domain: spi phys

text:
Ingrid Legriffon
email: ingrid.legriffon@onera.fr

NOISE PREDICTION OF A NEW GENERATION AEROSTAT

Keywords:

The wood or wind turbine markets, to name two examples, are confronted to the obstacle of having to transport heavy loads to and from areas that are accessible with difficulty. Airborne transportation is a solution. In this frame, a new generation aerostat is being developed, in partnership with Flying Whales. In order to make possible a commercial success of this kind of vehicle, the increasing sensitivity of people to aircraft noise has to be taken into consideration. If one wants to comply with future noise regulation applicable to this kind of aerostats, the noise impact for different operating conditions has to be estimated. Classic procedures like cruise, take-off and landing, as well as stationary flights are considered and evaluated. The aerostat is equipped with two propulsive propellers, four hovering propellers and two additional propellers for lateral control. The propulsive and control propellers are mounted vertically, the hovering propellers horizontally. Operating conditions will lead to flights above grounds with steep slopes and possibly dense vegetation. In this paper preliminary noise evaluations are presented for the most standard operating points that should occur. Given the sources' characteristic noise directivity, the vertically mounted propellers radiate directly into the field below the aerostat, where, in case of a stationary flight, people will be at work, loading the aerostat. The hovering propellers however radiate away from the aerostat, reaching maximum levels on the ground several hundreds of meters away from the aerostat itself, depending on the emission altitude and the ground slope. The relative contribution of each source depends on the operating condition. A parametric study helps to identify leads for noise reduction at the ground.

Introduction

Markets dealing with wind turbines or wood are in search of a more efficient way of transporting their goods. For now, tree trunks for instance, after being harvested, have to be moved by terrestrial transportation means to their location of processing. Especially in mountainous regions, the transportation of heavy loads can represent a problem that could be lifted by replacing trucks by aerostats.

If aerostats are to be commercialised, they will have to find their place in the already existing air traffic regulation system. One of the potential obstacles is the environmental impact; indeed they must not exceed acceptable noise levels.

A first preliminary aerostat design was developed, in partnership with Flying Whales. Being able to carry 60 tons of material and fly around 115 km/h, it will be approximately of 160 x 40 x 70 m size. The results presented in this paper on an eight-propeller configuration are preliminary calculations of tonal noise and will serve as reference test case. Ongoing discussions have led to an optimized propeller configuration with a total number of 32 propellers. ICSV26, Montreal, 7-11 July 2019

Noise calculation code

For the evaluation of the aerostat's noise impact on the ground, the in-house ONERA tool CAR-MEN-FLAP is used. CARMEN is a System Noise Prediction Tool making it possible to predict the sound pressure level footprint during a whole rotary wing aircraft trajectory simulation [START_REF] Malbéqui | Aircraft Noise Modelling and Assessment in the IESTA program[END_REF][START_REF] Legriffon | Aircraft Noise Modelling and Assessment in the IESTA program with focus on engine noise[END_REF]. It is composed of three modules: acoustic source models, installation effects and atmospheric propagation.

The noise source model used in this study, a tool called FLAP, includes a set of analytical models for predicting the noise radiated by a helicopter main and tail rotors, simple propellers etc. Its main difference with the ONERA more advanced HMMAP computation chain [START_REF] Beaumier | Description and validation of the ONERA computational method for the prediction of blade-vortex interaction noise[END_REF] is a lower CPU runtime and a much lower input data requirement, allowing its use at a preliminary stage in the design of new concepts. Its characteristics are obtained by a less fine modeling and the use of usual values for the input data. On the other hand, this low level of modeling makes it difficult to obtain an estimate in absolute levels, so it is preferable to make comparisons in relative levels to observe the trends [START_REF] Reboul | Semi-analytical modelling of helicopter main rotor noise[END_REF].

The installation effects module calculates the interaction of the waves emitted by the sources with the structure of the aircraft that can reinforce or mask the radiation. In the case of the aerostat we assume that the skin is perfectly transparent to acoustic waves. As a result, we do not consider masking or reflections for this case study.

This last module makes it possible through ray-tracing to propagate the sound from the aircraft to the ground taking into account meteorological effects, atmospheric absorption, the Doppler effect etc. In the case of this study, several calculation hypotheses are made. We consider a standard atmosphere, at 20 ° C, without wind. We also assume the flow entering the propellers to be perpendicular to the propeller. Upward winds that could rise up the slope are therefore not taken into account.

In view of the dimensions of the aerostat it was not possible to make a calculation including all propellers at the same time. Therefore each propeller is calculated separately and the sum of all the contributions is done during post-processing.

Preliminary aerostat and propeller design

A first round of design discussions lead to an aerostat design equipped with 8 propellers, composed of two propulsive propellers, four hovering propellers and two additional propellers for lateral control (see Figure 1 and Table 1 for coordinates, based on Flying Whales documents). After a first round of calculations, it was decided, in concertation with Flying Whales, to implement propellers of 6 blades, turning at 500 RPM and generating 800 kW. An aerodynamic parametrical study was done, which delivered the input needed for the FLAP calculations: blade geometry, thrust, torque and RPM. Since in FLAP the thickness of the blade is important, but not so much the shape of the blade, NACA00XX (where XX is the relative thickness) were used for all propellers.

Calculation set up

Several test configurations have to be evaluated to get an idea of the general impact of the aerostat on ground noise levels. Several altitudes, flight configurations and ground properties can and will be encountered during its missions. The extraction site will most probably be in mountainous environments, where the slope might be of varying importance. A representative value is chosen to be 30 degrees.

In the following chapters, the altitude is defined as the distance between the centre of gravity of the aerostat and the ground straight below (see Figure 2a).

Hovering configuration

The simplest configuration to treat is the one where the aerostat is hovering above the site of extraction where the workers load the wood. The aerostat is aerostatically balanced; it therefore doesn't need the lifting propellers in order to stay in the air.

Two potentially noisy configurations are to be considered in the hovering position. One where the lateral propellers are at work either to change the lateral orientation of the aerostat or to counteract cross winds; and one with working lift propellers when for instance altitude changes are engaged. ICSV26, Montreal, 7-11 July 2019

Configuration 1: Lateral propellers only, 30° ground slopealtitude 50m

In the case where the orientation of the aerostat has to be modified, for whatever reasons, the power given to lateral propellers can go up to 800 kW. The propellers turn at 500

In a situation where the aerostat is at 50 meters altitude and on a 30° sloped ground, the noise impact on the ground of each propeller is shown in Figure 3, the sum of both in Figure 4. The X coordinate corresponds to the projection of X' on the ground (which is at 30°, see Figure 2a) The loading noise being not exactly symmetrical in the propeller plane, but radiating slightly to the back of the propeller, the installation and orientation of the lateral propellers have a non-negligible influence on the ground noise maps. As can be seen in the propeller configuration (Figure 1a), Y7 (front) is facing right while Y8 (rear) is facing left, which gives the total footprint a "wavy" asymmetrical aspect. The maximum level directly below the front of the aerostat reaches 85 dB, while at 1 km on the lateral side (Y [m] direction) the levels fall far below 45 dB. In the propeller plane (X [m] direction) the noise reaches further distances, at 1 km the levels are still up to 60 dB.

Configuration 2: Lift propellers only, 30° ground slopealtitude 50m

In the case of a gain in height, the lift propellers Z can reach 800 kW each. The four lift propellers work identically; only the distance to the ground, variable due to the slope, has a modifying impact on the footprint (Figure 5 and Figure 6). The mountain slope leads to a bean shaped footprint with maximum levels of 92 dB below the aerostat, of course slightly shifted from the very centre because of the propeller directivities. The front propellers' footprint is more focalized, less wide spread than the rear propellers that are higher above ground and therefore emit on a larger surface. At 1.5 km lateral distance parallel to the mountain slope and downwards to the mountain (negative X), the levels still reach 65 dB. Upwards (up the mountain, positive X) the levels decrease more rapidly since the angle of incidence gets further from the propeller plane.

The propellers are reversible; an altitude change towards the ground will therefore lead to slightly lower values in the footprint.

Transition and Cruise

Configuration 3: Transition, 0° ground slopealtitude 150m

In the case of transition between hovering and advancing configuration, there is a phase where the X and Z propellers can function at the same time, before the aerostat even moves. If we consider 800 kW on the propulsion propellers and 400 kW on the lift propellers, with a zero advancing velocity, the noise footprint presents itself as shown in Figure 7 and Figure 8.

The 0° ground slope leads to a perfectly circular footprint of the lift propellers, which function at the same height at same power. The propulsive propellers face to the right (positive X), therefore the sound is slightly radiated to the back. The total footprint has a clear circular aspect with levels of 60 dB going as far as 1 km from the centre of the aerostat. The highest levels, around 72 dB, are however still encountered below the propulsive propellers. ICSV26, Montreal, 7-11 July 2019 Levels at take-off and landing are important for the surroundings of the hangar. Furthermore the path between hangar and extraction site might overfly populated regions. Noise levels therefore also have to be checked for flyovers at different altitudes. To cover two encountered configurations, a 150 m altitude flyover over a 30° ground slope and a 600 m altitude flyover over a 0° ground slope are evaluated. In both cases the X propellers are set to 800 kW each, while neither Y nor Z propellers are at work. The advancement of the aerostat happens parallel to iso-altitude lines (Figure 2b). The noise footprints and their analysis will be shown during the Conference.

Discussion

The above tested configurations are shown in dB. Displaying the results in dBA alters extremely the noise levels. Indeed the frequency range of the radiated sound is extremely low for a 6 blade propeller at 500 RPM, the BPF being 50 Hz. The A-weighting therefore drastically reduces the contribution of the, initially, most energetic tones and the final tonal levels on the ground never exceed 60 dBA for hovering configurations and 42 dBA for transitioning configurations (Figure 9).

1)

2)

3) Broadband propeller noise is not included yet, due to the current lack of validation of the models. Depending on the considered configuration, one can expect changes in the footprint when adding the broadband noise contribution. Indeed, in configurations where only vertical propellers are at work (X and Y), the self-noise (main broadband contributor), will stay below tonal noise levels, even expressed in dBA. When the horizontal propellers are working, however, the shadow zone, right below the propellers, will receive non negligible levels of self-noise. For the complete evaluation all noise sources will be considered. The same tendencies should be obtained when considering installed propellers. Indeed, aerodynamic perturbations created by structures (arm support….) surrounding the propellers will be responsible for an additional noise radiation at higher frequency and radiating mainly out of the propeller rotation plane. However, taking into account this kind of contribution is out of the scope of this preliminary study.

The author would like to thank Gabriel Reboul and Luis Bernardos Barreda for their contribution to this work.

Figure 1 :

 1 Figure 1: Propeller configuration

  a) Hover and transition configuration b) Cruise configuration, front view

Figure 2 :

 2 Figure 2: View of aerostat in 30° slope configuration

Figure 3 :Figure 4 :

 34 Figure 3: Tonal footprint in dB of rear and front lateral propellers Y at 800 kW

Figure 5 :Figure 6 :

 56 Figure 5: Tonal footprint in dB of rear and front lift propellers Z at 800 kW

Figure 7 :Figure 8 :

 78 Figure 7: Tonal footprint in dB of a) the four lift propellers Z at 400 kW, b) the two propulsive propellers X at 800 kW

Figure 9 :

 9 Figure 9: Total tonal footprints for Configurations 1), 2), 3) in dBA

Table 1 : Centre of Gravity and Propeller coordinates (the centre of the coordinate system being the nose of the aerostat)

 1

		X'	Y'	Z'
	Z1	-13.02 m	-28.21 m	0 m
	Z2	-13.02 m	28.21 m	0 m
	Z3	-112.99 m	-29.52 m	0 m
	Z4	-112.99 m	29.52 m	0 m
	X5	-96.33 m	-29.61 m	12.94 m
	X6	-96.33 m	29.61 m	12.94 m
	Y7	0 m	0 m	-15.57 m
	Y8	-144.5 m	0 m	10.5 m
	Centre of Gravity	-67.7 m	0 m	8.6 m


Mickael Delamare

Remi Boutteau

Xavier Savatier

Nicolas Iriart

Evaluation of an UWB localization system in static and dynamic

Keywords:

Applications in the context of the industry 4.0 need a precise localization. Indoor localization remains an open problem. Among the possible solutions, we see the emergence of Ultra Wide Band(UWB)-methods. The aim of this article is to evaluate an UWB system in order to estimate the position of a person in indoor environments. We have evaluated an UWB system to obtain results of the 3D localization of a moving person in buildings environment in real time. For that purpose, static and dynamic tests were established using a ground truth based on a motion capture system with a millimetric accuracy.

Introduction

Robotisation, especially in factories, leads to an increasingly close interaction between man and machine, a concept referred as cobotics. This evolution is accompanied by a growing demand for intuitive and efficient Human Machine Interfaces (HMIs) based on natural interaction. In this context, HMIs will involve the development of innovative hand-held human-machine interfaces relying on gesture-recognition to enable intuitive and non-intrusive control of industrial machinery. To achieve this task, accurate and very small form-factor sensors are required. The operator can himself evolve in a building or a workshop without being constrained by having cumbersome locating system. The capture of the movement or the posture must be coupled with a notion of accurate and absolute location in a building (workshop, warehouse); this information enables a natural and contextual interaction between the operator and a set of machines. Localization in indoor environment will be used in industry 4.0 or industry of the future which corresponds to a new way of organizing the means of production. This new industry is emerging as the convergence of the virtual world, digital design, management (finance and marketing) with real-world products and objects.

Observation and understanding of gesture and posture have been the subject of numerous studies. Many studies were presented regarding the gesture perception from a fixed sensor, the best known being the Kinect from Microsoft. However, all these solutions restrict the movements of the operator and limit the possibilities of natural interaction with a machine. Such as the distance or the field of view for a common use. Another approach is to observe the movement from a hand-held device. These solutions are generally based on inertial sensors such as accelerometers and gyroscopes; their assembly forms what is commonly called an IMU (Inertial Measurement Unit). IMU diffusion has increased with the development of MEMS technologies, which offer a good cost-to-performance ratio and is well adapted to the human size [START_REF] Dobkin | Wearable motion sensors to continuously measure real-world physical activities[END_REF].

These solutions are the basis for Attitude Heading Reference System (AHRS) measurement devices. They are attitude measurement units because they allow a measurement of the orientation of the sensor in the terrestrial reference frame, a measurement that can be significantly improved thanks to data fusion algorithms [START_REF] Madgwick | An Efficient Orientation Filter for Inertial and Inertial[END_REF]. A review of these filtering methods and the performance that can be achieved today with low-cost MEMS sensors can be found in [START_REF] Michel | On attitude estimation with smartphones[END_REF].

Indoors localization solutions based on radio-frequency systems are equivalent to a GPS. These approaches are increasingly being investigated with the use of trilateration methods by using a transmitter-receiver distance information, known as RSSI for Received Signal Strength Indicator. The RSSI is available in many telecommunication standards. More recently multilateration (measurement from transmission time differences called Time Difference of Arrival or TDoA between at least two transmitters and one receiver; transmitters being perfectly synchronized). The fact that the system to be located is itself active increases considerably the localization accuracy. There is a wide range of systems in this field. A review of these solutions shows that an accurate localization around 30cm is possible [START_REF] Mautz | Indoor positioning technologies[END_REF]. However, this performance degrades severely when there is no direct Line-Of-Sight between the terminals (fixed anchor in the building) and the receiver (Tag placed on the moving person) to be located. The accuracy of these solutions depends on the environment in which the system will be deployed, which is related to the use case. It should be noted that there is a strong excitement caused by the release of UWB radio solutions to the market wich promise to be even more efficient than the current ones.

The contribution of this work is a dynamic test with a millimeter accuracy ground truth in real time, to evaluate its precision and its accuracy, and to define if UWB localization sensors can be used for gesture recognition in 3D space.

This paper is divided into two parts. First, we study the performance a UWB-based localization sensor named "UWB" in the rest of this paper, and evaluate the specification in a free space surrounded by metallic objects such as robots, infrastructure or doors in our laboratory. Secondly, we propose a complete evaluation of the system behaviour in static and dynamic conditions to see if UWB can be used to obtain an accurate 3D trajectory for gesture recognition.

State of the art of indoor localization technologies

For human-machine Interaction in the context of industry 4.0, it is necessary to be able to locate the operator in a large environment (above 20m range) and with good accuracy (with a 0.1 meter accuracy). Localization in an indoor environment will be used in industry 4.0, based on Maultz thesis [START_REF] Mautz | Indoor positioning technologies[END_REF] there are 13 technologies shown in Table 1 that can answer indoor-localization.

Systems based on cameras for indoor localization approaches are used in different ways. The first one is to have a 3D building model as a reference. The second system is the socalled viewbased approach. It consists in taking the current view of a mobile camera and comparing it with previously captured view sequences. This system arrived at centimeter accuracy and can cover a building [START_REF] Niu | Resource-efficient and Automated Imagebased Indoor Localization[END_REF]. The third system is coded targets used for point identification to locate a person. The system can know where the person is with a centimeter accuracy but does not store the trajectory made by the person [START_REF] Liao | Design of a Smartphone Indoor Positioning Dynamic Ground Truth Reference System Using Robust Visual Encoded Targets[END_REF]. The fourth system is the projection of reference points in the environment. This system needs a direct view of the same surface and it can be used for tracking with a millimeter accuracy [START_REF] Tilch | Current investigations at the ETH Zurich in optical indoor positioning[END_REF]. The fifth system is using one camera or many cameras without reference by observing position change. This system can reach sub-centimeter accuracy and can cover 30m 2 .

Infrared systems based on active beacons or using natural radiation are mainly used for rough positional estimation or for detecting the presence of a person in a room. They have centimetermeter accuracy level and can cover 1-5 meters in static conditions. They are a common alternative to optical systems operating in the visible light spectrum. An accuracy of 4cm has been reported and people can be tracked up to a distance of 5m [START_REF] Khoshelham | Accuracy and Resolution of Kinect Depth Data for Indoor Mapping Applications[END_REF] and centimeter accuracy in a retail store [START_REF] Arai | Evaluation of Indoor Positioning System based on Attachable Infrared Beacons in Metal Shelf Environment[END_REF].

Tactile and polar systems have m-mm accuracy and can cover an entire room. The polar point method uses a distance measurement and an angular measurement from the same beacon to determine the coordinates of a nearby station. Tactile systems are high precision mechanical instruments which measure positions by touching an object with a calibrated pointer. We can not track an entire trajectory in 3D [START_REF] Mautz | Indoor positioning technologies[END_REF].

Localization systems based on propagation of sound waves have a centimeter accuracy and can cover 2-10 square meters. The sound is a mechanical wave so positioning systems use air and building materials as means of propagation [START_REF] Wang | ARABIS: an Asynchronous Acoustic Indoor Positioning System for Mobile Devices[END_REF]. Mechanical waves are not sufficiently accurate in indoor environments for industrial applications due to multipath which is a phenomenon that occurs when a radio signal propagates through several paths and is received on an antenna.

WLAN/WIFI systems have one meter of accuracy and can cover 20 -50m 2 . Distance estimation using WLAN is generally possible from RSSI (Received Signal Strength Indication), ToA (Time of Arrival), TDoA (Time Difference of Arrival) and RTT (Round-Trip Time). The accuracy of this kind of systems is not enough to handle an accurate trajectory estimation in the 3D space [START_REF] Gansemer | RSSI-based Euclidean Distance algorithm for indoor positioning adapted for the use in dynamically changing WLAN environments and multi-level buildings[END_REF] [START_REF] Cui | Novel WiFi/MEMS Integrated Indoor Navigation System Based on Two-Stage EKF[END_REF].

RFID has dm-m level of accuracy and can cover 1-50 m. Most RFID systems rely on proximity detection of permanently mounted tags to locate a person. The accuracy of an RFID system is directly related to the density of tags deployment and reading ranges so it can be expensive in large areas. RFID systems can not do 3D trajectory tracking because most of them rely on proximity detection of permanently mounted tags to locate mobile readers [START_REF] Shi | IKULDAS: An Improved kNN-Based UHF RFID Indoor Localization Algorithm for Directional Radiation Scenario[END_REF].

Pseudolites use a similar methods of localization as the Global Navigation System (GNSS) but in indoor environments. Several difficulties such as multipath mitigation, time synchronization and ambiguity solving have limited this system to few applications in GNSS-challenged environments such as open pit mines [START_REF]2010 7th International Symposium on Communication Systems, Networks & Digital Signal Processing (CSNDSP 2010)[END_REF] [START_REF] Fujii | Hyperbolic Positioning with Antenna Arrays and Multi-Channel Pseudolite for Indoor Localization[END_REF]. It can cover 10 -1000m 2 area and have a cm-dm accuracy.

Other radio-frequency systems such as Zigbee, bluetooth, Digital Television, Cellular networks, Radar, FM radio, Phones based on Digital Enhanced Cordless Technology have for best submillimeters accuracy and can cover 10-1000 square meters. However, performance levels and applicability vary greatly depending on several factors such as the use of preexisting reference infrastructure, pervasiveness of devices, signal ranges, power levels [START_REF] Mautz | Indoor positioning technologies[END_REF]. The best systems have an accuracy of 1m and can cover a building. Inertial navigation systems is usually fused with complementary sensors which provide absolute location information due to drift and have few meters accuracy [START_REF] Mautz | Indoor positioning technologies[END_REF]. Footmounted systems can make use of zero velocity during the foot is in stance stage and have therefore a lower drift and can improve the accuracy below 1m [START_REF] Renaudin | Optimal data fusion for pedestrian navigation based on UWB and MEMS[END_REF] of the travelled distance. Compared to IMUs mounted at other body parts [START_REF] Susi | Motion mode recognition and step detection algorithms for mobile phone users[END_REF] with drifts being typically larger.

System based on magnetic field has centimeter-accuracy and can cover 10 meters area [START_REF] Blankenbach | Position estimation using artificial generated magnetic fields[END_REF]. Different approaches range from systems dedicated for medical purposes using an artificial quasi static magnetic field with less than 1 m3 volume operating at mm-accuracy level. In indoor environments, with the same approach, we can have few meters accuracy covering storage aisles and a building [START_REF] Vandermeulen | Indoor localization Using a Magnetic Flux Density Map of a Building[END_REF] [1] but we can be perturbed by the magnetic field induced by electric motors inside industrial buildings.

Infrastructure systems are technologies that use the existing building infrastructure or embed additional infrastructure into the building materials such as Power Lines positioning, Floor Tiles, Fluorescent Lamps or leaky feeder cables as described in [START_REF] Mautz | Indoor positioning technologies[END_REF]. These systems have cm-m level of accuracy. 1: Indoor positioning technologies as described in [START_REF] Mautz | Indoor positioning technologies[END_REF] UWB (Ultra WideBand) is less expensive than others technologies and can be accurate even in Non-Line-Of-Sight (NLOS) conditions. It has the ability to carry signals through doors and other obstacles that tend to reflect signals with more limited bandwidth and higher power levels [START_REF] Dragomirescu | 60ghz Wireless Nano-Sensors Network for Structure Health Monitoring as Enabler for Safer, Greener Aircrafts[END_REF]. Syberfeldt et al. [START_REF] Syberfeldt | Localizing operators in the smart factory: A review of existing techniques and systems[END_REF] proposed a review of existing techniques and systems for locating operators in a smart factory. In this comparison, we can see that UWB has a high precision compared to others indoor localization system and a medium cost for the industry. Alarifi et al. [START_REF] Alarifi | Ultra wideband indoor positioning technologies: Analysis and recent advances[END_REF] established a Strengths, Weaknesses, Opportunities, Threats (SWOT) analysis of UWB systems. The main benefits of UWB systems are a low-power consumption and the ability to penetrate different kinds of materials. This is due to the very short pulses that do not interfere with most of the existing radio systems. The weakness of UWB is the synchronization: due to his short pulses, it may take time to synchronize. This article comforts our choice of UWB as the best system for indoor localization.

3 Experimental Setup and Evaluation

Experimental setup

We decided to evaluate a UWB system from Decawave since it seems to be the most accurate [START_REF] Ruiz | Comparing Ubisense, BeSpoon, and DecaWave UWB location systems: indoor performance analysis[END_REF]. To evaluate this system, four anchors must first be placed in the room used for indoor localization. We align anchors with laser measurements. One Anchor is chosen as reference (initialization at x=0 and y=0), and we must obtain the position of each anchor according to the initialization anchor as shown in Figure 1a. We obtain the position of each anchors with a VICON motion capture system. The area of testing in Figure 1a is in the lab with a LOS condition and in an industrial environment with a metallic structure, robots and a metallic door close to the testing area as shown in Figure 1b. The Tag is mounted on a support and placed on a wooden cart with a height of 0.7m to verify the trajectory in 3D in the inner area of the UWB system.

Tests and Evaluation

Static Measurement Precision The first test is to place the tag in the inner area of the UWB anchors. This test will give us the distribution of the UWB points when the tag is static. The results of the static test are given in Table 2. The mean error on the 3 XYZ axes is 1cm and the average range is 10cm. The values are distributed around the average value with a standard deviation of 0.011m. This means that the UWB system is not precise in a static situation, but has a high accuracy of 10cm on average. UWB is accurate up to 10cm in static and behaves like a sphere around the target with a range value of 10cm. When a person is not moving, we know where the person is with an accuracy of 10cm. In XY measurement we have 21cm of accuracy as shown in Table 3. That means we have 78% of precision for this trajectory in XY. We can use UWB for real time localization and in dynamic. We have 0.24cm of accuracy in 3D (XYZ) only 40% of values for Z-axis are precise, they are not around the mean value. The Z-axis is not trustable for dynamic localization and for motion gesture recognition. This result shows that, in dynamic localization, we can use UWB for motion tracking with X-Y axis in real time but not in 3D because the Z-axis is not trustable. Figure 2 highlights that the Z-axis measurements are wavy.

Static

Dynamic Measurement Evaluation and Precision of mapping

The third test is to realize a mapping of the inner area and outer area of the UWB system to evaluate its behaviour. We covered the maximum area and try to see if the accuracy/precision changed. Comparing to our first test we have an accuracy of 23cm in the inner area and 25cm in the outer area in 2D and 23cm and 24cm in 3D that is close to our first result in dynamic localization shown in Table 3 show that UWB is homogeneous for a covered area even outside of the area defined by its anchors in industrial LOS conditions. UWB is really good for dynamic localization in indoor environments. We lose precision compared to our static results. We had 10cm accuracy in static measurement, we had 0.24m accuracy in dynamic localization as shown in Table 4. Study of the influence of anchors This test was made to verify the behavior of UWB in the inner area of UWB in dynamics with four and six anchors. We place four anchors exactly as in the Figure 1a and one more on the floor in one corner of our cube. And then two more on the floor in corners. With the use of 4 anchors, the 3D positioning error is 0.24 ± 0.19cm with a Z error of 0.32 ± 0.29cm. The number of anchors mainly influences the Z measurement: with 6 anchors, the Z error is 0.16 ± 0.01cm while the 3D error decreases slightly: 0.20 ± 0.12cm.

Conclusion

In this article, we describe the behaviour of an Ultra WideBand system in static and dynamic cases by comparison with a ground truth obtained with a motion capture system. We have an evaluation of the precision and accuracy of the UWB system which is really good in the X-Y axes but not trustable along the Z-axis. We confirm that precision and accuracy are better by adding anchors when performing dynamic localization. UWB systems can not be used for gesture recognition. Nevertheless, they can be a really good choice for localization, even in dynamic, and can be more robust if we add more anchors. Z-axis needs to be improved, mostly in terms of precision, and this can be achieved by data fusion with other sensors. Our future works will be the improvement of the accuracy and precision of the system by the addition of an IMU and a barometer.

  (a) Four static anchors in purple are placed in a rectangle. The tag is placed in the area of the anchors in LOS. (b) Placement of anchors in the laboratory.

Fig. 1 :

 1 Fig. 1: Our UWB setup

Fig. 2 :

 2 Fig. 2: Trajectory made in the laboratory with LOS conditions in 2D and 3D with VICON (orange) and UWB (blue) in meters.

Table

	Technology	Typical Accuracy Typical Coverage
	Cameras	0.1mm-dm	1-10
	Infrared	cm-m	1-5m
	Tactile & Polar Systems um-mm	3-2000m
	Sound	cm	2-10m
	WLAN/WIFI	m	20-50m
	RFID	dm-m	1-50m
	Ultra WideBand	cm-m	1-50m
	High Sensitive GNSS	10m	'global'
	Pseudolites	cm-dm	10-1000m
	Other Radio Frequencies m	10-1000m
	Inertial Navigation	1%	10-100m
	Magnetic Systems	mm-cm	1-20m
	Infrastructure Systems cm-m	building

Table 2 :

 2 Comparison of mean localization errors and standard deviation with a static test in Line-Of-Sight condition. Dynamic Measurement Evaluation and Precision of a trajectory With the Vicon system [15], we will compare the exact 3D point of the Vicon with the 3D point of UWB in real-time. The first test we made was a trajectory inside the inner area of the UWB anchors. The test was made in the laboratory in LOS with industrial conditions.

  . These two tests

	Dynamic measure	X-axis Y-axis Z-axis 2D	3D
	Mean error 0.20m 0.22m 0.32m 0.21m 0.24m
	Range	0.73m 0.64m 0.87m 0.65m 0.75m
	Standard deviation 0.13m 0.14m 0.29m 0.135m 0.186m

Table 3 :

 3 Table of dynamic trajectory.

Table 4 :

 4 Errors of the dynamic measurements.


text:
Nicolas Deymier

Sebastien Pernet

X Ferrieres
email: xavier.ferrieres@onera.fr

Gerac

Study of a stable hybridization method to couple FVTD,GD scheme with FDTD/FEM scheme

Keywords: Hybrid method, finite element scheme, Galerkin discontinuous scheme, Maxwell's equations in time domain

Study of a stable hybridization method to couple

FVTD,GD scheme with FDTD/FEM scheme

Introduction

Current electromagnetic problems require the processing of complex structures in which geometrical details, computational time and size of the discrete problem are important factors to consider in the simulation. To increase the performances in terms of computation time and storage memory, the use of cartesian meshes is prefered, whereas near the geometry, to guarantee the precision, it is rather necessary to use a non-structured mesh. For each type of mesh or class of problems, there are different kinds of schemes more or less appropriate to solve it. This is due to the approximations made in the scheme which induce different kinds of errors on the solution. Then, to improve the simulation, a good idea consists in dividing the computational domain into different sub-domains where we apply the most appropriate numerical method to solve the Maxwell equations. In this strategy, different numerical schemes are coupled and the difficulty lies in having a stable and consistent hybrid scheme. In this paper, we propose a stable hybrid method allowing to take into account FV, FD, FEM and DG schemes. After the pre-sentation of the hybridization principle, by considering a leapfrog time discretization for the hybrid method, one shows that it exists a condition according to the schemes taken in the hybridization which ensures the conservation of an energetic quantity. This condition gives a stability condition of the hybrid method. Next, we give some results on the study of a propagative mode inside a wave guide to validate the proposed hybrid method.

Principle of the hybrid method

In this paper we present a hybrid method based on the coupling of some numerical schemes (FEM, DG, FD etc.) to solve the transient Maxwell equations. One of the main difficulties is to ensure the stability of the method at the space and time level. In the literature, it exists, for exemple, several approaches constructed from interpolation techniques which suffer from numerical instabilities. To overcome this problem, we propose to use a DG formalism in order to couple together in a stable manner the subdomains in which different numerical methods are used. Now, we briefly explain our approach. Let (Ω i ) i=1,••• ,N be a partition of the computational domain Ω, Σ i,j := Ω i ∩ Ω j , n i,j the unit normal to Σ i,j directed from Ω i et Ω j and V (i) is the set of neighbour subdomains of Ω i . In a first step, we write the Maxwell problem in Ω as a transmission one on the subdomains :

∀i = 1, • • • , N , ε ∂E i ∂t -∇ × H i = J in Ω i (1a) µ ∂H i ∂t + ∇ × E i = 0 in Ω i (1b) n i,j × E i = n i,j × E j on Σ i,j , ∀j ∈ V (i) (1c) n i,j × H i = n i,j × H j on Σ i,j , ∀j ∈ V (i) (1d)
Next, we rewrite (1) in a weak form by using a DG approach : ∀ϕ, ψ ∈ H(curl, Ω i ),

Ωi ε ∂E i ∂t -∇ × H i • ϕ dx = Ωi J • ϕdx + j∈V (i) Σi,j α i,j (n i,j × H i -n i,j × H j ) • ϕdγ (2a)
Suggested members of the Scientific Committee: Julien Diaz, J. Hesthaven

Ωi µ ∂H i ∂t + ∇ × E i • ψ dx = j∈V (i) Σi,j γ i,j (n i,j × E i -n i,j × E j ) • ψdγ (2b)
To ensure the equivalence of this reformulation with the original problem, the coefficients α i,j and γ i,j must be as follows :

1 -α i,j + α j,i = 0 and 1 -γ i,j + γ j,i = 0 α i,j + γ j,i = 0 and α i,j + γ j,i = 0

Stability

We now use in each subdomain Ω i an adapted spatial numerical scheme (FEM, DG, FDTD, FV) and a second order leapfrog scheme for the time discretization. To ensure the stability of the hybrid scheme, we study the evolution in time of a quantity given by Ω εE(x)

• E(x)dx + Ω νH(x) • H(x)dx.
More precisely, we have to prove that this quantity is maintained or decreased along the time. For example, by considering an hybridization between GD [START_REF] Cohen | A spatial high order discontinuous Galerkin Method to solve Maxwell's equation in time domain[END_REF] and FEM [START_REF] Deymier | New High order FDTD method to solve EMC problem[END_REF] methods, we have [START_REF] Deymier | Etude d'une méthode éléments finis d'ordre élevé et de son hybridation[END_REF] :

∆t ≤ 2 c 0 max(A 1 , A 2 , A 3 )
with

A 1 = ρ M -1 2 1 R1 M -1 2 1 + √ µ √ ε max ρ M -1 2 1 BE 1 M -1 2 1 A 2 = ρ M -1 2 1 BH 1 M -1 2 1 A 3 = 1 Λ K ρ M -1 2 2 R2 M -1 2 2 + √ µ √ ε ρ M -1 2 2 B2 M -1 2 2
with ρ(A) the spectrum radius, c 0 the waves speed, the matrices M2 , R2 , B2 the mass, stiffness and jump matrices for the DG scheme and M1 , R1 , BE 1 , BH 1 the same for FEM. Λ K is a coefficient which depends on the Jacobian matrix of the transformation between K and the unit element for the DG scheme.

Numerical validation

To validate our hydrid method, we propose to study a propagative mode inside a curved wave guide. The guide is divided into two parts on which a FEM and a DG scheme are respectively applied (see Figure 1). In Figure 2, we compare the results obtained with our hybrid FEM/DG method and with a DG method applied on all the problem. We can show on this figure the good agreement between the solutions obtained by our FEM/DG and the DG methods at a testpoint located inside the curved guide.

Conclusion

In this paper, we proposed a stable hybrid method between continuous and discontinuous Gakerkin schemes, in order to solve the Maxwell equations in time domain. We have specified how to establish a stability condition for two combined methods and we give, as example, a stability condition for a hybrid FEM/DG method. Finally, we showed a validation of this method by comparison to a reference DG solution, based on the computation of a propagative mode inside a curved wave guide.

Figure 1 :

 1 Figure 1: Curved guide geometry with the two domains for FEM/GD Hybrid method.

Figure 2 :

 2 Figure 2: Comparison between FEM/DG and DG approaches.


Kevin J Verdière

Frédéric Dehais

Raphaëlle N Roy

Spectral EEG-based classification for operator dyads' workload and cooperation level estimation

There is a growing momentum to design online tools to measure mental workload for neuroergonomic purposes. Most of the research focuses on the monitoring of a single human operator. However, in real-life situations, human operators work in cooperation to optimize safety and performance. This is particularly the case in aviation whereby crews are composed of a pilot flying and a pilot monitoring. The motivation of this study is to evaluate the possibility to apply an hyperscanning approach to estimate the mental workload of crews composed of two operators. We designed an experimental protocol in which ten crews (i.e. 20 subjects) had to perform a modified version of the NASA MATB-II during 8 five-minute blocks (i.e. 4 mental workload level configurations * 2 cooperation v. non cooperation conditions). Mental workload and cooperation level were classified using a traditional passive brain-computer interface pipeline that includes a spatial filtering step on frequency features. Our results disclosed that all mental states' estimations were significantly above chance level. Intra-subject classification accuracy for mental workload (2 classes) was 63% for the pilot flying and 58% for the pilot monitoring. As for cooperation level, the binary classification reached 57% for the pilot flying and 60% for the pilot monitoring. Regarding the team, intra-team classification accuracy of the workload configuration of the team (4-class) reached 35%. As for the team cooperation level, the binary classifier reached 60% of accuracy. The results are discussed in terms of hyperscanning applications.

I. INTRODUCTION

Mental workload is a cognitive state that has been studied for decades. It is generally considered to be the result of the difficulty of a task and the associated effort furnished by the operator [START_REF] Gevins | Electroencephalography (eeg) in neuroergonomics[END_REF]. This mental state is of major interest to the human factor community as its impact on task performance has long been assessed. Classical ways of measuring mental states are subjective measures (i.e. questionnaires) and objective but indirect measures such as behavioral measures (i.e. reaction times and accuracy) or Autonomous Nervous System's measures (e.g. cardiac activity). Recently, researchers have been designing new means of performing a direct mental state assessment through cerebral measurements leading to the emergence of a field called Neuroergonomics, and thanks to machine learning techniques to a field called Physiological Computing and passive Brain-Computer Interfaces. Thus, cerebral activity measured using an electroencephalogram (EEG) has been shown to be significantly altered by an increasing cognitive workload. Indeed, an increase in the workload of an operator is linked to a decrease in the amplitude of temporal features called event-related potentials [START_REF] Allison | Workload assessment of computer gaming using a single-stimulus event-related potential paradigm[END_REF]- [START_REF] Brouwer | Estimating workload using eeg spectral power and erps in the n-back task[END_REF] and a power decrease in the alpha band ([8 12] Hz) at centro-parietal sites jointly with an increase in power in the theta band ([4 7] Hz) at fronto-central sites [START_REF] Stipacek | Sensitivity of human eeg alpha band desynchronization to different working memory components and increasing levels of memory load[END_REF]- [START_REF] Roy | Mental fatigue and working memory load estimation: interaction and implications for eeg-based passive bci[END_REF].

Using dedicated classification pipelines on various cerebral measures several authors have been able to efficiently estimate an operator's mental workload in laboratory [START_REF] Roy | Efficient mental workload estimation using task-independent EEG features[END_REF], [START_REF] Roy | Mental fatigue and working memory load estimation: interaction and implications for eeg-based passive bci[END_REF], [START_REF] Durantin | Using near infrared spectroscopy and heart rate variability to detect mental overload[END_REF] or even in real life settings [START_REF] Gateau | In silico versus over the clouds: On-the-fly mental state estimation of aircraft pilots, using a functional near infrared spectroscopy based passive-bci[END_REF]- [START_REF] Dehais | Monitoring pilots mental workload using ERPs and spectral power with a six-dry-electrode EEG system in real flight conditions[END_REF]. Despite their interest, most of these studies have focused on the monitoring of a single operator. However, one has to consider that human operators generally work in a cooperative fashion to achieve common goals. A typical example is the aviation domain whereby crews are composed of a pilot flying (PF), who is in charge of controlling the aircraft trajectory, and of a pilot monitoring (PM), who is in charge of monitoring the aircraft status and communicating with air traffic controller [START_REF] Authority | Monitoring matters, guidance on the development of pilot monitoring skills[END_REF], [START_REF]Guidance material for improving flight crew monitoring[END_REF]. Hence, there is a need to implement monitoring solutions at the team level as episodes of high workload have been shown to disrupt cooperation [START_REF] Dehais | Pilot flying and pilot monitorings aircraft state awareness during go-around execution in aviation: A behavioral and eye tracking study[END_REF], [START_REF] Reynal | Pilot flying vs. pilot monitoring during the approach phase: An eye-tracking study[END_REF].

A recent field of research has tried to address this issue by identifying physiological proxies of cooperation over time. For instance, the physiological substrates of cooperation, also called 'physiological compliance', have been studied using protocols that involve teams of 2 (dyads) or more participants (for a review see [START_REF] Palumbo | Interpersonal autonomic physiology: A systematic review of the literature[END_REF]). Since the first 'hyperscan' (multiple brain recording [START_REF] Montague | Hyperscanning: simultaneous fmri during linked social interactions[END_REF]) some studies were performed in the field of game theory, decision making or cooperative v. competitive behavior. Yet only a few of them did actually relate to team workload (for a review on hyperscanning in Social Neuroscience see [START_REF] Babiloni | Social neuroscience and hyperscanning techniques: past, present and future[END_REF]). For example, Stevens and collaborators [START_REF] Stevens | Neuroergonomics: Quantitative modeling of individual, shared, and team neurodynamic information[END_REF] presented a quantitative model based on entropy measures to assess teams' neurodynamics during complex cooperative task performance (i.e. submarine piloting task or healthcare training). Also, Toppi and collaborators [START_REF] Toppi | Investigating cooperative behavior in ecological settings: an eeg hyperscanning study[END_REF] found significant differences in graph metrics computed from Partial Directed Coherence in PF-PM teams during simulated flights. Lastly, Korczowski and collaborators [START_REF] Korczowski | Single-trial classification of multi-user p300-based brain-computer interface using riemannian geometry[END_REF] demonstrated the performance of Riemannian geometry for classification of Multi-User P300-Based Brain-Computer Interface. However none of these two studies tried to classify and estimate operators' state using a passive Brain-Computer Interface (BCI) pipeline. This a very recent field of study and to our knowledge the efficient estimation of a team's workload through cerebral measures has not yet been published, and nor is it the case for a team's cooperation level. To meet this challenging goal, couples of participants had to perform a modified version of the NASA MATB-II in which we manipulated the levels of mental workload and cooperation. This experimental set-up aimed at reproducing the flying operational context as participants played either the role of a PF or a PM. With this protocol we hypothesized that, because mental workload and cooperation elicit different behaviors and different neurodynamics, [START_REF] Babiloni | Social neuroscience and hyperscanning techniques: past, present and future[END_REF]- [START_REF] Toppi | Investigating cooperative behavior in ecological settings: an eeg hyperscanning study[END_REF], a classifier based on spectral EEG features should be able to discriminate those mental states. To evaluate this hypothesis, mental workload and cooperation levels were classified using a traditional passive BCI pipeline that includes a spatial filtering step on frequency features.

II. METHODS

A. Participants

Twenty participants (i.e. 10 teams; 4 females; 25 years old in average ±7) underwent this experiment on a volunteer basis. They were recruited among the students of the ISAE-SUPAERO engineering school. All had normal or corrected-to-normal vision and no history of neurological or psychiatric disorders. The study was approved by the local ethic committee (IRB00011835-2019-05-28-1) and all participants gave their informed written consent.

B. Experimental Protocol

The participants took part in an experiment that included a modified version of the MATB micro-world [START_REF] Comstock | The multi-attribute task battery for human operator workload and strategic behavior research[END_REF]. Each couple performed 8 scenarios of 5 minutes each. During the whole experiment each participant was either Pilot Flying (PF) or Pilot Monitoring (PM), a role attributed randomly by the experimenter. The PF had to perform the System Monitoring (Sysmon) task using the keyboard along with the Tracking (Track) task using a joystick. The PM had to manage the Communications (Comm) with the mouse along with the Resource Management (Resman) Task using the numerical keyboard. Two levels of difficulty were modulated separately for each participant (i.e. Easy and Hard) which resulted in two mental workload conditions (i.e. Low and High). For the PF, only the Track difficulty was modulated by lowering its responsiveness and increasing its speed. For the PM, only the Resman task difficulty was modulated by increasing the flowrates and increasing the number and the duration of failed pump. Moreover, the participants were also asked either to cross-monitor and help their partner (cooperative condition) or not (control condition). Cross-monitoring refers to interacting directly with the partner' tasks without speaking (i.e. doing his/her task). Those modulations resulted in a total of 8 possible conditions (i.e. 8 blocks). All the conditions/blocks were pseudo-randomly presented.

C. Data Acquisition

The participants' subjective reports of workload were recorded thanks to the NASA TLX questionnaire [START_REF] Hart | Development of nasa-tlx (task load index): Results of empirical and theoretical research[END_REF]. Also, their performance was computed thanks to a score based on their performance to each of the MATB sub-tasks. Moreover, the participants' EEG were recorded at 256 Hz with two BioSemi ActiveTwo 64 active electrodes positioned according to the 10-20 system. The Common Mode Sense (CMS) active electrode and the Driven Right Leg (DRL) passive electrode were positioned next to POz. Data from the task and both EEG systems were synchronized and recorded with the help of Lab Streaming Layer [START_REF] Kothe | Lab streaming layer (lsl)[END_REF].

D. Classification Procedure

Classifiers trained on frequency features (theta, alpha and low beta power) were used to detect if we could discriminate the workload level for each participant (binary), and the workload configuration for each team (i.e. low/low, low/high, high/low or high/high, hence 4-class). In the same manner classifiers were trained to detect the cooperation level (always binary) for each subject, and for the team. To do so, a classification pipeline close to that used by Dehais and collaborators [START_REF] Dehais | Monitoring pilots mental workload using ERPs and spectral power with a six-dry-electrode EEG system in real flight conditions[END_REF] and by Roy and collaborators [START_REF] Roy | Mental fatigue and working memory load estimation: interaction and implications for eeg-based passive bci[END_REF] was used. The EEG data processing and classification were run using EEGLab (V14.1.2b) and Matlab (R2019a).

First, every block was cut into 2-sec epochs. Each epoch was preprocessed independently in order to potentially extend our method to online processing. The data were high-pass filtered (0.5 Hz) and noisy portions were removed using the ASR plugin of the toolbox available at [START_REF] Mullen | Real-time modeling and 3d visualization of source dynamics and connectivity using wearable eeg[END_REF]. Sources of noises were mainly due to movement and physiological noises (eg. Eye movement, cardiac activity). Next, for each epoch the frequency power in different frequency bands (theta [4 8] Hz, alpha [8 12] Hz and low beta [12 16] Hz) was computed. To compute these frequency power features, the EEG signals were filtered in each band using a 150-order FIR filter. Then, a Common Spatial Filter (CSP) was computed for each band and only 4 filters were kept. The features then consisted of the log variance of the spectrally and spatially filtered signal. In total there were 12 features per epoch (3 frequency bands*4 filters).

Lastly, a subject-dependent 2-class or 4-class (depending on the study) shrinkage Linear Discriminant Analysis (sLDA) classifier was used, as recommended in [START_REF] Lotte | A review of classification algorithms for eeg-based brain-computer interfaces: a 10 year update[END_REF], with a One-Versus-The-Rest (OVR) strategy for the 4-class. A 4-Fold Cross Validation procedure was applied by keeping one block (scenarios) of each class out per fold. All classifiers were trained using data from blocks different from the ones used for testing. The theoretical chance threshold was adjusted following the recommendations of [START_REF] Combrisson | Exceeding chance level by chance: The caveat of theoretical chance levels in brain signal classification and statistical assessment of decoding accuracy[END_REF].

E. Statistical Analyses

The subjective, behavioral, EEG and classification results were all statistically analyzed using the Statistica software. A repeated measures ANOVA with workload for PF and PM, cooperation and electrodes (WK PF x WK PM x COOP x ELECT) was used. Tukey HSD was applied to post-hoc tests to correct for multiple comparisons. For the sake of clarity and to facilitate the reading of the results only the data of 4 electrodes frequently cited in the literature were analyzed for the physiological analyses, namely Fz, Cz, Pz and Oz. Yet all 64 electrodes were used for the classification step.

III. RESULTS

A. Protocol validation

In order to validate the experimental protocol designed to modulate mental workload, we verified whether the participants did indeed feel a higher strain in the high load condition as compared to the low one, and whether their performance was decreased by an increase of workload.

1) Subjective Reports: As regards the subjective reports of workload measured thanks to the NASA TLX, in a general manner the operators who performed the task as pilot monitoring reported a higher workload when they underwent the task in the high difficulty condition (PM Difficulty) than in the low one (F(1,9)=3062.8, p < 0.01). In the same manner, the operators that performed the task as pilot flying reported a higher workload when they underwent the task in the high difficulty condition (PF Difficulty) than in the low one (F(1,9)= 29.32, p < 0.01). There was no significant differences in the subjective ratings regarding the cooperation condition.

2) Behavioral Data: Regarding the behavioral data, the operators' performance dropped when workload increased for the pilot flying (F(1,9)=5.21, p < 0.05), as well as when it increased for the pilot monitoring (F(1,9)=5.22, p < 0.05). There was no significant differences in performance regarding the cooperation condition.

B. EEG Data

The power of the three frequency bands of interest -theta, alpha and low beta-was modulated by both workload and cooperation. Indeed, the low beta power of the PF decreased significantly at Fz in the cooperation condition when PM had a high workload (p < 0.05). The low beta power of the PM significantly increased with an increase in workload of the PF (p < 0.05) and significantly decreased with an increase in workload of the PM herself (p < 0.01).

Alpha power of the PM significantly decreased at all sites with an increase in workload level of the PM in the control condition (p < 0.05); it also significantly decreased with cooperation when workload was low for the PM and high for the PF (p < 0.05). As for the PF, there was only a trend of increase in alpha power at Pz with increasing workload and cooperation (p = 0.08). This trend was mirrored by a trend for a decrease in theta power at all sites with increasing workload and cooperation (p = 0.08). Lastly, there was a trend for a decrease in theta power of the PM when the load of the PF increased (p = 0.07); there was also a trend for a decrease in theta power in the cooperation condition compared to the control condition (p = 0.06).

C. Classification Results

All classification results were significantly above the adjusted chance level. The workload condition of each operator was estimated in an intra-subject fashion using the pipeline described earlier. As illustrated by Figures 1, the binary classification reached 63% of accuracy for the pilot flying and 58% for the pilot monitoring (adjusted threshold: 57%). Also, using both operators the workload configuration (i.e. low/low, high/low, low/high or high/high) could be estimated with a 4-class classifier with an accuracy of 35% (adjusted threshold: 31%; Figures 2).

Regarding cooperation level estimation, the binary classification reached 57% using for the pilot flying, 60% using the pilot monitoring and 60% using the team (adjusted threshold: 57%; Figures 3 and4). There was a trend for a better cooperation estimation using both operators' features than only the PF ones (p = 0.07).

IV. DISCUSSION & CONCLUSION

The main goal of this study was to assess whether workload and cooperation level could be estimated using typical EEG features (i.e. spectral features: power in the theta, alpha and beta bands) and a classification pipeline using data from one single operator or the whole dyad. First, the protocol that was used did manipulate the workload of both operators as demonstrated by statistically significant subjective, behavioral and physiological modulations.

Next, it appeared that indeed both mental states could be estimated from the EEG spectral features of each operator with classification accuracies above the adjusted chance level with as high as 63% of accuracy for workload binary estimation which is inline with previous findings [START_REF] Roy | Mental fatigue and working memory load estimation: interaction and implications for eeg-based passive bci[END_REF]. Cooperation level was also classified as high as 60% independently of the workload level. Yet to our knowledge there is no literature to compare this result to. Interestingly there was not much benefit of using both operators' features since the classification performance of using one operator's features and using both operators' were not statistically different. However in a hyperscanning framework it might be relevant to assess operators' mental states using both single operators' features and dyadic features to ensure a correct decision on a given team's state by the automated system.

Interestingly enough there was a slight difference in workload estimation depending on the role (i.e. PF or PM). Indeed the workload estimation dropped to 58% on the PM. Her/his tasks might not elicit a workload level as high as the PF's one. This might also due to the fact that the model was trained as if there was only 2 conditions for a participant: Easy and Hard. The reality was that the workload of one participant (PF or PM) could be greatly influenced by the performance of the partner as the task was developed to have dependencies among subs-tasks. For example, while a scenario equated as an Easy one for a PM, if the PF performed poorly at the tracking task, this easy scenario could have been even harder than a hard one for the PM. This strong dependency, especially from the track to the resource management might be a reason for this accuracy gap. When evaluating a team member workload, it might be irrelevant to look only at one teammate difficulty regardless of their partners difficulty. Yet this implementation allowed This study showed that it is possible to detect workload level and cooperative states using spectral EEG features from a 2-second window. The results compare to classifier performance obtained with a fatigue inducing protocol [START_REF] Roy | Mental fatigue and working memory load estimation: interaction and implications for eeg-based passive bci[END_REF] where 65% were achieved. Moreover classifiers were tested with epochs from scenarii they were not trained on. This prevented us to spuriously increase the classification rate by detecting spectral similarities in contiguous epochs. Yet improvements still remain to be done in order to greatly increase the classification performance. For instance, the classification pipeline that was used was applied at the sensor level. It would be interesting to extend the analysis to the source level by using ICA [START_REF] Makeig | Independent component analysis of electroencephalographic data[END_REF] or LORETA [START_REF] Pascual-Marqui | Functional imaging with low-resolution brain electromagnetic tomography (loreta): a review[END_REF]. Also, a spatial filter was used to summarize spectral information from the electrodes. Instead, connectivity metrics could be used as features as previously demonstrated for mental state monitoring purposes on either a single operator or on dyads [START_REF] Verdière | Detecting pilot's engagement using fnirs connectivity features in an automated vs. manual landing scenario[END_REF], [START_REF] Toppi | Investigating cooperative behavior in ecological settings: an eeg hyperscanning study[END_REF], [START_REF] Charbonnier | Estimation of working memory load using EEG connectivity measures[END_REF], [START_REF] Charbonnier | EEG index for control operators mental fatigue monitoring using interactions between brain regions[END_REF]. In addition, although 10 couples were used, classification was done at the subject or team level. Another solution could be to perform intersubject or interteam prediction using linear regression methods [START_REF] Chiang | Cross-subject transfer learning on high-speed steady-state visual evoked potentialbased brain-computer interface[END_REF].

Further, practical limitations of this protocol (i.e. temporal constraints) compelled subjects to realize only one block per condition. Hence classification could not be performed over a single condition. Epochs were either classified as low or high regardless of the partner's task difficulty or the cooperative state. Therefore this might not reflect very accurately the actual workload experienced by the participants and more generally their mental states. Therefore, it would be useful to implement a more refined protocol considering levels of workload and with more repetitions in order to classify the exact same conditions. Moreover, this pipeline should be evaluated with a portable EEG system to get closer to ecological conditions. While this protocol open the way to real world setting condition, the practical application will still remain a great challenge.

Conversely while cooperation was also classified regardless of the workload level, it seems even more interesting that the classification level reached 60%. This results means that despite opposite levels of workload, cooperative behavior might elicit specific detectable and robust spectral EEG patterns. However one has to note that the protocol asks participants to cooperate but they were not required to do so. In other words, the classification could have been performed over the actual observed level of cooperation instead of the cooperative instructions.

To conclude, to our knowledge this study is the first one to try and assess dyadic mental workload and cooperation level using EEG spectral features and a classification pipeline. Hyperscanning is a promising tool for performance and security improvements in risky work settings and this promising study paves the way for mental state monitoring applications on teams of operators.

Fig. 1 .

 1 Fig. 1. Upper : Binary workload classification performance from a single operator's EEG data. Lower : Confusion matrices for the binary workload classification performance from a single operator's EEG data

Fig. 2 .

 2 Fig. 2. Upper : 4-class workload/configuration classification performance from two operators' EEG data. Lower : Confusion matrix for the 4-class workload classification performance from both operators' EEG data

Fig. 3 .Fig. 4 .

 34 Fig. 3. Binary cooperation level classification performance from each type of operator or both operators' EEG data

ACKNOWLEDGMENT

This study was supported by a PhD grant delivered by the DGA (Direction Générale de l'Armement).