Paul Akiki

Maya Hage

Jean-Claude Vannier

Mohamed Bensetti

Benjamin Dagusé

Mike Mcclelland

Performance comparison of a doubly-salient motor with multi-V-shape ferrite magnets

Keywords: Concentrated winding, multi-V ferrite magnets, torque ripple, Asymmetric poles, Design of Experiments, slot/pole combinations

This paper presents the analysis of a novel doubly salient structure with concentrated tooth winding and multi-V shape ferrite magnets. Permanent Magnet Synchronous Machines (PMSM) have been universally used with rare-earth magnets or with ferrite magnets and distributed winding. The proposed topology is presented as an improvement to PMSM for high torque and low-speed applications. It has low copper losses due to its short end-winding and benefits from a low cost by virtue of its lack of rare earth materials. This paper presents two slot/pole combinations: the 18/16 and the 12/10. A 2D Finite Element Analysis is used to investigate the average torque, the power factor and the torque ripple of each structure. It is shown that high performance is achieved for both motors. However, a parametric-analysis is performed on the 18/16 motor and shows that the saliency torque cannot be improved without reducing the torque and the power factor. As for the 12/10 motor, its main drawback is its high torque ripple. The torque ripple is reduced using two techniques; a rotor step skew and the use of an asymmetric pole shape. In this paper, a combination of both methods is proposed in order to reduce specific torque harmonics. Finally a comparison of the two motors is presented in order to determine which one is more suitable for the high torque and low speed application.

I. INTRODUCTION

Research and development of high torque motors in direct drive applications gained significant attention recently, especially in the field of machine-tools, conveyers, elevators, etc. Generally, such applications operate at low rotational speeds. The conventional drive system, which consists of using a high-speed motor with a mechanical speed reducer, has many drawbacks especially the additional mechanical losses caused by the speed reducer and its low reliability. Hence, the production of high torque at low speed in a direct drive configuration is becoming a challenge for the machine designers and researchers. Such a system would be more reliable and efficient than the classical one. Rare-earth magnets such as Neodymium-Iron-Boron (NdFeB) or Samarium-Cobalt (SmCo) are generally used. These magnets are capable of producing strong magnetic fields and are suitable for synchronous machines in high torque density applications.

The design of Permanent Magnet Synchronous Motors (PMSM) with high torque density is actively studied. Researchers investigated many topologies and different operating principles. In order to improve the torque, the double air-gap structure has been widely studied. Motors with 2 stators and 1 rotor with distributed winding [START_REF] Wang | Design of high-torque-density double-stator permanent magnet brushless motors[END_REF] or concentrated winding [START_REF] Zhao | Dual-stator Interior Permanent Magnet Vernier Machine Having Torque Density and Power Factor Improvement[END_REF], [START_REF] Alamoudi | A split tooth permanent magnet machine design for high torque applications[END_REF] are able to produce a high torque but the manufacturing process of such designs is very complicated.

Another approach to improve the torque is to increase the surface of the air-gap; this is done using an exterior rotor [START_REF] Sato | Improved ferrite magnet vernier machine for an in-wheel machine[END_REF]- [START_REF] Fan | Investigation of a New Flux-Modulated Permanent Magnet Brushless Motor for EVs, Investigation of a New Flux-Modulated Permanent Magnet Brushless Motor for EVs[END_REF]. A more novel operating principle emerged lately, known as flux switching. The magnets are on the stator side and the rotor is a passive magnetic circuit with poles similar to the one used in switched reluctance motors [START_REF] Zulu | Permanent-Magnet Flux-Switching Synchronous Motor Employing a Segmental Rotor[END_REF]- [START_REF] Zhou | Torque Density and Magnet Usage Efficiency Enhancement of Sandwiched Switched Flux Permanent Magnet Machines Using V-Shaped Magnets[END_REF]. When the magnets are placed on the stator, their temperature rise may be more easily managed and the risk of demagnetization is reduced [START_REF] Zhu | Analysis of a Novel Multi-Tooth Flux-Switching PM Brushless AC Machine for High Torque Direct-Drive Applications[END_REF]. Hybrid excitation flux switching machines were also studied [START_REF] Sulaiman | Design studies on high torque and high power density hybrid excitation flux switching synchronous motor for HEV applications[END_REF]- [START_REF] Hua | A Novel Hybrid Excitation Flux-Switching Motor for Hybrid Vehicles[END_REF]. The extra excitation winding offers a variable flux capability, but it makes the structure more complex and requires an additional inverter to supply the excitation coil.

The previously mentioned structures are mainly based on rare-earth magnets. However, the rising price of these magnets has led to an increase in the cost of the motor. In order to solve this problem, a variety of motors which do not use or with reduced rare-earth materials have been extensively developed for high torque density applications. An external rotor switched reluctance motor is presented in [START_REF] Torkaman | External rotor SRM with high torque per volume: design, analysis, and experiments[END_REF] but is reported to have issues with noise and vibration. The authors in [START_REF] Kim | Torque Density Elevation in Concentrated Winding Interior PM Synchronous Motor With Minimized Magnet Volume[END_REF] used Vshape magnets in the rotor in order to concentrate the flux and minimize the volume of the magnets. Another category of motors is the one that uses non rare-earth permanent magnets such as ferrite or alnico. The low magnetic field created by these type of magnets forces the designers to use them in a flux concentration configuration [START_REF] Kim | Investigation and Experimental Verification of a Novel Spoke-Type Ferrite-Magnet Motor for Electric-Vehicle Traction Drive Applications[END_REF] or to use them as an additional torque component in synchronous reluctance motors. This machine is called Permanent Magnet Assisted Synchronous Reluctance Motor (PMASynRM) with distributed stator winding [START_REF] Morimoto | Experimental Evaluation of a Rare-Earth-Free PMASynRM With Ferrite Magnets for Automotive Applications[END_REF], [START_REF] Prieto | Effect of magnets on average torque and power factor of Synchronous Reluctance Motors[END_REF].

In this paper, a novel electric machine design has been investigated. It is a doubly-salient structure with a concentrated tooth winding on the stator and multi-V shape ferrite magnets in the rotor. The main advantages of this structure are the high torque that can be achieved and the low Joule losses in the winding. In fact, the multi-V-shape configuration enhances the flux concentration phenomenon compared to the simple Vshape magnet, and the short end-coil of the concentrated tooth winding offers the possibility of reducing the copper losses which can increase the efficiency of the machine. This type of motor is shown to be a good candidate for high torque applications. However, there are very few technical papers that investigated the performance of these motors [START_REF] Kano | Torque Ripple Reduction of Saliency-Based Sensorless Drive Concentrated-Winding IPMSM Using Novel Flux Barrier[END_REF]. Hence, a comprehensive comparison and analysis of multi-V-shape magnet with concentrated tooth winding motors is necessary.

When designing motors for direct drive applications, two essential criteria have to be met: the first one is the ability to develop high torque at low speed and the second one is the smoothness of the torque produced. The slot/pole combination is a key parameter that affects the above mentioned criteria. Two different combinations will be studied in this paper: the 18/16 and the 12/10 motors. Thus, in the next two sections, 2D Finite Element Analysis (FEA) using FEMM coupled with MATLAB is conducted to evaluate the performances of the two structures in terms of electromagnetic torque, power factor and torque ripple. The results of an FEA simulation for each topology are presented and an analysis based on certain geometrical parameters is conducted in order to better understand how the drawbacks of each machine can be improved. Finally, a comparison of the two machines performance is given in order to determine which one is more suitable for the high torque and low speed application.

II. ANALYSIS OF THE 18/16 STRUCTURE

The structure with 9 stator slots and 8 rotor poles is often encountered since it develops a very smooth torque due to the fact that 9 and 8 have no common divider [START_REF] Meier | Permanent-Magnet SynchronousMachines with Non-OverlappingConcentrated Windings for Low-Speed Direct-Drive Applications[END_REF]. However, a rotating force acts on the stator because of the harmonic nature of this structure. This leads to the recommendation to only use multiples of this combination, in order to provide harmonic cancellation [START_REF] Meier | Permanent-Magnet SynchronousMachines with Non-OverlappingConcentrated Windings for Low-Speed Direct-Drive Applications[END_REF]. The first multiple of this elementary structure, for instance, the 18/16 structure is considered in this paper. This section presents the winding sequence of the stator. Then a reference machine is considered and its performance is shown. Next, the analysis of the saliency torque and the total torque is made. Finally, the torque ripple of the structure is presented.

A. Winding Configuration for the 18/16 Motor

The machine is a three phase motor (m = 3), and is designed with a non-overlapping concentrated tooth winding. A double layer winding is chosen so that the fundamental winding factor for the 18 slot/16 pole design is high and equal to 0.945 which makes this topology suitable for high torque production [START_REF] Meier | Permanent-Magnet SynchronousMachines with Non-OverlappingConcentrated Windings for Low-Speed Direct-Drive Applications[END_REF]. Each tooth has a concentrated coil and the mechanical angle between two consecutive coil-vectors is 20°. The complete vector diagram of the stator is given in Fig. 1 with tooth number 1 arbitrarily set at zero angle. In order to determine the proper winding for each coil, the mechanical angles (θ meca ) are converted to electrical angles (θ elec ) by using the following equation:

= ( 1
)
where p = 8 (number of pole pairs). The electrical angle is then matched with the closest relevant angle of a normal 3 phase vector diagram (Fig. 2). If the first coil is A+, the second one is at 160 electrical degrees so it is matched with 180 electrical degrees which corresponds to A-. This procedure is applied for every single tooth and leads to the following winding sequence: A+ A-A+, B+ B-B+, C+ C-C+. This winding pattern is repeated twice in order to cover the whole stator.

B. Motor Structure Investigation

The considered machine presents 2 layers of V-shape permanent magnets (PM) as shown in Fig. 3. A layer (or barrier) is mainly defined by 2 parameters presented in Fig. 4: δ is the barrier's tilt angle and k = θ/β is the ratio of the barrier's opening angle with respect to the half pole angle. Since each pole has 2 barriers, the index i is added to the parameter k in order to designate the barrier number 1 or 2. All poles are symmetrical so the same δ and k i values are applied to all of them. A reference machine is considered such that δ = 5°, k 1 = 0.6 and k 2 = 0.3. The specifications for the FEA of this structure are given in TABLE I. Fig. 5 shows the mean torque versus the current angle α (angle between the current vector and the q-axis) in electrical degrees (°elec). The maximum torque is obtained for α = 20°elec which implies that the d-component of the current (Id) is very small compared to its q-component (Iq).In fact, the mean torque is given by the following equation:

= 3 2 + - (2)
where ψ PM is the permanent magnet flux , L d and L q are the inductance in the d and q axis respectively. Thus, the maximum torque is achieved with I d << I q when (L d -L q ) is small which means that this machine presents a low saliency ratio (L d /L q ). With this knowledge, the current angle value at optimal torque (α opt ) represents the saliency of the structure: a high value of α opt reflects a high saliency ratio and vice versa.

Since the salient component of the torque is magnet-free, it is important to maximize the saliency ratio so that the same torque value is obtained with less magnet volume which reduces the motor's cost. The objective of the next paragraphs is to analyze the effect of barrier number and tilt angle on the torque and the power factor of the machine.

C. Saliency Torque Investigation

To better understand the salient component of the torque, the magnets are deliberately omitted. At this point, the structure becomes a synchronous reluctance motor. The torque is produced by the difference between L d and L q . A parametric FEA analysis is conducted. Fig. 6 represents the saliency torque with respect to the current angle for different values of δ from 0 to 15°. It shows that the optimal torque is obtained at α = 45°elec and that its value increases with the barrier tilt angle. Its maximum is found to be equal to 32 Nm. Fig. 7 shows the effect of the number of barriers on the saliency torque. The maximum torque increases significantly from 1 to 2 barriers, as would be expected since the field lines encounter a lower reluctance in the q-axis than in the d-axis, so the difference between L d and L q increases. However, a 3 barrier structure doesn't significantly improve the saliency torque. This is due to the limited geometrical space as a result of the high number of poles (16 poles). Thus, a two barrier structure is retained for further investigation.

D. Total Torque and Power Factor Analysis

The presence of PM in the flux barriers affects the torque and the Power Factor (PF) of the machine. The 2 barrier structure is considered with k 1 and k 2 defined as in TABLE I.

At first, a parametric FEA is conducted with constant PM volume and different values of δ. The results of the simulation are given in Fig. 8 for the mean torque and in Fig. 9 for the power factor. The optimal torque increases when the value of δ is higher, with practically a constant optimal current angle α opt = 30°elec. The maximum torque is 116 Nm. As for the PF, it is higher when δ is increased knowing that the PM volume remains constant. Therefore, the PF is improved when the ratio of the PM volume to the total barrier volume is high.

In a second phase, the PM volume is not kept constant and it completely fills the barriers for each value of δ (PM volume = barrier volume). Fig. 10 and Fig. 11 show that the optimal torque and the PF can achieve high values when δ is decreased (idem when PM volume is increased). However, α opt decreases when δ becomes smaller. Thus, the salient torque becomes negligible when compared to the PM torque if δ is decreased.

E. Torque Quality Verification

The torque of the reference machine (TABLE I) is computed for a whole electrical period as shown in Fig. 12. The current angle α = α opt = 20°elec so the optimal torque is obtained. The torque ripple (∆T) is calculated as follows:

Δ = - = (3)
where T pp is the peak-to-peak torque and T avg is the average torque. ∆T is found to be equal to 3.21 % which confirms that the 18/16 structure develops a smooth torque.

F. Conclusion for the 18/16 structure

The average torque, the Power Factor (PF) and the torque ripple of the 18/16 motor are investigated. The analysis of the results shows that this configuration produces a high torque at low rotational speeds with a reasonable PF. Also, the torque ripple is very low. However, a compromise has to be found if one seeks to maximize the saliency torque. In fact, increasing the barrier tilt angle δ improves the saliency torque but deteriorates the total torque and the PF.

Another quite common slot/pole combination is analyzed in the next section. It is the 12/10 structure. Since the greatest common divisor of the number of slots and the number of poles is equal to 2, then this configuration results in low unbalanced magnetic force and in low noise [START_REF] Verez | Impact of pole and slot combination on noise and vibrations of fluxswitching PM machines[END_REF].

III. ANALYSIS OF THE 12/10 STRUCTURE

In this section, the winding of the 12/10 structure is presented. Then, the performance of a reference machine is described. Next, the rotor skewing technique for torque ripple reduction is presented. This is followed by a Design of Experiments (DOE) which is carried out in order to investigate the asymmetric poles technique for torque ripple minimization. Finally, two particular strategies for combining these two methods are studied and an efficient method for torque ripple reduction is proposed. The following paragraphs are a preliminary study that analyzes the electromagnetic torque of the structure.

A. Winding Configuration for the 12/10 Motor

For the 12/10 structure, as for the 18/16 structure, the double layer non-overlapping concentrated tooth winding is chosen. The fundamental winding factor is equal to 0.933 so the structure would be suitable for high torque production [START_REF] Meier | Permanent-Magnet SynchronousMachines with Non-OverlappingConcentrated Windings for Low-Speed Direct-Drive Applications[END_REF]. The machine is a 3 phase motor, and the mechanical angle between two consecutive coil-vectors is 30°. Electrical angles are given by Eq.1 where p = 5. Using the same procedure described for the 18/16 motor, the winding sequence of the 12/10 structure is: A+ A-, B-B+ , C+ C-, A-A+ , B+ B-, C-C+. It is worth noting that the second half of the stator is acyclic compared to the first one, because one machine half contains an odd number of poles.

B. Performance of the Proposed Structure

The proposed motor has a rotor with 2 barriers as presented in Fig. 13. The layer geometrical parameters are showed in Fig. 4. A reference machine is defined with the parameters given in TABLE II. The results of the FEA for the mean torque with respect to the current angle are shown in Fig. 14. The maximum torque is 200 Nm with α opt = 30°elec. The power factor of this machine is given in Fig. 15, it is equal to 0.66 for α = 30°elec. For the 12/10 combination, the torque is periodic with a period of 60°elec which is equivalent to one sixth of an electric period. The torque ripple is shown in Fig. 16. It is calculated using Eq.3 and is equal to 33%. Therefore, a 12/10 motor is capable of producing a high torque at low speed with a reasonable power factor, but the main drawback of such structure is the torque ripple that is very high. A harmonic decomposition of the torque is presented in Fig. 17. The second (2 nd ) harmonic is the highest one; followed by the first (1 st ) harmonic. The objective of the next paragraphs is to reduce the torque ripple to less than 5%. Different techniques for minimizing the torque ripple fall typically into two major categories: the first concerns the machine design and the second is based on active control schemes [START_REF] Jahns | Pulsating torque minimization techniques for permanent magnet AC motor drives-a review[END_REF]. In this article, the first category is investigated. Two main techniques can be identified: rotor skewing and rotor magnetic design optimization. Skewing technique was studied during the last decade [START_REF] Deodhar | Modeling of skew using the flux-MMF diagram[END_REF] and it continued to be the subject of recent work with different motor types [START_REF] Chu | Reduction of On-Load Torque Ripples in Permanent Magnet Synchronous Machines by Improved Skewing[END_REF]- [START_REF] Li | A Novel Dual-Stator Flux Switching Permanent Magnet Machinewith Six Stator Slots and Four Rotor Poles Configuration[END_REF].As for the magnetic design of the rotor, it includes primarily the design of asymmetric rotor poles [START_REF] Sanada | Torque ripple improvement for synchronous reluctance motor using an asymmetric flux barrier arrangement[END_REF]- [START_REF] Pina | Modeling of Synchronous Reluctance Motors Aidedby Permanent Magnets with Asymmetric RotorPoles[END_REF].

C. Rotor Step Skewing

Since the 2 nd harmonic is the highest one, the skew angle (ψ skew ) is calculated in order to minimize it. The reduction of the 2 nd harmonic is achieved by shifting its phase by 180°elec.

Because it has a period of 30°elec the skew angle will be:

= 30 180 360 = 15° (4)
which corresponds to 3 mechanical degrees (Eq. 1 with p = 5).

Fig. 18 shows the initial torque and the torque with the step skew applied. The total torque is obtained by adding the two waveforms such that ∆T is reduced from 33% to 5%.

D. Asymmetric Pole torque ripple reduction

When designing the rotor of an electric motor, the torque ripple is reduced by using asymmetric poles. Fig. 4 denotes that the two main parameters of a barrier are the tilt angle δ and the ratio of the barrier's opening angle k.

1) Effect of the parameter δ

A series of simulations are performed with different values of δ while maintaining the same values of k and the same PM volume. The current angle is set to 30°elec. The results shown in Fig. 19 imply that varying δ between 0 and 15° keeps ∆T between 35% and 38.5% which is practically unchanged. Thus, the parameter δ does not influence the torque ripple directly. It can then be fixed at a value of 15°.

2) Effect of the parameter k

In order to study the influence of the barrier opening angle, four variables are defined: k ij with i = {1, 2} and j = {1, 2}. The index "i" corresponds to the magnetic pole type (North or South) and the index "j" corresponds to the number of the barrier.

A Design of Experiments (DOE) is carried out using the predefined 4 variables: k 11 , k 12 , k 21 and k 22 as inputs and the average torque, the 1 st and the 2 nd harmonic as outputs. Each variable has 4 levels defined within the following ranges:

• k 12 and k 22 ∈ [0.1, 0.3] • k 11 and k 21 ∈ [0.5, 0.7]
The variation limits are chosen in a way that guarantees the non-overlap of the barriers. The 4 levels of each variable are defined using the distances [-1, -0.5, 0.5, 1] with respect to the center of each interval. For instance, the k 12 interval center is 0.2 so this variable takes the following values: 0.1, 0.15, 0.25 and 0.3.The FEA is conducted at 40 A (rms) with a current angle α opt = 30°elec. Fig. 20, Fig. 21 and Fig. 22 show the results of the first order interaction between the inputs and the outputs.

According to Fig. 20, the highest torque value is obtained for k 11 = 0.7 (blue dashed line) and k 21 = 0.7. However, k 12 and k 22 are constant regardless of what value is set for k 11 and k 21 .

In Fig. 21, for k 11 = 0.7, the minimum amplitude of the 1 st harmonic is given for k 12 = 0.15, k 21 = 0.7 and k 22 = 0.25. The second row suggests a minimum value for k 12 = 0.25 (red continuous line), but this contradicts the analysis of the first row and increases the amplitude of the 1 st harmonic. Hence, the results of the first row, marked by black squares, are chosen.

As for the 2 nd harmonic, Fig. 22 shows that for k 11 set to 0.7, the minimum amplitude is reached for k 12 = 0.15, k 22 = 0.15 and k 21 =0.5. However, setting k 21 to 0.5 decreases the average torque according to Fig. 20. A compromise is made between maximizing the average torque and minimizing the amplitude of the 2 nd harmonic, so the value of 0.65 is chosen for k 21 . Black square markers are used to locate the selected values. A summary of the DOE results is given in TABLE III. The configurations that minimize either the 1 st or the 2 nd harmonic lead to an asymmetric pole structure.

3) Minimization of the 2 nd harmonic

As shown in Fig. 17 the 2 nd harmonic is the dominant harmonic amplitude. The configuration that minimizes the 2 nd harmonic is tested with k 11 = 0.7, k 21 = 0.65 and k 12 = k 22 = 0.15. The torque ripple and its harmonic decomposition are presented in Fig. 23 and Fig. 24. ∆T passes from 33% to 8.2%. The 2 nd harmonic is reduced significantly. However, the first harmonic remains relatively high and is responsible for the remaining torque ripple. To further reduce the torque ripple different strategies to combine the step skew and the asymmetric poles are investigated. Fig. 23. Torque ripple with the 2nd harmonic reduced using asymmetric poles Fig. 24. FFT of the torque with the 2nd harmonic reduced using asymmetric poles

E. Combination of Rotor Step Skewing and Asymmetric Poles

1) 1 st strategy: Reduction of the 2 nd harmonic using asymmetric poles and the 1 st harmonic by rotor step skewing

The minimization of the 2 nd harmonic using asymmetric poles leads to ∆T = 8.2%. The rotor step skew is used to reduce the 1 st harmonic which now becomes the largest (Fig. 24). Since its period is 60°elec, a phase shift of 180°elec is obtained with:

= 60 180 360 = 30° = 6° (5)
∆T decreases from 8.2% to 6% as shown in Fig. 25. The torque ripple reduction is not significant because of the high skew angle. In fact, skewing the rotor is equivalent to increasing the current angle. Adding 30°elec to α opt = 30°elec leads to a current angle of 60°elec which significantly decreases T avg, , it passes from 200 Nm to 145 Nm according to Fig. 14. Thus, the ratio given by Eq.3 does not improve much. 2) 2 nd strategy: Reduction of the 1 st harmonic by asymmetric poles and the 2 nd harmonic by rotor step skewing Based on the previous analysis, another strategy is proposed. The 1 st harmonic is reduced using asymmetric poles (TABLE III) and leads to ∆T = 11.63 %. The structure is then step skewed in order to reduce the 2 nd harmonic with = 15° = 3° . The result given in Fig. 26 shows that ∆T = 4.62%. Skewing the rotor by 15°elec does not decrease T avg significantly; it passes from 200 Nm to 187 Nm according to Fig. 14. Hence, the ratio given in Eq.3 is reduced.

3) Improved 2 nd strategy

As mentioned previously, the barrier tilt angle δ does not affect the torque ripple directly. However, reducing δ results in increasing the PM volume so that Tavg is increased and the ratio (Eq.3) further decreases. The result of the 2 nd strategy with δ = 5° is shown in Fig. 27. The following table summarizes the results for different values of δ. Changing the value of δ does not significantly affect the peakto-peak value of the torque but increases its average value so the torque ripple is further reduced. F. Conclusions on the 12/10 structure The performance of the 12/10 motor has been investigated. This structure is able to produce a high torque at low speed with an acceptable power factor. The main drawback of this configuration is the high torque ripple that it exhibits. However, the torque quality can be improved using rotor step skew but the average torque is decreased. As for the asymmetric rotor pole technique, it reduces the torque ripple but not below the target value of 5%. Different combinations of the above techniques are investigated. In this paper, the proposed strategy for the 12/10 motor reduces the 1 st harmonic using asymmetric poles and the 2 nd harmonic using rotor step skew with a low value of the barrier tilt angle. This combination reduces the torque ripple significantly without significantly reducing the average torque.

IV. COMPARISON OF THE 18/16 AND THE 12/10 STRUCTURES In terms of torque and power factor, both structures achieve a high average torque at low speed with a power factor of around 0.7. Since the two motors are doubly-salient structures, their optimal current angle is low and is equivalent to a low saliency torque. The 12/10 motor develops the highest torque at α opt = 30° (Fig. 14). As for the 18/16 motor, it has the highest torque for α opt = 20° and cannot attain an optimal current angle of 30° without reducing the average torque (Fig. 10).

The last comparison criterion is the quality of the torque. The 18/16 motor does not require further modifications in the structure to obtain low torque ripple since it develops a smooth torque. On the contrary, the 12/10 motor suffers from high torque ripple that can be reduced by using a combination of techniques but this may complicate the improved structure. The following table summarizes the main comparison points: The choice of structure that is more suitable for a high torque and low speed application depends whether the target is to design a motor that is relatively easy to manufacture, with satisfactory performances, or to minimize the PM volume despite the modifications made to the structure to obtain the desired performance.

Since the cost of ferrite magnets is low; one may favor the less complex structure. Thus, the 18/16 motor would be an appropriate choice and may be the subject of future work.

Torque [N.m]

V. CONCLUSION In this paper a novel doubly salient structure with concentrated tooth winding and multi-V shape ferrite magnets is studied. Two slot/pole combinations are investigated: the 18/16 and the 12/10. The performance of each machine is analyzed using 2D Finite Element Analysis (FEA). Both motors exhibit a high torque at low speed with a good power factor. The 18/16 develops a smooth torque without implementing any torque ripple reduction technique. On the other hand, the 12/10 structure can overcome its high torque ripple using appropriate rotor electromagnetic design.

A DOE is carried out and the analysis of the results leads to asymmetric pole configurations that can reduce specific torque harmonics. In addition, a combination of rotor step skew and the asymmetric pole technique is proposed for the 12/10 machine and leads to a torque ripple of 3.44% without significantly reducing the average torque.

Finally, the comparison of both motors shows their suitability for high torque and low speed applications. A compromise has to be made between the permanent magnet additional cost in the case of 18/16 machine and the rotor manufacturing complexity in case of the 12/10 machine.

Fig. 1 .Fig. 2 .

 12 Fig.1. Vector diagram of the stator with 18 slots Fig.2. Vector diagram of a 3 phase system

Fig. 3 .Fig. 4 .

 34 Fig.3. 18/16 motor structure

Fig. 5 .

 5 Fig.5. Torque vs current angle for the 18/16 reference machine

Fig. 6 .Fig. 7 .

 67 Fig.6. Saliency torque (without PM) for different values of δ

Fig. 8 .Fig. 11 .

 811 Fig.8. Torque for different values of δ with a constant PM volume

Fig. 12 .

 12 Fig.12. Torque ripple of the reference machine

Fig. 13 .Fig. 14 .Fig. 15 .Fig. 16 .Fig. 17 .

 1314151617 Fig.13. 12/10 motor structure

Fig. 18 .

 18 Fig. 18. Total torque ripple with a skew angle of 15°elec

Fig. 19 .

 19 Fig. 19. Torque ripple for different values of δ at constant PM volume

Fig. 20 .Fig. 21 .Fig. 22 .

 202122 Fig. 20. Results of the DOE for the average torque

Fig. 25 .

 25 Fig. 25. Total torque ripple using the 1st strategy

Fig. 26 .

 26 Fig. 26. Total torque ripple using the 2nd strategy

Fig. 27 .

 27 Fig. 27. Total torque ripple using the 2nd strategy with δ = 5°

TABLE I .

 I SPECIFICATIONS OF THE 18/16 REFERENCE MACHINE

	Specification	Value
	Stack length	200 mm
	Exterior diameter	260 mm
	PM remanent flux density	0.4 T
	Target average torque	190 Nm
	Target torque ripple	5%
	Rated speed	500 rpm
	Rated current	40 A (rms)
	δ	5°
	k1	0.6
	k2	0.3

TABLE II .

 II SPECIFICATIONS OF THE 12/10 REFERENCE MACHINE

	Specification	Value
	Stack length	200 mm
	Exterior diameter	260 mm
	PM remanent flux density	0.4 T
	Target average torque	190 Nm
	Target torque ripple	5%
	Rated speed	500 rpm
	Rated current	40 A (rms)
	δ	3°
	k1	0.6
	k2	0.3

TABLE III .

 III RESULTS OF THE DOE

	Objective	k11	k12	k21	k22	δ
	Maximize the average torque	0.7	No impact	0.7	No impact	15°
	Minimize the 1 st harmonic	0.7	0.15	0.7	0.25	15°
	Minimize the 2 nd harmonic	0.7	0.15	0.65	0.15	15°

TABLE IV .

 IV TORQUE RIPPLE USING THE 2 ND STRATEGY WITH DIFFERENT VALUES OF δ

	δ [°]	Tpp [Nm]	Tavg [Nm]	∆T [%]
	15	8	174	4,6
	10	7,1	183	3,8
	7,5	6,92	189,6	3,65
	5	6,7	196	3,44

TABLE V .

 V COMPARISON SUMMARY

		18/16 motor	12/10 motor
	Average torque	Good	Good
	Power factor	Good	Good
	Machine saliency	Very bad	Bad
	Torque ripple	Very good	Very bad


E Benoit

G Mauris

L Foulloy

Lamii / Cesalp

Fuzzy sensor for the perception of colour

The aim of this paper is to propose a new method for building a fuzzy partition on multi-dimensional spaces. This method is apply for creating fuzzy symbolic sensors which use multi-component measurements. Colour sensing is an interesting perception to apply this method. Indeed, men have good control on this sensing but can not explain it simply. Then, the fuzzy colour sensor can learn human perception of colour and does not need explicit information about colour perception mechanisms.

Introduction

Introduced since several years, fuzzy symbolic sensors, also called fuzzy sensors, are intelligent sensors which are able to receive, to produce and to handle fuzzy symbolic information [Foulloy 88], [Benoit 91]. This particularity allows them to be used as perceptive organs for symbolic controllers like fuzzy controllers and fuzzy expert systems. Furthermore, this kind of sensor can own the most advanced functionalities of intelligent sensors, like auto-adaptation and learning, by using artificial intelligence techniques as proposed by Zingales [Zingales 91].

Actual fuzzy sensors work on single-component measurements like distance, temperature and so one. In order to make fuzzy description of a multi-component measure like colour or smell, we propose an original fuzzy description method based on multi-dimensional fuzzy sets. In order to perform this method on a real sensor, we chose to build a fuzzy colour sensor which make the fuzzy description of the colour of a surface.

Fuzzy sensors

Fuzzy symbolic sensors are based on the translation of information from a numerical representation to a symbolic one. To perform a symbolic measurement, it is necessary to clearly specify the relation between symbols and numbers [Zadeh 71]. Introduce a set of symbols S. Let E be the set of all possible measurement values. An injective mapping from the symbolic set L in the set of the fuzzy subsets of measurements. This mapping called a fuzzy meaning and denoted τ : S ¡ F(E) associates any symbol to a fuzzy subset of measurements. Symbolic measurement is now obtained from a mapping, called a fuzzy description and denoted ι: E ¡ F(S). It associates any measurement to a fuzzy subset of the symbolic set S. There is a fundamental relation between fuzzy description and fuzzy meaning. If a symbol belongs to the description of a measurement, then the measurement belongs to the meaning of the symbol, i.e:

µ ι(x) (a) = µ τ(a) (x) ( 1 )
If the set of the symbol meanings is a fuzzy partition of E then we have a fuzzy nominal scale [Benoit 93], which is an extension to fuzzy subsets of the concept of nominal scale [Finkelstein 84]. For fuzzy sensors, we always impose to be in this case .

In the following example, a fuzzy telemeter use the set of symbols S={Close, Medium, Far}. We can see the fuzzy meaning of symbols and the fuzzy description of the measurement x=12 cm.

Benoit E., Foulloy L., Galichet S., Mauris G. "Fuzzy sensor for the perception of colour", IEEE World congress on Computational Intelligence, June 26 -July 2 1994, Orlando, USA, pp. 2008-2013

Fig. 1 3

Multi-component fuzzy sensors

When a sensor use several transducers, the measure is a vector of numerical values, and the measurement set is a multidimensional volume. Then, the meaning of each symbol must be a fuzzy set defined in this multi-dimensional volume. Furthermore the set of meanings has to be a fuzzy partition of the measurement set.

In this paper, we consider an initial knowledge about measurement. This knowledge is materialized by the meaning of symbols on a small subset V of the measurement set. Then the measurement set is partitioned in n-simplexes with the Delaunay triangulation method. A n-simplex in a n-dimensional space is a polyhedra with n+1 vertices. For example, a 2-simplex is a triangle and a 3-simplex is a tetrahedron. The points used to perform the triangulation are the elements of the set V.

The membership function of the meaning of each symbol is defined on each n-simplex by a multi-linear interpolation.

We suppose the restriction on a n-simplex of the membership function of the meaning of a symbol s is :

µ τ(s) (v) = µ τ(s) (x 1 ,x 2 , ..., x n ) = a 1 x 1 +a 2 x 2 + ... +a n x n +a n+1 (2)
The value of this function is known for the n+1 vertices of the n-simplex. So the n+1 factors a i can be calculated.

Where v i is the i th vertex of the n-simplex, and x i j is its j th component.

This process is performed on each n-simplex and for each symbol. Then we have a fuzzy nominal scale defined on E. This scale is an extension of the fuzzy nominal scale on V.

With this method, the knowledge needed to configure the sensor is very compact. It can be acquired during a learning phase by a communication with a system called teacher which can be a man or an expert system. During the learning phase, the teacher and the sensor analyse the same phenomenon, and the teacher gives its description to the sensor. The sensor increases its knowledge with its measure associated to the teacher description. Then it can build the fuzzy nominal scale.

Colour measurement

Human beings perceive electromagnetic light beams by four types of photochemical transducers: three cones for day vision and one rod for night vision. The photometric sensors give back information in relation to the received energy. The sensation of colour is generated by the different spectral sensitivities of the cones. The "blue" cones detects short wavelength, whereas the "green" and "red" cones detect respectively medium and long wavelengths.

The artificial sensing (for example the video camera) is based on three photometric transducers that recreate the effects of red, green and blue cones. For the fuzzy colour sensor, we use three photo-transistors with optical filters. The sensor τ(Close) τ(Medium) τ(Far)

x (cm) 15 12 10 µ 0 1

Close Medium Far

E S µ ι(12)

A M

1 -B = M x 1 1 ... x 1 n 1 ... ... ... … x n 1 1 + ... x n 1 + n 1 = A a 1 … a n 1 + = B µ τ s ( ) v 1 ( ) µ τ s ( ) v 2 ( ) ... µ τ s ( ) v n 1 + ( ) =
has three components : a light source, a sensing unit, and a measurement head. The sensing unit includes the transducers, a signal conditioner, and a computation device which performs signal processing, fuzzy description, and learning procedure.

4.1) Fuzzy description of RGB components

The responses of the detectors are normalized between 0 and 1, and then the colour space is simply a unit cube (R,G,B). This colour space is used as the measurement set of the fuzzy sensor. For partitioning the whole measurement universe, the vertices of tetrahedron must be characteristic points. Then, the smallest partition contains eight elements, and the vertices of the cube are characteristic measurements. Experiments show that for several basis colours, the learning need several characteristic points (2 or 3) for a symbol. Contrary to men, it makes an important difference between pale and dark colours.

4.2) Fuzzy description of chrominance

During a colour description in the common language, the luminosity is usually expressed separately. For example we can say "pale blue" or "dark red". In order to introduce this knowledge in the sensor, a non linear transform is applied on the RGB cube (see fig. below). Then, luminance and chrominance can be describe separately. The measurement set of the luminance is monodimensional, and its description is not developed in the paper. The measurement set of the chrominance is two-dimensional, it is called the chrominance plane of colour and it is used as the measurement set.

The experiments confirm the advantage of this representation : the sensor generally needs only one learning point by symbol. are especially adapted for sensing with unknown mechanisms, but easily controlled by a man. Indeed, the sensor does not need explicit information about these mechanisms to be configurated.

As the fuzzy colour sensor gives a fuzzy representation of the measure, it can be used in a symbolic control system. The method applied to build multi-dimensional fuzzy sets can be used in many applications. For example, pattern recognition needs to make a classification in a multi-dimensional space, and will be an interesting domain to develop this method.

Fig. 2

 2 Fig.2

Fig. 3

 3 Fig. 3 RGB cube before and after the transform


Denis Giri
email: denis.giri@supelec.fr

Maxime Rosenwald
email: maxime.rosenwald@supelec.fr

Benjamin Villeneuve
email: benjamin.villeneuve@supelec.fr

Sylvain Le Gallou
email: sylvain.legallou@supelec.fr

Renaud S Éguier
email: renaud.seguier@supelec.fr

Scale Normalization for the Distance Maps AAM

The Active Apearence Models (AAM) are often used in Man-Machine Interaction for their ability to align the faces. We propose a new normalization method for AAM based on distance map in order to strengthen their robustness to differences in illumination. Our normalization do not use the photometric normalization protocol classically used in AAM and is much more simpler to implement. Compared to Distance Map AAM performances of [1] and other AAM implementation which use CLAHE [2] normalization or gradient information, our proposition is at the same time much robust to illumination and AAM initialization. The tests have been drive in the context of generalization: 10 persons with frontal illumination from M2VTS database [3] were considered to build the AAM, and 17 persons under 21 different illuminations from CMU database [4] were used for the testing base.

I. INTRODUCTION

In the context of Man-Machine Interaction, face alignment (precise detection of key elements of the face: eyes, nose and mouth) is a necessary step for face recognition, gesture analysis and lip reading. The Active Appearance Models (AAMs) initially proposed by Cootes in [START_REF] Cootes | Active appearance models[END_REF] allow to detect finely the outlines of those key elements. To do so, the AAMs combine shape information with texture information. Indeed, the AAMs are based on a priori knowledge of shapes (points of interests connected to each other) and shape-free textures of a training database. They can thus be used to generate a set of plausible representations of shapes and textures of the learned objects. They also allow the search for objects in images by an optimization process on model parameters, in order to match the model as well as possible on the image zone containing the object.

The targeted applications are meant to be used on embedded systems (mobile phones, game consoles) in both indoors and outdoors environments. However, this implies a perfect robustness to illumination variations, and since the AAMs are partially based on texture analysis, they are quite sensitive to illumination conditions. We therefore propose a new normalization procedure dedicated to the AAM which use the Distance Map instead of gray level textures and compare it to standard methods that have already been proposed to address the specific problem of illumination robustness.

In the next section, we will present the different methods proposed by the scientific community to improve the AAM robustness illumination. In section III, different well known techniques and our proposition will be explain. The section IV will presents comparison and we will conclude in section V.

II. STATE OF THE ART

This illumination problem in AAM is far from new. Recently, [START_REF] Huang | Face alignment under variable illumination[END_REF] have proposed a two step method. They first used an edge-filtering pre-processing, using a Gabor transform, which allows the AAMs to roughly converge to the targeted face. And then, they used a patch filtering pre-processing, some kind of adaptive histogram equalization method, to refine the convergence. [START_REF] Gallou | Distance maps : A robust illumination preprocessing for active appearance models[END_REF] and [START_REF] Pujol | A supervised modification of the Hausdorff distance for visual shape classification[END_REF] used Distance Map instead of grey-level image texture. Distance Map (DM) are pictures in which each pixel level is equal to its distance to the nearest edge pixel. In [START_REF] Pujol | A supervised modification of the Hausdorff distance for visual shape classification[END_REF], six DM per person were made from six different grayscale pictures. This allowed to create an average DM that extracts the constant features of a face, using Hausdorff Distance [START_REF] Huttenlocher | Comparing images using the Hausdorff distance[END_REF]. [START_REF] Gallou | Distance maps : A robust illumination preprocessing for active appearance models[END_REF] clearly pointed out the qualities of DM when used with AAMs. Nevertheless, they implemented the classical AAM photometric normalization method which was time consuming and used some persons from CMU database to learn the model, which was tested on other persons from the same database. Therefore the AAM learned CMU background information which facilitates the convergence on the tests images.

In the next section, different techniques will be exposed before the presentation of our specific normalization.

III. PRE-PROCESSES

After having introduced the AAM, we will rapidly propose the different pre-processes to which we will compare our proposition explain in section III-C.

A. Active Appearance Models

The AAMs are a pattern recognition method proposed in the 90's (see [START_REF] Cootes | Active appearance models[END_REF] and [START_REF] Stegmann | Active appearance models: Theory, extensions and cases[END_REF]) for medical image processing and face analysis. They works in two phases:

• In the 1st phase, they learn how a human face looks like by creating a mathematical model, using a database of annoted face pictures. That model includes the memorization of the mean shape and the mean texture of a human face, and their main variation modes throw Principal Component Analysis (PCA), according to the picture learning database. A PCA on a shape training base and a PCA on a shape-free texture training base are applied respectively in order to create the statistical shape and texture models given by the formulas:

x i = x moy + Φ x * b x and g i = g moy + Φ g * b g (1)
with x i and g i are respectively the synthesized shape and texture, x moy and g moy the mean shape and the mean texture, Φ x and Φ g the matrices of eigenvectors of shape and texture covariance matrices and b x and b g the controlling vectors of the synthesized shape and texture.

Another PCA is then applied on several examples of b which is the concatenation of b x and b g in order to obtain the appearance parameter c:

b = Φ * c (2)
with Φ the matrix of PCA eigenvectors. c is a vector controlling b x and b g (equation 2) at the same time, that is to say the shape (first equation 1) and texture (second equation 1) of the model. Then, AAMs create a regression matrix by exploring the possibilities of the model it has just created, allowing the algorithm to predict how to adapt to any situation. • In the 2nd phase, the AAM seeks a face in a picture by minimizing the difference of the model's texture to the texture it is placed on. That minimization is done through a number of iterations of the following iterated algorithm. First, the AAMs use the regression matrix to determine which parameter has to be changed, and then, the model goes through a few tests in order to find the best value for that parameter. If a same illumination is used with all the pictures presented to this algorithm, then it will work perfectly well. However, due to the fact that the AAMs is based on textures, any slight modification in illumination will cause a huge loss in efficiency. To solve this problem, a photometric normalization has been introduced in that algorithm. It makes sure that each picture luminosity has the same first an second order statistics [START_REF] Stegmann | Active appearance models: Theory, extensions and cases[END_REF], thus improving the efficiency of the AAMs. However, this doesn't solve the main problem, which is the sensitivity to the angle of illumination. In order to solve this problem, following solutions have been formulated: adaptive histogram equalization, gradient texture, and distance maps.

B. Pre-processing for robustness to illumination variations 1) Adaptive histogram: As Fig 1 shows it, the classical

AAMs works on the original grayscale pictures and need few iterations to converge. Like [START_REF] Huang | Face alignment under variable illumination[END_REF], we perform a Contrast Limited Adaptive Histogram Equalization (CLAHE) [START_REF] Zuiderveld | Contrast Limited Adaptive Histogram Equalization[END_REF]. This pre-process divides the picture into 64 tiles, creates the mapping functions associated to these 64 tiles. Each pixel is then processed using the 4 adjoining tile's mapping functions, the color of the resulting pixel being a bilinear interpolation of the results given by these 4 mapping functions. The result is a smooth picture with a much more homogeneous illumination. As it can be seen in Fig 2, the AAM preceded by a CLAHE equalization need few iterations to converge 2) Gradient texture: CLAHE equalization improve the results in the context of profil or semi-profil illumination. For that reason, we extract the gradient norm of the CLAHE images to produce the model and the tests images illustrated in Fig 3 . However, since the gradient-processed pictures are not subject to a high variability of luminosity, the photometric normalization described above might not be necessary. To evaluate this assumption, two sets of tests will be made: with and without normalization.

3) Distance Map: Finally, we propose to test the usefulness of Distance Maps (DM) in AAMs based face alignment methods (see [START_REF] Gallou | Distance maps : A robust illumination preprocessing for active appearance models[END_REF] and [START_REF] Pujol | A supervised modification of the Hausdorff distance for visual shape classification[END_REF]). These DM are created first by extracting the edges out of a CLAHE processed picture, and then by assigning to each pixel a level corresponding to its distance to the nearest edge pixel. The DM is specified according to this equation :

DM [i, j] = min {k,l}∈{E} ( (i -k) 2 + (j -l) 2 ) (3)
with DM [i, j] the value of the DM in [i, j] coordinates pixel, and E the set of edges pixels coordinates. The idea is to provide the AAMs with edge information, which isn't sensitive to illumination. However, since the AAMs need textures to converge with a high efficiency, we provide them with a synthetic texture filed only with edge information. And although this idea is indeed related to the use of a gradient preprocess, the edge information is not limited to the pixels close to an edge, but spread throughout the entire picture. Therefore, the AAMs have a lot more informative texture to work with and can converge more easily. See

C. Scale Normalization

In the standard use of AAMs, photometric normalization is an important step of the algorithm. Indeed, it permits to compare all texture images despite their different gray level dynamics. At the same time, this normalization is done at every computation of the residual error which introduce complexity and increase time calculation. In addition, Distance Maps AAM of [START_REF] Gallou | Distance maps : A robust illumination preprocessing for active appearance models[END_REF] have been tested with the photometric normalization while gray level dynamics only vary according to the scale of the model. Indeed, informations contained in DM are distances between edges which are larger and smaller when the scale of the model is respectively larger and smaller. So we propose to replace the standard photometric normalization by a new normalization which consists only to multiply all DM pixels by a scalar. This factor is the scale of the model which is the first element of the pose parameter. This new normalization is faster than the photometric normalization, because mean and variance of texture is no longer computed. Instead of photometric normalization, the DM is multiplied by the current model scale given by the pose parameter T :

DM = (T [1] + 1) * DM, (4)
The

IV. RESULTS

Our AAM algorithm creates the face model in a 64 pixels*64 pixels window so that the mean texture contains 1430 pixels.

We will compare our proposition to the pre-processes presented in section III-B in the context of generalization : the AAM will use ten persons with frontal illumination from M2VTS database (Fig 7 ) to learn a face model and tests will be made on seventeen persons from CMU database (Fig 8) under twenty one different illuminations leading to 357 test images.

The robustness to the illumination angle will first be illustrated, followed by some tests focused on initialization sensitivity.

A. Sensitivity to the illumination

All following graphs represent the convergence percentage versus the angle of illumination. We consider that a model has converged if the localization error of the eyes and mouth center and the nose (as pointed in Fig 9) are under a threshold of Deye/4, Deye being the distance between the eyes.

Figure 10 shows the CMU acquisition system: each person is recorded under 21 different illuminations created by a "flash system" laid out from the left to right of faces. In the next graphs, an illumination of 1 means the light came from the left of the subject, and an illumination of 21, that it came from its right; a central illumination being around 10-12.

1) Grayscale pictures: Fig 11 shows how much a CLAHE

pre-processing brings to the AAM's robustness to the angle of illumination. We can indeed see that, with CLAHE, the AAMs get a 90% rate of successful convergence for the 10 most central illuminations, whereas without this pre-process, the AAMs only get a 90% success rate on 4 illuminations.

2) Gradient texture: On Fig 12, we compare the use of photometric normalization for gradient-processed pictures, and as we can see, it is fairly difficult to tell which one is best. We however retain the normed-gradient pre-process for the rest of the study for its slightly better results on average.

We can also see on Fig 13 that although a gradient pre-process brings a huge improvement for the extreme illuminations, it also brings a slight loss of about 10% of successful convergence when the illumination is more central. The gain obviously comes from the fact that gradient is less sensitive to illumination. And the loss comes from the fact that the density of information is quite low since only the areas close to an edge have information, while every pixel of a grayscale picture contains information. Therefore, the AAMs will necessarily have some trouble converging precisely with gradient-processed pictures. That lead [START_REF] Huang | Face alignment under variable illumination[END_REF] to chose a two step algorithm: first close in roughly on the targeted face using gradient-processed pictures, then precisely using grayscale pictures.

3) Distance Map: However, if we use a DM pre-processing with our specific normalization, a 2 step algorithm is no longer necessary to obtain a precise convergence whatever the illumination, as we can see in Fig 14.

The mean convergence ratio is still of 90% for the central illuminations, and doesn't go below 75% for the extreme illuminations, except for 1 single illumination. But this result would not be possible without our special normalization. As we can see in the Fig 15, if we use a classical photometric normalization as in [START_REF] Gallou | Distance maps : A robust illumination preprocessing for active appearance models[END_REF], we lose between 10% and 40% of successful convergence depending on the illumination considered.

B. Sensitivity to the initialization point

As we will see, these gains in term of illumination robustness come with a gain in terms of a less sensitivity to the initialization point. The X-axis in the following figures represent different initialization of the AAMs around the center of the face. We of course kept our results from the previous illumination tests, when the AAMs always started centered on the targeted face, but we also added 4 starting point on each side of that face, every 2 pixels. Cootes suggested in [START_REF] Cootes | Statistical models of appearance for computer vision[END_REF] that the model could be disrupted by 10% in translation. In our case, the face model is contained in a 64 pixels*64 pixels window so that the face model is around 40 pixels wide. So we expect to have an initialization robustness in translation of our algorithm at around 4 pixels.

As we can see in the

V. CONCLUSION

In this article, we have described a new normalization method for the AAM which use Distance Map instead of grey level pixels texture to improve the illumination robustness. This proposition was compared to other well known techniques dedicated to illumination sensitivity in the context of generalization, meaning that face Active Appearance Model was extracted from a specific database (M2VTS), tests being made on other persons in different environments (CMU). Our proposition is more robust both in terms of illumination angle (around 85% of successful convergence whatever the illumination), and in terms of initialization (it has an average of

Fig. 1 .

 1 Fig. 1. Example of a face search with the standard AAM.

Fig. 2 .

 2 Fig. 2. Example of a face search with the AAM and CLAHE process.

  perfectly.

Fig. 3 .

 3 Fig. 3. Example of a face search with the AAM and Gradient process.

Fig. 4 .Fig. 5 .

 45 Fig. 4. Example of a face search with the AAM and Distance Map process.

  Fig 5 presents the standard Distance Map creation of[START_REF] Gallou | Distance maps : A robust illumination preprocessing for active appearance models[END_REF] on a simple image in two scale. In the part of the figure5called "Regions of interest warped in a same size" we put the model in scale of one and two in the same size to have a comparison of the input image of the residual error when the same model is in scale of one and in a scale of two. We can easily see the problem of the normalization in the Region of interest: the gray level dynamics of DM of the same objet but in two different scale are very different. So, residual error is hedged.In the Fig 6 we can see improvements of Distance Maps with the new normalization : the gray level dynamics of Distance Maps with the new normalization of the same objet but in two different scale are noticeably the same. In this example the scale of the model (first line of Fig 6) is multiplied

Fig. 6 .

 6 Fig. 6. The new normalization of Distance Map.

Fig. 7 .

 7 Fig. 7. The 10 faces from M2VTS database used in the training phase of AAMs.

Fig. 8 .

 8 Fig. 8. The 17 faces from PIE database used in the searching phase of AAMs displayed under the 21 different illuminations.

Fig. 9 .

 9 Fig. 9. Error localization.

Fig. 10 .

 10 Fig. 10. The CMU system of acquisition: positions of 17 of 21 flashes (4 left flashes are not visible in this view) and the camera used for creating facial images.

Fig. 12 .

 12 Fig. 12. Convergence comparison between AAMs with Gradient pre-process (square) and AAMs with Gradient pre-process but without photometric normalization (o).

Fig. 13 .

 13 Fig. 13. Convergence comparison between AAMs with CLAHE pre-process (square) and AAMs with Gradient pre-process (o).

Fig. 14 .

 14 Fig. 14. Convergence comparison between AAMs with CLAHE pre-process (square) and AAMs with Distance Map pre-process with the new photometric normalization (o).

Fig. 15 .

 15 Fig. 15. Convergence comparison between AAMs with Distance Map preprocess [1](square) and AAMs with Distance Map pre-process with the new photometric normalization (o).

Fig. 16 .

 16 Fig. 16. Convergence comparison in translation between the standard AAMs (square) and AAMs with CLAHE pre-process (o) for only the 10 central illuminations of the PIE database faces.

  Fig 16 and 17, a CLAHE preprocessing is as interesting concerning the problem of initialization sensitivity as it was concerning the angle of illumination. Fig 17 concerns all the 17 faces and all the 21 illuminations of the CMU database, whereas Fig 16 only deals with the 10 central illuminations where CLAHE-processed pictures had a 90% of successful convergence ratio (Illuminations 4 to 14, see Fig 11). Fig 18, which only deals with the central illuminations

Fig. 17 .

 17 Fig. 17. Convergence comparison in translation between the standard AAMs (square) and AAMs with CLAHE pre-process (o) for the 21 illuminations of the PIE database faces.

Fig. 18 .

 18 Fig. 18. Convergence comparison in translation between AAMs with CLAHE pre-process (square), AAMs with Distance Map pre-process with the new photometric normalization (o) and AAMs with Gradient pre-process (tri) for only the 10 central illuminations of the PIE database faces.

Fig. 19 .

 19 Fig. 19. Convergence comparison in translation between AAMs with CLAHE pre-process (square), AAMs with Distance Map pre-process with the new photometric normalization (o) and AAMs with Gradient pre-process (tri) for the 21 illuminations of the PIE database faces.

10% more of successful convergence than a grayscale method, and this only on the central illuminations, where the grayscale methods still work). In the future, we might want to try and explore the possibility of having better results using an oriented edge extraction method and of course the Distance Map and specific normalization we described here.