNanopore software can be downloaded from http://lben.epfl.ch/page-79460.html.

IV. CONCLUSION

Nanopore sensing is a versatile technique; which can also be integrated, in more complex platforms such as optical tweezers, to do force measurement on molecular motors for example. In 2006 Keyser et al. [START_REF] Keyser | Direct force measurements on DNA in a solid-state nanopore[END_REF] published the first experiment of optical trapping force measurement of DNA translocating through a nanopore giving a direct measurement of the electrical force exerted on DNA during translocation. This recent concept of coupling nanopores to optical tweezers opened up a variety of new single molecule studies for biomolecules [START_REF] Trepagnier | Controlling DNA capture and propagation through artificial nanopores[END_REF][START_REF] Spiering | Nanopore Translocation Dynamics of a Single DNA-Bound Protein[END_REF]. This technique could be used to further explore molecular mechanics of transcription, to study forces applied by RNAP to DNA during transcription and give a more detailed view of the kinetic of transcription.

Compared to current single-molecule experiments done on RNAP [START_REF] Wang | Force and velocity measured for single molecules of RNA polymerase[END_REF][START_REF] Davenport | Single-molecule study of transcriptional pausing and arrest by E-coli RNA polymerase[END_REF][START_REF] Shaevitz | Backtracking by single RNA polymerase molecules observed at near-basepair resolution[END_REF] nanopore unfolding can remove structure by shearing rather than pulling. It can also open structures strictly sequentially as they pass through the nanopore. Such an experimental configuration more accurately simulates "natural" biological processes such as transcription [START_REF] Raillon | Nanopore sensing of single molecules application to RNAP-DNA complexes, fabrication of graphene-nanopore devices and translocation algorithm analysis[END_REF].

Figure 1 .

 1 Figure 1. a) 4 x 8 mm 2 silicon chip, KOH groove is visible in the center of the chip b) Optical image of a 50x 50 m 2 Si x N y . membrane (in green) in the center of the chip shown in a). This 220 nm thick membrane is composed of three stacked layers (20 nm low-stress Si x N y ., 100 nm SiO 2 and 100 nm low-stress Si x N y .) and is created by standard processes of photolithography, dry and wet etching. The small black dot in the center of the membrane corresponds to the thinned region c) TEM image of the thinned region; fabricated by electron beam lithography and etched down to a thickness of 20 nm. d) TEM images of several nanopore sizes. Taken from[START_REF] Raillon | Nanopore sensing of single molecules application to RNAP-DNA complexes, fabrication of graphene-nanopore devices and translocation algorithm analysis[END_REF].

Figure 2 .

 2 Figure 2. a) Schematics of the microfluidic cell b) I-V characteristic of nanopore in inset (diameter of 5.4 x 9.6 nm2) taken at 1 M KCl at room temperature, resulting experimental conductance is written in the graph c) Formula taken from Kim et al. [7] to calculate the theoretical conductance range for this nanopore with = [0° -45°]. Illustration taken from [3].

OpenNanopore

Figure 4 .

 4 Figure 4. Depiction of the OpenNanopore's tasks : Level fitting and creating database of fitted events.

Figure 3 .

 3 Figure 3. Concatenated events from experiment with RNAP-DNA complexes with RNAP halted at one end of the DNA template. Example of a current trace (in blue) after addition of RNAP-DNA complexes to the 16 x 19 nm pore in 1 M KCl solution with 50 mV applied. In red the fit obtained using the cumulative sum (CUSUM) algorithm. Illustration taken from [1].

ACKNOWLEDGMENT

Authors thank to D.T.L. Alexander for providing training and technical assistance with the transmission electron microscope. Nanopore fabrication was carried out in part in at the EPFL Center for Micro/Nanotechnology (CMI). Thanks to K. Lister (CMI) for technical support with electron-beam lithography.

*Research supported by the European Research Council (grant no. 259398, ProABEL: Nanopore integrated nanoelectrodes for biomolecular manipulation and design.


P Baraldi

M Compare

S Sauco

E Zio

Ensemble Neural Network-Based Particle Filtering for Prognostics

Particle Filtering (PF) is used in prognostics applications by reason of its capability of robustly predicting the future behavior of an equipment and, on this basis, its Residual Useful Life (RUL). It is a model-driven approach, as it resorts to analytical models of both the degradation process and the measurement acquisition system. This prevents its applicability to the cases, very common in industry, in which reliable models are lacking. In this work, we propose an original method to extend PF to the case in which an analytical measurement model is not available whereas, instead, a dataset containing pairs «state -measurement» is available. The dataset is used to train a bagged ensemble of Artificial Neural Networks (ANNs) which is, then, embedded in the PF as empirical measurement model.

The novel PF scheme proposed is applied to a case study regarding the prediction of the RUL of a structure, which is degrading according to a stochastic fatigue crack growth model of literature.

Introduction

Predictive Maintenance (PM) is an innovative maintenance paradigm, founded on the assessment of the current health state of an equipment (i.e., state identification) and the prediction of its future evolution (i.e., prognostics, [START_REF] Jarrell | Prognostics and Condition-Based Maintenance: A New Approach to Precursive Metrics[END_REF] [START_REF] Jardine | A review on machinery diagnostics and prognostics implementing condition based maintenance[END_REF]). This allows identifying problems in the equipment at the early stages of development and estimating the RUL (i.e., the residual time span before the degradation state reaches the threshold that leads to a loss of functionality). In principle, an accurate estimate of the RUL enables to run the equipment as long as it is healthy, thus providing additional time to opportunely plan and prepare the maintenance interventions for the most convenient and inexpensive times [START_REF] Jardine | A review on machinery diagnostics and prognostics implementing condition based maintenance[END_REF].

The development of prognostic systems capable of reliably predicting the occurrence of a faulty condition in the equipment mainly depends on the quality and quantity of the available information and data on its past, present and future behavior. In this respect, a typical distinction is made between data-driven and model-based approaches. In the former case, modeling of the evolution of the degradation process relies exclusively on process history data. Empirical techniques like Artificial Neural Network (ANN, e.g, [START_REF] Bishop | Neural Networks for Pattern Recognition[END_REF], [START_REF] Worden | Natural computing for mechanical systems research: A tutorial overview[END_REF]), Support Vector Machine (SVM, e.g. [START_REF] Hsu | A Practical Guide to Support Vector Classification[END_REF]), Local Gaussian Regression (LGR, e.g. [START_REF] Rasmussen | Gaussian Processes for Machine Learning[END_REF], [START_REF] Liu | Kernel Adaptive Filtering: A Comprehensive Introduction[END_REF]) are typical examples. In the latter case, a model of the degradation process is used to predict the future evolution of the equipment state and infer the RUL.

Physic-based Markov models (e.g., [START_REF] Samanta | Degradation modeling with application to ageing and maintenance effectiveness evaluations[END_REF], [START_REF] Yan | A dynamic multi-scale Markov model based on methodology for remaining life prediction[END_REF]), statistical distributions of failure times (e.g., [START_REF] Abernethy | The New Weibull Handbook[END_REF], [START_REF] Cox | Analysis of Survival Data[END_REF]), empirical degradation models (e.g., [START_REF] Kopnov | Optimal degradation process control by two-level policies[END_REF], [START_REF] Lam | Optimal maintenance policies for deteriorating systems under various maintenance strategies[END_REF]) are typical examples. If experimental or field degradation data are available, these can be used to calibrate the parameters of the model or to provide ancillary information related to the degradation state, within the state-observer formulation typical of a filtering problem with given state model; Kalman filtering (KF, e.g., [START_REF] Roweis | A unifying review of linear Gaussian models[END_REF], [START_REF] Hamilton | Time Series Analysis[END_REF]) and Particle Filtering (e.g., [START_REF] Arulampalam | A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking[END_REF]- [START_REF] Sikorska | Prognostic modelling options for remaining useful life estimation by industry[END_REF]) are typical examples. This work focuses on Particle Filtering (PF) for prognostics, in recognition of its capability of robustly predicting the future behavior of the equipment degradation, x , which is typically a quantity not directly observable, without requiring the strict hypotheses of the KF ( [START_REF] Arulampalam | A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking[END_REF]) on the linearity of the system state evolution and noise gaussianity. From the prediction of the future evolution of the degradation and knowledge of the failure threshold (i.e., the degradation value beyond which the equipment loses its function), one can assess the equipment RUL.

Previous works employing a PF scheme for prognostics (e.g., [START_REF] Arulampalam | A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking[END_REF], [START_REF] Orchard | A Particle Filtering-based Framework for On-line Fault Diagnosis and Failure Prognosis[END_REF], [START_REF] Vachtsevanos | Intelligent Fault Diagnosis and Prognosis for Engineering Systems[END_REF]) assume knowledge of the following information [START_REF] Gustaffson | Particle filtering with dependent noise[END_REF]:

1) The knowledge of the degradation model describing the stochastic evolution in time of the equipment degradation x (in general a multi-dimensional vector):

( 1) = ( ( ), ( ))

x t g x t t   ( 1
)
where g is a possibly non-linear vector function and () t  is a possibly non-Gaussian noise.

2) A set of measures (1),..., ( ) z z t of past and present values of some physical quantities z related to the equipment degradation x . Although z in general is a multi-dimensional vector, in this work it is considered as a mono-dimensional variable; then, the underline notation is omitted.

3) A probabilistic measurement model which links the measure z with the equipment degradation x :

( ) = ( ( ), ( ( )))

z t h x t x t  ( 2
)
where h is a possibly non-linear vector function and () x  is the measurement noise vector.

In practical cases where the analytical measurement model is not available, the PF scheme here described would not be directly applicable. To overcome this hurdle, in this work the challenge is notably to combine a data-driven approach for exploiting the measurement data, with a model-based approach, for exploiting degradation modeling. To the authors' best knowledge this is the first time that such issue is addressed in prognostics.

For example, piping of deep water offshore well drilling plants degrades due to a process of scale deposition which may cause a decrease, or even a plug, of the cross sections of the tubular. Giving the inaccessibility of the piping, it is usually impossible to acquire a direct, on line, measure of the scale deposition thickness. On the other side, research efforts are devoted to perform laboratory tests to investigate the relationships between the scale deposition thickness and other parameters which can be more easily measured during plant operation, such as pressures, temperatures and brine concentrations. The idea is to populate datasets with the values of the measurable parameters for different scale deposition thicknesses, and use the data to build data-driven models for predicting the scale deposition thickness [START_REF] Moura | Predictive maintenance policy for oil well equipment in case of scaling through support vector machines[END_REF].

Another example concerns the crack propagation in bearings of rotating machinery, which often results in damage to the bearings and consequent reduced efficiency, or even severe damage, of the entire motor system. In this respect, several studies have been performed for an analytical description of the crack propagation process in bearing (e.g., [START_REF] Green | Crack Detection in a Rotor Dynamic System by Vibration Monitoring[END_REF], [START_REF] Huang | Residual life predictions for ball bearings based on self-organizing map and back propagation neural network methods[END_REF]). However, a direct measure of the crack depth during online operation is usually not possible, and thus the classical PF scheme is not applicable. On the other hand, since the major tell-tale sign of a bad bearing is an increase in vibration, both in amplitude and complexity ( [START_REF] Harris | Rolling Bearing Analysis[END_REF], [START_REF] Seker | Elman's recurrent neural network applications to condition monitoring in nuclear power plant and rotating machinery[END_REF]), a possible approach consists in developing laboratory tests to relate the crack depth to the measurements of the vibrations which the crack induces in the assembly. From these tests, an empirical model which links the vibration measurement to the real crack depths may be obtained.

In this context, the specific novelty of the work here presented is the application of PF for prognostics in a case in which the measurement model is not available but a dataset containing a number of pairs made by the state and the corresponding measurement is available for exploitation by a data-driven approach. To do this, a technique based on the use of an ensemble of ANNs [START_REF] Carney | Confidence and prediction intervals for neural network ensembles[END_REF] is here embedded in the PF scheme. Bagging is used to generate the datasets for training the different ANN predictors whose output are, then, combined to give the ensemble output, which is characterized by a lower variance than the one of the single ANN predictor [START_REF] Breiman | Bagging Predictors[END_REF]. The key idea of bagging is to treat the available dataset T as if it were the entire population, and then create alternative versions of the training set, by randomly sampling from it with replacement.

An alternative way to cope with the issue considered in this work consists in the development of a completely data-driven approach. For example, one may use the analytical degradation model to generate samples of degradation evolutions, and, then, utilize them together with the measurement data in a 'traditional' data-driven approach (e.g., a Support Vector Machine) which directly predicts the system future degradation evolution. However, notice that traditional data-driven approaches, differently from the PF approach, are typically not able to continuously update in a Bayesian perspective the uncertainty on the prediction.

The remainder of the work is structured as follows: in Section 2 a brief review of the PF is reported;

in Section 3 the problem of the substitution of the measurement model and the technique to overcome this problem are presented. In Section 4 the technique is applied to a case study dealing with the physical phenomenon of the crack growth; Section 5 concludes the work.

Particle Filtering for prognostics

Particle Filtering (PF) is a model-based method whose application in prognostics aims at inferring the evolution of an equipment degradation state on the basis of a sequence of noisy measurements; it relies on Bayesian methods to combine a prior distribution of the unknown state with the likelihood of the observations collected, to build a posterior distribution. This technique is widely used in prognostics since it allows to take into account even non-linear systems and/or non-Gaussian noises. The prediction of the equipment degradation state, x , is performed by considering a set of s N weighted particles, which evolve independently on each other, according to the probabilistic degradation model of Equation 1. The basic idea is that such set of weighted random samples constitutes a discrete approximation of the true Probability Density Function (pdf) of the system state x at time t . Typically, in a PF scheme, when a new measurement is collected, it is used to adjust the predicted pdf through the modification of the weights of the particles. Roughly speaking, the smaller the probability of encountering the acquired measurement value, when the actual component state is that of the particle, the larger the reduction of the particle's weight. On the contrary, a good match between the acquired measure and the particle state results in an increase of the particle importance. This requires the knowledge of the probabilistic law which links the state of the component to the gathered measure (Equation 2). From this model, the probability distribution ( | ) P z x of observing the sensor output z given the true degradation state x is derived (measurement distribution). This distribution is then used to update the weights of the particles upon a new measurement collection (for further details see [START_REF] Arulampalam | A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking[END_REF], [START_REF] Orchard | A Particle Filtering-based Framework for On-line Fault Diagnosis and Failure Prognosis[END_REF], [START_REF] Cadini | Model-based Monte Carlo state estimation for condition-based component replacement[END_REF]). Schemes of the PF algorithm are presented in Figures 1 and2.

ANN

In this Section, we propose a method to estimate the pdf ( | ) P z x of the measurement z in correspondence of a given equipment degradation state x , in the case in which the analytical form of the measurement model is not known. The method, derived from [START_REF] Carney | Confidence and prediction intervals for neural network ensembles[END_REF] and [START_REF] Nix | Estimating the mean and the variance of the target probability distribution[END_REF], requires the availability of a dataset made of training N couples ( , ) nn xz . The estimated pdf ˆ( | ) P z x will be used in the PF scheme according to the scheme of Figure 3. Behind the method there is the hypothesis that the measurement model, which is unknown, can be written in the form:

( ) ( ) ( ) z x f x x   (3)
where () fx is a biunivocal mathematical function and the measurement noise () x  is a zero mean Gaussian noise.

The method is based on the use of a bagged ensemble of ANNs, which are employed to build an

interpolator () x  of the available training patterns   ( , ), 1.,..., n n training T x z n N 
. Since the obtained ANNs outputs depend on the training set, ANNs may suffer from instability. To overcome this issue, the use of a bagged ensemble of ANNs has been proposed (e.g., [START_REF] Breiman | Bagging Predictors[END_REF], [START_REF] Breiman | Combining predictors[END_REF]): each base interpolator of the ensemble is trained on different distributions of data according to a bootstrap technique. The key idea is to treat the available dataset as if it were the entire population, and then to create a number Empirical studies have established that bagging is a simple and robust method that generally increases the accuracy of a single learner [START_REF] Breiman | Bagging Predictors[END_REF], [START_REF] Breiman | Combining predictors[END_REF].

( ) ( ) = [ ( ) ( )] ( ) avg avg z x x f x x x       (5)
The left-hand side of Equation 5 is a random variable which represents the error of the ensemble output () avg x



with respect to the measurement () zx. This random error is made up of two contributions (right hand side of Equation 5):

1. The random difference ( )

( ) avg f x x  
between the unknown deterministic quantity ()

fx
and the ensemble output

() avg x 
. This quantity is a random variable, being

m x  .
2. The intrinsic noise () x  of the measurement process, whose variance is indicated by

2 () x  .
These two contributions are estimated by means of the procedures described in the following Sections 3.1 and 3.2.

Distribution of the model error variance

The procedure here used to estimate the distribution ( ( ) | ( )

) avg P x f x  of the ensemble output () avg x 
given the true value of () fx, is based on the assumption that the random variable ( ) ( )

avg f x x   is
gaussian with zero mean and standard deviation

() m x 
, which entails that ( ( ) | ( )

) avg P x f x  is
gaussian with mean () fx. Notice that residual errors in the output of the ANN are usually not caused by variance alone; rather, there may be biases in the output of the ANN, which invalidate the assumption that the mean of the distribution is zero. However, it is generally accepted that the contribution of the variance in the residual error of the ANN dominates that of the bias (see [START_REF] Stuart | Neural Networks and the bias/variance dilemma[END_REF] for further details on this). Furthermore, the bias in the output of an ensemble of NNs is expected to be smaller than that of the single ANN.

In order to estimate the model error variance 2 ()

m x
 , the technique in [START_REF] Carney | Confidence and prediction intervals for neural network ensembles[END_REF] , sampled with replacement from  .

For any subset * p  , =1,..., pP , the corresponding variance 2* ()

p x  is computed; then, the estimate 2 ˆ() m x  of the variance 2 () m x
 is calculated as their average value:

2 2* =1 1 ˆ( ) = ( ) P mp p xx P   (8)
Finally, the estimate of the regression distribution proposed by the method is:

2 ( ( ) | ( )) ( ( ), ( )
)
avg avg m P x f x N x x     (9)

Distribution of the measurement noise

In this Section, the technique proposed in [START_REF] Nix | Estimating the mean and the variance of the target probability distribution[END_REF] is applied to estimate the variance 2 () x  of the Gaussian zero mean noise () x  affecting the measurement equation (Equation 3).

From Equation 5, one can derive:

22 [ ( )] [ ( ) ( )] [ ( )] 2 {[ ( ) ( )] ( )} ( ) ( ) avg avg avg m Var z x Var f x x Var x E f x x x xx              ( 10
)
The last equality is due to the independence of the error

Finally, in order to estimate 2 () x  for a generic x , a single ANN is trained using the dataset . Finally, being () fx invertible, the distribution ( | ) P z x of the measurement z in correspondence of a given state x , is given by:

Estimate of the measurement distribution P(z|x)

22 ( | ) ( | ( )) ( ( ), ( ) ( )) avg m P z x P z f x N x x x       (12)

Description of the case study

In this Section, we apply the technique described in Section 3 for estimating the measurement distribution ( | ) P z x to a case study dealing with the crack propagation phenomenon in a component subject to fatigue load. The system state is described by the vector ( 1) = ( ) 3 10 (0.05 0.1 ( )) ( )

x t x t x t t         (13) 2 2 2
( 1) = ( ) ( )

x t x t t   (14)
( ) = ( ) ( ) ( ) 0.25 ( ) z t f x x x t x      (15)
where 1 () x  is a zero mean Gaussian noise, whose standard deviation depends on 1 x :

2 1 1 1 1 1 1 [ ( )] = 120 10 2 Std x x x     (16)
According to Equation 15, the function () fx is given by 1 0.25

x 

, which is, as required by the method, an invertible function. These degradation and measurement models have been derived from [START_REF] Orchard | A Particle Filtering-based Framework for On-line Fault Diagnosis and Failure Prognosis[END_REF].

Notice that the probabilistic measurement model of Equation 15has been intentionally taken simple, as the main interest of our work is the quantification of the uncertainty in the RUL prediction and not the ability of the ensemble in reproducing the measurement model. In this respect, the knowledge of the variance of the measurement noise is fundamental, as it determines the amplitude of the prediction intervals of the RUL estimates. Thus, it is the capability of correctly reconstructing the variance that plays a key role in the assessment of the potential of the proposed technique.

Estimate of the measurement distribution

avg x  : 22 1, 1, =1 1 = ( ( ) ( )) N test i avg i i test b f x x N    (17)
This value gives information on the accuracy of the estimate of fx , which is not available if the measurement equation (Equation 15) is not known. Thus, in general one can only compute:

The PI with 0.68 p   is given by:

2 2 2 2 1 1 1 1 1 1 1 垐 垐 ( ) ( ) ( ) ( ) ( ) ( ) ( ) avg m avg m x x x z x x x x             (20)
In order to verify whether the estimate of Notice also that the linearity of the prediction of the expected value of x 1 can be explained by averaging Equations 13 and 14: A scheme of the method used for the computation of these performance indicators is shown in Figure 11; the obtained values are reported in Tables 4 and5. P z x and on the prognostics performance of the Finally, the performance evaluator proposed in [START_REF] Saxena | Damage Propagation Modeling for Aircraft Engine Run-to-Failure Simulation[END_REF] has been computed to evaluate the prediction performance: where a 1 = 10, a 2 =13, n=100 is the number of simulated histories and d is the difference between the estimated RUL and its true value. To compute the value of this performance metric, the following procedure has been adopted:

2 2 2 2 [ ( 1)} = [ ( )] [ ( )] [ ( )] constant E x t E x t E t E x t      43
E x t E x t E x t E t E x t E x t            
1. Set the failure threshold to S T =7.

2. Simulate the evolution of the degradation process; this allows calculating the true value of the true RUL t RUL at t=80 as the difference between the time instant at which the component achieves ST and 80. Moreover, the set of measures sampled according to the measurement model are collected. The values of the performance indicators obtained in the case in which the RUL is predicted by using the 'traditional' PF approach (s=10.30) the 'data-driven' approach (s=10.65) turn out to be very close to each other.

Figure 1 :Figure 2 :

 12 Figure 1: Flowchart of a PF algorithm

Figure 3 :

 3 Figure 3: Information flowchart for the modified PF algorithm

  randomly sampling from it with replacement (i.e., every sample is returned to T after sampling so that a pattern could appear multiple times in the same bagged set * b T ). Using these training sets, the networks * =1 { ( ; )} B b b b xT  are built and the output () avg x  of the bagged ensemble is obtained by averaging the single ANN output according to:

Figure 4 :

 4 Figure 4: Scheme of a bagging ensemble of ANNs On the other hand, since PF requires the knowledge of the pdf ( | ) P z x , the estimate of () fx does

  .., bB  , i.e. different training sets would lead to different ensemble models and thus to different output () as the model error, its variance will be referred as model error variance and indicated by 2 ()



  which can be derived from the distribution ( ( ) | ( )) measurement noise () x  , according to Equation5. Since these two distributions are both Gaussian, with means and variances estimated as shown in Sections 3.1 and 3

12 (

 12 t , whose first element, 1 () xt, indicates the crack depth whereas the second element, 2 () xt, represents a timevarying model parameter that directly affects the crack growth rate. The evolution of this degradation process is described by the following two equations, which form a markovian system of order one:

B

  According to the technique illustrated in Section 3, an ensemble of = 200ANNs to estimate the noise variance 2 () x  is characterized by 5 tansigmoidal hidden neurons and one linear output neuron.The results are evaluated in terms of the following performance indicators, which are computed by considering

Figure 5 :

 5 Figure 5: Scheme of the proposed cross-validation 1. The square bias 2 b ; i.e., the average quadratic difference between the true value of

  that the computation of this indicator requires the knowledge of the

1 (

 1 MSE indicate satisfactory performance of the ensemble.2. The coverage of the Prediction Interval (PI) with confidence 0.68. This indicator is used to verify the accuracy of the estimate of the distribution( | ) P z x . A PI with a confidence level p  is defined as a random interval in which the observation



  provides a satisfactory approximation of the true pdf, we will consider how many times the measurement is the portion of data inside the p  -confidence interval, the more accurate is the estimation of the parameters of the Gaussian pdf. A graphical representation for the verification procedure is shown in Figure6.

Figure 6 :

 6 Figure 6: Verification of the coverage for PI In order to avoid over/under estimating the performance indicators 2 b and coverage, cross-

Figure 10

 10 Figure10shows the prediction of the crack depth evolution performed at

Figure 10 :X

 10 Figure 10: Comparison of the PF predictions with the true state evolution considering different cardinalities of the training set.To evaluate the impact of replacing the measurement equation with the ensemble of ANNs,

Figure 11 :

 11 Figure 11: Scheme for the evaluation of the prognostics performance

  It can be noticed that the coverage of the ensemble trained with 1000 training data is very close to 0.68; furthermore, even the other performance indicators are very close to those which would be obtained by considering the measurement equation. This result confirms that when the size of the training set is sufficiently large, the approximation of the distribution 1 ( | ) P z x is accurate and therefore it does not remarkably alter the outcome of the PF. On the contrary, the performance indicators obtained by considering the ensemble trained with 50 data are less satisfactory; this is due to the worse estimate of the 1 ( | ) P z x provided by the ensemble. In particular, the reduction of the PI width is due to the underestimate of the variance of 1 ( | ) P z x which results in a more peaked particles' distribution when a measurement is collected.In conclusion, the size of the training dataset has an influence both on the approximation of the

3 .

 3 Use the PF to estimate the component degradation state at t=80 and predict the RUL ˆRUL t .

5 .

 5 Perform n-1 times the steps 2-4 and compute s.

  requires to divide the

	The set	=1 mM ( )} com m x  = {	constitutes a sampling of	com M values from the distribution ( ( ) | P x 	avg	( )) x
	and its sample variance 2 ˆ() m x 	m could be used to approximate the unknown variance 2 () x 	of the
	ensemble output. Notice that the idea behind this procedure is that by estimating () fx with		() avg x	,
	one can approximate ( ( ) | ( )) P x f x 	by ( ( ) | P x . In order to improve the reliability and ( )) x
							avg	com	avg
	stability of 2 ˆ() m x 	, bagging is also performed on the values of  . Thus,	P bagging re-sampled sets
	of  are gathered:
		* pp = { } P 	=1			(7)
	where * p  is the	p -th subset containing	M values of		() com x
							B
	networks of the ensemble		() avg x	into	M smaller sub-ensembles, each one containing	K networks,
	and to consider the output		() com x m	, =1,..., mM of each sub-ensemble as:
	k K =1 xx K 1 ( ) = ( ) k   m com		(6)

Table 1 Performance indicators in case of 1000 and 50 training data over 25 cross-validations; the mean  std is reported

 1 Table 1 reports means and standard deviations of the performance indicators over the 25 cross-validations in the two cases.

	training data	1000	1000	50	50
	model	Ensemble	1 ANN	Ensemble	1 ANN
	b	2	0.0040 ± 0.0015 0.0097 ± 0.0060	0.0793 ± 0.0395	0.3877 ± 0.3441
	PI coverage	0.6758 ± 0.0366	-	0.5488 ± 0.1031	-
	Notice that when 1000 training couples 1 () avg x  Furthermore, notice that the ensemble outperforms a single ANN trained with all the 1000 training 1, ( , ) nn xz, 1,..., training are available, the ensemble output nN  is very accurate in the prediction of the function f(x), the bias being very small. patterns. With respect to the estimate of the distribution 1 ( | ) satisfactory approximation, being the coverage very close to 0.68. P z x , the proposed method provides a Using the smaller training set made by 50 training patterns, the accuracy of the 1 ( | ) P z x estimate decreases. Notice, however, that the prediction of the () more satisfactory than that of one single ANN. Table 2 reports the estimates of the two contributions 2  and 2  of the variance of the estimated fx value provided by the ensemble is still measurement distribution 1 ˆ( | )  is negligible with respect to the variance 2  of the measurement noise. Thus, the accuracy of the estimate of the PI is more sensible to the estimate of 2  . P z x . Notice that in this case study, 2 1000 training data Real value Var (P(z|x))= 2  + 2  0.4489±0.1359 0.4955±0.0621 -2  0.0243±0.0317 0.0005±0.0001 -50 training data 2  0.4886±0.0276 0.4095±0.1642 0.4900

Table 2 : Contributions to the

 2  value provided by Equation16. Notice that this comparison, which is done in this work to assess the performance of the methodology, is not possible in real industrial applications if the measurement model (Equations 15 and 16) is not available.

	( | ) P z x variance In this respect, Figures 7 and 8 show the estimate of 2  by 1000 training N  and 50 training N  1, ( , ) nn xz, 1,..., training () x 1 , pairs, respectively. The estimated values in the two cases of training sets formed nN  are compared with the true 2

Table 4 : Performance indicators at t=100

 4

			1000	training	50	training
		traditional	data		data
	coverage 0.6500	0.7000		0.6000
	PI width 1.3058	1.3226		1.2088
	MSE	0.3421	0.3464		0.3641

Table 5 : Performance indicators at t=120

 5

z of the measurement sensor, and is used to update, within a Bayesian framework, the prediction of the evolution of the degradation state, upon the acquisition of a measure. In practice, the measurement model may not be available in an analytical form; rather, there may be available a set of data which allows, through data-mining techniques, to build the measurement model. In this work, a technique based on an ensemble of ANNs has been investigated to this aim and applied to a case study derived from the literature. The verification conducted on the results shows that, when the training set is sufficiently large, a good approximation of the model may be obtained and its substitution in the PF does not significantly affect its performance. Additional effort will be dedicated in future works to improve the accuracy of the estimate when only a small training set is available and to extend the applicability of the technique also in those cases in which () fx is not biunivocal. Moreover, one more future objective is the substitution also of the model of the evolution of the system state for a data-driven model, like an ensemble of ANNs trained on the basis of an available dataset, with a procedure which may be inspired by the one presented in this work, in order to allow the usage of the PF in those cases where also an analytical model of the evolution of the system is unavailable.

is trained with much more patterns in the first case.

Crack depth prediction

The objective of this Section is to evaluate the performance of the overall PF scheme in the prediction of the crack depth evolution when the ensemble of ANNs is used to estimate the measurement distribution provided by the two ensembles with the distribution which would be obtained by using the true measurement equation for the particle with the highest difference between the weights computed through the analytical measurement model and through the considered technique (with 1000 training data). Table 3 reports the most significant numerical values for the comparison: the means and the standard deviations of the distributions and the weight w assigned to the particle upon the Bayesian update (before this, the weight w is the same in the three cases, since the resampling algorithm has been adopted, see [START_REF] Arulampalam | A Tutorial on Particle Filters for Online Nonlinear/Non-Gaussian Bayesian Tracking[END_REF]). Notice that the ensemble trained with 50 data provides a distribution characterized by variance lower than the analytical, and thus the weight assigned to the particle ( 1 5.93