Ho Si

Phuc Do Van Hung Nguyen

Hai-Canh Canh Vu

Benoît Iung

Phuc Do
email: phuc.do@univ-lorraine.fr

Benoit Iung

Dynamic maintenance grouping and routing for geographically dispersed production systems

Keywords: Grouping maintenance, Route scheduling, Economic dependence, Geographical dependence, Geographically Dispersed Production Systems, Local Search Genetic Algorithm

Introduction

In the recent years, with the growth of international trade, the development of distributed control, information, and logistic technologies, many manufacturing companies pursued the goal of building geographically dispersed production systems (GDPS) to ensure their competitiveness [START_REF] Matt | Trends towards distributed manufacturing systems and modern forms for their design[END_REF][START_REF] Tang | Scheduling technicians for planned maintenance of geographically distributed equipment[END_REF]. According to this concept, the production is done over a number of production sites which are geographically located far apart from each other. On the one hand, the GDPS is a key solution for optimizing production cost and product delivered cost as well as adapting customer's demands. On the other hand, the GDPS has to face many challenges concerning standards, regulation, production management, and especially, maintenance planning and optimization.

Firstly, in the framework of maintenance optimization, the dependencies between components have important impacts on the performance of a maintenance planning and need to be considered in the maintenance modelling and optimization [START_REF] Wildeman | A dynamic policy for grouping maintenance activities[END_REF][START_REF] Nicolai | Optimal maintenance of multi-component systems: a review[END_REF]. Unlike centralized systems, a GDPS system can be divided into two abstraction levels. At site level, a production site contains different components to perform specific production or service functions [START_REF] Matt | Trends towards distributed manufacturing systems and modern forms for their design[END_REF][START_REF] Phan | Multi-stage optimization for periodic inspection planning of geodistributed infrastructure systems[END_REF]. Therefore, each site can be seen as a multi-component system whose components may depend on each others. These dependencies are classically classified into three main types as in [START_REF] Wildeman | A dynamic policy for grouping maintenance activities[END_REF][START_REF] Nicolai | Optimal maintenance of multi-component systems: a review[END_REF][START_REF] Do | Dynamic grouping maintenance strategy with time limited opportunities[END_REF]: structural dependence (e.g. maintenance of a failed component implies maintenance of working components or, at least, dismantling them); stochastic dependence (i.e the condition of components influences the life distribution of other components) and economic dependence (i.e the cost of joint maintenance of a group of components does not equal the total cost of individual maintenance of these components). Recently, a fourth type of dependence, namely logistic dependence, has been introduced in [START_REF] Keizer | Condition-based maintenance policies for systems with multiple dependent components: A review[END_REF]. Logistic dependence exists when executing maintenance of several components require a same maintenance skill and/or a same type of spares parts. At GDPS system level, another dependence, called geographical dependence, exists if the total distance/time of the joint maintenance group of several components is smaller than the total distance/time of each individual component. This type of dependence may impact the maintenance planning and/or total maintenance cost. This is specially true when only one maintenance team located far from production sites is available for performing the maintenance on different sites. It should be noticed that, in literature, a large number of maintenance approaches has been introduced, developed and successfully applied to multi-component systems considering several types of dependencies.

A relevant overview on this topic is given in [START_REF] Keizer | Condition-based maintenance policies for systems with multiple dependent components: A review[END_REF]. Among existing maintenance approaches, dynamic grouping maintenance approach initially proposed in [START_REF] Wildeman | A dynamic policy for grouping maintenance activities[END_REF] seems to be an efficient one since it can take into account several kinds of dependencies between components and easily update the maintenance planing in dynamic contexts (varying deterioration rate of components, maintenance opportunities, etc.) [START_REF] Do | Dynamic grouping maintenance strategy with time limited opportunities[END_REF][START_REF] Vu | Maintenance grouping strategy for multi-component systems with dynamic contexts[END_REF]. However, this approach cannot be directly applied for the maintenance optimization of a GDPS due to the geographical dependence between components and sites.

Another challenge concerns the maintenance routing problem. It is interesting to determine the optimal route that the maintenance team should follow to maintain several production sites. To solve this problem, several studies focus on finding the optimal route that minimizes the travel distance/travel cost, see for instance [START_REF] Díaz-Ramírez | Aircraft maintenance, routing, and crew scheduling planning for airlines with a single fleet and a single maintenance and crew base[END_REF][START_REF] Al-Thani | A model and optimization-based heuristic for the operational aircraft maintenance routing problem[END_REF][START_REF] Goel | Workforce routing and scheduling for electricity network maintenance with downtime minimization[END_REF][START_REF] Camci | Maintenance scheduling of geographically distributed assets with prognostics information[END_REF]. Unfortunately, in the models proposed, the maintenance is usually considered as a constraint rather than the second optimization objective. Recently, papers [START_REF] Irawan | Optimisation of maintenance routing and scheduling for offshore wind farms[END_REF][START_REF] López-Santana | On the combined maintenance and routing optimization problem[END_REF] try to integrate both maintenance planning and routing into a global model. However, in these works, the dependencies between components do not count. Therefore, the issue on joint consideration of maintenance scheduling and routing of GDPS with taking into account the component dependencies remains widely open.

To face with the above challenges, the paper is addressing a dynamic grouping maintenance approach well adapted for GDPS systems. Maintenance planning and maintenance routing are jointly studied in a global model, considering several types of dependencies between components and sites (economic and geographical dependencies). For this purpose, cost structures and dependencies modelling are formulated and used as a basis for the development of the global model. A combination of the Local Search Genetic Algorithm (LSGA) and Branch and Bound method (BAB) is implemented to optimize the proposed model and determine the optimal maintenance routes and schedules. Moreover, several dynamic contexts which may occur with time are also studied and integrated in the optimization process. Thanks to this consideration, the proposed approach allows updating optimally the grouped maintenance planning and routing in presence of the dynamic contexts.

In relation to the approach proposed, the remainder of this paper is organized as follows. Section 2 is devoted to describe general assumptions and problem statement. The maintenance cost structure and dependencies modelling and formulation are presented in Section 3. A maintenance grouping and routing approach is then developed for GDPS in Section 4. Some numerical examples are investigated to illustrate the use and the performance of the proposed approach in Section 5. Finally, the conclusions deduced from this work are presented in the last section.

General assumptions and problem statement 2.1 System description

We consider a GDPS consisting of several independent production sites geographically located far apart from each other. Each production site is supported by several machines whereby each machine is composed of a set of components. In this study, only several critical components for each site are investigated. Indeed, a component is considered as a critical once if (i) its failure leads to a shutdown of the corresponding production site and (ii) the component's failure occurrence without any preventive maintenance intervention is important. In this context, the maintenance plays an important role to keep the components' proper operation and also to avoid their failure. Both corrective and preventive maintenance actions are therefore considered. For corrective maintenance (CM), as all components are critical, if a component fails, it is necessary to repair it as soon as possible to bring the corresponding production site to an operating state. In that sense, it is reasonable to assume that immediate minimal repair actions are performed on the failed components and that each CM action restores the failed component to "as bad as old" state.

All CM maintenance actions are done by a local maintenance team at each production site. The CM maintenance duration is short and can be neglected. To avoid the failure of components and sites, preventive maintenance (PM) actions are performed mainly on the critical components. Each PM action on a component brings the maintained component to be a new one (replacement action). All PM actions are done by a maintenance center team which may located far from production sites.

This assumption is realistic because PM maintenance resources are centralized at one maintenance center that can save logistic and maintenance cots. In that way, to perform a PM action on a given component of a production site, the maintenance team and all necessary maintenance resources (spare part, maintenance tools, etc.) need to be transported from the maintenance center to the maintained production site. As an example, a typical GDPS system composed of five production sites and one maintenance center are shown in Figure 1. The connections between production sites and maintenance center represent the possible routes to be followed by the maintenance team.

From an economical point of view, when several components are jointly maintained, the total maintenance cost may be reduced because (i) the maintenance preparation cost related to logistic preparation (e.g, scaffolding erecting, machine opening, maintenance tools, etc) can be shared (economic dependence) and (ii) the total travel distance/cost can be reduced (geographical dependence).

Since CM actions are performed by a local maintenance team as soon as each component's failure occurs, the paper is addressing a maintenance approach well adapted in finding an optimal maintenance and routing plan for all preventive maintenance actions of a GDPS system. Of course, the impacts of such a CM action and its cost need to be considered in the proposed maintenance model, see Section 4.

Problem statement and assumptions

In the framework of maintenance optimization for "centralized" multi-component system, economic dependence between components is investigated and integrated in various maintenance models through setup cost which is the cost paid for all logistic preparation of each maintenance action [START_REF] Wildeman | A dynamic policy for grouping maintenance activities[END_REF][START_REF] Nicolai | Optimal maintenance of multi-component systems: a review[END_REF]. In these maintenance models, single setup cost model (or identical setup cost) is used for all maintenance activities. This model cannot be directly applicable in the context of GDPS systems since the logistic preparation may be different for components located in different production sites. Moreover, as a characteristic of GDPS systems, geographical dependence, whereby the total travel distance/time can be reduced when several components are preventively maintained together, often exists between components. The latter need to be modelled and considered in the maintenance optimization process.

Concerning maintenance approaches, dynamic grouping maintenance trying to group several components to be jointly maintained to reduce maintenance costs seems to be a promising maintenance approach for maintenance optimization of "centralized" multi-component systems since it can better take into account the economic dependence between components and allows updating a maintenance planing in a dynamic context [START_REF] Wildeman | A dynamic policy for grouping maintenance activities[END_REF][START_REF] Nicolai | Optimal maintenance of multi-component systems: a review[END_REF][START_REF] Do | Dynamic grouping maintenance strategy with time limited opportunities[END_REF][START_REF] Vu | Maintenance grouping strategy for multi-component systems with dynamic contexts[END_REF]. However, to develop such an approach for the maintenance of a GPDS system faces many challenges in modelling, formulation and optimization process to take in consideration of geographical dispersion between the production sites and the maintenance center. Indeed, given a number of possible maintenance routes (the itineraries that the maintenance team should follow to perform the preventive maintenance of one or several components which may be located in different production sites) with different impacts on the setup cost and maintenance dates, the maintenance routing should be considered in the development of the maintenance grouping approach. The joint consideration of maintenance grouping and routing makes the developed model become a hyper-complex one. The finding of the optimal grouping solution and optimal maintenance route from the developed model is a NP-complete optimization problem. The latter leads to implement an intelligent search algorithm.

In addition, due to the characteristics of a GDPS system, several following situations may happen with time in reality:

1. Change of route and weather conditions: the maintenance routes and/or travel durations between different sites/sites and maintenance center may be changed over time due to specific reasons such as failure of a maintenance team's vehicles, bad weather conditions, or interruption of specific routes between production sites and maintenance center [START_REF] Bajaj | Some constrained shortest-route problems[END_REF][START_REF] Joksch | The shortest route problem with constraints[END_REF]; 2. Change of transportation capacity: the transportation means may be changed due to economic and/or technical reasons, e.g., failure or replacement of a vehicle with lower or higher capacity [START_REF] Bajaj | Some constrained shortest-route problems[END_REF][START_REF] Joksch | The shortest route problem with constraints[END_REF]. These kinds of the above situations, referred to "dynamic contexts" in this paper, may have significant impacts on the maintenance planning and routing. In the presence of such a dynamic context, the current maintenance grouped plan and maintenance route may be no longer optimal ones and need to be updated. The proposed maintenance grouping and routing approach should be a dynamic one which allows considering the impacts of a dynamic context and optimally updating the maintenance plan and route when the dynamic context occurs. In addition, according to different types of dynamic contexts, an appropriate updating process needs to be developed.

To answer these above scientific issues, the main objective of the paper is to develop a dynamic maintenance grouping and routing approach for a GDPS system. The proposed approach allows considering both economic and geographical dependencies between components, the impacts of maintenance routing on the grouping performance, and also the impacts of a dynamic context that may occur with time.

To develop our grouping and routing maintenance approach, the following additional assumptions are considered:

• Only several critical components are considered in each production site;

• Interruption of a production site does not impact the normal operation of the others;

• Only one maintenance team (repairman) of the maintenance center located far form production sites is considered;

• The maintenance team and necessary resources are always available and ready for all planned preventive maintenance actions;

• A specific repairman skill is required to perform the preventive maintenance of each component;

• Minimal repair CM actions with negligible duration are executed by local maintenance team.

Costs structures and dependencies modeling 3.1 Maintenance cost structure

As mentioned above, to do the PM of a component, the maintenance team and spare part have to be transported from the maintenance center to the production site where the component is located on.

The transportation costs should be included in the PM cost. Let C p i denote the cost of a PM action of component i located at site j.

C p i = C sp i + C dt ij + C lb i + S 0 ij + S tr i , (1)
where,

• Spare part cost, C sp i , is the cost of buying a new component which is used to replace the old one;

• C dt ij denotes the downtime cost which occurs when site j is stopped during the maintenance of component i. C dt ij can be calculated as

C dt ij = R dt j • ω i
, where R dt j and ω i are respectively the downtime cost rate of site j and the PM duration of component i;

• Labor cost C lb
i is paid for the related works of maintenance team. It is reasonable to consider that the higher the repairman skill is required, the more expensive the labor cost is. In this way,

C lb i = R lb (l i ) • ω i , where R lb (l i )
is the labor cost rate associated with the required repairman skill level l i . This skill level is the lowest one that guarantees the success of the PM action on the component;

• Site-preparation cost, S 0 ij , is associated with preparation tasks at site j such as scaffolding erecting, machine opening, etc. S 0 ij can be shared when several components of the same site are preventively maintained together. Note that the site-preparation cost may be different for different components located in the same site or even for identical components located in the different sites;

• Transportation cost, S tr i , is paid for the transportation of spare parts, repair tools and repair team from the maintenance center to the maintenance site j. Let L 0j and L j0 be the travel distances from the maintenance center (denoted by "0") to site j and back again respectively, the transportation cost can be calculated as

S tr i = R tr •(L 0j +L j0 )
, where R tr is the transportation cost rate. When several components are jointly maintained, S tr i can be reduced.

Dependencies modelling and formulation

Consider a group of several components G k , the economic dependence between the components indicates that the PM cost of the group (C p G k ) is not equal to the total PM cost of all the components in isolation, i.e.

C p G k = i∈G k C p i .
In literature, most of grouping maintenance models developed for "centralized" multi-component systems consider that the economic dependence comes from the saving of the setup cost ∆S 0 G k , and the penalty cost ∆H G k related to: (a) the reduction of components useful life if the maintenance dates are advanced; (b) the increase of component failure probability if the maintenance dates are postponed (see [START_REF] Wildeman | A dynamic policy for grouping maintenance activities[END_REF] for more details). Consequently, we have:

C p G k = i∈G k C p i -∆S 0 G k + ∆H G k (2)
From this model, in the case of GDPS system, it is necessary to extend it with regards to both geographical dependence and the repairman skill required for each preventive maintenance actions.

More precisely:

• Labor cost penalty ∆C lb G k . When components are jointly maintained, the maintenance team needs to complete all the maintenance tasks associated with the components group . Therefore, a polyvalent skill may be required. As consequence, the labor cost may be directly penalized.

• Transportation cost saving ∆S tr G k . It should be noticed that to replace an individual component, the maintenance team has to travel from the maintenance center to the maintenance site where the component is located on, and then come back to the maintenance center when the maintenance is completed. Otherwise, to do the PM on a group of several components, the maintenance team replaces sequentially all components of the group and returns to the maintenance center only when the maintenance of all the group's components is completed. The travel distance and travel time are reduced due to the geographical dependence between the components. For these above reasons, in the frame of a GDPS, the equation ( 2) should be rewritten as follows:

C p G k = i∈G k C p i -∆S 0 G k + ∆H G k (I G k ) + ∆C lb G k -∆S tr G k (I G k ) (3)
In the above equation, the penalty cost ∆H G k and the transportation cost saving ∆S tr G k are introduced as the functions of the maintenance route (I G k ), because it has direct impacts on the PM dates of components and on the travel distance of the maintenance team. For more explanation, let's consider the example in Figure 2. Assume that three components located in three different sites 1, 2 and 3 are preventively maintained together. To perform jointly the PM actions of the three components, the maintenance team can follow different maintenance routes from the maintenance center (MC): MC→ 1 → 3 → 2 → MC (Figure 2a), MC→ 2 → 3 → 1 → MC (Figure 2b), and MC 2c). It is clear that, with the same departure time from the maintenance center t G k , the arrival times at each site and the travel distance of the maintenance team depend on the selected maintenance route (see Figures 2a and2c). In addition, it should be noted that, in figures Given these above impacts of maintenance routes on the grouping performance, the maintenance routing optimization need to be jointly considered with the maintenance planning optimization.

→ 1 → 2 → 3 → MC (Figure
The cost model for joint preventive maintenance of several components shown in Equation ( 3) is used to calculate the total cost of a maintenance planning within a given horizon. The detailed description is presented in Subsection 4.3.

Dynamic maintenance grouping and routing approach for GDPS

The proposed approach is structured in 4 phases supporting both the maintenance grouping and routing planning (see Figure 3). In the first phase, the PM cycle/interval of each component is determined by minimizing its long-term maintenance cost rate (see Section 4.1). This PM cycle is then used to determinate the individual PM dates of each component in the planning horizon in phase 2 (see Section 4.2). In the third phase, the economic profit associated with the joint preventive maintenance of a group of components is firstly formulated based on the individual PM dates obtained in the previous phase. Optimization tools such as Local Search Genetic Algorithm and Brand and Bound are then applied to find the best grouping solution GS * (a set of exclusive groups), the optimal PM date of each group in GS * , and the optimal maintenance routes of each group in GS * . The best grouping structure is found by maximizing the total grouping economic profit in the considered horizon (see Section 4.3). Finally, the last phase is devoted to update the maintenance grouping and routing planning when (i) occurring a dynamic information related to maintenance resources or traffic conditions impacting the current maintenance grouping and routing planning, or (ii) a new planning horizon is needed (rolling horizon), see Section 4.4.

GDPS data

Individual maintenance optimization

The objective of this phase is to determine the optimal PM cycle of each component, which minimizes its long-term maintenance cost rate. Without loss of generality, Weibull distribution law is herein used as an example to model the components' failure behavior. The failure rate of component i, denoted r i (t), is given as follows

r i (t) = β i λ i x λ i β i -1 (4)
where, λ i (λ i > 0) and β i (β i > 1) are scale and shape parameters respectively.

It is assumed that component i is preventively replaced at every x i time unit. Its long-term maintenance cost rate can then be calculated as

φ i (x i ) = lim t→+∞ C i (t) t = C p i + C c i • x i 0 r i (t)dt x i + w i = C p i + C c i • x i λ i β i x i + w i . (5)
where:

• C c i •
x i 0 r i (t)dt is the average corrective cost of component i within the period [0 x i ];

• C i (t) is the cumulative CM and PM maintenance costs of component i until t;

• ω i denotes the PM duration of component i.

The optimal PM cycle of component i, denoted x * i , can be then determined by solving the following equation

x * i = arg min x i φ i (x i ) =⇒ dφ i (x i ) dx i x i =x * i = 0 ⇐⇒ (6)
C c i • (β i -1) • (x * i ) β i + C c i • β i • ω i • (x * i ) β i -1 -C p i • λ β i i = 0
The minimum maintenance cost rate is

φ * i = φ i (x * i ).

Individual planning

The objective of this step is to build an individual maintenance plan in a finite planning horizon P H = [t begin , t end ] based on the optimal PM cycle obtained in the previous step. To do this, the first PM date of each component i in the planning horizon is calculated as

t i 1 = x * i + t begin -t e i ,
where t e i is the total operational time of component i elapsed from the last replacement. The execution date of the m th PM of component i (m > 1) in the planning horizon is

t i m = t i m-1 + x * i + ω Σ i , where ω Σ i is the cumulative downtime of component i within interval [t i m-1 , t i m ].
The downtime can result from the PM maintenance of other components located on the same site. It is shown in [START_REF] Wildeman | A dynamic policy for grouping maintenance activities[END_REF][START_REF] Do | Dynamic grouping maintenance strategy with time limited opportunities[END_REF] that to ensure all components are taken into account in the maintenance decision, the planning horizon should be chosen in the way that each component is preventively carried out at least one time within the planning horizon. Therefore, t end = (t j 1 + ω j ) with t j 1 = max i=1:n

t i 1 .
It should be noticed that the individual PM dates of the tentative plan have to be redetermined when the next planning horizon is considered, or when short-term information (e.g., in presence of a dynamic context, maintenance opportunities, etc.) occurs. In the next subsection, these individual PM dates will be modified such that they can be jointly executed to reduce the maintenance cost.

Grouping optimization and maintenance routing

The objective of this step is to find the optimal way to group the above individual PM dates, which maximizes the grouping economic profit in the planning horizon. Moreover, in the GDPS context, the components of a group may be located in the different sites. So, the finding of the optimal maintenance routes that minimize the travel distance of the maintenance team is an important issue to be solved.

For these objectives, the maintenance grouping and routing model as well as optimization methods are presented in the next subsections.

Concept of maintenance group and economic profit formulation

Grouping concept Let's firstly consider a group G k of several components, which are tentatively maintained at their individual PM dates t i m with i ∈ G k . To be jointly maintained, each component of the group may be maintained earlier or latter regarding to its tentative PM date. Let t i m indicate the executed PM date of component i (t i m may differ from t i m ). To perform the components group, the maintenance team needs to go from the maintenance center to all the maintained sites by following a specific route before coming back to the maintenance center. The maintenance route prescribes the sequence of the sites that the maintenance team has to follow. A large number of possible routes usually exist that across all the maintenance sites with different travel distances. Let t G k denote the time that the maintenance team leaves the maintenance center (departure time) to maintain group G k , and I G k (j) = v means that with respect to the route I G k , site j is visited by the maintenance team at the v th order.

• If I G k (j) = 1, the maintenance team will visit first site j after leaving the maintenance center.

The maintenance team will arrive at site j at T AS j = t G k + d 0j , where d 0j is the travel time from the maintenance center to site j. T AS j is also the grouped PM date of components of group G k located at site j: t i m = T AS j . The maintenance team will leave site j at time T LS j = T AS j + i∈G k and site j ω i , and move to the next maintenance site.

• If I G k (j) = v > 1, the maintenance team will visit site j at the v th order. The actual PM dates of components of group G k located on site j are then t i m = T LS q + d qj , where q is the site that the maintenance team has previously visited at the (v -1) th order.

From the above analysis, each maintenance group G k is characterized by the four following parameters: components of group, departure time of the maintenance team t G k , and maintenance route I G k as well as the repairman skill level.

Economic profit of group G k . According to equation 3, the economic profit of group G k , denoted by EP G G k , can be determined as:

EP G G k (t G k , I G k ) = i∈G k C p i -C p G k = ∆S 0 G k + ∆S tr G k (I G k ) -∆H G k (I G k ) -∆C lb G k (7)
Now we have to calculate each part of the economic profit.

• The site-preparation cost saving ∆S 0 G k . This saving exists when several components of the same site are jointly maintained. Let nc k i denote the number of components of group G k located on site i, and ns k denote the number of sites containing, at least, one component of group G k .

If the preparation tasks at a site i are the same for the PM of a component as for a group of components located on the site, S 0 ij = S 0 ik = S 0 i , the site-preparation cost saving can be then calculated by the following equation:

∆S 0 G k = i∈G k S 0 ij -S 0 G k = ns k i=1 S 0 i • (nc k i -1) (8)
• The transportation cost saving ∆S tr G k (I G k ). This saving comes from the reduction of the travel distance of the maintenance team. Let L G k (I G k ) denote the total travel distance when the maintenance team follows the maintenance route I G k . We have:

∆S tr G k (I G k ) = i∈G k R tr i • (L 0j + L j0 ) -R tr G k • L G k (I G k ) (9)
where R tr G k denotes traveling cost rate for the PM of group G k . Without loss of generality, it is assumed that R tr i = R tr G k = R tr . The transportation cost saving can be then rewritten as follows:

∆S tr G k (I G k ) = R tr • i∈G k (L 0j + L j0 ) -L G k (I G k ) (10)
• The penalty cost ∆H G k (t G k , I G k ). This penalty cost occurs due to the changes of the PM dates from the tentative ones t i m to the grouped ones t i m and depends on both the departure time t G k and maintenance route of the repair team. The penalty cost can be calculated as, [START_REF] Wildeman | A dynamic policy for grouping maintenance activities[END_REF]:

H G k (t G k , I G k ) = i m ∈G k C c i • [( age i (t i m ) λ i ) β i -( age i (t i m ) λ i ) β i ] -(t i m -t i m ) • φ * i ( 11
)
where, age i (t) denotes the total operational time of component i until t.

• The labor cost penalty ∆C lb G k can be expressed as:

∆C lb G k = R lb G k ω G k - i∈G k R lb i • ω i (12)
where ω G k is the maintenance duration of group G k . If only one maintenance team is considered, it is then reasonable to assume that ω

G k = i∈G k ω i .
Economic profit of a grouping structure. A grouping structure is defined as a collection of mutually exclusive groups GS = {G 1 , G 2 , ., G ng } satisfying the two following conditions:

G 1 ∩ G 2 ∩ . . . ∩ G ng = ∅ and G 1 ∪ G 2 ∪ . . . ∪ G ng
covers all individual maintenance activities in the planning horizon. The total economic profit of a grouping structure GS can be calculated as:

EP S(GS) = G k ∈GS EP G G k (t G k , I G k ) (13)
EP S(GS) represents the performance of grouping structure GS. The grouping performance depends on grouping structure (GS), departure time of the maintenance team (t G k ) and maintenance route (I G k ) to maintain each group G k of GS.

Maintenance grouping and routing optimization

The issue to be solved at this step is how the optimization tools can be implemented to support the grouping and routing optimization problem, which is defined as:

(GS * , t * G k , I * G k ) = arg max GS,t G k ,I G k G k ∈GS EP G G k (t G k , I G k ) (14)
A combination of the Local Search Genetic Algorithm (LSGA) and Branch and Bound method (BAB) is proposed in this paper as an intelligent search approach to find the optimal grouping structure (GS * ), and the optimal maintenance routes I * G k (Figure 4). It should be noticed that the joint consideration of LSGA and BAB is well adapted for the GDPS problem because it allows reducing the search space of potential solutions (GS * and I * G k ). GA starts by randomly creating a set of possible grouping structures. At each GA's iteration, the grouping structures are compared based on their total economic profit (EP S). The relevant grouping structures with higher economic profits will be saved and improved by applying genetic operations such as crossover, mutation, and elitism. GA is stopped when stopping criteria such as the maximum iteration number is reached.

It should be noted that, at each iteration of GA, the calculation of the total economic profit of a specific grouping structure is not evident. Indeed, with the same grouping structure, the economic profit values can be different depending on the choice of departure times of the repair team, and the choice of maintenance routes. Consider a specific group G k of grouping structure GS, BAB algorithm should be applied to find the optimal maintenance route (I * G k ). Remember that BAB algorithm may provide a set of routes, denoted SI G k , with the same shortest travel distance, but the grouped PM dates of components are not the same (See again the example in Figure 2). That is the reason why the Local Search is integrated into the GA to search the best route among SI G k . The special settings of BAB and LSGA for the maintenance grouping and routing optimization problem are presented in annexes A and B.

Update and rolling horizon

The optimal grouping structure and maintenance routes obtained from the previous step need to be updated according to one of the two following reasons:

1. in presence of a dynamic context: As mentioned before, a dynamic item such as change of maintenance routes, change of transportation capacity or change of components characteristics (see again Section 2.2) may occur with time. In presence of such a dynamic context, the current grouping structure may no longer be the optimal one or even unusable. An adaptive maintenance planning is needed. To integrate such a dynamic context, we need to go back to "Individual planning" step and so on. A detailed illustration is presented in Subsection 5.4.

at the end of the current planning horizon:

A new maintenance planning for the next horizon is needed. New horizon can be constructed based on new required missions' interval. For this purpose, the rolling horizon procedure is used by going back to phase 2 of the optimization scheme to redefine all preventive maintenance activities in the new individual planning horizon and so on. The rolling horizon updating is illustrated in Subsection 5.4.

Numerical examples

The aim of this section is to show how the proposed grouping and routing approach can be used for the maintenance planning and maintenance updating of a GDPS with generated data, and to verify its performance in different maintenance cost settings.

Given data

Consider a typical GDPS in Figure 1 containing 5 geographically dispersed sites, and one maintenance center located far from these sites. The detailed distances between sites and between sites and maintenance center (MC) are given in Table 1. It should be noticed that, in this study, all parameters are given in arbitrary units, e.g., arbitrary time unit (atu), arbitrary distance unit (adu) or arbitrary cost unit (acu).

The average speed in moving of the maintenance team is AS = 25 (adu)/(atu). The travel time then can be easily determined by dividing the travel distance by the average speed, i.e.

d ij = L ij /AS.
The transportation cost rate is considered to be the same for all components R tr i = R tr , and is equal to 18 (acu/adu). For each site, 3 main critical components are considered in this study. The main characteristics related to the components site, the down time cost rate (R dt j ) and the preparation cost (S Site j ) are

given in Table 2. The data related to each component such as the shape and scale parameters of Weibull distribution, the spare part cost, the CM cost, PM time, the age at t begin as well as the repairman skill level are all reported in Table 3.

Finally, the labor cost rates R lb are fixed at 100, 200, 300 (acu) regarding to the required skill levels l i = 1, l i = 2 and l i = 3 respectively.

Optimal maintenance grouping and routing

The proposed grouping and routing approach is applied for the maintenance grouping and route scheduling of the considered GDPS. The results obtained from the individual maintenance planning, grouping maintenance planning and maintenance routing are all reported in the following paragraphs.

Individual maintenance planning. The PM is assumed to be carried out separately for each component of the GDPS. The maintenance team has to go to the maintained site and go back again each time whenever a component of the site is preventively maintained. By using the equations 1, 4, 5, 6, the transportation cost (S tr i ), the optimal PM cycle (x * i ) and the minimum maintenance cost rate (φ * i ) of each component are calculated and shown in Table 3. Based on the obtained PM cycle and given values of t e i , all individual PM dates are identified and reported in the same table.

In this example, each component is maintained only once in planning horizon P H = [0, t 5 1 + ω 5 ] = [0, 5500.5] (atu). If this individual maintenance plan is used, the average maintenance cost that has to be paid is equal to:

φ individual sys = 15 i=1 φ * i = 56.2 (acu) (15)
It should be noted that the transportation and setup costs respectively take 18.82% and 19.06% of the above cost. The reduction of the two costs are then crucial from the economic point of views.

The grouping maintenance is a promising solution to solve this problem.

Grouping maintenance planning. In order to reduce the setup and transportation costs, the individual PM activities determined in the previous phase are grouped. The joint use of LSGA and BAB is applied to find the optimal grouping structure. The obtained results are shown in Table 4 and Figure 5. The optimal grouping structure contains three groups. The components in each group are optimally selected to satisfy a number of factors such as the saving of transportation cost, the penalties related to PM execution and labor costs. Among these factors, the transportation cost saving takes the most important part (the highest value), and has the strongest impact on the composition of the groups. Indeed, the results in Figure 5 show that even the individual PM dates of components 13, 14, 15 of site 5 (the farthest site from the maintenance center) are not close to each other, these components are still grouped in a same group (group G 3 ). This is because the grouping of these components can help to significantly reduce the transportation cost. For this reason, the individual PM dates of components in an optimal group are not necessary to be close to each other as underlined by the other existing papers focusing on the grouping maintenance of centralized multi-component systems [START_REF] Wildeman | A dynamic policy for grouping maintenance activities[END_REF][START_REF] Do | Dynamic grouping maintenance strategy with time limited opportunities[END_REF]. From the economic point of view, the grouping maintenance plan helps to reduce 69.26% travel distance of the maintenance team as well as the transportation cost, and save up to 68.24% setup cost when compare to the individual maintenance. The reduction of travel distance is very important since it is not only meaningful from the economic point of view, but also sustainability one (reduce energy consumption, travel-related risks, environmental negative impacts). Along with the above advantages, the grouping maintenance also leads to some disadvantages and penalties. In fact, it makes the labor cost and the CM cost increase 14.70% and 259% respectively. Overall, the grouping maintenance helps to save up to 9.24% total maintenance cost when compare to the individual one.

G k of GS * ∆S tr ∆S Site ∆C lb H EP G EP S G 1 = {3 1 , 6 1 , 9 1 , 12 1 } 7722 0 0 1385.7 6336.3 28592.2 G 2 = {1 1 , 2 1 , 4 1 , 5 1 , 7 1 , 8 1 , 10
The average maintenance cost of the system, when the individual PM activities are grouped, is:

φ grouping sys = φ individual sys - EP S t end = 51.0 (acu) (16)
Maintenance route scheduling. To guarantee the above grouping performance, the maintenance team has to respect the optimal maintenance routes and the optimal departure times reported in Table 5.

Table 5: Optimal maintenance itineraries of the maintenance team

G k of GS * Departure time (t * G k ) Optimal maintenance route I * G k L * G k G 1 = {3 1 , 6 1 , 9 1 , 12 1 } 3649.4 MC → 2 → 3 → 4 → 1 → MC 345 G 2 = {1 1 , 2 1 , 4 1 , 5 1 , 7 1 , 8 1 , 10 1 , 11 1 } 3972.0 MC → 2 → 3 → 4 → 1 → MC 345 G 3 = {13 1 , 14 1 , 15 1 } 4585.6 MC → 5 → MC 304
According to the obtained results shown in Table 5, for example, to perform the PM of group G 1 , the maintenance team has to start from the maintenance center at 3649.4 (atu), then travels across the sites 2, 3, 4, 1, and returns to the maintenance center. The total travel distance of the round trip is equal to 345 (adu). When compared to the individual maintenance, the total travel distance is saved up to 55.42%. It should be noted that this optimal maintenance route is determined by the two following steps: the BAB is firstly looking for the shortest travel route (MC-2 -3 -4 -1-MC), the LSGA then decides in which direction the maintenance team has to go on. The saving of the group equals 6336.3 and 6291.2 with respect to the two directions (MC → 2 → 3 → 4 → 1 → MC) and MC (← 2 ← 3 ← 4 ← 1 ← MC) respectively. The final decision is then to go on the first direction.

Consider group G 2 , with the same optimal maintenance route as group G 1 , the travel distance as well as transportation cost can be saved up to 77.71%. Finally, for group G 3 containing 3 components of the same site number 5, the maintenance team has to go to the site only one time instead of three.

The travel distance and transportation cost are then reduced about 66.67% thanks to the grouping of these PM activities.

Sensitivity analyses

As mentioned before, the main intent of grouping maintenance is to save the transportation and setup costs. The grouping performance then strongly depends on the transportation cost rate and site-preparation cost.

Sensitivity analysis to the transportation cost rate

The aim of the subsection is to study the impact of transportation cost rate (R tr ) on grouping optimization process. To do this, the proposed grouping strategy is applied for different cases where the transportation cost rate is varied from 10 to 100 (acu), while the other given data remain unchanged.

The case where R tr = 0 is not considered because it rarely occurs in real life.

Grouping maintenance updating in dynamic contexts

The objective of this subsection is to present how the grouping maintenance plan can be updated when dynamic contexts occur. For this purpose, a dynamic context n o 1 "Change of maintenance routes" (see again Section 2.2) is considered. Assume that the optimal grouping solution presented in Table 5 is selected. After the maintenance of group G 1 , at 3849.4 (atu), the direct road between the maintenance center and site 5 is interrupted for a long period due to road maintenance activities. As a consequence, to go to site 5 from the maintenance center, the maintenance team has to travel on another road via site 2 with a longer distance. The travel distance of the new road is L 05 = L 02 + L 25 = 210 (adu). This means that a new logistic dependence between sites 2 and 5 occurs. In the presence of this situation, the current grouped maintenance planning and routing may be no longer optimal and need to be updated as soon as possible. To do this, the proposed grouping strategy is re-executed. The optimization process starts from the "Individual planning" step with a new horizon, namely H2, for which the beginning is equal to t begin H2 = 3849.4 (atu) and so on. At the end of the process, a new optimal grouped maintenance planning is provided and sketched in Figure 8. G i Hj indicates the group i of the horizon j. The maintenance routing results are shown in Table 8.

Table 8: Optimal maintenance itineraries after updating

G k of GS * t * G k I * G k L * G k G 1 = {1, 2, 4, 7, 10, 11} 3859.4 MC → 2 → 3 → 4 → 1 → MC 345 G 2 = {5, 8, 13, 14, 15} 4662.5 MC → 2 → 5 → 3 → MC 491 G 3 = {3, 6, 9, 12} 8370.6 MC → 1 → 4 → 3 → 2 → MC 345
The new results underline that components 1, 2, 4, 7, 10, 11 are maintained sooner than before, while the maintenance of components 5 and 8 are postponed and grouped to group G 2 H2 . From the logistic point of view, the new configuration of the group is reasonable. In fact, given the interruption of the direct road between the maintenance center and site 5, the maintenance team now starts from the maintenance center and then directly goes to site 2 instead of site 5. The solution with the direct connection between the maintenance center and site 5 no longer exists in the new grouping and routing solutions.

Conclusions

In this work, a dynamic maintenance grouping and routing for a geographically dispersed production system (GDPS) is proposed. The proposed approach provides simultaneously an optimal grouped maintenance planning and an optimal maintenance routing that the maintenance team has to follow during their maintenance works. The optimal solutions are reliable since the interactions between the maintenance planning and routing are jointly studied and integrated in the optimization process by proposing a combination of LSGA and BAB methods. Moreover, economic and geographical dependencies which have significant impacts on maintenance planing and routing are investigated and integrated in the proposed global maintenance model. Finally, several dynamic contexts which often occur in reality are also studied and make the proposed maintenance approach more flexible for real applications. To highlight the use and the advantages of the proposed grouping approach, a numerical example of a GDPS system consisting of 15 components located in five different sites is investigated. The obtained results show that the proposed maintenance strategy can help to reduce significantly the transportation and the preparation costs. The grouping performances have also been studied through different sensitivity analyses with different settings of the transportation cost rate and site-preparation cost. The dynamic grouping is then recommended for the maintenance planning of GDPS with high transportation and preparation costs from an economic point of view. Moreover, the ability to update the maintenance grouping and route plans in presence of a dynamic context. This paper extends the development of our research in the framework of a grouping maintenance and routing for a GDPS system which has been presented partially in [START_REF] Nguyen | A dynamic grouping maintenance strategy for geographically dispersed production systems[END_REF]. Our future research work will focus on the further investigations on the grouping maintenance planning and maintenance routing of GDPS with consideration of other dependencies such as stochastic and functional dependencies between components and sites. The BAB algorithm iteratively solves the maintenance routing problem by considering one level at a time starting from the top of the search tree (level 0) to the last level (level ns k + 1). In Figure 9, we consider the maintenance routing of group G k containing components 1, 2, 4, 5, 7, and 8 located in three different sites 1, 2 and 3. The BAB is done from the maintenance center (level 0) to the last level (level 4).

At a considered level v, the following steps are done:

• Estimate lower bound value of each node q ∈ HN v . The lower bound value of node q, denoted LB(q), indicates the minimum logistic cost (minimum travel distance), that we can obtain if we decide to travel across the node q.

• Select a node for expansion. Let EHN v be the set containing all nodes of level v (HN v ) and all unexpanded nodes of the previous levels. The node with the lowest value of the lower bound among all nodes in EHN v (the most promising node) is selected for the expansion.

• Expand the selected node. The node expansion is to identify all possible nodes that the maintenance team can directly travel from the selected node. The expanded node is called parent node, and the generated nodes are child ones. The BAB process then jumps to the level of the child nodes.

The only one problem now is how to estimate the lower bound value. Firstly, let L uv denote the that the number of components in a group cannot be bigger than the capacity of transportation vehicles (m sp ).

• Step 3: Evaluating the performance of grouping structure. The performance of a grouping structure in the population is assessed by its total profit economic EP S. To do this, for a group G k , the BAB is firstly applied to find the set of itineraries with the shortest distance (SI G k ). At the beginning, a route in SI G k is randomly chosen for each group G k . Based on the grouping structure and all selected routes, the grouping economic profit can be evaluated as follows:

EP S(GS) =    G k ∈GS EP G G k (t G k , I G k ) if ∀k, nc k ≤ m sp -∞ if ∃k, nc k > m sp
where, nc k is the number of components in group G k .

• Step 4: Elitism. The two best grouping structures of the current population are directly copied to the next generation in order to protect them from the high level of disruption.

• Step 5: Crossover. Crossover is performed to combine a pair of parent grouping structures to generate better grouping structures. To do this, two PM activities are firstly randomly chosen as the crossover points. And then, the elements between these points of the selected parent grouping structures are exchanged (see Figure 10A). The probability that the crossover is done for a pair of grouping structures is around 80%. • Step 6: Mutation. Mutation helps to prevent LSGA from capturing local optima. For each selected grouping structure, a maintenance activity of a group is randomly selected and then moved to another group (see Figure 10B). Mutation probability should be small to prevent LSGA from random search. It is usually chosen from 0.1% to 1%.

• Step 7: Local search. For each grouping structure in the new generation, Local Search is applied to choose and evaluate several routes in SI G k . The best route is saved for the next generation.

• Step 8: Stopping. LSGA is stopped when the maximum number of generations is reached.

Figure 1 :

 1 Figure 1: A typical GDPS containing 5 production sites and a centralized maintenance center

  2a and 2b, two different maintenance routes with the same travel distance can lead to different arrival times, in other words, different executed PM dates. The latter may impact the penalty cost which depends strongly on the change of executed PM dates.

Figure 2 :

 2 Figure 2: Impacts of maintenance routes on the PM dates and travel distance

Figure 3 :

 3 Figure 3: Dynamic grouping and routing for the maintenance of GDPS

Figure 4 :

 4 Figure 4: The principle of LSGA for the maintenance grouping and routing optimization problem

Figure 5 :

 5 Figure 5: Individual maintenance plan and optimal grouped maintenance plan

5 Figure 6 : 4 Figure 7 :

 5647 Figure 6: Sensitivity analysis of grouping economic profit to transportation cost rate

Figure 8 :

 8 Figure 8: Grouping maintenance updating in the presence of a road interruption

Figure 9 :

 9 Figure 9: Search tree for the group G k = {1, 2, 4, 5, 7, 8}

Figure 10 :

 10 Figure 10: Example of crossover and mutation operators.

Table 1 :

 1 Travel distances between the production sites and their maintenance center

	Site MC	1	2	3	4	5
	MC	-	80	56 120 131 152
	1	80	-	100 98	87 250
	2	56	100	-	68 103 154
	3	120	98	68	-	54 161
	4	131	87 103 54	-	209
	5	152 250 154 161 209	-

Table 2 :

 2 Components, downtime cost rate and site-preparation cost of each production site

	Site	1	2	3	4	5
	Component 1, 2, 3 4, 5, 6 7, 8, 9 10, 11, 12 13, 14, 15
	R dt j	295	315	348	364	206
	S Site j	200	160	120	80	160

Table 3 :

 3 Components' data and individual maintenance optimization results

	Component	λ i	β i	C sp i	C c i	w i	t e i	l i	S tr i	x * i	φ * i	t i 1
	1	2497 2.86 1745 568 10 1401 1	2880 5229.2 2.5727 3828.2
	2	3258 2.76 2526 672 16 2730 2	2880 7868.4 2.6872 5169.4

Table 4 :

 4 Optimal grouping structure and its economic profit

Acknowledgements

The authors would like to thank the Government of Vietnam for its partial financial support to this research.

The evolution of grouping economic profit when the transportation cost rate increases from 10 to 100 is plotted in Figure 6. The obtained results show that the bigger the transportation cost rate is, the higher the grouping economic profit is given. The grouping maintenance is therefore recommended for the GDPS with high transportation cost rates.

In addition to the grouping performance, the optimal grouping structure is also studied and reported for different values of transportation cost rate in Table 6. From the table, we can observe that when the transportation cost rate increases, the optimal grouping structure is configured such that the saving of the travel distance is maximal.

Sensitivity analysis to the site-preparation cost

The same study is carried out by varying the site-preparation cost from 0 to 500 (acu). Note that in this study, the site-preparation cost is considered to be the same for all sites, for all components, and denoted by S 0 . The proposed grouping strategy is applied for each value of the site-preparation cost.

The obtained results are presented in Table 7 and Figure 7.

Table 7: Sensitivity analysis of grouping structure to site-preparation cost

The same conclusion as in the case of the transportation cost rate can be deduced from the obtained results. The bigger the site-preparation cost is, the higher the grouping performance is. The

A Implementation of Branch and Bound

The most natural way to present the algorithm is to use search tree language. An example of the search tree for TSP with three sites and one maintenance center is shown in Figure 9. In the Figure ,   the root node (maintenance center) at the top of the tree represents the maintenance center, the nodes at level one represent all the sites that could be visited first (node 1, node 2, and node 3), the nodes at level two represent all the sites that could be visited in second (node 4, node 5, node 6, and node 7), etc. Generally, the horizontal set of all nodes at level v is denoted by HN v . Otherwise, the vertical set of nodes, denoted V N a→b , represents an entire route (a ≡ b ≡ 0) or a part of route from node a to node b. For example, in Figure 9, V N 0→8 denotes the part of route where the maintenance team travels from the maintenance center to node 3, node 6, and node 8 consecutively. distance between two sites u and v. L uv = +∞ if there is no direct route connecting the two sites.

The lower bound represents the smallest travel distance, that the routes traveling across node q can obtain, is calculated as:

• L 0→q is the total travel distance of the planned part of the routes from the maintenance center to node q. Consider node 2 in Figure 9, we have L 0→2 = L 02 .

• L q→0 is the expected total travel distance of the unplanned part of the routes from node q to the maintenance center. Since the route from node q to maintenance center is still unknown, the calculation of its total distance has to be done approximately. Consider a site u that the maintenance team has not yet visited u / ∈ V N 0→q , it is clear that the shortest distance to go to site u is L min u = min v∈U L vu . U is the set of sites in which the maintenance team could be before visiting site u. Consequently, we have:

For example, consider again node 2 in Figure 9, the maintenance team has already visited site 2. The expected travel distance of the unplanned part is:

After application of the above BAB, we obtain the optimal routes with the shortest travel distances for each group of grouping structure. However, the direction to go in each route has not been decided yet.

B Implementation of Local Search Genetic Algorithm

In this section, the main steps of LSGA is detailed knowing that LSGA is implemented to find not only the optimal grouping structure, but also the optimal maintenance routes. The principle of LSGA is summarized in Figure 4.

• Step 1: Coding. This step is aiming at defining the way to introduce a grouping structure in LSGA. A grouping structure is here represented by an array M . M (i m ) = j if maintenance activity i m is in group j.

• Step 2: Generating a population of grouping structures. LSGA creates randomly an initial population of grouping structures. To generate a grouping structure, the number of groups is randomly chosen in [1, n]. Next, all PM activities are randomly put into the chosen groups. Note


Xuan-Qui Pham

Naresh Kumar

Minh-Huong Ha-Thi

Isabelle Leray
email: isabelle.leray@ens-paris-saclay.fr

Sensitive and selective detection of uranyl ions based on aggregatebreaking mechanism

A highly selective fluorescent sensor based on salicylaldehyde azine derivative for the detection of uranyl cation was developed. The aggregation induced emission characteristics of compounds S1 and S2 were investigated and a strong emission of these derivatives was observed upon aggregation in organoaqueous solvent. The emission of these aggregated forms was found to be effectively quenched by uranyl cation. In water/acetonitrile (60/40; v/v), the aggregates of S2 gave the most obvious quenching effect. The effect of uranyl was shown to be destructive rather than constructive to the aggregation of the salicylaldehyde azine derivatives. An aggregate-breaking process was proposed to explain the destruction of the aggregates by the complexation with uranyl cation. S2 can be used as an efficient fluorescent sensor for uranyl cation in aqueous solvent. The sensor showed good selectivity towards uranyl and with a low detection limit up to ppb scale.

Introduction

Uranium, a radioactive element has been extensively used in the nuclear industry. The fissile isotope 235 U plays a principal role in the development of nuclear power plants and nuclear weapons, with 235 U being the first material pursued in the development of the atomic bombs deployed during World War II.

Atomic weapons and fissile materials are ongoing concerns for human safety. [1] 238 U has been used in advanced nuclear reactors as a source material for creating plutonium-239, which can in turn be used as a nuclear power source. Increasing human activities with uranium have consequently led to widespread pollution and environmental impact. The uranyl ion (UO 2 2+ ) is a naturally occurring oxycation found in minerals and has been reported to cause birth defects and immune system damage. [2] The maximum allowable concentration of uranyl in drinking water has been defined as 20 ppb by the World Health Organization. Keeping in view the importance of the uranyl ion, sensitive and selective protocols for the detection of these ions are in great demand. [3] Analytical techniques such as potentiometry, X-ray fluorescence, ICP-MS, and ion-chromatography have been used for uranyl detection. [4][5][6][7][8] Alternatively, absorbance or emission-based optical sensors can also provide unique advantages. For example, several inorganic fluorescent sensors have been reported such as phosphate or pyrophosphate salts. [9][10][11] One of the disadvantages is that they are often interfered by other cations at low temperature due to crystallization.

Several organic fluorescent sensors based on 2,6-pyridinedicarboxylic acid, [12] quinoxalinol salen ligands, [13] cyclic peptide, [14] clopidogrel, [15] polymer containing amidoxime, [16] and salicylaldehyde azine [17] were reported to detect uranyl cations up to ppm or ppb scale. However, the common problems of organic fluorescent sensors are a lack of selectivity from other lanthanides and the limitation of working in aqueous solution. [18][19][20][21][22][23][24] Our research group has been working on the design and the synthesis of fluorescent sensors for ions of biological or environmental significance. [25, 26][27-29]. In continuation of this work, we herein report two analogous compounds (S1 and S2). Their photophysical and complexing properties for uranyl ions have been investigated. The presence of nitro groups on aromatic rings in the S2 compounds might have an effect on the electron density at hydroxy and Schiff-base centers, and on the aggregation behavior in organoaqueous media. S2 was shown to be a highly selective and sensitive sensor for UO 2 2+ detection in aqueous solvent.

Figure 1. Structure of studied salicylaldehyde azine derivatives.

Experimental section

Synthesis

General procedure

All reagents were purchased from Aldrich and were used without further purification. 1 H and 13 C spectra were recorded on a JEOL-FT NMR 400 MHz spectrophotometer using CD 3 OD/DMSO-d 6 as solvent and tetramethylsilane as internal standard. Data are reported as follows: chemical shift in ppm (δ), multiplicity (s = singlet, d = doublet, t = triplet, m = multiplet), coupling constants J (Hz).

N,N/-bis(salicylidene)hydrazine) S1

Compound S1 was synthesized via a previously reported procedure. [30] Firstly, salicylaldehyde (500 mg, 4.098 mmol) was dissolved completely in 40 mL ethanol. Hydrazine hydrate (102 mg, 2.041 mmol) solution in ethanol (20 mL) was then added over at least 20 min. After that, the resulting reaction mixture was refluxed for 4 hours. After cooling to room temperature, a yellow solid was formed, filtered and washed with cold ethanol to give pure product in 90% yield.

UV-visible absorption spectroscopy

For all absorption spectroscopy measurements, Hellma quartz cells with an inner path length of 10 mm were used. Double beam Varian Cary-4000 and Cary-5000 spectrophotometers were used to record the UV-visible absorption spectra.

Steady state fluorescence spectroscopy

For all fluorescence spectroscopy measurements, Hellma quartz cells with an inner path length of 10 mm were used. Corrected emission spectra were obtained on a Jobin-Yvon SPEX Fluoromax-4 spectrofluorometer.

Photophysical and complexation studies

For studies in dilute solution, compounds S1 and S2 were dissolved in acetonitrile with [S1] = 5 µM and [S2] = 7 µM. For AIE studies, water was added as a second, poor-soluble solvent was added and increased gradually by each 10%, from 0% to 100%. The samples were put in the dark under a luminescence source to quickly evaluate their emission intensity. The fluorescence quantum yield of each sample was calculated using quinine sulfate in sulfuric acid 0.5 N as a reference. [32] In all experiments, the ligands were excited at 365 nm and fluorescence spectra was recorded at 550 nm. All spectroscopic data of the complexation were recorded after one hour in the dark to make sure that the aggregation behaviors were completed.

For selectivity studies, the detection limit towards uranyl was calculated based on the quenching response of S2 at a small concentration range of uranyl (0-3 µM). The following equation was used to calculate the detection limit: c limit = 3s / k, where s represents the standard deviation of S2 solution, c limit is the limit of detection and k is the slope of the working curve.

The concentration of S2 was 7 µM. All samples were excited at 365 nm and fluorescence intensities were recorded at 550 nm. The concentration of uranyl and competing cation were 20 µM and the reaction time was also one hour.

Dynamic Light Scattering

The sizes of aggregates were obtained by DLS by means of an analyzer Zetasizer Nano ZS ZEN 3600.

There is a 4 mW He-Ne laser, operating at 633 nm, and a photomultiplier detector capable of collecting backscattered light at 175°. The temperature during analysis was 25 °C.

Measurements of intensity were performed in a multi-acquisition mode with automatically adjusted correlograms. Average sizes of aggregates and distribution widths were calculated by fitting the correlogram with a cumulants algorithm.

Scanning Electron Microscopy

Electron images were obtained by The Hitachi S-3400N equipped with Secondary and Backscatter Electron Detectors. There is a Deben Peltier Coolstage to control moisture loss in low vacuum mode.

Results and discussion

Synthesis

Compound S1 and S2 were synthesized according to previously reported procedures [30,31] and can be obtained in high yields by the condensation of salicylaldehyde and 5-nitro salicylaldehyde, respectively, with hydrazine in ethanol.

Scheme 1. Synthesis of sensors S1 and S2.

Aggregation-induced emission properties

Scheme 2. Structure of S1 with free C-C; N-N rotation (left) and its emissive aggregate in water (right).

An emissive aggregate / nanosuspension was formed immediately after the injection of S1 solution in acetonitrile to water (Scheme 2), which might suggest that S1 has aggregation induced emission (AIE) characteristics in water/acetonitrile solution. In fact, in water/acetonitrile with a percentage of water less than 80%, S1 (5 µM) was well dispersed in the solution. Consequently, the molecules were conformationally flexible along with a free intramolecular rotation of carbon-carbon that leads to nonradiative decay processes. In this condition, fluorescence was quenched so that almost no emission was observed. When the percentage of water reached 80% or more, S1 molecules began to aggregate and free intramolecular rotation was restricted. Consequently, the non-radiative decay processes were hampered and the fluorescence intensity showed a corresponding increase (Figure and figure 3). Similar behavior was also reported for this molecule in the water/ethanol mixture. 4). This can be rationalized by the lower solubility of S2 due to the presence of two nitro groups.

The viscosity of a solution, which can be affected by temperature, can modify the fluorescence of a compound. To gain more insight into this effect, temperature dependence of the fluorescence properties of compound S2 was studied. For this purpose, propylene glycol was used to increase viscosity withdecreasing of temperature without crystallization. At low temperature, as the solvent becomes more viscous, the rotation of intramolecular bonds would become restricted. S2 and a reference fluorophore, BODIPY (Fig. S4), were dissolved in propylene glycol to monitor the fluorescence change with decreasing temperature. Fluorescence spectra of S2 during temperature variations and its comparison with temperature dependent fluorescence changes of BODIPY are shown in Figures 4 and5, respectively. Fluorescence spectra of BODIPY and S2 showed a shift to shorter wavelength as temperature decreased. Such blue shifts of fluorophores at lower temperature were reported previously. [33][34][35] Moreover, fluorescence enhancement by decreasing temperature was observed in both cases. From room temperature to -100°C, fluorescence intensity of BODIPY at 530 nm was increased about 2 times while fluorescence intensity of S2 at 520 nm was increased more than 10 times. The restriction of intramolecular rotation in S2 might explain this difference. The decrease of temperature could reduce the molecular collisions and the non-radiative pathways. Once the temperature became lower than the freezing point of propylene glycol (-59°C), rotational motion was mostly prevented, particularly for the case of AIE dyes like S2. The difference in fluorescence behavior between two molecules gives a clear confirmation of the effect of molecular rotation on the fluorescence characteristics of S2, where the fluorescence was dramatically enhanced in a rigid medium.

Complexing properties of sensors with the uranyl cation

The sensors were expected to form a complex with uranyl cations owing to the presence of nitrogen and oxygen atoms in the molecular scaffold. The complexation can disturb the aggregation behavior and have a significant influence on the fluorescence of the AIE dyes. Fluorescence changes of S1 (5 µM) and S2 (7 µM) in different water/acetonitrile mixtures were evaluated by adding an excess amount of uranyl cation (50 µM). All spectroscopic data were recorded after one hour in order to complete the complexation.

The addition of uranyl cation to well dispersed solutions of S1 and S2 did not enhance the fluorescence. However, fluorescence of S1 and S2 aggregates was partially quenched upon addition of uranyl after one hour. The fluorescence response of S1 and S2 aggregates at different water fractions with uranyl cation is shown in Figure 3 and Figure 4, respectively. A smaller fraction of water granted no significant fluorescence changes as aggregates were non-emissive in dilute solution. [S1] = 5 µM, λ exc = 365 nm. The addition of UO 2 2+ to S1 aggregates results in slight quenching of fluorescence as shown in Figure 3.

Similarly, a small fluorescence decrease was also observed for S2 aggregates at 80% water fraction. However, uranyl complexation with S2 aggregates at 60% water in acetonitrile caused significant fluorescence quenching (Figure 4). It should be noted that S2 possesses two electron withdrawing -NO 2 groups which stabilize phenolate form of S2 in solution and the complexation with uranyl is therefore more efficient. It might be a reason that efficient fluorescence quenching was observed for S2 compared to that for S1. As the response of S2 towards uranyl is more pronounced, we decided to use this ligand for the detailed complexation studies.

Subsequently, complexation kinetics of S2 with uranyl cation (10 µM) was investigated in water/acetonitrile (60/40; v/v). Diffusion in the visible region (Figure 5) which belongs to the aggregates slowly disappeared, implying that the aggregates were gradually destroyed. Interaction of uranyl with the aggregated form of S2 favors the release of individual molecules of S2 as indicated by the gradual increase of absorbance at 365 nm (Figure 5). The measured absorbance at 365 nm reached equilibrium after 30 minutes, suggesting that the minimum time to complete the complexation is about 30 minutes.

The complexation with uranyl was also performed in HEPES buffer/acetonitrile (pH = 7, 60/40; v/v). In comparison to water/acetonitrile system, a similar fluorescence response was noticed in this mixture, showing that the sensor can also work the same way in buffer solution. (Figure S2). Fluorescence titration of S2 with uranyl cation was also performed. Uranyl nitrate was added to aggregates of S2 in water/acetonitrile mixture (60/40; v/v).

Figure 6 shows the changes in fluorescence spectra and intensities at 550 nm as a function of uranyl concentration. The fluorescence titration data was consistent with the aggregate-breaking mechanism as discussed above. The addition of 10 µM of uranyl seemed to destroy the aggregates and considerably quenched the fluorescence. An aggregate-destructive mechanism upon adding uranyl cation was then proposed as shown in Figure 7. Complexation of S2 molecules with uranyl cation actually destroyed the formed aggregates to solubilize the molecules in the solution. Since the required quantity of uranyl for saturated titration was reasonably close to one equivalent, is it possible that the stoichiometry of S2uranyl complex is 1:1.

Sensitivity

The detection limit towards uranyl was calculated based on the response of S2 over a small concentration range of uranyl cation (Figure 12). The following equation was used to calculate the detection limit:

Where s represents the standard deviation of S2 solution, c limit is the limit of detection and k is the slope of the working curve. The limit of detection was found to be 6.2 ppb (23 nM), consistent with the ppb level of some other reported uranyl sensors [15,16]and exceeding others. [12,14]

Selectivity

In order to evaluate the selectivity of sensor S2 towards uranyl, fluorescence response was measured in the presence of other possible competing cations. It is to be noted that lanthanides have been well known as interfering cations in the nuclear industry analysis. For that reason, three lanthanides (La 3+ , Ce 3+ and Yb 3+ ) and other common cations (K + , Ca 2+ , Mg 2+ , Cd 2+ , Zn 2+ , Hg 2+ , Fe 3+ , Al 3+ ) were tested. To avoid the hydrolysis of metal cations, HEPES (pH 7.0) solution was used instead of pure water. In HEPES (pH 7.0)/acetonitrile solution, the absorbance or emission profile of S2 as well as the response with uranyl was very close with that in water/acetonitrile system (Figure S1 andS2). All samples were excited at 365 nm and fluorescence intensities were recorded at 550 nm. As shown in Fig. 13, the effect induced by an addition of 20 µM of competing metal ions were negligible. Upon the addition of 20 µM of uranyl ions, the full response was obtained, indicating that no significant interference results from the presence of these ions. In summary, sensor S2 can efficiently detect uranyl in the presence of a wide range of lanthanides and other common cations for practical application.

Conclusion

A series of salicylaldehyde azines have been synthesized and studied. In organoaqueous media, compounds S1 and S2 exhibited strong AIE characteristics. Due to oxygen and nitrogen binding sites, the molecules could form complexes with uranyl cations and quench the fluorescence. In the present research, it is to be noted that the effect of uranyl is somewhat more destructive rather than constructive to the aggregation. The strongest quenching effect was observed for the aggregates of S2 in water/acetonitrile (60/40; v/v). The fluorescence quenching is explained by an aggregate-breaking mechanism, as the fluorescent aggregates were destroyed by the complexation with uranyl cation. The proposed mechanism was further supported by DLS and SEM experiments. Sensor S2 shows good selectivity towards uranyl over lanthanides and other common cations, and allows a detection limit of 6.8 ppb for uranyl ions.

Figure 2 Figure 3 .

 23 Figure 2 Emission spectra of S1 (5µM) (left) and S2 (7 µM) (right) with different fraction H 2 O/CH 3 CN (v:v), λ exc = 365 nm

Figure 4 .

 4 Figure 4. Fluorescence spectra of S2 (in propylene glycol) when temperature decreases gradually to -100°C. [S2] = 10 µM. λ exc = 365 nm.

Figure 5 .

 5 Figure 5. Comparison of fluorescence spectra changes of reference BODIPY (Blue) and S2 (red) in propylene glycol at different temperatures. [S2] = 10 µM, λ exc = 365 nm, λ obs = 520 nm. [BODIPY] = 10 µM, λ exc = 510 nm, λ obs = 530 nm.

Figure 3 .

 3 Figure 3. Response of S1 aggregates in water (left) and in water/acetonitrile 9:1 (right) with UO 2 2+ (50 µM).

Figure 4 .

 4 Figure 4. Response of S2 aggregates in water/acetonitrile 8:2 (left) and 6:4 (right) with UO 2 2+ (50 µM). [S2] = 7 µM, λ exc = 365 nm.

Figure 5 .Figure 6 .

 56 Figure 5. Kinetic of absorbance of S2 (7 µM) in water/acetonitrile (60/40; v/v) upon adding uranyl 10 µM.Inset: absorbance at 365 nm over time.

Figure 7 . 2 2+Figure 11 .

 7211 Figure 7. Proposed quenching mechanism of S2 upon uranyl addition.

Figure 12 .

 12 Figure 12. Calibration curve of S2 (7 µM) with small range of [Uranyl] in water/acetonitrile (60/40; v/v). λ exc = 365 nm. Fluorescence intensities were recorded at 550 nm.

Figure 8 .

 8 Figure 8. Selectivity of S2 towards uranyl over other metal ions. Reaction time is one hour. Excitation wavelength was 365 nm and all fluorescence values were recorded at 550nm. [S2] = 7 µM, [UO 2 2+ ] = [competing cations] = 20 µM. Uranyl source: uranyl nitrate.

2.2. Spectroscopic measurement 2.2.1 Solvents and Salts. Acetonitrile from

	1 H NMR (CD 3 OD, 400 MHz): δ =
	11.40 (s, 2 H), 8.71 (s, 2 H), 7.38 (m, 4 H), 7.05 (d, 2 H), 6.97 (t, 2 H) ppm.
	N,N/-bis(5-nitro-salicylidene)hydrazine S2
	Compound S2 was synthesized using a similar procedure.[31] 2-hydroxy-5-nitrobenzaldehyde (500 mg,
	2.99 mmol) was dissolved in 30 mL ethanol, following by the addition of hydrazine hydrate (74.8 mg,
	1.50 mmol) solution in 15 mL ethanol. After that, the resulting reaction mixture was refluxed for 4
	hours. After cooling to room temperature, a yellow solid was formed, filtered and washed with cold
	ethanol to give pure product in 91% yield. 1 H NMR (DMSO, 400 MHz): δ = 9.08 (s, 2 H), 8.70 (d, 2 H),
	8.27 (dd, 2 H), 7.16 (dd, 2 H) ppm.
	Aldrich (spectroscopic grade) was employed as
	solvent for absorption and fluorescence measurements. Cations from Aldrich or Alfa Aesar,
	were of the highest quality available and vacuum dried over P 2 O 5 prior to use.

Acknowledgements

This work was supported by the National Research Agency program "DECRET" (ANR-13-SECU-0001).