R Ravaud

G Lemarquand
email: guy.lemarquand@univ-lemans.fr

T Roussel

Time-varying non linear modeling of electrodynamic loudspeakers

Keywords: Loudspeaker, Electrodynamic, Electrical Impedance PACS: 43-38 Ja

This paper deals with the time-varying nonlinear analytical modeling of the electrodynamic loudspeaker. We propose a model which takes into account the variations of Small signal parameters. The six Small signal parameters (R e , L e , Bl, R ms , M ms , C ms ) depend on both time and input current. The electrodynamic loudspeaker is characterized by the electrical impedance which, precisely measured, allows us to construct polynomial functions for each Small signal parameter. By using this analytical model, we propose to compare two identical electrodynamic loudspeakers.

One of them is supposed to be run in and the other one is not. The experimental methodology is based on a precise measurement. In all the paper, the time scale is assumed to be much longer than one period of the harmonic excitation.

Introduction

The reference model describing the electrodynamic loudspeaker designed by Thiele and Small [START_REF] Small | Closed-boxloudspeaker systems, part 1: Analysis[END_REF] predicts that the electrodynamic loudspeaker is both a linear system and a stationary one. This analytical model is very useful since it is simple to use. However, an electrodynamic loudspeaker exhibits nonlinearities which depend on time. Some authors, such as A.J.M Kaiser [START_REF] Kaizer | Modeling of the nonlinear response of an electrodynamic loudspeaker by a volterra series expansion[END_REF] and W. Klippel [3] [START_REF] Klippel | Loudspeaker nonlinearities -cause, parameters, symptoms[END_REF], have studied the nonlinearities of electrodynamic loudspeakers. These nonlinearities have become better and better known [START_REF] Noris | Nonlinear dynamical behavior of a moving voice coil[END_REF] [6] and some authors have proposed a new structure of loudspeaker with an ironless motor and without any outer rims and spider [START_REF] Berkouk | Contribution a l'etude des actionneurs electrodynamiques[END_REF] in order to eliminate these nonlinearities.

The other drawback of an electrodynamic loudspeaker is that it is an timevarying system [START_REF] Gander | Dynamic linearity and power compression in moving-coil loudspeaker[END_REF]. Indeed, the electrical resistance R e increases in time due to the heat produced by the voice coil. Then, the compliance C ms depends on time since the outer rim and the spider become more elastic because of the heat produced by the resistance. The Small signal model using lumped parameters does not forecast these time-varying phenomena, and such an time-varying analytic model taking into account these properties does not exist. In this paper, we put forward a way of characterizing experimentally the time dependence and the level dependence of the Small signal parameters. This experimental characterization allows us to compare two identical electrodynamic loudspeakers. One of them is supposed to be run in and the other one is not. The knowledge of the time necessary to break-in an electrodynamic loudspeaker is very important because this element of information gives indications about the physical properties of both the mechanical stiffness k and the mechanical damping parameter R ms . The first section presents the Small signal model using lumped parameters and the main nonlinearities of an electrodynamic loudspeaker. The second section presents the experimental methodology to identify the variations of the Small signal parameters. In the third section, the time dependence of the Small signal parameters and its consequences are discussed. The last section presents an analytical model which takes into account the variations of the Small signal parameters in time and according to the input current.

2 The Small signal model using lumped parameters and its limits

The Small signal model using lumped parameters

According to the Small signal model using lumped parameters, two coupled differential equations are necessary to describe the electrodynamic loudspeaker. One of them is called the electrical differential equation and is given by:

u(t) = R e i(t) + L e di(t) dt + Bl dx(t) dt (1)
The other one is called the mechanical differential equation and is given by:

M ms d 2 x(t) dt 2 = Bli(t) -R ms dx(t) dt - 1 C ms x(t) (2)
The parameters used in Eqs.( 1) and (2) are the following: Eqs. ( 1) and ( 2) allow us to define the electrodynamic loudspeaker electrical impedance Z e which is expressed as follows:

i(t)=coil current [A] u(t)=input voltage [V ]
Z e = R e + jL e w + Bl 2 R ms + jM ms w + 1 jCmsw (3)
Eq. ( 3) is well known and is often used to describe the electrodynamic loudspeaker. However, Eq.( 3) does not forecast the distortions created by an electrodynamic loudspeaker and the time dependence of the Small signal parameters. Moreover, if we take into account the eddy currents [START_REF] Vanderkooy | A model of loudspeaker driver impedance incorporating eddy currents in the pole structure[END_REF] which occur when the input frequency increases, the electrical impedance Z e should be written as follows:

Z e (i, t) = R e (i, t) + jR µ (i, t)L e (i, t)w jL e (i, t)w + R µ (i, t) + Bl(i, t) 2 R ms (i, t) + jM ms (i, t)w + 1 jCms(i,t)w (4)
where R µ (i, t) is the eddy current resistance. Z e (i, t) is a time-varying nonlinear transfer function; at each time and for different input currents, its value changes. In Eq. ( 4), we assume all the parameters depend on both time and input current. Strictly speaking, these dependences exist but it is very difficult to find them experimentally and to predict them analytically. All these parameters have not the same sensitivity both to input current and to time.

Moreover, some parameters vary a lot with the input current but do not create important distortions

Nonlinearities of electrodynamic loudspeakers

The nonlinearities that produce distortion phenomena can be classified into three categories. The first type corresponds to the motor nonlinearities and is described in section (2.2.1). The second type corresponds to the suspension nonlinearities and is described in section (2.2.4). The third type corresponds to the acoustical nonlinearities [START_REF] Lemarquand | Large bandwith loudspeaker emitting coherent acoustic waves: nonlinear inter-modulation effects[END_REF] and is not described here since these nonlinearities are not directly produced by the electrodynamic loudspeaker.

The motor structure

The force factor Bl is not uniform in the air gap. First, the force factor depends on the voice coil position. Indeed, the magnetic field induction B is the superposition of two fields. One of them is created by the permanent magnet and is time independent. This field crosses through the yoke pieces but only thirty per cents serves to move the coil. The other one is created by the coil and is time dependent. Klippel [START_REF] Klippel | Dynamic measurement and interpretation of the nonlinear parameters of electrodynamic loudspeakers[END_REF] proposed to model the force factor by using a polynomial writing.

Bl(x) = Bl 0 + Bl 1 x + Bl 2 x 2
(5)

The voice coil inductance

The coil self inductance depends on the moving part position. This dependence generates a reluctant force. This reluctant force is given by:

F rel (t) = 1 2 i(t) 2 dL e (x) dx (6)
We see that when L e does not depend on the voice coil position x, the reluctant force F rel (t) equals zero, it is one of the assumptions of the Small signal model using lumped parameters.

Eddy currents

The electrical conductivity of the iron is high enough to let the eddy currents appear in the iron yoke pieces of the motor. Vanderkooy [START_REF] Vanderkooy | A model of loudspeaker driver impedance incorporating eddy currents in the pole structure[END_REF] proposed a model which takes this phenomenon into account, the electrical impedance varies like L e √ w. The interaction between the eddy currents and the current in the coil generates a drag force F drag which can be written as follows:

F drag = η(i, x) dx(t) dt 1,7 (7)
where η(i, x) can be defined as the sensitivity of the drag force according to the eddy currents ; this one depends on input current and the position of the voice coil.

The suspension

A classical suspension is mostly made of rubber, impregnated fabric or molded plastic. The Small signal model using lumped parameters describes a suspen-sion as an ideal spring but an actual suspension shows non linear behaviour.

In consequence, its compliance C ms depends on the movement amplitude and the induced damping parameter R ms depends greatly on both the amplitude and frequency. More generally, many authors use the mechanical stiffness k which is defined by:

k = 1 C ms (8)
Like the force factor Bl, k can be written in terms of a polynomial function.

k(x) = k 0 + k 1 x + k 2 x 2 (9)
Such a model has been used by Klippel [3] to model the non linear behaviour of both the outer rim and the spider. However, such a model cannot take into account the effect of the hysteretic response of elastomers.

Time varying properties of the electrodynamic loudspeakers

The electrical resistance R e

Many authors studied the non stationnarities of electrodynamic loudspeakers as M.Gander [START_REF] Gander | Moving-coil loudspeaker topology as an indicator of linear excursion capability[END_REF], [START_REF] Gander | Dynamic linearity and power compression in moving-coil loudspeaker[END_REF] and showed that the Small signal parameters depend on time. The parameter which seems to be the most sensitive to time is the electrical resistance R e . The electrical resistance R e increases in time due to the heat produced by the coil:

R e (t) = ρ l S (1 + α∆T + ...) (10)
where α = 4.10 -2 K -1 for the copper, l is the electric wire length, S is the electric wire cross section area and ∆T is the temperature elevation due to the heat produced by the coil. The electrical resistance variation can modify both the outer rim and the spider properties. The heat produced by the electrical resistance due to the heat produced by the coil passes through to both the outer rim and the spider. Consequently, their temperature increases.

The increase in the temperature of the spider and the outer rim generates a modification of their mechanical behaviour.

Time dependence of the mechanical stiffness k

Although analytical models taking into account the time dependence of the mechanical stiffness k do not exist, the properties of the outer rim change in time on account of the heat produced by the electrical resistance due to the Joule effect. Experimentally, this dependence is visible on the electrical impedance and this phenomenon is discussed in this paper. The outer rim and the spider exhibit both viscous and elastic characteristics. The type of viscoelasticity which occurs in the case of an actual electrodynamic loudspeaker is non linear. In consequence, a volterra equation cannot be used to connect stress and strain and a simple model to describe such a behaviour does not exist. Indeed, the outer rim deformations are large and the outer rim properties change under deformations.

3 Improvement of the Small signal model using lumped parameters: experimental methodology

Introduction

This section presents a way of deriving the time dependence and the input current dependence of the Small signal parameters. For this purpose, an experimental way based on a measurement algorithm is described. The electrodynamic loudspeaker is characterized by the electrical impedance which, precisely measured, allows us to construct polynomial functions for each Small signal parameter. The knowledge of the Small signal parameter variations allows us to derive analytically the distortions created by the electrodynamic loudspeaker.

Principle of the measurement

In order to measure the electrical impedance of a loudspeaker, it must be placed in an anechoic chamber in a normalized plane. By varying the frequency and the input current, we can measure the electrical impedance. So as to increase the measurement precision when impedance variation is important, different measurement algorithms have been developed. Basically, the aim is to acquire more points when impedance variation is important and less information when impedance tends to be constant with frequency.

Measurement equipment and devices

The electrical impedance is measured by a Wayne Kerr wedge that has an excellent precision (10 -4 Ω). Different algorithms are used to determine at which frequencies impedance must be measured. Basically, points must be measured when electrical impedance reaches a maximum or when impedance variation with frequency is important. To do so, a dichotomic search of the maximum impedance is used first to measure accurately the impedance near the resonance frequency. The second algorithm is called in order to detect important variation of impedance while the first algorithm is called to refine measurement near impedance maxima.

Determination of the Small signal parameters

The Small signal parameters vary both in time and with the input current.

As it is very difficult to find the two dependences for each parameter, the measurement algorithm is first used to derive the time dependence and afterwards to derive the input current dependence. On the one hand, the input current level is fixed and the electrical impedance is measured each time. On the other hand, Thiele and Small variations in time are neglected and the electrical impedance is measured for many input currents. In each case, we work with three degrees of freedom. These three degrees of freedom are the time t, the input current i and the frequency f = w 2π . The measured value is always the electrical impedance Z e .

Nonlinear parameter variations

To determine the nonlinear parameter variations, two impedance layers are used. One of them can be called the experimental impedance layer Z (exp) e and is determined by using the measurement algorithm described in section (3).

The other one can be called the theoretical impedance layer Z (theo) e and is determined as follows: the Small signal parameters are assumed to vary with either the input current or time. In a first approximation, a polynomial writing is used to represent the dependence on the parameters with either the input current or time. The expansion is truncated after the 2nd term. Therefore, in the case of the input current dependence, we assume the electrical resistance R e and R µ to be constant; the Small signal parameters are expressed as follows:

Bl(i) = Bl(1 + µ Bl i + µ 2 Bl i 2 ) (11) R ms (i) = Rms(1 + µ Rms i + µ 2 Rms i 2 ) (12)
k(i) = k(1 + µ k i + µ 2 k i 2 ) (13) M ms (i) = M ms (1 + µ Mms i + µ 2 Mms i 2 ) (14) L e (i) = L e (1 + µ Le i + µ 2 Le i 2 ) (15)
and the electrical impedance becomes:

Z (theo) e1 (i) = R e + jR µ L e (i)w jL e (i)w + R µ + Bl(i) 2 Rms(i) + jM ms (i)w + k(i) jw (16)
Again, in the case of the time dependence, we assume that R µ is constant.

The Small signal parameters are expressed as follows:

R e (t) = R e (1 + ν Re t + ν 2 Re t 2 ) (17) Bl(t) = Bl(1 + ν Bl t + ν 2 Bl t 2 ) (18) R ms (t) = Rms(1 + ν Rms t + ν 2 Rms t 2 ) (19) k(t) = k(1 + ν k t + ν 2 k t 2 ) (20) M ms (t) = M ms (1 + ν Mms t + ν 2 Mms t 2 ) (21) L e (t) = L e (1 + ν Le t + ν 2 Le t 2 ) ( 22
)
and the electrical impedance becomes:

Z (theo) e2 (t) = R e (t) + jR µ L e (t)w jL e (t)w + R µ + Bl(t) Rms(t) + jM ms (t)w + k(t) jw (23)
A least square method is used to identify all the parameters in the both cases ;

this method is based on the Symplex algorithm. The principle of this algorithm is to minimize the difference ∆Z e between the experimental impedance and the theoretical impedance. In the case of the time dependence of the Small signal parameters, this difference is expressed as follows:

∆Z 1 e (t) = n=2 n=0 Z (exp) e (t) -Z (theo) e1 (t) 2 (24)
In the case of the input current dependence of the Small signal parameters, this difference is expressed as follows:

∆Z 2 e (i) = n=2 n=0 Z (exp) e (i) -Z (theo) e2 (i) 2 (25)
When the algorithm converges, all the values describing the nonlinear parameters are obtained and allow us to predict analytically the distortions created by the electrodynamic loudspeaker by solving the time-varying nonlinear differential equation.

Time dependence of the Small signal parameters

This section describes a temporal study of two electrodynamic loudspeakers.

The electrodynamic loudspeakers used are two woofers (Eminence Alpha). One of them is run in and the other one is not. First, the measurement algorithm presented in the previous section is used in order to derive all the non-linear parameters. Then, time-varying effects experimentally observed are discussed and physically interpreted. 2),( 6) and [START_REF] Berkouk | Contribution a l'etude des actionneurs electrodynamiques[END_REF]. In the previous section, the experimental impedance layer is determined with the measurement algorithm presented in section [START_REF] Klippel | Dynamic measurement and interpretation of the nonlinear parameters of electrodynamic loudspeakers[END_REF]. In this section, the experimental impedance is compared to the theoretical one calculated with the Small signal model using lumped parameters. For this purpose, the difference ∆Z 1 e (t) between the experimental impedance modulus and the theoretical impedance modulus is calculated for each frequency and at each time. This difference ∆Z 1 e (t) is represented in Fig. [START_REF] Kaizer | Modeling of the nonlinear response of an electrodynamic loudspeaker by a volterra series expansion[END_REF]. The mean difference ∆Z e is defined as the difference ∆Z 1 e (t) divided by the number of points necessary to plot the experimental impedance layer. By using the Small signal model using lumped parameters with constant parameters, the mean difference ∆Z e equals 0, 20Ω. and viscoelastic properties change with decreasing or increasing temperature.

Resonance frequency variation

Another interesting temporal effect is the resonance frequency variation. It is quite difficult to obtain the resonance frequency experimental measurement in time because its variation is very fast and the time necessary to get the measurement points by the algorithm is only about half a second. Fig. [START_REF] Noris | Nonlinear dynamical behavior of a moving voice coil[END_REF] shows the resonance frequency f res as a function of time. We see in this figure that the resonance frequency decreases in time. This effect can be explained since the mechanical stiffness of suspension ( spider, outer rim) depends on time. In consequence, the resonance frequency is not constant and depends also on time. In short, the decrease in mechanical stiffness generates the decrease in the resonance frequency.

f res (t) = 1 2π k -k 3 t -k 4 t 2 Mms (26)

Comparison between two loudspeakers: one of them is not run in and the other one is

This section presents an experimental comparison between two electrodynamic loudspeakers. One of them is supposed to be run in and the other one is not.

The electrodynamic loudspeaker which is run in has been used for one year.

In consequence, its mechanical properties have changed, particularly for the outer rim and the spider which have become both more elastic and worn.

For five hours, we measured continually the electrical impedance of the two electrodynamic loudspeakers. The experimental electrical impedance modulus Z e (t) of the electrodynamic loudspeaker which is not run in is represented in Fig. [START_REF] Dobrucki | Nonlinear distortions of woofers in fundamental resonance region[END_REF]. As said previously, Z e (t) is plotted at different instants and is a func- tion of frequency. In this figure, we see that the electrical impedance decreases in time and it is mainly due to the change of the mechanical properties. Another interesting point is that the resonance frequency varies quickly in time between t 0 and t 1 which corresponds to 8 seconds. This variation is probably due to the dry friction behaviour of the outer rim.

Fig. [START_REF] Berkouk | Contribution a l'etude des actionneurs electrodynamiques[END_REF] represents the electrical impedance modulus of the electrodynamic loudspeaker which is supposed to be run in. As in the previous case, Z e (t) is plotted at different instants and is a function of frequency. This figure shows that the decrease in electrical impedance modulus is less important for the woofer which is run in than the one which is not. This diminution is about 0, 4Ω for the woofer which is not run in, whereas this diminution is 0, 05Ω for the woofer which is run in. Moreover, the resonance frequency variation is less important for the woofer which is run in than the one which is not. This resonance frequency variation is about 1Hz for the woofer which is not, whereas this variation is 0, 4Hz for the woofer which is run in. Furthermore, the resonance frequency is very different between the two loudspeakers although they are both the same. The resonance frequency of the woofer which is run in is about 67Hz whereas the resonance frequency of the woofer which is not run in is about 79Hz. This resonance frequency discrepancy is probably due to the fabrication scattering and the change in time of the membrane mechanical properties.

Electrical impedance variation in time

The previous section shows that the electrical impedance varies in time. The aim of this section is to show that the electrical impedance does not vary in the same way according to the frequency measurement. For this purpose, we plot the electrical impedance for the two loudspeakers at two different fixed frequencies. One of them is at the resonance frequency and the other one is at 200

Hz. In The same experimental measurements are done with the electrodynamic loudspeaker which is not run in. Again, an experimental measurement is realized with a fixed frequency which equals the resonance frequency. Such an experimental measurement is represented in Fig. 10 This figure shows that the electrical impedance decreases in time. The behavior of the electrical impedance is very different according to the electrodynamic loudspeaker used at the resonance frequency. The figure [START_REF] Lemarquand | Large bandwith loudspeaker emitting coherent acoustic waves: nonlinear inter-modulation effects[END_REF] shows the electrical impedance modulus of the woofer which is not run in as a function of time. The fixed frequency equals 200Hz and the input current equals 100mA.

As seen previously in the case of the run in electrodynamic loudspeaker, the electrical impedance modulus increases in time. In Fig. [START_REF] Gander | Moving-coil loudspeaker topology as an indicator of linear excursion capability[END_REF], the electrical impedance modulus decreases in time. Moreover, we see that the electrical impedance modulus varies more at the resonance frequency than another frequency (here: 200Hz).

Running in an electrodynamic loudspeaker

The aim of this section is to show the time necessary to consider that an electrodynamic loudspeaker is run in. For this purpose, we use the electrical impedance modulus of the electrodynamic loudspeaker. We take a frequency which equals the resonance frequency, an input current which equals 100mA and we plot the electrical impedance modulus at each instant. Such an electrical impedance modulus is plotted in Fig. [START_REF] Kreyszig | Advanced Engineering Mathematics[END_REF]. This figure shows that the electrical impedance modulus does not vary after 10 4 s, which corresponds to about three hours. It can be concluded that this is the time necessary for breaking in this electrodynamic loudspeaker. The mean difference ∆Z e equals 0, 39Ω.

In table [START_REF] Small | Closed-boxloudspeaker systems, part 1: Analysis[END_REF], all the parameters and their expansions are described and the sensitivity to the least square is precise. This table shows that the parameter which is the more sensitive to the input current is the equivalent damping parameter R ms .

Obtaining the time-varying nonlinear differential equation

This section presents the time-varying nonlinear differential equation of the electrodynamic loudspeaker which is run in. For this purpose, we take into Ranking of the parameters according to their sensitivity to the least square algorithm parameters depend on time. To solve the time-varying nonlinear differential equation, a Taylor series expansion is used.

Discussion about the time-varying differential equation

It is noticeable that the temporal variations of the Small signal parameters do not create any important distortions. Indeed, if we assume all the Small signal parameters to be constant with the input current, the general differential equation of the electrodynamic loudspeaker is written:

ãd 3 x(t) dt 3 + b(t) d 2 x(t) dt 2 + c(t) dx(t) dt + d(t)x(t) = u(t) (32) with ã
= M ms L e Bl (33) b
(t) = M ms R e (1 + ν Re t + ν 2 Re t 2 ) Bl + R ms L e Bl (34) c(t) = R e (1 + ν Re t + ν 2 Re t 2 )R ms + Bl 2 + k(1 + ν k t + ν 2 k t 2 )L e Bl (35) d(t) = k(1 + ν k t + ν 2 k t 2 )R e (1 + ν Re t + ν 2 Re t 2 ) Bl (36)
The time-varying differential equation defined in Eq.( 32) is a hypergeometric equation and can be solved in the general case by using the theory of the Power Series Method [START_REF] Kreyszig | Advanced Engineering Mathematics[END_REF]. However, if we take u(t) = Ae (jwt) where A is a term of amplitude, the response does not contain terms in e (j2wt) ,e (j3wt) ,etc... In consequence, we deduct that the time dependence of the Small signal parameters does not generate any distortions.

Solving the nonlinear differential equation

The nonlinear differential equation can be solved at each time. By assuming the electrical resistance to be constant in time, the only parameter sensitive to time is the mechanical stiffness. To simplify the resolution of the time-varying nonlinear differential equation, we can write that at each time, the nonlinear differential equation is stationary. The distortions predicted by the nonlinear differential equation depend on time but can be solved at each time. The study of the nonlinear small signal parameters can be done with either the input current or with the position of voice coil. In fact, the relation between the input current i and the position x(t) of the voice coil is linear. Indeed, by using the classical approach, Laplace Law describes the movement of the voice coil at first order.

M ms d 2 x(t) dt 2 = Bli(t) (37)
If we consider that the current is varying sinusoidally in time, above the frequency resonance, the displacement of the voice coil is proportional to the Laplace force and in opposed directions. The displacement of the voice coil can be described by:

x = - Bli M ms w 2 ( 38
)
where w is the radian frequency of the input current. In consequence, it exists a parameter α which verifies:

x = αi (39)
where α = -Bl Mmsw 2 . All the Small signal parameters can be expressed as a Taylor series expansion. By inserting all these expansion series in Eq.( 28), we obtain a classical nonlinear differential equation. Its solution is given by Eq.( 40). The solution is developed until the order 2 (µ 2 ).

x(t) = x 0 (t) + µx 1 (t) + µ 2 x 2 (t) + ...

where x 0 (t) is the solution of the nonlinear differential equation of the electrodynamic loudspeaker when the terms with orders higher than zero are neglected, x 1 (t) is the solution of the nonlinear differential equation when the terms with orders higher than one and smaller than one are neglected, x 2 (t) is the solution of the nonlinear differential equation when the terms with orders higher than two and smaller than two are neglected. In short, the solution of the nonlinear differential equation of the electrodynamic loudspeaker is given by:

x(t) = A cos(wt) + B sin(wt) + C cos(2wt) + D sin(2wt) + ...

The terms A and B can be found by inserting A cos(wt)+B sin(wt) in Eq.( 27)

with an excitation u(t) which equals P sin(wt) where P is an amplitude. The terms C and D can be found by taking the terms with orders higher than one and smaller than one into account,etc...

Experimental and theoretical displacement spectrums

This section presents the experimental and the theoretical displacement spectrums of the electrodynamic loudspeaker which is run in. The theoretical displacement spectrum is obtained by calculating the Fourier transform of the solution given in Eq.( 41). The experimental displacement spectrum is obtained by using a laser Doppler velocimeter. The theoretical displacement spectrum is consistent with the experimental displacement spectrum. The theoretical and experimental first-harmonic and second-harmonic shows a very good agreement. However, the theoretical third-harmonic is lower than the experimental one. This discrepancy between the theoretical third-harmonic and the experimental one shows the limit of the use of a series Taylor expansion. It can be noted that the experimental spectrums have been measured at low frequencies. For higher frequencies, the theoretical model should take into account membrane modes.

Conclusion

The aim of this paper is the study of the time-varying effects and nonlinear effects of electrodynamic loudspeakers. A temporal study based on a very precise measurement shows the time dependence of the membrane mechanical stiffness k. However, this time dependence does not create any distortions. Moreover, two identical electrodynamic loudspeakers are compared and important time discrepancies are discussed. The resonance frequency between an electrodynamic loudspeaker which is run in and one which is not is extremely different and does not vary in time in the same way. Then, the time-varying nonlinear differential equation of the electrodynamic loudspeaker is solved by using a series Taylor expansion. For this purpose, the time-varying effects are neglected but can be taken into account by solving the nonlinear differential equation at different instants. The theoretical displacement spectrum is consistent with the experimental displacement spectrum.

x

  (t)=position of voice coil [m] Bl=electrodynamic driving parameter [T.m] R ms =mechanical damping parameter and drag force [N.s.m -1 ] C ms =mechanical compliance of suspension(spider, outer rim)[m.N -1 ] M ms =equivalent mass of moving voice coil, cone, air[Kg] R e =electrical resistance of voice coil[Ω]L e =inductance of voice coil[H]

4. 1

 1 Obtaining the experimental impedanceThe first step to derive the time dependence of the Small signal parameters is to use the experimental impedance layer. As explained previously, the current input current is fixed. A current which equals i = 100mA is injected in the electrodynamic loudspeaker. The electrodynamic loudspeaker used is supposed to be run in. The lower measurement frequency equals 50Hz and the upper measurement frequency equals 250Hz. The experimental impedance is measured for eight hours. Such an experimental impedance layer is represented in Fig.[START_REF] Small | Closed-boxloudspeaker systems, part 1: Analysis[END_REF]. It can be noted that the time-varying effects are not visible in this impedance layer but they are clearly shown in Figs.(

Fig. 1 .

 1 Fig. 1. Experimental three-dimensional representation of the electrical impedance modulus of the electrodynamic loudspeaker (x: time 0s to 3.10 4 s) (y: 0Hz to 200Hz) (z: 0Ω to 25Ω)

Fig. 2 .

 2 Fig. 2. Three-dimensional representation of the difference ∆Z 1 e (t) between the experimental impedance and the theoretical impedance ; the theoretical impedance is based on the Small signal model using lumped parameters with constant parameters (x: time 0s to 3.10 4 s) (y: 0Hz to 200Hz) (z: 0Ω to 25Ω) 4.2.2 Parameter sensitive to time

Fig. 3 .Fig. 4 .

 34 Fig. 3. Three-dimensional representation of the difference between the experimental impedance and the theoretical impedance ; the theoretical impedance is based on Small signal model using lumped parameters with variable mechanical stiffness (x: time 0s to 3.10 4 s) (y: 0Hz to 200Hz) (z: 0Ω to 25Ω)

Fig. 5 .

 5 Fig. 5. The resonance frequency [Hz] is a function of time [s]

Fig. 6 .

 6 Fig. 6. Electrical impedance modulus of the woofer which is not run in. The electrical impedance modulus [Ω] is a function of frequency [Hz] and is plotted at different instants around the resonance frequency.

Fig. 7 .

 7 Fig. 7. Electrical impedance modulus of the woofer which is run in. The electrical impedance modulus [Ω] is a function of frequency [Hz] and is plotted at different instants around the resonance frequency.

Fig. ( 8 )

 8 , the electrical impedance modulus of the woofer which is run in is a function of time. The fixed frequency equals 200Hz and the input current equals 100mA. This figure shows that the electrical impedance modulus increases in time. In Figure (9), we still plot the electrical impedance modulus

Fig. 8 .

 8 Fig. 8. Electrical impedance modulus of the woofer which is run in. The frequency equals 200Hz and the input current equals 100mA. The electrical impedance modulus is a function of time.

Fig. 9 .

 9 Fig. 9. Electrical impedance modulus of the boomer which is run in. The frequency equals the resonance frequency and the input current equals 100mA. The electrical impedance modulus is a function of time.

Fig. 10 .

 10 Fig. 10. Electrical impedance modulus of the woofer which is not run in. The frequency equals the resonance frequency and the input current equals 100mA. The electrical impedance modulus is a function of time

Fig. 11 .

 11 Fig. 11. Electrical impedance modulus of the woofer which is not run in. The frequency equals 200Hz and the input current equals 100mA. The electrical impedance modulus is a function of time.

Fig. 12 . 5 . 1

 1251 Fig. 12. Electrical impedance modulus of the woofer which is not run in. The frequency equals the resonance frequency and the input current equals 100mA. The electrical impedance modulus is a function of time.

Fig. 13 .

 13 Fig. 13. Experimental three-dimensional representation of the electrical impedance modulus of the electrodynamic loudspeaker (x:0.05A to 0, 2A) (y: 0Hz to 650Hz) (z: 0Ω to 25Ω)

Fig. 14 .

 14 Fig. 14. Three-dimensional representation of the difference ∆Z 2 e (i) between the experimental impedance and the theoretical impedance ; the theoretical impedance is based on the Small signal model using lumped parameters with constant parameters (x:0, 05A to 0, 2A) (y: 0Hz to 200Hz) (z: 0Ω to 6Ω) 5.2.2 Parameters sensitive to the input current

Fig. 15 .

 15 Fig. 15. Three-dimensional representation of the difference between the experimental impedance and the theoretical impedance ; the theoretical impedance is based on the Small signal model using lumped parameters with variable parameters (x: 0A to 0, 2A) (y: 0Hz to 200Hz) (z: 0Ω to 25Ω)

Fig. 16 .

 16 Fig. 16. Experimental and theoretical spectrums of the electrodynamic loudspeaker which is run in. The input current equals 100mA and the input frequency equals 100Hz.

Table 1

 1

	1	R ms	1.1(1 + 4.09i -8.36i 2 )	1.24	33%
	2	Bl	5.5(1 + 0.33i -1.02i 2 )	1.67	18%
	3	M ms	0.009(1 + 0.56i -0.22i 2 )	1.74	14%
	4	k	7440(1 -0.2i + 0.9i 2 )	1.86	8%
	5	L e	0.0017(1 -1.68i + 7.58i 2 )	1.98	3%
	6	R µ	2, 28	2.04	0%
	7	R e	3, 17	2.04	0%

account the nonlinear parameters defined in the previous section and we also take into account the time variation of the mechanical stiffness k. The timevarying nonlinear differential equation is defined by Eq.( 27) in the case when we also take into account the variation of the electrical resistance R e in time.

with

Solving the time-varying nonlinear differential equation

We explain here how to solve the equation defined in the previous section. We can point out that the coefficient a(i) defined in Eq.(28) is the only coefficient which is constant in time. We use the notation Re t and k t to indicate that these


Simon Flandin

Christine Vidal-Gomel

Raquel Becerril

Cyril Bossard

Magali Prost

Yohann Cardin

Gilles Kermarrec

ANALYZING THE COLLECTIVE ACTIVITY OF FIREFIGHTERS DURING URBAN FIRE SIMULATION

Keywords: Team sense-making, semi-open space, simulation, firefigthers

This chapter proposes the study of the collective activity of a team of firemen in a simulation situation. In reference to the Data/Frame theoretical model, this study analyzed team sensemaking through the articulation of individual activities. The methodology was inspired by the principles of in situ analysis developed within the NDM framework. Observation and communication data were recorded from 11 firefighters in training situations and completed by verbalization data collected during subjective re-situ interviews. Data analysis was based on the use of multi-score format. The results highlight the (im)possibilities of inter-individual interaction that are created throughout a training situation. The "Sensemaking Articulation of Global Activity" (SAGA) mode of representation makes the articulation of individual sensemaking visible. This study highlights the influence of the functional (mission of each agent) and spatial (position of each agent) configurations of the team on team sense-making during a maneuver. Within the team, two levels of understanding of the situation (macroscopic and microscopic) coexist with local and typical forms of coordination involving all or part of the team. As a result, the team sense-making appears as an enchainment of cycles of local sensemaking in which the team leader is the coordinator. All of these results allow us to suggest ways to improve the design of simulations for firefighting team training.

INTRODUCTION

This chapter presents an analysis of the activity of firefighters' teams in practical training situations designed for firefighters. More specifically, the objective is to analyze the team sense-making during a simulation in order to propose ways to improve it.

Simulation for training purposes

The use of simulation in a pedagogical perspective is a practice particularly exploited in domains considered as risky such as the military domain [START_REF] Grau | Conception et utilisation de la simulation pour la formation : pratiques actuelles dans le domaine militaire[END_REF][START_REF] Jensen | Sensemaking in military planning: a methodological study of command teams[END_REF]; aviation [START_REF] Rankin | Sensemaking following surprise in the cockpit-a re-framing problem[END_REF] or virtual teams [START_REF] Rafaeli | Sensemaking in virtual teams: The impact of emotions and support tools on team mental models and team performance[END_REF]. The main interest lies in the fact that simulation allows, without risk for the learner, to promote the acquisition of skills when performing specific tasks that are difficult to reproduce in reality. Its use allows the manipulation of problematic variables, such as the consequences of actions in risky situations, the complexity of technical and organizational systems or the temporality of the processes involved [START_REF] Samurçay | Exploitation didactique des situations de simulation[END_REF].

2 Within this framework, the simulator is defined as an "artifact that simulates (partially or totally) the functioning or behavior of a technical system, an installation, or a natural phenomenon" (Vidal-Gomel et al., 2011, p. 117). The latter is generally the result of modeling work on the real activity. It can be material (with interfaces for the trainees and possibly for the trainers) or purely symbolic (and not be a technological object per se). In the case of the training of firefighters that we have studied, the simulator is not a specific technological object but a global operational device defining the status and roles of each member of the team within a figurative environment [START_REF] Béguin | Working, learning, interacting through simulation[END_REF]. Although the studies carried out on work situations in the field of ergonomics psychology have largely studied the individual dimension, they point to the need to analyze collective activity [START_REF] Leplat | Activités collectives et nouvelles technologies[END_REF][START_REF] Hoc | Coopération humaine et systèmes coopératifs[END_REF]. At the same time, it appeared important for researchers (as well as for managers) to understand processes inherent to these situations leading, or not, to the passage of the skills of each individual to a collectively efficient team. This concern for the collective dimension was therefore logically integrated into the design of the training systems. The firefighting profession is characterized by the fact that it is not practiced in isolation but almost exclusively within a team based on a precise and perfectly established organizational system [START_REF] Lipshitz | What's burning ? The RAWFS heuristic on the _re ground[END_REF]. Collaboration between members of the firefighting team is essential in view of the plurality of risks, the evolving and uncontrollable nature of situations and the time pressure [START_REF] Samurçay | Cooperative work and decision making in emergency management[END_REF][START_REF] Klein | Team sensemaking[END_REF]. In order for there to be collective efficiency in the field of work, the necessity for individuals is that they be able to share the same task, i.e. the same goal and the same working conditions [START_REF] Leplat | Ergonomie et activit_es collectives[END_REF]. In the case of the firefighting teams we studied, this common goal is to stop an incident and rescue victims.

1.2.The team sense-making model (Klein et al., 2010)

In order to understand how a team functions, valuing sense-making by a collective in a situation remains an avenue of research to explore. By adapting their individual Data/Frame model to the collective, [START_REF] Klein | Team sensemaking[END_REF] attempt an approach aimed at specifically understanding "the process by which a team manages and coordinates its efforts to explain the current situation and anticipate future situations, particularly under uncertain and ambiguous conditions ». In this perspective, the authors take up the different activities that make up the original cyclical model and elevate them to their collective dimension (Figure 1). [START_REF] Klein | Team sensemaking[END_REF]. [START_REF] Klein | Team sensemaking[END_REF] extract from this team sense-making model various strategies that contribute to the collective construction of a cognitive framework appropriate to the relevant data of the situation. All these strategies are listed and detailed in Table 1.

Table 1. team sensemaking strategies adapted from [START_REF] Klein | Team sensemaking[END_REF] Team sense-making

Emerging strategies Recognize a frame

The team formulates criteria or rules used to identify the frame A team member announces what the frame is The team collaborates to identify the frame Question a frame Designate a team member to play the role of "devil's advocate" and raise doubts about the relevance of a frame The team creates rules or identifies triggers to alert that the frame may be irrelevant Team members speak up and discuss what could go wrong with using the frame Re-frame (compare) The team compares the frame and votes for one of them Team builds consensus on the most appropriate frame Leader announces which frame is most appropriate Re-frame (seek)

The individual suggests a frame that is adopted, modified, or rejected by the team after comparing frames Team speculates on data and suggests causal views: leader or team member combines views within a frame 4

To the best of our knowledge this theoretical model has only been applied within a study on air traffic control [START_REF] Malakis | Exploring team sensemaking in air tra_c control (ATC): insights from a field study in low visibility operations[END_REF]. The authors specifically studied team sensemaking processes performed by the air traffic management collective in very low visibility conditions. These collectives involve controllers located in the control tower and on the tarmac as well as possibly a team leader. An interesting point lies in the modulable character (in numerical terms and consequently of attribution of functions) of the collective according to the density of the traffic which, independently of the conditions inherent to the studied situations, implies a fortiori different coordination processes according to the moments when these situations take place. Using the critical decision analysis method, [START_REF] Malakis | Exploring team sensemaking in air tra_c control (ATC): insights from a field study in low visibility operations[END_REF] verified the operability of the model in the real conditions of a risky activity. In this way, they highlighted the sense-making processes developed collaboratively within these collectives as well as the strategies put in place specifically for the domain. These results allowed the development of efficient technological devices adapted to the real activity of air traffic controllers in difficult conditions (e.g. in low visibility situations).

This study is of real interest in the context of our work insofar as the group studied, although in continuous audio contact, is highly spatially dispersed. As a result, the accessibility to information is not the same for all the team members (especially in terms of visual information) and requires them to communicate more in order to share the same information. This element is also underlined by the authors, in the perspective of designing technological management devices, by taking into account the aircraft's piloting team. Although pilots were not interviewed in the study, [START_REF] Malakis | Exploring team sensemaking in air tra_c control (ATC): insights from a field study in low visibility operations[END_REF] point out the lack of shared situational awareness between them and the control team in that the weather information specifically provided to them is not entirely identical. As a result, this informational gap can lead to certain dysfunctions in the collective construction of meaning of a situation, especially if it takes place under difficult conditions.

OBJECTIVE AND THEORETICAL RATIONALE

(1) The main objective of this chapter is to report on the collective activity of the firefighting team in a practical training situation. To this end, we conducted an empirical study based on two assumptions. The fire department teams, in our case in an urban environment, are led to evolve in compartmentalized spaces partially preventing communication (verbal or visual) between the members. In order to determine the processes of team sense-making in a "fragmented" team [START_REF] Grosjean | Communication et intelligence collective : le travail à l'hôpital[END_REF], we start from the presupposition that this object can be understood from the articulation of individual sense-making.

(2) Taking into account the subjective and individual character of the agent in a collective requires an understanding of the experience of each member during the action and of their articulation. Therefore, our work is part of a naturalistic approach intended to account for the meanings that the team members construct through their permanent interaction with the simulation situation. We postulate the coexistence within the collective of different levels of understanding of the situation. This plurality of forms of understanding would be both the result of the different functions allocated to each member and of the (im)possibilities of interaction brought about by the context. The understanding of the situation could be organized according to a relation to a "framework" of sense-making at the individual level and possibly shared at a collective level (Team sense-making model; [START_REF] Klein | Team sensemaking[END_REF]

METHODOLOGY

The presuppositions presented above require the development of a specific methodology capable of accounting for the collective's agency in relation to environmental constraints. Thus, the method of multi-score transcription seems suitable in that it is a prerequisite for identifying

3.1.Context and participants

The study was carried out in the context of training sessions on urban fire management for fire managers organized by a French departmental fire service. The training sessions take the form of a full-scale simulation on a technical platform. During an emergency, the fire chief is the first officer to arrive on the scene with his team. His responsibility is to quickly take charge of the first emergency measures. The team leader is in charge of a response truck with five team members: the driver, the supply pair (BAL) and the attack pair (BAT). The driver's role is to drive the truck to the scene of the incident and possibly manage the water supply to the fire hoses for the team members attacking the fire. The BAL is in charge of supplying water to the fire hoses and possibly supporting the team members attacking the fire. The BAT's mission is to explore the scene of the incident and to attack the fire with the hoses. These functions, although perfectly defined, are likely to be modified during a maneuver according to the real needs of the field.

The study was conducted in collaboration with 11 volunteer firefighters participating in the fire chief training organized by a departmental fire service in France. At the time of data collection, their average age was 36 years (standard deviation: 7.62). At the time of the study, their experience as a firefighter was 12 years on average (SD 3.58). Participants were named using a code corresponding to the maneuver (between 1 and 3) followed by their position name (Chief, BAL-1, BAL-2, BAT-1, BAT-2): for example, code 3 BAT-1 corresponds to the leader of the attack pair (BAT) in maneuver 3.

3.2.Data collection

In this work, we were interested in three maneuvers performed during the training in full-scale simulation on a technical platform. These maneuvers will be numbered from 1 to 3 according to their chronological order during the training. Maneuver 1 corresponds to a fire response in a city's technical services. Maneuver 2 involves a fire in an apartment adjacent to a home for the elderly and involving a victim. Maneuver 3 involved a fire in a street with a heavy truck (with one victim). These maneuvers had a duration of 12'43", 18'10" and 10'17" respectively.

During these three maneuvers, the data collection procedure was applied each time to the entire intervention team except for the driver (played by a professional not involved in the training process). In this way, on each intervention, five trainees were involved, playing the roles of squad leader, BAT leader, BAT team member, BAL leader, BAL team member respectively.

The data collection procedure was based on in situ analysis methods. Three types of data were collected:

 Observational data on the activity of the trainees during the scenarios. These observational data were collected through the audiovisual recording of the behaviors during the maneuver. The situations were filmed from two points of view, both providing extrinsic data, using two types of digital video cameras. On the one hand, the use of a shoulder-mounted camera made it possible to record the team's activity from an external point of view (movement in space, gestures, postures). On the other hand, the use of an 6 head-mounted camera on the helmet of each trainee (see Figure 2) made it possible to report on their activity from the actor's own field of vision (participant's point of view in the course of the action).  Communication data involving the trainees during the simulations. These data are mainly recovered from the recording of the head-mounted camera.  Verbalizations obtained during individual interviews in subjective re-situ [START_REF] Rix | Enregistrement en perspective subjective située et entretien en re situ subjectif : une méthodologie de constitution de l'expérience[END_REF][START_REF] Rix-Lièvre | Différents modes de confrontation à des traces de sa propre activité[END_REF] directly following the execution of the maneuver on site. This form of interview, which gives access to intrinsic data, consists of confronting an actor with audiovisual traces of a period of his activity taken from his own point of view (in our case, via the cameras mounted on the helmets).

Data analysis

The analysis consisted in reconstructing the chronicle of the situations (temporal unfolding) by synchronizing the extrinsic data (behaviors and communications) and the intrinsic data (verbatim) collected for each participant. To do this, the analysis was based on the following 6 steps: (1) multi-score transcription;

(2) sequencing of the maneuvers;

(3) identification of individual sense-making; (4) categorization of the level of individual sense-making; (5) representation of the team sense-making; (6) validity of the analysis.

Initially, this work exploited the MUltI-SCOre Format (MUSICOF), which allows the analysis of collective activity in semi-open space (Guibourdenche et al., 2017). We performed a multi-score transcription using the video films, from all the cameras used simultaneously during the study situations. All of the participants' behaviors were reported and were supplemented with verbalizations from individual interviews with each participant. All these data were gattered together using MUSICOF for each maneuver. These tables are constructed along two axes: a horizontal axis to respect the temporal course of the situation; a vertical axis to respect the spatial configuration of the intervention sites. Figure 2 shows an example of the MUSICOF format used in this study. For each maneuver, the overall intervention environment was divided into different spaces that could reflect the (im)possibilities of interaction for the collective. For each of these predefined spaces, each member of the team is represented in the multi-span chart by two lines: the upper line for his or her behaviors and communications; the lower line for placing opposite his or her corresponding verbalizations collected during the interview.

The second step consisted in sequencing the maneuvers by detecting "moments of rupture" within the collective activity (45 in total). These moments of rupture correspond to changes in the collective in terms of spatial configuration (separation and gathering of team members during the maneuver) or functional configuration (orders and missions given to each member by the team leader). These different configurations will be presented in the results section.

In the third step, we identified the individual sense-making activities corresponding to behavioral markers such as communications and behaviors noted during the situation and/or verbalizations collected during interviews. The fourth step consisted in categorizing individual sense-making according to the level of individual understanding (377 individual activities in the whole study). The fifth step is related to the graphical representation of the team sense-making. For this purpose, we designed a representation mode called "Sense-making Articulation of Global Activity" (SAGA) which consists in illustrating, for each sequence identified during the situation, the articulation of team members sense-making (according to the Data/Frame 8 model) according to the spatial and functional configurations of the team. The figure 3 illustrates the spatial partitioning of a team in a semi-divided functional configuration of firemen with SAGA.

RESULTS

Individual sense-making

The sequencing procedure extracted 45 sequences from the three maneuvers studied. Maneuver 1 has 15 sequences, Maneuver 2 has 19 sequences and Maneuver 3 has 11 sequences.

The step of identifying individual sense-making following the Data/Frame theoretical model allowed us to distinguish 377 individual sense-making over the whole study. The distribution of these individual sense-making for each member during the 3 maneuvers is summarized in Tables 2,3, and 4. The number of occurrences of individual sense-making following the data/frame model [START_REF] Klein | Team sensemaking[END_REF] shows that two processes are particularly favored by firefighters. The recognition of the frame and the elaboration of the frame are the most mobilized by the firefighters whatever the role (leader/team member) or the maneuver involved.

From the 377 individual sense-making, a second analysis allowed us to distinguish two levels of individual sense-making: microscopic and macroscopic. The macroscopic level corresponds to the situation as a whole (type of incident, presence of victims, potential dangers, configuration of the site) and the type of maneuver applied to it (missions of each pair or partner, task planning). The microscopic level refers to the contextual elements (e.g. hydrant location, fire behavior, victim's health status, required equipment) and actions or procedures (e.g. fire attack, victim assistance, feeding) related to the execution of a specific mission. Over the course of the study, 182 individual sense-making were associated with a macroscopic level and 195 of these were associated with a microscopic level.

Highlighting of 6 typical structures of team sense-making

The 45 collective activity sequences identified from the 3 maneuvers were represented using SAGA for each of them. This step allowed the extraction of local structures of firefighting team sense-making. Specifically, these results highlight six typical structures of team sensemaking: Alertness, Binomial development process, Negotiation, Team sense-making standby, Mission Reassignment, and Team sense-making adjustment.

Alertness

The first structure of team sense-making corresponds to the first sequence of each maneuver. This takes place in the truck when the fire chief receives the departure message from the call center. During this sequence, the team is in a "grouped configuration" in the truck, which gives all members the opportunity to interact. The departure message from the call center gives the fire chief the address where the team will have to intervene and can then be more or less detailed on the characteristics of the incident. The fire chief then passes on to his team members the information he has gathered from the call center concerning the situation. This is illustrated in figure 4. He also gives them all the safety rules relative to the type of incident to be managed as well as certain information concerning the application of the future maneuver 10 (e.g. location of fire hydrants). To compensate for a possible lack of information, this moment can also be used by the fire chief to transmit to his team his possible assumptions about the situation (e.g. "We don't have the notion of a victim but I imagine that the truck must have a driver").

Binomial development process

The second structure concerns a binomial elaboration process (it appears six times in our data set). It corresponds to a transmission of information between the two members of the same binomial so that each of them can elaborate their respective microscopic framework. The transmission of information can be unidirectional in the case where only one of the two partners has access to the information and transmits it to the other. This case appears for example in maneuver 3, when the BAL attacks the fire. The BAL leader carries the lance but is unable to update his understanding of the situation because the headwind prevents him from seeing what is going on. It is the BAL team member behind him who shifts a little to see what is going on and gives him information as he goes along (e.g. "Maybe put yourself a little stronger.", "We'll move. We're going to get closer.", "That's okay, fire out apparently. I'll pass it on."). This transmission of information can also be bidirectional in the case where each of the partners gives the other the information that it considers relevant. This is the case during maneuver 1 when the TAO enters a smoky room in order to cut the electric meter and to extinguish the fireplace. The two partners exchange information on what they respectively consider relevant in their situation. This exchange then allows both parties to elaborate and align their respective microscopic frameworks. The structure of this team sense-making can be illustrated in Figure 5.

La m ise en éveil La première st ruct ure de con st ruct ion col lect ive de sens cor respon d à la première séquence de chacune des man oeuvres. Celle-ci a lieu dan s le cam ion lor sque le chef d'agr ès reçoi t le message de dépar t du CODIS. Lors de cet t e séquence, l'équipe est en "c on figu rat ion regr ou pée" dan s le cam ion ce qui don ne la possibilité à t ou s les membres d'int eragi r. Le message de dépar t du CODIS don ne au chef d'agr ès l'ad resse où l'équipe va devoi r int ervenir et peut ensuit e êt re plus ou moi ns dét ai llé sur les car actérist iques de l'incident . L e chef d'agr ès t r ansm et par l a suit e à ses équi pier s l es i nfor m at i ons qu'i l a pu r écolt er aupr ès du C OD I S concer nant l a si t uat i on. C eci est illust ré par la figu re 5. 8. Il leur t ran smet égal ement t ou t es les règl es de sécurité relat ives au type d'incident à gérer ai nsi que cert ai nes infor mat ion s con cernant la mise en ap plicat ion de la man oeuvre fut ure (e. g. emplacement des pot eau x à incendie). Pou r pal lier un évent uel man que d'infor mat ion , ce mom ent peut au ssi êt re mis à profi t par le chef d'agr ès pou r t ran smet t re à son équipe ses supposit ion s évent uelles sur la sit uat ion (cf. chap it re 4 ; e. g. " On n'a pas la notion de vi ct ime mais du coup, j'imagi ne qu e le camion il a forcém en t un chau↵eu r" ).

Negotiation

This structure (which appears 9 times) concerns moments of questioning by a member of the pair and presents three variants illustrated in figure 6. Globally, a member of the pair, by initiating a questioning of his microscopic framework, informs his partner who will also proceed to a questioning of his microscopic framework. An exchange of information between partners follows, which can be compared to moments of negotiation, and leads to one or other of the variants presented. Thus, this process of questioning can have a symmetrical structure insofar as the two partners will conclude either by preserving their microscopic framework (variant a) or by reframing it (variant b). These cases appear, for example, during a situation where the BAT is lost in the apartment where they have to rescue a victim and regularly question their microscopic frameworks in order to know if they have taken the right path in relation to what the team leader is asking. This questioning leads either to the preservation of their respective frames (considering that they have taken the right path and that they are close to finding the victim) or to the search for a new frame (considering finally that they have taken the wrong path and that they must find another one). This questioning can also present an asymmetrical structure (variant c) when, following a negotiation, one member of the pair preserves his microscopic frame while the other creates a new frame (re-framing). This situation arises, for example, during maneuver 1 when the BAL team member informs the BAL leader of his skepticism regarding the location of the supply division in relation to the location of the fire. The BAL Chief then reconsiders his action and moves the division in accordance with his teammate's remarks. The BAL leader therefore proceeds to refocus while the BAL team member preserves his initial microscopic frame.

le cas où chacun des par t enai res donne à l'aut re les infor mat ions qu'il juge pert inent e. C'est le cas lor s de la manoeuvre 1 (séquence 10) lor sque le BAT ent re dans un local enfumé afi n de couper le compt eur élect rique et d'ét eindre le foyer. Les deux par t enai res échangent des infor mat ions sur ce qu'ils jugent respect ivement pert inent s dans leur sit uat ion. Cet échange permet al or s aux deux par t is d'élab or er et de fai re concor der leur cadre microscopique respect if. La st ruct ure général e de cet t e const ruct ion col lect ive de sens peut êt re illust rée par la figure 5.9.

Mission reassignment

The fourth structure of team sense-making relates to moments of transition where a pair reports the result of its mission and/or its availability to the team leader (Figure 7). The team leader takes advantage of these moments to elaborate his macroscopic framework by taking into account information on the state of progress of the maneuver that he is implementing. Following this process of updating, he further clarifies the mission to the teammate or transmits a new mission to him. This structure, illustrated by figure 7, appears six times in our data. For example, during maneuver 1, the fire chief finds the BAT when he leaves the smoke-filled building. The latter gives him an account of what they have done and also of the significant elements that they have noted. The fire chief then explains their mission, insisting on the ventilation of the building in order to evacuate the smoke.

Figure 7. SAGA : Mission reassignment L a const r uct i on collect i ve de sens par négociat ion La t roi sième st ruct ure de const ruct ion col lect ive de sens por t e sur des m om ent s de r em ise en quest i on binôm iale.Cet t e st ruct ure,qui présent e t roi s var iant es, appar aˆıt neuf foi s sur l'ensemble de nos données. Ces t roi s for mes a, b et c sont illust rées en figure 5.10. Figur e 5.10: Les t roi s var iant es de la 3 e st ruct ure de const ruct ion col lect ive de sens : La remise en quest ion binômial e Global ement , un membre du binôme, en init iant une remise en quest ion de son cadre microscopique, en fai t par t à son par t enai re qui va égal ement procéder à une remise en quest ion de son cadre microscopique. S'ensuit un échange d'infor mat ions ent re par t enai res, pouvant s'appar ent er à des moment s de négociat ion, et about issant à l'une ou l'aut re des var iant es présentées. Ainsi, ce processus de remise en quest ion binômial e peut présent er une st ruct ure symét rique dans la mesure où les deux par t enai res vont conclure soi t sur une préservat ion de leur cadre microscopique (var iant e a) soi t sur un recadrage (var iant e b). Ces cas de figure appar ai ssent par exemple pour le BAT lor s de la manoeuvre 2 respect ivement lor s des séquences 15 et 17. Au cours de cet t e sit uat ion, le BAT est perdu dans l'appar t ement où ils doi vent secourir une vict ime et passent régulièrement par des remises en quest ion de leurs cadres microscopiques afi n de savoi r s'ils ont emprunté le bon cheminement par rappor t à ce que le chef d'agrès. Ces remises en quest ion about issent soi t à la préservat ion de leurs cadres respect ifs (en considérant qu'ils ont emprunté le bon cheminement et qu'ils ne sont pas loi n de t rouver la vict ime) soi t à la recherche d'un nouveau cadre (en considérant final ement qu'ils se sont t rompés de chemin et qu'ils doi vent en t rouver un aut re).

L a r éat t r i but ion de m i ssion

La quat rième st ruct ure de const ruct ion col lect ive de sens por t e sur des m om ent s de t r ansit i on où un bi nôm e r end com pt e du r ésult at de sa m ission et / ou de sa disp onibil it é aupr ès du chef d' agr ès. Le chef d'agr ès profi t e de ces moment s pour élabor er son cadre macroscopique en prenant en compt e des infor mat ions sur l'ét at d'avancement de la manoeuvre qu'il est en t rai n de met t re en place. A la suit e de ce processus de ré-act ual isat ion il précise davant age la mission au binôme ou lui t ransmet une nouvelle mission. Cet t e st ruct ure, qui est illust rée par la figure 5.11, appar aˆıt six foi s au sein de nos données. Par exemple, au cours de la manoeuvre 1 (séquence 12) , le chef d'agr ès ret rouve le BAT à sa sor t ie du bât iment enfumé. Ce dernier lui fai t un compt e-rendu de ce qu'ils ont e↵ect ué et égal ement des élément s significat ifs qu'ils ont relevés. Le chef d'agr ès leur précise par la suit e leur mission en insist ant sur la vent ilat ion du bât iment afi n d'y évacuer les fumées. 13 4.2.5. Team sense-making stand-by This structure (present 12 times in the data) concerns moments of waiting for a pair (or a single agent) when the latter has finished his mission and is available. These moments without any specific function allow the agents to elaborate their macroscopic framework by taking into account the activity of the fire chief and/or the other team members in order to update their understanding of the situation. This sense-making is directly dependent on the spatial configuration of the team and the possibilities of interaction that it offers to the inactive agents. This is illustrated by maneuver 2, during which the BAL is left without an assigned mission for a long time. During the first four sequences, the two partners constituting the BAL proceed to an elaboration of their respective macroscopic framework by taking into account mainly information concerning the activity of the team leader to which they have regular access. However, this possibility of interaction is abruptly interrupted when the fire chief enters the truck to pass the ambient message. This interruption then prevents the BAL from any elaboration of its macroscopic framework. This process of elaboration on the part of the BAL resumes immediately the next sequence when the fireman gets out of the truck. This structure of team sense-making is illustrated by Figure 8.

Team sense-making adjustment

The last structure of team sense-making (which appears only once) concerns a particular moment of questioning of the microscopic framework within a pair leading the partners to a process of reframing by comparing their microscopic and macroscopic frameworks (figure 9). Although this structure cannot be considered as typical of fire fighters sense-making, it can constitute a significant element of the collective activity that can be directly linked to a risk of collective underperformance. Indeed, the assignment of a mission to a pair (or to a single agent) means that the latter will mainly focus on the construction of its microscopic framework related to its objective. However, during the execution of this mission, the detection of certain information relative to the global situation (thus entering into their macroscopic framework) is likely to no longer fit into their microscopic framework. This disturbance may provoke a questioning of the framework, leading to a reframing process by comparing the microscopic and macroscopic frameworks. This is what happens during maneuver 2 when the BAT returns with his equipment to the corridor leading to the apartment

CH A P I T R E 5. É T U D E D E L ' A CT I V IT É C OLL E C T I V E D ' U N E É QUI P E D E SA P E U R S-P OMP I E R S
L a m ise en vei ll e de l a const r uct ion coll ect ive de sens La cinquième st ruct ure de const ruct ion col lect ive de sens concerne des m om ent s d'at t ent e d' un binôm e (ou d'un agent seul) lor sque celui-ci a t erminé sa mission et se ret rouve disponible. Ces moment s sans fonct ion spécifique permet t ent aux agent s de procéder à une élab or at ion de leur cadre macroscopique en prenant en compt e l'act ivité du chef d'agr ès et / ou des aut res équipiers afi n de réact ual iser leur compréhension de la sit uat ion. Ces moment s spécifiques appar ai ssent douze foi s sur l'ensemble de nos séquences.

Cet t e const ruct ion de sens se t rouve direct ement t ribut ai re de la configurat ion spat ial e de l'équipe et des possibilités d'int eract ion que celle-ci o↵re aux agent s inact ifs. Ceci est illust ré par la manoeuvre 2 lor s de laquelle le BAL se ret rouve longuement sans mission at t it rée (de la séquence 10 à la séquence 15) . Au cours des quat re premières séquences, les deux par t enai res const it uant le BAL procèdent à une élab or at ion de leur cadre macroscopique respect if en prenant principal ement en compt e des infor mat ions concernant l'act ivité du chef d'agr ès à laquelle ils ont régulièrement accès. Cependant , cet t e possibilité d'int eract ion s'int errompt brusquement lor sque le chef d'agr ès ent re dans le camion pour passer le message d'ambiance (séquence 14) . Cet t e int errupt ion empêche al or s le BAL de t out e élab or at ion de leur cadre macroscopique. Ce processus d'élab or at ion de la par t du BAL reprend aussit ôt la séquence suivant e lor sque le chef d'agr ès ressor t du camion. Cet t e st ruct ure de const ruct ion de sens peut s'illust rer par la figure 5.12. Figur e 5.12: 5 e st ruct ure de const ruct ion col lect ive de sens : At t ent e d'un binôme This is a post-print of the following chapter: Bossard C., Prost M., Cardin Y., & Kermarrec G. Analyzing the Collective Activity of Firefighters During Urban Fire Simulation, published in Simulation Training through the Lens of Experience and Activity Analysis, edited by Simon Flandin, Christine Vidal-Gomel, and Raquel Becerril Ortega, 2022, Springer International Publishing, reproduced with permission of Springer Nature Switzerland AG. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-89567-9_9 14 where the fire is located. At this point, the BAT's mission is to set up all the necessary equipment at the entrance to the apartment to attack the fire and rescue the victim inside. However, when he enters the corridor, he comes across the fire chief who is rescuing the witness who has been intoxicated by smoke. Taking into account this information, which is not related to their mission (microscopic) but to the situation as a whole (macroscopic), will create a disagreement in their understanding process. Indeed, the BAT leader and his teammate will stop all action (BAT teammate: "So there, we see that the fire chief, he takes out the witness he had [...] Now we ask ourselves, should we give the fire chief a hand? Should we abandon our mission? So we didn't really know what was going on. That's why we're watching a little bit."). The BAT will only resume its activity after the intervention of the trainers who will consider, within the framework of the simulation, that the witness has been rescued and that the fire chief can consequently give the executory mission to the BAT.

DISCUSSION

The main objective of this study was to report on the collective activity of the firefighting team in a practical training situation. This analysis was concretized by the implementation of a representation mode (SAGA) intended to put in visibility the articulation of the individual activities according to the functional and spatial configurations of the collective. The results of our study will be discussed according to 3 axes: 1) The articulation of the two levels of comprehension of the situation to be trained; 2) Change of role and function to enrich sense-making at individual and team levels; and 3) Typical structures of team sense-making to be taken into account to design new simulations. Figur e 5.13: 6 e st ruct ure de const ruct ion col lect ive de sens : Compar ai son ent re cadres macroscopique et microscopique Cet t e st ruct ure n'appar ai ssant qu'une seule foi s sur l'ensemble de nos données (manoeuvre 2, séquence 6) ne peut clai rement pas êt re considérée comme typique de l'act ivité des sapeurs-pompiers. Cependant elle peut const it uer à not re sens un élément significat if de l'act ivité col lect ive pouvant direct ement êt re lié à un risque de cont re-perfor mance col lect ive. En e↵et , l'att ribut ion d'une mission à un binôme (ou agent seul) fai t que ce dernier va principal ement se concent rer sur la const ruct ion de son cadre microscopique relat if à son ob ject if. Cependant , au cours de l'exécut ion de cet t e mission, la dét ect ion de cert ai nes infor mat ions relat ives à la sit uat ion gl obal e (donc ent rant dans leur cadre macroscopique) sont suscept ibles de ne plus s'accor der avec leur cadre microscopique. Cet t e pert urbat ion peut provoquer une remise en quest ion du cadre about issant à un processus de recadrage par compar ai son ent re les cadres microscopique et macroscopique. C'est typiquement ce qui se produit au cour de la manoeuvre 2 lor sque le BAT rent re avec son mat ériel dans le couloi r menant à l'appar t ement où se t rouve le foyer de l'incendie. A ce moment précis, le BAT a pour mission de met t re en place à l'ent rée de l'appar t ement t out le mat ériel nécessai re à l'at t aque du feu et au sauvet age de la vict ime s'y t rouvant . Cependant , lor sque celui-ci rent re dans le couloi r, This is a post-print of the following chapter: Bossard C., Prost M., Cardin Y., & Kermarrec G. Analyzing the Collective Activity of Firefighters During Urban Fire Simulation, published in Simulation Training through the Lens of Experience and Activity Analysis, edited by Simon Flandin, Christine Vidal-Gomel, and Raquel Becerril Ortega, 2022, Springer International Publishing, reproduced The functional diversity that characterizes the team results in each member understanding the situation according to his or her own objective, his or her own point of view. Indeed, by looking at the way in which each individual understands the situation and develops sense-making, we were able to highlight the coexistence of two levels of understanding within the collective: macroscopic and microscopic. Our results show that the team leader focuses exclusively on a macroscopic understanding of the situation. This aspect corresponds to his function, insofar as it requires him to understand the problem he is dealing with (recognition of the situation) and to deduce from it the missions he must entrust to his team members. In this way, from a personal point of view, he is rarely led to act directly on the situation, except on an ad hoc basis. Thus, his analytical work remains global with respect to the situation (type of incident, presence of victims, potential dangers, spatial context) and does not require an extremely "fine" understanding of the situation. Even if the specific and precise understanding of the elements of the situation characterizes more the activity of the crew members (BAT and BAL), our results show that all of them adopt both levels of understanding during a maneuver (macro and micro). The team members adopt a macroscopic level of meaning-making with respect to the situation until the team leader assigns them a specific mission. From then on, they turn to a microscopic meaningmaking process specific to the situation (e.g., rescuing a victim, extinguishing a fire) and partial understanding of the overall situation. It seems relevant to support the team leaders in their ability to orient the activity of each team member according to their function and the level of understanding that this function requires (macroscopic or microscopic). For example, a trainer could guide the activity of the officer in charge of entering an apartment with the lance in order to find a victim. In the case of such a mission, the agent enters into a microscopic sense-making process related to a specific objective to be reached. This help could thus concern precise elements such as the safety measures to be put in place before entering a closed room and then the clues to be taken into account in the smoky environment in order to understand the configuration of the place. Simulation has a particular interest here again by proposing realistic and credible situations, training the agents to identify and share significant information specific to the situation in order to build a macroscopic understanding when it is necessary for the team. Thus, in firefighting teams, the sense-making of the situation is done in action, mixing an individual activity focused on the mission to be achieved and a social activity focused on the understanding of the situation from the team's point of view. Finally, the training could be improved by asking the trainers to insist on the back and forth between these two levels of understanding of the situation for each member of the team. The training would then allow for modulated learning alternating between personalization and homogenization.

5.1The articulation of the two levels of comprehension of the situation to be trained

Change of role and function to enrich sense-making at individual and team levels

The consideration of team sense-making as an articulation of individual sense-making allowed us to note its heterogeneous character. Our results show a disparity of individual sense-making within the firefighting team as well as levels of understanding of the situation. This heterogeneity results from the influence of individual functions because a firefighting team is characterized by the diversity of roles allocated to each of its members. Although these roles have a strong influence, they do not entirely substitute for the functions actually performed in the field. The case of the fire chief is different because role and function overlap insofar as his responsibility is to direct his team members in order to resolve the incident in progress, which is relatively generic to be transposable from one situation to another. However, as far as his team members are concerned, the function of each one depends on the mission entrusted to him by the fire chief. It is not uncommon, for example, for the BAT, theoretically intended to extinguish the fire, to be called upon to manage the water supply instead of the BAL (example in maneuver 3 of our present study). In this way, depending on the missions dictated by the fire chief, the intervention team can take on different functional configurations during a maneuver, thus influencing the understanding of the situation of each individual. This opens up an opportunity for training firefighting teams, since it is not only a matter of training them to take on the role specific to their function, but also of teaching them to change roles during an intervention according to the needs of the situation. The representations SAGA show here all their relevance because they help to build 16 pedagogical scenarios in which the actors can train these adaptability skills through team sensemaking. Simulations offer interesting possibilities thanks to replay, individual and/or collective viewing (with the possibility of changing the point of view) to build a shared frame during debriefing sessions. Simulation allows learning by doing, being part of active pedagogies, where different relationships to the frame can be deployed. Thus, from a pedagogical point of view, it seems important that the trainers accompany the trainee fireman to pilot and manage the activity of his team throughout the situation. This aspect is already the object of interest in the training but in an informal way and always after the simulation activity (during the debriefing). Our study shows the importance of this team sensemaking skill, which allows us to recommend to simulation designers to fully integrate it into the scenarios and to make it a pedagogical activity in its own right.

Typical structures of team sense-making to be taken into account to design new simulations.

The heterogeneous nature of the collective construction of meaning also lies in the (im)possibilities of interaction in the environment. Alterations in the possibilities of communication (verbal or visual) constrain the members of the team because of the compartmentalized environments in which the teams have to evolve. According to the movements of each one during the maneuver, the team is led to present varied spatial configurations acting on the mechanisms of collective construction of meaning. It appears from then on "local" and "typical" structures of team sense-making. The configuration of the places, associated with the absence of remote communication devices (e.g. microphones), leads the members of the team to be able to communicate only with the people in the vicinity. We then observe "very localized" structures of team sense-making which take different forms according to the movements and the activity of each one. This phenomenon can be observed at different levels of the collective, either on a part of the team (e.g. a pair readjusting its understanding during its mission) or on its totality (the team leader who transmits information to the rest of the team gathered in the truck). Our results show regularities in the modes of coordination between team members leading us to identify 6 typical structures of team sense-making.

The team sense-making take a multitude of forms in the course of the missions entrusted to each pair (or team member) and of their movements within the environment continuously modifying the (im)possibilities of interaction between each individual. The set of typical structures of team sensemaking that could be extracted contributes to constitute cycles of local coordination corresponding mainly to the activity of the two pairs and intermingling to constitute the global activity of the team during a maneuver.

From a pedagogical point of view and in the perspective of progressive learning, these environmental constraints could be overcome by equipping the team members with microphones. This would allow them to exchange important information at any time, overcoming the need to be in close proximity to communicate. This system would facilitate the collective activity of the team and could be a step before training situations without the possibility of exchanges other than in immediate proximity. From there, a certain progressiveness could be established by leaving all communications between the trainee team leader and his team members free, then by reducing them as the training progresses (e.g. limiting the number of communications during a situation or only authorizing calls initiated by the trainee team leader and prohibiting calls from team members). These pedagogical situations would allow to train team sense-making, an "embedded" phenomenon where the agents need to share very precise and specific information about the situation (e.g. "headwind" in the results). Locating this relevant information in the situation, which is similar to affordances, requires specific training that must be taken care of by the training of teams.

In conclusion, the model of team sense-making used in this work appears useful for describing and understanding the back and forth between action, its effects and the frame for acting in a dynamic situation. The consequences for training are interesting because it implies to favor an intuitive

Figure 1 .

 1 Figure 1. Expanded data/frame diagram to team sense-making taken from Klein et al. (2010).

Figure 2 .

 2 Figure 2. Relationships between the reference spaces (represented by the floor plan on the upper left and the photos on the right) and the MUSICOF transcription

Figure 3 .

 3 Figure 3. An illustration of the Sensemaking Articulation of Global Activity (SAGA). Letter E elaborate a frame; Letter Q question a frame; Letter R reframe; Bold line radical impossibility for interaction; Discontinuous line limited possibility of interaction Finally, we ensured the validity of the analysis by relying on the 3 principles of Corbin and Strauss (2008): completeness, exclusivity and fidelity (sequencing, coding, inter-coder agreement calculations).

Figure 4 .

 4 Figure 4. SAGA : Alertness

Figur e 5

 5 Figur e 5. 8: 1 er st ruct ure de con st ruct ion col lect ive de sens : Le chef d'agr ès an non ce la sit uat ion

Figur e 5

 5 Figur e 5.9: 2 e st ruct ure de const ruct ion col lect ive de sens : Élabor at ion binômial e

  Cet t e remise en quest ion binômial e peut présent er égal ement une st ruct ure asymét rique (var iant e c) lor squ'à la suit e d'une négociat ion un membre du binôme va préserver son cadre microscopique al or s que l'aut re va passer par 220 Y OHA NN CA RDIN 5.2. R É SU LT ATS la créat ion d'un nouveau cadre (recadrage). Cet t e sit uat ion se présent e par exemple lor s de la manoeuvre 1 (séquence 5) lor sque l'équipier-BAL fai t par t au chef-BAL de son scept icisme quant à l'endroi t où ce dernier à poser la division d'al iment at ion par rappor t à la local isat ion du foyer d'incendie. Le chef-BAL va al or s reconsidérer son act ion et déplacer la division confor mément aux remar ques de son équipier. Le chef-BAL procède par conséquent à un recadrage al or s que l'équipier-BAL préserve son cadre microscopique init ial .

Figur e 5

 5 Figur e 5.11: 4 e st ruct ure de const ruct ion col lect ive de sens : Ré-at t ribut ion de mission

Figure 8 .

 8 Figure 8. SAGA : Team sense-making stand-by

Figure 9 .

 9 Figure 9. SAGA: Team sense-making adjustment

  ust em ent de const r uct ion collect i ve de sens La sixième st ruct ure de const ruct ion col lect ive de sens por t e sur un moment par t iculier de remise en quest ion du cadre microscopique au sein d'un binôme amenant les par t enai res à un pr ocessus de r ecadr age par compar aison ent r e l eur cadr e m icr oscopi que et m acr oscopique (Figure5.13).

  This is a post-print of the following chapter:Bossard C., Prost M., Cardin Y., & Kermarrec G. Analyzing the Collective Activity of Firefighters During Urban Fire Simulation, published in Simulation Training through the Lens ofExperience and Activity Analysis, edited by Simon Flandin, Christine Vidal-Gomel, and Raquel Becerril Ortega, 2022, Springer International Publishing, reproduced with permission of Springer Nature Switzerland AG. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-89567-9_9

		The team collaborates to synthesize competing frame
	Elaborate a frame	The team discusses and dismisses anomalous data as transient or otherwise
		insignificant signals
		Data synthesizing team members lead data "collector" activities to seek new
		data to verify the frame
		Synthesizing and collecting team members collaborate to discover new
		relationships that preserve or extend the frame

Table 1 .

 1 Distribution of individual sense-making of each member of firefighters team in maneuver 1.

	Maneuver 1	Recognize a	Elaborate a	Question	a	Re-frame	Re-frame
		frame	frame	frame		(seek)	(compare)
	Chief	2	20	2		1	0
	BAT-1	4	19	2		2	0
	BAT-2	4	16	3		1	0
	BAL-1	5	13	3		1	2
	BAL-2	3	11	1		0	0

Table 2 .

 2 Distribution of individual sense-making of each member of firefighters team in maneuver 2.This is a post-print of the following chapter: Bossard C., Prost M., Cardin Y., & Kermarrec G. Analyzing the Collective Activity of Firefighters During Urban Fire Simulation, published in Simulation Training through the Lens of Experience and Activity Analysis, edited by Simon Flandin, Christine Vidal-Gomel, and Raquel Becerril Ortega, 2022, Springer International Publishing, reproduced with permission of Springer Nature Switzerland AG. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-89567-9_9

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Table 3 .

 3 Distribution of individual sense-making of each member of firefighters team in maneuver 3

	Maneuver 3	Recognize a	Elaborate a	Question	a	Re-frame	Re-frame
		frame	frame	frame		(seek)	(compare)
	Chief	2	14	1		1	0
	BAT-1	7	16	2		2	0
	BAT-2	6	14	2		2	0
	BAL-1	3	22	1		0	0
	BAL-2	3	18	1		1	0

  This is a post-print of the following chapter:Bossard C., Prost M., Cardin Y., & Kermarrec G. Analyzing the Collective Activity of Firefighters During Urban Fire Simulation, published in Simulation Training through the Lens ofExperience and Activity Analysis, edited by Simon Flandin, Christine Vidal-Gomel, and Raquel Becerril Ortega, 2022, Springer International Publishing, reproduced with permission of Springer Nature Switzerland AG. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-89567-9_9

  with permission of Springer Nature Switzerland AG. The final authenticated version is available online at: https://doi.org/10.1007/978-3-030-89567-9_9

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