P Ginisty
email: pascal.ginisty@ifts-sls.com

R Girault

J Tosoni

E Dieude-Fauvel

J Olivier

J Vaxelaire

SLUDGE DEWATERING: INFLUENCE OF OPERATING PARAMETERS ON DRYNESS LIMIT DETERMINATION

Keywords: Dryness limit, sludge dewatering, flocculation, filtration-compression cell, drainage, polymer

Dewatering process efficiency, classically assessed by a parameter "dryness limit", is strongly affected by conditioned sludge properties and by operating conditions. The method to measure its parameter is based on a filtration-compression test, which depends significantly on operating conditions. A standard method is under progress in France to develop a better controlled procedure. This paper presents the impact of solids load, pressure and compression time, filter cloth, flocculation conditions, pre-thickening and storage time on the dryness limit for different kinds of sludge. A comparison with industrial devices was also made.

INTRODUCTION

The effectiveness and cost of sludge treatment and disposal operations are strongly affected by the volume to be treated and the solids concentration (or water content). Consequently, thickening and dewatering are significant steps for the total sludge processing train. They both have a real impact on subsequent operations (storage, pumping, transportation and handling). Sorensen [START_REF] Sorensen | Filtration of activated sludge[END_REF] reports that 30-50% of annual treatment operating costs relate to the sludge dewatering stage. Sludge conditioning generally enhances the removal of water during the thickening and dewatering process. Sludge is classically dewatered using centrifuge, filterpress, belt filter or screw filters. In every case, the process efficiency is strongly affected by sludge properties, and strongly linked to organic content, state of water and rheological properties [START_REF] Ruiz | Dewatering of urban residual sludges : Filterability and hydrotextural characteristics of conditioned sludges[END_REF]. That is why users and suppliers need a parameter to assess sludge dewaterability and a standard method for its measurement. Correlations were already highlighted between dewatered sludge dryness and simple parameters such as Capillary Suction Time (CST), dry and volatile matters, pH and conductivity, specific resistance to filtration, compressibility index, Mohlman index and centrifugation index, viscosity, drainability index [START_REF] Salzer | Les boues des usines de depollution urbaines[END_REF]. Limit water content, corresponding to the minimum water content of the sludge cake reached after a constant pressure filtration for an infinite operating time, is another important parameter that can be useful to describe and forecast the efficiency of the filtration process by a single mechanical action. The concept of the dryness limit was defined in the past French standard XP-T97001 Part 3 [START_REF]Essais des boues : Détermination des caractéristiques en liaison avec l'aptitude à la concentration (old French standard)[END_REF] developed in the early eighties. Suppliers and users of dewatering equipment need a parameter allowing the comparison of sludge dewaterability in referenced conditions. Despite the fact that "dryness limit" does not represent the dryness reached with industrial equipment, industrials agree that this is a fundamental datum giving guarantees on dewatering devices performances [START_REF] Gazbar | Assessment and improvement of performances of mechanical dewatering processes of sewage sludge[END_REF]. The problem of the XP-T97001 standard lies on the lack of information concerning main parameters (solids load, expression pressure and time) which strongly affect the dryness limit. A task group was recently created at the French standards authority (Afnor), in the frame of the French mirror group of CEN TC 308 "Sludge characterization" to improve the method of determination of dryness limit. It gathers French suppliers, users and universities. A first document FD-T 97001 [START_REF]Caractérisation des boues -part-1 : Détermination de la siccité limite » (French standard under progress)[END_REF] was written listing all the parameters which can influence the measurement and recommends to precise them when a dryness limit value is provided. The objective of the research is to study the role of every operating condition listed in FD-T 97001-1 relative to sludge dryness in order to recommend values for analysts for the development of a future standard. Previous communications [START_REF] Ginisty | Influence of flocculation on sludge thickening and dewatering[END_REF] [8] highlighted the role of 3 main parameters -solids load, pressure and compression time -on the dryness limit of a mineral and activated sludge and proposed a new procedure to reduce the duration of limit dryness experiments. This paper presents the influence of test duration, pressure, cake thickness, filter cloth, flocculation conditions, pre-thickening and storage on the dryness limit for different kinds of sludge (aerated, digested, water supply, industrial, mineral). Results of dryness limit are compared to the dryness reached with different industrial devices (centrifuge, belt press, filter press).

MATERIALS AND METHODS

Sludge and flocculants

Materials characteristics used in this study are summarized in table 1.

Flocculation and thickening

Prior to dewatering, sludges were flocculated to be more representative of industrial operating conditions. Sludge flocculation experiments were carried out with a new kind of device called "Bootest" developed by IFTS. This apparatus was initially used for validation of prEN 14742 standard concerning laboratory chemical conditioning procedure and already described in previous work [START_REF] Ginisty | New Laboratory Developments for sludge flocculation[END_REF]. Two flocculation tanks of 90 mm diameter each are stirred in similar conditions with measurement and control of time and speed mixing, impeller position (in function of the sludge volume). Flocs are transferred automatically from the flocculation tanks to the drainage part of the Bootest. Drainage cells are equipped with filter cloth reference Si030904 supplied by Rai-Tillières (French manufacturer).

Sludge dewatering

Dewatering tests were carried out with a filtration-compression cell of 70 mm internal diameter (figure 1). A perforated disk was located at the bottom of the cylinder to support a synthetic filtering medium (most of the tests were performed with the referenced medium 05-25302-SK 025 from Sefar Fyltis). The pressure was applied by a pneumatically driven-piston.

RESULTS AND DISCUSSION

Choice of operating conditions for a new procedure for dryness limit determination

The dryness of biological flocculated sludge usually slowly increases with compression time, especially for highly compressible sludges. It reaches a constant value after a long compression time, often greater than 16 hours [START_REF] Ginisty | Influence of flocculation on sludge thickening and dewatering[END_REF]. Consequently, the dryness limit of the filter-cake is generally not reached after a reasonable experimental time as illustrated in figure 2. A long dewatering time is not convenient for analysts and modifications of flocculated sludge properties during one day compression may occur. The cake dry solids content corresponding to this asymptote is called dryness limit. It corresponds to the cake dryness obtained after an infinite operating time (as defined in FD-T 97001-1 [START_REF]Essais des boues : Détermination des caractéristiques en liaison avec l'aptitude à la concentration (old French standard)[END_REF]). The standard development aims at determining reference conditions to extrapolate the dryness limit from a 4-hours test.

A simple mathematic model, classically used to fit consolidation behaviour [10] [11] is proposed to extrapolate cumulative curves of filtrate mass versus time obtained from a few hours experiment to an infinite time.

The determination of the slope of the linearized form of the model enables to assess the dryness limit (S ∞ )

Previous work [START_REF] Ginisty | Influence of flocculation on sludge thickening and dewatering[END_REF] showed that the model fits well the compression data obtained with flocculated sludges thickened by gravity drainage. With mineral sludges a good agreement between experimental and model data is obtained over the whole compression time. For flocculated activated sludge (which is more compressible than mineral sludge), model fits better with experimental data when the sludge is well preconsolidated, that is to say during the last 2 hours of the experiment as illustrated in figure 3. The comparison of sludge of different origins will be carried out on the basis of this method (extrapolation of data obtained after 2 hours of compression). It is well known that sludge dryness is strongly influenced by cake thickness, the higher the cake thickness the lower the dryness. The influence of this parameter is coupled with the compression time [START_REF] Raynaud | Experimental characterisation of activated sludge behaviour during mechanical expression[END_REF]. Previous results [START_REF] Ginisty | Influence of flocculation on sludge thickening and dewatering[END_REF] enabled to draft a new procedure where the reduction of cake thickness from 10±0.5 mm to 5±0.25 mm enables the decrease of compression time from 16 h to 4 h to obtain equivalent results in a filtration-compression cell. Figure 4 shows that cake thickness is a very sensitive parameter as a variation of 1.5 mm generates a variation of 2.5 points of dryness. The difficulty of the procedure lies on the fact that a preliminary test is necessary to adjust sludge mass to obtain the desired cake height (by determining cake porosity and solids density). Another possibility is to impose a given dry solids per filtration area unit but it may lead to different cake thicknesses. For example, the solids mass of sludge E needs to be increased from 1.5 kg DS/m 2 (loaded mass for sludge C) to 2.4 kg DS/m 2 to obtain the same cake dryness of 5 mm owing to differences in cake porosity (75.4% instead of 81.4%) and solids density (2.39 g/cm 3 instead of 1.59 g/cm 3 ).

Pressure has usually low influence on the final cake dryness obtained with urban sludge dewatering [START_REF] Gazbar | Assessment and improvement of performances of mechanical dewatering processes of sewage sludge[END_REF]. The behavior is generally different with mineral sludges. For example, the dryness limit of sludge F increases from 68 to 75% while pressure varying from 4 to 15 bar [START_REF] Ginisty | Influence of flocculation on sludge thickening and dewatering[END_REF]. High pressure (30 bar) can lead to floc breakage if they have a weak mechanical resistance. Similarly, pressure rise has also low influence as illustrated in figure 5 which compares 3 protocols for 4 hours compression time. Dryness limit (%)

Figure 5: Influence of pressure rise on dryness limit (flocculated sludge C) P1: 2bar-1h/3bar-1h/4bar-2h, P2: 2bar-0.5h/3bar-1.5h/4bar-2h, P3: 4bar, 4h

In the procedure, the applied pressure was 4 bar for an easy application in any filtration-compression cell.

Flocculation conditions may have a strong influence on dryness limit. The impact of 5 flocculation parameters (polymer cationicity, structure, dosing, mixing conditions and temperature) has been studied in previous work [START_REF] Ginisty | Dryness limit : a useful parameter to assess sludge dewatering[END_REF]. Polymer cationicity and structure influence the moisture distribution in the cake and the ability to liberate water by compression. Polymer dosing and mixing conditions mainly affect floc size distribution. Temperature affects mainly filtrate viscosity which has an impact on dewatering kinetics but not on the final cake dryness. Sludge flocculation has to be controlled very carefully. For this reason, a specific device (Bootest) and an operating procedure (prEN 14742) have been developed to form flocs in a repeatable way.

Other parameters (filter cloth, storage during 5 days, pre-thickening by gravity drainage or not) have been tested in previous work [START_REF] Ginisty | Dryness limit : a useful parameter to assess sludge dewatering[END_REF]. The results showed only a little influence of these parameters on sludge dryness.

The developed procedure consists in filtration-compression of flocculated and thickened sludge during 4 hours at 4 bar to form cakes of 5±0.25 mm thickness. The extrapolation of data obtained during the last 2 hours of compression with the mathematical model enables to calculate the so-called "dryness limit".

Comparison of dryness limit measured at lab scale and industrial data

The dryness limit aims at giving maximal sludge dryness that can be obtained by mechanical dewatering equipment. The value obtained at lab scale (31.5%) for an activated sludge (sludge D) was compared to the free water content measured by thermo-gravimetric tests which was assessed to 26.9±1.5%. This value is closed to the dryness obtained with the filter press (between 23 and 30% with a mean value of 25.8%). These results confirm that the dryness limit determined at lab scale is always higher than the dryness reached at industrial scale (table 2). This comparison was carried out with different devices like centrifuge (operating under conditions set to obtain the maximal dryness) and belt press. The ratio between the dryness obtained at industrial scale and the dryness limit depends on both the sludge nature and on the dewatering equipment. For activated sludge, the ratio varies from 0.8 (obtained with filter-press) to 0.5 (obtained with belt press). This ratio achieves 0.9 for digested sludges with centrifuge but falls to 0.6 with water supply sludges. This later is mainly composed of mineral matters and behaves differently from organic matters, A specific procedure could be imagined for this type of sludge.

CONCLUSIONS

The concept of "dryness limit" is a useful index to assess sludge dewaterability. It is measured at lab scale from a filtration-compression test. As the definition refers to the dryness obtained after an infinite time, the use of a mathematical model is necessary to extrapolate data obtained in a reasonable experiment time. The dryness limit significantly depends on final cake thickness, expression pressure and compression time. A consensus will have to be found to select these parameters for the development of a future standard. A new simple procedure has been developed to achieve tests in a reasonable time (4 hours) with a moderate pressure (4 bar) and a measurable cake thickness (5 mm) to have a reference value. Obviously, sludge flocculation has also an impact on the sludge dryness and should be carried out in a repeatable way, as recommended by the standard prEN 14742. The reference value of dryness limit should facilitate the discussion between end-users and suppliers of dewatering machines. Suppliers should give guarantees on their equipment performances on the basis of dryness limit according to their own experience. The ratio between dryness obtained at industrial scale and the dryness obtained at lab scale depends on dewatering equipment and sludge type. It varies from 0.5 to 0.9 which shows that the dryness obtained at lab scale (in the proposed reference conditions) represents a "limit" to sludge mechanical dewatering. Further work should be done to consolidate the experimental procedure and to carry out common tests with organisations involved in the project.

The authors acknowledge all the participants of the French mirror group for their contribution in this work and suppliers and end-users who provide all the sludges.

SYMBOLS

a, b, c: constant parameters DS: dry solids or dry matters S: sludge dryness S ∞ : dryness limit t: compression time (s) VM: volatile matters

Figure 1 :

 1 Figure 1: Filtration-compression cell Flocculated sludge thickened by gravity drainage was used for filtration-compression tests. The mass of filtrate was recorded against time (by a weighing scale connected to a computer). The cake final dry matter content was measured by drying at 105°C.

Figure 2 :

 2 Figure 2: Evolution of different flocculated sludges (A, B, C) dryness versus compression time

Figure 3 :

 3 Figure 3: Comparison model (linearized form)/experimental data (a) Mineral sludge (b) Activated sludge

Figure 4 :

 4 Figure 4: Influence of cake height on sludge dryness (flocculated sludge C)

Table 1 :

 1 Sludge and polymer characteristics

				Sludge			Flocculent
	Flocculated sludge	Type	WWTP	Dry solids (%)	Loss of Ignition (% DS)	Polymer	Supplier	Type	Dose (kg active matters/t DS)
	A		Varennes (03, F)	1	53	EM 640 BD	SNF Floerger	Structured, highly cationic	7
	B		M oulins (03, F)	3	72	EM 640 BD	SNF Floerger	Structured, highly cationic	7
	C	Activated	Rouquet (47, F)	3	61	EM 640 TBD	SNF Floerger	Structured, highly cationic	6
	D		Liege (B)	2.8	66	FeCl3 Setfloc 9112	Tessenderlo WVE GmbH	Structured, highly cationic	7
	E		Noyal (35, F)	3	61	EM 840 HIB	SNF Floerger	Structured, highly cationic	6
	F	M ineral synthetic	Kaolin + CaCl 2	10.2	0	AN 926 SH	SNF Floerger	Linear, weakly anionic	2
	G		Tours (37, F)	2.4	64	Zetag 8185	BASF	Linear, high cationicity	13
	H	Digested	Troyes (10, F)	3.4	60	EM 340 CT	SNF Floerger	Linear, medium cationicity	9
	I		Albi (81, F)	3.6	66	Zetag 9018	BASF	Structured, highly cationic	20

Table 2 :

 2 Sludge characteristics after dewatering

	Boue	Type	dewatering device	Lab dryness (S L )	dryness limit (S∞)	Industrial dryness (S i )	S L /S∞ (%) Si/S∞ (%)
	C	activated	centrifuge	25.5	28.1	20	91	71
	D	activated	filter press 25 bar	28.9	31.5	24.9	92	79
	E	activated	belt press	28.6	32.4	17	88	52
	G	digested	centrifuge	22.8	27.6	23	83	83
	H	digested	centrifuge	23.4	31.9	27	73	85
	I	digested	centrifuge	21	24.4	22	86	90
	J	water supply	centrifuge	47.8	49.3	30	97	61
	K	water supply	centrifuge	33.4	39.4	23	85	58
	L	food	centrifuge	20.8	21.8	19	95	87
	M	MBR	centrifuge	25.5	29.3	20	87	68


Antonio A Pereira

Quentin Leclere
email: quentin.leclere@insa-lyon.fr.

Assessment of acoustic pressure holograms from membrane velocity measurements

The aim of this paper is to show experimentally the possibility to assess acoustic pressure holograms using a light membrane and a scanning laser vibrometer. The velocity of a light membrane placed in an acoustic field can be measured without contact by means of a laser vibrometer. The ideal membrane must be optically reflective, acoustically transparent (as light as possible), impermeable, and mounted without tension. The measured velocity is equal for continuity reasons to the normal acoustic velocity, but differs from the acoustic velocity without the membrane because the membrane is never completely transparent to acoustic waves. A mass effect can be taken into account to correct this difference. Then, the acoustic pressure holograms can be deduced from velocity holograms using the 2D Discrete Fourier Transform. An experimental validation is carried out, acoustic pressures identified from laser measurements are compared to microphone measurements, with a very satisfying match over a wide frequency range.

Introduction

An acoustic pressure hologram is generally acquired by using a moving microphone (with a reference sensor) or a microphone array. The aim of this paper is to show experimentally the possibility to assess acoustic pressure holograms using a light membrane and a scanning laser vibrometer. The technique is based on the insertion of a light membrane in the studied acoustic field and on the measurement of its velocity by scanning its surface using a laser vibrometer. The possibility to measure the acoustic velocity in the air using a membrane has been investigated in a previous work [START_REF] Leclere | Particle velocity field measurement using an ultralight membrane[END_REF], and the theory of membrane-based holography is proposed in a second paper [START_REF] Leclere | Nearfield acoustic holography using a laser vibrometer and a light membrane[END_REF]. The main difficulty of the approach is that the membrane modifies the sound field : the membrane velocity (equal for continuity reasons to the normal acoustic velocity) is not equal to the normal acoustic velocity that would have existed without it. The aim of the previous works was to show the possibility to correct the membrane velocity to virtually remove its mass, for a plane wave in normal incidence [START_REF] Leclere | Particle velocity field measurement using an ultralight membrane[END_REF] or for any kind of wave [START_REF] Leclere | Nearfield acoustic holography using a laser vibrometer and a light membrane[END_REF]. The aim of the present study is to show the possibility to obtain acoustic pressures from membrane velocity measurements. Although it has been shown in [START_REF] Williams | Sound source reconstructions using a microphone array[END_REF] [4] that velocity-to-velocity NAH is more robust than pressure-to-velocity NAH, the assessment of acoustic pressure holograms remains necessary to compute the acoustic intensity through the membrane, or to compare it with some microphone measurements.

The first part of this work recalls the basic principles of membrane-based NAH, including the mass correction and the velocity to pressure transformation, which requires the use of an averaged k-space function. The second part is about the experimental validation : the acoustic pressure obtained by using membrane velocity measurements is compared to the acoustic pressure measured with a microphone in the same plane without the membrane.

Theory of membrane-based holography

The formulation of planar NAH based on acoustic velocity measurements [START_REF] Williams | Sound source reconstructions using a microphone array[END_REF] is similar to pressure-based NAH [START_REF] Bree | The microflown; a novel device measuring acoustical flows[END_REF], and has been experimented thanks to recently developed acoustic velocity sensors [START_REF] Maynard | Nearfield acoustic holography: I. theory of generalized holography and the development of NAH[END_REF]. The particle velocity is measured on the direction normal to the hologram plane, and its 2D Discrete Fourier Transform (DFT) allows the following expansion :

V z (x, y, z, ω) = n m V z nm (z, ω)e jknxx e jkmyy , ( 1
)
z being the direction normal to the measurement plane, with k nx = 2πn/L x , k my = 2πm/L y , and n, m positive or negative integers varying between limits defined by the spatial resolution, and L x and L y dimensions of the measurement surface.

The use of the 2D DFT implies that the acoustic field is periodical in the x and y directions, a period corresponding to the measurement surface. This induces non-physical discontinuities at the borders, generating artificial high wavenumbers. The classical solution to overcome this problem is to use spatial windows to zero edges of the measurement surface [START_REF] Williams | Continuation of acoustic near-fields[END_REF]. A more interesting approach is to find an extrapolation of the 2D acoustic field in order to extend the hologram [START_REF] Williams | Numerical evaluation of the rayleigh integral for planar radiators using the fft[END_REF], and to apply the spatial window to the extrapolated area, thus keeping the whole measured information intact (this is a kind of intelligent zero-padding : data is not extended by zeros but by physically pertinent values). The procedure is experimentally validated in [START_REF] Pezerat | Identification of vibration excitations from acoustic measurements using near field acoustic holography (nah) and the force analysis technique (fat)[END_REF].

The use of the membrane to assess the acoustic velocity is intrusive : the membrane itself modifies the sound field. Waves emitted by the source are indeed partially reflected by the membrane. However, these modifications can be corrected to obtain the acoustic velocity that would have existed without membrane (using a e -jωt time dependency):

Ṽ z nm (z, ω) = V z nm (z, ω) 1 - jµk nmz 2ρ , ( 2
)
where

k nmz = k 2 0 -k 2 nx -k 2 my or j k 2 nx + k 2 my -k 2 0 for respectively (k 2 nx + k 2 my ) < k 2 0 or (k 2 nx + k 2 my ) > k 2 0
, µ is the mass per unit area of the membrane, ρ the air density, and Ṽ z nm the (n, m) component of the corrected velocity. It is important to note that this correction does not take into account the possible multiple reflections between the source and the membrane ; this explains that the minimization of the membrane mass remains crucial as stated and illustrated in [START_REF] Leclere | Particle velocity field measurement using an ultralight membrane[END_REF], even with this correcting term.

The velocity-to-pressure transformation, applying the Euler equation to the (n, m) component of the 2D DFT, is given by

P nm (z, ω) = ωρ k nmz V z nm (z, ω) = G nm (ω)V z nm (z, ω). ( 3
)
This operation is well-posed for high spatial frequencies, because of the division by the term k nmz . Meanwhile, this division can induce a strong amplification when some components of the 2D DFT decomposition have wavenumbers in the vicinity of the acoustic wavenumber (k 2 nx + k 2 my ≈ k 2 0 ). This can potentially induce a large bias error because the transformation is applied to a Discrete Fourier Transform of the velocity field. A solution, proposed in [10] and used in this work, is to compute an averaged expression of G nm (ω) to avoid coincidence effects between the singularity and discretized wavenumbers of the 2D-DFT.

Experimental setup

An experiment has been carried out to validate the theoretical developments proposed in the previous sections. The acoustic source, already used in previous work [START_REF] Leclere | Nearfield acoustic holography using a laser vibrometer and a light membrane[END_REF], is a compression driver coupled to a copper tube (22 mm diameter) with 3 openings. The resulting acoustic source is equivalent to 3 correlated monopoles in the frequency range of interest. A light membrane (height 0.5m× width 0.35m, 45g/sqm) is placed at 5cm of the acoustic source, in a plane parallel to the one defined by the 3 openings of the studied source.

The membrane is maintained by a frame, without tension. The velocity of the membrane is measured by using a scanning laser vibrometer, using a 16 × 24 scan grid (2cm resolution). The acoustic pressure in the same plane (without the membrane) is measured with a microphone at 3 positions, at 5cm in front of each source.

Effect of the k-space averaging of the velocity-to-pressure operator

The pressure obtained using the velocity-to-pressure operator given in Eq. ( 3) is drawn in Figure 1, averaged on the whole measurement grid (384 points), with and without the averaged expression of G nm (ω). The regularization ef- Fig. 1. Averaged acoustic pressure identified using the measured membrane velocity, using the non averaged (---) and averaged (-) velocity-to-pressure operator .

fect of the k-space averaging operation is clear in Figure 1. The result of the non-averaged transformation exhibits strong non-physical peaks at several frequencies, overestimating by more than 10dB the pressure obtained using the averaged operator. This peaks can be said "non-physical" firstly because they do not appear on microphone measurements, and, moreover, because their frequencies depend on the size of zero padding (or extrapolation) used before the spatial DFT.

Results

The pressure identified from membrane velocity measurements and corrected using equation ( 2) is drawn in Figure 2 with the acoustic pressure measured without the membrane. The corrected pressure is very close to the measured acoustic pressure without the membrane, illustrating the possibility to virtually remove the membrane, and to precisely assess the acoustic pressure that would have been without it.

The measured velocity, only corrected by the acoustic impedance of the plane wave ρc, is also given in the same figure, to show the combined effect of the velocity-to-pressure transformation and the mass correction. The velocity-topressure transformation and the mass correction are preponderant respectively in low and high frequency. conclusion This paper illustrates experimentally the possibility to use a scanning laser vibrometer and a light membrane to assess acoustic pressure holograms. Although the NAH velocity-to-pressure operation is known to be well-posed for high spatial frequencies, a special care has to be taken to treat a k-space singularity generating potentially large errors. A solution, proposed in the literature for acoustic radiation computations, has been efficiently applied in the present work, and experimental results show the necessity to implement it systematically. An experimental comparison with directly measured acoustic pressures validates the velocity-to-pressure transformation as well as the membrane mass correction over a wide frequency range. This validation is very encouraging and shows that the membrane approach is able to provide the acoustic pressure as well as the normal acoustic velocity, and consequently the acoustic power crossing the membrane, and all these quantities with the high spatial resolution that can be reached by a laser vibrometer.

Fig. 2 .

 2 Fig. 2. Acoustic data averaged over 3 positions. Microphone acoustic pressure (-), membrane velocity * ρc (...) and membrane-based acoustic pressure (---) .


Laurent Pruvost

Q Leclère

E Parizet

Angular and temporal determinism of rotating machine signals : the diesel engine case

Keywords: Cyclostationarity, diesel engine noise, source separation PACS: 43.60.-c

published or not. The documents may come

Angular and temporal determinism of rotating machine signals: The diesel engine case Q. Leclere,

Introduction

Acoustic or vibration signals acquired on rotating machines operating in steadystate conditions are said to be cyclostationary [START_REF] Antoni | Cyclostationarity by examples[END_REF]. Cyclostationarity is the general framework to treat signals exhibiting periodical properties. The deterministic part of a cyclostationary signal is commonly defined by its purely periodic component, i.e. the expected value of the signal during a cycle, also called CS1 part (first order of cyclostationarity). This part can be estimated by averaging the signal over a large number of cycles [START_REF] Braun | Analysis of repetitive mechanism signatures[END_REF]. The random part of the signal is defined relatively to the deterministic part : it is the residual part resulting from the subtraction of the deterministic part from the total signal. This definition of the deterministic / random decomposition of a cyclostationary signal is attractive because of its simplicity. It can however be ambiguous when dealing with signals acquired on rotating machines running in steady-state conditions. The determinism of vibration or acoustic signals acquired on rotating machines is dual : firstly the occurrence of mechanical events (mechanical shocks, combustions in reciprocating engines...) is guided by the position of the main shaft of the machine : this is an angular determinism. Secondly, the response of the structure to excitations results from a convolution product in the time domain : it is a temporal determinism. This construction of signals in temporal and angular domains brings out the concept of fuzzy cyclostationarity [START_REF] Bonnardot | Comparaison entre les analyses angulaire et temporelle des signaux vibratoires de machines tournantes[END_REF]. The duality of the determinism is not a problem if the instantaneous speed is purely periodic (or constant). In this case, a signal purely periodic in angle will be purely periodic in time [START_REF] Bonnardot | Comparaison entre les analyses angulaire et temporelle des signaux vibratoires de machines tournantes[END_REF][START_REF] Antoni | Cyclostationary modelling of rotating machine vibration signals[END_REF]. Difficulties appear when the instantaneous rotation speed exhibits fluctuations from cycle to cycle, i.e. if the instantaneous speed is not purely periodic. In this case, the relation between temporal and angular domains is not deterministic. Cycle averaging operations, that are necessary to estimate deterministic parts of signals, will thus lead to different results in time or angle. The deterministic part of the signal in angle (resp. in time) will exhibit a random part in time (resp. in angle). The aim of this paper is to assess theoretically and experimentally the effect of speed fluctuations on angular and temporal deterministic parts of signals acquired on rotating machines. Sections 1 and 2 concern respectively the temporal and angular deterministic part. Simple and general considerations about sources in rotating machines lead to the expression of low pass filters and damping effects on deterministic parts. The last section is an experimental illustration in the case of a diesel engine operating at cold idle. In all the following, "time signals" or "angular signals" will stand for signals sampled with a constant step respectively in time or angle.

1 Extraction of the temporal deterministic part

synchronous averaging

The temporal deterministic part of a rotating machine signal corresponds to its expected value during one cycle in the time domain. It can be estimated by averaging it over a large number of cycles. The main difficulty of this averaging process is that consecutive cycles do not have the same number of samples because of cyclic speed variations. In fact, two cycle events separated by a constant value in angle will be separated by a varying delay in the time domain. It means that the resulting average does not correspond exactly to a cycle as defined relatively to the angle, but to a time portion of the signal corresponding approximately to the mean duration of a cycle. However, an angle reference corresponding to a given position of the main shaft is necessary to align those time portions before the averaging operation (position-locking in [START_REF] Braun | Analysis of repetitive mechanism signatures[END_REF]). A given time portion will thus be defined as the m points preceding the chosen angle reference together with the p points following it, T = (m+p)/f s corresponding approximately to a cycle duration (with f s the sampling frequency in Hz). Because of cyclic speed variations, the temporal deterministic part of a signal is necessarily defined together with a chosen angle reference. The choice of different angle references for the synchronization will lead to different results.

Effects of the synchronization error

Unfortunately, time portions corresponding to successive cycles cannot be exactly synchronized because of the discrete nature of acquired signals. The chosen angle reference is indeed localized between two time samples. Without resampling or interpolation techniques, a synchronization error is unavoidable, and corresponds to the delay between the reference and the nearest sample of the time portion. This error can be described by a random variable ∆ uniformly distributed between -1/(2f s ) and 1/(2f s ) (assuming the rotation speed and the sampling frequency are non commensurable). The effect of this error on the synchronous average can be obtained by considering its expected value. The Fourier decomposition of the deterministic part of the signal is expressed as follows

d(t) = n D n e j2πf n t , with f n = n T = n m + p f s . ( 1
)
Considering the synchronization error, the expected value of the synchronous average is given by

d(t) = E[d(t + ∆)] = n D n E[e j2πf n (t+∆) ] d(t) = n D n e j2πfnt E[e j2πfn∆ ] d(t) = n E[cos(2πf n ∆)]D n e j2πf n t (2)
Equation ( 2) brings out a frequency dependent bias factor, whose value is easily calculated considering the law of ∆ : It means that the synchronous average will give a biased estimation of the deterministic part. The bias factor is a function of the ratio f /f s , and varies between 1 (no bias) for f = 0 and 0.64 for f /f s = 1/2 (Nyquist frequency). The bias factor is drawn in figure 1.

b(f ) = E[cos(2πf ∆)] = f s πf sin πf f s ( 3
It can be noted that it is possible to use upsampling procedures to artificially increase f s . No information is created : the frequency content of the upsampled signals will remain zero above the original Nyquist frequency. However, it permits to align more precisely time portions before the averaging process by decreasing the synchronization error ∆.

Effects of cyclic speed variations

The dynamic response of the structure and its acoustic radiation are defined in the time domain. Thus, the temporal synchronous averaging is theoretically optimal to extract the response of the structure to an impact excitation occurring in the vicinity of the cycle event chosen for the synchronization. However, the alignment of cycle events occurring at significantly different angles will be lost, as illustrated in figure 2.

Considering a cycle event occurring at θ (with θ = 0 the synchronization angle), and a mean speed Ω(1 + ν) between 0 and θ (with ν the speed uncertainty), the time corresponding to θ is given by

t = θ Ω(1 + ν) (4)
In case of a moderated cyclic speed variation (-0.

1 < ν < 0.1), 1/(1 + ν) can t t t 0 θ 0 (synchronization angle) θ 1 θ 2 t 1 t 2 t 3 cycle #i cycle # i+1
Fig. 2. Misalignment of synchronized consecutive cycles using a time sampling be approximated by (1 -ν) :

t = θ Ω (1 -ν) = θ Ω -ν θ Ω = θ Ω + ∆ (5)
With ∆ = -νθ/Ω the random delay induced by the cyclic speed variations. The bias error induced by this delay when averaging several cycles is obtained, as for the previous section, by calculating the expected value of cos(2πf ∆) (see eq. ( 3)). Here, the difference is that the random delay is not uniformly distributed. Assuming that the cyclic speed uncertainty ν is a centered gaussian random variable with a standard deviation σ ν , ∆ is also a centered gaussian random variable, with a standard deviation σ ∆ = θσ ν /Ω. The expected value of the bias factor is finally given by

E[cos 2πf ∆] = +∞ -∞ cos(2πf t) 1 σ ∆ √ 2π e -t 2 /(2(σ ∆ ) 2 ) dt (6)
The integral in equation ( 6) is the expression of the Fourier transform of the gaussian function, which is also a gaussian function :

E[cos 2πf ∆] = F e -t 2 /(2(σ ∆ ) 2 ) σ ∆ √ 2π = e -2π 2 f 2 (σ ∆ ) 2 = e -2π 2 f 2 θ 2 (σν ) 2 /Ω 2 (7)
The bias factor is drawn in figure 3 for several values of θ and for the speed fluctuation observed on a diesel engine at cold idle (see section 3.2). It can be seen that the bias error behaves as a low-pass filter, with for instance an attenuation of 20dB at 500 Hz for a cycle event occurring at π after the synchronization angle (with σ ν = 4e -3). 2 Extraction of the angular deterministic part

Time to angle correspondence

There are two possibilities to obtain signals sampled respectively to the angle, and both are based on the use of an angular coder coupled to the main rotating shaft of the studied machine. This system provides a square signal with a period equal to the angular resolution. The first possibility is to drive the acquisition system with this clock signal, so as to obtain one sample by angle step. A difficulty of this method is that the anti-aliasing analogous filters must be adjusted on a varying sampling frequency. The second possibility is to record the angle signal, as well as other inputs, equally spaced in time, and to post process the time to angle transformation [START_REF] Fyfe | Analysis of computer order tracking[END_REF][START_REF] Bonnardot | Comparaison entre les analyses angulaire et temporelle des signaux vibratoires de machines tournantes[END_REF]. This second possibility has been chosen in this study, because it allows the processing of same signals sampled either in time or angle. The chosen sampling frequency must be adjusted in accordance with the angle resolution and the maximum instantaneous speed : the first harmonic of the signal of the angular coder must be lower than half the sampling frequency. A function t(θ) (time in function of the angle) is easily constructed from the clock signal, with a resolution that can be made higher than the resolution of the coder by upsampling the instantaneous speed, if needed. Then, signals are resampled in angle using an interpolation technique. The interpolation algorithm used for angular resampling is the piecewise cubic spline of the MATLAB software [START_REF]MATLAB 7 Data Analysis[END_REF].

Expression of the angular deterministic part in the time domain

The assessment of the angular deterministic part of signals expressed in angle is much easier than for the temporal deterministic part : it is not necessary to synchronize signals. It is sufficient to average consecutive signal portions with a number of samples corresponding to the number of sample in one cycle.

Then, it can be interesting to transform back this angular deterministic part in the time domain, for instance to compare it with the temporal deterministic part. This can be done by computing the cyclic average of the instantaneous rotation speed, the integration of which gives a cyclic average of the function t(θ), allowing to get back in time by using interpolation techniques.

Effects of cyclic speed variations

The occurrence of events generating vibration and noise in rotating machines is defined relatively to the rotation angle of the main shaft. Averaging in angle is theoretically advised if we are interested in the effective occurrence of events, for instance for diagnosis purpose or fault detection. Unfortunately, the response of the structure results from a convolution in the time domain. Thus, an averaging with respect to angle will bias the deterministic part of the response of the structure because of cyclic speed variations (see figure 4). Let us consider the Fourier expansion of the (temporal) response of the structure to the deterministic part of an excitation occurring at an angle θ = 0.

θ θ t 0 θ 0 t 1 t 2 t 3 θ 1 θ 2 cycle #i cycle # i+1
d(t) = n D n e j2πfnt (8)
The time -angle relation is expressed as in equation ( 5). The preceding expansion can thus be written in function of θ :

d(θ) = n D n e j2πf n (θ/Ω+∆) , (9)
with ∆ = -νθ/Ω.

It is important to note that Ω(1+ν) is the value during a given cycle realization of the instantaneous rotation speed average between 0 and θ. It is thus a function of θ, as well as the standard deviation of ν. However, σ ν will be considered as constant in the following for the sake of simplicity.

The expected value of the angular cyclic average is thus given by

d(θ) = E(d(θ)) = n D n e j2πf n θ/Ω E(e j2πf n ∆ ) (10)
The frequency dependent bias factor is identified in equation ( 10) :

b(θ, f ) = E(e j2πf ∆ ) = E[cos(2πf ∆)] (11)
This expected value is explicitly written as follows (see eq. ( 7)):

b(θ, f ) = e -2π 2 f 2 θ 2 (σν ) 2 /Ω 2 (12)
This attenuation is drawn in figure 5 in function of θ, for different values of frequency f , and considering Ω and σ ν constant (this is of course an approximation, but experimental observations provided in section 3.2 show that this is realistic at least for reciprocating engines). It results in a kind of virtual damping, with a damping factor increasing with the speed uncertainty and the frequency. It is clear that the less the structure is damped, the more this bias will affect its response when averaging with respect to angle.

3 Experimental comparison between the angular and temporal determinism of diesel engine signals

experimental setup

The experimental illustration proposed in this paper focuses on a diesel engine (1.9L, common rail injection, four in-line cylinders) operating at cold idle (about 850rpm). The engine is mounted on a bench in a semi-anechoic room. The instantaneous speed of the crankshaft is measured using an angle coder with a resolution of 0.5 deg. Several signals are recorded using a time sampling of 102400 Hz :

• 1 : cylinder pressure, • 2 : accelerometer on a crankshaft bearing cap, • 3 : acoustic pressure at about 1m from the engine, • 4 : angle coder.

Cyclic speed variations of the studied engine

The cyclic speed incertitude is the cause of theoretical differences between temporal and angular determinisms. It is thus of prime interest to estimate its magnitude on the studied experimental case. The average speed of the engine running at cold idle is 854rpm. When studying the population of speeds averaged over a cycle (for 213 cycles), the normalized standard deviation is equal to 0.26%. But if we look at the population of speeds averaged over a course (quarters of cycles corresponding to the duration between two consecutive TDC), the normalized standard deviation is increased to 0.45%. The instantaneous cyclic speed averaged over 213 consecutive cycles is drawn in figure 6, together with the standard deviation. Angular decelerations and accelerations preceding and following combustions are visible, the instantaneous speed standing between 780 and 890 rpm, (between -8% and +6% of the nominal speed). The normalized standard deviation is between 0.4 and 0.5 %, with peaks at about 0.6 % in the vicinity of TDCs. It means that the dispersion of the instantaneous speed is of the same order of magnitude as the dispersion observed on the speeds averaged over a course. The instantaneous speed uncertainty thus seems principally generated by the uncertainty of the averaged speed of a course, that can be explained by the combination of several physical unknowns like the exact fuel quantity injected in the cylinder or the auto-ignition delay. These observations legitimize assumptions made in section 2 : the dispertion of the cyclic speed is almost the same for the instantaneous speed and for averaged values over angle distances between 0 and π.

comparison of temporal and angular deterministic parts

Temporal and angular cyclic averages are computed using methods described in sections 1 and 2. Signals are recorded during 30s on the engine running at cold idle. Angular cyclic averages are transformed back into the time domain as described in section 2, to be compared to the time domain results. Angular and temporal deterministic parts of the microphone signal are drawn in figure 7 in function of time, the 0 corresponding to the TDC in the first cylinder, the cycle event chosen for the synchronization of the time averaging process.

Angular and temporal deterministic parts are clearly different. Four bursts are clearly identified, corresponding to the noise generated by the four combustions. For the angular deterministic part, the four bursts seem to have similar strengths. Concerning the temporal deterministic part, the burst following the TDC used for the synchronization (in the cylinder #1) is stronger than the preceding and the following ones (respectively cylinders #2 #3). The burst corresponding to the TDC in cylinder #4 is even lower. These observations are conform to theoretical expectations found in section 1. Time-frequency representations of time and angular deterministic parts are drawn in figure 8.

It is clear on the temporal deterministic part that the response of the engine to combustions #2, 3,and 4 is strongly attenuated over 1kHz, compared to the angular deterministic part. On the other side, the response to combus-tion in cylinder #1 (just after the TDC chosen for the synchronization), is clearly stronger on the temporal deterministic part, and its duration is longer. It confirms the results of section 2, forecasting a damping-like attenuation of the angular deterministic part, with a damping factor increasing with the frequency.

Quadratic values of temporal and angular deterministic parts of the pressure in cylinder #1, the bearing cap accelerometer and the microphone signals are drawn in figure 9, using an integration constant of 2ms. Signals are bandpass filtered between 0.5 and 12kHz. It can be seen on the cylinder pressure trace that temporal and angular deterministic parts are similar. The energy of this signal is indeed concentrated on a very short time corresponding to the combustion, the effect of cyclic speed fluctuations is thus negligible, the synchronization event used for the temporal cyclic averaging corresponding approximately to this combustion. It can be seen on the accelerometer and microphone traces that the temporal deterministic part is a little more energetic during the response to the combustion in the cylinder # 1, and much less in other cylinders. The studied accelerometer is placed on the bearing cap between cylinders # 2 and 3, explaining why the energy of the angular deterministic part is more important just after the combustion in this two cylinders.

Extraction and exploitation of random parts

The study of the deterministic part of signals is of prime interest for the monitoring of the studied rotating machine, because it represents its operation at the first order. The random part of the signals is the difference between the original signal and its deterministic part. It is important to note at this stage that a light underestimation of the deterministic part can induce in some situations large overestimations of the random part. The study of the random part can be very interesting, for example in identification problems where some sources have to be separated. It is known that the correlation between noise and vibration sources of a rotating machine, that induces difficulties in the identification of their own contributions to the total noise, is mainly due to their determinism [START_REF] Chung | Measurement of frequency reponses and the multiple coherence function of the noise-generation system of a Diesel engine[END_REF][START_REF] Yawata | Identification of internal noise sources in Diesel engines[END_REF]. Removing the deterministic part of signals is thus a clever way to help in their separation. Several studies recommend to remove the temporal deterministic part of signals for system identification problems [START_REF] Antoni | Effective vibration analysis of ic engines using cyclostationarity. part ii : New results on the reconstruction of the cylinder pressures[END_REF][START_REF] Badaoui | Separation of combustion noise and piston-slap in diesel engine-part i: Separation of combustion noise and piston-slap in diesel engine by cyclic wiener filtering[END_REF][START_REF] Pruvost | Diesel engine combustion and mechanical noise separation using an improved spectrofilter[END_REF]. The underlying idea of these works is to consider the structure of the rotating machine as an invariant filter. In this case, the input-output relationship between sources and responses can be separated into two systems, the first one between the deterministic parts of excitation and responses, and the second one between random parts of excitation and responses. Coherent contributions of other sources are supposed to be deterministic, the system between random parts can thus be thought to be less disturbed than the system between deterministic parts. The system identification has been implemented to the experimental case studied in this work. The aim is to identify the linear relationship between the pressure in cylinder #1 and the noise measured at 1m of the engine. The temporal deterministic / random separation of input and output signals has been realized as described in previous sections, and the transfer function has been estimated separately for the two systems using a H1 estimator (see [START_REF] Pruvost | Diesel engine combustion and mechanical noise separation using an improved spectrofilter[END_REF] for details). The magnitude of obtained transfer functions are drawn in figure 10. It can be seen that the transfer function obtained using the deterministic part is globally stronger than the one obtained using random parts. It can be explained by the contributions of coherent mechanical sources that are still present on the deterministic part of the response signal, but that are efficiently suppressed by using the random parts. The engine was running at cold idle for this example, an operating condition for which the mechanical noise is particularly strong. However, it is quite difficult to objectively determine the best estimation of the transfer function, the real one being unknown. But a previous work [START_REF] Pruvost | Diesel engine combustion and mechanical noise separation using an improved spectrofilter[END_REF] based on an important number of operating points brings out the superiority of the approach based on the suppression of the deterministic parts.

conclusion

The determinism of signals acquired on rotating machines is dual : mechanical events are determined in function of the angular position of the main shaft, and vibration and acoustic responses result from convolution operations in the time domain. If the cyclic rotation speed is purely periodic, this duality is transparent because the cyclic time-angle relationship is determined. But this situation is never perfectly achieved in real life, because the instantaneous rotation speed at a given cycle angle is never exactly the same from cycle to cycle, and this speed uncertainty is sometimes sufficient to induce different determinisms in time or angle. The effect of the speed uncertainty on the estimation of the deterministic part has been investigated in temporal and angular domains, and low pass filtering and damping effects have been quantified. The instantaneous speed uncertainty has been experimentally assessed in the case of a diesel engine, and the angular and temporal deterministic parts of vibration and acoustic signals have been assessed and compared, bringing out illustrations confirming theoretical expectations. An example of the application of the deterministic/random separation of signals has finally been proposed, illustrating the pertinence of such approaches for system identification problems.

Fig. 1 .

 1 Fig. 1. Bias factor generated by the synchronization error

Fig. 3 .

 3 Fig.3. Bias factors caused by cyclic speed variations on the synchronous average for events occurring at an angle θ from the synchronization angle. σ ν = 4e -3, Ω = 850rpm (cold idle)

Fig. 4 .

 4 Fig. 4. Misalignment of synchronized consecutive cycles using an angular sampling

Fig. 5 .

 5 Fig. 5. Attenuation of the response of the system to an excitation occurring at an angle θ = 0 caused by the averaging in the angular domain for different frequencies. σ ν = 4e -3

Fig. 6 .

 6 Fig. 6. Top : instantaneous cyclic speed averaged over 212 cycles, with confidence interval at ±2σ in dashed red line. Bottom : normalized standard deviation.

Fig. 7 .

 7 Fig. 7. Angular (black) and temporal (gray) cyclic averages (1m microphone signal). Vertical lines materialize TDCs, with the central one standing for the TDC used for the synchronization used for the time averaging.

Fig. 8 .

 8 Fig. 8. Time-frequency representations of angular (top) and temporal (bottom) cyclic averages (1m microphone signal).

Fig. 9 .

 9 Fig.9. Instantaneous quadratic values of angular (solid black) and temporal (dashed gray) cyclic averages for the cylinder pressure (top) accelerometer (center) and microphone (bottom) signals using a band-pass filter [0.5 12kHz], integration constant : 2ms .

Fig. 10 .

 10 Fig.10. Magnitude of transfer functions using deterministic parts (solid black line, o markers) and random parts (dashed gray line, × markers), averaged in third octave bands.


Nikola Maurová Paillereau
email: nikola.paillereau@mac.com

ASSESSING THE PHONETIC LEVEL IN L2 VOWELS PRODUCTION WITH THE VISUVO SOFTWARE: CASE OF CZECH LEARNERS ACQUIRING CONTRASTS BETWEEN FRENCH MID VOWELS e/ɛ, ø/oe ANDo/ɔ

Keywords: pronunciation assessment, vowels, formants, French as a Foreign Language (FFL), Czech

The VisuVo software is designed to visually compare formants of vowels as uttered by different speakers, in isolation and in different contexts or prosodic positions. Both researchers and teachers can use the software. VisuVo aims to evaluate the initial phonetic level of a learner and to trace the progress in L2 vowels realisation compared to a set of pre-recorded references. VisuVo has an interactive and simple interface to handle. Its features and output graphics are illustrated by a study of contrasts between the French mid vowels e/ɛ, ø/oe and o/ɔ produced in isolation and in symmetrical contexts /p, t, k, R/ by 10 native nonsouthern French speakers representing the reference, and 10 Czech learners of French to be tested.

INTRODUCTION 1.Teaching and Assessment in Phonetics

Since the appearance of the communicative approach in the 1970s, perfect pronunciation of L2 sounds is no longer an objective. Still, learners may wish to go unnoticed for their foreign accent and to speak, ideally, like natives [START_REF] Billières | Quelques problèmes soulevés par les différentes variétés d'accents dans les méthodes de français langue étrangère[END_REF]. Teachers should therefore compare the particularity of phoneticphonological systems of L1 and L2, their prosody and segments, their phonotactic rules and coarticulation patterns leading to allophonic variations [START_REF] Best | Nonnative and secondlanguage speech perception: Commonalities and complementarities[END_REF]. Coarticulation habits are language dependant [START_REF] Manuel | Universal and languageparticular aspects of vowel-to-vowel coarticulation[END_REF]. Once the vowels have been inserted in the spoken chain, the formant frequency values in the middle part of the vowels, on one side, and the direction of the formants during the transition between the vowel and the surrounding consonants, on the other side, depend on many factors, such as the language itself, surrounding consonants, prosodic position (initial, final, stressed, etc.), style (hyper-or hypo-articulated) and speech rate [START_REF] Lindblom | Spectrographicstudy of vowelreduction[END_REF]. The mastery of allophonic variations should therefore be included in the curriculum.

An objective evaluation of an exact phonetic level acquired by a learner is hardly possible on the sole basis of perceptual judgments. Human assessors can be helpful, of course, as they can normalise the incoming speech and categorise sounds without any big difficulty; they cannot, however, perform fine acoustic analyses enabled by modern technological means [START_REF] Ashby | Prototype categories in phonetics[END_REF]. The difficulty in objectively assessing different phonetic levels is reflected by the Common European Framework of Reference for Languages (CEFRL) [START_REF]Common European Framework of Reference for Languages: Learning, Teaching, Assessment[END_REF], which does not provide clear criteria for distinguishing between six levels of phonological skill (A1, A2, B1, B2, C1 and C2), and confuses levels C1 and C2. Progress in the acquisition of new phonological contrasts is gradual, and teachers should therefore appreciate different stages of phonetic progress [START_REF] Dickerson | The learner'sinterlanguage as a system of variable rules[END_REF]. Machines can help and, in this perspective,VisuVo(VISUalisation of VOwels) can be considered a tool for teachers to objectively assess different phonetic levels.

Acoustic Target

To study deviations in L2 pronunciation, researchers and teachers need to refer to a phonetic norm defined by native speakers' productions [START_REF] Flege | The Instrumental Study of L2 Speech Production: SomeMethodologicalConsiderations[END_REF]. The same vocalic timbre can be achieved with different articulatory strategies [START_REF] Riordan | Control of vocal-tract lenght in speech[END_REF], so that vowels are more easily defined in acoustic terms, that is in terms of their formant frequencies. The current French segmental system includes 3 nasal vowels and ten oral vowels /i, e, ɛ, a, u, o, ɔ, y, ø, oe/. Back vowels can be adequately defined by the first two formants(the upper formants have no perceptual weight [START_REF] Delattre | An experimentalstudy of the acousticdeterminants of vowelcolor : observation on the one-and two-formant vowelssythetisedfromspectrographic patterns[END_REF]), front vowels by the first three formants, and the vowel /i/ by the first four formants. A closer distance between F3 and F4 defines the French vowel /i/, so that F4 is important in the acoustic definition of vowels with /i/-like timbre [START_REF] Vaissière | Proposals for a representation of soundsbased on their main acousticperceptualproperties, Tones and Features[END_REF].

AIM OF THE STUDY

The objective of this paper is to present the VisuVo diagnostic tool. VisuVo is a piece of specialised software which can quickly and interactively generate three types of graphs representing vocalic formants from a large database. The graphs are vowel triangles, allophonic variations tracers and contrasts diagrams. They aim to highlight acoustic differences in the pronunciation of L2 vowels compared to pre-recorded L1 formant frequency values as a reference, and display learners' progress.

In this study, VisuVo illustrates three first formants (F1 to F3) of French mid vowels e/ɛ, ø/oe and two first formants of o/ɔ, as produced by 10 Czech learners and 10 native non-southern French speakers (reference). The Czech language has five phonologically short vowels /a, e, i, o, u/ (/e/ and /o/ being sometimes transcribed in recent Czech literature with /ɛ/ and /ɔ/) and five long ones /aː, eː, iː, oː, uː/. The Czech language (unlike French) does not make contrast between rounded/unrounded front vowels, nor between mid-open/mid-close vowels.

The question is to what extentCzech learners can acquire contrasts between e/ɛ, ø/oe and o/ɔ? Which are the consonantal contexts that facilitate learning of the three contrasts?

3.METHODOLOGY

Corpus and Speakers

The corpus, derived from a larger body [START_REF] Landron | Le corpus PhoDiFLE : un corpus commun de français langue étrangère pour une étude phonétique des productions de locuteurs de langues maternelles plurielles[END_REF], consists of the mid vowels /e, ɛ/, /ø, oe/ and /o, ɔ/ pronounced:

1. in isolation (i.e. between two short pauses so as to avoid coarticulatory phenomena), inserted in carrier sentences, such as « Tôt, il a dit<ô>commedanstôt. » ("Soon, he said <u> like in soon.") 2. intrisyllabiclogatoms CVCVCVC (where C = /p, t, k, R/) inserted in carrier sentences, such as « Le mot kaukaukaukepeutbiencoller. » ("The word kaukaukauke matches well.")

The corpus includes recordings of female speakers without any known hearing problems, namely:

1. Ten native non-southern French, aged between 21 and 48 (M = 28,5), 4 repetitions.

2. Ten Czech advanced learners (Learners 1 to 10), aged between 25 and 28 (M = 25,7), 10 repetitions.

Productions of French natives were used to define the French reference in the present study.

Recording and Data Processing

All instructions were given in writing. The recordings were made in a quiet room with a headband microphone AKGC 520 L and a sound card Edirol UA 25 connected to a Mac computer. The set of sentences was recorded with a sampling frequency of 44100 Hz and a sampling rate at 16 bits. Recordings were preceded by a training phase.

Ten target vowels of two corpuses were labelled and analysed using the Praat software [START_REF] Boersma | Praat: doingphonetics by computer[END_REF]. The formant values were automatically calculated with the formula To Formant (burg) of the Praat system (analysis window: 25 ms). All values taken semi-automatically were checked and corrected manually, when necessary.

RESULTS

Average Values

The differences in F1, F2 and F3 (in Bark, expressed as a percentage) of the mid vowels realised by the French speakers (FR) and Czech learners (CZ) are summarized in Table 1.

TheFrench native speakers realised the contrast between mid vowels with a systemic difference in F1. According to the consonantal context, the difference in F1 varies between 25 % and 34 % for the pair e/ɛ, between 23 % and 30 % for ø/oe, and between 26 % and 31 % for o/ɔ. The difference in F2 is equal to or less than 6 % for pairs e/ɛ and ø/oe, and between 13 % and 22 % for the pair o/ɔ. The difference in F3 doesn't exceed 3 % for all pairs.

TheCzech learners do not exhibit a difference in F1 and F2 between mid vowels e/ɛ and o/ɔ, except for F1 of e/ɛ produced in isolation and F2 of o/ɔ realised in a labial context where the difference represents 5 %. According to Flanagan [START_REF] Ashby | Prototype categories in phonetics[END_REF], a 5 % formant difference corresponds to a just noticeable difference for vowel formant frequencies F1 and F2, but it is probably not large enough to distinguish between two different phonemes. In contrast, vowels ø/oe are produced with a difference in F1 between 5 % (in certain contexts) and 15 % (in isolation). The difference in F3 never exceeds 1 %.

The average vocal formants of e/ɛ, ø/oe and o/ɔ produced by natives and learners, in different consonantal contexts and prosodic positions (the first, mid and the last vowels in logatoms) is illustrated in Figure 1generated by VisuVo. Finally, the strengthening of contrasts between e/ɛ and, in particular, ø/oe produced by the Czech learners in isolation is illustrated in Figure 2. We note a difference in mean values of F1.

Individual Variability

The study of 10 replicates of vowels individually performed by 10 learners shows that acoustic cues constituting contrasts vary from learner to learner. A quasi-systematic acoustic difference between pair vowels indicates that learners have created two different categories for the vowels in contrast.

Vowel triangles F1/F2 (in Bark) of Figures 3 and4 generated with VisuVo make it possible to compare performances of different learners according to phonetic contexts.

In isolation (Figure 3), Learner 2 does not distinguish between e/ɛ, but the majority of occurrences of ø/oe and o/ɔ have different F1 and F2 (yet the difference is lower than in natives). Learner 9 achieves e/ɛ and o/ɔ with a difference in two formants (again, the difference is lower than in natives). The contrast between ø/oe in Learner 9 is based on F2 contrary to F1 in natives.

In a dental context (Figure 4), Learner 2 produces the contrast e/ɛ with a difference in F2 primarily, and does not distinguish between ø/oe and o/ɔ. Learner 3 pronounces e/ɛ with a difference in F1 and F2, but, in contrast to natives, the [ɛ] is produced, on average, with a lower F1 than [e]. The contrasts between ø/ and o/ɔ are essentially based on F2.

CONCLUSION

Native French speakers systematically produce the contrast between mid vowels based on the main acoustic cue F1, traditionally correlated to the degree of aperture. These contrasts are an obvious phonetic difficulty for Czech learners who generally do not distinguish e/ɛ and o/ɔ, and realise the contrast ø/oe with less acoustic difference than natives. This result shows that the difficulty of acquiring four contrastive degrees of aperture instead of three is not the same for all vowels. Indeed, the contrast between phonemically new vowels ø/oe (two new phonemes for Czech learners) is more approximated than the contrasts between phonemically similar vowels e/ɛ and o/ɔ.

A detailed analysis of formant frequencies eased by the use of VisuVo shows that 1) performances in the production of contrasts vary from learner to learner, 2) some contexts appear to facilitate contrasts implementation, and 3) a number of potentially specific problems for a given learner can be easily identified. In order to objectively evaluate different stages of phonetic progress, teachers should be advised to complete their perceptive appreciation by visualisation of formant frequencies, as done easily by VisuVo.

Figure 1 :

 1 Figure 1:Average formants F1, F2 (F3) (in Bark) of vowels e/ɛ, ø/oe and o/ɔ produced in isolation (horizontal strokes) and in logatoms CVCVCVC (where C = p, t, k, R)in the first, second and the last vowelby 10 native French speakers (cross, 4

Figure 2 :

 2 Figure 2:Average formants F1, F2 and F3 (in Bark) of vowels e/ɛ, ø/oe produced in isolation by 10 Czechlearners (10 repetitions per speaker). Values takenat 1/3, ½ and 2/3 of vowellengths. The standard deviationis one.

Figure 3 :

 3 Figure 3: Triangle F1/F2 (in Bark) of 10 French oral vowelsrepeated in isolation 4 times by 10 natives (circle) and 10 times by Learner 2 (cross)

Figure 4 :

 4 Figure 4: Triangle F1/F2 (in Bark) of 10 French oral vowelsrepeated in logatomstVtVtVt 4 times by 10 natives (rhombus) and 10 times by Learner 2 (square) and Learner3 (triangle). Values takenathalf of the vowellengths.

Table 1 :

 1 Difference of average formants (in percentages) F1, F2 (F3) (in Bark) of vowels e/ɛ, ø/oe and o/ɔ produced in isolation (0) and in logatoms CVCVCVC where C = p, t, k, R by 10 native French speakers (FR, 4 repetitions per speaker) and 10 Czechlearners (CZ, 10 repetitions per speaker). Values takenathalf of vowellengths. Ctx Vw Diff. F1 % Diff. F2 % Diff. F3 % FR CZ FR CZ FR CZ 0