Francisco Javier Carrillo
email: francisco.carrillo@enit.fr

Frédéric Rotella
email: rotella@enit.fr

Some contributions to estimation for model-free control

Keywords: Parameter estimation, model-free control, adaptive ultra-local model control

This paper describes some contributions to Model Free Control (MFC). For example, its properties about disturbance rejection are analyzed. It is also shown that it is possible to propose new estimation methods for an extended version for MFC using time-varying parameters of an ultra-local model. In particular it is emphasized that these parameters can be estimated using alternative and standard adaptation methods. An application to a thermal process model illustrates one specific point of the new adaptive approach.

INTRODUCTION

During the last decade a new control strategy has been proposed in Fliess and Join (2008) and [START_REF] Fliess | Revisiting Some Practical Issues in the Implementation of Model-free Control[END_REF]. This control strategy is based on two specific features. On the one hand the use of an ultra-local model given by: [y(t)]

(n) = F (t) + α(t)u(t),

where :

• y(t) and u(t) are the scalar output and input of the system; • n is the derivation order of the proposed ultra-local model. Usually, and for practical applications, n = 1 or 2 is sufficient to describe during a short time period the system behavior; • F (t) is a time-varying function which transforms as a disturbance term the higher order terms and the complexity of the model; • α(t) is a time-varying gain. The advice given in papers on model-free control is to consider constant this gain and choose its value such that y (n) (t) and that αu(t) are "of the same magnitude". Let us mention here that this standpoint leads to fruitful practical applications. See for instance the concrete applications listed in [START_REF] Fliess | [END_REF] and the references therein. Nevertheless, one of the objective of our paper is to consider a time dependency of the gain α(t).

On the other hand the model-free control is designed following flatness-based principles (Sira-Ramirez and Agrawal (2004); [START_REF] Fliess | Flatness and Defect of Non-linear Systems: Introductory Theory and Examples[END_REF]; [START_REF] Lévine | Analysis and Control of Nonlinear Systems[END_REF]). Namely, for a desired reference trajectory on the system output, denoted r(t) and defined on a given time domain [0, t f ], the control is given by:

u(t) = 1 α(t) (r(t)) (n) -F (t) + R(p)e(t) , (2)
where:

• e(t) is the tracking error r(t) -y(t);

• R(p) is a rational function in the differential operator p [START_REF] Rotella | An Operational Standpoint in Electrical Engineering[END_REF]). Let us mention that the coefficients of R(p) may be time-varying functions; • α(t) and F (t) are the instantaneous estimated values for the coefficients α(t) and F (t) of the ultra-local model (1).

When the controller (2) is applied to the system, taking into account the ultra-local model, we obtain:

[y(t)] (n) = F (t) + α(t) α(t) (r(t)) (n) -F (t) + R(p)e(t) .
Let us introduce the following notations:

• k(t) = α(t) α(t) and λ(t) = 1 -k(t); • g(t) = F (t) -k(t) F (t); • S(p) = p n + k(t)R(p),
then the previous controller (2) yields the following closed loop system:

S(p)e(t) = λ(t) (r(t)) (n) -g(t). (3)
This relationship leads to the conclusion that estimators and the regulator R(p) must be designed such that t f 0 e(t) < E where E is the admissible error in the tracking objective.

As a particular case the adaptive control (2) is defined through the PID structure

R(p) = k P + k I p + k D p 1 + τ F p , (4)
where k P , k I and k D are the gains of the proportional, integral and derivative actions, respectively, and, τ F is the time-constant for the filtered derivative. Let us remark

r(t) + - (r(t)) (n) -F (t)-R(p)e(t) α(t) + n, F (t), α(t) + z(t) d(t) b(t) Fig. 1. Closed-loop control.
that the control with ( 4) is denoted by Fliess and Join (2008); [START_REF] Fliess | Revisiting Some Practical Issues in the Implementation of Model-free Control[END_REF] as an intelligent-PID controller.

We prefer here the adjective adaptive due to the fact that the coefficients of the controller (2) are adapted through the estimation of α(t) and F (t) with a differential equation (see for instance [START_REF] Becedas | Adaptive Controller for Single-link Flexible Manipulators based on Algebraic Identification and Generalized Proportional Integral Control[END_REF] or [START_REF] Wu | Continuous Adaptive Robust Controllers Guaranteeing Uniform Ultimate Boundedness for Uncertain Nonlinear Systems[END_REF]). Let us mention also that in the case where α(t) is fixed at the beginning to a given value (e.g. α(t)≡ 0.9 or 1) then the closed-loop controlled becomes:

(p n + R(p)) e(t) = F (t) -F (t),
(5) and the adaptation mechanism has a consequence on the right-side term of the error dynamics only. With respect to the proposed model, let us mention that some similar, but different, control strategy has been given in [START_REF] Ilchmann | Performance funnels and tracking control[END_REF]. The main difference is that in our approach are estimated the drift term and the input gain. Considering the estimation for α(t) we are led beyond the i-control and we are going towards adaptive control (acontrol).

In this paper we restrict the scope to single-input singleoutput systems. Nevertheless, the case of multivariable systems could be considered with the same guidelines as in [START_REF] Fliess | Vers une commande multivariable sans modèle[END_REF]; Fliess and Join (2008). The paper is organized as follows. Section 2 describes some remarks about disturbance rejection properties and the use of prior knowledge in the extended MFC. Section 3 proposes some alternative and standard parameter estimation methods for MFC. In section 4 an application to a thermal process is presented. Concluding remarks are given in section 5.

SOME REMARKS ON MODEL-FREE CONTROL

As it can readily be seen we have considered here a little bit more complex model than those used in the usual literature or applications on this topic by introducing the time-varying parameter α(t). Indeed we consider in the following this parameter as a parameter which must be estimated. This point of view leads to a light difference with the implementation of intelligent controllers, namely i-P and i-PI controllers which are using derivatives estimators. Nevertheless, we are in position to perform some remarks which reenforce the advantages for the free-model control. These comments are to be added to the proposed ones in D' Andrea-Novel et al. (2010); [START_REF] Fliess | Revisiting Some Practical Issues in the Implementation of Model-free Control[END_REF].

Implicit integral action

Let us suppose that the closed-loop control (2) is performed with exact estimations for F (t) and α(t) (Fig. 1) where b and d are disturbances. With e(t) = r(t) -z(t) and z

(t) = y(t) + b(t), we obtain [y(t)] (n) = F (t) + α(t) × 1 α(t) (r(t)) (n) -F (t) + R(p)e(t)] + d(t)} , = (r(t)) (n) + R(p)e(t) + α(t)d(t), thus we get (p n + R(p)) e(t) = -p n b(t) -α(t)d(t).
(6) When the closed-loop system is stable, the first consequence of this result is the reject of output perturbations b(t) = t i for i = 0 to n -1. In the case where integral

action are included in R(p), namely R(p) = R * (p) p m with m > 0, we obtain p n+m + R * (p) e(t) = -p n+m b(t) -p m (α(t)d(t)) . (7)
Obviously, when α(t)d(t) = t j , for j = 0 to m -1, the disturbance rejection is ensured.

A priori knowledge

The main advantage of the model-free control is to generate a control design without an a priori model for the system. In this framework, the reference trajectory to track is fixed at the beginning. Nevertheless, we are going to see that taking into account a dynamic model for the system can improve the convergence properties for the estimators or to see that the parameter α cannot be considered as a constant. Let us suppose that the system is described by the nonlinear input-output model

[y(t)] (ν) = Φ(y(t), u(t)), (8)
where Φ(y(t), u(t)) is a function which depends on inputoutput variables and their derivatives up to the (ν -1)-th order. Let us mention here that, in practice, the order ν of this model is greater or equal to n. Firstly, from the flatness standpoint, the first task is to generate the reference to track, r(t) such that r (n) (t) = Φ(r(t), u r (t)) where u r (t) stands for the control which ensures that y(t) = r(t).

Secondly, from the model (8) we can build

[y(t)] (n) = Φ(y(t), u(t))+ [y(t)] (n) -[y(t)] (ν) + α(t)u(t) -α(t)u(t),
where n is an arbitrary integer and α(t) an arbitrary possibly time-varying gain. Obviously, α(t) can be fixed at the beginning to 1, but the identification of F (t) in the ultra-local model (1) leads to

F (t) = Φ(y(t), u(t)) + [y(t)] (n) -[y(t)] (ν) -α(t)u(t).
We deduce that

α(t) = Φ(y(t), u(t)) + [y(t)] (n) -[y(t)] (ν) -F (t) u(t) . (9)
As a consequence, an estimator for F (t) may lead to a possibly time-varying gain α(t). Let us mention here that the construction of F (t) and α(t) is not unique for a given model. This fact will be proved in the parameter estimation section 3.

In order to be more precise consider the model of an active magnetic bearing used in De [START_REF] De Miras | Active Magnetics Bearing: a New Step for Model-free Control[END_REF]. This model can be written as

ÿ(t) = D(t) + λsign(i(t))i 2 (t) 2m (g -sign(i(t))y(t)) , ( 10
)
where the output is the displacement y(t), the control is the current i(t) in the coil, D(t) is a load disturbance, g the nominal gap between the coil and the shaft, m is the shaft mass and λ an electromagnetic constant parameter.

With n = 2, two models such as (1) can be deduced. On the one hand

ÿ(t) = D(t) + λsign(i(t))i 2 (t) 2m (g -sign(i(t))y(t)) -i(t) + i(t),
which leads to the identification [START_REF] De Miras | Active Magnetics Bearing: a New Step for Model-free Control[END_REF] which implies an estimation of F (t) only. On the other hand, another point of view, among others, can be used here. Namely, we can write (10) as

F (t) = D(t) + λsign(i(t))i 2 (t) 2m (g -sign(i(t))y(t)) -i(t), α(t) = 1. It is the model used in De
ÿ(t) = D(t) + λsign(i(t))i(t) 2m (g -sign(i(t))y(t)) i(t),
which leads to the identification

F (t) = D(t), α(t) = λsign(i(t))i(t) 2m (g -sign(i(t))y(t))
,

where the gain α(t) is a time-varying gain. To our point of view, the previous remark leads us to consider an estimator for α(t) too.

PARAMETER ESTIMATION

The first three subsections of this part are independent.

The first one points out the non uniqueness of the estimated model. The second one deals with some obtained tracking property. The third subsection proposes a new adaptation mechanism for the drift term and the input gain of the ultra-local model. In the fourth subsection an improvement is indicated for the case of a fast time-varying input gain.

In the following we take n = 1 in the ultra-local model (1).

Generalized inverse based estimator

A possibility for the estimation is to consider the ultralocal model (1) as the regressor

ẏ(t) = U (t)θ(t), ( 11
) where U (t) = [ 1 u(t) ] and θ(t) T = [ F (t) α(t) ].
Usually, the term α(t) is fixed at the outset or, in some cases as in [START_REF] Gédouin | Experimental Comparison of Classical PID and Model-free Control: Position Control of a Shape Memory Alloy Active Spring[END_REF]) is a nonlinear known function. The basic principle is to estimate the drift term F (t). The purpose of this section is to point out that, on the one hand, α(t) can be estimated too, and, on the other hand, this estimation introduces an arbitrary parameter which allows a significance of the parameter α(t). Indeed, the estimation θ(t) of θ(t) can be thought as the solution of the undetermined linear equation (11). As, for every t, rank (U (t)) = 1, this system is consistent (or compatible) which leads to θ

(t) = U (t) {1} ẏ(t) + I 2 -U (t) {1} U (t) z(t), (12)
where :

• U (t) {1} is an arbitrary generalized inverse of U (t), namely it fulfills the relationship (Ben-Israel and Greville ( 2003))

U (t)U (t) {1} U (t) = U (t); • z(t) is an arbitrary 2-dimensional vector. Because rank (U (t)) = 1, we get dim (ker {U (t)}) = rank I 2 -U (t) {1} U (t) = 1.
Consequently, if we denote v(t) a vector such that span {v(t)} = ker {U (t)}, the arbitrary part of ( 12) can be reduced to

I 2 -U (t) {1} U (t) z(t) = λ(t)v(t),
where λ(t) is the arbitrary scalar parameter. This parameter allows to span the solution set of (11) which can be written as

θ(t) = U (t) {1} ẏ(t) + λ(t)v(t),
The estimations of F (t) and α(t) are depending of this parameter which can be tuned with respect to some supplementary constraints.

Let us consider now a particular, but important, case. Let us chose the following generalized inverse for U (t)

U (t) {1} = 1 0 ,
which leads to

I 2 -U (t) {1} U (t) = 0 -u(t) 0 1 .
This particular case allows to consider λ(t) as the second component of z(t) and, the solution set can be read as :

F (t) = ẏ(t) -λ(t)u(t), α(t) = λ(t)
, where the meaning of the parameter appears clearly. As a first remark the case of constant λ(t) has been considered in [START_REF] Fliess | [END_REF], and secondly, we get

F (t) = ẏ(t) -α(t)u(t). ( 13
)
As another example let us take U (t) {1} = U (t) + the pseudo-inverse of U (t) (Ben-Israel and Greville ( 2003)). Namely,

U (t) + = 1 1 + u(t) 2 1 u(t)
,

which leads to I 2 -U (t) + U (t) = 1 0 0 1 - 1 1 + u(t) 2 1 u(t) u(t) u(t) 2 = 1 1 + u(t) 2 u(t) -1 [ u(t) -1 ] . With µ(t) = [ u(t) -1 ] z(t)
, the estimator can be read as

θ(t) = U (t) + ẏ(t) + µ(t) 1 1 + u(t) 2 u(t) -1 , = 1 1 + u(t) 2 ẏ(t) 1 u(t) + µ(t) u(t) -1 , = 1 1 + u(t) 2 ẏ(t) + µ(t)u(t) u(t) ẏ(t) -µ(t) ,
which leads to

F (t) = ẏ(t) + µ(t)u(t) 1 + u(t) 2 , α(t) = u(t) ẏ(t) -µ(t) 1 + u(t) 2 .
Let us remark that the elimination of µ(t) leads to the same relationship, namely F (t) = ẏ(t) -α(t)u(t). Nevertheless, the existence of the degree of freedom in the estimation induces that no a priori exact values for F (t) and α(t) exist independently of outer constraints.

For instance some outer constraints on the control (e.g. saturations,...) need α(t) > α min to ensure the implementation. With the parameters λ(t) or µ(t) this point can be obviously satisfied.

The formula (13) indicates clearly that two estimation strategies can be used. On the one hand, from the algebraic method presented in Fliess and Join (2008); [START_REF] Fliess | Revisiting Some Practical Issues in the Implementation of Model-free Control[END_REF]; [START_REF] Mboup | Numerical Differentiation with Annihilators in Noisy Environment[END_REF] we can obtain the estimation ẏ(t) of the first derivative of y(t). In this framework F (t) and α(t) has to be performed in two successive steps. An estimate α(t) of α(t) leads to the estimation F (t) = ŷ(t)α(t)u(t). The details can be found in the cited works. Let us mention here that the algebraic methods can be used or can be extended to the estimation of a gain α which can be considered as constant during a short period of time. For shortness sake the developments are not given in the present paper but will be the subject of future works. Indeed, we are interested in an adaptive estimation strategy to get F (t) and α(t).

Tracking for derivative

With the control

u(t) = ṙ(t) -F (t) + k (r(t) -y(t)) α(t) ,
and the estimator F (t) = ŷ(t) -α(t)u(t), where ŷ(t) is an estimator for the derivative of the output. We are led to write

u(t) = ṙ(t) -ŷ(t) + α(t)u(t) + k (r(t) -y(t)) α(t) .
The elimination of u(t) leads to ṙ(t) -ŷ(t) + k (r(t) -y(t)) = 0. With the error term e(t) = r(t)-y(t) the previous equation can be read as (k + p)e(t) = ŷ(t) -ẏ(t), where p stands for the derivative operator.

Let us suppose that k > 0 and lim t→∞ e(t) = 0, namely, the regulator ensures perfect tracking, then we have proved that the derivative estimator converges to the real derivative of the output signal. In other words, the estimation error and the tracking error are related through a filtering as ŷ(t) -ẏ(t) = 1 k + p e(t).

Adaptation mechanism

Let us suppose here that α and F are unknown constants such that:

ẏ(t) = F + αu(t) = θ T φ, (14)
where

θ T = [F α] and φ T = [1 u].
Due to the fact that the system output derivative is not measurable, we proceed by filtering as in the parametric estimation of continuous-time systems [START_REF] Baysse | Time Domain Identification of Continuous-time Systems with Time Delay using Output Error Methods from Sampled Data[END_REF]). Namely, considering the filtered signals y f (t) = G(p)y(t) and u f (t) = G(p)u(t), where G(p) is the transfer of the filter, yields the filtered version of the ultra-local model. Then, from ( 14) it can be written that

ẏf (t) = [ F α ] 1 f (t) u f (t) = θ T φ f (t),
where 1 f (t) stands for the filtered unit step G(p)H(t) where H(t) is the Heaviside step function and

φ T f (t) = [ 1 f (t) u f (t) ].
When the filter is supposed to be strictly proper ẏf (t) is obtained with the output filtering ẏf (t) = pG(p)y(t).

Then the filtered estimated ultra-local model is proposed as

ẏf (t) = θT φ f (t) = F α 1 f (t) u f (t) .
Because this estimator is to be used in an adaptive controller, the parameters can be obtained from the minimization of the following normalized quadratic criterion

J = min θ    1 2 ẏf -θT φ f 2 m 2    ,
where m 2 is chosen to satisfy that [START_REF] Ioannou | Robust Adaptive Control[END_REF]. For example we can use:

φ f m ∈ L ∞ as proposed in
m 2 = 1 + γφ T f φ f
, where γ > 0. The minimization can be then obtained using the gradient algorithm

ǫ = ( ẏf -θT φ f ) 1 + γφ T f φ f and θ = -Γ∇J( θ) = Γφ f ǫ.
Where the adaptive gain Γ is a symmetric definite positive matrix. This algorithm have good tracking alertness properties. In practice, first-or second-order filters G(p) with unit static gain provide good results. For example it can be used:

G(p) = c p + c ; G(p) = c 2 (p + c) 2 ;
Of course, some knowledge about the system bandwidth frequency is useful.

The convergence and stability properties of this new adaptive controller are under study and will be the subject of a future paper. In particular it could be necessary to use adaptive gradient with projection laws as discussed in [START_REF] Ioannou | Robust Adaptive Control[END_REF] to obtain a more robust design.

Estimation for a time-varying α(t)

In the case of time-varying functions F (t) and α(t) the previous procedure can be also used. In order to give a simplified description we consider here a first-order filter

G(p) = c c + p . The
G(p) = 1 1 + τ p = 1 -τ p + (τ p) 2 -• • • with τ = 1 c , we obtain ẏf (t) = F G(p)H(t) + α(t)u(t) -τ ( α(t)u(t) + α(t) u(t)) + τ 2 (α(t)u(t) + 2 α(t) u(t) + α(t)ü(t)) -• • • = F G(p)H(t) + α(t) 1 -τ p + (τ p) 2 -• • • u(t) + α(t) -τ + 2τ 2 p -3τ 3 p 2 + • • • u(t) + • • •
For simplicity sake, let us consider we look for estimations for α(t) and α(t). Thus taking into account the first terms in the previous series leads to the ultra-local (truncated) filtered model ẏf

(t) = F G(p)H(t) + α(t)u f (t) + α(t)u f f (t), where u f (t) = G(p)u(t) and u f f (t) = -τ + 2τ 2 p -3τ 3 p 2 + • • • u(t), = d dp 1 1 + τ p u(t) = - τ (1 + τ p) 2 u(t).
In this case the regressor can be written (using again that 1 f (t) stands for the filtered unit step):

ẏf (t) = ΘT Φ f (t) = F α α 1 f (t) u f (t) u f f (t)
, and, the previous adaptation strategy can be used.

EXAMPLE

The simplified model of the thermal process trainer Feedback PT320 is given by

y(t) = Ke -T d p u(t) (1 + τ 1 p)(1 + τ 2 p) ,
where the parameters K, T d ,τ 1 and τ 2 can vary because they depend on the operating point.

For a nominal point with medium air flow and temperature set-point of 40 • C (in the figure 2 the corresponding sensor voltage value is around 5 volts) the following values can be obtained [START_REF] Baysse | Time Domain Identification of Continuous-time Systems with Time Delay using Output Error Methods from Sampled Data[END_REF][START_REF] Baysse | Contributions à l'identification de modèles à temps continu[END_REF])

y(t) = 0.8e -0.22p u(t) (1 + 0.45p)(1 + 0.15p) .
The simulations results are obtained with an a-P controller (with k P = 3) using Matlab-Simulink. A second-order In order to evaluate the adaptation properties of the proposed estimation strategy the parameters of the process to be controlled are changed at time t = 35 seconds to:

y(t) = 0.6e -0.18p (1 + 0.35p)(1 + 0.15p) u(t),
which means a change of the operating point (e.g. the air flow has been increased). Simulation results are shown in the figure 2 for the behavior of the process (where it can be clearly seen the adaptation transients starting at t = 0 and t = 35 seconds and showing the good tracking alertness properties of the normalized gradient algorithm) and, in the figure 3 the time evolution of the parameters of the ultra-local model. Notice that the estimated parameters are not constant and the adaptation mechanism follows the process variations. In our simulation example, a control with a constant value for α could be used, nevertheless, our adaptation algorithm gives an admissible set of estimated varying parameters. Other simulations (not shown here due to space limitations) permit to see that the obtained regulation performances with the a-P controller have equivalent settling times to those obtained with a fixed PID tuned with the Ziegler-Nichols frequency response model as described in [START_REF] Aström | Advanced Pid Control[END_REF].

CONCLUSION

This paper proposes some contributions for the analysis and for the implementation of adaptive ultra-local model control. In particular it was proposed a new extended version of MFC using time-varying parameters. Indeed the simplest version considers that the α parameter is constant. Also alternative adaptive versions giving estimates for the parameters of the ultra-local model were proposed. Simulations were provided which point out the efficiency of the reference tracking and the good convergence properties. In the paper some other research lines have been proposed and will be the subject of next papers.

Fig. 2 .

 2 Fig. 2. Tracking with parameters change (black: controlled output, red: reference, 4 stands for 35 • C and 6 for 45 • C). estimation filter G(p) with c = 10 is used; γ = 1 and Γ = 500I, where I is the identity matrix. The initial value for the θ vector is θ(0) = 1 1 .

Fig. 3 .

 3 Fig. 3. Estimation with parameters change (black: F , red: α).


L Bensefa-Colas

M Telle-Lamberton

S Faye

J.-L Bourrain

M.-N Cr Epy

G Lasfargues

D Choudat

I Momas

Occupational contact urticaria: lessons from the French National Network for Occupational Disease Vigilance and Prevention (RNV3P)

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

Background Occupational contact urticaria (OCU) is an occupational contact dermatitis that can cause serious health consequences and disability at work. Objectives To describe OCU and its temporal trends by the main causal agents and activity sectors in a nationwide scheme in France. Methods Using data from the French National Network for Occupational Disease Vigilance and Prevention (RNV3P), we described OCU reported during the period 2001-10 and analysed the temporal trends of OCU and OCU attributed to the most frequent agents over the study period. Trends analyses were supported by reporting odds ratios using a logistic regression model with reference to 2001, or with time as a continuous variable. Results During the study period, 251 cases of OCU were reported in RNV3P, half of which were due to natural rubber latex, in particular in the health and social work activity sector (HSW). The number of these cases declined significantly over the study period (19% per year), and particularly after 2006. Conversely, the other causes of OCU did not decrease. Conclusions Using surveillance data from a French national network, this study has found that there was a significant decline in OCU due to natural rubber latex, particularly in the HSW, when powdered latex gloves were banned from French hospitals. Our results show the effectiveness of this preventive measure, and suggest that this practice should be extended to other sectors.

What's already known about this topic?

• Contact urticaria is known to be a frequent cause of occupational dermatosis, but statistics on occupational contact urticaria (OCU) are scarce.

What does this study add?

• For the first time, temporal trends in OCU were studied over a 10-year period using data from the French RNV3P network.

• The results show the effectiveness of latex exposure prevention measures for healthcare workers and the need for these measures to be extended to other sectors to reduce OCU in the workplace.

Occupational skin diseases (OSDs) are the second most common occupational health problem in Europe, after musculoskeletal disorders. [START_REF] Brun | European Agency for Safety and Health at Work. Expert Forecast on Emerging Chemical Risks Related to Occupational Safety and Health[END_REF] They represent 10-40% of all recognized occupational illnesses and are one of the most important emerging risks related to exposure to chemical, physical and biological risk factors. [START_REF] Brun | European Agency for Safety and Health at Work. Expert Forecast on Emerging Chemical Risks Related to Occupational Safety and Health[END_REF][START_REF]European Agency for Safety and Health at Work. Occupational Skin Diseases and Dermal Exposure in the European Union (EU-25): Policy and Practice Overview[END_REF] Occupational contact dermatitis (OCD) is the most frequently reported work-related skin disease in many countries. While less frequent than OCD, occupational contact urticaria (OCU) accounts for 1-8% of reported cases of occupational skin diseases. [START_REF] Nicholson | Evidence-based guidelines for the prevention, identification and management of occupational contact dermatitis and urticaria[END_REF] OCU can be defined as a type of urticaria for which the causal agents or exposure can be found partly or wholly in the work environment. [START_REF]European Agency for Safety and Health at Work. Occupational Skin Diseases and Dermal Exposure in the European Union (EU-25): Policy and Practice Overview[END_REF] It comprises physical urticaria, which can be made worse by occupational activities, and contact urticaria due to causative agents, proteins or chemicals, with an immunological or nonimmunological mechanism. [START_REF] Coz | Urticaria. In: Kanerva's Occupational Dermatology[END_REF] Because symptoms can be severe in certain circumstances, the problem of OCU needs to be addressed. However, while the causes of immunological contact urticaria are known, [START_REF] Bourrain | Occupational contact urticaria[END_REF][START_REF] Amaro | Immunological occupational contact urticaria and contact dermatitis from proteins: a review[END_REF][START_REF] Basketter | Immediate contact reactions[END_REF] only some of these causes have been identified as being related to workplace exposure. [START_REF] Coz | Urticaria. In: Kanerva's Occupational Dermatology[END_REF] Most publications on OCU are case reports or short series, and there have been only a few epidemiological studies. [START_REF] Coz | Urticaria. In: Kanerva's Occupational Dermatology[END_REF][START_REF] Kanerva | Statistics on occupational dermatoses in Finland[END_REF][START_REF] Kanerva | Statistical data on occupational contact urticaria[END_REF][START_REF] Cherry | Surveillance of occupational skin disease: EPIDERM and OPRA[END_REF][START_REF] Mcdonald | Incidence by occupation and industry of work-related skin diseases in the United Kingdom, 1996-2001[END_REF][START_REF] Turner | The incidence of occupational skin disease as reported to The Health and Occupation Reporting (THOR) network between 2002 and 2005[END_REF][START_REF] Williams | Occupational contact urticaria: Australian data[END_REF] Data concerning OSD in French workers are very limited. [START_REF] Bensefa-Colas | Occupational allergic contact dermatitis and major allergens in France: temporal trends for the period 2001-2010[END_REF] In France the only national statistics available come from Public Insurance Compensation. Even then, only OCU caused by latex proteins is compensated for and recorded. Furthermore, these data have certain biases: they do not take into account nonsalaried workers, and compensation criteria are based more on administrative criteria than on clinical diagnosis.

The most comprehensive information on OSD and OCU in France is issued from the French Occupational and Environmental Disease Consultation Centres, situated at 32 university hospitals: these make up the French National Network for Occupational Disease Vigilance and Prevention (RNV3P, R eseau National de Vigilance et de Pr evention des Pathologies Professionnelles). It was set up in 2000 and continuously monitors occupational diseases, including skin allergies. [START_REF] Bensefa-Colas | Occupational allergic contact dermatitis and major allergens in France: temporal trends for the period 2001-2010[END_REF][START_REF] Bonneterre | Programmed health surveillance and detection of emerging diseases in occupational health: contribution of the French national occupational disease surveillance and prevention network (RNV3P)[END_REF] Patients with suspected work-related diseases are referred to these centres, mainly by occupational physicians, general practitioners or specialists, such as dermatologists, in order either to obtain expert advice on the link between exposure and disease, or to obtain technical support. RNV3P is an occupational health surveillance scheme at the national level. [START_REF] Bonneterre | Programmed health surveillance and detection of emerging diseases in occupational health: contribution of the French national occupational disease surveillance and prevention network (RNV3P)[END_REF] In this context, the aim of this study based on RNV3P was to describe general features and to study temporal trends in notified OCU by activity sectors and main causal agents in France over the period 2001-10.

Material and methods

Data collection and study database

Data collection from RNV3P has been described previously. [START_REF] Bensefa-Colas | Occupational allergic contact dermatitis and major allergens in France: temporal trends for the period 2001-2010[END_REF] The experienced occupational physicians based in the 32 centres systematically complete standardized forms for each new referred patient and report all new cases of occupational diseases. Only the final diagnosis was used for data collection. [START_REF] Bensefa-Colas | Occupational allergic contact dermatitis and major allergens in France: temporal trends for the period 2001-2010[END_REF][START_REF] Bonneterre | Programmed health surveillance and detection of emerging diseases in occupational health: contribution of the French national occupational disease surveillance and prevention network (RNV3P)[END_REF] Data included diagnosed diseases (among them OSD and OCU), exposures and occupations and/or activity sectors. All data are coded using the standardized International Classification of Diseases 10th revision (ICD-10). [START_REF] Bonneterre | Programmed health surveillance and detection of emerging diseases in occupational health: contribution of the French national occupational disease surveillance and prevention network (RNV3P)[END_REF] The medical experts rated imputability, which is the evidence of association between the occupational exposure and the disease on a fourlevel scale including null, possible, probable and certain. The quality of data was optimized using computerized tools for coding and monitoring data consistency, regular quality training and centralized quality controls. [START_REF] Bensefa-Colas | Occupational allergic contact dermatitis and major allergens in France: temporal trends for the period 2001-2010[END_REF][START_REF] Bonneterre | Programmed health surveillance and detection of emerging diseases in occupational health: contribution of the French national occupational disease surveillance and prevention network (RNV3P)[END_REF] The study database consisted of 69 779 work-related disease events recorded in the RNV3P between 2001 and 2010, with completed data on occupational exposure (substances and occupation) and the potential association between occupational exposure and disease. [START_REF] Bensefa-Colas | Occupational allergic contact dermatitis and major allergens in France: temporal trends for the period 2001-2010[END_REF] The present analysis deals with 7146 cases of OSD (neoplasia excepted) considered as being probably or certainly associated with exposure (ICD-10 codes L00-L99) (Fig. 1).

The RNV3P network received approval for this study from the national board enforcing data protection legislation.

Case definition

Diagnosis of OCU was based on clinical investigation, mainly skin prick tests with commercially available suspected standardized allergens, or prick by prick (with fresh materials such as food). For a few allergens on determination of specific IgE, including latex and its recombinant allergens (Hev b1, Hev b3, Hev b5 and Hev b6Á02), diagnosis was made by several different commercial methods, including radioallergosorbent tests and, currently, enzyme-linked immunosorbent assay (Im-munoCAP 100; Phadia AB, Uppsala, Sweden). [START_REF] Coz | Urticaria. In: Kanerva's Occupational Dermatology[END_REF] Patients were assessed by experienced occupational medical experts, mostly dermatologists or allergists. The physicians took skin-test results and their occupational relevance into consideration when determining the causal relationship by providing a semiquantitative scale of work relatedness.

Cases were defined as all new OCU (ICD-10 codes L50 and L50Á0-L50Á9) notified from 2001 to 2010 that were considered to be probably or certainly associated with occupational exposure by the medical expert of each centre.

Data analysis

Descriptive analyses were performed on occupations, industrial activities and agents related to the OCU cases reported in RNV3P during the study period. Trend analyses were carried out when the numbers of cases were adequate (n ≥ 50) and were based on previously used methods. [START_REF] Bensefa-Colas | Occupational allergic contact dermatitis and major allergens in France: temporal trends for the period 2001-2010[END_REF][START_REF] Paris | Work-related asthma in France: recent trends for the period 2001-2009[END_REF][START_REF] Mcnamee | Measurement of trends in incidence of work-related skin and respiratory diseases, UK 1996-2005[END_REF] Analysed data consisted of the number of new notified cases in the national database for a given year. The odds (called reporting odds) of OCU or OCU related to specific occupational exposure (namely a causal agent, an industrial sector or both) for a given year were defined by the ratio between the number of OCU cases or OCU cases associated with this exposure and the number of all other cases of OSD in this year. The reporting odds ratio (ROR) [START_REF] Rothman | The reporting odds ratio and its advantages over the proportional reporting ratio[END_REF] for each year was calculated with reference to the year 2001 using a logistic regression model that controlled for age and sex; the dependent variable was OCU cases vs. other dermatitis, or OCU related to a specific exposure vs. other cases of dermatitis. The main predictorcalendar timewas treated here as a categorical variable, with each category parameter leading to an estimate of the corresponding year's ROR. Temporal trends were tested by the nonparametric Kendall rank correlation test between years, and the ROR was calculated for each year.

An alternative method considering calendar time as a continuous variable with a scale of years in the logistic model was also used. It led to an estimate of the annual change in ROR, the underlying hypothesis being that the trend would be a regular increase (or a regular decrease) in the ROR by a constant multiplicative factor.

Statistical analyses were performed using R software (https://www.r-project.org/). Statistical significance was defined as P < 0Á05.

Results

Sociodemographic data

During the study period 2001-10, 251 cases of OCU were recorded in the RNV3P network, with a clear predominance of women (176, 70Á1%). The link between disease and exposure was considered as certain in 163 cases (64Á9%). The mean age was 36Á3 AE 10Á6 years, with women significantly younger than men (P = 0Á005) (Fig. 2).

The most frequently reported industrial activities were health and social work activities (HSW), including 94 cases of OCU (41%), which were almost exclusively among women (85 cases). The second most frequently reported activity was manufacturing (41 cases, 18%), with a predominance of men (28 cases) (Table 1). The most frequently involved occupations were personal and protective service work (mainly personal care workers and to a lesser extent hairdressers), life science and health associate professionals (mainly nursing and midwifery professionals) and sales and services occupations, which were represented largely by helpers and cleaners (Table 1).

Causal agents

Physical factors were involved in 21 cases, including pressure (n = 9), cold (n = 3) and vibration (n = 1). Vegetal proteins were the most common cause of OCU (n = 143, 62%, physical OCU excepted) (Fig. 3). Among them, natural rubber latex (NRL) was predominant (n = 124), followed by plants, grains and vegetables (n = 15), wood (n = 3) and enzyme (n = 1). Animal proteins cases (n = 8, 3Á5%) were attributed to fish and seafood, meat, and insects. Hair bleaching products represented the most frequent nonprotein substance related to OCU (n = 9).

Among cases due to NRL, HSW was by far the most commonly involved activity sector (65%), followed by real estate, renting and business activities (9Á7%). However, there were no predominant occupations. Conversely, non-NRL cases came from a wide variety of activity sectors (Fig. 4).

Temporal trends

During the 2001-10 study period, the overall number of cases of OSD decreased significantly relative to all other occupational diseases in the RNV3P network, by an average of 6% per year (P < 0Á001, data not shown). Among OSD (Table 2), cases of OCU decreased significantly relative to all other cases of dermatitis (by an average of 9% per year, P < 0Á001). However, the trend results differed according to causal agents and sectors. We observed a significant decrease in reported cases of OCU related to NRL in the whole workforce (by an average of 15% per year, P < 0Á001), and the downward trend was significantly greater for cases restricted to NRL in the HSW sector (by an average of 19% per year, P < 0Á001). With reference to 2001, the odds of OCU due to NRL became significantly lower in the second part of the period (Fig. 5). Conversely, causes other than NRL did not show any significant trend.

Study population 127 685 health problems at work

Discussion

For the first time, we describe trends in cases of OCU for the main involved agents and industrial activities in a national occupational disease surveillance scheme. The present study covers a 10-year period. Half of the cases were due to NRL, in particular in the HSW sector, and the number of new cases decreased significantly over the 2001-10 study period. During this period other causes of OCU did not decrease. Before discussing these results, strengths and limitations of our data need to be addressed.

Firstly, under-reporting is a known bias in population-based registry studies, and under-reporting of true cases of OCU cannot be excluded in our reporting network. However, hospital-based occupational disease centres serve as a reference for physicians and specialists for the diagnosis of OCD including OCU, and we can suppose that capture of cases of OSD and OCU in these centres is far higher than the capture of work-related diseases as a whole. [START_REF] Bensefa-Colas | Occupational allergic contact dermatitis and major allergens in France: temporal trends for the period 2001-2010[END_REF] The main strength of our study is thus based on the occupational and medical expertise. Standardized diagnostic procedures for determining OCU are performed by trained occupational medical experts, who have the expertise to look for and highlight specific work-related allergens. [START_REF] Bensefa-Colas | Occupational allergic contact dermatitis and major allergens in France: temporal trends for the period 2001-2010[END_REF] Diagnosis is based on the patient's full medical history and assessment of exposure risks in the workplace, in combination with testing results in accordance with guidelines. [START_REF] Lachapelle | Patch Testing and Prick Testing[END_REF][START_REF] Gim Enez-Arnau | Contact urticaria and the environment[END_REF] The causal relationship between disease and agent was coded, which allows identification of contact urticaria that is probably or certainly work related. One strength of our study is that the RNV3P data are taken from multiple centres spread throughout France, thus reducing the potential bias that could result from region-specific industries. Furthermore, this network probably provides the only reliable statistics on OCU at a national level.

One limiting factor in our study is that it is based not on the entire French occupational population, but on a specific subpopulation captured by the centres. [START_REF] Bensefa-Colas | Occupational allergic contact dermatitis and major allergens in France: temporal trends for the period 2001-2010[END_REF][START_REF] Bonneterre | Programmed health surveillance and detection of emerging diseases in occupational health: contribution of the French national occupational disease surveillance and prevention network (RNV3P)[END_REF] In order to address this bias, we used the subgroup of all OSDs reported in our network as the reference population, with these data being supplied by the physicians who made the same clinical investigations for the diagnosis of contact dermatitis and urticaria. The study design allows measurement of the disproportionality of the occurrence of a specific OCU (case) relative to all other occurrences of all other OSDs in the network (not cases), thus enabling oversignals in the reporting database to be detected over a period of 1 year. [START_REF] Rothman | The reporting odds ratio and its advantages over the proportional reporting ratio[END_REF] These data can thus provide valid information on time trends in subgroups without direct reference to the whole population. [START_REF] Uter | Surveillance in occupational contact dermatitis[END_REF] Regarding temporal trends during the 2001-10 period, changes in disease recognition or in the strength of relationship between OCU and allergens could introduce a bias and compromise the consistency of diagnosis over time, an important criterion for valid estimation. [START_REF] Bensefa-Colas | Occupational allergic contact dermatitis and major allergens in France: temporal trends for the period 2001-2010[END_REF][START_REF] Mcnamee | Measurement of trends in incidence of work-related skin and respiratory diseases, UK 1996-2005[END_REF][START_REF] Shapiro-Mendoza | Recent national trends in sudden, unexpected infant deaths: more evidence supporting a change in classification or reporting[END_REF] However, no significant change in the diagnostic method has occurred during the study decade and we feel confident that there was no risk of bias due to under-reporting over the years due to reporter fatigue. [START_REF] Paris | Work-related asthma in France: recent trends for the period 2001-2009[END_REF][START_REF] Mcnamee | Measurement of trends in incidence of work-related skin and respiratory diseases, UK 1996-2005[END_REF] Indeed, inclusions in RNV3P were not based on voluntary reporting, and all diseases were systematically and mandatorily reported on the basis of financial contracts. [START_REF] Bensefa-Colas | Occupational allergic contact dermatitis and major allergens in France: temporal trends for the period 2001-2010[END_REF][START_REF] Bonneterre | Programmed health surveillance and detection of emerging diseases in occupational health: contribution of the French national occupational disease surveillance and prevention network (RNV3P)[END_REF] In addition, during the same period the total number of reported diseases in the network increased significantly.

Lastly, most of the national schemes have studied OSD without making any distinction between OCU and other OSDs (such as OCD), and information on the actual cause is not often reported. [START_REF] Diepgen | Occupational contact dermatitis. In: Kanerva's Occupational Dermatology[END_REF] Even when it is reported, the link with occupational exposure is most often unknown or unclear. The strength of our surveillance scheme is the availability of data on the sources of exposure, occupations, and activity sectors that are actually involved. This study describes the OCU case features, including time trends, in an occupational disease surveillance network for a disease that has been poorly documented in the literature. [START_REF] Kanerva | Statistics on occupational dermatoses in Finland[END_REF][START_REF] Kanerva | Statistical data on occupational contact urticaria[END_REF][START_REF] Cherry | Surveillance of occupational skin disease: EPIDERM and OPRA[END_REF][START_REF] Mcdonald | Incidence by occupation and industry of work-related skin diseases in the United Kingdom, 1996-2001[END_REF][START_REF] Turner | The incidence of occupational skin disease as reported to The Health and Occupation Reporting (THOR) network between 2002 and 2005[END_REF][START_REF] Williams | Occupational contact urticaria: Australian data[END_REF] Comparisons with data in other countries are very difficult: national occupational skin registries are scarce, and, as mentioned above, they mostly combine all subtypes of OSD and provide in the best cases an estimate of the incidence of occupational dermatosis. [START_REF] Turner | The incidence of occupational skin disease as reported to The Health and Occupation Reporting (THOR) network between 2002 and 2005[END_REF] Apart from OCU due to NRL, studies based on time series are very rare.

Men

Women Total

In our data, contact urticaria most frequently affected young women. Similar patterns have been shown in the U.K., [START_REF] Cherry | Surveillance of occupational skin disease: EPIDERM and OPRA[END_REF][START_REF] Mcdonald | Incidence by occupation and industry of work-related skin diseases in the United Kingdom, 1996-2001[END_REF] and more recently in a retrospective study in Australia. [START_REF] Williams | Occupational contact urticaria: Australian data[END_REF] In the RNV3P, the predominant sector involved in OCU was HSW, consisting mostly of healthcare workers, with a large proportion of women as previously described in the U.K. [START_REF] Mcdonald | Incidence by occupation and industry of work-related skin diseases in the United Kingdom, 1996-2001[END_REF][START_REF] Turner | The incidence of occupational skin disease as reported to The Health and Occupation Reporting (THOR) network between 2002 and 2005[END_REF][START_REF] Turner | Evaluating interventions aimed at reducing occupational exposure to latex and rubber glove allergens[END_REF] and Australia. [START_REF] Williams | Occupational contact urticaria: Australian data[END_REF] Conversely, according to statistics from Finland, the highest numbers of cases of OCU concerned farmers and domestic animal attendants. [START_REF] Kanerva | Statistical data on occupational contact urticaria[END_REF] In our study, at-risk occupations other than HSW were hairdressers, cleaners or machine operators. This differed slightly from other studies, with the differences being dependent on the socioeconomic fabric of the country. [START_REF] Doutre | Occupational contact urticaria and protein contact dermatitis[END_REF] The workers most commonly reported as being at risk of OCU in these studies include, in addition to HSW occupations, bakers, farmers and those in food preparation occupations, as well as veterinarians and domestic animal attendants, and hairdressers. [START_REF] Nicholson | Evidence-based guidelines for the prevention, identification and management of occupational contact dermatitis and urticaria[END_REF][START_REF] Coz | Urticaria. In: Kanerva's Occupational Dermatology[END_REF][START_REF] Bourrain | Occupational contact urticaria[END_REF][START_REF] Gim Enez-Arnau | Contact urticaria and the environment[END_REF] NRL was the predominant cause of OCU reported in the RNV3P network, followed by other vegetal proteins and by hair bleaching products. Allergy to NRL is actually a sensitization to Hevea brasiliensis proteins, and NRL is known to be the most common cause of OCU. [START_REF] Bourrain | Occupational contact urticaria[END_REF][START_REF] Amaro | Immunological occupational contact urticaria and contact dermatitis from proteins: a review[END_REF][START_REF] Doutre | Occupational contact urticaria and protein contact dermatitis[END_REF] Vegetal or animal proteins are the most commonly reported causes of OCU, [START_REF] Nicholson | Evidence-based guidelines for the prevention, identification and management of occupational contact dermatitis and urticaria[END_REF] with a less frequently reported cause being chemicals that involve an immunological or nonimmunological mechanism. [START_REF] Nicholson | Evidence-based guidelines for the prevention, identification and management of occupational contact dermatitis and urticaria[END_REF][START_REF] Coz | Urticaria. In: Kanerva's Occupational Dermatology[END_REF] Causal agents other than NRL reported in the literature are cow dander, food and animal products, and flours and grains. [START_REF] Nicholson | Evidence-based guidelines for the prevention, identification and management of occupational contact dermatitis and urticaria[END_REF][START_REF] Kanerva | Statistics on occupational dermatoses in Finland[END_REF][START_REF] Kanerva | Statistical data on occupational contact urticaria[END_REF][START_REF] Mcdonald | Incidence by occupation and industry of work-related skin diseases in the United Kingdom, 1996-2001[END_REF][START_REF] Turner | The incidence of occupational skin disease as reported to The Health and Occupation Reporting (THOR) network between 2002 and 2005[END_REF][START_REF] Williams | Occupational contact urticaria: Australian data[END_REF] However, it is surprising that animal proteins are involved in only a few cases in our network, one of the hypotheses being that OCU due to animal proteins was classified as protein contact dermatitis (PCD), for which the most frequent clinical presentation is a chronic or recurrent eczema, sometimes associated with exacerbation of urticarial reaction immediately after contact with the causal protein. [START_REF] Amaro | Immunological occupational contact urticaria and contact dermatitis from proteins: a review[END_REF] All of these factors could explain a probable misclassification of animal protein OCU as PCD to animal proteins, particularly for people handling foods. [START_REF] Amaro | Immunological occupational contact urticaria and contact dermatitis from proteins: a review[END_REF] Our data reveal that ammonium persulfates and other persulfates were probably the hair bleaching urticant causing

À0Á60 À0Á76 À0Á89 À0Á20 À0Á20 P-value 0Á016 0Á002 < 0Á001 0Á42 0Á42 ROR (years) b,d ROR 0Á91 0Á85 0Á81 0Á92 0Á98 CI 0Á87-0Á96 0Á80-0Á91 0Á74-0Á88 0Á83-1Á01 0Á92-1Á04 P-value < 0Á001 < 0Á001 < 0Á001 0Á098 0Á54
ROR, reporting odds ratio; CI, confidence interval. a Relative to all other occupational skin diseases (neoplasia excepted). b Annual RORs were defined as the ratio between the number of cases of OCU in each group and the number of all other occupational skin diseases for a given year, with reference to 2001 using a logistic regression model (controlled for age and sex). c Nonparametric Kendall rank correlation tau between years and the annual RORs. d Annual change in ROR for a year (x) vs. year (x À 1). OCU in hairdressers. [START_REF] Coz | Urticaria. In: Kanerva's Occupational Dermatology[END_REF][START_REF] Gimenez-Arnau | Immediate contact skin reactions, an update of contact urticaria, contact urticaria syndrome and protein contact dermatitis -"a never ending story[END_REF] They were the third most common cause of OCU in the Australia study. [START_REF] Williams | Occupational contact urticaria: Australian data[END_REF] Physical exposure is associated with cases referred to as physical contact urticaria, which is considered a subgroup of contact urticaria. [START_REF] Coz | Urticaria. In: Kanerva's Occupational Dermatology[END_REF][START_REF] Doutre | Occupational contact urticaria and protein contact dermatitis[END_REF] In these cases the origin is not purely occupational, and exacerbations can be triggered by direct contact with the physical agent during workplace activities. This can result in deep oedema or shock, for example after exposure to a cold environment. Although it is conventionally classified separately, this specific syndrome is an important issue, particularly because of occupational consequences and the risk of professional exclusion. [START_REF] Coz | Urticaria. In: Kanerva's Occupational Dermatology[END_REF][START_REF] Bourrain | Occupational contact urticaria[END_REF] In our network, the wearing of gloves, materials handling and repeated contacts in some cases caused delayedpressure urticaria in the workplace. Such clinical settings have been rarely described in the literature.

Over the course of the study period, the sector most commonly involved in OCU related to NRL was the HSW sector. In other studies, sensitization and clinical allergy to NRL have also been reported more frequently in the HSW sector, the most common clinical manifestation being contact urticaria. [START_REF] Amaro | Immunological occupational contact urticaria and contact dermatitis from proteins: a review[END_REF][START_REF] Doutre | Occupational contact urticaria and protein contact dermatitis[END_REF][START_REF] Valks | Allergic contact urticaria from natural rubber latex in healthcare and non-healthcare workers[END_REF][START_REF] Jolanki | Incidence rates of occupational contact urticaria caused by natural rubber latex[END_REF] NRL is known to have been a serious occupational health hazard for healthcare workers during the 1990s and 2000s, [START_REF] Bousquet | Natural rubber latex allergy among health care workers: a systematic review of the evidence[END_REF] especially for those with a high exposure to latex gloves highly powdered with protein. [START_REF]Latex Allergy: Occupational Aspects of Management. A National Guideline[END_REF] Indeed, use of NRL medical gloves in France increased 10-fold in the years 1980-90 following the emergence of the HIV infection epidemic. [START_REF]Control on Natural Rubber Latex Medical Gloves Market[END_REF] At that time, prevalence studies showed that 2-17% of exposed healthcare workers were sensitized to NRL, while the rate was < 1% in the general population. [START_REF] Basketter | Immediate contact reactions[END_REF][START_REF] Gim Enez-Arnau | Contact urticaria and the environment[END_REF][START_REF] Doutre | Occupational contact urticaria and protein contact dermatitis[END_REF][START_REF] Valks | Allergic contact urticaria from natural rubber latex in healthcare and non-healthcare workers[END_REF][START_REF] Jolanki | Incidence rates of occupational contact urticaria caused by natural rubber latex[END_REF][START_REF] Liss | Latex sensitization: occupational versus general population prevalence rates[END_REF][START_REF] Tang | Latex sensitisation in healthcare workers in Singapore[END_REF][START_REF] Reunala | Latex allergy and skin[END_REF] Regarding time-trend analysis, during the 2001-2010 study period we observed a significant decrease in the overall number of cases of OCU reported in the RNV3P network, with an annual decline of 9%. Cases due to NRL among HSW decreased significantly at a rate of 19% per year, and since 2006 the difference from 2001 has been statistically significant. This decrease occurred concomitantly with the French recommendations since approximately 2004 to use low-protein, nonpowdered latex gloves and latex-free gloves as preventive measures in hospitals. Indeed, in 2004 the French National Agency for Medicine and Health Products Safety carried out a market survey on latex medical gloves, and in 2005 it confirmed the interest in powder-free gloves in the management of latex allergy risk in hospitals, in parallel with restricted use of latex gloves if alternatives existed. [START_REF]Control on Natural Rubber Latex Medical Gloves Market[END_REF][START_REF]Control on Natural Rubber Latex Medical Gloves Market[END_REF] Indeed, the introduction of powder-free gloves began with experiments in some French hospitals and was extended to most hospitals after 2004-05. Recommendations to reduce exposure to latex gloves in the workplace have been made by many countries (the U.S.A. and several European countries among them), which has resulted in a decrease in latex allergy. [START_REF] Reunala | Latex allergy and skin[END_REF][START_REF]Preventing allergic reactions to natural rubber latex in the workplace[END_REF][START_REF] Kujala | A review of current literature on epidemiology of immediate glove irritation and latex allergy[END_REF][START_REF] Allmers | Decreasing incidence of occupational contact urticaria caused by natural rubber latex allergy in German health care workers[END_REF] However, Bousquet et al. have pointed out a lack of appropriate studies to assess the effect of these policies. [START_REF] Bousquet | Natural rubber latex allergy among health care workers: a systematic review of the evidence[END_REF] The decline of NRL-induced OCU observed in our data in the HSW sector in France, particularly during the second part of the last decade following the hospital-wide interventions, suggests the effectiveness of such preventive actions.

Conversely, in sectors other than HSW, NRL-induced cases of OCU have remained relatively stable according to data from the RNV3P network, suggesting a need to extend public health policy to reduce exposure to NRL from latex gloves in these other sectors. Latex gloves should not be used in the workplace when they are not necessary (as in the agri-food, hairdressing and cleaning sectors).

Lastly, no trend was apparent for non-NRL cases of OCU over the 2001-10 study period. It is important that future occupational health policies take urticant exposure into account, in order to reduce exposure in the different sectors shown in our analysis that could be at risk, such as manufacturing, social and personal service activities, and the automobile industry. Further research is needed to identify sensitizers and their sources of generation in the workplace (in particular proteins in the agri-food and research sectors), and to limit exposure by substitution, reduction of exposure, containment (e.g. use of robotics), the use of protective equipment and ventilation. It is also necessary to provide information and training for workers about allergens and safety, and to refer workers with OCU to physicians who have expertise to make the appropriate workplace adjustments.

In conclusion, we have used data taken from the RNV3P over a 10-year period to study, for the first time, the causes of OCU in the workplace by activity sector and time frame. The significant decrease in OCU related to NRL in the HSW sector following preventive measures enforced in the middle 2000s in French hospitals would appear to endorse the efficacy of such measures. As OCU related to other agents has been shown to be stable, we suggest that other occupational groups and sectors could also benefit from preventive measures.

FitnessFig 1 .

 1 Fig 1. Flow chart of the study population: occupational skin diseases recorded in the French National Network for Occupational Disease Vigilance and Prevention, 2001-10. a Environmental diseases without any opinions on association with exposure on clinical file. b Occupational skin diseases probably or certainly work related.

Fig 2 .

 2 Fig 2. Distribution of work-related cases of urticaria reported in the French National Network for Occupational Disease Vigilance and Prevention, 2001-10, by age group and sex (n = 251).

Fig 5 .

 5 Fig 5. Annual reporting odds ratios for occupational contact urticaria due to natural rubber latex in the health and social work sector reported in the French National Network for Occupational Disease Vigilance and Prevention, 2001-10 (n = 124), with 2001 as the reference year. CI, confidence interval.

Table 1

 1 Industrial sectors and occupations of patients with occupational contact urticaria reported in the French National Network for Occupational Disease Vigilance and Prevention by sex, 2001-10 (n = 251)

Table 2

 2 Annual distribution and trends of occupational contact urticaria (OCU) reported in the French National Network for Occupational Disease Vigilance and Prevention by selected causal agents and/or activity sectors, a 2001-10

					Other than health
	OCU group	All cases	Natural rubber latex (NRL)	Health and social work: NRL	and social work: NRL	Other than NRL
	Total	251	124	74	50	127
	2001	29	19	17	2	10
	2002	34	17	11	6	17
	2003	37	15	10	5	22
	2004	32	19	9	10	13
	2005	29	20	9	11	9
	2006	21	11	4	7	10
	2007	15	8	6	2	7
	2008	28	7	4	3	21
	2009	18	6	3	3	12
	2010	8	2	1	1	6
	Kendall tau on annual RORs b
	Kendall tau c

Funding sources

The study network was funded by the French Agency for Food, Environmental and Occupational Health and Safety (ANSES), the National Health Insurance System for Employees (CNAM-TS) and the National Health Insurance System for Agricultural Workers (CCMSA). Any opinions and conclusions expressed herein are solely those of the authors.

Values are n (%). a Missing data, n = 24. b P < 0Á001 for comparison of activity sectors per sex, or occupations per sex, using a v 2 -test.


Remarkable response of hollow thermoplastic microspheres-elastomer matrix composites in uniaxial tension

In the last few years, the mechanical response of hollow thermoplastic microsphereselastomer matrix composites has been investigated. The large majority of the studies focuses on their compressive properties and particularly on the stress-strain response. In the present paper, large strain uniaxial tension experiments are conducted on thermoplastic microspheres filled polyurethane elastomer. Six volume fractions of microspheres are considered. Thanks to a two-camera setup and digital image correlation measurements, the volumetric response of the materials is extensively analyzed. As a major result, the remarkable volumetric behaviour is highlighted: the hydrostatic pressure vs. volume change curves admit several extrema that may be read as the macroscopic signature of the complex microstructural phenomena involved during deformation. Moreover, it is shown that the size of the volumetric loading-unloading hysteresis loop is directly related to the volume fraction of microspheres in the materials.

Introduction

Polymer syntactic foams, i.e. materials made of microspherical inclusions embedded in a matrix, are employed in various applications for their buoyant and/or acoustic behaviours, their compressive strength but also their thermal insulation properties [START_REF] Gupta | Applications of polymer matrix syntactic foams[END_REF]. In most of cases, glass microspheres are considered in rigid thermoset resins [START_REF] Gupta | Comparison of tensile and compressive characteristics of vinyl ester/glass microballoon syntactic foams[END_REF] or elastomer [START_REF] Brown | A multiscale study of damage in elastomeric syntactic foams[END_REF] matrices.

For the last few years, new thermoplastics microballoons/elastomer matrix composites have been developed. They are made of hollow thermoplastics microspheres (HTMs in the following, commercial name Expancel) encapsulating a gas [START_REF] Curd | Geometrical and mechanical characterisation of hollow thermoplastic microspheres for syntactic foam applications[END_REF]) that act as fillers in silicone [START_REF] Shorter | The mechanical behaviour of elastomers when hollow microspheres are used as a particulate filler[END_REF] or polyurethane [START_REF] Yousaf | Compression properties of polymeric syntactic foam composites under cyclic loading[END_REF] elastomer matrix. In a large majority of studies devoted to these materials, the focus is laid on their compressive properties: such experimental results are proposed by [START_REF] Paget | Syntactic foam under compressive stress: Comparison of modeling predictions and experimental measurements[END_REF]; [START_REF] Yousaf | Compression properties of polymeric syntactic foam composites under cyclic loading[END_REF]; [START_REF] Smith | Modelling hollow thermoplastic syntactic foams under high-strain compressive loading[END_REF]. These investigations being very recent, only few attempts of modelling have been published; roughly speaking authors are trying to account for the (reversible) buckling of the HTMs by different approaches: simple physical models [START_REF] De Pascalis | Predicting the pressure-volume curve of an elastic microsphere composite[END_REF], numerical or analytical homogenization techniques [START_REF] Shrimali | A simple explicit model constructed from a homogenization solution for the large-strain mechanical response of elastomeric syntactic foams[END_REF], or phenomenological compressible constitutive equations [START_REF] Smith | Modelling hollow thermoplastic syntactic foams under high-strain compressive loading[END_REF].

For uniaxial tension, and to the best of our knowledge, only two studies report experiments on dumbbell samples:

• [START_REF] Shorter | The physical behaviour of elastomers containing hollow spherical fillers[END_REF] present the loading curves of an unfilled and three HTMs filled silicone elastomers. It is shown that for low strain, higher the microspheres content, higher the stiffness; the inverse phenomenon is observed for large strain (> 175% strain).

• [START_REF] Yousaf | Tensile properties of all-polymeric syntactic foam composites: experimental characterization and mathematical modelling[END_REF] propose a thorough investigation of the cyclic response of HTMs/polyurethane elastomer syntactic foams up to 50% strain. Among the results, it is shown that the presence of microballoons highly increases the size of the loading-unloading stress-strain hysteresis loop.

These two studies focus on macroscopic stress-strain unidimensional response but do not investigate the compressibility of these materials, even if this property is of major importance in applications.

In the following, the uniaxial tensile response of HTMs filled polyurethane elastomer is reported. Experimental methods are presented in the next section: materials and samples, then the two-camera setup are described. Results are presented and discussed in Section 3. First, the data treatment is detailed. Then, after the presentation of classical stress-strain results, the focus is laid on the volumetric response of the materials: hydrostatic pressure vs. volume change curves are drawn and their comprehensive analysis is proposed. Finally, a short conclusion closes the paper.

Methods

Materials and samples

Materials are made of a polyurethane elastomer matrix filled with HTMs. Six volume fractions of HTMs (which will be sometimes referred to as "porosity" in the following) are considered: 0, 5, 10, 15, 20, and 25% (nominal data given by the supplier). The volume fraction of each specimen has been verified with the following method. First, the density of the polyurethane matrix is considered independent of the HTMs volume fraction: it is equal to the one of the 0% material. Second, samples being produced by a cutting punch, their in-plane geometry is assumed well-established. The thickness of specimen is measured by a caliper with a precision of ± 0.01 mm, and the weight by a balance with a precision of ± 0.002 g. Then the actual porosities are calculated. The corresponding results are given in Table 1, each of them corresponds to the mean value of three measurements on three different samples. In the following, the actual values will Nominal porosity (%) 5 10 15 20 25 Actual porosity (%) 4.6 ± 0.10 9.3 ± 0.33 13.5 ± 0.18 17.5 ± 0.14 23.2 ± 0.18 Table 1: Nominal and actual volume fractions of HTMs in the five filled materials.

be considered for the computations, but for the sake of simplicity the nominal ones will be used in the presentation of the results.

The geometry of the dumbbell samples are shown in Figure 1(left). sketches the uniaxial tensile test, and introduces the notations: l 0 × w 0 × t 0 strain gauge deforms into l × w × t with the force F . Practically, l 0 is about 20-25 mm. Thus, we define

• the three stretch ratios

λ = l l 0 , λ w = w w 0 , λ t = t t 0 , (1)
respectively in the longitudinal, width, and thickness directions,

• and the nominal (first Piola-Kirchhoff) and true (Cauchy) stresses:

P = F w 0 × t 0 , σ = F w × t .
(2)

Experimental set-up

The experimental apparatus is shown in Figure 2. Uniaxial tensile experiments are con- ducted with a Instron ElectroPulse E10000 (linear-torsion all electric-dynamic machine); it is equipped with a 1 kN load cell and high pressure grips. During the experiments, displacement is prescribed at speed 10 mm/min, during the whole cycle (both loading and unloading). For each porosity, the experiments are conducted twice, on different samples. Both displacement and force F are recorded at 20 Hz.

In addition to these global measurements, local surface measurements of strain are carried out. For this purpose, two Prosilica GT6600 29 Mpix cameras (resolution 6576×4384 Pix 2 ) with 100 mm Zeiss Makro-planar 2/100ZF lenses record the deformation of the sample throughout the test: the front face camera records the deformation of the face normal to the thickness, and the side face camera records the deformation of the face normal to the width (see Fig. 2). Then, Digital Image Correlation (DIC) provides the three stretch ratios of Eq. ( 1). The method used here is almost similar of the one of [START_REF] Crevoisier | Volume changes in a filled elastomer studied via digital image correlation[END_REF], with two cameras facing the two sides of the sample. Here, due to large strain no parasitic bending occurs, then the authors assume that the strain field measured on both sides are equal to the strain field on the corresponding opposite hidden faces. Note that a more precise technique would consist in using two sets of two cameras and in performing stereo correlation on two opposite sides of the sample [START_REF] Wu | Strain localisation and damage measurement by full 3d digital image correlation: application to 15-5ph stainless steel[END_REF]. From a practical point of view, the gauge length of the specimens is covered with a black paint speckle as shown in Figure 3. Displacement and strain fields are computed thanks to VIC-2D software (Correlated Solutions). Mean values of the logarithmic strain tensor are calculated thanks to a virtual strain gauge (black rectangles in Fig. 3). The dimensions of these gauges are about 15 × 4.5 mm 2 for the front face (Fig. 3(top)) and 15 × 1.5 mm 2 for the side face (Fig. 3(bottom)). The corresponding optical and DIC parameters are summarized in Tables 2 and3, respectively.

Camera

Allied Vision Technology Prosilica GT6600

Results and discussion

All data investigated here are available in [START_REF] Coret | Images and data accompanying article: Remarkable response of hollow thermoplastic microspheres-elastomer matrix composites in uniaxial tension[END_REF]. Thus, in the following we sometimes choose to not present the results for all porosities.

Isotropy

Classically, isotropy of such materials is assumed. Thanks to the two cameras, it is possible to verify this assumption. As examples, Figure 4 presents the comparison of λ w and λ t for 0% and 20% filled materials. For all volume fractions (not shown here), results are identical: λ w = λ t during all the experiments. Thus, all materials are isotropic.

In the following, only λ w will be considered when necessary. Indeed, its measurement is more precise than the one of λ t because the analysed surface is larger in the width direction (see Fig. 3).

Repeatability, averaging and smoothing

As mentioned above, experiments are conducted twice for a given material. In all cases, measurements are repeatable and reproducible. Then a mean curve is calculated for each material. This curve is a bit noisy due to the sampling frequency of the force measurement (20 Hz) and to the low measured values of the loading force as compared to the load cell capacity (1 kN). Then, it is smoothed by a Savitzky-Golay filter with a polynomial of degree 2 (Scipy documentation, 2021). This process is illustrated in Figures 5 and6 for the 0% and 20% filled materials respectively. Similar results are obtained for the four other materials.

Through the rest of the paper, all analyses will be performed considering smoothed mean curves.

Classical results in uniaxial tension

Standard results of uniaxial tensile tests are depicted in Figure 7. The left-hand side plot shows the evolution of the transversal stretch ratio (λ w = λ t ) with respect to the longitudinal one (λ), and the right-hand side plot shows the stress-strain loading-unloading curves.

From a general point of view, these results are very classical and looks like the ones obtained with pure elastomers: stress-strain curves exhibit the traditional hysteresis loop. Nevertheless, a more precise comparison of the curves leads to the following comments.

• At first sight, the λ w vs. λ evolution curves are very similar whatever the volume fraction of HTMs. Moreover, the corresponding hysteresis loops between loading and unloading are very small.

• All stress-strain curves admit the same shape and the same initial stiffness. Loading curves exhibit differences in stiffness for λ 1.6 -1.7: the higher the porosity of HTMs, the more the stiffness decreases. An opposite trend has been observed by [START_REF] Shorter | The physical behaviour of elastomers containing hollow spherical fillers[END_REF], but the initial stiffness of the materials were highly different from one to another. Moreover, it is to note that the curve of the 15% material does not follow the general trend: for λ = 2.5, it is above the 5% and 10% curves.

• All stress-strain curves present a hysteresis loop between loading and unloading: the higher the volume fraction of HTMs, the larger the hysteresis loop. This observation is similar to the one of [START_REF] Yousaf | Tensile properties of all-polymeric syntactic foam composites: experimental characterization and mathematical modelling[END_REF] for small strain (λ = 1.25 and 1.4).

• At λ = 1 on the unloading curves, there is almost no compressive stress. We can roughly conclude that viscous effect are negligible for small strain rates (about 5.10 -3 s -1 at small strain). This result is in accordance with the one of Yousaf et al ( 2022) who measure about 5% strain for max(λ) = 1.25 and about 7-8% for max(λ) = 1.4 at zero-stress on the unloading curves, whatever the fraction of HTMs.

We argue that the viscoelasticity of the composite depends on the viscous properties of the elastomer matrix and not on the HTMs volume properties.

Compressibility

As stated above, the response of the filled materials seems to be quite close to the one of standard elastomers under uniaxial tensile loading conditions. Nevertheless, it is wellknown that the major feature of HTMs-elastomer composites is their volumetric response. Thus, in the following we propose a complete analysis of this feature. This approach resembles to the method proposed in Smith et al ( 2021) for compressive loading conditions. First, we consider only kinematic quantities. Both the Poisson ratio ν (generalized to large strain) and the volume ratio J (Jacobian determinant of the deformation gradient tensor) are calculated:

ν = - log λ w log λ and J = λ × λ w × λ t = λ × λ 2 w .
(3)

The corresponding results are plotted in Figure 8. For both quantities, the curves exhibit hysteresis loops which size increases with the volume fraction of HTMs. It is to note that this response was not predictable by examining the evolution of lateral stretch in Fig. 7(left). As shown in Fig. 8(left), the results for λ < 1.2 are not relevant (division by log λ with λ near 1). For larger values, ν varies between 0.47 and 0.51. It reveals that the materials are almost incompressible, but the shape of the curves highlight a complex response "around" incompressibility. This complexity becomes obvious when examining the evolution of J depicted in Fig. 8(right). Except the curve of the pure polyurethane (0%), all curves admit a large hysteresis loop, with several changes of slope during the cycle. It is important to note again that it corresponds to very small changes in volume: between -0.5% to 4% for the material with 25% HTMs.

Volumetric response

To further investigate this unusual phenomenon, we consider now the stress-strain volumetric response of the materials. In this way, the hydrostatic pressure is calculated. It is defined as

p = - 1 3 trσ, ( 4
)
where σ is the Cauchy stress tensor related to the nominal stress tensor P by

σ = (det F ) -1 P F T , (5)
F being the deformation gradient tensor and • T the transposition operator. Recalling that in the principal directions of deformation (length, width and thickness directions of the sample, see Fig. 1) F is the diagonal tensor which contains the stretch ratios, the Cauchy stress in the loading direction reduces to P/λ 2 w and all other components of σ are null. Thus,

p = - 1 3 P λ 2 w . (6)
As this pressure is always negative in uniaxial tension (because P ≥ 0), -p is used to plot the graphs. Nevertheless, we have to keep in mind that the pressure is positive, i. the curve of the virgin material (0%) is classical for a quasi-incompressible elastomer: it presents a small hysteresis and for a change in volume of about 0.5% (J = 1.005), the pressure increases sharply with the volume change. Second, all the other curves have the same complex shape: they present a hysteresis loop that increases with the HTMs volume fraction. Moreover, they exhibit a non-monotonous form with several extrema. In order to investigate the features of these hysteresis loops, some descriptive notations are introduced. Consider the schematic hysteresis loop depicted in Figure 10. During a C. The minimum of the loading part. It is to note in Fig. 9 that for 15% and 20%, J 1 (it went back to the undeformed volume) for -p 1 MPa. For 25%, the volume has diminished for the same pressure. D. It is the maximum loading point, it corresponds to λ 2.5 and to the maximum pressure borne by the material. The unloading begins and the volume continue to increase until point E. E. This is the maximum change in volume attained during the cycle. After this point, the volume decreases through the rest of the unloading path.

F . It is the end of the cycle; at this point λ = 1. There is a remanent change in volume.

With our results, it is difficult to know if it is irreversible (damage) or if the sample will recover its initial dimensions (viscous effect).

To continue the discussion, four additional quantities are introduced: the pressure jumps

∆(-p) 1 = -(p(C) -p(B)) and ∆(-p) 2 = -(p(E) -p(C)) (7)
and the volume change jumps

∆J 1 = J(C) -J(B) and ∆J 2 = J(E) -J(C), (8)
as shown in Fig. 10. surprising observation: both volume change jumps evolve linearly with the HTMs volume fraction. For pressure, it is not exactly similar: the data corresponding to 15% are not exactly aligned with other points (see Fig. 12(right)). It is related to the previous observation of Fig. 7(right) in which the 15% stress-strain curve is above the 5% and 10% ones. In our opinion, this discrepancy may be due to defects in the 15% material (even if the two tests were almost superimposed); but it does not mitigate the remarkable characteristics of the phenomena highlighted in the present paper.

Conclusion

In this paper, a thorough analysis of uniaxial tensile experiments on polyurethane elastomer filled with hollow thermoplastics spheres has been conducted. Thanks to a twocamera setup and digital image correlation, the surprising volumetric response of such materials has been exhibited. Even if the lateral stretch and nominal stress vs. loading stretch curves are very classical and look like the ones of standard elastomers, the change in volume vs. pressure curve exhibits several slope changes in the loading-unloading hysteresis loop.

This remarkable macroscopic response is the signature of complex microstructural phenomena; as emphasized by [START_REF] Yousaf | Tensile properties of all-polymeric syntactic foam composites: experimental characterization and mathematical modelling[END_REF] in the case of uniaxial extension it might be explained by the "debonding of microspheres from the matrix material". Such possible explanations necessitate further investigation, and we hope that the present observations will help to understand and model the mechanical response of HTMs filled elastomers.

  Figure 1: Sample. Left: dimensions (mm). Right: notations.

Figure 2 :

 2 Figure 2: Experimental set-up with camera positioning.

Figure 3 :

 3 Figure 3: Virtual strain gauges on undeformed samples. Top: front face. Bottom: side face.

Figure 4 :

 4 Figure 4: Isotropy of the materials. Porosity: 0% (left), 20% (right). The red and blue lines correspond to two different experiments.

Figure 5 :

 5 Figure 5: Lateral stretch ratio (left) and nominal stress (right) vs. extension. Porosity: 0%. In blue and red: raw data of the two experiments; in black: the corresponding averaged and smoothed curve.

Figure 6 :

 6 Figure 6: Lateral stretch ratio (left) and nominal stress (right) vs. extension. Porosity: 20%. In blue and red: raw data of the two experiments; in black: the corresponding averaged and smoothed curve

Figure 7 :

 7 Figure 7: Lateral stretch ratio (left) and nominal stress (right) vs. stretch ratio for all materials.

Figure 8 :

 8 Figure 8: Poisson ratio ν (left) and change in volume J (right) vs. extension. The loading-unloading path is shown by the black arrows.

  Figure 9: Volumetric response of the six materials.

Figure 10 :

 10 Figure 10: Description of the volumetric response. Definition of the extrema and the jumps, example of the 25% filled material.

  Figure 11: Analysis of volumetric curves. Left: extrema; Right: jumps.

Table 2 :

 2 Image acquisition parameters.

	Dynamic range, image 8 bits
	Lens	100 mm Zeiss Makro-planar 2/100ZF
	Field of view	110 × 73 mm 2
	Patterning technique	Black spray paint
	DIC Software	VIC-2D version 8.
	Subset shape function 6-tap spline
	Strain formulation	Logarithmic
	Matching Criterion	NSD

Table 3 :

 3 DIC parameters.