Mikhael Tannous

Patrice Cartraud

David Dureisseix

Mohamed Torkhani

A beam to 3D model switch for rotor dynamics applications

Keywords: Rotor dynamics, Finite elements, Switch, Energy consistency

A typical accidental slowing down of a turbine presents a rotor-stator contact that may be limited to a small interval of the whole simulation period. Such engineering problems involving slender structures with local or non-linear phenomena restricted in time require a 3D model for a better understanding of the local or non-linear phenomena, whereas a simplified beam model can be sufficient for simulating the linear phenomena occurring for a long period of time.

This paper proposes a strategy that enables to switch from a beam model to a 3D model during a transient rotor dynamics analysis, and thus, allows to reduce the computational cost while preserving a good accuracy.

The simulation starts with a beam model, and at the switch instant ts, the 3D solution is initialized as the sum of a displacement corresponding to the classical Timoshenko kinematics assumption and a 3D correction that accounts, for instance, for cross-section deformation. This is performed on three consecutive time steps (the switch instant, the previous and the following steps), thus allowing to make velocity and acceleration corrections.

The method is proved to be energetically sound and is validated through comparisons with a reference solution corresponding to the 3D model solution computed during all the simulation.

Introduction

Many industrial problems in transient dynamics, such as the simulation of turbine accidents, require a 3D model in order to accurately account for local effects such as rubbing, that occur along a small period of time. However, a 3D model for the entire structure used during the whole simulation will result in an unaffordable computational cost even on the best nowadays computational machines and softwares. We, therefore, present a method that can reduce dramatically the computational cost, for problems where the 3D non-linearities are restricted in space and time.

To solve problems for which non-linearities are restricted in time, one can use a time integration scheme switching technique. In fact, when non-linear phenomena occur, such as contact interactions, small time steps are needed to ensure an accurate modeling of the physical phenomenon. In such cases, an explicit integration method is well suited to reduce the computational cost. However, for the complementary part of the problem which is linear, an implicit method presents the advantage of unconditional stability, thus making it possible to use larger time steps. An algorithm that enables one to switch automatically between explicit and implicit integration scheme thus significantly reduces the computational cost. Narasimhan and Lovell [START_REF] Narasimhan | Predicting springback in sheet metal forming: an explicit to implicit sequential procedure[END_REF] and Jung and Yang [START_REF] Jung | Step-wise combined implicit-explicit finite element simulation of autobody stamping processes[END_REF] proposed, respectively, an explicit to implicit and implicit to explicit time integration switches for sheet metal forming applications. Explicit to implicit and implicit to explicit switches were used in Lo et al [START_REF] Lo | Assessment of efficiency for a hybrid explicit/ implicit code simulation of a multiple impact crash scenario[END_REF] for improving the computational cost of the simulation of impact crash problems. In Noels et al [START_REF] Noels | Combined implicit-explicit algorithms for non-linear structural dynamics[END_REF][START_REF] Noels | Automatic time stepping algorithms for implicit numerical simulations of non-linear dynamics[END_REF], the authors developed automatic criteria for time integration scheme switching techniques and applied it for non-linear structural dynamics. This technique has also been applied in Noels et al [START_REF] Noels | Combined implicit/explicit algorithms for crashworthiness analysis[END_REF][START_REF] Noels | Combined implicit/explicit time-integration algorithms for the numerical simulation of sheet metal forming[END_REF] to metal forming simulation and in Noels et al [START_REF] Noels | Automatic time stepping algorithms for implicit numerical simulations of blade/casing interactions[END_REF] for a blade/casing interaction simulation. These explicit/implicit and implicit/explicit switches have been recently implemented in the industrial finite element code Code_Aster based on the research work of Mahjoubi et al [START_REF] Mahjoubi | Coupling subdomains with heterogeneous and incompatible time steps[END_REF] when implicit and explicit domains are not located in the same area, and a domain decomposition-like method is used to couple them. For phenomena that are restricted in space, i.e. to a small part of the computational domain, a wide range of methods has been developed. These approaches are always in progress and can be divided into exact (or direct) methods and iterative ones. The most popular exact approaches are the static condensation techniques and the exact structural reanalysis methods, such as used in Hirai [START_REF] Hirai | An exact zooming method for finite element analyses[END_REF], Hirai et al [START_REF] Hirai | An exact zooming method[END_REF]. Adaptive meshing techniques can be used for a local refinement of a 3D model, see for example Plaza et al [START_REF] Plaza | A 3D refinement/derefinement algorithm for solving evolution problems[END_REF]. Volume patches such as Arlequin enable to superpose two different domains, e.g. a beam model and a 3D model. Applications examples can be found in Ben Dhia [START_REF] Dhia | Multiscale mechanical problems: the Arlequin method[END_REF], Ben Dhia and Rateau [START_REF] Dhia | The Arlequin method as a flexible engineering design tool[END_REF], Cottereau et al [START_REF] Cottereau | A stochastic-deterministic coupling method for continuum mechanics[END_REF], Ghanem et al [START_REF] Ghanem | Arlequin framework for multi-model, multitime scale and heterogeneous time integrators for structural transient dynamics[END_REF]. Beam to 3D connections or shell to 3D connections, enable to account accurately for local 3D phenomena, while the rest of the model is less computationally expensive thanks to the beam or shell elements. Many applications in the literature exist such as the mixed beam-3D model used by Kettil and Wiberg [START_REF] Kettil | Application of 3D solid modeling and simulation programs to a bridge structure[END_REF] for the simulation of a bridge deformation.

The iterative domain decomposition methods can be divided into overlapping and non-overlapping domain decomposition methods. Multi-scale methods with patch are overlapping domain decomposition methods that enable to have a local zoom on the domain; the superposition methods consist in making a local correction on a global domain, such as the finite element patches Lions and Pironneau [START_REF] Lions | Domain decomposition methods for CAD[END_REF], Glowinski et al [START_REF] Glowinski | Finite element approximation of multi-scale elliptic problems using patches of elements[END_REF] and the harmonic patches He et al [START_REF] He | Accelerating the method of finite element patches using approximately harmonic functions[END_REF].

Non-overlapping domain decomposition methods can be classified into three main categories: the primal approaches Mandel [START_REF] Mandel | Balancing domain decomposition[END_REF], the dual approaches (FETI method) that appeared in the early 1990s Farhat and Roux [START_REF] Farhat | A method of finite element tearing and interconnecting and its parallel solution algorithm[END_REF], and the hybrid or mixed approaches such as FETI-DP, which is an improved version of the FETI method, that combines the advantages of the dual and primal approaches Farhat et al [START_REF] Farhat | FETI-DP: a dual-primal unified FETI method -Part I: A faster alternative to the two-level FETI method[END_REF]. FETI has also a multi-scale version used in Mobasher Amini et al [START_REF] Amini | A micro-macro strategy for ship structural analysis with FETI-DP method[END_REF] and Mobasher Amini et al [START_REF] Amini | Multi-scale domain decomposition method for largescale structural analysis with a zooming technique: application to plate assembly[END_REF] for the computation of ship structures where windows are some centimeters wide, whereas the structure of the ship is hundreds of meters long. For similar applications we also find the micro-macro approaches, see Ladevèze et al [START_REF] Ladevèze | A micro-macro and parallel computational strategy for highly heterogeneous structures[END_REF].

Regarding local non-linear phenomena, FETI was enhanced to deal with large number of subdomains and can take geometric non-linearities into account Farhat et al [START_REF] Farhat | The second generation FETI methods and their application to the parallel solution of large-scale linear and geometrically non-linear structural analysis problems[END_REF], and was adapted for contact problems in Avery et al [START_REF] Avery | A numerically scalable dual-primal substructuring method for the solution of contact problems Part I: The frictionless case[END_REF], Avery and Farhat [START_REF] Avery | The FETI family of domain decomposition methods for inequality-constrained quadratic programming: application to contact problems with conforming and nonconforming interfaces[END_REF], Dureisseix and Farhat [START_REF] Dureisseix | A numerically scalable domain decomposition method for the solution of frictionless contact problems[END_REF]. In Alart et al [START_REF] Alart | Additive Schwarz method for nonsymmetric problems: application to frictional multicontact problems[END_REF] we find an adapted Schwarz method for frictional contact problems. In Gendre et al [START_REF] Gendre | Non-intrusive and exact global/local techniques for structural problems with local plasticity[END_REF][START_REF] Gendre | A two-scale approximation of the Schur complement and its use for non-intrusive coupling[END_REF], the authors developed an algorithm that enables to replace the global mesh by a finely meshed local zone, in order to take local nonlinear effects into consideration with low computational effort. The use of beam to 3D connections or shell to 3D connections can also be useful for non-linear local phenomena. In Andrieux and Varé [START_REF] Andrieux | A 3D cracked beam model with unilateral contact. Application to rotors[END_REF], a beam to 3D connection was successfully used for a study of local cracking in a turbine rotor.

Turbine accident problems present non-linear phenomena that are restricted both in time and space. For non-linearities restricted in space, i.e. for the time period where no contact interactions take place, a beam model is sufficient to model the slowing down of the turbine as done in Roques et al [START_REF] Roques | Modeling of a rotor speed transient response with a radial rubbing[END_REF]. However, in this reference the authors also used the beam model for local rotor stator interactions modeling. To be able to accurately account for the local rotor stator interactions, a 3D local model is mandatory. The remaining parts of the turbine do not exhibit non-linear local phenomena and can be modeled by beam elements. Therefore, a model that mixes beam and 3D elements, connected with appropriate constraints, can be very useful to model non-linearities restricted in space. This approach has been proposed in Tannous et al [START_REF] Tannous | A beam to 3D model switch for transient dynamic analysis[END_REF][START_REF] Tannous | A beam to 3D model switch for transient dynamic analysis[END_REF] for transient dynamic applications excluding overall rotations, based on the PhD of Tannous [START_REF] Tannous | Développement et évaluation d'approches de modélisation numérique couplées 1D et 3D du contact rotor-stator[END_REF].

Therefore, this research article goes one step further and addresses the issue of reducing the computational cost for non-linear phenomena restricted in time and for rotor dynamic applications. The simulation starts at t = t0 with a beam model for a linear simulation, and switches at t = ts1 to a 3D model when a non-linear phenomenon is to take place. The simulation switches back at t = ts2 to the beam model for of the rest of the simulation that ends at tf, if no more non-linear phenomenon is present as illustrated in Fig. 1. This strategy, called the switch method, presents several difficulties when applied to rotor dynamics applications in comparison with a switch method for transient dynamic problems excluding overall rotations. In fact, the beam and the 3D solutions of the same rotor dynamics problem are slightly phase shifted. This make the switch method a challenging task since the solutions shift leads to a non-negligible difference between the 3D and the beam solutions at the switch instant. This issue as well as other difficulties are addressed in the scope of this paper. This paper presents a beam to 3D model switch. The 3D to beam model switch is not the subject of this research work. The switch method is independent from the switch instant choice. This latter is chosen arbitrarily in this research article for sake of simplicity, since the main objective of this article is to present the switch from a methodological and academic point of view such a way the method works whatever the switch instant is. However, the switch has to be performed in the linear stage preceding the appearance of non-linear phenomena. This represents the main switching criteria for all type of applications. For a rotorstator contact problem, when a rotor to stator contact is detected on the beam model at a given instant tc, the switch instant is calculated by ts = tcn ∆t, where ∆t is the time step and n is a safety factor that enables to perform the switch sufficiently far from any non-linearity. Moreover, since this paper is focused on the switch process, linear problems are considered.

Unbalanced rotor dynamics modeling

The loss of a terminal blade of a turbine creates an unbalance of mass M at a distance d from the axis of rotation, which rotating at an angular velocity ω. This produces an unbalance force F = M d ω 2 applied where the mass breakdown took place. We are interested in the dynamic response of such an unbalanced rotor.

Different modeling techniques enable to describe the dynamic response of the unbalanced rotor. Beam based models, such as described in Section 2.1, are simple and efficient models. They are of satisfactory precision if no local phenomena are observed. If local phenomena occur, such as a rotor to stator contact/friction interactions, 3D elements are required to accurately capture these effects. Such a modeling technique is detailed in Section 2.2 and is computationally expensive.

Note that in the following, we present the beam modeling as well as the 3D modeling of an unbalanced rotor. The finite element software that we are using in the scope of this research paper is Code_Aster developed by the Research and Development section of EDF [START_REF]Code_Aster: a general code for structural dynamics simulation under GNU GPL licence[END_REF]. Code_Aster proposes a beam modeling of an unbalanced rotor in the Galilean frame, whereas the 3D modeling of the unbalanced 3D rotor, taking into account the gyroscopic effects of the 3D elements recently developed in the scope of the PhD thesis of Ghanem [START_REF] Ghanem | Contributions à la modélisation avancée des machines tournantes en dynamique transitoire dans le cadre Arlequin[END_REF], takes place in the rotating frame. In this article, we therefore use for rotor dynamics modeling, the rotating frame for the 3D model, and the Galilean frame for the beam model. The gyroscopic matrix of the 3D elements is dependent on the rotation velocity. The rotor dynamic problem is non-linear if the rotation velocity is an unknown of the dynamic problem. Code_Aster deals with rotor dynamic problems in which the rotating velocity is given. We, therefore, for the following application examples deal with a constant and given rotating velocity; though the switching technique itself is fully applicable to rotor dynamic problems for which the rotating speed is an unknown.

Beam modeling of a rotor subjected to unbalance loading

Let us consider a rotor as schematically shown in Fig. 2. An unbalance load F = M d ω 2 is triggered by the loss of a mass M located at point PM at a distance d from the axis of rotation of the rotor turning with an angular speed ω.

The equivalent beam model of the rotor is show in Fig. 3, with a discrete rigid disk. In other terms, the inertia and mass properties of the disk are affected to the beam node that corresponds to the disk position, namely point PN in Fig. 3. The disk deformation is not taken into account in such a simplified model.

The fundamental dynamic equation of a beam model subjected to a rotation unbalance Fb in the Galilean frame Rg, where Ubg is the beam displacement vector, reads: In these conditions and in the frame Rg, the unbalance Fb has two components: one along to the x-axis named Fx = M d ω 2 cos(ωt), and the other along the y-axis direction Fy = M d ω 2 sin(ωt).

3D modeling of a rotor subjected to unbalance loading

The fundamental equation of motion of a 3D rotor model, as the one shown in Fig. 2, subjected to unbalance, in the rotating frame R at an angular velocity ω, reads:

(

,

, and are respectively the displacements, velocities and accelerations of the 3D model. M3D, G3D(ω), A3D and K3D are respectively the mass, gyroscopic, damping and stiffness matrices of the 3D model.

is the unbalance force written in R. has a fixed direction in R and a module F3D = M d ω 2 . Note that in the rotating frame R, the gyroscopic matrix G3D(ω) is the matrix that takes into account the gyroscopic effects of the 3D elements as well as the Coriolis and dragging forces, Lalanne and Ferraris [START_REF] Lalanne | Dynamique des Rotors en Flexion[END_REF].

Beam to 3D model switching

Since the beam modeling of the unbalanced rotor is described in the Galilean frame and the 3D modeling in the rotating one, switching for one model to another supposes firstly to use the same frame for both the models. We, therefore, need to make a frame transition for the beam solution (from the Galilean to the rotating frame), before switching to the 3D model.

Frame transfer matrix

We consider that the rotation of the rotor is occurring around its z-axis as illustrated in Figs. 2 and3. The beam displacements , velocities and accelerations written in the Galilean reference Rg are transferred to the rotation frame R and are denoted respectively , and , by using a frame transfer matrix Qb. The frame transition can be summarized by the following expressions:

(3) 2

Note that for a beam model, with 6 degrees of freedom, the frame transfer matrix reads:

cos -sin 0 sin cos 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 cos -sin 0 sin cos 0 0 0 1 (4)
where θ represents the angle of the rotation of the rotor from its initial position.

Basics of the switch

A beam model simulation starting at t = 0 is to be switched for a 3D model simulation at t = ts. Starting with the 3D model at t = ts requires the collection of the beam model solution at ts and transforming this solution to have a suitable 3D model initialization at the same instant. The construction of the 3D solution at t = ts relies on the decomposition of the solution in three main components:

1. A rigid body motion (rotation). This part of the solution is already decoupled from the two other parts of the solution, since in Code_Aster the rotation velocity is given and the 3D solution is written in the rotating frame. 2. A beam solution corresponding to rigid body cross-sections (Timoshenko kinematical assumption),

. A projector matrix P, introduced in Tannous et al [START_REF] Tannous | A beam to 3D model switch for transient dynamic analysis[END_REF] and recalled in Appendix A, can be defined to transform the beam displacement vector into a 3D rigid body displacement per beam section P . Since the beam and the 3D solution are expressed in different frames, the beam solution is first transformed to the rotating frame by Eq. ( 4), to give P .

A 3D correction denoted with

, expressed in the rotating frame.

The 3D solution at t = ts, in the rotating frame, reads:

(

Therefore, 3D dynamics Eq. ( 2) leads to:

, and are three corrective terms. However, since we have one equation with three unknowns, additional assumptions should be made.

First strategy

In a first step, we neglect the velocities and accelerations corrections ( and ) and compute the displacements corrections at t = ts in a static computational step:

- - - (7)
The computations of and can be done in the same way as , using Eq. ( 4). The 3D model can therefore be initialized at t = ts with: [START_REF] Noels | Automatic time stepping algorithms for implicit numerical simulations of blade/casing interactions[END_REF] This strategy is quite cheap from a computational cost point of view, but the strong assumption consists in neglecting and . At a consequence, they initiate, at the switch instant, a transient stage with high frequency oscillations, mostly on the accelerations of the 3D solution. To stabilize the solution after switching, and as proposed in Tannous et al [START_REF] Tannous | A beam to 3D model switch for transient dynamic analysis[END_REF], one can filter these high frequency oscillations by introducing a numerical damping in the time integration scheme (HHT integration scheme Hilber et al [START_REF] Hilber | Improved numerical dissipation for time integration algorithms in structural dynamics[END_REF] for example), or make velocities and accelerations corrections (triple static switch procedure also discussed in Tannous et al [START_REF] Tannous | A beam to 3D model switch for transient dynamic analysis[END_REF]). This later method, proved to be efficient, eliminates completely the transient stage and provides a stable 3D switch solution. It is briefly presented in the following and is used in all the application examples of this article.

Second strategy

The second strategy, i.e. the triple static switch, consists on making three static switches by solving Eq. ( 7) at the switch instant ts, one time preceding ts and denoted ts-1 and at one time step following ts and denoted ts+1. The velocities at t = ts will be computed according to the finite difference formula:

∆ (9)
The accelerations are computed in order to preserve the dynamic equation of the 3D model at ts, and thus at ts is the solution of:

- - (10)
where is computed with Eq. ( 5), and is computed with Eq. ( 9). If an implicit time integration scheme is used, e.g. one of Newmark time integration schemes family, then the accelerations will automatically be computed by the finite element software such a way they respect Eq. ( 10) as indicated by Géradin and Rixen [START_REF] Géradin | Mechanical vibrations: theory and application to structural dynamics[END_REF].

Energy consistency of the switch

The precision of the switch is checked by comparing the switch solution with a 3D reference solution computed along the whole simulation period. Another method to check the validity and the robustness of the switch is to check its energy consistency. This is a procedure widely used in the literature. Noels et al [START_REF] Noels | Automatic time stepping algorithms for implicit numerical simulations of non-linear dynamics[END_REF][START_REF] Noels | Combined implicit/explicit time-integration algorithms for the numerical simulation of sheet metal forming[END_REF] used this procedure to demonstrate the stability of an implicit/explicit time integration scheme switch method.

We consider a mechanical system rotating at an angular speed ω around an axis with a corresponding inertia I. In the rotating frame, F is the external load, U is the displacement vector, M and K are the mass and stiffness matrices. The kinetic energy can then be written as the sum of two components. The first component is related to the rotating inertia, namely, Wcr = ½ Iω 2 , and the second component is related to the deformation of rotor Wcd = ½ . The deformation energy reads: [START_REF] Hirai | An exact zooming method[END_REF] The work of the external forces Wf is computed by: [START_REF] Plaza | A 3D refinement/derefinement algorithm for solving evolution problems[END_REF] Without dissipative sources, the kinetic energy theorem leads to: [START_REF] Dhia | Multiscale mechanical problems: the Arlequin method[END_REF] where cst is a constant that depends on the problem being solved. If the external force is constant, one gets a constant energy balance:

-

In our study case, the unbalance is a constant (it is a function of time for a short period before it reaches its given value, and the switch takes at an instant at which the unbalance is constant). Therefore, the energy consistency (i.e. the fact that the switch does not remove nor insert energy in the 3D solution after switching) can be checked by computing the total energy Wt of the 3D solution after switching, and verifying that this later is constant and is close to the total energy of the 3D reference solution.

Application example on rotor dynamics

Let us consider a 3D rotor model, as the one shown in Fig. 2, made up of a steel material with a density ρ = 7800 kg/m 3 , a Young modulus E = 2.1 10 11 N/m 2 and a Poisson ratio ν = 0.3.

The half cross-section of the rotor is presented in Fig. 4. Table 1 gives the rotor dimensions. The rotor disk itself is modeled as a rigid part with a young modulus a hundred times higher than that of the rotor. The 3D rotor is meshed with quadratic elements and contains 1883 nodes with 3 degrees of freedom (dof) each, while its equivalent beam model with Hermite elements contains 43 nodes with 6 dof each.

In the following example, the rotor is pinned at its two extremities and is rotating at an angular velocity ω = 300 rpm and is subjected to a 1 kg unbalance at point PM as illustrated in Fig. 2. The studied time evolution spreads on 0.5 s, and is solved by the Newmark implicit mean acceleration scheme with 8000 time steps (∆t = 6.25 10 5 s). Note that applying the unbalance abruptly (at the first time step) will generate high frequency oscillations in the accelerations and velocities. This fact is illustrated in Fig. 5: dividing the time step by two, leads to a doubled acceleration.

To address this issue, the unbalance is applied according to a given progressive time law. The rotor excitation will depend on this law 1 but the switch method itself can manage all loading conditions. Fig. 6 shows two different unbalance laws. In the first, the unbalance F(t) is applied linearly during 0.01 s, and is kept constant afterwards. In the second, F(t) follows a more progressive evolution law, with null derivatives at t = 0 and at t = tm, instant at which the unbalance reaches its stable constant value. The switch instant is ts = 0:25 s. After switching, the 3D solution is compared to a 3D reference solution computed along the whole simulation period (0.5 s). Fig. 5. Influence of the size of the time step if the unbalance is applied abruptly at the first time step. 1 Imposing the unbalance according to a given law has the effect of not generating numerical high frequency oscillations. However, it may excite some high eigen-frequencies of the rotor, since such loading functions include a large series of high frequencies, even though the loading is smooth. We first present an application example for the first unbalance loading law, and for a 300 rpm rotating velocity.

Fig. 7 shows the displacements of point PN along the x-axis in the rotating frame (see Fig. 2)). The 3D solution after switching is compared to the 3D reference solution.

The results in Fig. 7 are transformed to the Galilean frame, and the displacements of point PN of the beam model in its Galilean frame are added, thus resulting in Fig. 8.

We can note the presence of two vibration frequencies, the first one is that of the global rotation of the rotor. The second one is a modulation and represents the vibration of the rotor around its stable deflection posture (while rotating). This later is excited by the unbalance law, and is a physical response of the rotor. A Fast Fourier Transform (FFT) of this modulation shows a frequency close to 256 Hz, which is an eigenfrequency of the rotor2 . As seen in Zoom 1 of Fig. 8, a shift exists between the 3D reference solution and the beam solution. This shift, that also can be seen on Figs. 7 and9, is due a slight difference (around 1 %) between the eigen-frequencies of the beam and the 3D models, which in turn leads to a shift between the beam and the 3D solutions and not to the switch method. Having an enough slender beam and refining the 3D mesh model contributes to reducing this difference.

For the displacements results, the shift is noticed on the modulations (second eigen-frequency and not the first), but the evolutions of the two solutions are very similar and present very close amplitudes.

For the velocities and accelerations, this shift can be seen on the first eigen-frequency. Though at the switch instant, the beam at the 3D reference solutions may have anti-phase velocities and accelerations (Figs. 10 and11), the amplitudes are very similar. In the following, and for a better clarity of the figures, the results are shown for t ∈ [0.24 s, 0.26 s]. Note that the same conclusions are also obtained on a point that does not belong to the neutral fiber of the rotor, such as point PM on which the unbalance force is applied and for which the velocities and accelerations results are presented in Fig. 9. The 3D switch solution at t = ts is constructed from a beam solution (

) at which a 3D correction ( ) is added. This implies that the 3D switch solution has the same deflection as the beam model at the switch instant. The 3D correction is mainly a cross-section deformation and cannot adjust the shift between the beam and the 3D solutions. Therefore, after switching, the 3D switch solution ''clings'' on the beam solution and has the same eigen-frequencies as the 3D reference solution. Thus, the shift is never compensated as shown on the displacements results in Fig. 8 as well as on the velocities (Fig. 10) and acceleration (Fig. 11) results. This is inevitable since it is not possible to have identical beam and 3D solutions behaviors 3 .

In spite of the phase shift between the beam solution and the 3D solution, the switch enables one to have a very good approximation of the 3D reference solution. The behavior of the 3D switch solution and the 3D reference solution is almost the same if the phase shift is isolated (same natural frequencies, amplitudes, etc.). No perturbations (high frequency oscillations, divergences, etc.) exist in the 3D switch solution. The switch allows to save computational cost while preserving a good accuracy.

Analyzing the energy consistency of the switch confirms the robustness of this later: no parasite energy is inserted nor removed from the solution at the switch instant. No energy disturbance occurs on the kinetic, deformation and total energy values at the switch instant. As previously explained in Section 3.3, the kinetic energy has two components: the first is related to the rotation of the rotor around its main axis and has a value of Wcr = ½ Iω 2 = 19.632 J in our case, and the second is related to the vibrational movement of the rotor (Wcd) and has a much lower main value. Wcr is constant because the rotational velocity is constant, and Wcd oscillates. The switch does not disturb any of the two kinetic energy components. Fig. 13 shows the deformation energy of the beam model, 3D reference model and the 3D switch model. We can notice that the nominal deflection of the rotor is established during the unbalance loading phase t ∈ [0, tm]. After this phase, the rotor vibrates around its stable equilibrium position. Thus, his strain energy oscillates around a constant value. After switching, the value of the strain energy of the 3D switch model is consistent with that of the beam model and the 3D reference model, and no oscillations are found.

Fig. 14 shows the total energy, computed according to Eq. ( 14), of the beam, 3D reference and 3D switch models. Once the unbalance reaches its constant value (at 0.01 s in our case), the total energy is a constant and that is obviously seen in Fig. 14. The 3D reference model and the 3D switch models have almost the same total energy. The switch does not insert nor remove energy from the system.

In the following, another application example is shown. The same physical and numerical conditions of the previous example are maintained in this following example, except the rotational velocity. The unbalance is applied according to the loading law of study case one of Fig. 6. The rotational velocity is increased to 1500 rpm, in order to show the robustness of the switch on another study case, and a higher rotational velocity. Results are shown on point PN along the x-axis direction. Note that the same conclusions are obtained along the y-axis direction and on other points belonging to the rotor. Fig. 15 shows the displacements results in the rotating frame. Velocities and accelerations are presented in Fig. 16. A simple comparison between Figs. 7 and 15 shows that the response of the rotor has the same modulations frequency as the preceding example. However, it is obvious, especially on Figs. 7b and15b, that the amplitudes of those modulations are increased due to the increased rotating velocity (from 300 rpm to 1500 rpm). The loading time law is not the only factor that can increase the amplitude of the response. The rotation velocity is a key factor. Analyzing the energy curves illustrates the robustness of the switch on higher rotational velocity cases. For a better clarity, the kinetic energy is presented in the time interval t ∈ [0.2 s, 0.3 s] in Fig. 17. It is obvious that the kinetic energy of the 3D switch solution is closer to that of the beam model than to that of the 3D reference solution. Differences exist between the beam and the 3D reference solutions, for the reasons previously discussed.

At the switch instant, the 3D switch solution clings on the beam one. This explains why the kinetic energy of the 3D switch solution (for both the components: the component resulting from the overall rotation and the one due the vibration of the rotor around its stable equilibrium position) is closer to that of the beam one than to that to the 3D reference solution kinetic energy.

This can be less visible on the strain energy (see Fig. 18). The strain energy of the 3D switch solution is very close to that of the 3D reference solution. The total energy is constant and do not present any perturbation. The 3D reference solution and the 3D switch solution have practically the same total energy as illustrated by Fig. 19.

The increase in the rotational velocity leads to more intensified vibrations of the rotor. However, the switch method preserve its accuracy and robustness. We thereafter, present a third and last application example for which the rotation velocity is ω = 300 rpm, but the loading is imposed progressively on a 0.1 s time interval (see Fig. 6). The following results are obtained on point PN in the rotating frame.

Fig. 20 shows the displacements results on point PN, while Fig. 21 shows the velocities and acceleration results of point PN around the switch instant in the rotating frame. In the following a comparison of this study case with the first one, i.e., with an imbalance established on 0.01 s and a 300 rpm rotational velocity is performed. By comparing the displacements of the first study case (Fig. 20) and those of this study case (Fig. 7b), one can conclude that imposing the imbalance progressively reduces the amplitudes of the modulations. However, the modulations retain the same natural frequency in both the study cases.

This fact is also highlighted by comparing the velocities and accelerations of the two study cases, i.e., by comparing Figs. 9a and21a.

In this study case, due to a smoother application of the imbalance, the rotor vibrates less violently around its stable equilibrium position. The kinetic and strain energies (Fig. 23) show small oscillations. The switch does not perturb the energetic stability of the system (no parasite energy is inserted nor removed, no oscillations are found on the energy curves, etc.). Moreover, a closer look to the kinetic energy curve Fig. 22 shows that in spite of the weakness of the kinetic energy component that counts for the vibration of the rotor around its stable equilibrium position Wcd, with respect to the component that count for the overall rotation Wcr, i.e., Wcd ≪ Wcr, the switch does not introduce parasite energy in any of the components.

The total energy (Fig. 24) is constant once the imbalance is stable.

Limits of the strategy

The presented strategy is simple, efficient and easy to implement for the different applications considered previously. However, one may demand if for some application cases, the switch method will not work or lead to unreliable results. This section presents an insight into the theoretical conditions that, if accomplished, make the switch efficient for any type of application, even for complex geometries, loads, boundary conditions, etc. These conditions, as explained later, can be resumed by the necessity of having the orthogonality of vectors and . Moreover, understanding the strategy's limits begins by examining the causes that make it difficult to strictly satisfy this condition.

Optimal strategy if the orthogonality of vectors and is satisfied

Switching from the beam to the 3D model, according to the first switching strategy, leads to a transient stage depicted by high frequency oscillations that can be attenuated by numerical damping. This is why strategy two was proposed. The latter, thanks to velocities and accelerations corrections make it possible to switch correctly without passing through a transient stage. Let us first discuss the main causes that are behind the transient stage that appear after switching when the first strategy is used and then discuss why strategy two is better and finish by understanding what are the possible limits of strategy two.

The basics of the switch is that results from a beam computation that is based on a rigid body assumption, and is a 3D correction that accounts for a rigid-body cross-section deformation. Therefore, the two vectors should be orthogonal. In other words, since is a pure 3D solution, then its construction should not depend on , since the latter is generated from a beam solution. It also means that counts only for the cross-section deformation and is not related to the beam deflection, since the later is taken into account in . The fundamental equation of motion of a 3D model at t = ts is described by: [START_REF] Cottereau | A stochastic-deterministic coupling method for continuum mechanics[END_REF] From we obtain:

It can be demonstrated that if we have a coincidence between the beam and the 3D models shape functions, in addition to very fine meshes and a non-lumped 3D mass matrix, then we can write: [START_REF] Kettil | Application of 3D solid modeling and simulation programs to a bridge structure[END_REF] as well as . Taking into account that is the beam solution which fulfills , then Eq. ( 16) leads to: [START_REF] Lions | Domain decomposition methods for CAD[END_REF] Since we have the assumption and (see Eq. ( 8)), we obtain the following orthogonality condition: [START_REF] Glowinski | Finite element approximation of multi-scale elliptic problems using patches of elements[END_REF] As explained earlier, the computation of P T turns to be cumbersome, so that the orthogonality condition will be written as follows:

∀ , (20)
Having the orthogonality of vectors and satisfied implies that the construction of vector does not depend on the beam solution. In other words, is a vector that counts for the cross-section deformation but is not related to the beam deflection since that latter is taken into account in the beam solution.

Satisfying the orthogonality condition implies practically that the 3D solution at the switch instant has exactly the same deflection as the beam solution.

is a correction vector that brings the required complementary information for the construction of the 3D solution, i.e., the cross-section deformation. However, Eq. ( 17) are practically never satisfied. The main difficulty is not having non lumped mass matrices (it is possible in most finite element software), but in the compatibility of the beam and 3D shape functions. However, a sufficient fine 3D mesh contributes to a better approximation of Eq. ( 17).

The orthogonality condition can also be seen from a different point of view, that of the contribution of each solution component ( and ), in the deformation energy of the 3D solution at the switch instant.

A closer look into the strain energy of the beam and the 3D models will give a better significance of the orthogonality condition, and of the meanings of it to be verified or not.

The strain energy of the beam model is:

The deformation energy of the 3D model taking into account the symmetry of the stiffness matrix is: [START_REF] Farhat | A method of finite element tearing and interconnecting and its parallel solution algorithm[END_REF] from the orthogonality condition and Eq. ( 17) one has:

thus the strain energy of the 3D model is equal to the strain energy corresponding to the cross-section deformation and the strain energy of the beam. Therefore, when switching no parasite energy should appear.

Non verifying the orthogonality condition consequences

The orthogonality condition cannot be respected unless Eq. ( 17) are true. However, due to the difference in the shape functions used for a beam model and those used for a 3D one (the space discretization is not hierarchically nested), it is not possible to satisfy the orthogonality condition of and exactly. Thus, and that implies that, when the first switching strategy is considered, a parasite energy is created when switching and is depicted by high frequency oscillations that appear immediately after switching and are attenuated by numerical damping. Not verifying the orthogonality condition also means that the beam deflection and the 3D reference model deflection at the switch instant are not equal. This fact can be seen in all the illustrative applications of this article (see for example Figs. 10 and11) and is schematized in Fig. 25. It is due to the fact that the natural frequencies of the two models are very close but not equal. The switch leads to a 3D solution that is equivalent but not equal to the reference one. When the triple static switch is considered, the difference between the 3D reference solution and the beam solution leads no more to a transient stage since the difference is compensated by velocities (and subsequently accelerations) corrections. Thus, no numerical damping is needed.

Limits of the strategy: discussion and examples

When the difference between the beam and the 3D solution is very important, the switch has no meaning and that is the main limit of the strategy.

In the following, the previous rotor with same loading and boundary conditions is considered. It is set to rotate at ω = 15 000 rpm (equivalent to 250 Hz). This velocity is very close to a natural frequency of the rotor. In fact, the beam rotor has a natural frequency of 253.76 Hz while its equivalent for the 3D one is 255.59 Hz. Even though the difference is small and is due to normal modeling differences (see Section 5.2), this will lead to non-negligible behavior differences as shown in Fig. 26. In such a case, the switch should not be performed. Note, however, that this difference does not lead the switch to diverge, but rather to a solution that is different from both. However, switching is useful when the beam and the 3D models give similar results which here means at a rotation speed sufficiently far from natural frequencies. When the triple static switch is performed, no parasite energy is introduced in the system. The efficiency of the switch is not reduced, if lot of physical high frequencies are excited. It is only the difference between the beam and the 3D solution that may limit the switch. It can be reduced when the rotor is sufficiently slender, the 3D mesh is fine, etc.

The main advantage of the switch is its ease of implementation and none intrusive aspect. However, an intrusive switch in which the orthogonality of and is overcome is to be proposed in a future publication.

Conclusions

This article proposes a strategy that enables one to reduce the computational cost for the simulation of the accidental slowing down of turbines. This strategy is simple, efficient, robust and preserve the accuracy when a 3D description is required only on a small part time domains.

Despite an inevitable phase shift between the 3D reference solution and the beam solution, the switch enables to produce a 3D solution that represents a good approximation of the 3D reference solution. This 3D switch solution is initialized from the beam solution and has the same natural frequencies of the 3D reference solution. The proposed approach is also energetically sound and enables a significant computational cost saving.

Although this article illustrated the switch from a beam model to a full 3D model, limiting the size of the 3D zone to the area where non-linear phenomena is to take place can be achieved by performing a switch from a beam model to a hybrid beam-3D model. A hybrid beam-3D model can be obtained as done in Tannous et al [START_REF] Tannous | A beam to 3D model switch for transient dynamic analysis[END_REF].

This switch method can be applied to more diverse applications, such as local plasticity or thermoplasticity, cracking, and several other kinds of local linear or non-linear effects as long as the switch is performed in the linear stage preceding any non-linearity.

The switch is a non-intrusive approach that was developed on Code_Aster, and can be easily implemented on a commercial finite element software.

Fig. 1 .

 1 Fig. 1. Beam to 3D switch.

( 1 )

 1 Mb, Ab and Kb represent respectively the mass, damping and stiffness matrices of the beam model. Gb(ω) is the gyroscopic matrix. This later is a function of the rotating velocity ω.

Fig. 2 .

 2 Fig. 2. A simple rotor with a disk.

Fig. 3 .

 3 Fig. 3. Beam model of the rotor.

Fig. 4 .

 4 Fig. 4. Dimensions of the rotor. l1 l2 e r R d 0.25 0.25 0.0125 0.025 0.125 0.25625

Fig. 6 .

 6 Fig. 6. Unbalance loading time imposing law.

Fig. 7 .

 7 Fig. 7. Displacements results along the x-axis of point PN (rotating frame).

Fig. 8 .

 8 Fig. 8. Displacements along the x-axis of point PN (Galilean frame).

Fig. 9 .

 9 Fig. 9. Velocities and accelerations results along the x-axis of point PM (rotating frame)

Fig. 10 .

 10 Fig. 10. Velocities results along x-axis of point PN (Galilean frame).

Fig. 11 .

 11 Fig. 11. Accelerations results along x-axis of point PN (Galilean reference).

Fig. 12 .

 12 Fig. 12. Kinetic energy Wc = Wcr + Wcd.

Fig. 13 .

 13 Fig. 13. Deformation energy Wd.

Fig. 14 .

 14 Fig. 14. Total energy Wt = Wc + Wd.

Fig. 15 .

 15 Fig. 15. Zoom on the displacements results at the switch instant for ω = 1500 rpm (rotating frame).

Fig. 16 .

 16 Fig. 16. Velocities and accelerations results (rotating frame).

Fig. 17 .

 17 Fig. 17. Kinetic energy for ω = 1500 rpm.

Fig. 18 .

 18 Fig. 18. Strain energy for ω = 1500 rpm.

Fig. 19 .

 19 Fig. 19. Total energy for ω = 1500 rpm.

Fig. 20 .

 20 Fig. 20. Displacements results for the second loading law (rotating frame).

Fig. 21 .

 21 Fig. 21. Velocities and accelerations results for the second loading law (rotating frame).

Fig. 22 .

 22 Fig. 22. Kinetic energy for the second loading law.

Fig. 23 .

 23 Fig. 23. Strain energy for the second loading law.

Fig. 24 .

 24 Fig. 24. Total energy for the second loading law.

Fig. 25 .

 25 Fig. 25. Non verification of the orthogonality condition.

Fig. 26 .

 26 Fig. 26. Different behavior of a beam and a 3D model simulating the same physical problem and loading.

The first three natural frequencies of the

3D rotor model are 255.597 Hz, 255.772 Hz and 374.534 Hz. Those of the beam rotor model are 253.73 Hz (double mode) and 372.15 Hz.

The same conclusions and quality of the results shown in Fig.8is also obtained on the y-axis direction and on each point belonging to the rotor.

Acknowledgments

The authors thank the French National Research Agency (ANR) in the frame of its Technological Research COSINUS Program. (IRINA, Project ANR 09 COSI 008 01 IRINA).

Appendix A. Generating is obtained through a projector matrix P which transforms the beam displacement vector into a 3D rigid body displacement per beam section. It is noteworthy to say that the 3D mesh and the beam mesh cannot be totally disconnected in order for the switch to be done. To be able to construct the displacement of a node on the 3D mesh, we should have the displacements and rotations of the beam node that has the same position along the beam. In other words, the beam model should be a projection of the 3D mesh on its neutral axis. However, it is not easy to build P because it depends on the relationship between the beam mesh and the 3D mesh, which may change from one cross-section to another. Instead, we will generate as a whole. Let n the number of cross-sections. Gi, with i = 1…n, is a point belonging to the neutral axis of the crosssection i. Each cross-section of the 3D beam model is constituted of mi 3D nodes. Note that the number of nodes may differ from one cross-section to another. Nij, with j = 1…mi is a node that belongs to the i th crosssection of the 3D model.

is the displacement of Nij computed for a cross-section rigid body displacement. The cross-section to which belongs Nij has Gi on its neutral axis. The i th beam node, which has the same coordinates as Gi, has a displacement and a rotational displacement . With the finite element software used, such as Code_Aster or Abaqus, we write a python loop that manages to compute , , for each node Nij as follows:

where is a vector oriented from Nij to Gi. Point Nij has , , for coordinates. Suppose 0, therefore Eq. (A.1) reads:


L Brocolini

E Parizet

P Chevret

Effect masking noise on cognitive performance and annoyance in open plan offices

Keywords: open-plan office noise, task performance, cognitive workload, annoyance, sound sources, speech intelligibility

 to deal with fluctuating noise as speech babble. Fifty-five subjects performed a serial memory task in four STIt (non-stationary STI) conditions (from 0.38 to 0.69) while STI values were kept constant (around 0.36). No significant difference appeared between the decreases in performance observed with multiple levels of intelligibility. However, an inter-individual variability appeared in performance measurements. The best performers seemed to be less affected by the high level of intelligibility condition than the other ones.

Introduction

Developed in the 1950's, the concept of the "open-plan" office is now widespread in the workplace. While offering many advantages in terms of layout and facilitating communication between colleagues, this way of organising the workspace had two major disadvantages. The feeling of privacy is lessened and noise level is increased causing discomfort for individuals working in this type of environment. Currently, it appears that noise is a major nuisance factor in open-plan offices [START_REF] Amstutz | Etude SBiB -Enquête suisse dans les bureaux[END_REF] in spite of a relatively low noise level (less than 65 dB(A)) [START_REF] Landström | Exposure levels, tonal components, and noise annoyance in working environments[END_REF]. Consequently, regulations in terms of noise levels in the workplace [START_REF] Directive | 10/EC of the European Parliament and of the Council of 6 February 2003 on the minimum health and safety requirements regarding the exposure of workers to the risks arising from physical agents (noise)[END_REF] are not representative of the actual situation. Furthermore, it seems that the noise nuisance experienced in open-plan offices affects work satisfaction [START_REF] Leather | Noise, psychosocial stress and their interaction in the workplace[END_REF] and employee health [START_REF] Pejtersen | Indoor climate, psychosocial work environment and symptoms in open-plan offices[END_REF], and that this exposure to noise can reduce employee performance depending on the types of task to be carried out and the characteristics of the noise present in the workplace [START_REF] Beaman | Auditory distraction from low-intensity noise: a review of the consequences for learning and workplace environments[END_REF].

Numerous studies have been carried out over a number of years based on the effects of noise on performances in workspaces [START_REF] Kaarlela-Tuomaala | Effects of acoustic environment on work in private office rooms and open-plan offices-longitudinal study during relocation[END_REF], [START_REF] Szalma | Noise effects on human performance: a meta-analytic synthesis[END_REF]. However, very few have focussed on the nature of the various sources present in open-plan offices. The layouts of open-plan offices give rise to a multitude of sound sources: conversations or half-conversations, phone ring tones, machine noise (printers, photocopiers, computer keyboards), people moving around, ventilation systems, etc. Although conversations are most often thought of as being the most annoying noise source, phone ring tones can also be a significant annoyance. According to a field survey, Boyce found that out of 200 workers, 67% were upset by phone ring tones [START_REF] Boyce | Users' assessments of a landscaped office[END_REF]. For Sundstrom et al., out of more than 2000 employees, 54% said they were upset by noise, particularly from people speaking and ringing telephones [START_REF] Sundstrom | Office noise, satisfaction, and performance[END_REF]. In 2005, Banbury and Berry showed through a field survey that out of 88 employees, continuously-ringing telephones (which were not answered) were more annoying than other people's conversations followed by phone ring tones [START_REF] Banbury | Office noise and employee concentration: Identifying causes of disruption and potential improvements[END_REF]. More recently, Pierrette et al. had a questionnaire filled out by 237 employees of 7 French companies [START_REF] Pierrette | Noise effect on comfort in openspace offices: development of an assessment questionnaire[END_REF]. In this study, it emerged that intelligible conversations caused the most significant annoyance followed by unintelligible conversations, phone ring tones and lastly the noise of machines such as printers. In view of the latest results, we wanted to check that these effects could be measured by experiments carried out in the laboratory. Indeed, although there have been numerous studies carried out in a controlled environment of the effect of speech on performance, not many have been carried out on the influence of other sound sources. In a laboratory context, Shelton et al. showed that in a lexical decision task, performance was reduced in the presence of phone ring tones (compared with the same task under silent conditions) [START_REF] Shelton | The distracting effects of a ringing cell phone: An investigation of the laboratory and the classroom setting[END_REF]. This result was also demonstrated by Martellotta et al. [START_REF] Martellotta | Laboratory study on the effects of office noise on mental performance[END_REF]. In this study, the environments of individual offices characterised in particular by telephones, affect performance in a memory task and the annoyance felt. Likewise, the environments of open-plan offices, in which the presence of voices is the largest factor, also have a strong impact on performance and annoyance. In addition, these environments affect the Stroop test the most (compared with other sound environments mostly characterised by low frequency components). In order to provide more in-depth knowledge on the nature of the various sound sources present in open-plan offices, the first experiment carried out in this paper has therefore dealt with the influence of the type of sound source upsetting a cognitive task. Using a serial memory task, the performance of a number of listeners disturbed by various sound sources was measured along with the annoyance felt.

Secondly, we focussed on a single type of sound source -the intelligible speech signalfor which the level of intelligibility varied. The noise of speech is very widespread in openplan offices and it is recognised that the intelligibility of the speech is a major nuisance factor. Widely used to measure the intelligibility of a signal, the STI (Speech Transmission Index) [START_REF] Commission | Sound system equipment-Part 16: Objective rating of speech intelligibility by speech transmission index[END_REF] is a good indicator of the nuisance when the speech signal is masked by a stationary noise. A number of authors have demonstrated the influence of intelligibility on nuisance and performance [START_REF] Ellermeier | Is level irrelevant in' irrelevant speech'? Effects of loudness, signal-to-noise ratio, and binaural unmasking[END_REF]- [START_REF] Haka | Performance effects and subjective disturbance of speech in acoustically different office types-a laboratory experiment[END_REF]. However, the STI does not take account of the influence on intelligibility of a masking noise such as the one pervading an open-plan office (due to other conversations). Indeed, this noise has a fluctuating character which encourages intelligibility. One of the main reasons is a phenomenon called "listening in the gaps" which enables a listener to take in the information contained in the non-masked portions of the target signal in order to reconstruct the meaning. So for a given STI value, intelligibility will be better in the case of a fluctuating noise. Rhebergen et al. have proposed an indicator which takes account of the fluctuating nature of the mask. This indicator is the eSII, for extended Speech Intelligibility Index [START_REF] Rhebergen | A speech intelligibility index-based approach to predict the speech reception threshold for sentences in fluctuating noise for normalhearing listeners[END_REF], [START_REF] Rhebergen | Extended speech intelligibility index for the prediction of the speech reception threshold in fluctuating noise[END_REF]. The basic principle is that the speech signal and the noise are segmented into portions of short duration. The SII is calculated for each portion using the current standard (ANSI S3.5-1997) [START_REF] Ansi | S3. 5-1997, Methods for the calculation of the speech intelligibility index[END_REF]. The global intelligibility index eSII is then the average of the SII values over the whole duration of the processed signal. Using the calculation method of the eSII and applying it to the STI (this being the indicator which is mostly used in all studies on open-plan offices), the STIt is an average of the sliding STIs calculated over a short time window (of the order of 12.5 ms). Thus, given an equal STI between a stationary masking noise and a fluctuating one, the STIt is larger the greater the fluctuations. Through the second experiment carried out in this paper, we wanted to know whether the STIt could be a good indicator of nuisance in the case where the noise masking the target signal is fluctuating. The second experiment therefore consisted of measuring the performance of listeners during a serial memory task while they were in the presence of a signal masked by ambient noises which fluctuated to a greater or lesser extent but which had the same STI.

Experiment 1 2.1 Objectives

Using a questionnaire distributed to the employees of a number of French companies, Pierrette et al. were able to highlight a number of troublesome sound sources in open-plan offices [START_REF] Pierrette | Noise effect on comfort in openspace offices: development of an assessment questionnaire[END_REF]. Intelligible conversations appear to be the sound source most often heard, followed by phone ring tones, people moving around, machines such as printers operating and lastly unintelligible conversations. However, the hierarchy in terms of annoyance is different: non-intelligible conversations appear in second position behind intelligible conversations. After this come phone ring tones, machine noise and people moving around. From these results, the objective of experiment 1 presented in this paper was to confront individuals with these sound scenarios in the laboratory in order to assess the impact of these acoustic conditions on the perceived annoyance along with performance measured by means of an intellectual activity such as a serial memory task.

Subjects

Thirty-five individuals took part in the experiment. Among these thirty-five individuals, twenty-eight were recruited from outside the laboratory and were paid, the others were postgraduate students of the Acoustic Vibrations Laboratory. The group of subjects was made up of seventeen women and eighteen men. Their median age was 41, the youngest was aged 23 and the oldest 59.

All participants underwent audiogram testing in the audiometric booth of the laboratory. The total hearing loss was calculated as the average of the hearing losses at frequencies 500 Hz, 1000 Hz, 2000 Hz and 4000 Hz (weighted in the case of asymmetric losses) in accordance with the recommendations of the International Bureau for Audiophonology (BIAP) [START_REF] Audiophonology | BIAP Recommendation 02/1 bis -AUDIOMETRIC CLASSIFICATION OF HEARING IMPAIRMENTS[END_REF]. Among the 35 participants, 21 had no hearing loss, 9 had an impairment between 21 and 22 dB H.L. and 5 had an impairment between 24 et 30 dB H.L. Again according to the recommendations of the BIAP, this represents a slight hearing loss. Thus we have assumed that no subject had a hearing impairment liable to call into question the validity of the experiment.

Performance task

For each sound condition, the individuals have to memorise ten lists of ten words in French (presented visually) and repeat them orally (one list after the other). The words have been chosen from the lexical lists produced by D. Dubois and J. Poitou [START_REF] Dubois | Normes catégorielles' et listes lexicales. 'Normes catégorielles' (liste de termes) pour vingt-deux catégories sémantiques[END_REF]. Among twentyfive lexical categories, five categories were selected: Animals, Fruits, Vegetables, Birds, Clothing. Each category had thirty words (the most frequently used [START_REF] Dubois | Normes catégorielles' et listes lexicales. 'Normes catégorielles' (liste de termes) pour vingt-deux catégories sémantiques[END_REF]): "dog, cat, horse, lion, elephant, etc." for the "Animals" category, "apple, pear, orange, cherry, banana, etc." for the "Fruits" category, etc. The five categories appear twice during the same sound condition in a random order and the ten words from each list were also chosen randomly from among the thirty in each category.

Each list of words was announced on the screen by an image which was displayed for five seconds (so that the participant was prepared for the first word on the list to appear). Each word was displayed on the screen for two seconds (MS Sans Serif 48 point font). The words appeared one after the other without a pause. After the tenth word, the subject had twenty seconds to say out loud the words they had remembered. A microphone was used to record their answers. A pause of fifteen seconds followed the repeat-back phase, then a new series started: five seconds announcement, twenty seconds to memorise (10 words x 2 secs), twenty seconds of repeating back, fifteen seconds break, and so on through the ten series.

Sound stimuli

During this experiment, five sound conditions were used, relating to the four types of sound source and a control condition which consisted of a wide band background noise similar to a ventilation system. The sources were the sound sources identified as troublesome during the study by Pierrette et al. [START_REF] Pierrette | Noise effect on comfort in openspace offices: development of an assessment questionnaire[END_REF], namely: machine noise (printers), intelligible speech, unintelligible speech and lastly phone ring tones. All signals used were built up from sound samples lasting a few seconds found on the Internet [START_REF]Universal-Soundbank[END_REF]- [START_REF] Rfi | Cours de français[END_REF]. More details regarding each of the sources are given in the following paragraphs.

Background noise (Control)

The background noise used during this experiment came from the "Universal Soundbank" website [START_REF]Universal-Soundbank[END_REF]. This is the noise of a ventilation system lasting a few seconds which was repeated in order to obtain a continuous signal lasting ten minutes. The level of this background noise was set at around 35 dB(A) at the position of the listener.

Printers (P)

The sounds of printers were also retrieved from the "Universal Soundbank" site [START_REF]Universal-Soundbank[END_REF]. These were three samples of respectively 12.5, 16 and 19.5 seconds. The first was the characteristic noise of an "inkjet" printer while the other two were of "laser" printers. Each of these samples was repeated twelve times to obtain thirty-six samples in total.

Intelligible speech (I-S)

From the "Audio-lingua" website [START_REF]expérimentation pédagogique du C. R. D. P. de l'académie de Versailles[END_REF], the intelligible speech database had thirty-six different samples. This involved individuals speaking on various subjects in French. Each sample was cut to obtain twelve files of duration 12.5, 16 or 19.5 seconds. Half of the samples were women's voices and half men's.

Non intelligible speech (N-I-S)

To obtain non-intelligible speech signals, nearly fifty sound extracts of intelligible speech (the shortest about twenty seconds and the longest about a minute) were retrieved from the "RFI" website [START_REF] Rfi | Cours de français[END_REF]. These were from French courses. From these conversations, 12.5 seconds were selected randomly from eight different files (also selected randomly) and were mixed together. Using the same procedure, eleven other samples of 12.5 seconds were built up along with twelve of 16 seconds and twelve of 19.5 seconds.

Phone rings (P-R)

In the same way as for printers, the sounds of telephones ringing were extracted from the "Universal Soundbank" website [START_REF]Universal-Soundbank[END_REF]. Four different ring tones were used, each being reworked into a sample lasting 12.5 seconds, one of 16 seconds and one of 19.5 seconds. Four types of ring tone were provided of three different durations making twelve samples. These signals were repeated three times to end up with a total of thirty-six samples.

For each sound sample, thirty-six samples were placed end-to-end (in a random order for each subject), with a one-second interval in between giving a total sound signal length of ten minutes. The background noise was emitted with a level L Aeq,10min of about 35 dB(A) while the sound sources superimposed on the background noise were played with a level L Aeq,10min of about 50 dB(A). All samples had been previously equalised to a level of L Aeq,12.5s = L Aeq,16s = L Aeq,19.5s = 50 dB(A). The sound levels were chosen to approximate to the actual situation in an open-plan office [START_REF] Pop | Acoustic descriptors for open plan offices -Evaluation of field measurements[END_REF].

Procedures

Research setting

The experiment took place in an audiometric booth in the laboratory. All stimuli were presented via a loudspeaker (Tapco S8) placed about 1 metre from the floor and from the listener behind the computer screen. The reproduction chain was frequency-corrected (31band ULTRA-CURVE PRO DSP8024 equaliser) such that the frequency response of the loudspeaker at the listening position was flat (the standard deviation of the level was 1.4 dB over all third octave bands between 40 and 12500 Hz).

Before starting the experiment, each participant had undergone audiogram testing (Oscilla USB-300 Screening Audiometer/AudioConsole 2.3.8). It was then explained to the individual that the experiment consisted of memorising lists of ten words and repeating back as many as possible (the responses were recorded using a directional microphone placed between the listener and the computer screen). To prevent the subjects saying too many words, it was explained to them that the number of "correct" words would be counted (+1) and that a penalty (-1) would be applied for "incorrect" words. To ensure the procedure was understood, an example with only two lists of words and without any sound source was then carried out in the presence of the experimenter. Then, all participants started the experiment with a background noise to familiarise them with the experiment. Lastly, they all carried out the requested task in the presence of each sound condition (background noise, machines, intelligible speech, unintelligible speech, telephones) in a random order based on a Latin square (5x5) [START_REF] Bradley | Complete counterbalancing of immediate sequential effects in a Latin square design[END_REF] to obviate any order effect. At the end of each sound condition, the participants had to answer a French version of the NASA-TLX questionnaire (see 2.5.3). Lastly, at the end of the experiment, they answered an annoyance questionnaire.

Performance measurement

The performance measured for each listener consisted of a sum of the words correctly repeated from which the number of incorrect words was subtracted. In order to assess the impact of the various sound conditions, all performances were expressed relative to that measured when the background noise only was played (the second presentation, the first was only used for learning). In other words, the measured data did not represent the raw performance but a decrease in performance calculated as the difference between the performance obtained in the control situation and the performance obtained with each sound condition:

Workload measurement

Developed at the end of the 80's, the NASA-TLX (Task Load Index) [START_REF] Hart | NASA Task Load Index (TLX) V1. 0 Users Manual[END_REF], [START_REF] Hart | NASA-task load index (NASA-TLX); 20 years later[END_REF] makes it possible to assess the work load through six questions. Each of these questions relates to a component of the work load: mental demand, physical demand, temporal demand, performance, effort, frustration. The questions are assessed on a scale of 0 to 100. Secondly, a weight is allocated to each component. NASA-TLX is a weighted mean of the six scores. NASA-RTLX (Raw Task Load Index) is a simplified version, namely, non-weighted and enables similar results to be obtained in less time [START_REF] Hart | Development of NASA-TLX (Task Load Index): Results of empirical and theoretical research[END_REF].

Each participant completed the NASA-RTLX using a graphic interface developed under Matlab after each sound condition. In the same way as for performance, the work load linked to the task carried out was expressed relative to that measured during the transmission of the background noise only. So as to work with theoretically positive data, the increase of NASA-RTLX was calculated as follows:

Annoyance measurement

The annoyance felt was measured again using the Matlab graphic interface. Unlike NASA-RTLX, the annoyance was measured at the end of the experiment after hearing all the sound conditions. The question asked was as follows: "At which point did the sound sources affect you in accomplishing the task requested?". A button on which was written the name of the sound source allowed the user to listen to it again for five seconds. Beside each source, a continuous scale allowed the subjects to score the annoyance felt using a cursor. Five points on each scale were marked with the words: "Not at all", "Slightly", "Moderately", "Very", "Extremely" [START_REF] Fields | Standardized General-Purpose Noise Reaction Questions for Community Noise Surveys: Research and a Recommendation[END_REF] giving the participants an idea of where to place the cursor. The position of the cursor was converted into a score between 0 (not at all annoying) and 100 (extremely annoying). To analyse the results, the score for each annoyance consisted of an increase in the annoyance level between each sound source and the background noise:

Results

Performance

The decreases in average performance according to the sound source are shown in figure 1. On average, the decrease in performance was the greatest when the sound source was intelligible speech (6.8%) followed by unintelligible speech (3.4%), printers (2.7%) and lastly phone ring tones (1.9%).

In order to check whether there was a significant difference between the various sound conditions, a repeated measures analysis of variance was carried out with one dependent variable: the decrease in performance, and one independent variable: the type of sound source. This analysis of variance showed that the sound condition had a significant effect on the decrease in performance (F(3,102) = 5.7, p = 0.0012). An Honest Significant Difference test (HSD), whose p values are given in table 1, shows that the decrease in performance is significantly greater in the presence of intelligible speech in comparison with other sound sources as can be seen from figure 1. A second repeated measures analysis of variance was carried out this time including the "age" and "sex" factors. This analysis did not reveal a link between the decrease in performance and the age or sex of the subjects.

NASA-RTLX

The most significant increase in cognitive load is obtained with intelligible speech (8.7%). However, unintelligible speech and phone ring tones can cause an extra cognitive load which is relatively close (7.8% and 6.8%). Only printers lead to a relatively low increase in NASA-RTLX (3.7%). This is confirmed by the one-way repeated measures analysis of variance carried out with the increase in NASA-RTLX as dependent variable and the type of source again as independent variable. Again, the results of this analysis are significant (F(3,102)=2.9, p=0.0408). The sound condition therefore has an influence on the increase in the cognitive load associated with a serial memory task.

The analysis of figure 2 combined with a Tukey post-hoc test shows that there is no significant difference between the "Printers", "Unintelligible speech" and "Phones" conditions. Likewise, there is no significant difference between the "Intelligible speech", "Unintelligible speech" and "Phones" conditions. On the other hand, the "Printers" and "Intelligible Speech" sound conditions are significantly different (see Table 2).

Annoyance

In the case of an increase in the annoyance felt, the results are similar to the increase in NASA-RTLX, even if the order of magnitude is greater. On average, the increase in annoyance felt is similar during intelligible speech, unintelligible speech and phone ring tone conditions (respectively 55.9%, 50.5% and 51.7%). The increase in annoyance felt with the printers is however mostly less (29.6%). A repeated measures analysis of variance confirms this significant effect of the sound condition (F(3,102)=15.3, p=0.0000). With regard to figure 3 and the Tukey difference test (see Table 3), it appears that "Intelligible speech", "Unintelligible speech" and "Phones" are not significantly different in effect. On the other hand, the increase in annoyance is significantly lower under the "Printers" condition than in the three other sound conditions. We also note that with regard to the annoyance felt, the age and sex of the subjects once more had no significant effect after a three-way repeated measures analysis of variance.

Discussion

The aim of experiment 1 was to assess the impact of various sound sources on performance in carrying out an intellectual task as well as on the perceived annoyance. The results obtained for performance measurement were expected and in agreement with what had been shown on numerous occasions: the performance in a memory task decreases in the presence of intelligible speech [START_REF] Hongisto | A model predicting the effect of speech of varying intelligibility on work performance[END_REF], [START_REF] Liebl | Combined effects of acoustic and visual distraction on cognitive performance and wellbeing[END_REF]- [START_REF] Ebissou | Use of the Speech Transmission Index for the assessment of sound annoyance in open-plan offices[END_REF]. On the other hand, the results obtained in terms of annoyance were less expected. No significant difference appeared between intelligible speech, unintelligible speech and phone ring tone signals. However, during a field survey by Pierrette et al. [START_REF] Pierrette | Noise effect on comfort in openspace offices: development of an assessment questionnaire[END_REF], intelligible conversations were by far the most annoying sound sources. Although it is difficult to provide an explanation as to these results, they are however confirmed by the analysis of the NASA-RTLX. Indeed, although having been evaluated using a slightly different procedure (NASA-RTLX was evaluated after each sound condition while the annoyance was evaluated at the end of the experiment), the results were similar. Intelligible speech is significantly different from printer noise, but is not more annoying than unintelligible speech. Although less efficient in the presence of intelligible speech, the individuals did not however feel more troubled. However a number of studies have shown a significant difference between these two sound sources in terms of annoyance [START_REF] Haka | Performance effects and subjective disturbance of speech in acoustically different office types-a laboratory experiment[END_REF], [START_REF] Schlittmeier | The impact of background speech varying in intelligibility: Effects on cognitive performance and perceived disturbance[END_REF] and work load [START_REF] Ebissou | Use of the Speech Transmission Index for the assessment of sound annoyance in open-plan offices[END_REF]. However, these results have been obtained with parameters associated with different stimuli which were used in our experiment. For example, in the study by Schlittmeier et al. [START_REF] Schlittmeier | The impact of background speech varying in intelligibility: Effects on cognitive performance and perceived disturbance[END_REF], the stimuli were present at a level at 35 dB(A) while in our case, the sounds were broadcast at 50 dB(A). Likewise, Haka et al. [START_REF] Haka | Performance effects and subjective disturbance of speech in acoustically different office types-a laboratory experiment[END_REF] show a variation in annoyance according to intelligibility using single-voice signals transmitted at 48 dB(A). In our study, no difference was visible between an intelligible signal with a single voice and unintelligible speech with multiple voices. These different parameters may in part explain the differences in the results obtained.

Anyhow, the speech signal remains a special sound source which led us on to test the influence of the level of intelligibility in experiment 2.

3 Experiment 2

Objectives

The objective of experiment 2 was to evaluate the influence of ambient speech on performance in the case where the background noise was fluctuating. Under experimental conditions similar to experiment 1, the performance of the listeners during a serial memory task was measured in the presence of a target voice and a masking noise. A mix of different voices was used to achieve a masking noise with varying degrees of fluctuation. Five sound conditions were tested:

-1 stationary noise only as control condition -1 male voice (target) + stationary noise (mask) -1 male voice (target) + 5 voices (mask) -1 male voice (target) + 3 voices (mask) -1 male voice (target) + 1 voices (mask) With regard to the mask, the higher the number of voices, the more the mask tended to become stationary. For this reason, if the average spectral content of each mask used was identical, the Speech Transmission Index (STI) would remain identical while the STIt would be higher the more the masking signal fluctuated.

Subjects

Fifty-five individuals took part in experiment 2. The group of subjects was made up of twenty-nine women and twenty-six men. Their median age was 44, the youngest was aged 31 and the oldest 61. They were all paid for taking part. All participants underwent audiogram testing in the audiometric booth in the laboratory and the total hearing loss was calculated (see 2.2). Among the subjects, 41 had a total hearing loss of between 20 and 22 dB H.L, 13 had an impairment between 23 and 29 dB H.L and one participant had a hearing impairment of 34 dB H.L. Regarding these hearing losses, no subject was discounted.

Performance task

The performance task was strictly the same as that used during experiment 1 (see 2.3).

Sound stimuli

Five sound conditions were used, corresponding to four masking levels of a target voice and one control condition which consisted of a normalised LTASS speech noise [START_REF] Byrne | An international comparison of longterm average speech spectra[END_REF] without target voice.

Control

The control condition used during this experiment was 22 seconds of white noise generated using Matlab then LTASS normalised. The level of this background noise was set at around 47 dB(A) at the position of the listener.

Clear speech

The target voice came from recordings available from the Collège National d'Audioprothèse. More precisely, it involved a "Man" reading phrases from Combescure [START_REF]Listes de phrases de Combescure[END_REF], Fournier [START_REF]Listes de phrases de Fournier[END_REF], along with lists from the Hearing in Noise Test (HINT) [START_REF]Listes de phrases HINT (Hearing In Noise Test)[END_REF]. All the available recordings were juxtaposed and cut into 40 samples of 22 seconds. These 40 samples were all normalised using the LTASS speech spectrum.

Masking sounds

The masking noise was made up of men's and women's voices. From the "Audio-lingua" website [START_REF]expérimentation pédagogique du C. R. D. P. de l'académie de Versailles[END_REF], it involved individuals speaking on various subjects in French. All the available signals were juxtaposed and cut into 90 samples of 22 seconds after having removed as many "blanks" as possible from the various speeches. Each of these 90 samples were normalised using an LTASS speech spectrum.

For each listener taking part in the experiment, the 1-voice mask was from these 90 samples, the 3-voice mask was a mix of 3 samples and the 5-voice mask a mix of 5 samples. All masking signals were equalised at the same level L eq,22s . The 4 th masking noise was a stationary noise. This was the same signal as that used for the control condition.

To avoid any possible confusion between the target signal and the mask (particularly in the case of the "1 voice (target) + 1 voice (mask)" sound condition), the masking signals were temporally inversed. In this way, the average spectrum remained unchanged, the same as the STI, and there was no possible confusion between the target signal and the masking signal.

The signal-to-noise ratio (target/mask) was set to -4 dB, i.e. a STI of approximately 0.35. A STI value such as this corresponds to the area where heightened decrease in performance is at its greatest in the predictive model of decrease in performance developed by Hongisto et al. [START_REF] Hongisto | A model predicting the effect of speech of varying intelligibility on work performance[END_REF]. The STI and STIt were systematically calculated for each stimulus created (4 masks x 10 repetitions x 55 participants). Figure 4 shows the averages of 550 STI and STIt values calculated for each masking condition. The average STI was 0.35 with the stationary masking noise and 0.36 for the other masks (5 voices, 3 voices, 1 voice). The variation in STI as expected was minimal and the standard deviation was greater the lower the number of voices present in the mask and therefore the higher the modulation. The average STIt calculated on the other hand was 0.38 with the stationary mask, 0.51 with the 5-voice signal, 0.56 with the 3-voice signal and 0.69 with the 1-voice signal. There again, the standard deviation was greater the higher the modulation of the masking signal. Only a few STIt values of the "3voice" condition were less than those of the "5-voice" condition. Overall, the 4 masking conditions were very different from one another from the STIt point of view. The difference between the average STIt calculated (0.38) and the STI calculated (0.35) for the stationary mask is explained by the method of calculating spectra in the octave band used. Indeed, for very short times (12.5 ms) the digital filters used with Matlab underestimate levels in the lowest octave bands.

During experiment 1, the stimuli were emitted throughout the period when the subjects were carrying out the requested cognitive task, namely during the word memorising and repeat-back phase (see 2.3 for more details of the cognitive task). In this new experiment, taking into account the signals available, the stimuli were only transmitted during the memorising phase.

Procedures

The sequence of experiment 2 was almost the same as for experiment 1 with a few exceptions (see 2.5). The main difference was in the fact that the participants in experiment 2 did not assess annoyance. Only the performance (see 2.5.2) and the cognitive load (see 2.5.3) were measured.

Results

Performance

The average performance decrease values are given in figure 5. On average, the decrease in performance was 3.71% when the mask was a stationary noise, 2.22% when the mask was made up of 5 voices, 3.56% with 3 voices and 3.05% with 1 voice. These results are compliant with those found by Ellermeier and Hellbrück (Exp. 2B) [START_REF] Ellermeier | Is level irrelevant in' irrelevant speech'? Effects of loudness, signal-to-noise ratio, and binaural unmasking[END_REF] which predicted a decrease in performance of about 3% for an STI of 0.35. This decrease in performance seemed reasonably stable whatever masking noise was used. To confirm this, a repeated measures analysis of variance was carried out with one dependent variable: the decrease in performance and one independent variable: the type of masking. This analysis of variance showed that there was no significant effect due to the fluctuation of the masking noise on the decrease in performance (F(3,162) = 1.3, p = 0.2927). In addition to the analysis of variance, a comparison test with a standard (0) of the percentage decrease in performance was carried out. The results of this test are shown in table 4. The fact that the percentage decrease in performance is statistically non-zero implies that adding a voice worsens the performance in comparison with the control situation which does not have a target signal. Je reste perplexe sur le t-test. Pourquoi tu ne fais pas un tuckey ? Et, je ne vois pas ce que tu appelles « standard (0) ». To explore these results in greater depth, a hierarchical clustering (Ward's method) was carried out on the raw performance obtained for five sound conditions -control (control1 was used for learning and control2 was used as reference), stationary, 5 voices, 3 voices and 1 voice. This classification highlighted two groups of individuals. Group 1 comprised 21 individuals and group 2 34. The first group of 21 people had consistently better performances (whatever the condition) than those in the second group of 34 subjects as can be seen in figure 6 -no relationship between this classification and the data specific to the subjects (gender, age, hearing) could be identified. Now, the decrease in performance is similar between the two groups except under the condition with a single masking voice (see Figure 7). A mixed repeated measures analysis of variance (one factor within subjects, one factor between subjects) showed that the interaction between the two factors is significant (F(3,159)=3.5, p=0.0177). Figure 7 shows that the effect resides in the "one masking voice" condition (corresponding to the highest STIt). The decrease in performance is therefore significantly greater for subjects with worse performances overall.

NASA-RTLX

The results of the increase in work load are similar to those obtained for the decrease in performance (see Figure 8). As before, a one-way repeated measures analysis of variance carried out with the rate of increase in NASA-RTLX as dependent variable and the masking sound again as independent variable. Again, the results of this analysis were not significant (F(3,102)=1.9, p=0.124). The fluctuation in masking noise therefore has no influence on the increase in the cognitive load associated with a serial memory task. Following this variance analysis, a comparison test with a NASA-RTLX increase standard was also carried out. The results of this comparison test may be seen in table 5. Once again, the significant differences relative to 0 of the increase in NASA-RTLX for each sound condition show that extra work load is required when one voice is added to the signal.

Likewise for performance, a mixed repeated measures analysis of variance with the "group" factor was carried out with the percentage increase of NASA-RTLX as dependent variable. This time, the results show no significant effect whether of the mask or the group or the interaction between the two. However, it is worthwhile noting that if the groups were formed on the basis of raw performance, the segmentation of these two groups is similar in the measurement of the cognitive load (je ne comprends toujours pas, est-ce que tu veux dire que tu obtiendrais la même segmentation pour la performance que pour la charge cognitive. Si c'est le cas, la phrase n'est pas correcte me semble-t-il). Whatever the sound condition, the memory task was less demanding for group 1 (the better performers) than for group 2 as can be seen in figure 9.

Discussion

In this experiment, no significant difference appeared between the decreases in performance observed with multiple levels of mask modulation. These results therefore seem to contradict the proposal to use the STIt temporal index as indicator of performance in the case where the masking noise of a speech signal fluctuates. It also goes counter to the other indicators such as the fluctuation force as proposed by Schlittmeier et al. in particular [START_REF] Schlittmeier | Algorithmic modeling of the irrelevant sound effect (ISE) by the hearing sensation fluctuation strength[END_REF]. According to the authors, the performance in a short-term memory task is directly linked to the fluctuating force of the stimulus. Now, in our experiment, the fluctuation force is naturally greater for the "1 target voice + 1 voice" (Fs = 0.65 vacil) mix than for the "1 voice + stationary noise" (Fs = 0.1 vacil) mix and is therefore not representative of performance. On the other hand, the results obtained did not completely contradict the study carried out by Haapakangas et al. [START_REF] Haapakangas | Effects of five speech masking sounds on performance and acoustic satisfaction. Implications for open-plan offices[END_REF]. In this study, the performance during a serial memory task was measured in the presence of a speech masked by five different noises. Among the five masks, there was in particular a pink noise, ventilation noise and music containing words. Although not having been measured according to an objective criterion such as the fluctuation force, it appeared clear according to the authors that the ventilation noise and the pink noise were more stationary in time than the musical mask. However, the decreases in performance measured with these three masks (with equivalent STI) were not significantly different. Between subject differences appeared for the condition "1 target voice + 1 voice". The listeners in the group with higher performance seemed less affected by the noise. Ebissou et al. [START_REF] Ebissou | Use of the Speech Transmission Index for the assessment of sound annoyance in open-plan offices[END_REF] have already shown that there is a difference in performance specific to the subjects, but this difference was visible whatever the sound condition (variable STI). In our case only the "1 target voice + 1 masking voice" condition highlighted a difference between the two groups of subjects. For the other sound conditions, the two groups seemed similar.

Regarding the work load measured via the NASA-RTLX, no significant impact was found between the various sound conditions which confirms the results previously found on the subject of performance.

Conclusion

The two experiments presented in this paper have highlighted under laboratory conditions a significant effect of intelligible speech on the performance achieved during a serial memory task (in comparison with other sound sources such as unintelligible speech, phone ring tones and printers). This effect is not found, however, through a subjective measurement of the work load or an evaluation of the annoyance although this has been shown during field surveys [START_REF] Pierrette | Noise effect on comfort in openspace offices: development of an assessment questionnaire[END_REF]. Furthermore, no effect on performance was observed due to the fluctuation of a masking signal. However, the relationship between STIt and the intelligibility of the speech in a fluctuating noise has been confirmed in the literature. These contradictory results could mainly be explained by the short period of exposure. As the effects of the factors for the various conditions were of the second order (as the STI was equal under these conditions), the subjects were able to concentrate their cognitive resources during the ten minutes of each condition.

So, for the future, longer duration tests might be a path which would be worthwhile exploring further.

Figure 1 :

 1 Figure 1: Decrease in performance with sound sources. (Mean values are presented with their corresponding standard errors)

Figure 2 :

 2 Figure 2: Increase in RTLX with sound sources. (Mean values are presented with their corresponding standard errors)

Figure 3 :

 3 Figure 3: Increase in annoyance with sound sources. (Mean values are presented with their corresponding standard errors) Table3: HSD test p-values Sound source P I-S N-I-S P-R P 0.0001* 0.0002* 0.0001* I-S 0.0001* 0.5830 0.7524 N-I-S 0.0002 0.5830 0.9927 P-R 0.0001 0.7524 0.9927

Figure 4 :

 4 Figure 4: Mean values of STI and STIt for each masking sound (Mean values are presented with their corresponding standard deviations).

Figure 5 :

 5 Figure 5: Decrease in performance with masking sound (Mean values are presented with their corresponding standard errors).

Figure 6 :

 6 Figure 6: Performance with masking sound for the two groups of listeners (Mean values are presented with their corresponding standard errors).

Figure 7 :

 7 Figure 7: Decrease in performance with acoustic condition for the two groups of listeners (Mean values are presented with their corresponding standard errors).

Figure 8 :

 8 Figure 8: Increase in Raw Task Load Index with masking sound (Mean values are presented with their corresponding standard errors).

Figure 9 :

 9 Figure 9: NASA-RTLX with acoustic condition for the two groups of listeners (Mean values are presented with their corresponding standard errors).

  way repeated measures analysis of variance (condition, age, sex) shows that neither age nor sex has any effect on the increase in NASA-RTLX, nor any interaction whatsoever.

		Table2: HSD test p-values
	Sound source	P	I-S	N-I-S	P-R
	P		0.0356*	0.1166	0.3223
	I-S	0.0356*		0.9606	0.7316
	N-I-S	0.1166	0.9606		0.9495
	P-R	0.3223	0.7316	0.9495
	A three-

Table 4 : one sample t-test for percentage of decrease in performance

 4

	Mask	%DP	Ref	t	dl	p
	Stationary	3.71	0	3.96	54	0.0002
	5 voices	2.22	0	2.71	54	0.0089
	3 voices	3.56	0	3.70	54	0.0005
	1 voice	3.05	0	3.13	54	0.0028

Table 5 : one sample t-test for percentage of increase in Raw Task Load Index

 5

	Mask	%IRTLX	Ref	t	dl	p
	Stationary	5.71	0	3.32	54	0.0016
	5 voices	4.43	0	2.22	54	0.0307
	3 voices	6.76	0	3.65	54	0.0006
	1 voice	7.45	0	4.32	54	0.0001

Funding

This project was funded by ANSES (Agence nationale de sécurité sanitaire, de l'alimentation, de l'environnement et du travail), in the frame of the Environment-Health-Work Program, with the support of Governmental Offices for Environment and Work. A major portion of the work was conducted within the CeLyA (Centre Lyonnais d'Acoustique) [ANR-10-LABX-60] research network.