Benjamin Mathieu
email: benjamin.mathieu@univ-amu.fr

Antonin Abillama

Malvina Martinez

Laurence Mouchnino

Jean Blouin

KEEPING IN TOUCH WITH OUR HIDDEN SIDE

Keywords: Body representations, Somatosensory target, Body image, Body schema

Previous studies have shown that the sensory modality used to identify regions of the body hidden from sight, but frequently viewed, influences the type of the body representation employed for reaching them with the finger. The question then arises as to whether this observation also applies to body regions which are rarely, if ever, viewed. We used an established technique for pinpointing the type of body representation used for the spatial encoding of targets which consisted of assessing the effect of peripheral gaze fixation on the pointing accuracy. More precisely, an exteroceptive, visually dependent, body representation is thought to be used if gaze deviation induces a deviation of the pointing movement. Three lightemitting diodes (LEDs) were positioned at the participants' eye level at -25 deg, 0 deg and +25 deg. Without moving the head, the participant fixated the lit LED before the experimenter indicated one of the three target head positions: topmost point of the head (vertex) and two other points located at the front and back of the head. These targets were either verbal-cued or tactilecued and the participants had to reach them with their index finger. We analysed the accuracy of the movements directed to the topmost point of the head, which is a well-defined, yet out of view anatomical point. Based on the possibility of the brain to create visual representations of the body areas that remain out of view, we hypothesized that the position of the vertex is encoded using an exteroceptive body representation, both when verbally or tactile-cued. Results revealed that the pointing errors were biased in the opposite direction of gaze fixation for both verbal-cued and tactile-cued targets, suggesting the use of a vision-dependent exteroceptive body representation. The enhancement of the visual body representations by sensorimotor processes was suggested by the greater pointing accuracy when the vertex was identified by tactile stimulation compared to verbal instruction. Moreover, a control condition showed that participants were more accurate in indicating the position of their own vertex than the vertex of other people. Together, our results suggest that the position of rarely viewed body parts are spatially encoded by an exteroceptive body representation and that non-visual sensorimotor processes are involved in the constructing of this representation.

INTRODUCTION

Our daily experience shows that we can touch any part of our body with our hands. Remarkably, this includes touching regions that we rarely see (e.g., top of the head, back). This capacity provides evidence for the existence of internal body representations and for the access of the arm motor system to these representations.

Much of our knowledge on the control of pointing movements to regions of our body comes from studies in which subjects had to indicate with the index finger different positions on their contralateral arm hidden from view [START_REF] Sirigu | Multiple representations contribute to body knowledge processing: evidence from a case of autotopagnosia[END_REF][START_REF] Blangero | Influence of gaze direction on pointing to unseen proprioceptive targets[END_REF][START_REF] Sarlegna | The effect of target modality on visual and proprioceptive contributions to the control of movement distance[END_REF][START_REF] Mikula | Vibrotactile information improves proprioceptive reaching target localization[END_REF][START_REF] Manson | Auditory cues for somatosensory targets invoke visuomotor transformations: Behavioral and electrophysiological evidence[END_REF][START_REF] Goettker | Somatosensory target information is used for reaching but not for saccadic eye movements[END_REF]. Generally, subjects point fairly accurately to these positions (errors <~2 cm). As a key finding, studies show that the sensory modality used to locate such targets have an impact on the type of body representation used to encode their position [START_REF] Sirigu | Multiple representations contribute to body knowledge processing: evidence from a case of autotopagnosia[END_REF][START_REF] Manson | Auditory cues for somatosensory targets invoke visuomotor transformations: Behavioral and electrophysiological evidence[END_REF][START_REF] Mueller | Effector movement triggers gaze-dependent spatial coding of tactile and proprioceptive-tactile reach targets[END_REF]. Body positions identified by tactile stimuli would be encoded using an interoceptive, somatosensory-based, body representation if the eyes or head remain still between the stimulation and the response. On the other hand, body positions defined by auditory or verbal cues would be encoded in an exteroceptive, visually-based, body representation (see [START_REF] Vignemont | Body schema and body image-Pros and cons[END_REF] for a review of different body representation taxonomies).

Visual calibration of proprioception is required for building coherent somatosensory body representations [START_REF] Harrar | Eye position affects the perceived location of touch[END_REF]. The question then arises as to whether somatosensory-based body representations are still used to locate body areas which are rarely viewed, even when defined by tactile stimulation. We addressed this issue by asking adult participants to touch with their index finger different points on their head (notably the vertex) indicated either verbally or by tactile stimulation. We used an established technique for pinpointing the type of body representation used for the spatial encoding of targets which consisted of assessing the effect of peripheral gaze fixation on the pointing accuracy [START_REF] Blangero | Influence of gaze direction on pointing to unseen proprioceptive targets[END_REF][START_REF] Manson | Auditory cues for somatosensory targets invoke visuomotor transformations: Behavioral and electrophysiological evidence[END_REF][START_REF] Mueller | Effector movement triggers gaze-dependent spatial coding of tactile and proprioceptive-tactile reach targets[END_REF]. The rationale for using this method is that the encoding of a target position is gaze-dependent when using an exteroceptive, visually-based, representation: in this case, the pointing errors are biased in the opposite direction to the gaze. For instance, with left fixation, subjects will usually point to the right of a target located straight-head [START_REF] Blangero | Influence of gaze direction on pointing to unseen proprioceptive targets[END_REF][START_REF] Manson | Auditory cues for somatosensory targets invoke visuomotor transformations: Behavioral and electrophysiological evidence[END_REF][START_REF] Mueller | Effector movement triggers gaze-dependent spatial coding of tactile and proprioceptive-tactile reach targets[END_REF]. Inversely, the spatial encoding of a target with an interoceptive body representation would be gaze independent: in this case, the pointing accuracy is not affected by gaze direction.

Clues exist in the literature suggesting that an exteroceptive body representation could be favoured over interoceptive representation for localising rarely viewed body positions identified by tactile stimulation. Indeed, studies have shown that coherent visual representations, including of human bodies, can be built using partial visual information [START_REF] Fuentes | Body image distortions in healthy adults[END_REF].

This opens the possibility of building a relatively accurate visual representation using available, yet incomplete visual feedback of the body. Vision of others' bodies [START_REF] Gallagher | How the Body Shapes the Mind[END_REF] could contribute to this cognitive construction of body parts that remain out of view. On the basis of these psychophysiological findings, we hypothesized that the spatial positions of body areas which are rarely if ever viewed (e.g., the vertex) are encoded using an exteroceptive body representation, both when they are verbally or tactile-cued. Accordingly, we predicted that the accuracy with which individuals point to these body areas will be biased if gaze direction is deviated from straight-ahead.

METHODS

Experimental set-up

Before running the experiment, the experimenter marked the position of the vertex (i.e., the topmost point of the cranium [START_REF] Gray | Anatomy, descriptive and surgical[END_REF]) on the stretch fabric cap worn by the participant. The vertex is located at the intersection point of the nasion-inion line and of the left and right tragus line.

Then, the participant was seated in semi-darkness with the head vertical and aligned with the trunk. Light-emitting diodes (LEDs) were positioned eye level ~57 cm in front, at -25 deg (left), 0 deg (central) and +25 deg (right) with respect to the cyclopean eye (Fig. 1). These LEDs served to control gaze direction during the trials. Three small spheres, each 10 cm apart, were fixed on the table, in the participants' fronto-sagittal plane (the closest at 20 cm from the participants). These spheres served as starting positions for the right index finger. The view of the finger in its initial position helped maintain proprioception calibration during the movement initiation [START_REF] Harrar | Eye position affects the perceived location of touch[END_REF].

Data recordings

The endpoint position of the index finger on the head was recorded using a digitizing stylus (120 Hz, Polhemus Fastrak). Head position (i.e., X and Y coordinates) was tracked using a 2.5 cm electromagnetic sensor (120 Hz, Polhemus Fastrak) embedded in the cap at the back of the head. The position of the eyes was recorded by EOG (250 Hz, Coulbourn Instruments) and displayed on the computer screen. EOG recordings allowed to verify the participant's ocular behavior during the experiment. The few trials in which the participants failed to maintain their ocular deviation were deleted and repeated.

Experimental conditions

The task of the participants was to indicate different points on their head with the tip of the index finger. This task was performed with three gaze deviations (i.e., left, center, right), in two conditions (i.e., Verbal, Tactile) which differed according to the cue modality used to indicate these targets.

Verbal-cue condition

At the start of each trial, the experimenter verbally indicated one of the 3 finger starting positions (i.e., far, middle or close). Once in place, the participant sent the verbal message "ready". Then, the following lighting sequence of the fixation LEDs started. From 0 to 1.5 s: lighting of the central LED; from 2 to 10 s: lighting of either the left, central or right LED. The participant had to fix the lit LED without moving the head. After ensuring that the participant fixated the final lit LED by looking at the EOG signal, the experimenter indicated one of the 3 points of the head (hereafter referred to as the targets) that the participants had to reach immediately with the index finger. These points were described and named as follows: the topmost point of the head (top, i.e., vertex), the mid-distance between the eyes and the topmost point of the head (front) and the mid-distance between the rearmost and the topmost points of the head (back). Without moving the eyes or the head, the participants had to touch, as accurately as possible, the target with the tip of their index finger.

Tactile-cue condition

This condition was similar to the Verbal-cue condition. Instead of verbally identifying the targets, the experimenter touched the targets using a Semmes-Weinstein monofilament (caliber: 6.65; force: 4.38 N). To this end, the experimenter held the filament perpendicularly above the target before descending it until the filament bowed upon contact with the head. Immediately after the tactile stimulation, the participants had to touch with their finger where they felt they had been touched on their head. The use of the monofilament ensured that the sensory stimulation evoked by the touches was similar across gaze and cue conditions, and across participants.

In both conditions, the participants were instructed not to rush their response. Standing behind the participants, the experimenter slipped a digitalizing stylus under the index to record the middle of the touched area on the head. Then, the experimenter touched 4 other points of the head with the stylus. The third of which was the actual vertex, while the others were nearby random positions on the head. Touching the head at random positions diminished the possibility of the participants obtaining error feedback about their pointing accuracy. Questioned after the experiment, all participants confirmed that they did not realize that the third position touched by the stylus on their head corresponded to the actual target position. Only trials using the vertex as the target were analyzed. The use of the front and back targets, and of the different starting positions minimized the risk of participants implementing stereotyped pointing responses to the vertex. For this reason, the front and back targets were not defined precisely.

For each Cue and Gaze condition, 12 trials used the vertex target, 2 trials used the front target and 2 trials used the back target. The order of presentation of the targets and of the fixation LED was pseudorandom. 14 participants started the experiment with the Tactile-cue condition.

Prior to each experimental condition, participants performed a series of 7 familiarization trials comprising all combinations of ocular fixation with the front and back targets (i.e., 6 trials) and 1 trial using the top target and the central fixation.

Others (control condition)

The identification of the vertex of other people can be thought of as being exclusively based on visual representations [START_REF] Sirigu | Multiple representations contribute to body knowledge processing: evidence from a case of autotopagnosia[END_REF]. It is therefore possible to assess the accuracy with which one localizes the vertex on the basis of a (hypothetically pure) visual representation by asking participants to indicate the vertex of other people. In a control condition, the participants located with their index finger the vertex of 6 adult volunteers (aged between 21 and 56 years) wearing a black fabric cap. During the test, the volunteers were seated, eyes closed, in a lighted room with the head vertical and aligned with the trunk. The experimenter positioned the tip of the digitizing stylus at the point of the head indicated by the participants. The participants were then asked to move around the seated volunteer and were allowed to correct the position of the stylus, before the experimenter marked its position. Then, in the absence of the participants, the actual vertex position of the volunteers was also marked on the cap before this and the participants' perceived vertex positions were recorded using the stylus. This control condition was performed either before or after the Verbal-cue or Tactile-cue conditions.

Data analyses

The effect of Gaze and Cue-target conditions on pointing accuracy was assessed by computing the radial error, which was defined as the 2D euclidean distance between the finger end position and the actual vertex position. Previous studies have shown that gaze direction had a greater impact on pointing movements in the medio-lateral direction than in the antero-posterior direction when subjects have their head aligned with the trunk [START_REF] Blangero | Influence of gaze direction on pointing to unseen proprioceptive targets[END_REF][START_REF] Manson | Auditory cues for somatosensory targets invoke visuomotor transformations: Behavioral and electrophysiological evidence[END_REF][START_REF] Mueller | Effector movement triggers gaze-dependent spatial coding of tactile and proprioceptive-tactile reach targets[END_REF]. Pointing accuracy was then further analyzed by computing the lateral (X coordinates) and longitudinal (Y coordinates) errors. These errors were respectively defined as the signed distance between the perceived and the actual vertex positions in both X and Y coordinates. Positive lateral errors indicated that the participants perceived the vertex to the right of the actual vertex. Positive longitudinal errors indicated that the vertex was perceived in front of the actual vertex.

The variability (i.e., standard deviation of the mean) in estimating the vertex position was computed for each Cue-target condition. This variable provides an estimate of the reliability of the representation used to locate the vertex when identified by either tactile or verbal cues.

The continuous recording of the head position indicated that the participants succeeded in minimizing head movements during the trials. Notably, looking at a peripheral target had no effect on the lateral head position as indicated by the results of one way ANOVAs which did not show significant effect of Gaze on the lateral positions of the head measured at the lighting of the fixation LED and at the time the touched position was measured (p>0.05 for both cuetarget conditions). On average (all Cue-target and Gaze conditions), the participants moved their head by 0.12 ±0.27 cm in the transverse plane between the recordings of the perceived and of the actual vertex positions (recordings separated by 2.6 s, on average). To cancel out the effect of these small head movements on the assessment of the participants' performance, prior to the error calculation, we subtracted X (medio-lateral) and Y (antero-posterior) head displacements measured between the two recordings, from the X and Y coordinates of the measured vertex position.

The effect of Gaze and of Cue-target conditions was tested using 3 Gaze (left, center, right) x 2 Cue-target (verbal, tactile) repeated measures analyses of variance (ANOVAs). We also compared the mean errors (radial, lateral, longitudinal) measured while the participants gazed at the central LED in both the Verbal-cue and Tactile-cue conditions with those measured in the Others control condition. These data were submitted to separate one-way ANOVAs with three levels (i.e., tactile, verbal, others). The alpha level was set at 0.05 for all statistical contrasts. Significant effects were further analyzed using Newman-Keuls post-hoc tests. Note that additional ANOVAs, not reported here, did not show significant Gender main or interaction effects on the 3 types of errors (all p>0.05).

RESULTS

Radial error

As a first salient finding, the amplitude of the radial error significantly differed according to the type of cue indicating the vertex (F1,26 = 28.29; p<0.001; η 2 p = 0.27, Fig. 2A). The radial error was smaller in the Tactile-cue (1.04 ±0.44 cm) than in the Verbal-cue (1.38 ± 0.57 cm) conditions. The ANOVA did not reveal significant effect of Gaze (F2,26 = 0.13; p>0.05) or significant interaction Cue-Target x Gaze (F2,26 = 0.42; p>0.05).

The variability of the radial error was significantly different between the two Cue-target conditions (F1,26 = 27.94; p<0.001; η 2 p = 0.26; Fig. 2B). This variability was smaller when the participants indicated their vertex position in the Tactile-cue (0.70 ± 0.28 cm) than in the Verbal-cue (0.88 ± 0.30 cm) conditions.

Lateral error

The participants perceived their vertex to the left of its actual position with right gaze fixation (-0.15 ± 0.48 cm) and to the right with left gaze fixation (0.11 ± 0.48 cm). This bias was confirmed by the ANOVA which revealed a significant effect of Gaze on the lateral error (F2,26 = 4.20; p<0.05; η 2 p = 0.10, Fig. 2C) and by the post-hoc comparison which showed a significant difference between left and right gaze fixations (p<0.05). The perceived vertex position in the gaze-centered condition did not significantly differ from that measured in gaze-deviated conditions (both p>0.05). Importantly, the perceived lateral position of the vertex did not significantly differ between the Verbal-cued and the Tactile-cued target conditions (F1,26 = 3.42; p>0.05) and the interaction Gaze x Cue-target was not significant (F2,26 = 0.03; p>0.05).

Longitudinal error

The longitudinal error was not significantly different between the Verbal-cue and Tactile-cue conditions (F2,26 =0.0007; p>0.05) or between the different gaze fixations (F2,26 = 0.79; p> 0.05).

The interaction Gaze x Cue-target was also not significant (F2,26 = 0.49; p>0.05).

Perceived self versus others vertex position

Radial error

Participants were more accurate in indicating the position of their own vertex than the vertex of other people. This was confirmed by the one-way ANOVA (Others, Tactile, Verbal) which showed a significant effect of Condition on the radial errors (F2,26 = 15.27; p<0.001; η 2 p = 0.39, Fig. 2D). Post-hoc comparison revealed that the radial error significantly differed between each condition. The radial errors were greatest in the Others condition (1.83 ± 0.71 cm) and smallest in the Tactile-cue conditions (1.03 ± 0.46 cm). As it can be seen in Fig. 2d, two participants were identified as outliers in the boxplot of the radial errors in the Others condition. To ensure that the larger radial error in the Others condition was not due to these participants, we performed another ANOVA without them. The significant effect of condition was preserved (F2,24 = 13.09; p<0.001; η 2 p = 0.37) as well as all pairwise comparisons (all p<0.05).

Lateral and longitudinal errors

The ANOVA revealed a significant effect of Condition on the lateral error (F2,26 = 4.05; p< 0.05; η 2 p = 0.14). The Post-hoc analyses showed that the lateral error in the Others condition (-0.29 ± 0.45 cm) was significantly greater than in the Tactile-cue condition (0.01 ± 0.35 cm, p<0.05), but not significantly different to the Verbal-cue condition (-0.13 ± 0.48 cm, p>0.05).

The longitudinal error did not significant differ (F2,26 = 1.50; p>0.05) between Tactile-cue (-0.02 ± 1.06 cm), Verbal-cue (0.10 ± 1.35 cm), and Others conditions (0.51 ± 1.16 cm).

DISCUSSION

Previous studies have shown that the sensory modality used to identify regions of the body influences the type of the body representation employed for reaching them with the finger [START_REF] Sirigu | Multiple representations contribute to body knowledge processing: evidence from a case of autotopagnosia[END_REF][START_REF] Manson | Auditory cues for somatosensory targets invoke visuomotor transformations: Behavioral and electrophysiological evidence[END_REF].

More specifically, identifying the body areas with an auditory and tactile cue respectively prompts the use of an exteroceptive (visually-based) and interoceptive (somatosensory-based) body representations when the eyes and head remain stationary. This scenario appears to be less straightforward when the target consists in a rarely, if ever, viewed area of the body, as in the present study. Indeed, when pointing to the tactile-cued vertex, our participants presented gazedependent errors: they pointed to the right of the vertex when fixating to the left, and vice versa (i.e., same directional biases as in previous studies using visual targets or auditory-cued targets on the arm [e.g., 5]). In agreement with our hypothesis, these effects of gaze direction on the finger endpoint position are consistent with the predominantly use of an exteroceptive body representation. One interpretation for this novel finding could be that visual body representations are used to localize body parts that cannot be identified through visualsomatosensory integration. We shall focus much of our discussion on the bases of this interpretation.

Whilst the targets used in previous studies were generally located on the contralateral arm [START_REF] Sirigu | Multiple representations contribute to body knowledge processing: evidence from a case of autotopagnosia[END_REF][START_REF] Blangero | Influence of gaze direction on pointing to unseen proprioceptive targets[END_REF][START_REF] Sarlegna | The effect of target modality on visual and proprioceptive contributions to the control of movement distance[END_REF][START_REF] Mikula | Vibrotactile information improves proprioceptive reaching target localization[END_REF][START_REF] Manson | Auditory cues for somatosensory targets invoke visuomotor transformations: Behavioral and electrophysiological evidence[END_REF][START_REF] Goettker | Somatosensory target information is used for reaching but not for saccadic eye movements[END_REF], our participants had to indicate the position of their vertex with the tip of their finger.

The peculiarity of this body location is that it is rarely, if ever, viewed on ourselves. Our results therefore lead to the paradox that the spatial position of a tactile stimulation on a part of the body that is regularly viewed would be encoded through a somatosensory-based representation [START_REF] Sirigu | Multiple representations contribute to body knowledge processing: evidence from a case of autotopagnosia[END_REF][START_REF] Sarlegna | The effect of target modality on visual and proprioceptive contributions to the control of movement distance[END_REF][START_REF] Manson | Auditory cues for somatosensory targets invoke visuomotor transformations: Behavioral and electrophysiological evidence[END_REF] while the position of a touch on a rarely viewed body part would be encoded through a visually-based representation (present results). This apparent paradox could be resolved by considering that the intrinsic and extrinsic body representations are co-constructed [START_REF] Pitron | Beyond differences between the body schema and the body image: insights from body hallucinations[END_REF] and that the weight given to each representation is context-dependent.

An accurate somatosensory mapping of the body space requires cross sensory calibration [START_REF] Van Beers | When feeling is more important than seeing in sensorimotor adaptation[END_REF]. For sighted persons, this calibration is principally achieved through vision [START_REF] Harrar | Eye position affects the perceived location of touch[END_REF][START_REF] Pitron | Beyond differences between the body schema and the body image: insights from body hallucinations[END_REF]. The possibility to regularly see our upper limbs and therefore refresh their somatosensory mapping through vision could enhance the reliability of the intrinsic body representation for encoding the spatial position of tactile stimuli on the arm. The reliability of the intrinsic body representation for locating hidden parts of the body such as the vertex, appears hampered by the impossibility to co-register their positions with somatosensory and visual inputs. The lack of visual calibration could also have an exacerbated detrimental effect for localizing body areas with little density of somatosensory receptors, as is the case for the top of the head [START_REF] Mehrabyan | Tactile and thermal detection thresholds of the scalp skin[END_REF].

In this context, an extrinsic body representation appears most suitable for coding the vertex position. Seeing ourselves from a first or a third (e.g., through a mirror) perspective, and seeing someone else's body [START_REF] Gallagher | How the Body Shapes the Mind[END_REF] would be fundamental to constructing what has been referred to as the long-term visual body representation (for a review, see [START_REF] Pitron | Beyond differences between the body schema and the body image: insights from body hallucinations[END_REF]). This body representation could also benefit from the capacity of the brain to construct coherent consolidated representations, or to re-actualise them, on the basis of partial visual information [START_REF] Fuentes | Body image distortions in healthy adults[END_REF].

Furthermore, sensorimotor-derived processes could also be involved in the construction of visual body representations [START_REF] Mancini | A supramodal representation of the body surface[END_REF]. For instance, sensorimotor experience gained during a lifetime could have a key role in enhancing the spatial resolution of the visual representation of the vertex. Putting on a sweatshirt or a hat, or washing your hair are examples of sensorimotor activities that might improve the visual representation of this unseen body area. This idea is supported by the fact that our participants showed smaller radial and lateral errors when indicating the position of their own vertex, than the vertex of other people. It seems reasonable to assume that the task of localizing the vertex on another person's head is essentially based on visual representations (see [START_REF] Sirigu | Multiple representations contribute to body knowledge processing: evidence from a case of autotopagnosia[END_REF]). Our results therefore further stress the importance of non-visual sensorimotor processes for constructing body representations, including those of visual origin. This is in line with the proposal that intrinsic and extrinsic body representations are coconstructed [START_REF] Pitron | Beyond differences between the body schema and the body image: insights from body hallucinations[END_REF].

The enhancement of visual body representations by sensorimotor processes is also suggested by the greater pointing accuracy showed by the participants when their vertex was identified by tactile stimulation compared to verbal instruction (i.e., smaller radial error associated with smaller variability). Previous studies have reported improved position sense with tactile stimulation [START_REF] Mikula | Vibrotactile information improves proprioceptive reaching target localization[END_REF][START_REF] Goettker | Somatosensory target information is used for reaching but not for saccadic eye movements[END_REF]. Our results indicate that this finer spatial resolution of the somatosensory mapping (which could be short-lived) can benefit visually-based extrinsic body representations. The interdependence between somatosensory-based and visually-based body representations is also revealed in the so-called rubber hand illusion [START_REF] Ehrsson | That's my hand! Activity in premotor cortex reflects feeling of ownership of a limb[END_REF]. This illusion arises from the simultaneous brushing of the hand of the subject, which is hidden from view, and of a facsimile of a human hand viewed in front of the subject. After a few minutes of exposure to this somato-visual context, the subjects perceive the fake hand as being the real hand, consistent with a close link between visual and somatosensory body representations.

  Participants 27 right-handed participants (mean age: 23.8 ± 2.4 years, 14 women) with normal or corrected to normal vision volunteered for the experiment. Informed consent was obtained before the start of the experiment which conformed to the Declaration of Helsinki for experiments involving humans.

Figure 1 .

 1 Figure 1. Schematic representation of the experimental set-up and procedure. The figure depicts the time course of a trial involving the middle starting position of the finger and a rightward gaze fixation. EOG: electro-oculography.

Figure 2 :

 2 Figure 2: Boxplots of radial [A] lateral [C] errors measured in the different Cue-target and Gaze conditions and of radial errors [D] in the Tactile-cue condition and in the Verbal-cue and Others conditions (both with centered-gaze fixation). The cross represents the mean, the horizontal line represents the median. The lower and upper edges of the box correspond respectively to the 1st and the 3rd quartiles. The length of the whiskers represent the ranges of the bottom 25% and top 25% of the data values, excluding outliers which are represented by individual dots (i.e., data at least 1.5 times the interquartile range from the edge of the box). [B] Variability of the radial error in the Tactile-cue and Verbal-cue conditions. *p<0.05; **p<0.005; ***p<0.001.

Acknowledgments

The authors thank Fanny Goetz for her help at various stages of this research project. We thank F. Buloup for developing the software Docometre used for data processing and acquisition.


Fabienne Anfosso
email: fabienne.anfosso@lcpc.fr.

Fabienne Anfosso-Lédée

The development of a new tire-road noise measurement device in France

Traffic noise emission is largely influenced by the road surface properties. These acoustical properties are evaluated by measuring the noise generated by tires rolling on it. Usually this is achieved with static pass-by measurements, but many advantages were found in developing continuous dynamic measurements in the close proximity of a rolling tire. An equipment was designed in France, where three microphones are mounted near the contact zone between the road surface and the tire of a test vehicle. With this equipment, it is possible to evaluate the tireroad noise generated at different speeds ranging from 50 km/h up to 130 km/h, but at a constant pace along a road section. The development of such a method for the evaluation of road surface properties, requires that the specific effects of the vehicle, the tire and external noise contributions are mitigated and removed if necessary. A great care was paid on the investigation of the aerodynamic noise contribution due to the displacement of the microphones along with the vehicle. Experiments were made indoors, in an airflow produced by a wind turbine, in order to qualify and evaluate the turbulent air flow around the microphones, and design appropriate windshields. Additional experiments performed outdoors on real measurement conditions confirmed that when using standard windshields, the tire-road noise level is more than 10 dB(A) higher than the airflow noise contribution, which makes this later negligible. Further investigations on the possible perturbing sources were made, like the vibration of the mounting system, the influence of the engine noise, the effect of the type or width of measurement tire, and the effect of external noise due to other vehicles in the traffic flow.

RÉSUMÉ

Le bruit du trafic routier est largement influencé par les propriétés des revêtements de chaussée. Ces propriétés acoustiques sont en général évaluées par une mesure statique de bruit de roulement au passage de véhicules. Mais une demande forte s'est exprimée en France pour le développement d'une méthode de mesure en continu du bruit de roulement, permettant d'évaluer les performances acoustique des revêtements de chaussée, aussi bien en milieu urbain que sur le réseau interurbain. Un dispositif de mesure a été développé, dans lequel trois microphones mesurent le bruit à proximité d'un pneumatique d'un véhicule d'essai en roulement. Cinq véhicules ont été instrumentés à l'identique dans 5 laboratoires différents, afin de tester la reproductibilité de la méthode. A l'aide de cet équipement, il est possible de mesurer le bruit généré par le contact pneumatique -chaussée à différentes vitesses entre 50 et 120 km/h, mais par pas de distance constants au long d'une section routière. La longueur de ces segments constants correspond à un nombre entier de tours de roue, que l'on peut adapter à l'objectif de la mesure.

Il est nécessaire que les effets spécifiques du véhicule, du pneumatique ou du bruit extérieur soient maîtrisés et éliminés si nécessaire. Des recherches approfondies ont porté sur la contribution du bruit aérodynamique dû au déplacement du système de mesure avec le véhicule. Des expérimentations en laboratoire à l'aide d'un ventilateur simulant le flux d'air à différentes vitesses d'un véhicule en déplacement, ont permis de qualifier et quantifier le flux turbulent autour des microphones. Différents dispositifs anti-vent ont pu être testés. Des mesures réelles sur le véhicule ont ensuite confirmé que les niveaux de bruit de roulement mesurés avec des protections standards sont supérieurs de plus de 10 dB(A) aux bruits aérodynamiques, ce qui rend ces derniers négligeables. Des recherches complémentaires ont été menées sur les sources perturbatrices potentielles, telles que les vibrations du système de montage, l'influence du bruit moteur, du type et de la largeur du pneumatique, et du bruit extérieur dû aux autres véhicules du trafic.

1-INTRODUCTION

Road traffic noise is a major and growing environmental problem in France and other European countries. Reducing the noise emitted at the source is of a great interest, especially in dense urban areas where the space for noise barriers is limited. Engine and transmission noise have been drastically reduced over the twenty past years, and as a consequence, the tire-road contact is now the main source of noise generation on light vehicles driving above 30 km/h (above 60 to 80 km/h for trucks). In order to reduce this tire-road noise, the improvement of pavement properties is promising, and differences as much as 12 dB(A) have been obtained between noisy and quiet pavements in France. But technological improvements require that evaluation tools are available. The evaluation of noise properties of pavements is useful for classifying the road pavements in terms of noise reduction potential, for assessing the noise reduction of a newly laid pavement, and for monitoring the aging of a road section or network. The current method for evaluating these noise properties is a pass-by measurement method. It will be presented first. Then the continuous dynamic measurement method developed in France will be presented next, with a description of all the investigations performed in order to assess the quality of the method.

2-THE EVALUATION OF NOISE PROPERTIES OF ROAD PAVEMENTS

2.1-Pass-by measurements

The wider used method for measuring tire-road contact noise is the pass-by measurement method, in which the A-weighted maximum sound pressure level L Amax of a passing vehicle is measured by a microphone located in the road near field, 7.50 m from the road axis and 1.20 m above the road surface. Each vehicle run is characterized by L Amax and the vehicle speed measured with a radar. For road surface characterization, this measured noise must be independent of the tire and vehicle characteristics. Thus, a large number of vehicles picked up from a real traffic flow are measured, and a statistical analysis is performed, by calculating a logarithmic regression of the L Amax vs. speed data. With this regression curve, it is possible to define the A-weighted reference sound pressure level at the reference speed, which is, after correction for temperature effects, the reference indicator for acoustic performance of the road pavement. The reference speed depends on the type of vehicles (passenger car or dual or multi axle trucks) and the type of road (highway, main road, local road...). The same procedure can be followed for each third octave frequency band, and a reference noise spectrum usually ranging from 100 Hz to 5 kHz can be derived. The measurement procedure, also known as Statistical Pass-By method (SPB) is described in an international standard ISO 11819-1 [START_REF]Acoustics : Measurement of the influence of road surfaces on road traffic noise -Part 1 : the statistical pass-by method[END_REF].

This procedure shows an acceptable reliability (less than 1 dB(A) repeatability and 1.5 dB(A) reproducibility). The method is appropriate for the characterization of road noise environment, because it includes all types of vehicles in a real traffic. By use of propagation models, it is possible in some simple cases, to estimate from SPB measurements the equivalent sound pressure levels (L eq ) at façade of building -the indicator for legal requirements [START_REF] Bérengier | The efficiency of road pavements for traffic noise reduction -a state of the art in France[END_REF]. This procedure is however a "static" method, the road surface properties are evaluated at a specific spot where the microphone is set. It is not possible to check on non-homogeneity of the pavement. Furthermore, drastic site conditions are required, where no obstacle must be present in the vicinity (no building, no barrier or earth-berm…), no slope, no curve, the surface between the road platform and the microphone position must be flat and homogeneous… These drastic requirements makes it almost impossible to operate in dense urban areas, where noise problems are the most critical.

2.2-Continuous measurements, or close proximity method

Because of these limits, it can be of a great advantage to perform continuous dynamic measurements within a traffic flow. The principle of the method consists in fixing a microphone to a wheel, close to the tire-road contact zone, and to measure the noise continuously while the tire is rolling. The measurement can be performed on the test tire of a trailer, or on the tire of a vehicle. In the case of the trailer, the tire fitted with the measurement equipment is usually covered by an enclosure in order to limit the noise pollution by the surrounding traffic and aerodynamic flow. The difficulty is then to make this enclosure as sound absorbent as possible in order to limit the sound reflections inside the enclosure. In the case of measurements on the tire of a test vehicle, the microphones are likely to be more exposed to aerodynamic and other perturbing noise sources. Many different types of tires can be tested in order to make the method as independent of the tire characteristics as possible, but with the restriction that they must fit to the vehicle or trailer. Consequently, only tires with approximately the same size can be tested. The operating principle consists in collecting a large amount of sample data -i.e. average noise level and speed data on road segments -and to estimate an average noise level at a reference speed by a statistical analysis on these data. This analysis can be a regression or a simple arithmetic average after speed correction. Road segments are typically a few meter long.

2.3-A state of the art on close proximity method

Many such measurement systems exist around the world, most of them being trailers. The agreement between measurements with these devices is an important issue. A standard method is still under discussion at the International Standardization Organization, but a comprehensive description exists in a draft document [START_REF]Acoustics : Measurement of the influence of road surfaces on road traffic noise -Part 2 : the close-proximity method[END_REF]. A round robin test was organized in 2000 between many CPX devices, but a good agreement could not be proved. In France, a comparison between four existing devices was performed on a motorway section with four different road surfaces. The agreement, although acceptable in terms of classification on global noise performance, was not fully satisfying, especially for the porous road surface where unexplained discrepancies occurred [START_REF] Gautier | Comparaison entre mesures au passage et mesures en champ proche -Bilan d'une expérimentation[END_REF]. For this reason, a research project for developing a new method was initiated. This method is intended for the acoustical classification of road surfaces (expert method), the assessment of road surface acoustic performances (check of conformity of production), and for the monitoring and diagnosis of road surface condition on a network. The method must be valid on short (100 m long) or on long (50 to 100 km) sections, on dense urban roads or on fast inter-urban roads. Five vehicles were identically equipped in five Public Works Laboratories, so that the reproducibility of the method can be estimated.

3-THE MEASURING SYSTEM

3.1-The test vehicle

The measurement device is a self powered vehicle, a passenger car Renault Scénic, only used for acoustic measurements. The reference tire configuration is Michelin Energy XH1 reference 195/60/R15, the mileage of which is approximately 1000 km during the tests presented later in the paper. This is a standard configuration, commonly available on the market. A set of 3 microphones is fitted to the vehicle, near the back right wheel. This position is chosen in order to be as far as possible from the engine -i.e. back wheel -and as far as possible from the exhaust pipe -i.e. right side on this car. Two microphones (#1 and #2) are fixed to the car body, on the side of the tire according to ISO [START_REF]Acoustics : Measurement of the influence of road surfaces on road traffic noise -Part 2 : the close-proximity method[END_REF] positions, i.e. 0.20 m from the axe of the wheel, and 0.10 cm above the road surface (figure 1). They are mounted on streamlined bars made from model aircraft building material. A third microphone (#3) is fixed on the trailer coupling, at the rear of the wheel in the horn. It is positioned at 0.80 m from the axe of the wheel, at 0.15 m above the road surface. This position has been used for many years in France, in the city of Paris especially, where the lateral positions where thought to be too dangerous for pedestrians.

The acoustic data acquisition system

The data are acquired on a 5 channel system : 3 are dedicated to the acoustic signals measured on the 3 microphones, one is for the tachometric information taken from the dashboard, and an additional channel can be used for audio comments from the operator during the measurements. The tachometry delivers an indication of the distance run (and subsequently the speed), and fixes the "period" on which the noise level is integrated. Therefore, instead of being time-averaged, the noise levels measured at each microphone are averaged on constant length segments, the distance of which can be fixed from one to several wheel rotations. In this way, on a complete road section, noise levels are evaluated on segments that can be easily localized, and that all have the same length whatever the driving speed of the test vehicle. An infra-red sensor located on the car body, starts the acquisition on the 5 channels simultaneously, when a retro-reflecting surface (honeycomb type) it met on the road side. It is possible to measure several times the tire-road noise at different speeds and to evaluate exactly the same road segment. For the acoustic classification of a road material, or the conformity of production, a refined evaluation is needed and short segments can be used (1 or 2 wheel rotation long). For the acoustic monitoring of a large part of a network, larger segments must be considered (10 to 50 wheel rotations for instance). In this paper, measured road segments will be 2 m long (one wheel rotation), and a regression on 8 runs at different speeds will be performed to derive the average noise level at the required speed.

4-QUALITY ASSESSMENT OF THE METHOD

The effect of vibrations

The vibrations at the microphone locations were measured at different driving speeds of the vehicle. An example is shown in figure 2 for the front bar vibration at 130 km/h. The objective was to optimize the mounting system of the microphone support (eg. fixed on the chassis instead of the car body or wheel axle, pre-strained supporting bar…), and to quantify the vibration levels borne by the microphones. It appears that these vibration levels are quite important at very low frequencies, between 20 and 50 Hz. These frequencies are much lower than tire-road noise frequencies, typically ranging from 100 Hz to 5 kHz. In this range, vibration levels are not exceeding 10 to 20 ms -2 at the driving speed 130 km/h. This would generate disturbing noise levels much lower than tire-road noise levels.

4.2-The effect of aerodynamic noise

The main concern with such a mobile system is to get rid of disturbing noise due to the displacement of the measuring system in the air. This produces aerodynamic noise and vibration of the system. The objectives of the research is :

to analyze the aerodynamic effects in the vicinity of the measuring microphones ; to evaluate the temporal and spectral contributions of this noise to the tire-road noise to design, if necessary, the relevant mounting and shielding systems First, a simulation was performed in a test laboratory where a wind turbine produces air flows at different speeds. The turbulent nature of the air flow around the microphone was observed, and the wind speed around the microphone quantified, using Pitot tube sensors. The aerodynamic noise was estimated for different speeds of air flow, and for different sorts of windshields : a standard windshield (round shape), a thin wind and rain shield, a nose cone, a turbulent screen, a streamlined windshield (Figure 3). It is observed that the noise of air flow is rather high, it can reach up to 90 dB(A) at 100 km/h even with a windshield. The nose cone and turbulent screen are less efficient than the standard windshield and the streamlined windshield for reducing the aerodynamic noise. Furthermore, the actual wind speed in the vicinity of the microphones was measured outdoors on the test vehicle in real driving conditions (figure 4). These measurements confirmed that the speed of air flow on the lateral microphones (#1 and 2) is close to the vehicle speed (figure 5). Of course it is much lower at the rear microphone position (#3) because it is partly protected by the tire and the car body, but this could not be evaluated with such sensors.

Figure 5. Flow noise vs. vehicle noise

A special streamlined windshield was designed by calculating the optimal "water drop" shape, and smoothing the surface by laser cutting in the foam and covering the external surface with a nylon film. The aerodynamic noise measured in the laboratory with such a protection gave similar (just slightly lower) levels than the standard windshield. In situ tests are currently proceeding. Finally, a chart is drawn, showing the limits of aerodynamic noise in relation to the vehicle speed range (figure 6). The tire-road noise level must be in the upper part or the chart to be air flow noise immune. All these investigations has been made also in the frequency domain. Similar limit curves are available for each third octave band ranging from 400 Hz to 5 kHz, and need to be compared to measured tire-road noise spectra. So far, on the measured road surfaces, the tire-road noise levels were well inside the "immune zone". That means that the air-flow noise was negligible during the measurements.

The engine noise and other perturbing sources

It was not possible to measure the tire-road noise with the engine off, because in this case, the tachymetric information is lost and the acoustic acquisition system does not run. The driving condition with the clutch disengaged was however investigated and compared at low speed with the gear engaged at different ratio. The results presented in figure 7 show a very small deviation, lower than 1 dB(A), even at 50 km/h in the 3 rd gearbox ratio. Here again, the resulting levels derive from a regression on 8 runs, and an averaging over the 200 m long section of Dense Asphalt Concrete (BBSG 0/10). It can be concluded that the engine noise contribution is negligible even at low speed, when the vehicle is driven at the optimal engine speed (i.e. 4 th or 5 th gear ratio). A perturbation was observed on some measurements that could be attributed to exhaust pipe noise radiation. This is particularly noticeable on the microphone #3 located behind the tire. The other two are further and partly screened by the tire. The noise emitted by the engine plus the exhaust system was measured as a function of the engine speed, at the three microphone positions when the vehicle does not move (no tire-road noise). Noise spectra measured at microphone #3 are presented in figure 8 for a few engine speeds. At 4000 rpm, it can reach 85 dB at 125 Hz (engine rotation fundamental frequency), and 400 Hz (exhaust pipe resonance). Then, the engine speed as a function of driving speed was recorded in normal driving conditions at optimal gear ratios. Thus, the contribution of engine + exhaust system to the measured tireroad noise level is estimated as a function of the driving speed. This can be resumed in a graph as illustrated in figure 9, where the "immune" zone for tire-road noise is defined, according to the vehicle speed range. For instance, tire-road sound pressure levels above 81 dB(A) when measured at the microphone #3 at a driving speed 85 km/h, are acceptable. Below 81 dB(A), they are contaminated by exhaust or engine noise. As for aerodynamic noise, this comparison should be repeated for each 1/3 octave band. But the analysis of the data obtained, clearly shows that except around the 400 Hz frequency band for microphones #3, the measured tireroad noise levels measured so far are not contaminated by engine and exhaust noise. Other potential perturbing noise sources are still under test at present : influence of the other tires on the car, influence of other vehicles in the traffic. These problems will be addressed by simulations. A noise representative of a vehicle passing in the same or opposite direction will be introduced in an uncontaminated measurement, and the effect on the averaging over the length of the measured segment will be estimated. The influence of the other front tire on the measurement, will also be addressed by modeling the sound propagation.

The influence of the tire characteristics

In the ISO project [START_REF] Bérengier | The efficiency of road pavements for traffic noise reduction -a state of the art in France[END_REF], it is required to perform and average on the noise emitted by 4 different tires, the specific description and composition of which is defined in details in the document. Note that a simple reference tire like a slick tire would not be appropriate because it generates noise far too peculiar. This strong restriction on the tire characteristics can make the measurements impossible when no tire on the market fulfil (anymore) the requirements. As an alternative, it was decided to use tires commonly available on the market. When they need to be replaced by new tires, a calibration test on a reference road surface will have to be performed in order to adjust the results if necessary. This procedure has been applied successfully over 10 years for controlled pass-by measurements in France. In a first stage, the tests are performed with one reference set of tires defined previously. But many tests were performed to investigate the effect of the size and of the type of tire, on different pavements. The global results in dB(A) at 90 km/h on 5 different sections and for 12 different sets of tires are presented in Table 1. They result from a regression analysis on 8 runs, and are all corrected for a 20°C temperature :

L Aeq (20°C) = L Amax (T) + 0. The road pavements are ranging from a noisy one (Surface Dressing 0/14) to a rather low noise one (Very Thin Asphalt Concrete 0/6). The results show that the maximum deviation between tested tires is between 0.4 and 2.7 dB(A), and the standard deviation lower than 1 dB(A). It must be specified however the tested tires were common tires, and no selection of noisy quiet tires was intended. An example in Figure 10 of spectral result for 7 new tires on a Dense Asphalt pavement, shows that no particular frequency effect can be noticed.

5-THE RELATION BETWEEN CLOSE PROXIMITY and PASS-BY METHODS

The obvious question raised when developing a new methodology is "how will it correlated with existing method", in other words, what is the correlation between close proximity noise levels (CPX) measured on the mobile system, and pass-by noise levels (SPB) ? Actually, the measured sound pressure levels are different, and this difference depends on the type of road surface (porous or non porous) and on the measurement site configuration. Sound pressure levels with CPX measurements are much higher because they are measured much closer to the noise source. The noise source is also not the same : in CPX measurements it is one single tire, but in SPB it is a large number of vehicles. And finally, the propagation path of the sound wave is very different in both cases. In the SPB case, the sound wave interacts with the road environment and may be more or less attenuated when the road surface is porous, or when the shoulder is made of grass. The sound pressure level difference between CPX and Pass-By measurements varies between 21 and 25 dB(A) at lateral microphones (#1 and 2), and between 17 and 20 dB(A) at the rear microphone (#3). It seems that pavements having an open porosity give higher differences than dense pavements (except for the porous asphalt, but it is a clogged one, and porosity may be low). It would be interesting to measure this difference on highly porous pavements, especially because noise measurements methods are definitely designed for those quietest pavements.

An approach for modeling the sound propagation between the tire and CPX microphones and between the vehicle and the SPB microphone has been initiated and give consistent predictions with these experimental results [START_REF] Anfosso-Lédée | Modeling the local propagation effects of tire-road noise[END_REF]. They also predict a higher noise level difference in the case of porous pavements.

6-CONCLUSIONS

In this paper, a new mobile system for measuring tire-road noise is presented. It is intended to be used for the evaluation of road surface noise performances, during a classification scheme, for the assessment of legal requirements, or for diagnostic or monitoring of road surface condition. A lot of investigations were made in order to assess the significance of the measurements, and it was shown that the possible perturbing noise sources are negligible compared with current tire-road noise measured. Although the design of the test device seems quite simple, the measured results are relevant. Repeatability, reproducibility will be checked in a near future, along with a further investigation on the correlation with pass-by measurements.

7-ACKNOWLEDGEMENT

The present research project is a collective contribution of LCPC and 5 Public Works Regional Laboratories (LRPC) : Autun, Clermont-Ferrand, Paris (Est), Lille and Strasbourg. Special thanks go to MM Y. Pichaud, J.F. Le Fur, L. Ségaud and L. Toussaint for their contribution to the measurements and analysis. The financial supports of the Ministry for Environment, of the Ministry for Public Works, Transportation and Housing (Road Department (DR), and Research Department (DRAST)), of the Regional Council of Pays de la Loire, are also acknowledged.

8-REFERENCES

Figure 1 .

 1 Figure 1. Position of the 3 microphones and mounting systems

Figure 2 .

 2 Figure 2. Vibration levels at the front bar (mic.#1) at 130 km/h

Figure 3 .

 3 Figure 3. Noise levels relative to the speed of air flow, for different windshields

Figure 4 .

 4 Figure 4. in situ measurements of wind speed (3 pitot tubes) around the microphone

Figure 6 .

 6 Figure 6. Limit curve for aerodynamic noise disturbance with standard windshield

Figure 7 .

 7 Figure 7. Noise level at the 3 microphones as a function of engine regime

Figure 8 .

 8 Figure 8. Engine + exhaust noise spectrum at microphone #3

Figure 9 .

 9 Figure 9. Engine + exhaust noise levels at mic. #3 relative to engine or vehicle speed

Figure 10 .

 10 Figure 10. Spectral results for different tires at 90 km/h on a DAC 0/10

Table 1 . Noise levels at 90 km/h with different tires and pavements [LCPC, LRPC Strasbourg]

 1 1 (T°C -20)

	Road pavement	L Aeq 90 km/h [dB(A)]	Mic.1	Mic.2	Mic.3
	Dense Asphalt Concrete	7 tires (new) : 4 makes ; 3 width (185-195-205)
	(BBSG) 0/10	Average	98.2	98.0	94.7
	LCPC Test Track	Max deviation	0.8	1.2	1.5
		Standard deviation	0.3	0.4	0.5
	Dense Asphalt Concrete	4 tires : 3 makes ; 3 width (185-195-205)
	(BBSG) 0/10	Average	100.6	100.7	98.6
	(RN 422)	Max deviation	0.9	1.1	1.4
		Standard deviation	0.4	0.5	0.7
	Thin Asphalt Concrete	6 tires : 3 makes ; 3 width (185-195-205)
	(BBm) 0/10	Average	98.2	98.2	96.2
	Lohr Test Track	Max deviation	2.7	1.8	2.3
		Standard deviation	1.0	0.7	0.8
	Surface Dressing (ES) 10/14 6 tires : 3 makes ; 3 width (185-195-205)
	(RN 422)	Average	102.6	102.3	99.6
		Max deviation	0.9	1	1.5
		Standard deviation	0.4	0.4	0.7
	Very Thin Asphalt Concrete 3 tires : 2 makes ; 3 width (185-195-205)
	(BBTM) 0/6 Type 2	Average	96.7	97.8	93.6
	(RN 420)	Max deviation	0.4	0.5	1
		Standard deviation	0.2	0.3	0.5

Table 2 . Difference CPX / Pass-By levels of the test vehicle on 200 m sections at 90 km/h

 2 Some preliminary investigations have been performed first by comparing the CPX noise level with a simultaneous pass-by noise level of the CPX test vehicle. This was performed on a test track on 2 road pavements, one is a Dense Asphalt Concrete, the other a Porous Asphalt Concrete but significantly clogged. The results are presented in Table 2 below. Another investigation was made on trafficked road, on 4 different sections, but this time comparing SPB statistical level (for passenger cars only) with CPX noise level at 90 km/h. The results are shown in Table 3

	∆L Aeq [200m] 90 km/h (dB(A))	Mic. #1	Mic. #2	Mic. #3
	Dense Asphalt Concrete (BBSG) 0/10	21.9	23.2	19.3
	Porous Asphalt Concrete (BBDr) 0/10	21.9	24.6	17.1

Table 3 . Difference between CPX and SPB noise levels at 90 km/h [LRPC Strasbourg]

 3


Jin-Kao Hao
email: hao@eerie.eerie.fr

François Trousset

Jean-Jacques Chabrier

Prototyping an Inconsistency Checking Tool for Software Process Models

Keywords: Software process modeling, inconsistency checking, Prolog application ---------

Software process modeling has attracted much research effort in Software Engineering.

However, there is little work reported for the verification of process models. In fact, the verification is often either performed by hand or it is left to the enacting mechanism to detect inconsistencies during execution. Since process models are becoming more and more powerful and complex, their verification is also becoming increasingly difficult and critical. Our proposition is that in the same way as we need process modeling to facilitate software manufacturing, we need special tools to help verify the consistency of software process models. This paper presents part of our research and our experience in designing and prototyping such a tool for the verification of software process models in the ALF project (Esprit No.1520). The tool helps verify the partial consistency of process models by statically detecting various inconsistencies. This prototype uses techniques developed in different fields such as compilation, constraint solving and logic. To our knowledge, this is the first tool of its kind designed for the static checking for process models.

Introduction

Recently, there has been growing interest in the software process: the process for software manufacturing. Taking a view originating from the software process is an important advance in Software Engineering. According to Mark Dowson, "we are part of an industry that manufactures (and maintains and evolves) large, complex artifacts --software systems. We would like our products to be of high quality and reasonable cost and to be delivered on time and within budget. The only way to achieve these objectives is to focus on the manufacturing process --the software process" [Dowson 91]. Informally, a software process is a set of activities for producing and evolving software systems throughout the software life cycle. Associated with the process view is process modeling. A process model is a static description which specifies the general features of a class of software processes, but not those features specific to a particular process. In other words, a process model governs each process of this modeled class.

A process model can thus be tailored to different processes by instantiating the process model entities with specific tools, objects, and other resources. The relationship between a process model and processes modeled by the model can be considered as an inheritance relation.

In fact, suppose that we have a Software Process Model, SPM, which models the Software Processes, SP1, ..., SPk. Suppose also that SPM possesses certain properties, then each process SPi derived from SPM will inherit these properties, specified in the initial process model. The process modeling activity, like the program writing activity, is not free of error. Thus, as properties are inherited from the model to software processes, it becomes evident that it will be of great benefit to detect and eliminate as many of those errors as possible (called inconsistencies in this paper) in a given process model before giving it to an enacting mechanism for execution or interpretation. The static detection of inconsistencies is part of what we call the verification of software process models.

Although process modeling has attracted much research effort, there is relatively little reported work for the verification of process models. In fact, the verification is often either performed by hand or it is left to the enacting mechanism to detect inconsistencies during execution. Since process models are becoming more and more powerful and complex, their verification is also becoming increasingly difficult and critical. Our proposition is that in the same way as we need process modeling to facilitate software manufacturing, we need special tools to help verify the consistency of software process models. This paper reports part of our research and our experience in designing and prototyping such a tool for the static verification of software process models in the ALF project (Esprit No.1520). The tool helps verify the partial consistency of process models by statically detecting various inconsistencies. This prototype uses techniques developed in different fields such as compilation, constraint solving and logic. It especially uses "general type solving techniques" developed in [Trousset 92] to deal with specific typing problems in process modeling. Additionally, our experience shows, once again, that Prolog is a very good candidate for rapid and evolving prototyping in some research areas.

The presentation is organized as follows: section 2 briefly reviews the MASP concepts, the process model proposed in the ALF project as well as the MASP/DL, the description formalism of MASPs; in section 3, we present the strategy used for prototyping our checking tool as well as the technical choices such as the prototyping environment and language; section 4 gives an overview of the tool itself and the techniques used in the tool; section 5 discusses future work; the last section concludes the paper with some observations and perspectives.

Software Process Modeling in the ALF Project

As with any programming language where a compiler depends on the syntax and semantics of the language, a verification tool for software process models depends on the syntax and semantics of the description formalism used for process modeling. In order to present our inconsistency tracker, we will give a brief reminder of the MASP concept, the software process modeling in the ALF project and the MASP/DL, the associated description language.

Process Modeling -the MASP Concepts

In ALF, software processes are modeled in terms of MASPs [Benali et al. 89,Griffiths et al. 89] OP -OPerator types specify classes of operators. An operator type is defined by a name, a signature, and a pre-and a post-condition. The signature specifies the types of input/output objects manipulated by the operator type. The pre-and the postconditions specify respectively constraints which must be satisfied before and after activating an operator of the operator type. An operator type may be instantiated by an existing tool (e.g. a C compiler) or a tool defined itself by a MASP which specifies a process submodel. This second kind of operator description introduces the notion of MASP-structure (MASP-hierarchy). EX -Each EXpression definition consists of three parts: a name, an optional event and a logic expression. By naming expressions, it is possible to refer to them by their names without rewriting them. This is similar to macro definition and expansion. The event part of an expression defines the moment to evaluate the logic expression part. Expressions are used as part of pre-and post-condition of operator types, characteristics, and the condition part of rules (see below). The expression model is optional. RU -RUles describe under which conditions execution of an operator may be attempted.

A rule contains two components. The first is an expression, the second is the name of an operator. The expression part of the rule and the pre-condition part of the concerned operator together constitute the necessary condition of the operator's execution. The rule model is optional.

OR -ORderings specify constraints on the order in which operators may be executed.

Orderings are used to specify that certain operators can be executed concurrently, sequentially, optionally, simultaneously or repeatedly. This part is optional.

CH -CHaracteristics are expressions which should be true in each state of a software process. Characteristics can be used to describe integrity constraints and software process goals. This part is optional.

Process Modeling Formalism -the MASP Definition Language

Generally speaking, we can distinguish two ways of representing software process models. First, process models can be described with the aid of an informal or narrative formalism such as natural languages and flowcharts, which has been long employed by many organizations. Second, they can be described by means of a formal notation such as programming language-like formalisms, which is exemplified by the process programming [Osterweil 87]. The discussion about the advantages and drawbacks of the informal and formal approaches can be found elsewhere; for example, see [Keller 88,Lehman 87,Osterweil 87].

The process modeling in the ALF project is based on the second approach. A formal language with well defined syntax and semantics was developed. This is the MASP Definition Language (MASP/DL for short). MASP/DL is a powerful, yet very complex formal modeling language. Given that there is no space to present the entire language, here, we only give an example of a MASP written in MASP/DL. This will help the reader to grasp the outline of the language.

An Example of MASP Written in MASP/DL

This MASP models a simplified "edit<->compile" development cycle and is by no means realistic. It should be noted that MASPs developed in the ALF project are far more complicated, and always organized into a hierarchy. However, this MASP does highlight some important modeling aspects with the MASP/DL. All object types are declared in the object model; they are all descendants of a predefined object type "sys-object". Object types are structured into a hierarchy. Four operator types are defined. Each operator is composed of a precondition, the operator type (which may be a basic tool or another MASP) and the types of objects involved, a postcondition and the mode of the operator type (the interactive mode indicates that the operator can be invoked by the user). The rule model represents part of the process knowledge. For example, the third rule says that we terminate the process if all c_module are successfully compiled. The ordering specifies that an object _m of type c_module can be edited any number of times (though at least once) before being compiled and then the compilation errors are displayed if necessary.

Inconsistencies in MASPs

Evidently, inconsistencies (including syntax errors) may be introduced when writing MASPs. This situation is very similar to that of writing programs in any programming language. However the problem here is much more difficult due to the complexity of the MASP/DL. Moreover, we must verify not only the syntax and semantics of the MASP/DL, but also part of the semantics of the models specified by the MASPs.

Inconsistencies in a MASP can be roughly classified into three categories, called A, B and C respectively (syntax errors are not classified here).

A Class: Errors concerning declaration/references. The following examples show this kind of error.

A rule refers to an operator name which is not defined in the operator model, or the arity of the reference does not fit its definition. Any reference to an undefined entity (object, attribute, link, expression, ...) is also an error.

A parameter of an operator type has double definition. An entity (object, attribute, link, expression, ...) has double definition. and so on.

B Class: Typing problems. Some typing problems in MASPs are similar to that of any programming language. However, due to the complexity of the MASP/DL, typing problems here are more general and difficult than those found in traditional languages. Consequently, the checking and inferencing methods developed in the compiler construction for type checking are in general not sufficient. We will come back to the discussion later. Now let us look at an example.

An Example of a Typing Problem

This MASP describes a fictitious model for applications development in which an application is composed of modules of three different languages L1, L2 and L3. L2 modules can have inclusion files (incl), those of L3 both inclusion files and generic types (generic_type), and those of L1 generic types. An operator type (compile) is defined to allow compiling applications. The precondition of the operator type is an expression which defines the kind of applications which can be compiled. As will be shown in section 4, the expression cannot be typed correctly since there is no possible type for the variable _m satisfying both the declarations for the objects and the 2) in a conjunction of logic expressions which are used in different components of a MASP. For example, inconsistencies may occur between an operator and a rule. More precisely, if the conjunction Pre(Oper(R)) and Cond(R) is always false, then there is an inconsistency because the rule can never be used. Similar inconsistencies may occur for the interaction between operators, rules, orderings and characteristics.

The presentation above gives only a partial view of the different inconsistencies in MASPs, other inconsistencies are also possible. For example, cycles may exist in rules, in an object model due to subtyping etc. See [Chabrier et al. 89] for more detail.

Having presented the problems with which our Inconsistency Tracker For MASPs (ITFM for short) is confronted, we are now ready to describe our prototyping strategy for the design of the tool itself.

Prototyping Strategy

A prototype is a simplified model and can be built rapidly and modified easily. However, a prototype is itself a piece of software, even a complex system. This implies that a prototype cannot be built in an "ad hoc" way. In order to be productive, a prototype should be built with great care. It needs good preparation, and good organization. It also needs appropriate techniques and tools. In other words, it needs a good prototyping strategy.

The prototyping strategy used is similar to that of [Penedo 86]. The following steps have been established and followed for the prototype development:

• Identify research issues. Given the variety of inconsistencies that may be encountered in MASPs, we have identified the following research issues for investigation during the prototyping excises. * Internal representation of MASPs. MASPs are written in MASP/DL. MASP texts may be very complex. How to represent MASPs internally constitutes the first question to be answered. An appropriate internal representation is needed in order for the ITFM to track various inconsistencies, both syntactic and semantic. A good representation will facilitate the implementation of the prototype while a bad one complicates the task. * Type solving (A & B Class inconsistencies). As we have seen above, type inconsistencies in MASPs may be difficult to track. The purpose of the type-checkers here is not really to synthesize the type of each expression from the types of its subexpression. Instead we want to deduce, from declarations, the possible types of each variable (a variable represents an undeclared identifier or a subexpression, and may have several possible types) in an expression, and if needed, the types for each subexpression can be synthesized from the types of each variable. We use the term "type-solving" to distinguish this difference with traditional typechecking problem. We need more general, more powerful methods to deal with typing problems in MASPs. * Logical level inconsistency checking (C Class inconsistencies). The fact that a MASP involves only types (not concrete objects) implies that the ITFM must deal with general logic expressions. Also, the MASP/DL allows the using of extra logic structures (predifined predicates of the MASP/DL) inside expressions we must deal with. Finally, an expression may contain non quantified variables (called free variables). Special techniques are then needed to track logic inconsistencies.

• Propose possible solutions. For each identified research issue, we have studied possible solutions. * The internal representation of MASPs is dependent on the prototyping language and environment. Following our experience with Prolog, we have decided to represent MASPs as Prolog facts in Prolog's database (see §4.1). If we had chosen another language, other representations, e.g. a database would have been used to store MASPs. * Type solving. The essential point of a type system is to decide whether each variable of an expression can be typed correctly. This problem can be restated in another way; i.e. we want to know if each variable can have at least one possible type while satisfying all the concerned declarations. This statement is very similar to the definition of the Finite Constraint Satisfaction Problems [Hao & Chabrier 90,91,Chabrier et al. 91]. Indeed, this problem can be dealt with using constraint solving techniques. Techniques for general typing problems developed in [Trousset 92] are considered applicable. This will be discussed in the next section.

* Logic inconsistency checking. As expressions are first order predicates, methods in logic programming can be applied. However, due to the impure features (predefined predicates) and the generality of the expressions in MASPs, the direct application of predicate logic will lead to superfluous processing. This problem is solved by using rewriting techniques to express the predefined semantics of these predicates.

• Choose prototyping environments. The development environment and the languages used may have a great influence on the success of prototyping activities. Our experiences with Prolog as well as that of others, has convinced us of its suitability for prototyping. Sepia Prolog [Meier et al 88] is chosen as our basic development language. A workstation under Unix constitutes the working environment.

• Build and experiment with the prototype.

• Identify further work.

An Overview of the ITFM Tool

This section gives an overview of the ITFM prototype, its organization and the techniques used in the prototype.

The ITFM is essentially composed of four independent modules: a parser, two typecheckers, and a contradiction checker. Figure 1

Parser

The role of the parser is to take a MASP as its input, parse it and produce an internal representation in Prolog of the given MASP. In this representation, each component of the MASP is coded into several Prolog facts. For example, given the definition of an operator type in a MASP: it will be translated into the following set of Prolog facts:

oper_type(21, operator_2, 'compile, non-interactive). oper_args(21, operator_2, 1, '_m', name('c_module'), in). oper_args(21, operator_2, 2, '_o', name('obj_module'), out). oper_args(21, operator_2, 3, '_err', name('e_file'), out). oper_prec (22, operator_2, 3, eval('ready_for_compilation',[name('_m'), 'TRUE'])). oper_post (23, operator_2, 3, eval('o', [name('_m'), name('_o'), [])).

In this representation, every syntactic detail of the definition is recorded. Besides, other information such as the line number and position number of each parameter of the operator type is added in order to convey diagnostics in case of the detection of errors.

The parser essentially uses the syntax-directed techniques developed in compilation [Aho et al. 86]. It works with the formal definition of the MASP/DL grammar. During the parsing phase, syntax errors are reported whenever detected. However, the ITFM stops after reporting a syntax error. This is reasonable since the ALF project supposes that MASPs are written with the MASP/Editor that guarantees the syntactic correctness of MASP texts. There are two interesting points to note. First, instead of producing a parse tree as in a compiler, our parser produces Prolog facts which represent exactly the relevant syntactic information of a given MASP (irrelevant information, for example ';' is eliminated). Second, the choice of Prolog as our prototyping language makes this phase simple, it should be noted that Prolog was initially invented for natural language processing.

Type-Solving

Type-checker 1. Its role is to track most of the inconsistencies defined in the A class, i.e.

errors concerning declarations/references. The checker consists of a set of checking rules specifying the condition of each kind of inconsistency. Thanks to the internal representation of MASPs and the deduction mechanism of Prolog, the writing of checking rules is easy. For example, the checking rule for duplicated operator definition says that we should first collect all the operator names of a MASP in a list, and then verify if there are two identical names in the list. The type-checker 1 directly uses the syntactic information represented by the internal representation. During the checking, some semantic information is deduced and stored in the Prolog database. At the end of the type-checker 1, the first internal representation is transformed into the second representation (always in the form of Prolog facts) replacing some syntactic information (e.g. the names) with some semantic information (e.g. a link to their definition). This representation constitutes the starting point of the type-checker 2 which is based on constraint solving methods. In figure 2, the constraint solver poses no problem, since we know that well studied constraint solving techniques exist. Once the TP is transformed into a CSP, we know how to solve it by using constraint solving techniques. So the typing problem now involves making the transformation. For a given TP, there are many ways to transform it into a CSP. However, whatever transformation is used, the resulted CSP will be equivalent if the transformation used is sound and correct.

The transformation prototyped in the type-checker 2 is now briefly presented using a simple example. The main idea is to associate a solver variable for each expression variable, each subexpression and to consider each expression to be checked as a set of constraints on these variables, each variable having all possible types as its domain at the beginning.

Let us look again at the MASP example_2 given in section 2. We want to check the expression of the precondition of the operator compile. At the beginning, the variable _a already has a specific type application, while _m, _i, _g can be any type defined in the object model. The semantic of the predicate "has_module(_a, _m, NO_KEY)" says there is a link called "has_module" from _a (of type application) to _m (of unknown type). First, we check if such a link exists. The answer is yes because in the object model the type application is effectively extended with a link "has_module". Next, from the definition for the links, we know that the destination of a link of type has_module is a_module or c_module. Therefore the type of _m belongs to {a_module, c_module}. The second predicate of the expression "has_include(_m, _i, NO_KEY)" says there are links named "has_include" from _m to _i.

Checking the object model, we know the object c_module or p_module have been extended

with such a link. We thus deduce that the type of _m belongs to {c_module, p_module}. In the same way, we deduce, from the third predicate "has_generic(_m, _g, NO_KEY)" that the type of _m must belong to {a_module, p_module}. Since the three predicates are connected by AND, the type of _m must belong to the intersection of the sets {a_module, c_module}, {c_module, p_module} and {a_module, p_module} which is empty. That means the variable _m can never have any type as specified in the process model. In order for _m to have a valid type, several possibilities exist. For example, we can change one AND connector in the expression to an OR connector. We can change the destination of the link "has_module" to module. In this case, _m will have the unique type p_module. This second modification implies that the type-checker 2 takes into account the notion of subtype.

Logic Checker

The role of logic checking is to detect contradictions in logic expressions. The kind of expressions the solver has to deal with are expressions of the first order predicate calculus (not limited to Horn clauses). The checker is just an implementation of the general resolution principle. However, as expressions can contain predicates predefined in the MASP/DL, also called meta-predicates, which have their own semantics (e.g. IS_A_LINK_TYPE( t : LINK_TYPE ) is a meta-predicate asserting that t is a link type of the type LINK_TYPE ), the algorithm used by the checker is extended with a set of "rewriting rules" which describe the semantics of these predicates. These rewriting rules allow clauses to be rewritten efficiently according to the semantics of the predicates. Rewritten clauses are then treated as others by the general resolution rule. Another point is that as we need the results in a short delay (as permitted by humans), the resolution is limited to a certain number of inference steps, depending on the size of the expression to be checked. Due to this limitation and mainly to the semi-decidable nature of first order logic, the checker cannot always give a firm (affirmative or negative) result when it stops its resolution.

Importation

Another feature of the tool is that it takes into account the importations of object/operator types. In fact, object and operator types can be shared by several MASPs via importation. For example, an object type can be imported from another MASP and used locally by, say, operator types. However, if the imported object type does not exist, i.e. if it is not defined in the indicated MASP nor imported from another MASP, there is an inconsistency. This kind of inconsistency is detected by the tool. Importations can be nested, i.e. an imported object/operator type in a MASP can be imported again by another MASP. The tool takes into account this point by considering the transitive closure of the importations.

Future work

While the tracking of A and B class inconsistencies is efficient and deterministic, the tracking of logic contradictions may be very long. The reason for this is the complexity of the problem and the combinatorial nature of the technique used. We are looking for other more efficient techniques to deal with this problem.

Other work concerns the checking of several related MASPs. As shown in the second section, a process model may be organized into a hierarchy of several MASPs. The presentation above only concerns the inconsistency checking of a single MASP. However, even if each MASP is locally consistent, inconsistencies may still exist among a hierarchy of MASPs. In order to track this kind of inconsistency, more knowledge about the hierarchy is needed.

Conclusion

Software process modeling is an important advance in Software Engineering. The verification of the consistency of software process models is becoming more and more critical.

Tools for this verification would be very helpful. In this paper, we have presented such a verification tool: ITFM. The tool is capable of tracking syntactic errors, semantic inconsistencies, typing problems and logic contradictions in MASPs enforcing the partial correctness of MASPs.

The idea of treating general typing problems as constraint problems, which was developed in our early research, was partially prototyped and validated in the ITFM. Choosing Prolog as prototyping language has facilitated our task. We believe that the techniques explored and prototyped in the ITFM could also be useful and usable in other verification tools for process models. Finally, the ITFM itself is currently being used by the ALF project consortium to verify various process models. It has proven indispensable especially when MASPs are large and complicated. To our knowledge, this is the first tool of its kind designed for the static checking for process models.

  precondition of the operator type. *C Class: This kind of inconsistency can be expressed as a contradiction in a logic expression or in a conjunction of logic expressions. In order to simplify our presentation, we introduce some notations. Let OP be an operator, then Pre(Op) and Post(Op) represent respectively the logic expression part of the pre-and post-condition of Op. Let R be a rule, then Cond(R) is the logic expression of the condition part of the rule R and Oper(R) the operator used in R. We also use Charact(M) to designate the logic expression of the characteristic of the MASP M. With these notations, logical inconsistencies can be defined at two levels. 1) in an expression which is a Pre(Op) or Post(Op), a Cond(R) or still a Charact(M). For example, if Pre(Op) is always false, then the precondition Pre(Op) of the operator Op can never be satisfied. This inconsistency means that Op can never be executed. Similar inconsistencies may occur in Post(Op), Cond(R) or Charact(M).

  Fig. 1 Organization of the ITFM

  compile : (IN _m : c_module; OUT _o: Obj_module; OUT _err: e_file

  . MASP stands for Model for Assisted Software Process. A MASP M is composed of six

elements <OM, OP, EX, RU, OR, CH> (some elements are optional) where OM -Object Model specifies the object types involved in the MASP as well as the relationship between those object types. The object model is the PCTE object model

[Bourdier et al. 88]

which is based on the Entity Relation model.

  Type-checker 2. Its role is to track B class inconsistencies. That is, given an expression, it checks if each variable of the expression can have at least one possible type which satisfies all the related declarations. Such a typing problem can be considered as a finite constraint satisfaction problem CSP(V,D,C) (since the set of types defined is finite) where V={V1, V2, ..., Vn}, a set of variables. D={D1, D2, ..., Dn}, a collection of sets of possible values for each variable of V, Di called domain of Vi. C={C(Vi1, Vi2, ..., Vij) | C is a relation on Vi1, Vi2, ..., Vij of V}.Given a Problem TP, we first need to transform the problem into an equivalent CSP. Then solving the CSP means solving the initial TP. This is presented in figure2.

	Typing Problem	Translator	Finite Domain CSP	Constraint Solver
		Fig. 2 : Structure of the type-checker 2

Acknowledgements:

The authors would like to thank all the members of the ALF consortium: GIE Emeraude (France), CSC (Belgium), Computer Technologies Co. (Greece), Grupo de Mecanica del Vuelo, S.A. (Spain), International Computers Limited (United Kingdom), Cerilor (France), University of Nancy-CRIN (France), University of Dortmund-Informatik X (Germany), Catholic University of Louvain (Belgium) and University of Dijon-CRID (France).

 -----------------------------------------------------------------------------------------------------------* This work was partially supported by the ALF Project (Esprit No. 1520). The work was completed when the first two authors were at the Centre de Recherche en Informatique de Dijon.