Mohamed Trabelsi
email: mohamed.trabelsi@ensam.eu

Eric Semail
email: eric.semail@ensam.eu

) Ngac

Ky Nguyen
email: ngacky.nguyen@ensam.eu

Fabien Meinguet
email: fabien.meinguet@thalesaleniaspace.com

Open-Switch and Open-Phase Real Time FDI Process for Multiphase PM Synchronous Motors

Keywords: Aerospace safety, five-phase PMSM, multiphase elctric drive, inverter fault, closed-loop control, fault detection and identification, open-phase. I

This paper deals with the real time Fault Detection and Identification (FDI) process of inverter Open Switch Fault (OSF) and Open Phase Fault (OPF) in five-phase PMSM designed for aerospace applications in which the electric drive system has particular operating characteristics either in healthy states or in the faulty ones. Two original contributions are considered in this paper. They consist in normalizing the input variables of the FDI process applied to multiphase system and compensating the noise (switching and sensors noises) and dccomponent resulting from the fault occurrence. The proposed strategy uses multiple normalized criterias derived from the measured phase currents and the references currents obtained from the outputs of the speed controllers. The FDI shows independence with respect to transient states and to switching and measurement noises. Moreover, it can be easily included in an existing software without any additional sensors. The validity of the proposed method is verified by Matlab/Simulink simulation tests.

INTRODUCTION

Five-phase Permanent Magnet Synchronous Motor (PMSM) considered in this work is being studied for an aerospace Thrust Vector Control (TVC) system. The TVC system controls the orientation of the nozzle in order to define the trajectory of the rocket, as shown in Fig. 1. The proposed solution is composed of two electromechanical five-phase PMSM which replace the classical structure based on two hydraulic actuators. More details about the general functioning principle are given in [START_REF] Dos Santos Moraes | Fault tolerant dual-motor drives : sinzing of power electronic[END_REF] and [START_REF] Dos Santos Moraes | A comparative study of two fault-tolerant dual-motor drive topologies under short circuit inverter switch fault[END_REF] but for six-phase PMSM that is more adaptable to high power and presents more degrees of freedoms (DoF) especially under short-circuit fault. The choice of any phase number depends essentially of the fault number that can be tolerated in the system. The studied system in this work uses two five-phase PMSM which are electrically independents. However, the selected structure is considered sufficient for opened switch or phase faults tolerance. Each motor uses a five-leg Voltage Source Inverter (VSI) fed by batteries which replace the hydraulic tank. In TVC system, one of important constraints is that the drive has to continue to operate under fault conditions.

These aerospace systems are exposed to hard aerospace environmental and functional conditions inducing faults essentially related to the VSI. In previously published statistical studies [START_REF] Hanna | Medium-voltage adjustable-speed drives users' and manufactures' experiences[END_REF], the percentage of faults for three-phase variable-speed drives was evaluated to about 60% due to the experiences of user during the first year of operation. In addition, 70% of these faults were related to power switches of the VSI, such as short-circuit fault and open-circuit fault. The impact of a short-circuit fault is usually destructive with classical star coupled drives and needs either special VSI with two transistors in series or with supplementary components such as triac or special architecture such as open-windings drives [START_REF] Nguyen | Fault-tolerant operation of an open-end winding five-phase PMSM drive with shortcircuit inverter fault[END_REF]. It is the reason why only opened switch or opened phase faults will be considered in this paper without any additional power component in comparison with normal operation.

For classical three-phase systems, reviews of FDI methods have been already given in [START_REF] Bin | A literature review of IGBT fault Diagnostic and protection methods for power inverters[END_REF] before 2009 and recently in [START_REF] Gao | A Survey of Fault Diagnosis and Fault-Tolerant Techniques-Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches[END_REF]. They can be classified as model based methods [START_REF] Campos-Degado | An observer-based diagnosis scheme for single and simultaneous open-switch faults in induction motor drives[END_REF], [START_REF] Jung | An MRASbased diagnosis of open-circuit fault in PWM voltage-source inverters for PM synchronous motor drive systems[END_REF] or signal based methods. The first ones need an accurate system model to achieve a robust algorithm. Techniques based on analysis of the signals require the measurement of inverter outputs (currents or voltages). Methods based on voltage analysis, addressed in [START_REF] Karimi | FPGA-based real-time power converter failure diagnosis for wind energy conversion systems[END_REF]- [START_REF] Trabelsi | PWM-switching pattern-based diagnosis scheme for single and multiple open-switch damages in VSIfed induction motor drives[END_REF], have a major drawback because an extra hardware or extra sensors are usually needed for real time implementation. Techniques based on currents have been reported in [START_REF] Abramik | A diagnostic method for on-line fault detection and localization in VSI-fed ac drives[END_REF]- [START_REF] Zidani | A fuzzy-based approach for the diagnosis of fault modes in a voltage-fed PWM inverter induction motor drive[END_REF] with extension, in [START_REF] Estima | A new Approach for real-time multiple open-circuit fault diagnosis in voltage-source inverter[END_REF]- [START_REF] Wu | A real-time multiple open-circuit fault diagnosis method in voltage-source-inverter fed vector controlled drives[END_REF], to multiple-fault occurrence. However, these techniques have been developed for conventional systems with balanced threephase currents and sinusoidal back-EMFs of PMSM drives and cannot be applied directly to multiphase systems for fault diagnostic purposes. In fact, while working with multiphase PMSM drives, usually the back-EMFs contain multiple harmonic components such as third, fifth, seventh and ninth harmonic. Consequently, the reference and the measured phase currents can be distorted with the same components, when using the Maximum Torque Per Ampere (MTPA) control strategy, resulting thus in false alarms when applying the conventional FDI strategies.

Regarding the multiphase systems, there are only a few works [START_REF] Salahifar | Fault detection and fault tolerant operation of a five phase PM motor drive using adaptative model identification approach[END_REF], [START_REF] Salehifar | Observer-based open transistor fault diagnosis and faulttolerant control of five-phase permanent magnet motor drive for application in electric vehicles[END_REF] that address specifically the FDI problem for multiphase systems especially under inverter switch faults. In [START_REF] Salahifar | Fault detection and fault tolerant operation of a five phase PM motor drive using adaptative model identification approach[END_REF], [START_REF] Salehifar | Observer-based open transistor fault diagnosis and faulttolerant control of five-phase permanent magnet motor drive for application in electric vehicles[END_REF], a five-phase Permanent Magnet machine with trapezoidal electromotive force is considered. Injection of third harmonic current, which is one of the specificity of this kind of machine in terms of control, is taken into account and possibility of detection and identification is validated but without consideration on robustness.

In the proposed paper, the FDI algorithm, based on analysis of the currents, considers, as in [START_REF] Salahifar | Fault detection and fault tolerant operation of a five phase PM motor drive using adaptative model identification approach[END_REF], [START_REF] Salehifar | Observer-based open transistor fault diagnosis and faulttolerant control of five-phase permanent magnet motor drive for application in electric vehicles[END_REF], injection of a third harmonic of current but, as in [START_REF] Estima | A new Approach for real-time multiple open-circuit fault diagnosis in voltage-source inverter[END_REF]- [START_REF] Estima | A new algorithm for real-time multiple open-circuit fault diagnosis in voltage-fed PWM motor drives by the reference currents errors[END_REF], introduces a normalization of the currents in order to prevent the generation of false alarms.

In the first paragraph, faults effects in a five-phase machine are presented and analyzed. In the second paragraph, a FDI with normalization is given including, for a robust identification of the nature of fault, a compensation of fault effect. The last paragraph provides simulation results and test of robustness in case of torque load variations.

II. MULTIPHASE SYSTEM STRUCTURE AND OPERATING

CHARACTERISTICS UNDER INVERTER FAULTS The early step in this work consists in analyzing the overall electric drive system performances and dynamics under fault conditions. This step aims essentially to design a robust FDI process with respect to the following problematic questions:

 Which pertinent variables that will be selected for a robust FDI process design?  Is the designed FDI easy for real time integration in the existing electric drive system with respect to the cost function and the complexity?  Is the designed FDI robust for all operating conditions?

In other words, what is the sensivity of the FDI process to the parameters variation, the noises and the transient states?  How fast is the FDI process, permitting a minimum time delay between the fault occurrence and the fault identification? Moreover, in order to develop low-cost FDI process, it is strongly desirable to avoid the use of extra sensors. So, FDI process based on currents are attractive in comparison with those based on voltages. For this reason, it is chosen in this work that the fault effects analysis will be achieved only regarding the dynamic of the measured phase currents which will be used then as input variables for the proposed FDI process.

A. System structure and VSI topology

This section consists in analyzing the effects of OSF and OPF on the five-phase PMSM. A simplified scheme of the considered electric drive, including the power electronic part, the electric machines and its control, is shown in Fig. 2. It is composed of a five-leg VSI, a five-phase vector-controlled PMSM and a variable load generated through three-phase PMSM.

The VSI, composed of five legs (Fig. 2), is fed by a constant voltage source provided through a capacitive dc-link. Each leg features two power switches (T k , T k+5 , k =1, 2, 3, 4, 5) with anti-parallel connected freewheeling diodes ( D K , D K + 5 ). The VSI is controlled by the gate switching signals ( S K , S K + 5 ) ∈ { 0 , 1 } . The gate signal S K or S K + 5 is equal to "1" when the switch is conducting and equal to "0" when the switch is open.

The output currents of the VSI, in the original frame, can be expressed in steady states as follows:

( )

2 n 1 5 h i ( t ) I sin h p t n h 1 π Ω - ∞ = -  =             (1)
where, n=1,..,5 represents the phase current (i a , i b , i c , i d , and i e ), h is the order of the current harmonics, I h is the magnitude of the hth current harmonic, and pΩ is the electrical fundamental frequency.

For the PMSM under study, only the first and the third harmonics are considered but the algorithm could be extended to non-sinusoidal machines having more harmonics. So, the output currents of the VSI given in (1) can be reduced, for a healthy condition, as follows:

( ) ( )

2 2 1 3 i ( t ) I sin p t n 1 I sin 3 p t n 1 n 5 5 π π Ω Ω = -- + --                   (2)

B. Inverter Fault Effects Analysis

The OSF and OPF effects analysis are achieved using the electric drive structure shown in Fig. 2. The parameters of the five-phase PMSM are given in Table . I. All results are obtained in closed loop control and without system reconfiguration after fault occurrence. However, the pre-fault control, as well as the post-fault control, are achieved without any change in the control loops (speed and current loops) or in the maximum torque per ampere algorithm (MTPA), as shown in Fig. 2. The reference currents (i dq-ref ) are provided from the outer speed loop and the MTPA strategy.

Simulated results on FEA under healthy and faulty conditions are shown in Fig. 3, Fig. 4 and Fig. 5. Three fault modes are investigated: an open switch fault, open phase fault, and OSF or OPF in the case of non-sinusoidal back-EMFs (with 3rd harmonic). During both healthy conditions and faulty modes, the reference speed and the load torque are set to 1000 rpm and 15 Nm, respectively. For both normal operating condition and post-fault operation mode of the electric drive system, the VSI is built from the power switches and OSF or OPF in the case non-sinusoidal back-EMFs (with 3rd harmonic). During both healthy conditions and faulty modes, the reference speed and the load torque are set to 1000 rpm and 15 Nm, respectively. For both normal operating condition and post-fault operation mode of the electric drive system, the VSI is built from the power switches considering transistors and antiparallel diodes.

Simulation results addressed in Fig. 3 and Fig. 4 present respectively the time domain waveforms of the phase currents (Fig. 3a and Fig. 4a), the spectrogram of the faulty phase a (Fig. 3b and Fig. 4b) and the spectrogram of one healthy phase b (Fig. 3c and Fig. 4c) for both healthy and faulty conditions.

1) Healthy condition of the VSI:

In the first test, the electric drive system operates without any fault. It is observed that the phase currents are sinusoidal. These results are confirmed by the spectrogram of the phase current, showing thus the fundamental component and low amplitude highfrequency noise and switching effects.

2) Single open switch or open phase faults: In the second test (Fig. 3), an open switch fault is considered for the VSI at t =0.1018 s. In this case, the open circuit fault is applied to the upper transistor T1 of the first inverter leg (phase a) during permanent operating mode of the electric drive system. It is observed that the dynamic performances of the system are affected only when the current of the faulty inverter leg is nullified (because of the open-circuit fault of T1). During the rest of the period when the current ia(t) becomes negative, the electric drive system performances are similar to the healthy state. Regarding the double OSF of T1 and T6, resulting in an open phase fault case (Fig. 4), its occurrence results in similar effects but over a fundamental current period because two transistors are involved in this case. Although the OSF (T1) or the OPF (T1 and T6), the five-phase PMSM is still capable to operate but with torque and speed ripples, leading to more stress and thermal cycling in the power switches and other functional blocks in the electromechanical conversion chain.

It should be noted that the fault occurrence, regardless the fault type (single or multiple) and location, creates an asymmetry in the electric drive system, resulting in a periodic oscillation of the PMSM output torque. All these mechanical new-constraints induce in the motor several harmonic components even in the healthy phases: the currents have not sinusoidal shapes immediately after the fault occurrences because of the effect of mutual inductances between the phases. Each type of inverter fault (OSF or OPF) draws a particular form and modification of the phase currents, with a particular harmonic content. This characteristic is observed when examining the spectrograms depicted in Fig. 3.b-c and Fig. 4.b-c. They contain harmonics multiplying by fundamental current frequency in addition to the dc component which is observed in all phase currents under an OSF. Regarding the amplitudes of the observed harmonic components in the other healthy phases (e.g phase b (Fig. 3(c)), they are different in comparison with the spectrogram of the faulty phase a. For the healthy phase b, it is observed in the current ib(t) an increase of the fundamental harmonic and the apparition of a third harmonic component.

ia(A) ib(A) ic(A) id(A) ie(A

3) 3rd harmonic effect on the five-phase PMSM: Results addressed in Fig. 5 are obtained in pre-fault operation and post-fault operation of the electric drive system with a third current harmonic component applied to the five-phase PMSM according to MTPA strategy. As, in the previous tests, the reference speed and the load torque are set to 1000 rpm and 15 Nm, respectively. If in time representation the currents appear as complex, the spectrum of current contain, in OSF and OPF, the same component harmonic as previously.

III. PROPOSED REAL-TIME FDI PROCESS

The block diagram of the proposed FDI is illustrated in Fig. 6. It consists in five main steps:

1) Step_I : Fault profiles extraction in the decoupled subspaces d1q1 and d3q3 frames. This step permits to take into account the dynamic of the electric drive system in closed-loop operation. These fault quantities are expressed by

f ( t ) i ( t ) i ( t ) d1q1 d1q1_ ref d1q1_ mes = - (3)
f ( t ) i ( t ) i ( t ) d 3q3 d 3q3 _ ref d 3q3 _ mes = - (4)
The fault profiles f dq (t) are positive or negative when an OSF or OPF occurs in the VSI. They are close to zero under healthy condition. These quantities contain all faulty conditions of the VSI and are achieved for all operating points of the five-phase PMSM.

2) Step_II : Generation of equivalent fault profiles in original frame abcde. It consists mainly in applying successively the Park-inverse and generalized Concordiainverse transformations [START_REF] Campos-Degado | An observer-based diagnosis scheme for single and simultaneous open-switch faults in induction motor drives[END_REF] and [START_REF] Jung | An MRASbased diagnosis of open-circuit fault in PWM voltage-source inverters for PM synchronous motor drive systems[END_REF] to the fault profiles obtained in the first step.

The equivalent Concordia fault profiles can be obtained by • For the rotating d1q1-frame :

[ ] 1 d 1q1 f P ( ) f αβ θ -     =     (5)
• For the rotating d3q3-frame :

[ ] 1 xy d 3q3 f P(3 ) f θ -     =     (6)
However, the new fault profiles in original frame are a function of quantities [f αβ-xy (t)] as follow: fault profiles genration in d1q1 frame fault profiles genration in d3q3 frame

1 i d mes 1 i q mes i d ref 1 i q ref 1 i d mes 3 i q mes 3 i d ref 3 i q ref 3
[ ] t n x y t xy 0 5 f ( t ) C f ( t ) 2 C αβ αβ           =                 (7)
where, [f n (t)] =[ f abcde (t)], FDI process (fault profiles f n (t) and the measured phase currents i n (t)) without any conditioning. Unfortunately, the reliability is then very low under mechanical operating conditions change, as speed and load changes. A way to overcome this problem consists in normalizing these quantities. In fact, since these variables are the phase currents or derived from the phase currents, they can be normalized according to the sum of Concordia current modulus for each decoupled subspace as follows:

π π π π αβ π π π π =               (8)

C xy

π π π π π π π π =               (9
2 2 2 2 i i i i i i i s xy x y 9 5 h1 h3 I I 2 5 α αβ β = + = + + + = +          (10)
Here, it is clear that the current modulus i s  depends on the first and third harmonic components. For copper-losses optimization purposes in PMSM, the current vector is generally co-linear with the EMFs vector (Maximum Torque Per Ampere (MTPA) strategy [START_REF] Kestelyn | A vectorial approach for generation of optimal current references for multiphase permanent-magnet synchronous machines in real time[END_REF]). As a result, the ratio of the third current harmonic and the first one is the same as the ratio of the third back-EMF harmonic and the first one. As a consequence, it is thus quite easy to express the third harmonic component I h3 as a fractional ratio of the first harmonic I h1 as follow:

h3 h1 I .I ρ = ( 1 1 )
Hence, the total current modulus ( 10) can be simply reduced to:

( )

1 9 9 5 5 h1 h3 i I 1 I s 5 5 2 2 ρ ρ = + = +        (12)
It is clear that the current modulus i s  is a constant and depends only of the peak value of the first harmonic or the third harmonic, and the ratio ρ . These parameters can be easily experimentally fixed by measuring the back-EMFs of the PMSM. Finally, the normalized input variables of the FDI process are obtained:

i a,b,c,d ,e i (t) nN i i xy f a,b,c,d ,e f (t) nN i i xy αβ αβ = + = +     (13)
where,

2 5 2 2 i (t) sin p t (n 1) sin 3( p t (n 1) ) nN 5 5 9 5 5 π π Ω ρ Ω ρ = -- + -- +                       
Here, it should be noted that the fault profiles is normalized in the same way as the phase current since they are derived from them.

One of the important features is to work with normalized input variables of the diagnostic process, allowing the FDI strategy to be more independent of the transient states. Such objective is justified when using equation ( 13) since there is no dependence with the amplitude of the current vector. The normalized quantities i nN (t) are approximately within the range of ( ) ( )

2 5 5 5 9ρ ± +
. Regarding the f nN (t), they are close to zero under healthy condition of the electric drive system and are approximately within the range of ( ) ( )

2 5 5 5 9ρ ± +
for the faulty one.

4)

Step_IV : Fault Diagnostic. This step consists in two successive actions, fault detection and fault identification. For the fault detection, there are five diagnosis variables d n (t) which are obtained from the average absolute values of the normalized fault profiles f nN (t), expressed by

n f (t) nN d ( t ) ( t ) = ( 1 4 )
Under normal operating condition, these variables are close to zero. Contrariwise, the OSF or OPF occurrence in the VSI results in a positive d n value, variable according to the fault location.

The fault identification could be achieved in principle by determining the polarity of the average normalized phase currents ) (t i nN . With fig. 3, it appears that ) (t i nN are flowing in negative (resp. positive) direction if the OSF occurs in the upper (resp. lower) switch. In fact, as observed in section II, the OSF or OPF results in arbitrary deformation of the phase currents with an important induced dc current component and noise in the healthy inverter legs, affecting thus the reliability and robustness of such the simple identification. A way to avoid this problem and improve the immunity of the proposed algorithm to false alarms consists in compensating the noise and dc component induced in the normalized phase currents i nN (t). The following variables are then introduced for identification:

i i ( t ) f ( t ) d ( t ) d nN nN n Th i (t) nNC ( t ) d ( t ) d nN n Th if if - = <   >  (15)
In order to obtain a normalized value, the following variables are then considered for the identification step:

( t ) ( t ) i (t) nNC I (t ) n i (t) nNC ε = + (16)
with ε ,a constant value obtained by computation, under healthy condition of the VSI, by

1 10 i (t) nNC ε = ( 1 7 )
ε allows to guarantee a non-zero value for the denominator of I n (t).

Finally, the fault diagnosis signals which allow a robust FDI of the OSF and OPF can be formulated by equation [START_REF] Estima | A new Approach for real-time multiple open-circuit fault diagnosis in voltage-source inverter[END_REF] considering the following thresholds:

• d Th is the used threshold for fault detection.

P if 0 if N if ε ε ε < < ≤ = + = + +  <   >    ≥           (18)
The thresholds d Th , I Thp and I ThN have been evaluated by several simulation tests for both a healthy and a faulty operation conditions. Also, their dependence on the operating conditions, transient states, noise and dc component is reduced.

IV. FDI PROCESS PERFORMANCES EVALUATION RESULTS

This section presents a summary of the main simulation results conducted on the simulation software presented in Fig. 2. The parameters of the five-phase PMSM are given in Table I. In a first step, for a healthy VSI, different tests have been carried out to evaluate the robustness and the immunity of the proposal to false alarms especially during the load torque change. Then, two fault modes are investigated: an open switch fault and open phase fault. Another similar test is carried out to show the robustness of the proposed real time FDI Process under 3rd harmonic injection in the five-phase PMSM.

Simulation results depicted in Fig. 7 show the time-domain waveforms of the line currents, the detection variable d n (t) and the identification variable I n (t), respectively. This test addresses the FDI process performances under load change for a healthy operating conditions, and then, when an open circuit fault occurs in the upper switch T1 of the inverter leg a. The five-phase PMSM is running at 1000 rpm. Firstly, fast transient processes are induced by a change in the load torque from no-load to 20Nm and then from 20 Nm to 10Nm. However, it observed that the diagnosis variables remain unchanged, showing thus the immunity of the proposed strategy to false alarms under load change. The open circuit fault is caused to the upper MOSFET T1 at t = 0.048 s, by keeping its switching signal permanently in "Off" state. After the fault occurrence, the phase current i a suddenly drops to zero and is limited now to flow only in the negative direction, while the other currents have a light deformation and are flowing in negative and positive directions. Regarding the variable d n , it is observed that it increases immediately and converges to the positive level near to 0.3, corresponding to an OSF in T1. However, fast detection is achieved at t = 0.049 s, since is take only 1 ms to detect the fault condition in the power inverter (with a time delay near to 12% of the fundamental current period). Concerning the fault identification step, it is observed that only I a (t) exceeds threshold I Thp and successfully indicates the fault occurrence of MOSFET T1 at t = 0.05s, which takes a delay of 0.002 ms (23% of the fundamental current period).

The simulation results presented in Fig. 8 address the diagnosis technique capabilities when an open phase fault occurs in the VSI. On this figure, the simulation waveforms of the phase currents, the detection variable d n (t) and the identification variable I n (t) are presented. The FDI robustness is analyzed for two cases. The first one concerns the change in the load torque in healthy condition with 3rd harmonic component of the back-EMFs. The second case is related to the fault detection and identification effectiveness with 3rd harmonic component of the back-EMFs. The fast transient processes are induced by a step increase and then a step decrease of the load torque. The transient response is clearly visible on the phase currents, which suddenly change during a short lived interval. Regarding the detection and identification variables, it is expected that they remains always unchanged during these transient states, showing thus the high immunity of the proposed algorithm against false alarms. The OPF is caused to the inverter first leg a at t = 0.051s, by keeping simultaneously the switching signals (S1 and S6) permanently in "Off" state when the phase current i a (t) is positive. Regarding the diagnosis results, it is expected that fast fault detection is achieved at t = 0.052s when d a (t) exceeds the threshold d TH = 0.1, since it is taken only a delay of 1ms. The fault identification of the MOSFET T1 is quickly achieved at t = 0.053s when I a (t) exceeds the fixed negative threshold I ThN . Then, the fault identification of transistor T6 is achieved at t= 0.0568s when the phase current i a (t) becomes negative. I a (t) remains unchanged close to zero corresponding to the open phase fault of first leg-a.

V. CONCLUSION This paper presents a diagnostic method of open circuit switch faults in multiphase VSI feeding a five-phase PMSM. The procedure of fault detection and identification is based on multiple normalized criteria derived from the measured phase currents. Particular operating characteristics and behavior when using multiphase PMSM are considered here to improve the robustness and the immunity of the FDI process. The obtained simulation results show that the proposed technique is effective and robust for detection and localization of the OSF or OPF in a Permanent Magnet five-phase machine.

Fig. 1 :

 1 Fig.1 : Considered Thrust Vector Control system (TVC). (a) Torque generation for 3 inclination cases of the thrust, (b) Upper view of actuators axis and inclination angle φ.

Fig. 2 :

 2 Fig.2 : Configuration of the electromechanical conversion chain used in the TVC System .

  Fig.3: waveforms of the phase currents and their corresponding spectrogram for a healthy VSI and an open switch fault (OSF) of transistor T1. (a) Phase currents waveforms. (b) Spectrogram of the phase current ia (t). (c) Spectrogram of the phase current ib (t).

Fig. 4 :

 4 Fig.4: Time-domain waveforms of the phase currents and their corresponding spectrogram for a healthy VSI and an open phase fault (OPF). (a) Phase currents waveforms. (b) Spectrogram of the phase current ia (t). (c) Spectrogram of the phase current ib (t).

Fig. 6 .

 6 Fig. 6. Block diagram of the proposed real time FDI process

) 3 )Fig. 5 :

 35 Fig.5: Time-domain waveforms of the phase currents and their corresponding spectrogram for a healthy VSI, an OSF and an OPF with non-sinusoidal back-EMFs of the PMSM. (a) Phase currents waveforms. (b) Spectrogram of the phase current ia (t). (c) Spectrogram of the phase current ib (t).

  0

Table .

 .

				I : FIVE PHASE PMSM PARAMETERS
	R (Ω)	Lm(H)	Ls		p	P (kW)	Imax	dc-bus
	9.1 mΩ	3.1 mH	0.9 mH	7	10.5	125A	48V
	Phase currents (A)	-50 0 50
		0.08	0.085	0.09	0.095	0.1	0.105	0.11	0.115	0.12
					(a) Time (s)

  • I ThP and I ThN are the thresholds used for fault identification. P and N denote, respectively, the positive and negative states of the diagnosis variables.

	d (t ) n	0 P if if	f (t) nN f (t) nN	(t) (t)	d d Th Th
			( t ) ( t ) (t) (t) nNC nNC i i	I Thp
	I (t ) n	I	ThN	( t ) ( t ) (t) (t) nNC nNC i i	I	Thp
			( t ) ( t ) (t) (t) nNC nNC i i	I ThN

  Time domain waveforms of the phase currents, the detection variable d n (t) and the identification variable I n (t). A change of the load torque, and then at 0.048s, an open circuit fault of MOSFET T1 in leg a with sinusoidal currents.

	n (A)	50		i a (t)	i b (t)	i c (t)	i d (t)	i e (t)
	Phase currents i	-50 0		Load change					OSF operation
		0.4	0	0.02 d a (t)	0.04 d b (t)	0.06 d c (t)	0.08 d d (t)	d e (t)	0.1
		0.3
	d n (t)	0.2
		0.1
		0
		0	0.02	0.04	0.06	0.08	0.1
				I a	(t)	I b	(t)	I c	(t)	I d	(t)	I e (t)
		0
	(t)
	I n	-0.5
		-1
			0	0.02	0.04	0.06	0.08	0.1
	Fig.7.							Time (s)

  Time domain waveforms of the phase currents, the detection variable d n (t) and the identification variable I n (t). Open circuit fault of two MOSFET (T1 and T6) resulting in an open phase fault with nonsinusoidal currents.

	n (t)(A)	50		i a (t)	i b (t)	i c (t)	i d (t)	i e (t)
	Phase currents i	-50 0		Load change				OSF operation
		0.6 0.8	0	0.02 d a (t)	0.04 d b (t)	d c (t)	0.06	d d (t)	0.08	d e (t)	0.1
	d n (t)	0.2 0.4
		0
				0.02	0.04		0.06		0.08		0.1
		1
		0.5
	I n (t)	0
	-0.5		I a (t)	I b (t)	I c (t)	I d (t)		I e (t)
		-1
			0	0.02	0.04		0.06		0.08		0.1
						Time (s)
	Fig.8.

Acknowledgment

This work is a part of a project "3MTolerant" of MEDEE pole supported by the regional council of France Region-Nord-Pas-De-Calais.


Guillaume Sahuquet

Ronny Gueguen

Samuel Mer

Adrien Toutant

Françoise Bataille

Gilles Flamant
email: gilles.flamant@promes.cnrs.fr

Particle flow stability in tubular fluidized bed solar receivers

Introduction

• Molten salt is the commonly used heat transfer fluid in solar towers, but solar salt has limited operating temperatures which limit the efficiency of the power block.

• To overcome this issue and reduce costs, new particle receivers are under development worldwide as the fluidized particle-in-tube of the french National Center for Scientific Research. A pilot-scale test unit is currently under construction at Thémis, France, in the framework of the Next-CSP H2020 project [1]. A smaller cold mock-up was constructed to study the hydrodynamics of the particle suspension flow at PROMES laboratory.

• Depending on the values of two main parameters (namely the particle flowrate and the secondary air flowrate) the particle flow is either stable or unstable. When an instability occurs the total pressure in the system decreases and there are significant variations of the particle flowrate.

• Objective: Define a stability diagram of the particle flow in order to determine the secure operating conditions for the full-scale unit.

Methodology

• Material: olivine with a Sauter diameter of 30.0 μm (group A of the Geldart classification) [2]

• Fluidization in a dispenser thanks to a homogeneously distributed air flowrate. By applying pressure, the fluidized bed passes into a 3m-long transparent glass tube of 4.5 cm internal diameter and is collected in a fluidized bed collector, creating a particle flowrate G P .

• A secondary air flowrate q ae is applied at an injection nozzle of diameter d ae at the bottom of the tube.

• Analysis method: The stability of the particle flow is studied as a function of the secondary air flowrate q ae (Nm3/s) and of the solid mass flux G P (kg/(m².s)).

• Stability diagram for q ae in [0 -0,39] Nm 3 /s and G P in [0 -200] kg/(m².s) : Two specific values of q ae delimit two main domains.

• Unstable area: For values of q ae under a threshold air q unstable , the mass flow is unconditionally unstable.

• Stable area: For values of q ae above a threshold q stable , the particle flow is unconditionally stable.

• Transition area: Between q unstable and q stable , the mass flow is either stable or unstable depending on the value of G P .

This work is part of the Next-CSP project that has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 727762.

[1] http://next-csp.eu/

References Conclusion

Schematic (a) and 3D (b) representation of the cold mock-up

• A secondary aeration at the bottom of the tube is a necessary condition to get a stable particle flow.

• The aeration flowrate must overcome a given threshold to reach unconditional particle flow stability.

• The thinner the nozzle's diameter the smaller the air flowrate necessary to get unconditional stability.

• The boundaries of these domains depend on the nozzle's diameter defined as an increase of q unstable and q stable with d ae .

• The evolution of q unstable and q stable is linear for nozzle's diameters between 0,5mm and 3mm.

Results

[ 2 ]

 2 Kang Q., Flamant G., Dewil R., Baeyens J., Zhang H.L., Deng Y.M., 2019. Particles in a circulation loop for solar energy capture and storage. Particuology 43, p. 149-156. DOI: 10.1016/j.partic.2018.01.009


domain: spi phys

text:
Pedro Mecê
email: pedrofbmece@gmail.com

Jules Scholler

Kassandra Groux

Kate Grieve

Claude Boccara

Adaptive glasses wavefront sensorless Full-Field OCT for high-resolution retinal imaging over a

Keywords: Optical Coherence Tomography, Adaptive Optics, Retinal Imaging, Photoreceptors, Nerve Fiber Layer

INTRODUCTION

Optical coherence tomography (OCT) revolutionized ophthalmology in the 1990s owing to its high axial resolution, which enabled clinicians to distinguish the retinal layers in-vivo. [START_REF] Huang | Optical coherence tomography[END_REF] Although the axial resolution of OCT is sufficient to resolve retinal features at a micrometer scale, the lateral resolution is limited by ocular aberrations. [START_REF] Jarosz | High temporal resolution aberrometry in a 50-eye population and implications for adaptive optics error budget[END_REF] Owing to its capacity to correct for ocular aberrations in real-time, adaptive optics (AO) has become the primary technique to achieve high lateral resolution in the retina. [START_REF] Gofas-Salas | High loop rate adaptive optics flood illumination ophthalmoscope with structured illumination capability[END_REF] When coupled to OCT, AO has enabled micrometer resolution in all spatial dimensions for in-vivo retinal imaging, [START_REF] Jonnal | A review of adaptive optics optical coherence tomography: technical advances, scientific applications, and the future[END_REF] contributing to the understanding of retinal function [START_REF] Azimipour | Functional retinal imaging using adaptive optics swept-source oct at 1.6 mhz[END_REF] and diseases. [START_REF] Lassoued | Measuring dysfunction of cone photoreceptors in retinitis pigmentosa with phase-sensitive ao-oct[END_REF] Nevertheless, the high lateral resolution achieved with AO comes with a cost of a small field-of-view (FOV), which is limited by the isoplanatic patch of the eye (around 2 o × 2 o ) 7 but also by the trade-off between the spatial sampling of the scan and the acquisition speed, in order to avoid image distortion due to involuntary fixational eye motion. [START_REF] Mecê | Fixational eye movement: a negligible source of dynamic aberration[END_REF] Most importantly AO-OCT systems are complex and cumbersome, requiring long imaging sessions to acquire a large FOV. [START_REF] Jonnal | A review of adaptive optics optical coherence tomography: technical advances, scientific applications, and the future[END_REF] These limitations have prevented the translation of AO-OCT from the research lab to clinics. Much recent work has aimed at addressing these limitations, by reducing the AO-OCT system complexity and footprint through the use of conjugated lens-based wavefront sensorless AO, [START_REF] Verstraete | Wavefront sensorless adaptive optics oct with the done algorithm for in vivo human retinal imaging[END_REF][START_REF] Jian | Lens-based wavefront sensorless adaptive optics swept source oct[END_REF] or by increasing the FOV to 4 o × 4 o using multi-conjugate AO. [START_REF] Brunner | Single-volume ao-oct imaging of retinal pigment epithelial cells at an extended field of view[END_REF] However, the former still presents a small FOV because of the limited isoplanatic patch of the eye and spatial sampling of the scan, and the latter adds complexity as two deformable mirrors are necessary.

In this manuscript, we propose a lens-based sensorless AO approach using a multi-actuator adaptive lens (MAL) positioned in front of the examined eye, i.e. without strict pupil conjugation, in a technique we call the adaptive-glasses approach. The proposed optimization scheme does not require any calibration step and is therefore straightforward to implement in existing systems without increasing system footprint or optical complexity. We implemented the adaptive-glasses approach in our compact time-domain full-field OCT (henceforth, named FFOCT) system. FFOCT was found to behave differently to conventional imaging systems and Fourier-domain OCT with regards to optical aberrations. The lateral resolution of FFOCT is less affected by symmetric aberrations (i.e. defocus and astigmatism), [START_REF] Barolle | Manifestation of aberrations in full-field optical coherence tomography[END_REF] which dominate in the eye, owing to the use of a spatially incoherent source. This interesting feature was recently highlighted for high-resolution retinal imaging over a field-of-view of 3.5 o × 3.5 o , without apparent anisoplanatism. [START_REF] Mecê | Coherence gate shaping for wide field high-resolution in vivo retinal imaging with full-field oct[END_REF] Nevertheless, although symmetrical aberrations may not be adversely affecting the resolution in FFOCT, the presence of aberrations still provokes a loss of signal-to-noise ratio (SNR). Low SNR strongly impacts the robustness of FFOCT imaging, especially at large pupil size, and prevents imaging of retinal layers other than photoreceptors. [START_REF] Mecê | Coherence gate shaping for wide field high-resolution in vivo retinal imaging with full-field oct[END_REF][START_REF] Mecê | High-resolution in-vivo human retinal imaging using full-field oct with optical stabilization of axial motion[END_REF] Here, we show that the use of the adaptive glasses approach to correct for ocular aberrations can considerably increase the SNR and robustness of FFOCT, enabling imaging of different retinal layers with 3D cellular resolution over a 5 o × 5 o FOV acquired in a single shot, while retaining a compact system design. To the best of our knowledge the presented method is the first to ally 3D high-resolution, wide FOV, high acquisition rate and small system footprint, which are essential characteristics for clinical deployment.

METHODS

Description of the FFOCT system

Figure 1(a,b) presents the optical and mechanical schematic of the FFOCT system, outlining the low optical complexity and reduced footprint (50cm × 30cm). Figure 1(c) shows the first FFOCT prototype, which was recently installed at the Quinze-Vingts National Ophthalmology Hospital (Paris, France). To date, five different users (two of which trained) have already used the systems alone to acquire retinal images from subjects. The main components of the custom-built FFOCT system used in this study have been previously described in detail elsewhere. [START_REF] Mecê | High-resolution in-vivo human retinal imaging using full-field oct with optical stabilization of axial motion[END_REF] In brief, the FFOCT comprises a light-emitting diode (LED) with central wavelength of 850nm (30nm bandwidth), used as a spatially incoherent illumination source, giving a theoretical axial resolution of approximately 8 µm in water. The illumination beam is split into reference and sample arms by a 50:50 cubic beam splitter (BS). For the reference arm, a microscope objective is used with a silicon mirror placed at the focal plane of the objective. For the sample arm, the subject's eye was aligned along the optical axis. The back-scattered photons from both arms are recombined by the same BS and focused onto a high-speed CMOS camera (Q-2A750-Hm/CXP-6, Adimec) for FFOCT imaging. The size of an individual pixel of the FFOCT camera corresponds to 1µm in the retinal plane. The FFOCT coherence gate geometry was shaped to fit the retinal curvature and dispersion was compensated using a 20mm N-BAK1 optical window in the sample arm. [START_REF] Mecê | Coherence gate shaping for wide field high-resolution in vivo retinal imaging with full-field oct[END_REF] The FFOCT system is coupled through a dichroic mirror with a spectral-domain (SD) OCT system, with central wavelength of 930nm (60nm bandwidth). The SD-OCT was used to track and correct for eye axial motion by driving at 50Hz loop rate a fast voice-coil translation stage on which the FFOCT reference arm is mounted (see [START_REF] Mecê | High-resolution in-vivo human retinal imaging using full-field oct with optical stabilization of axial motion[END_REF] for further details). The correction in real-time of axial eye motion enables the FFOCT to acquire en-face images at a given depth in the retina. The SD-OCT has an A-scan rate of 36kHz. We chose to scan over a line of 2 o FOV at 140 Hz, providing a good trade-off between acquisition speed and SNR. [START_REF] Mecê | High-resolution in-vivo human retinal imaging using full-field oct with optical stabilization of axial motion[END_REF] For both FFOCT and SD-OCT channels, the beam diameter at the pupil is 7.5mm.

Adaptive-Glasses Wavefront Sensorless Approach

Since the phase modulation of FFOCT is performed almost randomly through the axial eye motion, [START_REF] Mecê | High-resolution in-vivo human retinal imaging using full-field oct with optical stabilization of axial motion[END_REF] the brightness of FFOCT retinal images varies from one image to another, making the FFOCT signal an unreliable merit function for wavefront correction. We therefore use the brightness of the SD-OCT B-scan as a surrogate for the FFOCT SNR optimization. Once these two wavelengths are close, correcting aberrations using the brightness of SD-OCT as a merit function is also suitable for FFOCT. B-Scans were averaged in the lateral dimension, and used for three purposes: 1) tracking the eye axial motion for correction in real-time, 2) guiding positioning of the FFOCT coherence gate at the layer of interest, and 3) as a merit function for the wavefront optimization. The merit function can be applied for any retinal layer of interest to automatically adjust the MAL shape to favor imaging in that particular layer. The MAL (Dynamic Optics srl, Italy) is composed of 18 actuators and can correct up to the fourth Zernike order. [START_REF] Verstraete | Wavefront sensorless adaptive optics oct with the done algorithm for in vivo human retinal imaging[END_REF] It has a transmission of 94% in the near infrared and a response time of less than 2ms. The MAL is positioned 2-3 cm in front of the subject's cornea, i.e. without strict pupil conjugation. It has a 10mm diameter, meaning that it is large enough to avoid vignetting and resolution loss which would occur with a smaller numerical aperture. Its diameter and position favor anisoplanatic correction through wavefront sensorless optimization similar to a pupil-conjugated scheme. [START_REF] Mertz | Field of view advantage of conjugate adaptive optics in microscopy applications[END_REF][START_REF] Pozzi | Plug-and-play adaptive optics for commercial laser scanning fluorescence microscopes based on an adaptive lens[END_REF] To perform the optimization, we used the DONE algorithm 17 which had three major advantages for the problem we wished to solve. First, it does not require evaluation of the merit function gradient, hence mitigates the MAL hysteresis by limiting the number of times that voltages are updated. Second, the DONE algorithm is very stable due to the use of regularization and is therefore well suited for noisy experimental data. Finally, as we use the actuator voltages as input degree of freedom, no calibration step is necessary since no modal decomposition is used. The DONE algorithm models the unknown merit function using a Random Fourier Expansion (RFE)

g(x) = D k=1 c k cos(ω T k x + b k
) fit to the experimental data using a least square approach. It iteratively finds a minimum of the merit function on a compact set X ⊆ [V min , V max ] d representing each actuator voltage (where d = 18 is the number of actuators) by updating the RFE at each new measurement, and using this RFE as a surrogate of the merit function for optimization. The number of iterations was set to 50, for a total of 1s optimization duration. Further details on the hyperparameters and the optimization steps can be found elsewhere. [START_REF] Scholler | Adaptive-glasses time-domain ffoct for wide-field high-resolution retinal imaging with increased snr[END_REF]

Imaging Acquisition and Processing

Retinal imaging was performed on three healthy near-emmetropic subjects (age range 25-31). Research procedures followed the tenets of the Declaration of Helsinki. Informed consent was obtained from subjects after the nature and possible outcomes of the study were explained. The study was authorized by the appropriate ethics review boards (CPP and ANSM -IDRCB number: 2019-A00942-55). Each subject was seated in front of the system and stabilized with a chin and forehead rest and asked to fixate a target. To maximize pupil diameter, image acquisition was performed in a dark room. Images were acquired just after wavefront optimization in parallel with real-time correction of axial eye motion. As the DONE algorithm has a high robustness to noise, subjects could blink during the wavefront optimization routine. Image sequences were composed of 150 frames acquired at 300 Hz. During image acquisition, the total power entering the eye from the FFOCT illumination source and the SD-OCT scanning source were respectively 1.3 mW (for the 0.5 s of image acquisition) and 0.25 mW (continuous scanning), which are below the ocular safety limits established by the ISO standards for group 1 devices. Since the phase of FFOCT was randomly modulated by the residual tracking error of axial motion, and to eliminate the incoherent terms, we adopted a 2-phase demodulation, [START_REF] Mecê | High-resolution in-vivo human retinal imaging using full-field oct with optical stabilization of axial motion[END_REF] consisting of subtracting one image from the next and taking the absolute value. Next, images with a very low or absent signal, mainly due to an insufficient phase shift between consecutive images were automatically detected, and then excluded before registration and averaging. We used the ImageJ plugin MosaicJ [START_REF] Thévenaz | User-friendly semiautomated assembly of accurate image mosaics in microscopy[END_REF] to stitch together five images into a 12 o × 12 o FOV. A photoreceptor density map was computed using a fully automated algorithm based on modal spacing as described in. [START_REF] Cooper | Fully automated estimation of spacing and density for retinal mosaics[END_REF] Retinal fundus images of all subjects were also acquired with Spectralis scanning-laser ophtalmoscope (SLO -Heidelberg Engineering, Germany).

RESULTS

Increasing SNR with the Adaptive-Glasses Approach

Figure 2 shows the capacity of the adaptive-glasses approach to correct for ocular aberrations and, thus, increase the SNR at the same time for the SD-OCT and FFOCT when imaging the retina in-vivo. An example of the wavefront optimization time series achieved with the DONE algorithm is presented in Fig. 2(a). Here, the brightness from the cone outer segment tips (COST) was used as a merit function. An overall increase of the SD-OCT brightness can be noticed, with a maximum increase happening at the COST layer (black arrow in Fig. 2(b)), outlining that the focal plane position was optimized for this given layer. Figure 2(c,d) present retinal images acquired with FFOCT from the same subject, at 4 o temporal, before and after correcting ocular aberrations with the adaptive glasses approach. Different amounts of averaging (N = 1, 10, 40, 100 images) are presented. Owing to the wavefront correction, a considerable increase of SNR can be obtained. Figure 2(e) presents the Spectral signal-to-noise ration (SSNR) as a function of the amount of averaged images with and without wavefront correction. An overall increase of 6dB of SSNR was obtained. An equivalent SSNR is obtained for N=40 without correction and N=1 with correction. The SSNR was computed using the power spectral density (PSD) radial average data, highlighted in Fig. 2(f,g), as a ratio of the photoreceptor mosaic spatial frequency (green pale column) and noise spatial frequency (400 cycles/mm -red pale column).

The PSD data in Fig. 2(f,g) gives interesting information about FFOCT for retinal imaging. First, note that ocular aberrations do not behave as simply low-pass spatial filters as for conventional imaging systems, nevertheless aberrations affect the SNR almost equally for all spatial frequencies. Second, even without correcting for ocular aberrations, it is possible to detect the photoreceptor mosaic spatial frequency on a single non-averaged image (N=1), which is an important information to compute photoreceptor-based biomarkers such as spacing and density. Finally, using a simple strategy such as image averaging, it is possible to image photoreceptors without any aberration correction. However, this comes with a cost for the temporal resolution, making it hard to fully explore the high acquisition rate of the FFOCT, i.e. 300Hz, to monitor individual photoreceptors and inner-cellular dynamics. Owing to the adaptive-glasses approach, individual photoreceptors can be monitored over time with a 6ms resolution, while photoreceptor-based biomarkers can be robustly computed from the spatial frequency value.

Simultaneous High-Resolution Cross-Section and En-Face Views of the Retina in Real-Time

During each imaging session, SD-OCT B-scans are displayed in real-time. Thanks to the adaptive-glasses approach, cones formed characteristic, bold, hyper-reflective dots at the level of the inner/outer segment (IS/OS) and COST, as presented in Fig. 3(a) for a single non-averaged B-scan. Using the SD-OCT and the axial motion stabilization, one can precisely position the FFOCT coherence gate at the retinal layer of interest and explore the high axial resolution of FFOCT (i.e. 8µm) to obtain, in real-time, en-face images from the IS/OS and COST with a 5 o × 5 o FOV, as it is shown in Fig. 3(b-d). Images were acquired as close as 1 o temporal to the fovea. Photoreceptor mosaic from IS/OS and COST appeared similar, but COST signal was typically smaller than IS/OS, consistent with previous studies using AO-OCT. [START_REF] Reumueller | Three-dimensional composition of the photoreceptor cone layers in healthy eyes using adaptive-optics optical coherence tomography (ao-oct)[END_REF][START_REF] Reumueller | Three-dimensional assessment of para-and perifoveal photoreceptor densities and the impact of meridians and age in healthy eyes with adaptive-optics optical coherence tomography (ao-oct)[END_REF] Although similar, the mosaics from IS/OS and COST are not completely identical as it is shown in the false color composite image Fig. 3(e), where IS/OS coded in red, and COST in green. Signal overlap (yellow) is dominant. Green and red signal might be linked to difference of cone reflectivity, alignment, cone outer segment tip renewal and the better depiction of cone signals at the COST layer.

Depth-Resolved Wavefront Optimization for Inner Retina Imaging

Although the FFOCT coherence gate can be precisely positioned at the retinal layer of interest, a mismatch of the coherence gate and focal plane positions (defocus aberration) produces low SNR FFOCT images. At the fullaperture, e.g. for a 7-mm pupil diameter, the depth of focus is approximately ten times thinner than the retina, making focus position an essential step. [START_REF] Mecê | Optical incoherence tomography: a method to generate tomographic retinal cross-sections with non-interferometric adaptive optics ophthalmoscopes[END_REF] If the merit function does not take into account the retinal layer of interest, the wavefront optimization is biased to the photoreceptor layer, [START_REF] Camino | Depth-resolved optimization of a real-time sensorless adaptive optics optical coherence tomography[END_REF] preventing high SNR FFOCT images of the inner retina. To mitigate this limitation, we implemented a depth-resolved wavefront optimization, where only the brightness of the layer of interest is considered, optimizing the focal plane position to the coherence gate position. Owing to this procedure, we were able to image photoreceptor IS/OS (Fig. 4(a)) and nerve fiber layer (NFL -Fig. 4(b)) and at the same retinal region with ease, here at 8 o nasal. Green arrows, in SD-OCT B-scans, indicate the retinal layer selected as a merit function for the wavefront optimization. Owing to the high axial resolution of the FFOCT, images of NFL at different depths can be obtained, as it is shown in Fig. 4(b). Yellow and red arrows show vessels being covered by the NFL as the coherence gate position moves towards the inner retina. Blue arrow points to a vessel, where it is possible to identify the vessel wall (image on the center) and the surface reflection (image on the right). One interesting retinal feature revealed by FFOCT is micron-sized hyper-reflective spots along the axon bundles (see yellow dashed box for a magnified image). These spots were already previously visible with confocal AO-SLO. [START_REF] Beykin | Discovery and clinical translation of novel glaucoma biomarkers[END_REF] Their micrometer dimension is consistent with axonal varicosities. [START_REF] Beykin | Discovery and clinical translation of novel glaucoma biomarkers[END_REF][START_REF] Wang | Varicosities of intraretinal ganglion cell axons in human and nonhuman primates[END_REF] Moreover, previous studies, using AO-SLO, had shown that the reflectivity of individual spots varies dramatically over time, potentially being indicative of axonal transport. [START_REF] Beykin | Discovery and clinical translation of novel glaucoma biomarkers[END_REF] This phenomenon can also be observed in the FFOCT, but with a significantly larger FOV, higher acquisition rate and with an one order of magnitude better axial resolution. Another interesting feature observed with FFOCT is the inner limiting membrane (ILM), as it is shown in Fig. 5. As we move from NFL towards ILM, horizontal nerve fibers give place to vertical "fiber-like" structures that might be collagen fibers that can be found in young subjects in the vitreous body close to the ILM. The PSD from the dashed white boxes also reveal the vertical "fiber-like" structure, as the vertical frequency signature from NFL becomes horizontal when close to the ILM.

Allying 3D High Resolution with Wide Field-of-View

One important hurdle of AO-OCT for clinical translation is the challenge of allying high-spatial resolution with a wide FOV, which is beneficial for clinical applications. Indeed, the dense sampling of the scan required comes with a cost of low acquisition rate and image distortion due to eye motion. Moreover, aberration correction using AO is limited by the eye's isoplanatic patch to a small 2 o × 2 o FOV. The combination of FFOCT and the adaptive-glasses approach opens a new avenue to wide FOV high-resolution retinal imaging in a compact imaging system (system footprint: 50cm × 30cm). Figure 3(b) presents a 5 o × 5 o FOV image obtained in a single shot (0.5s acquisition duration), as close as 1 o from the foveal center, where photoreceptors can be resolved over almost the entire FOV (limited only by the retinal curvature). Zoomed areas highlight that no apparent anisoplanatic effect in terms of spatial resolution is observed.

The wide FOV obtained in a single shot facilitates important tasks in the clinical environment to diagnose retinal disorders at early stages, such as image montaging and the computation of photoreceptor-based biomarkers. [START_REF] Litts | Photoreceptor-based biomarkers in aoslo retinal imaging[END_REF] Figure 6 shows two wide FOV montages from two different subjects, where the asterisk indicates the foveal center. Photoreceptor density is color coded and was consistent with the literature 28 except within 0.5 o of the fovea, where photoreceptors were not resolved but were nevertheless automatically detected using the proposed method by. [START_REF] Cooper | Fully automated estimation of spacing and density for retinal mosaics[END_REF] The montage of

CONCLUSION

We proposed the adaptive glasses approach as a wavefront sensorless AO method favoring small footprint and low optical complexity. We successfully applied this approach to in-vivo retinal imaging using FFOCT to increase SNR that were previously affected by ocular aberrations. Owing to the combination of the adaptive-glasses approach with the FFOCT, we achieved 3D high-resolution retinal image over a 5 o × 5 o FOV at 300Hz in a single shot, without major anisoplanatism influence. To the best of our knowledge, this is the first demonstration of AO successfully coupled to time-domain FFOCT for retinal imaging. We demonstrated that the performance achieved facilitate important tasks in the clinical environment such as image montaging and the computation of photoreceptor-based biomarkers. Photoreceptors were resolved as close as 0.5 o from the foveal center. We also showed that different retinal layers can be imaged, such as COST, IS/OS, NFL, ILM. Although we mainly illustrated the proposed approach for dual-channel SD-OCT and FFOCT retinal imaging, it can be adapted to other imaging modalities and samples. Finally, the combination of the adaptive glasses approach with FFOCT tackles those challenges that have so far prevented transfer of AO-OCT technology from bench to clinics.

Figure 1 .

 1 Figure 1. Optical (a) and mechanical (b) drawing outlining the low optical complexity and reduced footprint of the custom-built FFOCT for retinal imaging. (c) Prototype installed at the Quinze-Vingts National Ophthalmology Hospital.

Figure 2 .

 2 Figure 2. (a) Values of the merit function during wavefront optimization, for a total of 1 second duration. (b) Lateral average of an SD-OCT B-scan highlighting the increased signal after aberration correction. Black arrow points to the retinal layer used for wavefront optimization, i.e. COST. (c,d) FFOCT images of COST layer for different amounts of averaging (N = 1, 10, 40, 100) without (c) and with (d) aberrations correction using the adaptive-glasses approach. (e) Spectral SNR (SSNR) as a function of the number of averaged images with and without correcting for ocular aberrations. (f,g) PSD of images shown in (c) and (d) outlining the gain of SNR and how aberrations affect retinal images acquired with FFOCT. Green and red pale column are the spatial frequencies used to compute the SSNR, the former being the photoreceptor mosaic spatial frequency. Note that dB values were computed from amplitude (not intensity) signal of the FFOCT. Scale bar: 50µm

22

 22

Figure 3 .

 3 Figure 3. (a) Single non-averaged image of SD-OCT B-scan after correction of ocular aberrations using the adaptiveglasses approach, where individual photoreceptors from IS/OS and COST can be resolved. (b) 5 o × 5 o FOV en-face FFOCT image acquired simultaneously to (a) at COST layer. Individual photoreceptors can be resolved without any apparent anisoplanetism in terms of spatial resolution. (c,d) FFOCT image acquired at same retinal location at the IS/OS and COST layers respectively. (d) is a magnified image from (b) (yellow box). (e) False color composite image of images (c) and (d) outlining the similarities and differences between the IS/OS (red) and COST (green) mosaics.

Figure 4 .

 4 Figure 4. (a,b) SD-OCT retinal cross-section and FF-OCT en-face image acquired after optimizing the wavefront correction for the IS/OS and NFL layers respectively. Green and yellow dashed boxes indicate the magnified images location from the IS/OS and NFL level respectively. Individual photoreceptors and putative axonal varicosities (inside red circles) can be observed. Green arrows point to the retinal layer selected as a merit function for the wavefront optimization. Yellow and red arrows show vessels being covered by the NFL as the coherence gate position moves towards the inner retina. Blue arrow points to a vessel, where it is possible to identify the vessel wall (image on the center) and the surface reflection (image on the right). Scale bar: 100µm.

Figure 5 .

 5 Figure 5. (a) SD-OCT B-scan where dashed lines indicate the depth position where the en-face FFOCT images (b) were acquired. White dashed boxes indicate the region of the en-face image where the PSD was computed (bottom right of each image). Scale bar: 200µm.

  Fig 6(a) is composed of 5 images acquired at different retinal locations at COST layer, ranging from 11 o nasal to 7 o temporal, for a total 18 o × 5 o FOV (see Fig 6(b) for a fundus image acquired with the Spectralis SLO). The montage of Fig 6(d) is composed of 6 images acquired at different retinal locations at IS/OS layer (the foveal umbo is visible), ranging from 11 o nasal to 5 o temporal, and from 5 o superior to 6 o inferior in the central portion (see Fig 6(d) for a fundus image acquired with the Spectralis SLO). Magnified images and their respective PSD are also presented. The total time necessary to obtain such images (including subject alignment, image acquisition and processing) is about 20min. For comparison, an instrument with a 2 o × 2 o FOV (i.e.the typical size of the eye's isoplanatic patch) would need to stitch around 60 images to obtain the same image area with an image processing time multiplied by at least a factor of 10.[START_REF] Laslandes | Increasing the field of view of adaptive optics scanning laser ophthalmoscopy[END_REF][START_REF] Chui | Adaptive-optics imaging of human cone photoreceptor distribution[END_REF]

Figure 6 .

 6 Figure 6. (a) FFOCT image montage from Subject 1 at COST level, with a total 18 o × 5 o FOV, composed of five images stitched together. The color map and code represent the computed photoreceptor density.(b,c) Fundus image acquired with Spectralis SLO from Subjects 1 and 2 respectively outlining the retinal location where the FFOCT image montages were acquired. (d) FFOCT image montage from Subject 2 at the IS/OS level composed of six images stitched together ranging from 11 o nasal to 5 o temporal, and from 5 o superior to 6 o inferior in the central portion. Magnified images of 0.7 o × 0.7 o , chosen to be representative of different eccentricities, and their respective Fourier transforms are also shown. Scale bar for montages: 1mm. Scale bar for magnified images: 50µm.

ACKNOWLEDGMENTS

We thank Michel Paques and José Sahel for their clinical expertise and support. We also thank Yao Cai and Mathias Fink for technical support. HELMHOLTZ grant, European Research Council (ERC) (610110), IHU FOReSIGHT [ANR-18-IAHU-0001], Region Ile-De-France fund SESAME 4D-EYE [EX047007], French state fund CARNOT VOIR ET ENTENDRE [x16-CARN 0029-01], Fondation Visio grant, CNRS pre-maturation grant.


Laudin Molina
email: laudin.molina@imt-atlantique.fr

Élisa Blanchard
email: elisa.blanchard@imt-atlantique.fr

Christophe Couturier
email: christophe.couturier@imt-atlantique.fr

Jean-Marie Bonnin
email: jm.bonnin@imt-atlantique.fr

Be aware of the capture effect: a measure of its contribution to BLE advertisements reception

Keywords: BLE, BLE advertisement, capture effect, cochannel interference, collisions

The Bluetooth Low Energy (BLE) networks use three channels to broadcast advertisements. These advertisements and other BLE frames are subject to collisions. The collision probability increases as the number of devices increases. Nonetheless, because of the capture effect, receivers may correctly decode some of the frames involved in a collision. Recent studies proposed models and simulations for the BLE discovery process, showing the impact of the advertisement collisions as well as the importance of an appropriate selection of the parameters related to the discovery process. The impact of the capture effect in these studies is unclear. Here we report the impact of the capture effect on the BLE advertisements. In particular, we show that the capture effect systematically increases the advertisement reception rate. We establish upper and lower bounds to quantify the contribution of the capture effect to the packet delivery ratio in dense scenarios. We make measurements in a controlled environment (a Faraday box) to show the presence of the capture effect in networks with 2 to 14 advertisers. Empirical results show that for 14 devices the capture effect increases the advertisement delivery rate by 2.95 % on average, with a peak of 7.8 %. Using simulations to recreate dense scenarios (up to 1000 advertisers) we show that the capture effect can increase the packet delivery ratio by up to 25 %. Our results have implications in the performance analysis of the discovery process and provide insights for the design of BLE applications and protocols that leverage on BLE advertisements.

I. INTRODUCTION

BLE is a popular network technology that is widely deployed in consumer devices. For example, it is present in smartphones, wearable, and home appliances. BLE is inexpensive, lightweight, and energy-efficient. It can provide networking features such as mesh architecture and connectivity to the Internet. Among the applications and use cases we can include wireless connectivity, asset tracking, and location services. In the context of the COVID-19 pandemic many applications leverage BLE proximity capabilities for contacttracing purposes. All this may lead to scenarios with numerous BLE devices. For instance, a shopping mall with location services, where the different stores and departments advertise their products, and at the same time, visiting pedestrians carry a contact-tracing application.

Advertisements are at the core of BLE. BLE relies on BLE advertisements for device and service discovery as well as for non-connected features, such as direction finding and opportunistic communications.

Like other wireless technologies, BLE suffers from cochannel interference that causes advertisement collisions. During a collision, the receiver may lose all colliding advertisements or decode one of them if there is a capture effect. One drawback of BLE is its lack of an evolved mechanism for collision avoidance. Thus, collisions are responsible for slow and incomplete discoveries. A lot of works [START_REF] Hernández-Solana | Proposal and Evaluation of BLE Discovery Process Based on New Features of Bluetooth 5.0[END_REF]- [START_REF] Renzler | Improving the efficiency and responsiveness of smart objects using adaptive BLE device discovery[END_REF] (section III) have already studied the BLE discovery, with the focus mainly on the trade-off between discovery time, advertisement frequency, scan duration, and scan frequency. These works usually rely on simulations or mathematical models that assume that the receiver loses all advertisements in a collision, thus minimizing the capture effect. Other works [START_REF] Landsiedel | Chaos: Versatile and efficient all-to-all data sharing and innetwork processing at scale[END_REF], [START_REF] Roest | Enabling the Chaos Networking Primitive on Bluetooth LE[END_REF] exploit the capture effect in context of BLE without measuring the influence of the capture effect.

In this paper we address the question of what is the impact of the capture effect on the advertisements?. The answer to this question will allow more accurate simulation and mathematical models.

We describe an intuitive off-line strategy to quantify the impact of the capture effect (section IV). Then, using an empirical evaluation (section V), with up to 14 advertisers in a controlled environment, we observe that the capture effect systematically increases the advertisement packet delivery ratio (PDR). Empirical results with 14 devices show an average increase of 2.95 %, with a peak of 7.8 %. Finally, using simulations at a larger scale (section VI) we describe the potential maximal PDR gain due to the capture effect and establish lower and upper bounds for the expected advertisement PDR.

II. BACKGROUND A. BLE Advertisements

BLE is a short-range communication system that supports connection-oriented and connectionless communications [START_REF]Bluetooth Core Specifications 5.2, en-US[END_REF]. BLE operates in the 2.4 GHz ISM band. There are 40 channels, with channels 37, 38 and 39 dedicated to advertisements.

Advertisements are at the core of BLE. Advertisements enable network and service discovery, they also allow the transmission of data periodically. For example, Beacons (e.g., Apple's iBeacon and Google's Eddystone) use advertisements to periodically broadcast data. Devices transmit advertisements during transmission events, where frames are broadcast on the advertisement channels (fig. 1). Equation [START_REF] Hernández-Solana | Proposal and Evaluation of BLE Discovery Process Based on New Features of Bluetooth 5.0[END_REF] gives the time between two consecutive advertisement events, where advInterval is a configurable value in the range [20 ms, 10 485.759 375 ms] in steps of 0.625 ms. advDelay is a pseudo-random value in the range [0 ms, 10 ms]. This random advDelay perturbs the time between advertising events and reduces the chances for collisions. Note that BLE advertising does not implement any recovery procedure.

T advEvent = advInterval + advDelay (1)
In Bluetooth 5.2 [START_REF]Bluetooth Core Specifications 5.2, en-US[END_REF] there are two classes of advertisements: legacy and extended. Legacy advertisements use a single frame that is broadcast on the advertising channels. Legacy advertising frames have a maximum length of 47 B, for a maximum advertisement data length of 31 B. Extended advertisement increases the payload limit to 254 B and uses two frames. The advertiser transmits a first frame on the advertisement channels. This first advertisement points to a second frame transmitted in one of the other 37 channels. Additionally, there are different types of advertisements depending on the advertisement and the BLE device (directed or not, connectable or not, scannable or not). In this work we focus on legacy non-connected non-scannable advertisements named ADV NONCONN IND. We are interested in the ADV NONCONN IND because the receiver does not generate traffic and only uses the advertisement channels.

Advertisements use a Gaussian Frequency Shift Keying (GFSK) modulation at 1 Msym/s, therefore 47 B advertisements use 376 µs for wireless transmission.

While advertiser devices broadcast advertisement frames the scanners periodically monitor the advertising channels. BLE defines two parameters: scanW indow is the time spent listening to a given channel; and scanInterval is the duration between the start of two consecutive scan windows. For energy efficiency considerations, devices can return to sleep mode between scanning windows. Note that when scanInterval = scanW indow the device scans continuously. This is the configuration that we use for our experiments.

B. Capture Effect

The capture effect is the ability of certain radios to correctly decode a frame in presence of interference from other transmitters at the same carrier frequency [START_REF] Whitehouse | Exploiting the capture effect for collision detection and recovery[END_REF]. If one signal carrier is higher than the sum of the interfering signals, the receiver will decode the stronger signal with a high probability [START_REF] Gezer | Capture effect in IEEE 802.15.4 networks: Modelling and experimentation[END_REF]. This difference between signals, also called capture ratio [START_REF] Roberts | ALOHA packet system with and without slots and capture[END_REF], depends on the transmitter hardware and the signal strength level, and can be below 1 dB [START_REF] Son | Experimental study of concurrent transmission in wireless sensor networks[END_REF].

Whitehouse, Woo, Jiang, et al. [START_REF] Whitehouse | Exploiting the capture effect for collision detection and recovery[END_REF] identifies two types of collisions: stronger-first and stronger-last. In stronger-first collisions, the packet with the stronger signal comes first, the receiver synchronizes with the stronger packet and the weaker signal does not interfere. In stronger-last collisions, the packet with the strong signal comes last, the receiver first synchronizes with the weak signal and then fails to complete the reception because the stronger signal captures the channel and corrupts the ongoing reception. With the stronger-last collision, the receiver likely loses both packets.

Accordingly, the analysis presented in this paper assumes that when two or more advertisements overlap two scenarios may happen: Total Collision in which the scanner loses all advertisements or Capture Effect in which the scanner decodes one advertisement. The simulations and emulations presented in this paper follow an optimistic approach for the Capture Effect and assume that the scanner always decodes the first arriving frame. This optimistic, yet realistic [START_REF] Kosunalp | Experimental Study of Capture Effect for Medium Access Control with ALOHA[END_REF], approach is reasonable to draw an upper bound. Total Collision results in the worst possible PDR for a given scenario, i.e., a lower bound.

III. RELATED WORK

There is a significant amount of literature available on the performance of BLE discovery process. Likewise, few authors have studied the capture effect and BLE but mainly as part of concurrent transmissions [START_REF] Nahas | Concurrent Transmissions for Multi-Hop Bluetooth 5[END_REF]. However, the impact of the capture effect on the advertisements in the context of regular, non-concurrent, BLE networks remains understudied.

The Bluetooth specification [START_REF]Bluetooth Core Specifications 5.2, en-US[END_REF] gives guidelines for the transmission of the BLE advertisements, which are a core part of the BLE discovery process. There is extensive work done around the BLE discovery process [START_REF] Hernández-Solana | Proposal and Evaluation of BLE Discovery Process Based on New Features of Bluetooth 5.0[END_REF]- [START_REF] Renzler | Improving the efficiency and responsiveness of smart objects using adaptive BLE device discovery[END_REF], however, these works neglect the capture effect. Hernández-Solana, Perez-Diaz-de-Cerio, Valdovinos, et al. [START_REF] Hernández-Solana | Proposal and Evaluation of BLE Discovery Process Based on New Features of Bluetooth 5.0[END_REF] experimentally model the behavior of BLE scannable undirected advertising events. Then, the authors develop a mathematical model to obtain the measure of the potential capacity. Authors use the "nondetection probability due to collisions" to derive a model to evaluate the performance of the BLE discovery process. In particular, to estimate the probability to detect all devices within a given delay as well as to estimate the average time required to discover all the devices. Both, the analytical and the simulation model, assume that any overlap between two packets results in the receiver losing both packets. In the case of non-scannable advertisers, neglecting the capture effect would likely result in a lower bound. This work lacks of an estimation for the potential results on real scenarios.

Network flooding techniques take advantage of the capture effect [START_REF] Roest | Enabling the Chaos Networking Primitive on Bluetooth LE[END_REF], [START_REF] Nahas | Concurrent Transmissions for Multi-Hop Bluetooth 5[END_REF] and allow different devices to transmit simultaneously. Roest [START_REF] Roest | Enabling the Chaos Networking Primitive on Bluetooth LE[END_REF] evaluates the capture effect in the context of Chaos, "a communication primitive that allows all-to-all communication" [START_REF] Landsiedel | Chaos: Versatile and efficient all-to-all data sharing and innetwork processing at scale[END_REF]. Chaos leverage the time synchronization and the capture effect to perform concurrent transmission over the BLE stack. The authors focus the analysis of the capture effect on scenarios where advertisers transmit simultaneously.

In this context, the empirical results show that simultaneous advertisements require a delta signal-to-noise ratio (SNR) of more than 7 dB to achieve a capture effect in over 90 % of the collisions. However, the authors do not detail the capture effect for the regular BLE advertisements, where nodes use a random delay (advDelay) to avoid simultaneous transmission. Al Nahas, Duquennoy, and Landsiedel [START_REF] Nahas | Concurrent Transmissions for Multi-Hop Bluetooth 5[END_REF] and Roest [START_REF] Roest | Enabling the Chaos Networking Primitive on Bluetooth LE[END_REF] evaluate different combinations of encoding, power transmission and time delta and conclude that concurrent transmissions with the same data are feasible regardless of the BLE mode. For the particular case of BLE advertisements encoded at 1 Mbit/s, the capture success for power delta below 2 dB is 0 and reaches 50 % when the power delta increases to 4 dB [START_REF] Nahas | Concurrent Transmissions for Multi-Hop Bluetooth 5[END_REF]. Because of the focus on network flooding using concurrent transmissions the evaluations assume almost complete overlap of packets with the same data, for instance, Al Nahas, Duquennoy, and Landsiedel [START_REF] Nahas | Concurrent Transmissions for Multi-Hop Bluetooth 5[END_REF] limit the evaluation up to a time delta of 1.75 µs. This is not the case for regular BLE network, where there is no restriction in the content or packet overlap.

In the context of wireless sensor networks (WSNs) Kosunalp, Mitchell, Grace, et al. [START_REF] Kosunalp | Experimental Study of Capture Effect for Medium Access Control with ALOHA[END_REF] developed a model for pure ALOHA networks that takes into account the impact of the capture effect. The model shows the increase in the throughput of pure ALOHA thanks to the capture effect. The experimental evaluation is based on IEEE 802.15.4 devices without the clear channel assessment (CCA) and back-off procedures. In the model, the authors defined a capture coefficient, which is a function of the packet overlap and the length of the packet in bytes.

We focus on the impact of the capture effect on the BLE discovery process, specifically the effects on the BLE advertisement's PDR. Different from the previous works, we focus on the regular BLE advertisements transmitted by a different number of advertisers, without explicit synchronization. Because of the number of configurations that affect the capture effect in the BLE networks, we aim to draw upper and lower bounds to quantify the PDR gains due to the capture effect.

IV. QUANTIFYING THE CAPTURE EFFECT

To measure the impact of the capture effect we compare empirical results with emulations of Total Collision and Capture Effect. The comparisons use the advertisement's PDR as the performance metric.

We empirically measured the PDR on 14 different experiments, each with a given number of advertisers. These experiments happened in a controlled and well-known scenario. Using the data from these experiments we emulated two scenarios: Total Collision and Capture Effect. The difference between the empirical results and the emulation for Total Collision is the PDR gain due to the capture effect. Analogously, the difference between the empirical results and the emulation for Capture Effect is the potential maximal PDR gain.

The emulations take the advertisement reception sequence (section IV-A) for each experiment and estimate the PDR for the scenarios Total Collision and Capture Effect. The emulations begin by identifying, in the reception sequence, the advertisements that overlap. Note that the time stamp resolution is 31 µs, thus we consider that two advertisements, A and B, overlap if the end of A and the beginning of B are within 62 µs. As discussed in section II-B, in Total Collision the scanner misses all the advertisements in a collision, in Capture Effect the scanner always decodes the first of the advertisements involved in a collision.

A. Advertisements Reception Sequence

We rely on a BLE sniffer to reconstruct the reception sequence. This is because we cannot record the transmission sequence at the transmitter due to hardware limitations.

To complete the advertisements missed by the sniffer due to collisions the advertisers piggyback the time stamp of the six previous transmissions. Then, for every missing advertisement we estimate the reception time stamp, trx i , as

trx i = t rx j - (t tx j -t tx i ).
Where t tx i is the transmission time stamp for the missing advertisement and t tx j is the transmission time stamp of a subsequent advertisement correctly decoded by the sniffer.

B. Experimental setup

We investigated the effects of the interference between BLE advertisers in a controlled and isolated environment. We used a Faraday box that measured 13 x 20 x 28 cm. It provided isolation of 90 dB at 3 GHz. We did not register any external BLE nor Wi-Fi interference inside the box. Notice that the Faraday box did not prevent internal signal reflections.

The materials were: 1 CC2540 USB dongle as BLE sniffer, 8 Texas Instrument CC2640R2F wireless MCU Launch-Pad™ [START_REF]LAUNCHXL-CC2640R2 SimpleLink™ Bluetooth® Low Energy CC2640R2F wireless MCU LaunchPad™ development kit -TI.com[END_REF] development kits (CC2640) and 7 Nordic Semiconductor nRF52840 Development Kits [START_REF]The nRF52840 Bluetooth LE, Bluetooth mesh, Thread and Zigbee development kit for the nRF52811 and nRF52840 SoCs[END_REF] (nRF52). These two models have the antenna printed on the circuit board. One of the CC2640 devices operated as a scanner and the others as advertisers. Each device always operated in the same mode, i.e., advertiser or scanner. The sniffer software was the SmartRF™ Packet Sniffer, from Texas Instruments. The firmware of the BLE devices allowed keeping track of the advertisements transmitted by each of the advertisers and received by the scanner. The BLE scanner used a modified version of the firmware ble5 simple central cc2640r2lp app, version 3.20.0.21, provided by Texas Instrument1 . The BLE CC2640 advertisers used a modified version of the firmware ble5 simple broadcaster cc2640 app, provided by Texas Instrument. The nRF52 advertisers used a modified version of the firmware ble app beacon pca10056 s140 provided by Nordic Semiconductor.

Table I summarizes the BLE parameters used in the experiments.

C. Platform Calibration

Our goal is to measure the impact of the capture effect using the PDR. Thus we ensured that collisions are the only possible cause for missing frames. Also, we aimed for controlled and reproducible experiments. This is why we empirically verified that: (1) all devices perform similarly; (2) the position of the devices ensures that the scanner and the sniffer decoded the advertisements with a signal strength above -70 dB, which is the sensitivity threshold [START_REF]Bluetooth Core Specifications 5.2, en-US[END_REF]. We verified each device independently.

Empirical results confirm that all devices perform equally. During the calibration phase the PDR was 100 % for all devices. The receiver signal strength indicator (RSSI) was -27 dBm in all 14 calibration experiments.

V. EMPIRICAL EVALUATION OF THE CAPTURE EFFECT

The empirical evaluation consisted of one BLE sniffer, that allowed us to reconstruct the transmission sequence, one BLE scanner to measure the actual PDR, and 14 BLE advertisers used to generate the advertisements. There were 14 experiments, each with N advertisers, with N ranging between 1 and 14.

Figure 2 presents the average PDR and 95 % confidence interval for the empirical results (circles), emulation Total Collision (crosses), and emulation Capture Effect (triangles). Each experiment trial lasted 600 s and we did 10 trials. Figure 2 shows that the PDR decreases as the number of advertisers increases. The PDR decreases because the collision's probability increases with the number of advertisers.

The PDR corresponding to the empirical results ranges between the PDR of Total Collision and the PDR of Capture effect. In fig. 2, the Empirical Result's curve indicates that all empirical scenarios resulted in a PDR that is consistently lower than the Emulation Capture Effect. This is because the emulation Capture Effect assumes that the receiver always decodes one of the overlapping frames, which is an optimistic approach that provides an upper bound. During the field trials, however, some collisions result in the receiver losing all the overlapping advertisements. The difference between the Empirical Results and the Emulation Total Collision represents the theoretical maximal PDR gain for our test bed.

The PDR obtained empirically is consistently higher than the emulation Total Collision. This is because, in the field trials, a fraction of the collision results in the capture effect, while the emulation Total Collision assumes that the receiver loses all the advertisements involved in a collision. Note that the emulation represents a lower bound, that is, the worst PDR that one can expect for the test bed. For the scenario with two advertisers the average PDR for the Emulation Total Collision and the empirical results are 99.15 % and 99.40 %, respectively, for a PDR increase of 0.25 %. In our test bed the largest impact happens with 14 advertisers, with a maximum increase of 7.8 %. The average average increase for the scenario with 14 advertisers is 2.95 %, where the average PDR for Total Collision and the empirical results are 89.59 % and 92.54 %. As we will discuss in section VI, the network reaches a critical point around 170 advertisers, thus it is reasonable to expect that the difference with Total Collision will consistently increase as the number of advertisers increases, up to that point. Note that the occurrence of capture effect depends on various factors, notably the signal strength difference and the arrival time of the frames. For a detailed discussion about the causes of the capture effect we refer the interested reader to [START_REF] Son | Experimental study of concurrent transmission in wireless sensor networks[END_REF]. Figure 3 shows the impact of the capture effect on the advertisement PDR. The figure summarizes the difference between the empirical results and Emulation A (Total Collision). Results show that the capture effect increased the PDR for all configurations. Although the Box Plots overlap, we observe that with more advertisers the capture effect has a larger impact. The largest impact corresponds to the configuration with 14 advertisers, were one advertiser experienced an increase of 7.8 %. Negative values are because the accuracy of the time stamps is not precise enough. As a consequence, the emulation failed to detect some collisions that are within the measurement error. One way to avoid these negative values is to improve the accuracy, which depends on the manufacturer and hardware specifications. An alternative is to add an error threshold when detecting collisions, however this increases false positives while detecting the collisions. We prefer to limit the false positives and have conservative results.

The gap between the empirical results and emulation B represents the potential PDR gain for a scenario that favors the capture effect. Different from our test bed, in a typical scenario advertisers operate in different conditions (e.g., different distances to the scanner), which favors the capture effect with the consequently PDR gain. Section VI establishes upper and lower bounds for the contribution of the capture effect to the advertisement PDR.

VI. POTENTIAL PDR GAIN

In this section, we discuss the maximal advertisement PDR gain due to the capture effect using two simulation models. We developed an ad-hoc simulator 2 using Python 3.8. For each of the advertisers, the simulator generates an array of advertisements, each advertisement includes time stamps for the beginning and end of the transmission. As shown in fig. 1, the interval between the advertisements of the same advertise (T advEvent) has two components: advInterval, which is constant, and advDelay, which is variable. The simulator randomly selects advDelay from the range [0 ms, 10 ms], with steps of 625 µs. The simulator then checks for collisions by comparing the transmission time stamps.

The simulations model ideal scenarios, without external interference or variations on the radio. One simulation models Total Collision. This simulation results in the worst possible PDR for a given scenario, i.e., a lower bound. A second simulation models Capture Effect. This second simulation provides the best possible PDR for a given scenario, i.e., an upper bound. The simulator considers that the scanner can decode all the advertisements that it receives (i.e., signal strength is above the sensibility level) unless there is a collision. The simulations use the same parameters used in the empirical evaluation (Table I). They include configurations with up to 1000 advertisers. Each simulation lasts 200 s and we did 30 trials for each configuration.

Figure 4 shows the PDR resulting from the two simulations and the two emulations versus the number of advertisers. Squares represent the simulation Total Collision, stars represent the simulation Capture Effect, crosses represent the em- Figure 4 shows that the PDR of the simulations is consistent with the PDR of the emulations. Simulation results are within the 95 % confidence interval of the emulations.

The results of the simulations show that the gap between the Total Collision and Capture Effect increases with the number of advertisers until it reaches a maximum and then decreases until the PDR tends to 0. The maximum difference is 25 %. It occurs with 170 advertisers, where the PDR goes from 24 % to 49 %. That is, the capture effect has the potential to increase the PDR by up to 25 %, when compared to the worst case (Total Collision). Already with 30 advertisements the capture effect has the potential to increase the PDR by 10 %. Note that, as shown in section V, empirically some collisions result in capture effect.

For a scenario to reaches the upper bound denoted by the emulation Capture Effect, the receiver shall always decode one advertisement when there is a collision. One can design a hypothetical scenario by carefully configuring the advertisers so that the received signal strength from the different advertisers is different enough, e.g., the signals differ by about 4 dB [START_REF] Son | Experimental study of concurrent transmission in wireless sensor networks[END_REF]. In addition, the receiver shall continuously search for preambles, even during an ongoing reception. By continuously searching for a preamble, the receiver could resynchronize if a stronger signal comes [START_REF] Whitehouse | Exploiting the capture effect for collision detection and recovery[END_REF].

VII. CONCLUSIONS

In this paper we have presented an evaluation of the impact of the capture effect on the BLE advertisements. We have proposed to use the Capture Effect and Total Collision as the upper and lower bounds for the PDR, respectively. The upper bound assumes an ideal scenario in which all collisions result in capture effect. The lower bound assumes that, during a collision, the receiver loses all advertisements.

The evaluation included empirical and simulation results. The analyzed scenarios have confirmed that the capture effect impacts BLE by systematically increasing the advertisement PDR. In an isolated test bed, where all the devices performed similarly, and with 14 advertisers, the capture effect increased the advertisement PDR by up to 7.83 %, with an average increase of 2.95 %. This effect increases with the number of advertisers until 170 advertisers at which point the potential impact decreases until the PDR tends to zero. The theoretical peak of the gain between Total Collision and Capture Effect is 25 %.

These findings provide data that will allow more accurate simulation and analytical models for the BLE discovery and other BLE procedures, especially in dense scenarios. Furthermore, the results give insights into the scalability of the applications that rely on advertisements (e.g., beacons) as well as the feasibility of technologies that leverage on the capture effect (e.g., concurrent transmission).

As a future work, we plan to extend the test bed to further study characterize the capture effect, both in an isolated environment (e.g., the Faraday box) and in field tests outside the Faraday box. There are two factors to take into consideration for the experiments outside the Faraday box:

(1) the coexistence with other technologies operating in the ISM bands (e.g., Wi-Fi); (2) device positioning. With the new test bed we aim to describe the conditions that cause capture effect in BLE advertisements. For instance, we will study the signal strength and the arrival time of the overlapping advertisements. This will allow us to propose a model for use in simulations. Additionally, understanding the characteristics of capture effect in BLE networks will allow to design algorithms to better deal with collisions, for instance, by adjusting the transmission power to either favor or reduce the capture effect, according to the application needs. Another perspective is the study of undesirable consequences, where, for example, the capture effect may lead to uneven channel access.

Figure 1 .

 1 Figure 1. BLE advertising events and interval between consecutive advertising events.

Figure 2 .

 2 Figure 2. Comparison of the empirical and emulation PDR vs. the number of active advertisers, N . The figure shows the average and 95 %-confidence interval.

Figure 3 .

 3 Figure 3. Box plot with the difference between the PDR of the empirical results and the PDR of the emulation Total Collision.

Figure 4 .

 4 Figure 4. PDR of the simulation results vs. number of active advertisers, N in logarithmic scale. The figure shows the average and the 95 %-confidence interval

Table I PARAMETERS

 I USED IN THE EMPIRICAL EVALUATION.

	Parameter	Value
	scanInterval	10 s
	scanW indow	10 s
	advInterval	100 ms
	Payload size of the BLE advertisements 31 B
	BLE channel	38

2

  Available at https://gitlab.inria.fr/learning-bluetooth/ble simulator

		100
				10 %
	PDR (%)	50		25 %
			Simulation Total Collision
		0	Simulation Capture Effect
			Emulation Total Collision
			Emulation Capture Effect
		10 0	10 1	10 2	10 3
			Number of advertisers (N )

https://dev.ti.com/tirex/explore/node?a=krol.2c 3.20.00.21&node= AJ7WahFdRdIjVx0FM.obdg krol.2c 3.20.00.21

VIII. ACKNOWLEDGMENTS

This work is supported by the Région Bretagne (France), who funded the project Chantier 3.0.