P Morra

O Semeraro

D S Henningson

Carlo Cossu

Resolvent Analysis: With or Without Eddy Viscosity?

HAL is

Introduction

Coherent streamwise streaks, i.e. spanwise alternated high-and low-velocity regions elongated in the streamwise direction, account for most of the fluctuating energy in wall-bounded turbulent shear flows. Their ubiquity in transitional and turbulent flows has been related to the 'lift-up' effect where low-energy quasi-streamwise vortices immersed in a shear flow lead to high-energy streamwise streaks. Much attention has been given to the computation of optimal energy amplifications associated to the lift-up effect and of the associated optimal inputs and outputs for the linear initial-value problem and the response to harmonic and stochastic forcing.

In the case of turbulent flows, two distinct approaches have been followed to the definition of the linear operator used for the computation of optimal energy amplifications. In the first approach the Navier-Stokes equations are rewritten in terms of perturbations to the turbulent mean velocity; the instantaneous and averaged (Reynolds stresses) perturbation nonlinear terms are accounted for as an external input which forces the response via the linear operator (see e.g. [START_REF] Malkus | Outline of a theory of turbulent shear flow[END_REF][START_REF] Butler | Optimal perturbations and streak spacing in wall-bounded turbulent shear flow[END_REF][START_REF] Farrell | Optimal excitation of three-dimensional perturbations in viscous constant shear flow[END_REF][START_REF] Mckeon | A critical-layer framework for turbulent pipe flow[END_REF] among others and [START_REF] Mckeon | The engine behind (wall) turbulence: Perspectives on scale interactions[END_REF] for a review). In the second approach the 'incoherent' part of turbulent Reynolds stresses is included in the linear operator with an eddy-viscosity (ν t ) model (see [START_REF] Reynolds | Stability of turbulent channel flow, with application to Malkus's theory[END_REF][START_REF] Reynolds | The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments[END_REF][START_REF] Bottaro | Formation of secondary vortices in a turbulent square-duct flow[END_REF][START_REF] Del Álamo | Linear energy amplification in turbulent channels[END_REF][START_REF] Cossu | Optimal transient growth and very large scale structures in turbulent boundary layers[END_REF][START_REF] Pujals | A note on optimal transient growth in turbulent channel flows[END_REF][START_REF] Hwang | Amplification of coherent streaks in the turbulent Couette flow: an inputoutput analysis at low Reynolds number[END_REF][START_REF] Hwang | Linear non-normal energy amplification of harmonic and stochastic forcing in turbulent channel flow[END_REF] among others and [START_REF] Cossu | Self-sustaining processes at all scales in wall-bounded turbulent shear flows[END_REF] for a review). We will refer to the former approach as 'ν-model' and to the latter as 'ν t -model'.

Most of the comparisons between statistics of real turbulent flows and the predictions based on the two mentioned linear models, and in particular those where the resolvent modes are computed, are, however, either qualitative or concern integrated energy densities and (integrated) spatial spectra (the Fourier transform of the second-order velocity spatial correlations). Also, most of these analyses, with the notable exception of [START_REF] Illingworth | Estimating large-scale structures in wall turbulence using linear models[END_REF], lack a detailed quantitative comparison of the performance of the ν and ν t models.

A major source of difficulty for the comparison of turbulent statistics to predictions of linear models resides in the presence of a wide range of temporal frequencies involved in turbulent processes, even at selected spatial scales which can not be separated when considering spatial correlations tensors. In the context of Karhunen-Loève decompositions (proper orthogonal decompositions, POD) the use of the spatio-temporal correlation tensor R(x, x + ∆x, t, t + τ ) and of its Fourier-transform where the effect of different frequencies can be separated has led a direct connection between the spectral-POD modes and resolvent modes (see e.g. [START_REF] Picard | Pressure velocity coupling in a subsonic round jet[END_REF][START_REF] Semeraro | Stochastic and harmonic optimal forcing in subsonic jets[END_REF][START_REF] Towne | Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis[END_REF]) based on the ν-model.

The scope of this investigation is, inspired by this recent progress, to evaluate the respective performance of the ν-model and the ν t -model in the estimation of the velocity spatio-temporal power spectral density and power cross-spectral density. The turbulent channel flow at Re τ = 1007 is used as a testbed for this analysis because of the large inhomogeneity of ν t in this flow which enhances potential differences of the two models.

Background

We consider the dynamics of coherent perturbations in a turbulent flow of an incompressible fluid of kinematic viscosity ν in the channl between two infinite parallel walls located at y = ±h. We denote the streamwise, wall-normal and spanwise coordinates by x, y and z, respectively.

In the 'ν t -model', the evolution of small coherent perturbations to the turbulent mean flow is modelled with linearised equations which include the effect of the turbulent Reynolds stresses by means of an eddy viscosity ν t corresponding to the turbulent mean flow profile U = (U (y), 0, 0) [START_REF] Reynolds | Stability of turbulent channel flow, with application to Malkus's theory[END_REF][START_REF] Reynolds | The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments[END_REF][START_REF] Del Álamo | Linear energy amplification in turbulent channels[END_REF][START_REF] Pujals | A note on optimal transient growth in turbulent channel flows[END_REF]. Considering dimensionless variables based on the reference length h and the reference velocity (3/2)U bulk , where U bulk is the constant mass-averaged streamwise velocity, this model reads:

∂u ∂t + ∇u • U + ∇U • u = -∇p + ∇ • ν T ∇u + ∇u T + f , (1)
where u = (u, v, w) and p are the coherent perturbation velocity and pressure, ν T (y) = ν + ν t (y) is the total effective viscosity and f is the forcing term (note that in dimensionless units ν T = (1 + ν t /ν)/Re, where Re = (3/2)U bulk h/ν ). The incompressibility condition ∇ • u = 0 completes these equations. The eddy viscosity is modelled with the semi-empirical expression proposed by Cess [START_REF] Cess | A survey of the literature on heat transfer in turbulent tube flow[END_REF], as reported in [START_REF] Reynolds | Stability of turbulent channel flow, with application to Malkus's theory[END_REF]:

ν t ν = 1 2 1+ κ 2 Re τ 2 9 (1-y 2 ) 2 (1+2y 2 ) 2 (1-e y + /A ) 2 1/2 - 1 2 ,
(2) where y ∈ [-1, 1], y + = Re τ (1 -|y|) and Re τ = u τ h/ν is the Reynolds number based on the friction velocity u τ . The von Kármán constant is set to κ = 0.426 and the constant A = 25.4 as in [START_REF] Pujals | A note on optimal transient growth in turbulent channel flows[END_REF][START_REF] Hwang | Linear non-normal energy amplification of harmonic and stochastic forcing in turbulent channel flow[END_REF].

In the 'ν-model' (a.k.a. 'quasi-laminar model'), turbulent Reynolds stresses and nonlinear terms are both included in the forcing term f so that the linear model reduces to Eq. ( 1) but now only including the molecular kinematic viscosity ν T = ν [START_REF] Butler | Optimal perturbations and streak spacing in wall-bounded turbulent shear flow[END_REF][START_REF] Farrell | Stochastic forcing of the linearized Navier-Stokes equation[END_REF][START_REF] Mckeon | A critical-layer framework for turbulent pipe flow[END_REF].

The system invariance to translations in wallparallel directions leads to consider the Fourier-modes û(α, y, β, t)e i(αx+βz) and f (α, y, β, t)e i(αx+βz) of streamwise and spanwise wavenumbers α = 2π/λ x and β = 2π/λ z . Eq. ( 1) can be reduced to the following linear system, expressed in terms of the state vector q = [v, ωy ] T formed with the wall-normal components of the velocity and vorticity Fourier modes:

∂ q ∂t = Aq + B f , (3)
where û = Cq and q = Dû (the explicit expressions of the operators A, B, C and D can be found e.g. in [START_REF] Hwang | Linear non-normal energy amplification of harmonic and stochastic forcing in turbulent channel flow[END_REF]). As the system is linearly stable, the to deterministic can be analysed in the frequency domain considering the harmonic forcing f = f e -iωt with the harmonic response ue -iωt related by:

u = H f ; H = -C(iωI + A) -1 B ( 4
)
where H is the resolvent operator (or transfer function). When the forcing is stochastic so is the response and one has to consider velocity second-order spatio-temporal correlation tensor

R(ξ, y, y , ζ, τ ) = u(x, y, z, t)u * (x + ξ, y , z + ζ, t + τ ) , (5)
where denotes ensemble averaging and * denotes complex conjugate transpose. The (spatio-temporal) power cross-spectral density tensor S(α, y, y , β, ω) is obtained through Fourier transform of R in ξ, ζ and τ .

The tensor S can also be obtained directly as the average of the Fourier transform u of the velocity [START_REF] Bendat | Random data: analysis and measurement procedures[END_REF] and the stochastic forcing power cross-spectral density tensor P can be defined similarly:

S(α, y, y , β, ω) = u(α, y, β, ω) u * (α, y , β, ω) (6) P(α, y, y , β, ω) = f (α, y, β, ω) f * (α, y , β, ω) . ( 7
)
An estimation S (est) = HPH * of the velocity power cross-spectral density tensor is obtained by replacing the linear expression of Eq. ( 4) in Eq. [START_REF] Reynolds | The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments[END_REF]. Further assuming that P = p(α, β, ω) I (where I is the identity operator), as e.g. in [START_REF] Farrell | Optimal excitation of three-dimensional perturbations in viscous constant shear flow[END_REF][START_REF] Hwang | Amplification of coherent streaks in the turbulent Couette flow: an inputoutput analysis at low Reynolds number[END_REF][START_REF] Hwang | Linear non-normal energy amplification of harmonic and stochastic forcing in turbulent channel flow[END_REF], then S (est) reduces to:

S (res) = pHH * (8)
which is the basic expression used in resolvent analyses.

The scope of this study is to determined the accuracy of the estimation provided by Eq. ( 8). 3 Direct numerical simulation and statistics

The velocity correlations have been estimated trough a direct numerical simulation of the turbulent channel flow at Re τ = 1007 in a domain of extension L x = 3 and L z = 1.5 corresponding to the size of the most energetic large-scale motions (LSM) in the channel [START_REF] Del Álamo | Scaling of the energy spectra of turbulent channels[END_REF] and representing the minimum flow unit for the self-sustainment of coherent LSM [START_REF] Hwang | Self-sustained process at large scales in turbulent channel flow[END_REF]. The simulations have been performed using the pseudospectral SIMSON code which uses Fourier expansions in the streamwise and spanwise directions, where periodicity is enforced, and Chebyshev expansions in the wallnormal direction to solve the three-dimensional timedependent incompressible Navier-Stokes equations in the channel [START_REF] Chevalier | A Pseudo-Spectral Solver for Incompressible Boundary Layer Flows[END_REF]. A total of N x = 128, N y = 129, N z = 128 points have been used with a uniformly spaced grid in x and z and Gauss-Lobatto points in y. This corresponds to a grid spacing ∆x + = 23, ∆z + = 12 and to ∆y + min = 0.3 near the wall and ∆y + max = 24 at the channel centre. This chosen grid is coarser than those typically used in DNS at this Reynolds number to keep the data analysis manageable.

As shown in Figure [START_REF] Malkus | Outline of a theory of turbulent shear flow[END_REF], despite the moderate extension of the domain and the relatively coarse grid, the computed mean flow and the rms fluctuation profiles are in reasonable agreement with those of [START_REF] Lee | Direct numerical simulation of turbulent channel flow up to Re τ ≈5200[END_REF] obtained in the much larger domain L x = 25, L z = 9.5 with a finer grid (∆x + = 11, ∆z + = 5) We have further verified Cess's analytic fit by comparing the mean flow profile and the corresponding eddy viscosity to the ones issued by DNS data.

The analysis of the premultiplied streamwise kinetic energy spectral density αβE uu (α, y, β) = αβ ∞ -∞ S uu (α, y, y, β, ω)dω, evaluated in the y + = 15 and y = 0.5 planes (not shown here) shows that the most energetic structures at y = 0.5 have spatial scales corresponding to the dimensions of the LSM flow unit λ x = L x = 3, λ z = L z = 1.5 (corresponding to α ≈ 2, β ≈ 4) while the most energetic structures at y + = 15 have spatial scales λ +

x ≈ 450 and λ + z ≈ 100 (corresponding to α ≈ 14, β ≈ 63 at Re τ = 1007) typical of the near-wall self-sustained process. We will therefore focus on these two sets of (α, β), corresponding to (λ x = 3, λ z = 1.5) and (λ + x = 450, λ + z = 100), which represent the dynamics of large-scale and near-wall The power cross-spectral density tensor has therefore been computed for the two considered (α, β) pairs. The initial transient of the simulation is discarded and statistics and samples are accumulated starting from t = 95000. Welch's method with Hamming windowing and 75% overlap is then used to compute the velocity power cross-spectral density S using a total of N s = 8001 snapshots of the DNS solutions with sampling interval (∆t) s = 0.25 for a total acquisition time T max = 2000 for the small scales, and using N s = 20001 snapshots sampled every (∆t) s = 0.5 for a total acquisition time T max = 10000 for the large scales. The average temporal step of the DNS during the acquisition time is ∆t = 0.0106, i.e. ∆t + = 0.35. Data have also been averaged between the two walls.

The streamwise velocity power spectral density profiles S uu (α, y, y, β, ω) = u(α, y, β, ω) u * (α, y, β, ω) are reported in Figure (2) as a function of the phase speed c = ω/α, expressed in wall units, and of the wall normal coordinate for the considered (α, β) pairs. The peaks of these distributions are found at ω max = 4.3 and ω max = 1.4 for the near-wall and large-scale peaks, respectively. These peaks correspond to the two phase velocities c + max ≈ 10 and c + max ≈ 20 and their wall-normal locations (y + max ≈ 15 and y max ≈ 0.4 -0.5) approximatively correspond to the wall-normal position where

U + = c + .

Estimations from resolvents

The capacity of the ν t and the ν linear models to reproduce statistics of the turbulent flow via the estimation S (res) = pHH * given by Eq. ( 8) is tested by first assuming a (temporal) white noise forcing where p = p does not depend on ω and p is chosen such that the estimated total spectral power of the streamwise velocity matches the one issued from direct numerical simulations, i.e. uu (α, y, y = y, β, ω)) estimated with the ν t -model on the wall-normal coordinate and the phase speed c + with (white-noise) flatspectrum stochastic forcing (top panels) and colourednoise stochastic forcing (bottom panels) for the near-wall structures with λ + x = 450, λ + z = 100 (left panels) and the large-scale structures with λ x = 3, λ z = 1.5 (right panels). The mean velocity profile U + is reported as a dashed black line. The colour-scale is the same as the one used to represent direct numerical simulations data in Figure [START_REF] Butler | Optimal perturbations and streak spacing in wall-bounded turbulent shear flow[END_REF] noise forcing (top panels), the ν-model does not select the correct values and locations of the power spectral density peaks, which are predicted at too large c + values (and therefore too large ω values) and are located near the channel center (out of view in the top left panel). The power spectral density appears also to be too narrowly concentrated near the line U + = c + when compared to the DNS data of Figure ( 2) both for near-wall and large-scale structures. The estimation improves for the case of colored noise (bottom panels), where the selective (in ω) forcing is able to drive the response peaks nearer their DNS values. Even in this case, however, the power spectral density remains too narrowly concentrated and therefore too large near the U + = c + curve (the uniform dark red regions in bottom and right panels which are strongly offscale).

The use of the ν t model leads to a significant improvement, as shown in Figure ( 4), of the response near the channel centre because the effective eddy diffusivity dampens (where the eddy viscosity is high) and smoothens the critical layer peaks. The ν t -model is able to select a reasonable y + max -c + max location of the crossspectral peak for buffer-layer structures even with whitenoise stochastic forcing (top panels). For large-scale structures (top right panel), however, the amplitude of the response is still over-predicted near the channel centre and near the wall. The estimation based on the ν t model is further improved when the coloured-spectrum forcing is used (bottom panels), in particular for the large-scale case (bottom right panel)

Conclusions

In this study the 'measured' spatio-temporal power cross-spectral density S (dns) = u(α, y, β, ω) u * (α, y , β, ω) obtained by direct numerical simulation of plane channel flow at Re τ = 1007, has been compared to the estimation S (res) = pHH * based on the resolvent operator H which implicitly assumes that the spatio-temporal power cross-spectral density of the forcing is of the form P = p I. In this type of analysis the contribution of each temporal frequency ω to the spatial energy spectral density can be analysed separately. The comparison has been performed for structures with spatial scales typical of buffer-layer structures (λ + z = 100, λ + x = 450) and of large-scale motions (λ z = 1.5, λ x = 3).

Two distinct linear models have been considered for the evaluation of H, respectively including ('ν t model') or not (the quasi-laminar model or 'ν model') an eddy viscosity modeling the turbulent Reynolds stresses. Two types of forcing power spectra p(ω) have been considered: white noise (flat forcing power spectrum p = p) and 'coloured' noise (power spectrum where p(ω) is chosen so as to match the power spectrum of the estimated streamwise velocity power spectral density to the measured one).

Qualitatively correct estimations of power crossspectral density distributions and of the dependence of the power spectral density wall-normal distributions on the frequency (or, equivalently, the phase speed) are found when using the ν t model resolvent. On the contrary, generally overestimated values of the streamwise velocity power spectral density which are (too) narrowly concentrated near the critical layer are found when using the ν model which is also unable to even qualitatively reproduce the c + max -y + max values of the peak amplitude of the power spectral density for buffer-layer structures. It is also found that in all cases, as expected, estimations are improved by using the appropriately coloured input power spectrum p(ω) instead of white noise as already observed in [START_REF] Zare | Colour of turbulence[END_REF] using a different methodology.

The interpretation of these results is as follows: in the ν model the effect of turbulent Reynolds stresses resides only in the forcing and the associated power crossspectral density P while in the ν t model the effect of turbulent Reynolds stresses is included in the resolvent H. As a consequence, when no accurate information on P is available, which is the rule at high Reynolds numbers, and it is therefore assumed that P = pI, the ν t model performs much better than the ν-model because the effect of the turbulent Reynolds stresses is embedded in H. It is, however, likely that the ν model could perform equally well in the case where a realistic modelling of the forcing cross-spectral tensor P could be obtained leading to the estimation S (res) = HPH * . In this second case the scale selection would be dictated by P instead of H.

The similarity of resolvent modes computed with the ν-model and experimental SPOD modes previously observed in in turbulent jets [START_REF] Semeraro | Stochastic and harmonic optimal forcing in subsonic jets[END_REF][START_REF] Schmidt | Spectral analysis of jet turbulence[END_REF][START_REF] Towne | Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis[END_REF] can be understood by recalling that in free shear-flows the turbulent eddy viscosity usually only weakly depends on the radial coordinate and therefore the resolvent based on the ν-model coincides with the one based on the ν t -model except for a rescaling by ν/ν T of the Reynolds number and provided that the solution domain is not too long in the streamwise direction.

Further progress in the estimation of S (dns) could certainly come from a better modelling of the Reynolds stress tensor in the linear operator and from the modelling of P related to the regeneration mechanism of the vortices in the self-sustained processes [START_REF] Waleffe | Hydrodynamic stability and turbulence: Beyond transients to a self-sustaining process[END_REF][START_REF] Hwang | Self-sustained process at large scales in turbulent channel flow[END_REF][START_REF] Hwang | Self-sustained processes in the logarithmic layer of turbulent channel flows[END_REF][START_REF] Cossu | Self-sustaining processes at all scales in wall-bounded turbulent shear flows[END_REF]. These research directions are currently actively pursued.

Figure 1 :

 1 Figure 1: Comparison of direct numerical simulations in the LSM flow unit (DNS-LSM) at Re τ = 1007 to those in [22] (L&M) and to Cess's model at Re τ = 1000 in terms of mean flow profiles (left panel) and rms velocity profiles (right panel) from the DNS-LSM (lines with symbols) compared to those of L&M (lines)

Figure 2 :

 2 Figure 2: Dependence of the power spectral density S (dns) uu (α, y, y = y, β, ω)) issued from DNS data on the phase speed c + = ω + /α + and the wall-normal coordinate for buffer-layer structures with λ + x = 450, λ + z = 100 (left panel) and large-scale structures with λ x = 3, λ z = 1.5 (right panel). The mean velocity profile U + is reported as a dashed black line. Data from the direct numerical simulation in the LSM flow unit at Re τ = 1007

1 - 1 1 - 1 1 - 1 1 - 1

 11111111 S uu (est) (α, y, y, β, ω)dydω = ∞ -∞ S uu (dns) (α, y, y, β, ω)dydω. As a second case, colored noise is assumed with p(ω) such that at each selected frequency ω: S uu (est) (α, y, y, β, ω)dy = S uu (dns) (α, y, y, β, ω)dy. The results obtained with the ν-model are reported in Figure (3) where the y-profiles of the estimated streamwise velocity power spectral density versus the phase speed c + are shown analogously to Figure (2). For white-

Figure 3 :

 3 Figure 3: Dependence of S (est) uu (α, y, y = y, β, ω)) estimated with the ν-model on the wall-normal coordinate and the phase speed c + with (white-noise) flatspectrum stochastic forcing (top panels) and colourednoise stochastic forcing (bottom panels) for the near-wall structures with λ + x = 450, λ + z = 100 (left panels) and the large-scale structures with λ x = 3, λ z = 1.5 (right panels). The mean velocity profile U + is reported as a dashed black line. The colour-scale is the same as the one used to represent direct numerical simulations data in Figure (2).

Figure 4 :

 4 Figure 4: Dependence of S (est)

Acknowledgment

Direct numerical simulations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at NSC, HPC2N and PDC


Clement Colin

Antoine Martin

Improving mental time travel abilities to support the collection of needs: a pilot study

Keywords: Prospective ergonomics, mental time travel, needs anticipation

Several branches stemming from the field of human-centered design have tackled the discovery of user needs in early design phases. Within one of these approaches, prospective ergonomics, this study is calling for new methods in order to better elicit needs from the user. The study draws from the research on future-oriented cognition regarding how people imagine the future. We then report on a pilot study on the effect of two future projection tasks on the elaboration of user needs.

Introduction

For several years the field of human-centered design has been moving toward new approaches applied to the design of yet-unknown or ill-defined future products or services [START_REF] Mckim | Experiences in visual thinking[END_REF][START_REF] Sterling | Shaping Things[END_REF][START_REF] Hey | Analogies and metaphors in creative design[END_REF]Robert and Brangier, 2009 etc.). One of these approach, prospective ergonomics, has been defined by Robert and Brangier as "the part of ergonomics that attempts to anticipate human needs and activities so as to create new artifacts that will be useful and provide a positive user experience". Some past and current projects in prospective ergonomics have dealt with the future of energy [START_REF] Martin | Hydrogen Energy Technologies' Acceptance Review and Perspective: Toward a Needs' Anticipation Approach[END_REF] mobilities [START_REF] Brangier | An Interview Process to Anticipate Future Needs[END_REF] and software [START_REF] Nelson | Analyzing Interaction Dynamics at the Fuzzy Front-End of Innovation Projects: A Tool for Prospective Ergonomics[END_REF]. As of today, prospective ergonomics does not incorporate developments from cognitive psychology regarding the individual's ability to imagine a future. Since prospective ergonomics aims to anticipate future uses and needs it is then of the foremost importance to enable users and experts to better think, experience and verbalize probable futures in order to collect ideas and representations, build and explore scenarios. Thus, understanding how people project themselves into the future could be a stepping stone in order to develop new needs and uses anticipation methods. The goal of the study is to assess the effect of two consecutive future projection tasks on the expression of future needs. Other independent variables were manipulated (they won't be reported in details in the paper): the topics (energy for housing and transportation), the collection tools (sentence completion tests vs. open-ended questions), system definition level (yet-unknown vs. ill-defined). We chose to vary the system definition level because it offers value for use cases in prospective ergonomics where practitioners are asked either to explore needs and uses related to ill-defined or to yet-unknown socio-technical systems.

Mental time travel

Back in 1781, Kant penned the concept of anticipation in his essay the Critique of Pure Reason ("All cognition, by means of which I am enabled to cognize and determine a priori what belongs to empirical cognition, may be called an anticipation.") and Bergson penned the concept of élan vital (1907) a kind of future-oriented spontaneity. This ability to project oneself in the future has been termed mental time travel [START_REF] Suddendorf | Mental time travel and the evolution of the human mind[END_REF], future thinking [START_REF] Atance | Episodic future thinking[END_REF], envisioning the future (Buckner and Carroll, 2007), future-oriented cognition [START_REF] D'argembeau | Frequency, characteristics and functions of future-oriented thoughts in daily life[END_REF][START_REF] Osvath | The future of future-oriented cognition in non-humans: theory and the empirical case of the great apes[END_REF] etc. According to [START_REF] Schacter | Episodic future thinking: Mechanisms and functions[END_REF], it is the ability to consider an experience by mentally creating a realistic scenario that combines image, thought and action; it is what allow us to anticipate future events [START_REF] Eustache | La mémoire du futur[END_REF]. Here we will use the term mental time travel defined by Doris Bischof-Köhler as the capacity to "represent oneself at every possible instant in the past and in the future and to imagine the desires and motives at each of those instants independently of one's present motivational state". The central hypothesis of mental time travel (or MTT) is that the ability to imagine a future relies on memory systems. In 1985, Endel Tulving distinguished 2 types of memories linked to 2 types of anticipation: the anticipation of personal events (using the episodic memory) and the anticipation of general events (semantic memory) on the basis of patients (such as K.C.) with damaged episodic memory that were unable to imagine a personal future (the so-called episodic foresight ability) yet they were able to imagine a general future [START_REF] Kwan | Medication reconciliation during transitions of care as a patient safety strategy: a systematic review[END_REF]. Using fMRI, [START_REF] Viard | Mental time travel into the past and the future in healthy aged adults: an fMRI study[END_REF] confirmed that neuronal regions activated while envisioning the future are the same as those activated when proceeding to remembrance. Structures shared between episodic memory and future-oriented cognition have been identified as the hippocampus [START_REF] Hassabis | Patients with hippocampal amnesia cannot imagine new experiences[END_REF], the cingulate cortex, the prefrontal cortex and the precuneus [START_REF] Viard | Mental time travel into the past and the future in healthy aged adults: an fMRI study[END_REF]. The contribution of semantic memory has been less studied but [START_REF] Irish | Exploring the content and quality of episodic future simulations in semantic dementia[END_REF] concluded that semantic dementia patients also had a reduced ability to episodic foresight. The root cause might be that there is no strict biological separation between semantic and episodic memory systems [START_REF] Squire | The medial temporal lobe[END_REF][START_REF] Balota | Semantic memory[END_REF][START_REF] Greenberg | Interdependence of episodic and semantic memory: evidence from neuropsychology[END_REF]. Despite this growing literature, recommendations are rare regarding stimulation methods of the MTT ability. To describe these methods, we will use the umbrella term future projection task (Raffard et al., 2012;[START_REF] Bonn | Visualizing the good life: a cross-cultural analysis[END_REF]

Future projection tasks

Some researchers have started to propose ideas for the design of future projection tasks. D'Argembeau and Van der Linden (2012) underline that improving the quality of MTT is dependent on the specificity of the explored episode/situation and the quality of the sensorycontextual representation. Thus, [START_REF] Irish | The pivotal role of semantic memory in remembering the past and imagining the future[END_REF] recommend to follow two steps to project oneself in the future i) build an image of the event and its context, on the basis of memories and ii) develop and enrich the representations of the event. For the study, two existing future projection tasks have been adapted to an online survey format. The tasks were used as primers, a common tool in the fuzzy front end of design projects (e.g. [START_REF] Nelson | I'd like to be under the sea": Contextual cues in virtual environments influence the orientation of idea generation[END_REF]. Cognitive priming is the use of stimuli to elicit specific ideation or mental processes. The two future projection tasks are: the Guided Imaginary Projection [START_REF] Allinc | The Guided Imaginary Projection, a New Methodology for Prospective Ergonomics[END_REF] and the Future Thinking Task [START_REF] Macleod | Recovery of positive future thinking within a high-risk parasuicide group: Results from a pilot randomized controlled trial[END_REF]. Guided Imaginary Projection (GIP) is the mental, first-person exploration of a scenario related to a future service/product with the help of the design practitioner. Here the researcher's guidance took the form of an audio recording instructing to relax and to imagine a specific situation with as much details as possible [START_REF] Noël | Future-oriented mental time travel in individuals with disordered gambling[END_REF], then the respondent was asked to fill a form with a description of the situation he/she envisioned thus shifting the originally oral verbalization of the GIP to a text format. The Future Thinking Task (FTT) is a kind of verbal fluency task where the participant is asked to name a number of future experiences that will happen to him at different times in the future (e.g. one week, one year, ten years), then he is tasked with evaluating the likelihood and valence of each event. For the sake of brevity, FTT was adapted in the following manner: the respondents were asked to list three experiences that could happen in their future.

Method

Participants

Participants were recruited through web communities with interests relative to the topics of the study (i.e. energy for housing and transportation). A total of 205 respondents were included for analysis (70 females, 129 males and 6 who did not specify their gender). They were between the age of 17 and 77 (mean = 43.6, standard deviation = 15.0). Among all participants 17 were excluded (4 for not answering the questionnaire, and 13 for failing to perform one of the future projection tasks).

Procedure

Participants were randomly assigned to a set of 16 different online surveys (see Table 1) using the "random redirector" code [START_REF] Fergusson | Random redirect using Google Apps Script[END_REF] with the independent variables being:

-Topic (energy for housing or transportation) -System definition level (ill-defined or yet-unknown) -Future projection tasks (with or without) -Collection tool (open-ended questions or sentence completion test) First, participants were introduced to one of the two topics. Each topic was parted in two possible conditions: yet-unknown or ill-defined. (e.g. "This study aims to collect your thoughts on a possible future for the car. In this scenario, cars are mostly autonomous and shared." for the illdefined condition and "This study aims to collect your thoughts on the future of the car." for the yet-unknown condition). Then, depending on the modality, participants were either led to project themselves into the future using two consecutive future projection tasks (adapted from GIP and FTT, see 3.2) or went on to the next step without any projection task occurring. Future projection tasks were i) to listen to a 1-min audio recording asking the participant to imagine in as much detail as possible an experience with a future vehicle (or house) then to write it down, and ii) to list 3 things they think will happen to them in their future. Finally, they had to answer either a sentence completion test (e.g. "In the future, using a car, I will feel safe if ...") or an equivalent open-ended questionnaire (e.g. "In the future, when you will use a car, what would make you feel safe?"). Each of these conditions comprised 7 items regarding different modality of a future experience (safety, pleasure, privilege, compatibility with own lifestyle, anger, importance, usefulness to others). The survey ended with socio-demographical questions and a self-rated expertise scale (adapted from [START_REF] Johanna | The development and psychometric evaluation of a multidimensional measurement instrument of professional expertise[END_REF]. Collected data were coded by a first user researcher and then cross-checked by a second one. Two dependent variables were extracted from the transcripts for these preliminary results: fluency (number of unique needs generated per participant) and elaboration (average word count per need). These variables (together with flexibility and originality) are commonly used to assess creativity [START_REF] Lubart | Psychologie de la créativité[END_REF].

Preliminary results

ANOVA tests were run to measure the effect of the independent variables (namely future projection tasks, collection tool, system definition level, topic; see 3.2 for details). ; p = .034, h 2 p = .020) with a higher elaboration with future projection tasks than without (M=8.09, SD= 4.21 and M=7.03, SD=3.74) (see Figure 1).

Figure 1: Box plot of elaboration depending on future projection tasks A significant effect was also observed for collection tools (F(1,189) =0.720 ; p < .001, h 2 p = .058) with a higher elaboration for the open-ended questions over the sentence completion test (M=8.68, SD= 4.89 and M=6.60, SD=2.84). A significant effect was observed for system definition (F(1,189) =4.290 ; p = .040, h 2 p = .019) with a higher elaboration for ill-defined systems over yet-unknown systems (M=8.04, SD= 4.19 and M=6.94, SD=3.69). There was no effect of the topic (F(1,189) =1.282 ; p = .259, h 2 p = .006). For both fluency (r(203) = -.025, p = .722) and elaboration (r(203) = .52, p = .462) there was no correlation with self-rated expertise.

Conclusion

The study illustrates the effect of two future projection tasks on needs' elaboration (in average one more word has been collected with the projection task). No significant effects on fluency has been found. More detailed studies will be necessary to calibrate and further test the effect of the tasks. The treatment of additional dependent variables (originality, flexibility) will also help to better measure the effects. Other significant effects on elaboration were identified such as better results when the participants answered the open-ended questions (vs. the sentence completion tests). No effect of expertise on elaboration nor fluency was detected. The effects could be explained by the positive result of the projection tasks on the quality of participants' representations thus stimulating the evocation of needs [START_REF] Loup-Escande | Needs' elaboration between users, designers and project leaders: Analysis of a design process of a virtual realitybased software[END_REF] and reducing the psychological distance when thinking about distant (time/space) objects [START_REF] Trope | Construal-level theory of psychological distance[END_REF]. This study is a starting point in elaborating methods to support the collection of future needs for prospective ergonomics and other foresight-oriented fields. Current work is underway in prospective ergonomics to integrate such methods in user research interviews.

Limits

The first limit comes from the design of the survey: it was possible for participants to skip the audio recording of the modified GIP (or at least not fully follow the projection task guidelines) and still answer the verification questions. Despite being significant, the difference between the presence/absence of future projection tasks on the average elaboration is not very strong and calls for i) designing more refined future projection tasks, ii) comparing several tasks to determine which is the best, iii) checking if the projection tasks are successful.

To assess the quality of needs collected we used two criteria derived from the psychology of creativity (fluency and elaboration) with two others (originality and flexibility) still to be assessed. It is probable that we could use better suited criteria such as those proposed by [START_REF] Barré | Persona logical thinking: improving requirements elicitation for multidisciplinary teams[END_REF] who suggests using only usefulness, fluency and originality as relevant metrics for evaluating needs.

Directions for future research

As we discussed earlier both episodic memory and semantic memory have a role in MTT, in future studies it would be important to find future projection tasks that can stimulate both in order to collect needs specifics of each. The work from Pettersson and Karlsson (2014) -while not referring to semantic/episodic memory -is an interesting inspiration regarding the specificity of stimuli. Two projection tasks where used i) collage and images of future cars/cities (general concepts), ii) enactment of future experiences (personal concepts) within a very rough prototype of a car. For the first one the researchers collected mainly general insights (on life, architecture, technology) while for the second one they collected more personal insights (on interactions). Since MTT uses past experiences from the memory systems, future studies could take it into account by opening up to tools used to elicit a better recollection of past memories/problems that could give rise to a more efficient MTT. Such tools could provide or elicit imagery, a sense of presence, a narrative structure, a spatial setting/context, feelings of familiarity etc. [START_REF] Hassabis | Patients with hippocampal amnesia cannot imagine new experiences[END_REF][START_REF] Rubin | Belief and recollection of autobiographical memories[END_REF][START_REF] Wagner | Parietal lobe contributions to episodic memory retrieval[END_REF].

In addition to mental time travel, other cognitive processes could be candidates for priming such as counterfactual thinking and perspective taking. These processes, together with MTT, were primed successfully by a group of researchers (Fredericks et al., 2019) in order to improve the quality of new venture ideas in entrepreneurs. Additional methods could also be of use such as methods from the field of problem solving. To conclude with, the ubiquity of digital devices might have effects on the way humans use their brain [START_REF] Barr | The brain in your pocket: Evidence that Smartphones are used to supplant thinking[END_REF][START_REF] Ward | Brain Drain: The Mere Presence of One's Own Smartphone Reduces Available Cognitive Capacity[END_REF] following the (re)location of much of our memories to electronic devices. This is not new and the transfer of memories to external media has continuously increased since the successive discoveries of writing, printing, audio recording etc. Could this remodel or compromise our memory systems to the point where our ability to imagine the future is altered? How can we take this into account when eliciting future needs? Could studying the data traces left in phones, computers, social media… be another opportunity to find new needs?

  Regarding fluency, there was no effect of topic (F(1,189) =3.851 ; p = .051, h 2 p = .017), future projection tasks (F(1,189) =2.291 ; p > .05, h 2 p = .010) , collection tools (F(1,189) =0.720 ; p > .05, h 2 p = .003) or system definition level (F(1,189) =2.230 ; p > .05, h 2 p = .010). Regarding elaboration, there was a significant effect of future projection tasks (F(1,189) =4.550

Table 1 :

 1 Table summarizing the construction of the eight possible conditions that were applied to the two topics (energy for housing or transportation)

		Ill-defined systems			Yet-unknown systems
	Without future	With future projection	Without future	With future
	projection tasks		tasks	projection tasks	projection tasks
	Open-ended ques-tions	Sentence comple-tion test	Open-ended ques-tions	Sentence comple-tion test	Open-ended ques-tions	Sentence comple-tion test	Open-ended ques-tions	Sentence comple-tion test

Acknowledgement

This work was supported partly by the French PIA project « Lorraine Université d'Excellence », reference ANR-15-IDEX-04-LUE. This work has also been partly supported by a CIFRE grant by ANRT on behalf of the French Ministry of Higher Education, Research and Innovation.


Pauline Maurice
email: pauline.maurice@inria.fr

Jernej Camernik

Dasa Gorjan

Benjamin Schirrmeister

Jonas Bornmann

Luca Tagliapietra

Daniele Pucci

Serena Ivaldi

Jan Babic

Session 7 -Experiences / Prospects

INTRODUCTION

Work-related musculoskeletal disorders (MSDs) are the first cause of occupational disease in developed countries and therefore represent a major health issue [START_REF] Parent-Thirion | Fifth european working conditions survey, publications office of the european union[END_REF]. MSDs develop when biomechanical demands exceed the worker's physical capacity. In this regard overhead work is often cited as a MSDs risk factor [START_REF] Grieve | Overhead work: Identification of evidence-based exposure guidelines[END_REF][START_REF] Sluiter | Criteria document for evaluating the workrelatedness of upper-extremity musculoskeletal disorders[END_REF]. Overhead work yet remains very common on assembly lines, especially in the automotive industry. Indeed many complex tasks cannot be fully automatized because they still require human cognitive skills. One solution to relieve workers while keeping them in control of the task execution is then to assist them with an exoskeleton [START_REF] De Looze | Exoskeletons for industrial application and their potential effects on physical work load[END_REF]. Recently several industrial exoskeletons have been developed to support arms and/or tool weight during overhead tasks [START_REF] Sylla | Ergonomic contribution of able exoskeleton in automotive industry[END_REF][START_REF] Rashedi | Ergonomic evaluation of a wearable assistive device for overhead work[END_REF][START_REF] Spada | Analysis of exoskeleton introduction in industrial reality: Main issues and eaws risk assessment[END_REF][START_REF] Theurel | Physiological consequences of using an upper limb exoskeleton during manual handling tasks[END_REF][START_REF] Otten | Evaluation of a novel active exoskeleton tasks at or above head level[END_REF][START_REF] Huysamen | Evaluation of a passive exoskeleton for static upper limb activities[END_REF][START_REF] Weston | Biomechanical evaluation of exoskeleton use on loading of the lumbar spine[END_REF]. Many of them showed promising results regarding the reduction of physical workload. However, these studies present only partial assessments of the benefit provided by the exoskeletons. They exclude some important aspects like side-effects, adaptation, or user acceptance. In this work we present an exhaustive assessment of a novel passive exoskeleton for overhead work.

METHOD

The benefit provided by the use of an exoskeleton cannot be assessed solely based on the reduction of effort in the targeted limb. An exoskeleton is a wearable device, therefore its use might disrupt human movements or require additional effort. Supplemental effort can be caused by the weight of the device or, with passive exoskeletons, by the transfer of force from one joint to another. In addition, users' opinion of the device also affects its effectiveness. An exoskeleton that is ill-perceived by the user might remain unused, or cause psychological stress if use is imposed. Therefore we propose an assessment process that addresses the following aspects:

• Task performance: The task performance should be at least as good with the exoskeleton as without it.

• Fatigue: The exoskeleton should reduce metabolic demand and delay the apparition of fatigue.

• Physical effort: The exoskeleton should relieve the limb that is directly impacted.

• Side-effects: The exoskeleton should not significantly increase effort in limbs that are not directly impacted, nor cause bad postures. • Adaptation: Using the exoskeleton should not require a long training nor cause after-effects at removal.

• Acceptance: Users should feel better when using the exoskeleton compared to when not using it.

A. Exoskeleton Description

Within the European project AnDy [START_REF] Ivaldi | Anticipatory models of human movements and dynamics: the roadmap of the andy project[END_REF], the provided exoskeleton prototype is an upper-limb passive exoskeleton intended for supporting the weight of the arms, and possibly of manipulated tools, while the user is working overhead. This exoskeleton does not enhance the human's strength, but renders his/her arms virtually weightless, thereby relieving the shoulder joint. Being passive, hence without motors, the exoskeleton is light, not bulky, and easy to wear.

B. Experiment

Twelve participants performed an overhead pointing task with a portable tool, with and without the exoskeleton (Fig. 1). The participants' physical and physiological state was monitored with whole-body inertial motion capture, ground reaction force, EMG on shoulder and back muscles (right anterior deltoid and right erector spinae longissimus), oxygen consumption, and heart rate. The tool motion was recorded with optical motion capture to evaluate accuracy and completion time. Following the experiment, the perceived workload was assessed with the NASA Task Load Index (NASA-TLX) [START_REF] Hart | Development of nasa-tlx (task load index): Results of empirical and theoretical research[END_REF]. In addition, participants answered a questionnaire and a semi-directed interview was conducted to evaluate technology acceptance.

C. Measures

a) Task performance: Task performance was assessed with the movement accuracy and completion time.

b) Fatigue: Oxygen consumption and heart rate were used to evaluate objective metabolic demand and fatigue, while the NASA-TLX indicated subjective fatigue. Evolution of task performance over time was used as an additional indicator for fatigue.

c) Physical Effort: Given that the exoskeleton aimed at supporting the arms weight, the shoulder joint was directly impacted by the use of the exoskeleton. Therefore, activation of the anterior deltoid and estimated shoulder torque were used to assess the physical demand on the impacted limb. Joint torques were computed with inverse dynamics based on the recorded whole-body kinematics and ground reaction force [START_REF] Latella | Whole-body human inverse dynamics with distributed microaccelerometers, gyros and force sensing[END_REF]. d) Side-effects: Activation of erector spinae and back and hip torques were used to assess potential increase in effort in non-directly impacted limbs. Joint angles obtained by whole-body kinematics served to evaluate postural changes.

e) Adaptation: The tool 3D trajectory as well as trajectories of the shoulder, elbow and back in joint space were used to compare movement strategy with and without the exoskeleton. Evolution of task performance over time was used to detect learning and after-effects.

f) Acceptance: Score obtained in the technology acceptance questionnaire was used to quantitatively assessed acceptance of the exoskeleton, while opinions expressed during the interview served to shed light on some of the questionnaire answers.

RESULTS

Comparison of the two conditions with and without exoskeleton revealed that muscle activation, oxygen consumption and heart rate were significantly reduced when using the exoskeleton. Conversely, task performance was affected neither positively nor negatively. Importantly, the reduction in overall workload observed with objective measurements was also observed in subjective measurements: the task not only was, but also felt, less demanding when wearing the exoskeleton. Eventually, acceptance score was high and participants all said that they would choose to use the exoskeleton again for such a task.

CONCLUSION

Future work will be directed towards evaluating the exoskeleton on different tasks, including bending, crouching and walking to assess its transparency and potential disturbances of the users movements. Experiments on industrial sites are also planned. Furthermore, results from the evaluation will serve to guide the development of an intuitive adaptation of the level of support provided by the exoskeleton.

ACKNOWLEDGMENT

This work has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No.731540 (An.Dy). The content of this publication is the sole responsibility of the authors. The European Commission or its services cannot be held responsible for any use that may be made of the information it contains.

Fig. 1 .

 1 Fig. 1. Experimental set-up and sensors used to assess the exoskeleton.